Difference between revisions of "User:Maximilian Janisch/latexlist/latex/1"

Revision as of 11:37, 1 September 2019

List

1. ; $3 + 5$ ; confidence 0.136

2. ; $A , B , C \in C$ ; confidence 0.982

3. ; $( - ) ^ { * } : C ^ { 0 p } \rightarrow C$ ; confidence 0.505

4. ; $s = s ( ( A ^ { * } ) ^ { ( B ^ { * } ) } , ( B ^ { * } ) ^ { ( C ^ { * } ) } )$ ; confidence 0.907

5. ; $R el$ ; confidence 0.544

6. ; $d ( A , B ) : B ^ { A } \cong A ^ { * } B ^ { * }$ ; confidence 0.988

7. ; $4$ ; confidence 0.531

8. ; $S ^ { * } = S$ ; confidence 0.463

9. ; $B ^ { A } \cong ( A ^ { * } \otimes B )$ ; confidence 0.992

10. ; $B$ ; confidence 0.895

11. ; $C$ ; confidence 0.838

12. ; $( S , g )$ ; confidence 0.978

13. ; $3$ ; confidence 1.000

14. ; $D$ ; confidence 0.538

15. ; $5$ ; confidence 0.885

16. ; $F _ { 3 }$ ; confidence 0.996

17. ; $\operatorname { dim } ( S ) = 4 n + 3$ ; confidence 0.958

18. ; $\geq 7$ ; confidence 0.562

19. ; $( 4 n + 3 )$ ; confidence 1.000

20. ; $Z = S \nmid F _ { \tau }$ ; confidence 0.763

21. ; $\{ \xi ^ { \alpha } , \eta ^ { \alpha } , \Phi ^ { \alpha } \} \alpha = 1,2,3$ ; confidence 0.761

22. ; $4 n$ ; confidence 0.999

23. ; $m > 3$ ; confidence 0.916

24. ; $7$ ; confidence 0.937

25. ; $\eta ^ { \alpha } ( Y ) = g ( \xi ^ { \alpha } , Y )$ ; confidence 0.932

26. ; $S ( p )$ ; confidence 0.693

27. ; $T ^ { 2 } \times SO ( 3 )$ ; confidence 0.990

28. ; $SO ( 3 )$ ; confidence 0.940

29. ; $\Phi ^ { \alpha } ( Y ) = \nabla _ { Y } \xi ^ { \alpha }$ ; confidence 0.798

30. ; $\dot { i } \leq n$ ; confidence 0.190

31. ; $n \geq 1$ ; confidence 0.967

32. ; $SU ( 2 )$ ; confidence 0.811

33. ; $11$ ; confidence 1.000

34. ; $b _ { 2 } \neq b _ { 4 }$ ; confidence 0.995

35. ; $SU ( m ) / S ( U ( m - 2 ) \times U ( 1 ) ) , SO ( k ) / SO ( k - 4 ) \times Sp ( 1 )$ ; confidence 0.164

36. ; $0$ ; confidence 0.311

37. ; $m = 4 n + 3$ ; confidence 0.997

38. ; $\hat { v } ^ { ( S ) }$ ; confidence 0.182

39. ; $b _ { 2 } \neq b _ { 6 }$ ; confidence 0.994

40. ; $\operatorname { Sp } ( ( m + 1 ) / 4 )$ ; confidence 0.694

41. ; $\xi ( \tau ) = \tau _ { 1 } \xi ^ { 1 } + \tau _ { 2 } \xi ^ { 2 } + \tau _ { 3 } \xi ^ { 3 }$ ; confidence 0.998

42. ; $U ( 1 ) _ { \tau } \subset \operatorname { SU } ( 2 )$ ; confidence 0.671

43. ; $\sum _ { k = 1 } ^ { n } k ( n + 1 - k ) ( n + 1 - 2 k ) b _ { 2 k } = 0$ ; confidence 0.782

44. ; $\{ I ^ { 1 } , R ^ { 2 } , \hat { P } \}$ ; confidence 0.143

45. ; $S ^ { 3 } / \Gamma$ ; confidence 0.633

46. ; $k$ ; confidence 0.208

47. ; $\tau = ( \tau _ { 1 } , \tau _ { 2 } , \tau _ { 3 } ) \in R ^ { 3 }$ ; confidence 0.999

48. ; $C ( S )$ ; confidence 0.946

49. ; $$m$$ ; confidence 0.499

50. ; $\{ \xi ^ { 1 } , \xi ^ { 2 } , \xi ^ { 3 } \}$ ; confidence 1.000

51. ; $_ { \nabla } ( G / K )$ ; confidence 0.326

52. ; $$n + 2$$ ; confidence 1.000

53. ; $4 n + 3$ ; confidence 1.000

54. ; $15$ ; confidence 1.000

55. ; $5$ ; confidence 0.574

56. ; $s ^ { 2 }$ ; confidence 0.942

57. ; $\alpha = 1,2,3$ ; confidence 0.734

58. ; $\lambda = \operatorname { dim } ( \delta ) - 1$ ; confidence 0.702

59. ; $$Z = G / U ( 1 ) . K$$ ; confidence 0.948

60. ; $$1$$ ; confidence 0.742

61. ; $\operatorname { dim } ( O ) = 4$ ; confidence 0.996

62. ; $\operatorname { im } ( S ) = 7$ ; confidence 0.799

63. ; $U ( ( m + 1 ) / 2 )$ ; confidence 0.997

64. ; $F _ { \tau } \subset F _ { 3 } \subset S$ ; confidence 0.996

65. ; $\xi ^ { \mathscr { L } } = I ^ { \mathscr { L } } ( \partial _ { r } )$ ; confidence 0.127

66. ; $G _ { 2 } / \operatorname { Sp } ( 1 ) , \quad F _ { 4 } / \operatorname { Sp } ( 3 ) , E _ { 6 } / SU ( 6 ) , \quad E _ { 7 } / \operatorname { Spin } ( 12 ) , \quad E _ { 8 } / E _ { 7 }$ ; confidence 0.614

67. ; $g ( \xi ^ { \alpha } , \xi ^ { b } ) = \delta _ { \alpha b }$ ; confidence 0.989

68. ; $p = ( p _ { 1 } , \dots , p _ { n } + 2 )$ ; confidence 0.447

69. ; $O = G / \operatorname { Sp } ( 1 ) . K$ ; confidence 0.187

70. ; $z$ ; confidence 1.000

71. ; $S = SU ( m ) / S ( U ( m - 2 ) \times U ( 1 ) )$ ; confidence 0.541

72. ; $$T ^ { n }$$ ; confidence 0.616

73. ; $( C ( S ) , \overline { g } )$ ; confidence 0.418

74. ; $Sp ( 0 )$ ; confidence 0.378

75. ; $s ^ { 3 }$ ; confidence 0.948

76. ; $D$ ; confidence 0.661

77. ; $$\xi = I ( \partial _ { r } )$$ ; confidence 0.869

78. ; $$n \geq 0$$ ; confidence 0.996

79. ; $\Gamma \subset SU ( 2 )$ ; confidence 0.951

80. ; $b _ { 2 } i + 1 ( S ) = 0$ ; confidence 0.920

81. ; $m = 2 i + 1$ ; confidence 0.871

82. ; $[ \xi ^ { \alpha } , \xi ^ { b } ] = 2 \epsilon _ { \alpha b c } \xi ^ { c }$ ; confidence 0.322

83. ; $\xi ( \tau )$ ; confidence 0.999

84. ; $$S ( p ) = U ( 1 ) _ { p } \backslash U ( n + 2 ) / U ( n )$$ ; confidence 0.916

85. ; $1 > 1$ ; confidence 0.983

86. ; $b _ { 2 } ( s ) \leq 1$ ; confidence 0.580

87. ; $0$ ; confidence 0.355

88. ; $1$ ; confidence 0.998

89. ; $2$ ; confidence 1.000

90. ; $\tau _ { 1 } ^ { 2 } + \tau _ { 3 } ^ { 2 } + \tau _ { 3 } ^ { 2 } = 1$ ; confidence 0.974

91. ; $T ^ { 2 } \times \operatorname { Sp } ( 1 )$ ; confidence 0.987

92. ; $( C ( S ) , \overline { g } ) = ( R _ { + } \times S , d \nu ^ { 2 } + r ^ { 2 } g )$ ; confidence 0.265

93. ; $k > 7$ ; confidence 0.997

94. ; $\operatorname { Sp } ( n + 1 ) / \operatorname { Sp } ( n ) , \quad \operatorname { Sp } ( n + 1 ) / \operatorname { Sp } ( n ) \times Z _ { 2 }$ ; confidence 0.901

95. ; $SO ( 4 n + 3 )$ ; confidence 0.906

96. ; $t$ ; confidence 0.637

97. ; $P = \cup _ { n _ { 1 } , \ldots , n _ { k } , \ldots } \cap _ { k = 1 } ^ { \infty } E _ { n _ { 1 } } \square \ldots x _ { k }$ ; confidence 0.192

98. ; $\{ E _ { n _ { 1 } } \ldots n _ { k } \}$ ; confidence 0.382

99. ; $$\sigma \delta$$ ; confidence 0.999

100. ; $A _ { x _ { 1 } } ^ { \prime } \ldots x _ { k } = A _ { 1 } \cap \ldots \cap A _ { x _ { 1 } } \ldots x _ { k }$ ; confidence 0.061

101. ; $x _ { 1 } , \ldots , A _ { x _ { 1 } } \ldots x _ { k } , \ldots ,$ ; confidence 0.104

102. ; $\{ A _ { n _ { 1 } } \ldots n _ { k } \}$ ; confidence 0.200

103. ; $A _ { x } _ { 1 } \ldots x _ { k } x _ { k + 1 } \subset A _ { x _ { 1 } } \ldots x _ { k }$ ; confidence 0.139

104. ; $M$ ; confidence 0.626

105. ; $x$ ; confidence 0.475

106. ; $\pi$ ; confidence 0.772

107. ; $K$ ; confidence 0.738

108. ; $K _ { 0 } ( B ) ^ { + }$ ; confidence 0.993

109. ; $K _ { 1 }$ ; confidence 0.970

110. ; $C ( S ^ { 2 n } )$ ; confidence 0.540

111. ; $\tau ( x y ) = \tau ( y x )$ ; confidence 0.993

112. ; $\theta = 1 - \theta$ ; confidence 0.998

113. ; $$H$$ ; confidence 0.998

114. ; $n > 0$ ; confidence 0.998

115. ; $K _ { 0 } ( \varphi ) = \alpha$ ; confidence 0.993

116. ; $z \in G$ ; confidence 0.715

117. ; $f : G \rightarrow R$ ; confidence 0.996

118. ; $C ^ { * }$ ; confidence 0.866

119. ; $( K _ { 0 } ( A ) , K _ { 0 } ( A ) ^ { + } , \Sigma ( A ) )$ ; confidence 0.990

120. ; $D$ ; confidence 0.683

121. ; $I \mapsto I$ ; confidence 0.782

122. ; $K _ { 0 } ( \varphi ) : K _ { 0 } ( A ) \rightarrow K _ { 0 } ( B )$ ; confidence 0.977

123. ; $f ( G ^ { + } ) \subseteq R ^ { + }$ ; confidence 1.000

124. ; $h$ ; confidence 0.307

125. ; $( K _ { 0 } ( A ) , K _ { 0 } ( A ) ^ { + } , \Sigma ( A ) )$ ; confidence 0.990

126. ; $K _ { 0 } ( A )$ ; confidence 0.745

127. ; $H ^ { + } = G ^ { + } \cap H$ ; confidence 0.999

128. ; $\square ^ { * }$ ; confidence 0.982

129. ; $K _ { 0 } ( \varphi )$ ; confidence 0.924

130. ; $x _ { 1 } , x _ { 2 } , y _ { 1 } , y _ { 2 } \in G$ ; confidence 0.943

131. ; $( G , G ^ { + } )$ ; confidence 1.000

132. ; $25$ ; confidence 0.396

133. ; $\theta = \theta ^ { \prime }$ ; confidence 0.994

134. ; $y \leq x$ ; confidence 0.998

135. ; $\alpha : K _ { 0 } ( A ) \rightarrow K _ { 0 } ( B )$ ; confidence 0.991

136. ; $\alpha ( K _ { 0 } ( A ) ^ { + } ) = K _ { 0 } ( B ) ^ { + }$ ; confidence 0.997

137. ; $K _ { 0 } ( A ) ^ { + }$ ; confidence 0.988

138. ; $K _ { 0 } ( \varphi ) = K _ { 0 } ( \psi )$ ; confidence 0.842

139. ; $A _ { \theta } \cong A _ { \theta }$ ; confidence 0.999

140. ; $f$ ; confidence 1.000

141. ; $\geq 0$ ; confidence 1.000

142. ; $4$ ; confidence 0.978

143. ; $2 n$ ; confidence 1.000

144. ; $\alpha ( \Sigma ( A ) ) = \Sigma ( B )$ ; confidence 0.988

145. ; $\varphi : A \rightarrow B$ ; confidence 0.999

146. ; $\alpha ( \Sigma ( A ) ) \subseteq \Sigma ( B )$ ; confidence 0.978

147. ; $x _ { i } \leq z \leq y _ { j }$ ; confidence 0.967

148. ; $K _ { 0 }$ ; confidence 0.936

149. ; $\tau \mapsto K _ { 0 } ( \tau )$ ; confidence 0.994

150. ; $x \in G$ ; confidence 0.737

151. ; $K _ { 0 } ( \tau ) ( [ p ] _ { 0 } - [ q ] _ { 0 } ) = \tau ( p ) - \tau ( q )$ ; confidence 0.889

152. ; $y \in H$ ; confidence 0.503

153. ; $K _ { 0 } ( I ) \rightarrow K _ { 0 } ( A )$ ; confidence 0.923

154. ; $x , y \in A$ ; confidence 0.906

155. ; $x > 0$ ; confidence 0.700

156. ; $A _ { \theta }$ ; confidence 0.786

157. ; $( K _ { 0 } ( B ) , K _ { 0 } ( B ) ^ { + } , \Sigma ( B ) )$ ; confidence 0.997

158. ; $\tau : A \rightarrow C$ ; confidence 0.987

159. ; $i$ ; confidence 0.450

160. ; $\varphi , \psi : A \rightarrow B$ ; confidence 0.980

161. ; $\Sigma ( A )$ ; confidence 0.626

162. ; $x \in H ^ { + }$ ; confidence 0.518

163. ; $y \in G ^ { + }$ ; confidence 0.943

164. ; $1$ ; confidence 0.989

165. ; $x _ { i } \leq y _ { j }$ ; confidence 0.993

166. ; $K _ { 0 } ( B ) = Z + \theta Z$ ; confidence 0.898

167. ; $K _ { 1 } ( A ) = 0$ ; confidence 0.997

168. ; $( K _ { 0 } ( A ) , K _ { 0 } ( A ) ^ { + } )$ ; confidence 0.951

169. ; $t$ ; confidence 0.354

170. ; $i$ ; confidence 0.570

171. ; $SL _ { 2 } ( C )$ ; confidence 0.910

172. ; $Q = \sum _ { j = 0 } ^ { \infty } Q _ { j } z ^ { - j } , Q _ { j } = \left( \begin{array} { c c } { h _ { j } } & { e _ { j } } \\ { f _ { j } } & { - h _ { j } } \end{array} \right)$ ; confidence 0.875

173. ; $( g )$ ; confidence 0.981

174. ; $$= \operatorname { exp } ( x P _ { 0 } z + \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } ) g ( z ) . . \operatorname { exp } ( - x P _ { 0 } z - \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { \gamma } )$$ ; confidence 0.382

175. ; $( 1 )$ ; confidence 0.515

176. ; $C [ t ] = C [ t _ { 1 } , t _ { 2 } , \ldots$ ; confidence 0.593

177. ; $q ^ { ( l ) } = 2 i \frac { \tau _ { l } + 1 } { \tau _ { l } } , r ^ { ( l ) } = - 2 i \frac { \tau _ { l } - 1 } { \tau _ { l } }$ ; confidence 0.315

178. ; $$A K N S$$ ; confidence 0.971

179. ; $C ^ { \infty } ( s ^ { 1 } , SL _ { 2 } ( C ) )$ ; confidence 0.430

180. ; $\phi$ ; confidence 0.476

181. ; $X _ { i } \in \operatorname { sl } _ { 2 } ( C )$ ; confidence 0.209

182. ; $P ^ { ( l ) } = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) z + \left( \begin{array} { c c } { 0 } & { q ^ { ( l ) } } \\ { r ^ { ( l ) } } & { 0 } \end{array} \right)$ ; confidence 0.416

183. ; $$h$$ ; confidence 0.644

184. ; $\frac { \partial } { \partial t _ { k } } F _ { i j } = \frac { \partial } { \partial t _ { i } } F _ { j k }$ ; confidence 0.932

185. ; $t = ( t _ { x } )$ ; confidence 0.458

186. ; $\phi _ { - } ^ { - 1 } \frac { \partial } { \partial t _ { \mu } } - Q _ { 0 } z ^ { \mu } \phi _ { - } = \frac { \partial } { \partial t _ { \mu } } - Q ^ { ( n ) }$ ; confidence 0.140

187. ; $C$ ; confidence 0.175

188. ; $5$ ; confidence 0.571

189. ; $L ( \Lambda _ { 0 } )$ ; confidence 0.993

190. ; $k$ ; confidence 0.504

191. ; $\phi ( x , t , z ) =$ ; confidence 0.998

192. ; $\left. \begin{array} { l } { i \frac { \partial } { \partial t } q ( x , t ) = i q t = - \frac { 1 } { 2 } q x x + q ^ { 2 } r } \\ { i \frac { \partial } { \partial t } r ( x , t ) = i r t = \frac { 1 } { 2 } r x - q r ^ { 2 } } \end{array} \right.$ ; confidence 0.260

193. ; $\phi = \phi _ { - } \phi _ { + }$ ; confidence 0.996

194. ; $\frac { \partial } { \partial t } P _ { 1 } - \frac { \partial } { \partial x } Q _ { 2 } + [ P _ { 1 } , Q _ { 2 } ] = 0$ ; confidence 0.971

195. ; $A _ { 1 } ^ { ( 1 ) }$ ; confidence 0.822

196. ; $( \tau _ { l } )$ ; confidence 0.726

197. ; $Q ^ { ( n ) } = \sum _ { j = 0 } ^ { n } Q _ { j } z ^ { n - j }$ ; confidence 0.991

198. ; $8$ ; confidence 0.857

199. ; $8$ ; confidence 0.804

200. ; $$L$$ ; confidence 0.550

201. ; $t _ { n }$ ; confidence 0.933

202. ; $F _ { j k } ^ { ( l ) } : = \frac { \partial } { \partial t _ { j } } \frac { \partial } { \partial t _ { k } } \operatorname { log } ( \tau _ { l } )$ ; confidence 0.981

203. ; $\phi _ { - } ( x , t , z ) = \operatorname { exp } ( \sum _ { i = 1 } ^ { \infty } \chi _ { i } ( x , t ) z ^ { - i } )$ ; confidence 0.963

204. ; $K P$ ; confidence 0.846

205. ; $\pi$ ; confidence 0.434

206. ; $\phi _ { + } = \operatorname { exp } ( \sum _ { j = 1 } ^ { \infty } \phi _ { j } ( x , t ) z ^ { j } )$ ; confidence 0.999

207. ; $( \partial / \partial t _ { x } ) - Q _ { 0 } z ^ { x }$ ; confidence 0.284

208. ; $0.00$ ; confidence 0.237

209. ; $F _ { j k } =$ ; confidence 0.626

210. ; $$= \frac { 1 } { 2 } \operatorname { Tr } ( \sum _ { r = 0 } ^ { j } ( j - r ) Q _ { r } Q _ { k + j - r } + \frac { 1 } { 2 } \sum _ { r = 0 } ^ { j } ( r - k ) Q _ { r } Q _ { k + j - r } )$$ ; confidence 0.240

211. ; $N$ ; confidence 0.183

212. ; $i$ ; confidence 0.889

213. ; $g ( z )$ ; confidence 0.996

214. ; $\tau ( t ) = ( \tau _ { l } ( t ) ) _ { l \in Z }$ ; confidence 0.585

215. ; $$L : = P _ { 0 } \frac { d } { d x } + P _ { 1 } = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) \frac { d } { d x } + \left( \begin{array} { c c } { 0 } & { q } \\ { r } & { 0 } \end{array} \right)$$ ; confidence 0.711

216. ; $P ^ { ( l ) }$ ; confidence 0.869

217. ; $F _ { j k } = \frac { \partial } { \partial t _ { j } } \frac { \partial } { \partial t _ { k } } \operatorname { log } ( \tau )$ ; confidence 0.976

218. ; $q ^ { ( l + 1 ) } = - ( q ^ { ( l ) } ) ^ { 2 } r ^ { ( l ) } + q ^ { ( l ) } \operatorname { log } ( q ^ { ( l ) } ) , r ^ { ( l + 1 ) } = \frac { 1 } { q ^ { ( l ) } }$ ; confidence 0.906

219. ; $Q ^ { ( n ) } : = Q _ { 0 } z ^ { n } + Q _ { 1 } z ^ { n - 1 } \ldots Q _ { n }$ ; confidence 0.716

220. ; $\partial / \partial x = \partial / \partial t _ { 1 }$ ; confidence 0.401

221. ; $\Leftrightarrow [ \frac { \partial } { \partial x } - P , \frac { \partial } { \partial t _ { n } } - Q ^ { ( n ) } ] = 0$ ; confidence 0.947

222. ; $P = P _ { 0 } z + P _ { 1 } : = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) z + \left( \begin{array} { l l } { 0 } & { q } \\ { r } & { 0 } \end{array} \right)$ ; confidence 0.374

223. ; $\sum _ { i = 0 } ^ { \infty } X _ { i } z ^ { - i }$ ; confidence 0.831

224. ; $P _ { 1 }$ ; confidence 0.674

225. ; $L ( \psi ) = z \psi$ ; confidence 0.998

226. ; $P _ { 1 } = \left( \begin{array} { c c c } { 0 } & { \square } & { q } \\ { r } & { \square } & { 0 } \end{array} \right) , Q _ { 2 } = \left( \begin{array} { c c } { - \frac { i } { 2 } q r } & { \frac { i } { 2 } q x } \\ { - \frac { i } { 2 } r _ { x } } & { \frac { i } { 2 } q r } \end{array} \right)$ ; confidence 0.352

227. ; $Q$ ; confidence 0.380

228. ; $s = \sum _ { i > 0 } C \lambda ^ { i } \left( \begin{array} { c c } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) \oplus \sum _ { i > 0 } C \lambda ^ { - i } \left( \begin{array} { c c } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) \oplus C _ { i }$ ; confidence 0.161

229. ; $12$ ; confidence 0.590

230. ; $Q _ { 0 } = P _ { 0 }$ ; confidence 0.896

231. ; $Q$ ; confidence 0.095

232. ; $z \in C$ ; confidence 0.369

233. ; $\phi - ^ { 1 } ( \frac { \partial } { \partial x } - P _ { 0 z } ) \phi _ { - } = \frac { \partial } { \partial x } - P$ ; confidence 0.173

234. ; $\frac { \partial } { \partial t _ { m } } P - \frac { \partial } { \partial x } Q ^ { ( m ) } + [ P , Q ^ { ( r ) } ] = 0 \Leftrightarrow$ ; confidence 0.156

235. ; $Q _ { 1 } = P _ { 1 }$ ; confidence 0.999

236. ; $( \partial / \partial x ) - P _ { 0 } z$ ; confidence 0.947

237. ; $i$ ; confidence 0.474

238. ; $F _ { j k }$ ; confidence 0.974

239. ; $P _ { n + 1 } = \sum _ { i = 0 } ^ { n + 1 } u _ { i } ( \frac { d } { d x } ) ^ { i }$ ; confidence 0.947

240. ; $s l _ { 2 }$ ; confidence 0.247

241. ; $( 2 \times 2 )$ ; confidence 1.000

242. ; $P$ ; confidence 0.462

243. ; $\frac { \partial } { \partial t _ { n } } Q = [ Q ^ { ( n ) } , Q ] , n \geq 1$ ; confidence 0.137

244. ; $T$ ; confidence 0.973

245. ; $L ^ { Y } ( X , Y )$ ; confidence 0.431

246. ; $0 \leq S \leq T \in L ( X )$ ; confidence 0.657

247. ; $\varepsilon \in X$ ; confidence 0.430

248. ; $Y$ ; confidence 0.894

249. ; $r _ { ess } ( T )$ ; confidence 0.259

250. ; $$T : X \rightarrow Y$$ ; confidence 0.863

251. ; $X = 1 ^ { p }$ ; confidence 0.914

252. ; $T$ ; confidence 0.750

253. ; $x | < e$ ; confidence 0.841

254. ; $| e | | < 1$ ; confidence 0.271

255. ; $S < T$ ; confidence 0.984

256. ; $r _ { e . s s } ( T ) \in \sigma _ { ess } ( T )$ ; confidence 0.088

257. ; $Y = L ^ { 1 } ( \mu )$ ; confidence 1.000

258. ; $5$ ; confidence 0.396

259. ; $S , T \in L ( X )$ ; confidence 0.814

260. ; $r ( S ) \leq r ( T )$ ; confidence 0.998

261. ; $\sigma _ { ess } ( T )$ ; confidence 0.490

262. ; $1 \leq p < \infty$ ; confidence 0.999

263. ; $0 \leq S \leq T$ ; confidence 0.838

264. ; $X = c 0$ ; confidence 0.759

265. ; $| x | | \leq 1$ ; confidence 0.929

266. ; $1 - \alpha$ ; confidence 0.993

267. ; $A$ ; confidence 0.952

268. ; $74$ ; confidence 0.550

269. ; $3$ ; confidence 0.891

270. ; $\beta _ { 1 } , \ldots , \beta _ { p }$ ; confidence 0.501

271. ; $Z = X \Gamma + F$ ; confidence 0.500

272. ; $\Sigma _ { 1 } = X _ { 4 } ^ { \prime } \Sigma X _ { 4 }$ ; confidence 0.322

273. ; $x$ ; confidence 0.751

274. ; $z = \Gamma y$ ; confidence 0.946

275. ; $s \times p$ ; confidence 0.642

276. ; $( i , j )$ ; confidence 0.935

277. ; $B$ ; confidence 0.651

278. ; $0$ ; confidence 0.969

279. ; $M _ { E }$ ; confidence 0.680

280. ; $( n$ ; confidence 0.239

281. ; $Z _ { 13 }$ ; confidence 0.481

282. ; $T _ { 1 }$ ; confidence 0.446

283. ; $P$ ; confidence 0.403

284. ; $j = 1 , \ldots , p$ ; confidence 0.616

285. ; $2$ ; confidence 0.985

286. ; $$c$$ ; confidence 0.324

287. ; $\hat { \eta } _ { \Omega } = X \hat { \beta }$ ; confidence 0.485

288. ; $t$ ; confidence 0.895

289. ; $R = V _ { 33 } ^ { - 1 } V _ { 32 }$ ; confidence 0.628

290. ; $\leq F _ { \alpha ; q , x - \gamma }$ ; confidence 0.345

291. ; $a ^ { \prime } \Theta$ ; confidence 0.987

292. ; $y _ { 1 } , \dots , y _ { j }$ ; confidence 0.424

293. ; $\sqrt { 3 }$ ; confidence 0.281

294. ; $X _ { 3 }$ ; confidence 0.593

295. ; $MS _ { e } = SS _ { e } / ( n - r )$ ; confidence 0.793

296. ; $X \beta$ ; confidence 0.414

297. ; $\sum _ { i j k } ( y _ { i j k } - \eta _ { i j } ) ^ { 2 }$ ; confidence 0.779

298. ; $N$ ; confidence 0.740

299. ; $Z _ { 1 } M _ { E } ^ { - 1 } Z _ { 1 } ^ { \prime }$ ; confidence 0.548

300. ; $2$ ; confidence 0.672

301. ; $Y , B , E$ ; confidence 0.984

302. ; $8$ ; confidence 0.593

303. ; $E [ Z _ { 32 } , Z _ { 33 } ] = 0$ ; confidence 0.584

304. ; $2$ ; confidence 0.473

305. ; $1$ ; confidence 0.458

306. ; $t _ { 1 } , t _ { 2 } , \ldots$ ; confidence 0.731

307. ; $$M _ { E } = \sum _ { i j k } ( y _ { i j k } - y _ { i j . } ) ^ { \prime } ( y _ { i j k } - y _ { i j } )$$ ; confidence 0.159

308. ; $Z _ { 12 }$ ; confidence 0.917

309. ; $p \times p$ ; confidence 0.711

310. ; $H ^ { \prime }$ ; confidence 0.219

311. ; $e _ { j k }$ ; confidence 0.169

312. ; $Z _ { 32 } , Z _ { 33 }$ ; confidence 0.917

313. ; $a ^ { \prime } \Theta$ ; confidence 0.275

314. ; $x$ ; confidence 0.968

315. ; $( q , n - r )$ ; confidence 0.777

316. ; $( r - q ) \times p$ ; confidence 1.000

317. ; $7$ ; confidence 0.945

318. ; $i = 1 , \ldots , m$ ; confidence 0.480

319. ; $q = 1$ ; confidence 0.790

320. ; $N ( 0 , \Sigma _ { 1 } )$ ; confidence 0.996

321. ; $z _ { 1 }$ ; confidence 0.669

322. ; $y , \beta , e$ ; confidence 0.936

323. ; $= \operatorname { sin } \gamma q$ ; confidence 0.055

324. ; $c ^ { \prime } \beta = \eta$ ; confidence 0.492

325. ; $( 1 \times p )$ ; confidence 1.000

326. ; $B$ ; confidence 0.738

327. ; $\hat { \eta } \omega$ ; confidence 0.852

328. ; $n - r$ ; confidence 0.377

329. ; $m \times 1$ ; confidence 0.995

330. ; $X ^ { \prime } X \hat { \beta } = X ^ { \prime } y$ ; confidence 0.277

331. ; $6$ ; confidence 0.612

332. ; $Z _ { 12 } - Z _ { 13 } \Sigma _ { 33 } ^ { - 1 } \Sigma _ { 32 }$ ; confidence 0.727

333. ; $\hat { \psi } \pm S \cdot \hat { \sigma } \hat { \psi }$ ; confidence 0.134

334. ; $\psi \in L$ ; confidence 0.533

335. ; $\alpha$ ; confidence 0.905

336. ; $\Gamma = B X$ ; confidence 0.884

337. ; $H _ { j } : X _ { 3 } \beta _ { j } = 0$ ; confidence 0.980

338. ; $\hat { \eta } \Omega$ ; confidence 0.902

339. ; $Z _ { 0 } = Z _ { 12 } - Z _ { 13 } R$ ; confidence 0.674

340. ; $f ( Z _ { 1 } )$ ; confidence 0.795

341. ; $\Theta$ ; confidence 0.834

342. ; $\psi = \sum _ { i = 1 } ^ { q } d _ { i } \zeta _ { i }$ ; confidence 0.961

343. ; $y$ ; confidence 0.478

344. ; $M _ { H }$ ; confidence 0.989

345. ; $y _ { i j k }$ ; confidence 0.873

346. ; $E ( Z _ { 3 } ) = 0$ ; confidence 0.631

347. ; $( \alpha , \beta , \gamma ) ^ { \prime } = \beta$ ; confidence 1.000

348. ; $M _ { E } = Z _ { 3 } ^ { \prime } Z _ { 3 }$ ; confidence 0.783

349. ; $( 1 , t _ { j } , \ldots , t _ { j } ^ { k } ) ^ { \prime }$ ; confidence 0.604

350. ; $m \times s$ ; confidence 0.983

351. ; $SS _ { H } = \sum _ { i = 1 } ^ { \Psi } z _ { i } ^ { 2 }$ ; confidence 0.251

352. ; $$q \times 1$$ ; confidence 1.000

353. ; $\operatorname { dim } ( \Omega ) = r$ ; confidence 0.998

354. ; $E ( Z _ { 2 } )$ ; confidence 0.857

355. ; $( p \times p _ { 1 } )$ ; confidence 0.958

356. ; $22$ ; confidence 0.710

357. ; $\sigma ^ { 2 }$ ; confidence 0.864

358. ; $\| d \| ^ { 2 } \sigma ^ { 2 }$ ; confidence 0.982

359. ; $n > m$ ; confidence 0.980

360. ; $S$ ; confidence 0.868

361. ; $$I$$ ; confidence 0.738

362. ; $a$ ; confidence 0.607

363. ; $$n \times n$$ ; confidence 0.980

364. ; $\mu$ ; confidence 0.780

365. ; $$MS _ { e }$$ ; confidence 0.884

366. ; $$( n - r ) F$$ ; confidence 1.000

367. ; $$H : X _ { 3 } B X _ { 4 } = 0$$ ; confidence 0.914

368. ; $$E ( Z _ { 13 } ) = 0$$ ; confidence 0.388

369. ; $\Omega$ ; confidence 0.783

370. ; $$( A + \delta A ) \hat { x } = \hat { \lambda } \hat { x }$$ ; confidence 0.467

371. ; $$A + \delta A$$ ; confidence 0.999

372. ; $$A A ^ { + } A = A$$ ; confidence 0.999

373. ; $$A _ { i } \in R ^ { n \times n }$$ ; confidence 0.952

374. ; $$x + \delta x$$ ; confidence 0.997

375. ; $$A x = b$$ ; confidence 0.981

376. ; $$\sigma _ { i } ( A ) - \sigma _ { 1 } ( \delta A ) \leq \sigma _ { i } ( A + \delta A ) \leq \sigma _ { i } ( A ) + \sigma _ { i } ( \delta A )$$ ; confidence 0.987

377. ; $$A x - \hat { \lambda } x = - \delta A x$$ ; confidence 0.499

378. ; $$1 / | y ^ { i } _ { x ^ { i } } ^ { * }$$ ; confidence 0.245

379. ; $$X$$ ; confidence 0.962

380. ; $$\frac { \| ( A + \delta A ) ^ { + } - A ^ { + } \| } { \| ( A + \delta A ) ^ { + } \| _ { 2 } } \leq \mu \| A ^ { + } \| _ { 2 } \| \delta A _ { 2 }$$ ; confidence 0.551

381. ; $$\| \delta b \| \leq \epsilon \| b \|$$ ; confidence 0.440

382. ; $$3$$ ; confidence 0.899

383. ; $6$ ; confidence 0.907

384. ; $$D : \mathfrak { D } \rightarrow A$$ ; confidence 0.505

385. ; $$D _ { 2 }$$ ; confidence 0.967

386. ; $$( 1 / z ) d z$$ ; confidence 0.991

387. ; $$d [ ( \omega ) ] = 2 g - 2$$ ; confidence 0.588

388. ; $$\alpha _ { j k } = \alpha _ { k l }$$ ; confidence 0.439

389. ; $2$ ; confidence 0.729

390. ; $$L \subset F$$ ; confidence 0.990

391. ; $$B i$$ ; confidence 0.539

392. ; $$\omega P _ { i } P _ { j }$$ ; confidence 0.938

393. ; $$p | D _ { i }$$ ; confidence 0.587

394. ; $a$ ; confidence 0.856

395. ; $$A$$ ; confidence 0.998

396. ; $$L ] = \lambda$$ ; confidence 0.859

397. ; $$\varphi _ { L } : A \rightarrow P ^ { 4 }$$ ; confidence 0.936

398. ; $$\sum _ { n = 0 } ^ { \infty } f ^ { ( n ) } ( \lambda _ { n } ) P _ { n } ( z )$$ ; confidence 0.754

399. ; $$A _ { 1 } ^ { * }$$ ; confidence 0.975

400. ; $$z | > 1$$ ; confidence 0.823

401. ; $$F _ { 0 } = f$$ ; confidence 0.979

402. ; $$A \subset Y$$ ; confidence 0.990

403. ; $$B _ { j } \in B$$ ; confidence 0.414

404. ; $$t \rightarrow \infty$$ ; confidence 0.998

405. ; $$\psi \in \Gamma$$ ; confidence 1.000

406. ; $$\Lambda _ { S 5 } T$$ ; confidence 0.591

407. ; $$\operatorname { Mod } ^ { * } S = \operatorname { Mod } ^ { * } L _ { D }$$ ; confidence 0.117

408. ; $$D$$ ; confidence 0.984

409. ; $$\tilde { \Omega }$$ ; confidence 0.505

410. ; $X \in X$ ; confidence 0.278

411. ; $$h ^ { - 1 } ( F _ { 0 } )$$ ; confidence 0.995

412. ; $$A ^ { \# }$$ ; confidence 0.967

413. ; $$Z _ { G } ( - q ^ { - 1 } ) \neq 0$$ ; confidence 0.985

414. ; $$C _ { W } ( X )$$ ; confidence 0.985

415. ; $$V$$ ; confidence 0.987

416. ; $$M$$ ; confidence 0.455

417. ; $$0 \leq t _ { 1 } \leq \ldots \leq t _ { k } \leq T$$ ; confidence 0.863

418. ; $$c ( x )$$ ; confidence 0.998

419. ; $$P _ { V } ^ { \# } ( n )$$ ; confidence 0.472

420. ; $$\overline { H }$$ ; confidence 0.950

421. ; $$n \equiv a ( \operatorname { mod } b )$$ ; confidence 0.605

422. ; $$A _ { \alpha } ( x ) = o ( \frac { x } { \operatorname { log } x } )$$ ; confidence 0.911

423. ; $$\sigma ( n ) > \sigma ( m )$$ ; confidence 0.996

424. ; $$< 1$$ ; confidence 0.999

425. ; $$H ( x ) > ( 1 - \varepsilon ) ( \operatorname { log } x ) ^ { 2 }$$ ; confidence 0.997

426. ; $$x _ { k + 1 } = M ^ { - 1 } ( N x _ { k } + b )$$ ; confidence 0.894

427. ; $$[ M ^ { - 1 } A ] x = [ M ^ { - 1 } b ]$$ ; confidence 0.783

428. ; $$A = L + D + U$$ ; confidence 0.995

429. ; $$\phi : \Omega \rightarrow \Omega _ { t }$$ ; confidence 0.989

430. ; $$X \leftarrow ( U - 1 / 2 ) / ( \sqrt { ( U - U ^ { 2 } ) } / 2 )$$ ; confidence 0.910

431. ; $$X \leftarrow m + s ( U _ { 1 } + U _ { 2 } - 1 )$$ ; confidence 0.929

432. ; $$R ( f )$$ ; confidence 1.000

433. ; $$\int _ { H } f d m = \int _ { \Omega } R _ { 1 } f d P _ { 1 } = \int _ { \Omega } R _ { 2 } f d P _ { 2 }$$ ; confidence 0.794

434. ; $$y ( 0 ) = x$$ ; confidence 0.978

435. ; $$( I + \lambda A )$$ ; confidence 0.992

436. ; $$\partial X ^ { \prime \prime }$$ ; confidence 0.986

437. ; $$p ^ { * } y \leq \lambda ^ { * } p ^ { * } x$$ ; confidence 0.875

438. ; $$7$$ ; confidence 0.986

439. ; $$x ^ { \prime } > x$$ ; confidence 0.689

440. ; $$l ( D ) \geq \chi ( G ) - 1$$ ; confidence 0.970

441. ; $$\chi ( G ) < \operatorname { girth } ( G )$$ ; confidence 0.791

442. ; $$z \rightarrow 0$$ ; confidence 0.986

443. ; $$m$$ ; confidence 0.259

444. ; $$N p$$ ; confidence 0.998

445. ; $H _ { \hat { j } }$ ; confidence 0.205

446. ; $$d ( m )$$ ; confidence 0.930

447. ; $$k _ { 1 } = 2$$ ; confidence 0.992

448. ; $$\beta : S \rightarrow B / L$$ ; confidence 0.984

449. ; $$n > 1$$ ; confidence 0.998

450. ; $$A = A _ { 1 } \cap \ldots \cap A _ { n }$$ ; confidence 0.254

451. ; $$\approx 3$$ ; confidence 0.590

452. ; $$\sim 2$$ ; confidence 0.512

453. ; $$\operatorname { ad } X$$ ; confidence 0.415

454. ; $$\mathfrak { a } / W$$ ; confidence 0.438

455. ; $$( g )$$ ; confidence 0.376

456. ; $$\lambda \neq \mu$$ ; confidence 0.997

457. ; $$U _ { j } ^ { * } ( \xi )$$ ; confidence 0.987

458. ; $$X \in Ob \odot$$ ; confidence 0.251

459. ; $$l \mapsto ( . l )$$ ; confidence 0.425

460. ; $$T ^ { * }$$ ; confidence 0.984

461. ; $$K _ { X } ^ { v } \otimes L ^ { i }$$ ; confidence 0.368

462. ; $$\lambda < 1$$ ; confidence 0.995

463. ; $$W E = R . F . I$$ ; confidence 0.845

464. ; $$1 / ( 1 - \lambda )$$ ; confidence 0.977

465. ; $$X = \xi ^ { i }$$ ; confidence 0.662

466. ; $$f \times ( O _ { X } )$$ ; confidence 0.620

467. ; $$b ( t ) = F ( t ) + \int _ { 0 } ^ { t } K ( t - s ) b ( s ) d s$$ ; confidence 0.998

468. ; $$\operatorname { Ai } ( x )$$ ; confidence 0.619

469. ; $$w ^ { \prime \prime } ( z ) = z w ( z )$$ ; confidence 0.701

470. ; $$10 ^ { 16 }$$ ; confidence 1.000

471. ; $$\gamma m$$ ; confidence 0.719

472. ; $$\{ U _ { i } \}$$ ; confidence 0.984

473. ; $$f ( \psi ( z ) )$$ ; confidence 0.994

474. ; $$\int _ { - \infty } ^ { + \infty } \operatorname { ln } \| \operatorname { exp } ( i t f _ { \alpha } ) \| \frac { d t } { 1 + t ^ { 2 } } < \infty$$ ; confidence 0.982

475. ; $$\mu _ { f } ( E ) = \int _ { E } f d x$$ ; confidence 0.622

476. ; $$D = d / d t$$ ; confidence 0.954

477. ; $$C / \Omega$$ ; confidence 0.538

478. ; $$A _ { k } ^ { 2 }$$ ; confidence 0.983

479. ; $$( 2 n - 2 p )$$ ; confidence 1.000

480. ; $$x \in A ^ { p } ( X ) = A ^ { * } ( X ) \cap H ^ { 2 p } ( X )$$ ; confidence 0.669

481. ; $$p = n - 1$$ ; confidence 0.999

482. ; $$D ( x _ { 0 } ) = 0$$ ; confidence 0.998

483. ; $$x _ { 0 } ^ { 3 } x _ { 1 } + x _ { 1 } ^ { 3 } x _ { 2 } + x _ { 2 } ^ { 3 } x _ { 0 } = 0$$ ; confidence 0.999

484. ; $$\tau : G \times V \rightarrow V$$ ; confidence 0.995

485. ; $$G _ { X } = \{ g \in G : g x = x \}$$ ; confidence 0.901

486. ; $$V ^ { 1 }$$ ; confidence 0.987

487. ; $$\tau \in V o c$$ ; confidence 0.532

488. ; $$( K / k )$$ ; confidence 0.875

489. ; $$f _ { 1 } = \ldots = f _ { m }$$ ; confidence 0.889

490. ; $$L / K$$ ; confidence 0.986

491. ; $$N _ { 0 }$$ ; confidence 0.151

492. ; $$1 \leq h _ { m } \leq h . \phi ( m )$$ ; confidence 0.774

493. ; $$f ( x ) - P _ { n } ^ { 0 } ( x )$$ ; confidence 0.810

494. ; $$q ( V )$$ ; confidence 0.977

495. ; $$| K _ { i } | = | i K _ { V ^ { J } } |$$ ; confidence 0.620

496. ; $$M = 10 p _ { t x } - p _ { g } - 2 p ^ { ( 1 ) } + 12 + \theta$$ ; confidence 0.369

497. ; $$p _ { g } \neq 1$$ ; confidence 0.708

498. ; $$H$$ ; confidence 0.957

499. ; $$m = \nu ( P )$$ ; confidence 0.995

500. ; $$H \times H \rightarrow H$$ ; confidence 0.989

501. ; $$A _ { \alpha } \subseteq A$$ ; confidence 0.993

502. ; $$\forall x _ { k }$$ ; confidence 0.834

503. ; $$\Omega _ { p } ^ { * } = \Omega _ { p } \cup \{ F _ { i } ^ { * } : F _ { i } \in \Omega _ { f } \}$$ ; confidence 0.985

504. ; $$L _ { \Omega }$$ ; confidence 0.997

505. ; $$\operatorname { Red } : X ( K ) \rightarrow X _ { 0 } ( k )$$ ; confidence 0.991

506. ; $$p \in C$$ ; confidence 0.958

507. ; $$b a P$$ ; confidence 0.779

508. ; $$M \times N$$ ; confidence 0.757

509. ; $$U - \text { a.p. } \subset S ^ { p } - \text { a.p. } \subset W ^ { p } - \text { a.p. } \subset B ^ { p } - \text { a.p. } \quad p \geq 1$$ ; confidence 0.179

510. ; $$\{ f ( x ) \overline { \phi } _ { \lambda } ( x ) \}$$ ; confidence 0.564

511. ; $$\pi _ { k } ( x )$$ ; confidence 0.899

512. ; $$i : A \rightarrow X$$ ; confidence 0.601

513. ; $$O ( n ^ { 2 } \operatorname { log } n )$$ ; confidence 0.568

514. ; $$f _ { 1 } = ( P _ { n } \ldots P _ { 1 } ) ^ { 1 } f$$ ; confidence 0.568

515. ; $$\| f _ { 1 } - P _ { U \cap V ^ { J } } f \| \leq c ^ { 2 l - 1 } \| f \|$$ ; confidence 0.287

516. ; $$1 \rightarrow \infty$$ ; confidence 0.982

517. ; $$\partial M ^ { n + 1 } = K ^ { n }$$ ; confidence 0.516

518. ; $$X \subset Y$$ ; confidence 0.590

519. ; $$\alpha \neq 0$$ ; confidence 0.947

520. ; $$N ( R ) \neq 0$$ ; confidence 0.997

521. ; $$Z ( A ) = A \cap Z ( R )$$ ; confidence 0.998

522. ; $$| \alpha | = \sqrt { \overline { \alpha } \alpha }$$ ; confidence 0.964

523. ; $$\alpha _ { i } + 1$$ ; confidence 0.659

524. ; $$\phi = \operatorname { am } z$$ ; confidence 0.783

525. ; $$= v : q$$ ; confidence 0.846

526. ; $$c _ { q }$$ ; confidence 0.425

527. ; $$f \in C ( \partial D )$$ ; confidence 0.993

528. ; $$f ( t ) = \psi ( \phi ( t ) )$$ ; confidence 0.999

529. ; $$R > 0$$ ; confidence 1.000

530. ; $$x <$$ ; confidence 0.424

531. ; $$a \in V$$ ; confidence 0.699

532. ; $$f ( S )$$ ; confidence 0.968

533. ; $$s = s ^ { * } \cup ( s \backslash s ^ { * } ) ^ { * } U \ldots$$ ; confidence 0.271

534. ; $$R ^ { n } \subset C ^ { k }$$ ; confidence 0.407

535. ; $$f$$ ; confidence 0.816

536. ; $$I Y \subset O$$ ; confidence 0.739

537. ; $$X \equiv 0$$ ; confidence 0.220

538. ; $$0.96$$ ; confidence 1.000

539. ; $$\Gamma _ { n } ^ { \alpha } ( H ) _ { \alpha } ^ { 8 }$$ ; confidence 0.595

540. ; $$h \in \operatorname { Diff } ^ { + } ( M )$$ ; confidence 0.591

541. ; $$Z = \int _ { A } D A \sqrt { \operatorname { det } ( / \partial _ { A } ^ { * } / \partial _ { A } ) } \operatorname { exp } [ - \| F \| ^ { 2 } ]$$ ; confidence 0.921

542. ; $$\rho _ { 0 n + } = \operatorname { sin } A$$ ; confidence 0.354

543. ; $$\times \frac { \partial ^ { m + n } } { \partial x ^ { m } \partial y ^ { n } } [ x ^ { \gamma + m - 1 } y ^ { \prime } + n - 1 _ { ( 1 - x - y ) } \alpha + w + n - \gamma - \gamma ^ { \prime } ]$$ ; confidence 0.072

544. ; $$L u \equiv \frac { \partial u } { \partial t } - \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = 0$$ ; confidence 0.607

545. ; $$F _ { b }$$ ; confidence 0.450

546. ; $$f \in F$$ ; confidence 0.988

547. ; $$( L _ { 2 } )$$ ; confidence 0.999

548. ; $$n > r$$ ; confidence 0.999

549. ; $$\hat { W } \square _ { \infty } ^ { \gamma }$$ ; confidence 0.199

550. ; $$d _ { 2 n - 1 } = d _ { 2 n }$$ ; confidence 0.797

551. ; $$S _ { 2 } ^ { \gamma }$$ ; confidence 0.562

552. ; $$m \geq r$$ ; confidence 0.999

553. ; $$\operatorname { inf } _ { u \in \mathfrak { N } } \| x - u \| = \operatorname { sup } _ { F \in X ^ { * } } [ F ( x ) - \operatorname { sup } _ { u \in \mathfrak { N } } F ( u ) ]$$ ; confidence 0.144

554. ; $$L ( f )$$ ; confidence 0.998

555. ; $$\phi _ { k } ( t _ { k } ) = 1$$ ; confidence 0.994

556. ; $$X = H$$ ; confidence 0.599

557. ; $$P _ { 0 } ( z )$$ ; confidence 0.963

558. ; $$L _ { p } ( E )$$ ; confidence 0.872

559. ; $$\operatorname { deg } P \leq n$$ ; confidence 0.996

560. ; $$D ^ { 0 } f = f$$ ; confidence 0.998

561. ; $$\{ x _ { n j } ^ { \prime } \}$$ ; confidence 0.273

562. ; $$\operatorname { sup } _ { x \in \mathfrak { M } } \| x - A x \|$$ ; confidence 0.679

563. ; $$y _ { t } = t - S _ { \eta _ { t } }$$ ; confidence 0.968

564. ; $$H _ { k + 1 } ( f ( M ) )$$ ; confidence 0.998

565. ; $$\| T _ { M } \|$$ ; confidence 0.918

566. ; $$F ( z ) = z + \alpha _ { 0 } + \frac { \alpha _ { 1 } } { z } + \ldots$$ ; confidence 0.619

567. ; $$\overline { B } = C F ( \Delta ^ { \prime } )$$ ; confidence 0.999

568. ; $$1 ^ { 1 } = 1 ^ { 1 } ( N )$$ ; confidence 0.689

569. ; $$L f \theta$$ ; confidence 0.169

570. ; $$p / p$$ ; confidence 0.977

571. ; $$b _ { i } = \alpha _ { i } \alpha _ { 1 }$$ ; confidence 0.437

572. ; $$r ^ { \prime } < r$$ ; confidence 0.977

573. ; $$\alpha \geq b$$ ; confidence 0.978

574. ; $$r$$ ; confidence 0.805

575. ; $$\phi _ { x y } a \leq b$$ ; confidence 0.847

576. ; $$\operatorname { Arg } f$$ ; confidence 0.692

577. ; $$0 \notin f ( \partial D )$$ ; confidence 0.904

578. ; $$\operatorname { arg } f$$ ; confidence 0.862

579. ; $$\beta ( A )$$ ; confidence 0.999

580. ; $$M ( A ) = V \backslash N ( A )$$ ; confidence 0.983

581. ; $$\Omega ^ { p } [ V ]$$ ; confidence 0.985

582. ; $$S _ { E } = \{ \omega \in \hat { G } : E + \omega \subseteq E \}$$ ; confidence 0.881

583. ; $$g ( u ) d u$$ ; confidence 0.997

584. ; $$\Phi ^ { ( 3 ) } ( x )$$ ; confidence 0.986

585. ; $$J _ { \nu } ( x ) \sim \sqrt { \frac { 2 } { \pi x } } [ \operatorname { cos } ( x - \frac { \pi \nu } { 2 } - \frac { \pi } { 4 } ) \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \alpha _ { 2 n } x ^ { - 2 n }$$ ; confidence 0.755

586. ; $$f ( x ) \sim \sum _ { n = 0 } ^ { \infty } a _ { n } \phi _ { n } ( x ) \quad ( x \rightarrow x _ { 0 } )$$ ; confidence 0.754

587. ; $$M \subset G$$ ; confidence 0.949

588. ; $$Y$$ ; confidence 0.441

589. ; $$P \rightarrow \Sigma$$ ; confidence 0.991

590. ; $$f ( \lambda ) = ( \frac { \sigma ^ { 2 } } { 2 \pi } ) | \phi ( e ^ { i \lambda } ) | ^ { - 2 }$$ ; confidence 0.996

591. ; $$\mathfrak { A } _ { s _ { 1 } }$$ ; confidence 0.833

592. ; $$A = S ^ { \prime }$$ ; confidence 0.502

593. ; $$20$$ ; confidence 0.906

594. ; $$W _ { N } \rightarrow W _ { n }$$ ; confidence 0.076

595. ; $$\psi ( t _ { i } )$$ ; confidence 0.991

596. ; $$L ( \Sigma )$$ ; confidence 0.983

597. ; $$\sigma ( 1 ) = s$$ ; confidence 0.805

598. ; $$\phi ( t ) \equiv$$ ; confidence 0.467

599. ; $$\dot { x } = A x$$ ; confidence 0.608

600. ; $$x _ { y } + 1 = t$$ ; confidence 0.287

601. ; $$t _ { + } < + \infty$$ ; confidence 0.793

602. ; $$p < .5$$ ; confidence 1.000

603. ; $$Y _ { i } = 2 X _ { i } - 1$$ ; confidence 0.991

604. ; $$\{ A \rangle$$ ; confidence 0.294

605. ; $$\epsilon - \delta$$ ; confidence 0.998

606. ; $$| x$$ ; confidence 0.207

607. ; $$e$$ ; confidence 0.314

608. ; $$A ( \iota X A ( x ) )$$ ; confidence 0.456

609. ; $$\exists x A$$ ; confidence 0.894

610. ; $$x ^ { * } ( x ^ { * } y ) = x \wedge y$$ ; confidence 0.991

611. ; $$( x ^ { * } y ) ^ { * } z = ( x ^ { * } z ) ^ { * } ( y ^ { * } z )$$ ; confidence 0.974

612. ; $$\mathfrak { p } \supset b$$ ; confidence 0.356

613. ; $$( L ( \lambda ) )$$ ; confidence 1.000

614. ; $$\rho = ( 1 / 2 ) \sum _ { \alpha \in \Delta ^ { + } } \alpha$$ ; confidence 0.628

615. ; $$\{ \mu _ { i } \} _ { i = 1 } ^ { s - 1 } = \{ w . \lambda \} _ { w \in W ^ { ( k ) } }$$ ; confidence 0.489

616. ; $$\mathfrak { F } _ { \lambda }$$ ; confidence 0.661

617. ; $$L _ { p } ( R )$$ ; confidence 0.962

618. ; $$\left( \begin{array} { l l } { A } & { B } \\ { C } & { D } \end{array} \right)$$ ; confidence 0.965

619. ; $$V ^ { * } - V$$ ; confidence 0.998

620. ; $$V _ { n } = H _ { n } / \Gamma$$ ; confidence 0.724

621. ; $$\mu = \delta _ { X }$$ ; confidence 0.951

622. ; $$U ( y ) = \int _ { \Gamma } f ( x ) d \beta _ { Y } ( x )$$ ; confidence 0.820

623. ; $$x \in J$$ ; confidence 0.908

624. ; $$V ^ { \pm } \times V ^ { - } \times V ^ { \pm } \rightarrow V ^ { \pm }$$ ; confidence 0.809

625. ; $$T _ { K } ( K )$$ ; confidence 0.995

626. ; $$\frac { c _ { 1 } } { n } \leq ( | K | | K ^ { \circlearrowright } | ) ^ { 1 / n } \leq \frac { c _ { 2 } } { n }$$ ; confidence 0.421

627. ; $$\| T \| T ^ { - 1 } \| \geq c n$$ ; confidence 0.835

628. ; $$T : L _ { \infty } \rightarrow L _ { \infty }$$ ; confidence 0.978

629. ; $$| x _ { y } \| \rightarrow 0$$ ; confidence 0.611

630. ; $$l ^ { \infty } ( N )$$ ; confidence 0.759

631. ; $$\left( \begin{array} { c } { y - p } \\ { \vdots } \\ { y - 1 } \\ { y _ { 0 } } \end{array} \right) = \Gamma ^ { - 1 } \left( \begin{array} { c } { 0 } \\ { \vdots } \\ { 0 } \\ { 1 } \end{array} \right)$$ ; confidence 0.427

632. ; $$f ( \zeta ) > 0$$ ; confidence 0.996

633. ; $$m _ { 1 } \in M _ { 1 }$$ ; confidence 0.998

634. ; $$M _ { d } ^ { * } = M _ { d }$$ ; confidence 0.900

635. ; $$v ( \lambda ) = ( y _ { 0 } + \lambda ^ { - 1 } y _ { - 1 } + \ldots + \lambda ^ { - p } y - p ) y _ { 0 } ^ { - 1 / 2 }$$ ; confidence 0.241

636. ; $$E _ { 2 }$$ ; confidence 0.994

637. ; $$\alpha \in S _ { \alpha }$$ ; confidence 0.784

638. ; $$D \cup \Gamma$$ ; confidence 0.999

639. ; $$\lambda _ { 0 } + \ldots + \lambda _ { n } = 1$$ ; confidence 0.986

640. ; $$X _ { s } = X \times s s$$ ; confidence 0.533

641. ; $$\alpha _ { i } \in \Omega$$ ; confidence 0.833

642. ; $$\{ \xi _ { t } \}$$ ; confidence 0.990

643. ; $$\{ \xi _ { t } ( s ) \}$$ ; confidence 1.000

644. ; $$\delta _ { i k } = 0$$ ; confidence 0.900

645. ; $$f ( x ) = a x + b$$ ; confidence 0.931

646. ; $$f ( n ) \equiv 0 ( \operatorname { mod } p )$$ ; confidence 1.000

647. ; $$\| A \| _ { \infty }$$ ; confidence 0.981

648. ; $$b _ { i }$$ ; confidence 0.854

649. ; $$\pi ( m )$$ ; confidence 0.999

650. ; $$A _ { i } \Gamma \cap A _ { j } = \emptyset$$ ; confidence 0.946

651. ; $\operatorname { inf } _ { d } \int _ { \Theta } L ( \theta , d ) \frac { p ( x | \theta ) \pi ( \theta ) } { p ( x ) } d \nu ( \theta )$ ; confidence 0.420

652. ; $\theta = \theta _ { i }$ ; confidence 0.949

653. ; $D = \{ d _ { 1 } , d _ { 2 } \}$ ; confidence 0.998

654. ; $P _ { \theta } ( d x ) = p ( x | \theta ) d \mu ( x )$ ; confidence 0.550

655. ; $\delta ( x ) \in D$ ; confidence 0.997

656. ; $\pi ( \theta _ { 1 } ) = \pi _ { 1 }$ ; confidence 0.999

657. ; $\pi ( \theta _ { 2 } ) = \pi _ { 2 }$ ; confidence 0.999

658. ; $( X , B X )$ ; confidence 0.566

659. ; $\delta ^ { * } ( x ) = \left\{ \begin{array} { l l } { d _ { 1 } , } & { \text { if } \frac { p ( x | \theta _ { 2 } ) } { p ( x | \theta _ { 1 } ) } \leq \frac { \pi _ { 1 } } { \pi _ { 2 } } \frac { L _ { 12 } - L _ { 11 } } { L _ { 21 } - L _ { 22 } } } \\ { d _ { 2 } , } & { \text { if } \frac { p ( x | \theta _ { 2 } ) } { p ( x | \theta _ { 1 } ) } \geq \frac { \pi _ { 1 } } { \pi _ { 2 } } \frac { L _ { 12 } - L _ { 11 } } { L _ { 21 } - L _ { 22 } } } \end{array} \right.$ ; confidence 0.853

660. ; $\int _ { \Theta } L ( \theta , d ) \frac { p ( x | \theta ) \pi ( \theta ) } { p ( x ) } d \nu ( \theta ) = E [ L ( \theta , d ) | x ]$ ; confidence 0.885

661. ; $\rho ( \pi , \delta ) = \int _ { \Theta } \rho ( \theta , \delta ) \pi ( d \theta )$ ; confidence 0.993

662. ; $\delta ^ { * } = \delta ^ { * } ( x )$ ; confidence 0.998

663. ; $= \int _ { X } d \mu ( x ) [ \int _ { \Theta } L ( \theta , \delta ( x ) ) p ( x | \theta ) \pi ( \theta ) d \nu ( \theta ) ]$ ; confidence 0.736

664. ; $( \Theta , B _ { \Theta } )$ ; confidence 0.937

665. ; $d ^ { x }$ ; confidence 0.785

666. ; $\int \int _ { \Theta } L ( \theta , \delta ( x ) ) P _ { \theta } ( d x ) \pi ( d \theta ) =$ ; confidence 0.604

667. ; $L _ { i j } = L = ( \theta _ { i } , d _ { j } )$ ; confidence 0.694

668. ; $p ( x ) = \int _ { \Theta } p ( x | \theta ) \pi ( \theta ) d \nu ( \theta )$ ; confidence 0.972

669. ; $\rho ( \theta , \delta ) = \int _ { Y } L ( \theta , \delta ( x ) ) P _ { \theta } ( d x )$ ; confidence 0.192

670. ; $L _ { 22 } < L _ { 21 }$ ; confidence 0.945

671. ; $\rho ( \pi , \delta ) = \int _ { X } [ \pi _ { 1 } p ( x | \theta _ { 1 } ) L ( \theta _ { 1 } , \delta ( x ) ) +$ ; confidence 0.977

672. ; $\rho ( \theta , \delta )$ ; confidence 1.000

673. ; $\pi _ { 1 } + \pi _ { 2 } = 1$ ; confidence 0.992

674. ; $= \int \int _ { \Theta } L ( \theta , \delta ( x ) ) p ( x | \theta ) \pi ( \theta ) d \mu ( x ) d \nu ( \theta ) =$ ; confidence 0.774

675. ; $E [ L ( \theta , d ) | x ]$ ; confidence 0.361

676. ; $\delta \rho ( \pi , \delta )$ ; confidence 0.650

677. ; $( D , B _ { D } )$ ; confidence 0.999

678. ; $\rho ( \pi , \delta _ { \epsilon } ^ { * } ) \leq \operatorname { inf } _ { \delta } \rho ( \pi , \delta ) + \epsilon$ ; confidence 0.972

679. ; $\pi = \pi ( d \theta )$ ; confidence 0.979

680. ; $\delta = \delta ( x )$ ; confidence 0.981

681. ; $\rho ( \pi , \delta ^ { * } ) = \operatorname { inf } _ { \delta } \int _ { \Theta } \int _ { X } L ( \theta , \delta ( x ) ) P _ { \theta } ( d x ) \pi ( d \theta )$ ; confidence 0.586

682. ; $( \epsilon > 0 )$ ; confidence 0.999

683. ; $+ \pi _ { 2 } p ( x | \theta _ { 2 } ) L ( \theta _ { 2 } , \delta ( x ) ) ] d \mu ( x )$ ; confidence 0.612

684. ; $\{ P _ { \theta } : \theta \in \Theta \}$ ; confidence 0.633

685. ; $\rho ( \pi , \delta )$ ; confidence 1.000

686. ; $i , j = 1,2$ ; confidence 0.881

687. ; $\pi ( d \theta ) = \pi ( \theta ) d \nu ( \theta )$ ; confidence 0.998

688. ; $= \{ \theta _ { 1 } , \theta _ { 2 } \}$ ; confidence 1.000

689. ; $\delta ^ { * } ( x )$ ; confidence 0.978

690. ; $x \in X , \delta ^ { * } ( x )$ ; confidence 0.710

691. ; $\delta _ { \epsilon } ^ { * }$ ; confidence 0.648

692. ; $L ( \theta , d )$ ; confidence 0.992

693. ; $L _ { 11 } < L _ { 12 }$ ; confidence 0.994

694. ; $$s ( z ) = q ( z )$$ ; confidence 1.000

695. ; $$s ( z )$$ ; confidence 1.000

696. ; $$\Psi _ { 1 } ( Y ) / \hat { q } ( Y ) \leq \psi ( Y ) \leq \Psi _ { 2 } ( Y ) / \hat { q } ( Y )$$ ; confidence 0.236

697. ; $$x = ( x _ { 1 } + \ldots + x _ { n } ) / n$$ ; confidence 0.514

698. ; $$| f ( z ) | < 1$$ ; confidence 0.992

699. ; $$f \in B ( m / n )$$ ; confidence 0.956

700. ; $$L ( r ) = \int _ { 0 } ^ { 2 \pi } | z f ^ { \prime } ( z ) | d \theta = O ( \operatorname { log } \frac { 1 } { 1 - r } )$$ ; confidence 0.970

701. ; $$E X _ { 2 j } = \mu _ { 2 }$$ ; confidence 0.517

702. ; $$X _ { 1 }$$ ; confidence 0.637

703. ; $$L ( t )$$ ; confidence 0.967

704. ; $$\phi = \Pi ^ { \prime } \Pi ^ { - 1 }$$ ; confidence 0.997

705. ; $$P ( s S ) = P ( S )$$ ; confidence 0.219

706. ; $$k _ { z } = K _ { z } / \| K _ { z } \|$$ ; confidence 0.674

707. ; $$D \times D \in \Gamma ^ { 2 }$$ ; confidence 0.230

708. ; $$a ( z )$$ ; confidence 0.948

709. ; $$p _ { i } = \nu ( \alpha _ { i } )$$ ; confidence 0.832

710. ; $$d : N \cup \{ 0 \} \rightarrow R$$ ; confidence 0.953

711. ; $$x = \frac { 1 } { n } \sum _ { j = 1 } ^ { n } x$$ ; confidence 0.315

712. ; $$\Omega = S ^ { D } = \{ \omega _ { i } \} _ { i \in D }$$ ; confidence 0.591

713. ; $$P ^ { \prime }$$ ; confidence 0.871

714. ; $$p \leq 2$$ ; confidence 1.000

715. ; $$B _ { n } ( x + 1 ) - B _ { n } ( x ) = n x ^ { n - 1 }$$ ; confidence 0.672

716. ; $$/ N = T$$ ; confidence 0.692

717. ; $$\alpha = ( k + 1 / 2 )$$ ; confidence 0.643

718. ; $$1 - \frac { 2 } { \sqrt { 2 \pi } } \int _ { 0 } ^ { \alpha / T } e ^ { - z ^ { 2 } / 2 } d z = \frac { 2 } { \sqrt { 2 \pi } } \int _ { \alpha / \sqrt { T } } ^ { \infty } e ^ { - z ^ { 2 } / 2 } d z$$ ; confidence 0.722

719. ; $$\nu = a + x + 2 [ \frac { n - t - x - \alpha } { 2 } ] + 1$$ ; confidence 0.213

720. ; $$2 \operatorname { exp } \{ - \frac { 1 } { 2 } n \epsilon ^ { 2 } \}$$ ; confidence 0.999

721. ; $$K ( t ) \equiv 1$$ ; confidence 0.999

722. ; $$= 0 \text { as. } \cdot P _ { \theta _ { 0 } } ]$$ ; confidence 0.233

723. ; $$0 < \epsilon < i ( \theta _ { 0 } )$$ ; confidence 0.998

724. ; $$\omega ( x y ) = \omega ( x ) \omega ( y )$$ ; confidence 0.999

725. ; $$+ \frac { \alpha } { u } [ \alpha ( \frac { \partial u } { \partial x } ) ^ { 2 } + 2 b \frac { \partial u } { \partial x } \frac { \partial u } { \partial y } + c ( \frac { \partial u } { \partial y } ) ^ { 2 } ] +$$ ; confidence 0.828

726. ; $$x _ { i } ^ { \prime \prime } = x _ { i } ^ { \prime }$$ ; confidence 0.895

727. ; $$w = \pi ( z )$$ ; confidence 0.987

728. ; $$\Theta f$$ ; confidence 0.864

729. ; $$K > 0$$ ; confidence 0.999

730. ; $$F ^ { 2 } = \beta ^ { 2 } \operatorname { exp } \{ \frac { I \gamma } { \beta } \}$$ ; confidence 0.990

731. ; $$F . C _ { i j k } = I m$$ ; confidence 0.621

732. ; $$( 1 - \Delta ) ^ { m } P _ { \alpha } ( x ) = P _ { \alpha - 2 m } ( x )$$ ; confidence 0.951

733. ; $$V _ { k } \varphi ( x ) = \varphi ( x - h )$$ ; confidence 0.922

734. ; $$\mu \in R$$ ; confidence 0.990

735. ; $$\overline { B } ^ { \nu }$$ ; confidence 0.987

736. ; $$( Id - \Delta ) ^ { \nu }$$ ; confidence 0.560

737. ; $$\overline { \Xi } \epsilon = 0$$ ; confidence 0.326

738. ; $$P _ { 1 }$$ ; confidence 0.928

739. ; $$E _ { \theta } \{ T \}$$ ; confidence 0.560

740. ; $$b ( \theta ) \equiv 0$$ ; confidence 0.580

741. ; $$\hat { R } ( c )$$ ; confidence 0.613

742. ; $$0 < c < 1$$ ; confidence 0.979

743. ; $$\operatorname { Re } _ { c _ { N } } = n$$ ; confidence 0.069

744. ; $$F _ { n } ( z _ { 0 } ) = 0$$ ; confidence 0.993

745. ; $$| w | < r _ { 0 }$$ ; confidence 0.478

746. ; $$F _ { n } ( z )$$ ; confidence 0.855

747. ; $$\sum _ { n = 1 } ^ { \infty } l _ { k } ^ { 2 } \operatorname { exp } ( l _ { 1 } + \ldots + l _ { n } ) = \infty$$ ; confidence 0.545

748. ; $$x \in G _ { n }$$ ; confidence 0.415

749. ; $$( \tau = \text { const } )$$ ; confidence 0.589

750. ; $$w _ { 2 } ( F )$$ ; confidence 0.966

751. ; $$B = \{ b _ { i } : i \in I \}$$ ; confidence 0.985

752. ; $$H _ { m }$$ ; confidence 0.869

753. ; $$H _ { k } \circ \operatorname { exp } ( X _ { F } ) = \operatorname { exp } ( X _ { F } ) ( H _ { k } )$$ ; confidence 0.992

754. ; $$\mu _ { n } ( t ) = 0$$ ; confidence 0.990

755. ; $$\lambda _ { n } ( t ) = v$$ ; confidence 0.997

756. ; $$u = q ( x ) \text { on } g$$ ; confidence 0.462

757. ; $$\vec { u } = A _ { j } ^ { i } u ^ { j }$$ ; confidence 0.648

758. ; $$R _ { y } ^ { t }$$ ; confidence 0.060

759. ; $$S _ { T }$$ ; confidence 0.992

760. ; $$U ( t ) = \sum _ { 1 } ^ { \infty } P ( S _ { k } \leq t ) = \sum _ { 1 } ^ { \infty } F ^ { ( k ) } ( t )$$ ; confidence 0.917

761. ; $$K ^ { * }$$ ; confidence 0.777

762. ; $$2 \int \int _ { G } ( x \frac { \partial y } { \partial u } \frac { \partial y } { \partial v } ) d u d v = \oint _ { \partial G } ( x y d y )$$ ; confidence 0.204

763. ; $$q \in Z ^ { N }$$ ; confidence 0.950

764. ; $$0 \leq \lambda _ { 1 } ( \eta ) \leq \ldots \leq \lambda _ { m } ( \eta ) \leq \ldots \rightarrow \infty$$ ; confidence 0.714

765. ; $$A A ^ { T } = ( r - \lambda ) E + \lambda J$$ ; confidence 0.999

766. ; $$n _ { 1 } = 9$$ ; confidence 0.822

767. ; $$X _ { 1 } \times X _ { 2 }$$ ; confidence 0.987

768. ; $$0 \leq \delta \leq ( n - 1 ) / 2 ( n + 1 )$$ ; confidence 0.999

769. ; $$\tau ^ { n }$$ ; confidence 0.408

770. ; $$r ^ { 3 } / v \ll 1$$ ; confidence 0.747

771. ; $$\leq \frac { 1 } { N } \langle U _ { 1 } - U _ { 2 } \} _ { U _ { 2 } }$$ ; confidence 0.419

772. ; $$M _ { A g }$$ ; confidence 0.870

773. ; $$P T ( C ) \in G$$ ; confidence 0.971

774. ; $$\| x + y \| _ { p } = \| u + v \| _ { p }$$ ; confidence 0.572

775. ; $$n ( z ) = n _ { 0 } e ^ { - m g z / k T }$$ ; confidence 0.985

776. ; $$H = \sum _ { i } \frac { p _ { i } ^ { 2 } } { 2 m } + \sum _ { i } U ( r _ { i } )$$ ; confidence 0.992

777. ; $$E = \sum _ { i = 1 } ^ { M } \epsilon _ { i } N _ { i }$$ ; confidence 0.900

778. ; $$N = \sum _ { i = 1 } ^ { M } N$$ ; confidence 0.965

779. ; $$E$$ ; confidence 0.999

780. ; $$F ( x ) = f ( M x )$$ ; confidence 1.000

781. ; $$d s ^ { 2 } = \frac { d u ^ { 2 } + d v ^ { 2 } } { ( U + V ) ^ { 2 } }$$ ; confidence 0.972

782. ; $$\Omega _ { M } ( \rho ) \in V _ { M } ^ { V ^ { n } }$$ ; confidence 0.820

783. ; $$( x \vee C x ) \wedge y = y$$ ; confidence 0.985

784. ; $$( M )$$ ; confidence 1.000

785. ; $$h \in \Omega$$ ; confidence 0.914

786. ; $$\sum \frac { 1 } { 1 }$$ ; confidence 0.251

787. ; $$\partial ^ { k } f / \partial x : B ^ { m } \rightarrow B$$ ; confidence 0.717

788. ; $$99$$ ; confidence 0.271

789. ; $$\tilde { \mathfrak { N } } = \mathfrak { N } \backslash ( V _ { j = 1 } ^ { t } \mathfrak { A } ^ { \prime \prime } )$$ ; confidence 0.082

790. ; $$\omega _ { i } = 1$$ ; confidence 0.972

791. ; $$M _ { 1 } \cup M _ { 2 }$$ ; confidence 0.994

792. ; $$x ^ { \sigma } = x$$ ; confidence 0.948

793. ; $$t _ { f } ( n )$$ ; confidence 0.917

794. ; $$\frac { 2 ^ { n } } { \operatorname { log } _ { 2 } n \cdot \operatorname { log } _ { 2 } \operatorname { log } _ { 2 } n } < l _ { f } ( n ) < \frac { 2 ^ { n } } { \operatorname { log } _ { 2 } n }$$ ; confidence 0.504

795. ; $$\beta \neq - \alpha$$ ; confidence 0.992

796. ; $$\Delta _ { - } = - \Delta _ { + }$$ ; confidence 0.970

797. ; $$[ e _ { i } f _ { j } ] = h _ { i }$$ ; confidence 0.684

798. ; $$\alpha _ { i j } \neq 0$$ ; confidence 0.797

799. ; $$\alpha _ { i } \in R$$ ; confidence 0.443

800. ; $$\operatorname { lim } \mathfrak { g } ^ { \alpha } = 1$$ ; confidence 0.737

801. ; $$9 -$$ ; confidence 0.467

802. ; $$\alpha _ { k } = a _ { k k } - v _ { k } A _ { k - 1 } ^ { - 1 } u _ { k }$$ ; confidence 0.522

803. ; $$\mathfrak { M } _ { n }$$ ; confidence 0.373

804. ; $$\mathfrak { h } \subset \mathfrak { g }$$ ; confidence 0.959

805. ; $$A = R ( X )$$ ; confidence 0.988

806. ; $$\partial M _ { A } \subset X \subset M _ { A }$$ ; confidence 0.891

807. ; $$\Gamma \subset M _ { A }$$ ; confidence 0.920

808. ; $$| \hat { \alpha } ( \xi ) | > | \hat { \alpha } ( \eta ) |$$ ; confidence 0.745

809. ; $$\hat { G } \backslash G$$ ; confidence 0.582

810. ; $$f ( e ^ { i \theta } ) = \operatorname { lim } _ { r \rightarrow 1 - 0 } f ( r e ^ { i \theta } )$$ ; confidence 0.451

811. ; $$N ^ { * } ( D )$$ ; confidence 0.999

812. ; $$F ^ { \prime } ( w )$$ ; confidence 0.999

813. ; $$U ^ { N }$$ ; confidence 0.743

814. ; $$N ^ { * } ( \Omega )$$ ; confidence 0.996

815. ; $$\Phi ( \theta )$$ ; confidence 1.000

816. ; $$f ^ { * } ( z ) = \operatorname { lim } _ { r \rightarrow 1 - 0 } f ( r z )$$ ; confidence 0.445

817. ; $$B = H ^ { \infty } \subset H _ { \psi } \subset N ^ { * }$$ ; confidence 0.752

818. ; $$n ^ { \prime } = - n + m - 1$$ ; confidence 0.993

819. ; $$t _ { 0 } \in \partial S$$ ; confidence 0.816

820. ; $$C _ { \alpha }$$ ; confidence 0.664

821. ; $$K$$ ; confidence 0.981

822. ; $$K ^ { + }$$ ; confidence 0.992

823. ; $$L u = \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } - \frac { \partial u } { \partial t } = 0$$ ; confidence 0.466

824. ; $$t \in S$$ ; confidence 0.474

825. ; $$k ^ { \prime } = 1$$ ; confidence 0.991

826. ; $$\pi _ { i } / ( \pi _ { i } + \pi _ { j } )$$ ; confidence 0.304

827. ; $$1 \rightarrow K ( n ) \rightarrow B ( n ) \rightarrow S ( n ) \rightarrow 1$$ ; confidence 0.993

828. ; $$( i i + 1 )$$ ; confidence 0.886

829. ; $$\Pi ^ { \prime \prime }$$ ; confidence 0.914

830. ; $$P _ { 1 / 2 }$$ ; confidence 0.996

831. ; $$\omega ^ { - 1 }$$ ; confidence 0.909

832. ; $$H ^ { * } ( O ( n ) ) \rightarrow H ^ { * } ( B ( n ) )$$ ; confidence 0.999

833. ; $$\sum h _ { ( 1 ) } \otimes h _ { ( 2 ) }$$ ; confidence 0.516

834. ; $$\lambda _ { W } : V \otimes W \rightarrow W \otimes V$$ ; confidence 0.988

835. ; $$U _ { q } ( \mathfrak { g } )$$ ; confidence 0.626

836. ; $$L _ { p } ( T )$$ ; confidence 0.938

837. ; $$X$$ ; confidence 0.601

838. ; $$G ( u )$$ ; confidence 0.489

839. ; $$P \{ \mu ( t + t _ { 0 } ) = j | \mu ( t _ { 0 } ) = i \}$$ ; confidence 0.724

840. ; $$t _ { 1 } + t$$ ; confidence 0.973

841. ; $$P \{ \xi _ { t } \equiv 0 \} = 1$$ ; confidence 0.670

842. ; $$\int _ { 0 } ^ { 1 } \frac { 1 - G ( s ) } { F ( s ) - s } d s < \infty$$ ; confidence 0.998

843. ; $$P _ { C } ^ { 1 }$$ ; confidence 0.433

844. ; $$r ^ { 2 }$$ ; confidence 1.000

845. ; $$\operatorname { dim } ( V / K ) = 1$$ ; confidence 0.998

846. ; $$R [ H \times H$$ ; confidence 0.981

847. ; $$( \oplus _ { b } G _ { E B } b )$$ ; confidence 0.179

848. ; $$P _ { I } ^ { f } : C ^ { \infty } \rightarrow L$$ ; confidence 0.321

849. ; $$\alpha ^ { i }$$ ; confidence 0.739

850. ; $$f ( x ) = x ^ { t } M x$$ ; confidence 0.999

851. ; $$\frac { \partial N _ { i } } { \partial t } + u _ { i } \nabla N _ { i } = G _ { i } - L _ { i }$$ ; confidence 0.250

852. ; $$B \otimes K ( H )$$ ; confidence 0.796

853. ; $$Q ( H ) = B ( H ) / K ( H )$$ ; confidence 0.959

854. ; $$M _ { t } : = \operatorname { sup } _ { s \leq t } W _ { s }$$ ; confidence 0.396

855. ; $$\operatorname { lim } _ { n \rightarrow \infty } \nabla f ( x _ { n } ) = 0$$ ; confidence 0.985

856. ; $$x _ { + } = x _ { c } + \lambda d$$ ; confidence 0.719

857. ; $$\nu : Z ( K ) \rightarrow V \subset \operatorname { Aff } ( A )$$ ; confidence 0.915

858. ; $$\operatorname { dim } A = 2$$ ; confidence 0.998

859. ; $$0 \leq i \leq d - 1$$ ; confidence 0.993

860. ; $$d = \operatorname { dim } A$$ ; confidence 0.989

861. ; $$P _ { \alpha }$$ ; confidence 0.384

862. ; $$V _ { Q }$$ ; confidence 0.244

863. ; $$A$$ ; confidence 0.535

864. ; $$F _ { m }$$ ; confidence 0.945

865. ; $$n \geq 2 ^ { 13 }$$ ; confidence 0.999

866. ; $$n = p$$ ; confidence 0.858

867. ; $$d \geq n$$ ; confidence 0.956

868. ; $$2 ^ { 12 }$$ ; confidence 0.999

869. ; $$\frac { \partial v } { \partial t } - 6 v ^ { 2 } \frac { \partial v } { \partial x } + \frac { \partial ^ { 3 } v } { \partial x ^ { 3 } } = 0$$ ; confidence 0.944

870. ; $$\rho _ { j \overline { k } } = \partial ^ { 2 } \rho / \partial z _ { j } \partial z _ { k }$$ ; confidence 0.185

871. ; $$h : H \rightarrow ( C \bigotimes T M ) / ( H \oplus \overline { H } )$$ ; confidence 0.332

872. ; $$D ^ { \perp }$$ ; confidence 0.893

873. ; $$T : A _ { j } \rightarrow A$$ ; confidence 0.526

874. ; $$v = u ^ { 2 } +$$ ; confidence 0.633

875. ; $$X _ { t } = 2.632 + 1.492 X _ { t - 1 } - 1.324 X _ { t - 2 } + \epsilon _ { t } ^ { ( 2 ) }$$ ; confidence 0.949

876. ; $$CW ( 9.63 )$$ ; confidence 0.827

877. ; $$\Sigma _ { 12 } = \Sigma _ { 2 } ^ { T }$$ ; confidence 0.747

878. ; $$K _ { X } K _ { X }$$ ; confidence 0.800

879. ; $$C A$$ ; confidence 0.232

880. ; $$X \backslash K _ { X }$$ ; confidence 0.934

881. ; $$E ( \lambda )$$ ; confidence 1.000

882. ; $$\underline { C } ( E ) = \operatorname { sup } C ( K )$$ ; confidence 0.963

883. ; $$f$$ ; confidence 0.647

884. ; $$0 \leq j < k$$ ; confidence 0.995

885. ; $$( f \in H _ { C } ( D ) )$$ ; confidence 0.513

886. ; $$f \in H _ { c } ( D )$$ ; confidence 0.898

887. ; $$\rho \in C ^ { 2 } ( \overline { \Omega } )$$ ; confidence 0.996

888. ; $$E \times E$$ ; confidence 0.999

889. ; $$\nabla ^ { \prime } = \nabla$$ ; confidence 0.998

890. ; $$s _ { m } = r - s - \operatorname { rank } M _ { m } - 1$$ ; confidence 0.443

891. ; $$\epsilon ( \sigma ) = 1$$ ; confidence 0.993

892. ; $$1$$ ; confidence 0.897

893. ; $$t \otimes _ { k } K$$ ; confidence 0.618

894. ; $$\mu = \beta \nu$$ ; confidence 0.406

895. ; $$\lambda : V \rightarrow P$$ ; confidence 0.999

896. ; $$1 / \mu = d S / d \sigma$$ ; confidence 0.936

897. ; $$\psi ( z ) : = \frac { d } { d z } \{ \operatorname { log } \Gamma ( z ) \} = \frac { \Gamma ^ { \prime } ( z ) } { \Gamma ( z ) }$$ ; confidence 0.998

898. ; $$\operatorname { log } \Gamma ( z ) = \int _ { 1 } ^ { z } \psi ( t ) d t$$ ; confidence 0.962

899. ; $$F ( 1 _ { A } ) = 1 _ { F A }$$ ; confidence 0.901

900. ; $$( \alpha \circ \beta ) ( c ) _ { d x } = \sum _ { b } \alpha ( b ) _ { a } \beta ( c ) _ { b }$$ ; confidence 0.330

901. ; $$\alpha \rightarrow \dot { b }$$ ; confidence 0.200

902. ; $$e \in E$$ ; confidence 0.839

903. ; $$( \alpha _ { e } ) _ { é \in E }$$ ; confidence 0.403

904. ; $$Z [ X _ { é } : e \in E$$ ; confidence 0.114

905. ; $$1 \leq i \leq n - 1$$ ; confidence 0.993

906. ; $$Ab ^ { Z C } \approx Ab ^ { C }$$ ; confidence 0.662

907. ; $$\Omega _ { 0 } \times \{ x _ { 0 }$$ ; confidence 0.971

908. ; $$x = x ^ { 0 }$$ ; confidence 0.989

909. ; $$F ^ { - } ( \zeta _ { 0 } )$$ ; confidence 0.984

910. ; $$\psi = \psi ( s )$$ ; confidence 0.998

911. ; $$u ( x _ { 0 } ) = u _ { 0 }$$ ; confidence 0.932

912. ; $$L u = \sum _ { | \alpha | \leq m } \alpha _ { \alpha } ( x ) \frac { \partial ^ { \alpha } u } { \partial x ^ { \alpha } } = f ( x )$$ ; confidence 0.358

913. ; $$y _ { n + 1 } = y _ { n } + \frac { h } { 2 } ( f _ { n + 1 } + f _ { n } )$$ ; confidence 0.957

914. ; $$- w$$ ; confidence 0.598

915. ; $$- u _ { 3 }$$ ; confidence 0.803

916. ; $$A _ { j } A _ { k l } = A _ { k l } A _ { j }$$ ; confidence 0.372

917. ; $$V ( t ) = - V ( s )$$ ; confidence 1.000

918. ; $$\Gamma$$ ; confidence 0.974

919. ; $$x \in \operatorname { Dom } A$$ ; confidence 0.300

920. ; $$\partial I ^ { p }$$ ; confidence 0.973

921. ; $$E \| X _ { k } \| ^ { 3 + \alpha } < \infty$$ ; confidence 0.604

922. ; $$f \in C ^ { k }$$ ; confidence 0.918

923. ; $$( a b \alpha ) ^ { \alpha } = \alpha ^ { \alpha } b ^ { \alpha } \alpha ^ { \alpha }$$ ; confidence 0.173

924. ; $$D _ { p }$$ ; confidence 0.949

925. ; $$C \rho _ { p } C ^ { \prime }$$ ; confidence 0.884

926. ; $$\tilde { Y } \square _ { j } ^ { ( k ) } \in Y _ { j }$$ ; confidence 0.172

927. ; $$b \neq 0$$ ; confidence 1.000

928. ; $$y ^ { \prime \prime } - y > f ( x )$$ ; confidence 1.000

929. ; $$V ( \Lambda ^ { \prime } ) \otimes V ( \Lambda ^ { \prime \prime } )$$ ; confidence 0.996

930. ; $$\phi : \mathfrak { g } \rightarrow \mathfrak { g } ( V )$$ ; confidence 0.515

931. ; $$\chi \pi _ { \alpha }$$ ; confidence 0.268

932. ; $$\pi _ { 0 }$$ ; confidence 0.537

933. ; $$A$$ ; confidence 0.992

934. ; $$\alpha _ { \nu } ( x ) \rightarrow b _ { \nu } ( x ^ { \prime } )$$ ; confidence 0.798

935. ; $$\pi _ { \mathscr { q } } ( F )$$ ; confidence 0.437

936. ; $$c _ { q } ( \xi ) = \kappa ( \eta ^ { q } )$$ ; confidence 0.820

937. ; $$B G$$ ; confidence 0.998

938. ; $$\kappa ( \eta ^ { q } ) \in H ^ { 2 q } ( B )$$ ; confidence 0.856

939. ; $$E X ^ { 2 n } < \infty$$ ; confidence 0.974

940. ; $$t _ { k } \in R ^ { 1 }$$ ; confidence 0.998

941. ; $$b _ { k } ^ { \prime } = ( - 1 ) ^ { k + 1 } b _ { k }$$ ; confidence 0.930

942. ; $$X = \frac { 1 } { n } \sum _ { j = 1 } ^ { n } X$$ ; confidence 0.670

943. ; $$p ( x ) = \frac { 1 } { ( 2 \pi ) ^ { 3 / 2 } \sigma ^ { 2 } } \operatorname { exp } \{ - \frac { 1 } { 2 \sigma ^ { 2 } } ( x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } + x _ { 3 } ^ { 2 } ) \}$$ ; confidence 0.970

944. ; $$k ( C ^ { * } )$$ ; confidence 0.992

945. ; $$g = 0 \Rightarrow c$$ ; confidence 0.793

946. ; $$\tau = \tau ( E )$$ ; confidence 0.992

947. ; $$x _ { j } = \operatorname { cos } ( \pi j / N )$$ ; confidence 0.826

948. ; $$C _ { \omega }$$ ; confidence 0.073

949. ; $$h ^ { * } ( pt )$$ ; confidence 0.903

950. ; $$\Omega _ { 2 n } ^ { 2 } \rightarrow Z$$ ; confidence 0.476

951. ; $$\xi _ { 1 } ^ { 2 } + \ldots + \xi _ { k - m - 1 } ^ { 2 } + \mu _ { 1 } \xi _ { k - m } ^ { 2 } + \ldots + \mu _ { m } \xi _ { k - 1 } ^ { 2 }$$ ; confidence 0.818

952. ; $$j = 1 : n$$ ; confidence 0.980

953. ; $$T ( 0 ) = 0$$ ; confidence 0.574

954. ; $$\lambda \in \Lambda$$ ; confidence 0.954

955. ; $$f = \sum _ { i = 1 } ^ { n } \alpha _ { i } \chi _ { i }$$ ; confidence 0.422

956. ; $$+ \frac { 1 } { 2 } \sum _ { 0 < u \leq \sqrt { x / 3 } } ( [ \sqrt { x - 2 u ^ { 2 } } ] - u ) + O ( \sqrt { x } )$$ ; confidence 0.498

957. ; $$\theta \leq 1 / 2$$ ; confidence 0.991

958. ; $$a ( r )$$ ; confidence 0.924

959. ; $$N = L . L$$ ; confidence 0.482

960. ; $$Q / Z$$ ; confidence 0.664

961. ; $$( k \times n )$$ ; confidence 1.000

962. ; $$\phi ( x ) = [ ( 1 - x ) ( 1 + x ) ] ^ { 1 / 2 }$$ ; confidence 0.999

963. ; $$\phi ( x ) \equiv 1$$ ; confidence 0.999

964. ; $$\phi ( x ) = ( 1 - x ) ^ { \alpha } ( 1 + x ) ^ { \beta }$$ ; confidence 0.998

965. ; $$x ( t ) : R \rightarrow R ^ { n }$$ ; confidence 0.947

966. ; $$20$$ ; confidence 0.225

967. ; $$j \leq n$$ ; confidence 0.544

968. ; $$[ \gamma ]$$ ; confidence 1.000

969. ; $$x \in D _ { A }$$ ; confidence 0.542

970. ; $$x _ { n } \in D _ { A }$$ ; confidence 0.553

971. ; $$K ( f )$$ ; confidence 0.998

972. ; $$C = C ( f )$$ ; confidence 0.996

973. ; $$f : D \rightarrow \Omega$$ ; confidence 1.000

974. ; $$\mu ( E ) = \mu _ { 1 } ( E ) = 0$$ ; confidence 0.998

975. ; $$\mu _ { 2 } ( C R ) = 0$$ ; confidence 0.984

976. ; $$F = \{ f ( z ) \}$$ ; confidence 0.999

977. ; $$\Delta = \tilde { A } + \hat { B } - \hat { C }$$ ; confidence 0.152

978. ; $$g : Y \rightarrow Z$$ ; confidence 0.951

979. ; $$Q ( t ) : S ^ { \prime } \rightarrow S ^ { \prime }$$ ; confidence 0.764

980. ; $$\phi ^ { h } ( pt )$$ ; confidence 0.800

981. ; $$1 B S G$$ ; confidence 0.389

982. ; $$N \gg n$$ ; confidence 0.849

983. ; $$B O _ { m } \times B O _ { n } \rightarrow B O _ { m } + n$$ ; confidence 0.775

984. ; $$B P \square ^ { * } ( B P )$$ ; confidence 0.987

985. ; $$\Omega _ { f r } ^ { i }$$ ; confidence 0.443

986. ; $$O ( X ) = \oplus _ { n = - \infty } ^ { + \infty } O ^ { n } ( X )$$ ; confidence 0.863

987. ; $$x _ { i } / ( e ^ { x _ { i } } - 1 )$$ ; confidence 0.947

988. ; $$( S _ { \omega } ^ { c } ( e ) T ) [ M ] \in Z$$ ; confidence 0.570

989. ; $$\Omega$$ ; confidence 0.892

990. ; $$M U ^ { * } ( X )$$ ; confidence 0.986

991. ; $$( n )$$ ; confidence 0.998

992. ; $$\Omega _ { fr } ^ { - i } = \Omega _ { i } ^ { fr } = \pi _ { i + N } ( S ^ { N } )$$ ; confidence 0.922

993. ; $$e ^ { x _ { i } } - 1$$ ; confidence 0.882

994. ; $$im ( \Omega _ { S C } \rightarrow \Omega _ { O } )$$ ; confidence 0.230

995. ; $$\partial N$$ ; confidence 0.677

996. ; $$b _ { i + 1 } \ldots b _ { j }$$ ; confidence 0.553

997. ; $$l _ { i } ( P ) \leq l _ { i } < l _ { i } ( P ) + 1$$ ; confidence 0.413

998. ; $$V _ { 3 }$$ ; confidence 0.998

999. ; $$\operatorname { lm } c _ { 3 } = 0$$ ; confidence 0.496

1000. ; $$\{ x _ { n } > 0 \}$$ ; confidence 0.980

1001. ; $$u ( x ) = w ( x _ { n } ) \operatorname { exp } i ( x _ { 1 } \xi _ { 1 } + \ldots + x _ { n - 1 } \xi _ { n - 1 } )$$ ; confidence 0.744

1002. ; $$M$$ ; confidence 1.000

1003. ; $$\operatorname { cd } _ { p } ( X ) \leq \operatorname { cohcd } ( X ) + 1$$ ; confidence 0.970

1004. ; $$( U ) = n - 1$$ ; confidence 0.999

1005. ; $$cd _ { l } ( Spec A )$$ ; confidence 0.637

1006. ; $$x g = \lambda x$$ ; confidence 0.984

1007. ; $$u \mapsto \rho ( u ) - \operatorname { Tr } ( \text { ad } u ) \in \operatorname { End } _ { K } ( M )$$ ; confidence 0.830

1008. ; $$A ^ { G } = \{ \alpha \in A : g \alpha = \alpha \text { for all } g \in G \}$$ ; confidence 0.750

1009. ; $$Z G$$ ; confidence 0.957

1010. ; $$f : S ^ { m } \rightarrow S ^ { n }$$ ; confidence 0.195

1011. ; $$\pi _ { n } ( E ) = \pi$$ ; confidence 0.997

1012. ; $$\square ^ { 1 } P ^ { i } = P$$ ; confidence 0.776

1013. ; $$i ^ { * } ( \phi ) = 0$$ ; confidence 0.997

1014. ; $$\beta \circ \beta = 0$$ ; confidence 0.978

1015. ; $$\alpha : H ^ { n } ( : Z ) \rightarrow H ^ { n + 3 } ( : Z _ { 2 } )$$ ; confidence 0.262

1016. ; $$\pi ^ { 1 } ( X )$$ ; confidence 0.999

1017. ; $$C ^ { \infty } ( D ( \Omega ) )$$ ; confidence 0.935

1018. ; $$\beta _ { 0 }$$ ; confidence 0.851

1019. ; $$[ \sigma ] = [ \alpha _ { 1 } ^ { \alpha _ { 1 } } \ldots a _ { n } ^ { \alpha _ { n } } ]$$ ; confidence 0.729

1020. ; $$\overline { \overline { A } } = \vec { A }$$ ; confidence 0.649

1021. ; $$\phi \in \Phi$$ ; confidence 0.995

1022. ; $$F \subset U$$ ; confidence 0.980

1023. ; $$x 0$$ ; confidence 0.689

1024. ; $$C ( S ^ { n } )$$ ; confidence 0.498

1025. ; $$f \in L _ { 1 } ( G )$$ ; confidence 0.969

1026. ; $$\Pi ^ { N } \tau$$ ; confidence 0.183

1027. ; $$\beta Y \backslash Y$$ ; confidence 0.989

1028. ; $$X = 0$$ ; confidence 0.554

1029. ; $$\overline { f } : \mu X \rightarrow \mu Y$$ ; confidence 0.995

1030. ; $$| \alpha ( z ) |$$ ; confidence 0.916

1031. ; $$\{ d F _ { i } \} _ { 1 } ^ { m }$$ ; confidence 0.930

1032. ; $$\partial _ { r }$$ ; confidence 0.315

1033. ; $$f : K \rightarrow K$$ ; confidence 0.997

1034. ; $$d = ( d _ { n } )$$ ; confidence 0.939

1035. ; $$\pi J ( s ) = \operatorname { sin } \pi s \int _ { r } ^ { \infty } \delta ^ { s - 1 } f ( - \delta ) d \delta + \frac { r ^ { s } } { 2 } \int _ { - \pi } ^ { \pi } e ^ { i \theta s } f ( r e ^ { i \theta } ) d \theta$$ ; confidence 0.764

1036. ; $$\int _ { - \infty } ^ { \infty } ( P ( x ) / Q ( x ) ) d x$$ ; confidence 0.988

1037. ; $$J ( s ) = \operatorname { lim } J _ { N } ( s ) = 2 ( 2 \pi ) ^ { s - 1 } \zeta ( 1 - s ) \operatorname { sin } \frac { \pi s } { 2 }$$ ; confidence 0.964

1038. ; $$f ( z ) = 1 / ( e ^ { z } - 1 )$$ ; confidence 0.999

1039. ; $$O _ { A } = O _ { D } / J | _ { A }$$ ; confidence 0.748

1040. ; $$DT ( S )$$ ; confidence 0.583

1041. ; $$p _ { i } \in S$$ ; confidence 0.931

1042. ; $$U ( A ) \subset Y$$ ; confidence 0.995

1043. ; $$P ( A | B ) = \frac { P ( A \cap B ) } { P ( B ) }$$ ; confidence 0.724

1044. ; $$x _ { 0 } \in V ^ { n }$$ ; confidence 0.974

1045. ; $$\dot { \phi } = \omega$$ ; confidence 0.997

1046. ; $$A _ { 3 }$$ ; confidence 0.999

1047. ; $$\Omega ^ { \prime } = \| \Omega _ { \alpha } ^ { \prime \beta } \|$$ ; confidence 0.913

1048. ; $$P _ { i j } = \frac { 1 } { n - 2 } R _ { j } - \delta _ { j } ^ { i } \frac { R } { 2 ( n - 1 ) ( n - 2 ) }$$ ; confidence 0.947

1049. ; $$\varepsilon$$ ; confidence 0.504

1050. ; $$g \in S ^ { 2 } \varepsilon$$ ; confidence 0.445

1051. ; $$N = N \times \{ 1 \} \times \{ 0 \}$$ ; confidence 1.000

1052. ; $$C ^ { \infty } ( \tilde { N } )$$ ; confidence 0.330

1053. ; $$\gamma$$ ; confidence 0.764

1054. ; $$\tau _ { 2 } \Theta = - \Theta$$ ; confidence 0.618

1055. ; $$f ^ { \prime } ( z _ { 0 } )$$ ; confidence 0.967

1056. ; $$0 < \beta \leq 2 \pi$$ ; confidence 0.997

1057. ; $$( x ^ { 2 } / a ^ { 2 } ) + ( y ^ { 2 } / b ^ { 2 } ) = 1$$ ; confidence 0.891

1058. ; $$\operatorname { arg } z = c$$ ; confidence 0.995

1059. ; $$f ( \zeta )$$ ; confidence 0.995

1060. ; $$D \subset D _ { 1 }$$ ; confidence 0.990

1061. ; $$\leq ( n + 1 ) ( n + 2 ) / 2$$ ; confidence 0.994

1062. ; $$f ^ { \prime } ( x _ { 1 } ) \equiv 0$$ ; confidence 0.424

1063. ; $$A . B$$ ; confidence 0.944

1064. ; $$m = p _ { 1 } ^ { \alpha _ { 1 } } \ldots p _ { s } ^ { \alpha _ { S } }$$ ; confidence 0.462

1065. ; $$\mu ( d )$$ ; confidence 1.000

1066. ; $$\alpha ( x ) - b ( x ) = f ( x ) g ( x ) + p h ( x )$$ ; confidence 0.849

1067. ; $$q = p ^ { r }$$ ; confidence 0.892

1068. ; $$\int _ { - \pi } ^ { \pi } f ( x ) d x = 0$$ ; confidence 0.988

1069. ; $$r \uparrow 1$$ ; confidence 0.659

1070. ; $$X = R ^ { n }$$ ; confidence 0.975

1071. ; $$f _ { i } : D ^ { n } \rightarrow M _ { i }$$ ; confidence 0.449

1072. ; $$f _ { 2 } \circ f _ { 1 } ^ { - 1 }$$ ; confidence 0.997

1073. ; $$X \in V ( B )$$ ; confidence 0.996

1074. ; $$E = T B$$ ; confidence 0.999

1075. ; $$X : B \rightarrow T B$$ ; confidence 0.984

1076. ; $$Y \in T _ { y } ( P )$$ ; confidence 0.991

1077. ; $$\omega ^ { k } = d x ^ { k }$$ ; confidence 0.878

1078. ; $$f _ { x } ^ { - 1 }$$ ; confidence 0.443

1079. ; $$X _ { X } \in T _ { X } ( M )$$ ; confidence 0.414

1080. ; $$T _ { s ( x ) } ( E ) = \Delta _ { s ( x ) } \oplus T _ { s ( x ) } ( F _ { x } )$$ ; confidence 0.402

1081. ; $$T ( M )$$ ; confidence 0.884

1082. ; $$B \rightarrow H$$ ; confidence 0.991

1083. ; $$E _ { 1 } \rightarrow E _ { 1 }$$ ; confidence 0.970

1084. ; $$\neg \neg \exists x R \supset \exists x R$$ ; confidence 0.760

1085. ; $$\int _ { \alpha } ^ { b } p ( t ) \operatorname { ln } | t - t _ { 0 } | d t = f ( t _ { 0 } ) + C$$ ; confidence 0.687

1086. ; $$D ^ { + } = \cup _ { k = 1 } ^ { m } D _ { k }$$ ; confidence 0.835

1087. ; $$\forall x \in D _ { k } : \mu _ { k } \Delta u + ( \lambda _ { k } + \mu _ { k } ) \text { grad div } u = 0$$ ; confidence 0.915

1088. ; $$T ^ { * }$$ ; confidence 0.527

1089. ; $$\alpha \wedge ( d \alpha ) ^ { n }$$ ; confidence 0.989

1090. ; $$\alpha = d t + \sum p _ { i } d q _ { i }$$ ; confidence 0.858

1091. ; $$\alpha \wedge ( d \alpha ) ^ { s } ( x ) \neq 0$$ ; confidence 0.978

1092. ; $$W ^ { m + 1 }$$ ; confidence 0.972

1093. ; $$\Lambda _ { n } ( \theta ) - h ^ { \prime } \Delta _ { n } ( \theta ) \rightarrow - \frac { 1 } { 2 } h ^ { \prime } \Gamma ( \theta ) h$$ ; confidence 0.843

1094. ; $$u ^ { k } = u ^ { k - 1 } - \Delta \lambda _ { k } \phi ^ { \prime } ( u ^ { k - 1 } ) ^ { - 1 } \phi ( u ^ { 0 } )$$ ; confidence 0.687

1095. ; $$\frac { d u } { d \lambda } = - \phi ^ { \prime } ( u ) ^ { - 1 } \phi ( u ^ { 0 } )$$ ; confidence 0.984

1096. ; $$\{ \alpha _ { n } \} _ { n = 0 } ^ { \omega } \quad \text { and } \quad \{ b _ { n } \} _ { n = 1 } ^ { \omega }$$ ; confidence 0.788

1097. ; $$D \subset R$$ ; confidence 0.995

1098. ; $$I \rightarrow \cup _ { i \in l } J _ { i }$$ ; confidence 0.225

1099. ; $$f ^ { - 1 } ( F )$$ ; confidence 0.999

1100. ; $$U = U ( x _ { 0 } )$$ ; confidence 0.991

1101. ; $$y _ { 0 } = A _ { x }$$ ; confidence 0.344

1102. ; $$B \circ A$$ ; confidence 0.963

1103. ; $$x - y \in U$$ ; confidence 0.997

1104. ; $$i B _ { 0 }$$ ; confidence 0.998

1105. ; $$( T ^ { * } ( t ) = T ( t ) )$$ ; confidence 0.991

1106. ; $$631$$ ; confidence 0.381

1107. ; $$e ^ { i } ( e _ { j } ) = \delta _ { j } ^ { s }$$ ; confidence 0.182

1108. ; $$\mathfrak { A } _ { E }$$ ; confidence 0.121

1109. ; $$v _ { ( E ) } = v$$ ; confidence 0.188

1110. ; $$\rho < 1$$ ; confidence 0.998

1111. ; $$P s$$ ; confidence 0.529

1112. ; $$J ( \alpha )$$ ; confidence 1.000

1113. ; $$N = N _ { 0 }$$ ; confidence 0.799

1114. ; $$d y _ { t } = h ( x _ { t } ) d t + d w _ { t } ^ { 0 }$$ ; confidence 0.993

1115. ; $$A _ { n } x _ { n } = y _ { n }$$ ; confidence 0.869

1116. ; $$P Q$$ ; confidence 0.981

1117. ; $$A _ { n } : E _ { n } \rightarrow F _ { n }$$ ; confidence 0.561

1118. ; $$c _ { 1 } = f ^ { \prime } ( 0 ) = 1$$ ; confidence 0.991

1119. ; $$\int _ { - \pi } ^ { \pi } d \mu ( \theta ) = 1$$ ; confidence 0.969

1120. ; $$( f _ { 1 } + f _ { 2 } ) ( x ) = f _ { 1 } ( x ) + f _ { 2 } ( x )$$ ; confidence 0.957

1121. ; $$M ^ { \perp } = \{ x \in G$$ ; confidence 0.985

1122. ; $$r _ { u } \times r _ { v } \neq 0$$ ; confidence 0.643

1123. ; $$F [ f ^ { * } g ] = \sqrt { 2 \pi } F [ f ] F [ g ]$$ ; confidence 0.818

1124. ; $$F [ f ] = \frac { F [ g ] } { 1 - \sqrt { 2 \pi } F [ K ] }$$ ; confidence 0.997

1125. ; $$X _ { 1 }$$ ; confidence 0.237

1126. ; $$\sum _ { K \in \mathscr { K } } \lambda _ { K } \chi _ { K } ( i ) = \chi _ { I } ( i ) \quad \text { for all } i \in I$$ ; confidence 0.223

1127. ; $$\{ x _ { k } \}$$ ; confidence 0.963

1128. ; $$x _ { k + 1 } = x _ { k } - \alpha _ { k } p _ { k }$$ ; confidence 0.819

1129. ; $$\alpha _ { i } < b _ { i }$$ ; confidence 0.878

1130. ; $$i _ { k } = k - n [ k / n ] + 1$$ ; confidence 0.964

1131. ; $$\alpha _ { i } : A _ { i } \rightarrow X$$ ; confidence 0.918

1132. ; $$\pi _ { i } : S \rightarrow A$$ ; confidence 0.579

1133. ; $$\prod _ { i \in l } ^ { * } A _ { i }$$ ; confidence 0.474

1134. ; $$A ^ { * } B$$ ; confidence 0.976

1135. ; $$C X Y$$ ; confidence 0.226

1136. ; $$B _ { 1 }$$ ; confidence 0.988

1137. ; $$\{ X _ { t } : t \in T \}$$ ; confidence 0.835

1138. ; $$m ( S ) ^ { 2 } > ( 2 k + 1 ) ( n - k ) + \frac { k ( k + 1 ) } { 2 } - \frac { 2 ^ { k } n ^ { 2 k + 1 } } { m ( 2 k ) ! \left( \begin{array} { l } { n } \\ { k } \end{array} \right) }$$ ; confidence 0.753

1139. ; $$\eta _ { Y | X } ^ { 2 } = 1 - E [ \frac { D ( Y | X ) } { D Y } ]$$ ; confidence 0.635

1140. ; $$\operatorname { lm } z ( x ) = 1$$ ; confidence 0.908

1141. ; $$C ( n ) = 0$$ ; confidence 1.000

1142. ; $$\sum _ { 2 } = \sum _ { \nu \in \langle \nu \rangle } U _ { 2 } ( n - D \nu )$$ ; confidence 0.960

1143. ; $$D U$$ ; confidence 0.990

1144. ; $$( \nabla _ { X } U ) _ { p }$$ ; confidence 0.933

1145. ; $$e _ { i } = \partial / \partial x ^ { i } | _ { p }$$ ; confidence 0.599

1146. ; $$\Gamma ( C ) = V$$ ; confidence 0.882

1147. ; $$| w | < 1 / 16$$ ; confidence 0.877

1148. ; $$Y _ { j } = i$$ ; confidence 0.850

1149. ; $$E _ { 8 }$$ ; confidence 0.860

1150. ; $$\frac { F _ { n } ( - x ) } { \Phi ( - x ) } = \operatorname { exp } \{ - \frac { x ^ { 3 } } { \sqrt { n } } \lambda ( - \frac { x } { \sqrt { n } } ) \} [ 1 + O ( \frac { x } { \sqrt { n } } ) ]$$ ; confidence 0.444

1151. ; $$E _ { e } ^ { t X } 1$$ ; confidence 0.078

1152. ; $$1 \leq n \leq N$$ ; confidence 0.763

1153. ; $$V _ { 0 } ^ { n } = V _ { j } ^ { n } = 0$$ ; confidence 0.626

1154. ; $$\sqrt { 2 }$$ ; confidence 0.191

1155. ; $$t \mapsto \gamma ( t ) = \operatorname { exp } _ { p } ( t v )$$ ; confidence 0.936

1156. ; $$X *$$ ; confidence 0.383

1157. ; $$F T op$$ ; confidence 0.332

1158. ; $$q = 59$$ ; confidence 0.998

1159. ; $$7$$ ; confidence 0.254

1160. ; $$M _ { k } = C _ { k }$$ ; confidence 0.997

1161. ; $$E _ { x } ( s )$$ ; confidence 0.467

1162. ; $$H ( K )$$ ; confidence 0.395

1163. ; $$N = \mu / ( n + 1 )$$ ; confidence 0.992

1164. ; $$P ( x ) = \sum _ { j = 1 } ^ { \mu } L j ( x ) f ( x ^ { ( j ) } )$$ ; confidence 0.718

1165. ; $$x ^ { 3 } + y ^ { 3 } - 3 a x y = 0$$ ; confidence 0.887

1166. ; $$j = \frac { 1728 g _ { 2 } ^ { 3 } } { g _ { 2 } ^ { 3 } - 27 g _ { 3 } ^ { 2 } }$$ ; confidence 0.284

1167. ; $$\sum _ { i = 1 } ^ { n } S _ { i } S _ { i } ^ { * } < I$$ ; confidence 0.253

1168. ; $$n = \infty$$ ; confidence 1.000

1169. ; $$T _ { 1 } ( H )$$ ; confidence 0.995

1170. ; $$u : H \rightarrow H ^ { \prime }$$ ; confidence 0.987

1171. ; $$| \alpha | = \sum _ { l = 1 } ^ { d ^ { 2 } } \alpha _ { l }$$ ; confidence 0.447

1172. ; $$C = R _ { k m m } ^ { i } R _ { k } ^ { k k m }$$ ; confidence 0.081

1173. ; $$\Sigma _ { S }$$ ; confidence 0.760

1174. ; $$( \sigma ^ { t } f ) ( t ^ { \prime } ) = f ( t + t ^ { \prime } )$$ ; confidence 1.000

1175. ; $$H C ^ { 0 } ( A )$$ ; confidence 0.945

1176. ; $$z$$ ; confidence 0.525

1177. ; $$( u = const )$$ ; confidence 0.538

1178. ; $$- \infty < z < \infty$$ ; confidence 0.577

1179. ; $$F \in L ^ { * }$$ ; confidence 0.961

1180. ; $$+ \frac { 1 } { 2 \alpha } \int _ { x - w t } ^ { x + c t } \psi ( \xi ) d \xi + \frac { 1 } { 2 } [ \phi ( x + a t ) + \phi ( x - a t ) ]$$ ; confidence 0.187

1181. ; $$D x$$ ; confidence 0.713

1182. ; $$\operatorname { gr } D _ { X }$$ ; confidence 0.395

1183. ; $$f ^ { * } N = O _ { X } \otimes _ { f } - 1 _ { O _ { Y } } f ^ { - 1 } N$$ ; confidence 0.906

1184. ; $$V _ { V }$$ ; confidence 0.082

1185. ; $$= g ( \overline { u } _ { 1 } ) - \overline { q } = g ( \overline { u } _ { 1 } ) - v _ { M }$$ ; confidence 0.711

1186. ; $$( US )$$ ; confidence 0.980

1187. ; $$( L )$$ ; confidence 0.982

1188. ; $$= \operatorname { min } _ { k \in P } c ^ { T } x ^ { ( k ) } + u _ { 1 } ^ { T } ( A _ { 1 } x ^ { ( k ) } - b _ { 1 } )$$ ; confidence 0.488

1189. ; $$0 \leq k < 1$$ ; confidence 0.997

1190. ; $$2$$ ; confidence 0.110

1191. ; $$f : S \rightarrow C$$ ; confidence 0.674

1192. ; $$S _ { p } ^ { n + p } ( c ) = \{ x \in R _ { p } ^ { n + p + 1 }$$ ; confidence 0.809

1193. ; $$u _ { n } + 1 - k$$ ; confidence 0.616

1194. ; $$\tau _ { n } ( t ) = \frac { 1 } { 2 \pi } \frac { 2 ^ { 2 n } ( n ! ) ^ { 2 } } { ( 2 n ) ! } \operatorname { cos } ^ { 2 n } \frac { t } { 2 }$$ ; confidence 0.804

1195. ; $$= d ( w ^ { H _ { i } } | v ^ { H _ { i } } ) \cdot e ( w ^ { H _ { i } } | v ^ { H _ { i } } ) . f ( w ^ { H _ { i } } | v ^ { H _ { i } } )$$ ; confidence 0.435

1196. ; $$D \subseteq g H g ^ { - 1 }$$ ; confidence 0.970

1197. ; $$\alpha \in C \cup \{ \infty \}$$ ; confidence 0.176

1198. ; $$\pi ^ { \prime } : X ^ { \prime } \rightarrow S ^ { \prime }$$ ; confidence 0.952

1199. ; $$\kappa ^ { \prime } \cong \kappa \otimes O \Lambda$$ ; confidence 0.541

1200. ; $$\lambda ^ { m }$$ ; confidence 0.955

1201. ; $$\pi ( \chi )$$ ; confidence 0.978

1202. ; $$C ^ { \infty } ( G )$$ ; confidence 0.980

1203. ; $$L \cup O$$ ; confidence 0.130

1204. ; $$M _ { 1 } = H \cap _ { k \tau _ { S } } H ^ { \prime }$$ ; confidence 0.307

1205. ; $$m - 2 r$$ ; confidence 1.000

1206. ; $$Z \in X$$ ; confidence 0.820

1207. ; $$m _ { B } ( A ) = 0$$ ; confidence 0.968

1208. ; $$m B$$ ; confidence 0.535

1209. ; $$S ^ { 4 k - 1 }$$ ; confidence 0.950

1210. ; $$H = C ^ { n }$$ ; confidence 0.847

1211. ; $$F \in Hol ( D )$$ ; confidence 0.805

1212. ; $$\zeta ( s ) = \sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { s } }$$ ; confidence 0.995

1213. ; $$\Omega _ { X / Y } ^ { 1 }$$ ; confidence 0.919

1214. ; $$\phi : A \rightarrow A$$ ; confidence 0.991

1215. ; $$s ^ { \prime } : Y ^ { \prime } \rightarrow X ^ { \prime }$$ ; confidence 0.953

1216. ; $$R ^ { i } F = H ^ { i } \circ R ^ { * } F$$ ; confidence 0.941

1217. ; $$f t = g t$$ ; confidence 0.997

1218. ; $$f : X ^ { \cdot } \rightarrow Y$$ ; confidence 0.209

1219. ; $$\Pi \stackrel { D } { 3 } = F _ { \sigma \delta }$$ ; confidence 0.232

1220. ; $$E = N$$ ; confidence 0.995

1221. ; $$\sum _ { \mathfrak { D } _ { 1 } ^ { 1 } } ( E \times N ^ { N } )$$ ; confidence 0.290

1222. ; $$\sum _ { \sim } D _ { n + 1 } ^ { 0 }$$ ; confidence 0.204

1223. ; $$k [ ( T _ { i j } ) _ { 1 \leq i \leq d } ]$$ ; confidence 0.679

1224. ; $$| \hat { b } _ { n } | = 1$$ ; confidence 0.209

1225. ; $$G r$$ ; confidence 0.809

1226. ; $$1 \leq u \leq \operatorname { exp } ( \operatorname { log } ( 3 / 5 ) - \epsilon _ { y } )$$ ; confidence 0.512

1227. ; $$1 \leq u \leq 2$$ ; confidence 0.976

1228. ; $$u > 1$$ ; confidence 0.987

1229. ; $$q _ { 2 } \neq q _ { 1 }$$ ; confidence 0.828

1230. ; $$\Delta ^ { m } y _ { n } = \sum _ { k = 0 } ^ { m } ( - 1 ) ^ { m - k } \left( \begin{array} { c } { m } \\ { k } \end{array} \right) y _ { n + k }$$ ; confidence 0.786

1231. ; $$| u - v | \leq \operatorname { inf } _ { w ^ { \prime } \in K } | u - w |$$ ; confidence 0.210

1232. ; $$Z _ { h }$$ ; confidence 0.217

1233. ; $$\overline { G } = G + \Gamma$$ ; confidence 0.752

1234. ; $$t = t _ { 0 } = x _ { 0 } ( 0 )$$ ; confidence 0.983

1235. ; $$u \leq \theta u$$ ; confidence 0.794

1236. ; $$\operatorname { rank } ( A _ { i } ) = \operatorname { rank } ( B _ { i } )$$ ; confidence 0.983

1237. ; $$A = \sum _ { i = 0 } ^ { d } A _ { i } u _ { A } ^ { i }$$ ; confidence 0.523

1238. ; $$G ( G / F _ { 1 } ) = G _ { 1 }$$ ; confidence 0.998

1239. ; $$\operatorname { ord } ( \theta ) = \sum e$$ ; confidence 0.833

1240. ; $$G \neq 0$$ ; confidence 0.999

1241. ; $$\{ A \}$$ ; confidence 0.999

1242. ; $$\theta = \Pi _ { i } \partial _ { i } ^ { e _ { i } ^ { e _ { i } } }$$ ; confidence 0.142

1243. ; $$x \neq \pm 1$$ ; confidence 0.956

1244. ; $$( \operatorname { sin } x ) ^ { \prime } = \operatorname { cos } x$$ ; confidence 1.000

1245. ; $$( \frac { u } { v } ) ^ { \prime } = \frac { u ^ { \prime } v - u v ^ { \prime } } { v ^ { 2 } }$$ ; confidence 0.958

1246. ; $$( \operatorname { arccos } x ) ^ { \prime } = - 1 / \sqrt { 1 - x ^ { 2 } }$$ ; confidence 0.996

1247. ; $$\Delta \rightarrow 0$$ ; confidence 0.981

1248. ; $$x _ { 2 } ( t )$$ ; confidence 0.998

1249. ; $$\dot { x } = f ( t )$$ ; confidence 0.623

1250. ; $$x _ { 1 } ( t _ { 0 } ) = x _ { 2 } ( t _ { 0 } )$$ ; confidence 0.998

1251. ; $$0 < l < n$$ ; confidence 0.998

1252. ; $$= \Phi ( z ) \operatorname { exp } \{ \frac { z - t } { \pi } \int \int _ { S } \frac { A ( \zeta ) w ( \zeta ) + B ( \zeta ) \overline { w ( \zeta ) } } { ( \zeta - z ) ( \zeta - t ) w } d \xi d \eta \}$$ ; confidence 0.918

1253. ; $$W _ { 2 } ^ { p }$$ ; confidence 0.986

1254. ; $$L u = \operatorname { div } ( p ( x ) \operatorname { grad } u ) + q ( x ) u$$ ; confidence 0.840

1255. ; $$R _ { L } = H ( V )$$ ; confidence 0.569

1256. ; $$( x - x _ { 0 } ) / ( t - t _ { 0 } ) = u _ { 0 }$$ ; confidence 0.980

1257. ; $$n - m$$ ; confidence 0.998

1258. ; $$\partial x / u = \partial t / 1$$ ; confidence 0.967

1259. ; $$\sum _ { n = 1 } ^ { \infty } | x _ { n } ( t ) |$$ ; confidence 0.933

1260. ; $$| x ( t ( t ) ) \| \leq \rho$$ ; confidence 0.117

1261. ; $$\dot { x } ( t ) = A x ( t - h ) - D x ( t )$$ ; confidence 0.986

1262. ; $$2 \pi \alpha$$ ; confidence 0.461

1263. ; $$z = \phi _ { i }$$ ; confidence 0.976

1264. ; $$s ^ { \prime } ( \Omega ^ { r } ( X ) )$$ ; confidence 0.911

1265. ; $$\int _ { S } \omega$$ ; confidence 0.561

1266. ; $$\omega \in \Omega ^ { d } [ X ]$$ ; confidence 0.948

1267. ; $$\hat { V }$$ ; confidence 0.359

1268. ; $$d \omega = d \square ^ { * } \omega = 0$$ ; confidence 0.954

1269. ; $$\partial M$$ ; confidence 0.831

1270. ; $$u _ { R } ^ { k } ( x ) = \sum _ { i = 1 } ^ { n } u _ { i } a _ { i } ^ { k } ( x )$$ ; confidence 0.362

1271. ; $$u ( x _ { i } )$$ ; confidence 0.997

1272. ; $$r \in F$$ ; confidence 0.671

1273. ; $$b _ { 0 }$$ ; confidence 0.363

1274. ; $$r : h \rightarrow f ( x _ { 0 } + h ) - f ( x _ { 0 } ) - h _ { 0 } ( h )$$ ; confidence 0.388

1275. ; $$\frac { \partial u } { \partial t } + u \frac { \partial u } { \partial x } = D \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } }$$ ; confidence 0.994

1276. ; $$X _ { 1 } \cup X _ { 2 } = X$$ ; confidence 0.917

1277. ; $$\operatorname { dim } X \times Y < \operatorname { dim } X + \operatorname { dim } Y$$ ; confidence 0.994

1278. ; $$\{ fd ( M )$$ ; confidence 0.531

1279. ; $$[ V ] = \operatorname { limsup } ( \operatorname { log } d _ { V } ( n ) \operatorname { log } ( n ) ^ { - 1 } )$$ ; confidence 0.618

1280. ; $$< \operatorname { Gdim } L < 1 +$$ ; confidence 0.485

1281. ; $$d ( I ^ { n } ) = n$$ ; confidence 0.754

1282. ; $$s \in Z$$ ; confidence 0.983

1283. ; $$G$$ ; confidence 0.797

1284. ; $$w _ { N } ( \alpha ) \geq n$$ ; confidence 0.879

1285. ; $$y = y _ { 0 } - a n$$ ; confidence 0.836

1286. ; $$a x + b y = 1$$ ; confidence 0.602

1287. ; $$z = r \operatorname { cos } \theta$$ ; confidence 0.866

1288. ; $$\operatorname { li } x / \phi ( d )$$ ; confidence 0.594

1289. ; $$s = - 2 \nu - \delta$$ ; confidence 0.945

1290. ; $$C _ { 0 } ^ { \infty } ( \Omega ) \subset L _ { 2 } ( \Omega )$$ ; confidence 0.992

1291. ; $$H ^ { p } ( d \theta / 2 \pi )$$ ; confidence 0.994

1292. ; $$C ( G )$$ ; confidence 1.000

1293. ; $$0 < \lambda _ { 1 } ( \Omega ) \leq \lambda _ { 2 } ( \Omega ) \leq$$ ; confidence 0.992

1294. ; $$\sigma > h$$ ; confidence 0.998

1295. ; $$s = 0$$ ; confidence 0.992

1296. ; $$L y = g$$ ; confidence 0.990

1297. ; $$K = \overline { K } \cap L _ { m } ( G )$$ ; confidence 0.866

1298. ; $$| \{ Z \} _ { n } | \rightarrow \infty$$ ; confidence 0.988

1299. ; $$\sigma _ { i } ^ { z }$$ ; confidence 0.702

1300. ; $$e ( B / A ) f ( B / A ) = n$$ ; confidence 0.996

1301. ; $$f ( B / A ) = 1$$ ; confidence 0.999

1302. ; $$t _ { 8 } + 1 / 2 = t _ { n } + \tau / 2$$ ; confidence 0.248

1303. ; $$R _ { 2 } : x ^ { \prime } \Sigma ^ { - 1 } ( \mu ^ { ( 1 ) } - \mu ^ { ( 2 ) } ) +$$ ; confidence 0.981

1304. ; $$x d y$$ ; confidence 0.999

1305. ; $$\gamma$$ ; confidence 0.589

1306. ; $$c * x = \frac { 1 } { I J } \sum _ { i j } c _ { j } = \frac { 1 } { I } \sum _ { i } c _ { i } x = \frac { 1 } { J } \sum _ { j } c * j$$ ; confidence 0.068

1307. ; $$\lambda _ { 3 } = K \sum _ { i j } \frac { \delta _ { i j } ^ { 2 } } { \sigma ^ { 2 } }$$ ; confidence 0.991

1308. ; $$R = \sum _ { i = 0 } ^ { n - 1 } Z ^ { i } G J G ^ { * } Z ^ { * i } =$$ ; confidence 0.906

1309. ; $$T _ { 1 } T _ { 2 } ^ { - 1 } T _ { 3 }$$ ; confidence 0.997

1310. ; $$Z ^ { * }$$ ; confidence 0.508

1311. ; $$| f _ { i } | < 1$$ ; confidence 0.997

1312. ; $$R - F R F ^ { * } = G J G ^ { * }$$ ; confidence 0.996

1313. ; $$\sigma _ { k }$$ ; confidence 0.198

1314. ; $$x \in D _ { B }$$ ; confidence 0.620

1315. ; $$| w - \beta _ { 0 } | = | \zeta _ { 0 } |$$ ; confidence 0.997

1316. ; $$| F _ { 0 } ^ { \prime } ( \zeta _ { 0 } ) | \leq | F ^ { \prime } ( \zeta _ { 0 } ) | \leq | F _ { \pi / 2 } ^ { \prime } ( \zeta _ { 0 } ) |$$ ; confidence 0.854

1317. ; $$\operatorname { ln } F ^ { \prime } ( \zeta _ { 0 } ) | \leq - \operatorname { ln } ( 1 - \frac { 1 } { | \zeta _ { 0 } | ^ { 2 } } )$$ ; confidence 0.488

1318. ; $$d _ { n } \ll p _ { n } ^ { \theta }$$ ; confidence 0.957

1319. ; $$\psi ( x ) = x - \sum _ { | \gamma | \leq T } \frac { x ^ { \rho } } { \rho } + O ( \frac { X } { T } \operatorname { log } ^ { 2 } x T + \operatorname { log } 2 x )$$ ; confidence 0.429

1320. ; $$\pi ( y ) - \operatorname { li } y > - M y \operatorname { log } ^ { - m } y$$ ; confidence 0.899

1321. ; $$\zeta ( \sigma + i t ) \neq 0$$ ; confidence 0.991

1322. ; $$\sum _ { i \in I } \prod _ { j \in J ( i ) } \alpha _ { i j } = \prod _ { \phi \in \Phi } \sum _ { i \in I } \alpha _ { i \phi ( i ) }$$ ; confidence 0.170

1323. ; $$\prod _ { i \in I } \sum _ { j \in J ( i ) } \alpha _ { i j } = \sum _ { \phi \in \Phi } \prod _ { i \in I } \alpha _ { i \phi ( i ) }$$ ; confidence 0.076

1324. ; $$\alpha \sum _ { i \in I } b _ { i } = \sum _ { i \in I } a b _ { i }$$ ; confidence 0.661

1325. ; $$\| \hat { f } \| = \| f \| _ { 1 }$$ ; confidence 0.870

1326. ; $$A ( \vec { G } )$$ ; confidence 0.484

1327. ; $$\operatorname { lim } _ { n \rightarrow \infty } f g _ { n } = f$$ ; confidence 0.784

1328. ; $$\operatorname { lim } _ { x \rightarrow \infty } e ^ { - x } \sum _ { n = 0 } ^ { \infty } \frac { s _ { n } x ^ { n } } { n ! }$$ ; confidence 0.659

1329. ; $$[ A : F ] = [ L : F ] ^ { 2 }$$ ; confidence 0.997

1330. ; $$\sigma > 1 / 2$$ ; confidence 0.999

1331. ; $$\gamma _ { k } < \sigma < 1$$ ; confidence 0.998

1332. ; $$\Delta _ { D } ( z )$$ ; confidence 0.999

1333. ; $$D \backslash K$$ ; confidence 0.979

1334. ; $$x \square ^ { j }$$ ; confidence 0.818

1335. ; $$p _ { 1 } / p _ { 2 }$$ ; confidence 0.981

1336. ; $$y ^ { \prime } ( b ) + v ( b ) y ( b ) = \gamma ( b )$$ ; confidence 0.998

1337. ; $$y ^ { \prime } ( b ) + \psi y ( b ) = \beta$$ ; confidence 0.993

1338. ; $$\sum _ { m = 1 } ^ { \infty } u _ { m n n }$$ ; confidence 0.852

1339. ; $$O \subset A _ { R }$$ ; confidence 0.132

1340. ; $$A _ { 0 } ( G )$$ ; confidence 0.996

1341. ; $$\infty \in G$$ ; confidence 0.992

1342. ; $$\overline { U }$$ ; confidence 0.299

1343. ; $$A ( D ) ^ { * } \simeq A / B$$ ; confidence 0.981

1344. ; $$f ( q ) = 1 / ( \sqrt { 5 } q ^ { 2 } )$$ ; confidence 1.000

1345. ; $$Y ( t ) \in R ^ { m }$$ ; confidence 0.934

1346. ; $$T : L ^ { 1 } \rightarrow X$$ ; confidence 0.986

1347. ; $$\delta ( t )$$ ; confidence 1.000

1348. ; $$S _ { g } ( w _ { 0 } )$$ ; confidence 0.921

1349. ; $$A \stackrel { f } { \rightarrow } B = A \stackrel { é } { \rightarrow } f [ A ] \stackrel { m } { \rightarrow } B$$ ; confidence 0.193

1350. ; $$\propto \| \Sigma \| ^ { - 1 / 2 } [ \nu + ( y - \mu ) ^ { T } \Sigma ^ { - 1 } ( y - \mu ) ] ^ { - ( \nu + p ) / 2 }$$ ; confidence 0.904

1351. ; $$T$$ ; confidence 0.914

1352. ; $$\Sigma \Omega X \rightarrow X$$ ; confidence 0.748

1353. ; $$74$$ ; confidence 0.496

1354. ; $$V \not \equiv W$$ ; confidence 0.489

1355. ; $$\varphi$$ ; confidence 0.858

1356. ; $$\Sigma - 1$$ ; confidence 0.852

1357. ; $$h ^ { i } ( w ) = g ^ { i } ( w )$$ ; confidence 0.992

1358. ; $$T p ( A _ { y } ) = A$$ ; confidence 0.900

1359. ; $$Y \rightarrow J ^ { 1 } Y$$ ; confidence 0.987

1360. ; $$\Gamma _ { q }$$ ; confidence 0.846

1361. ; $$L ( u ) + \lambda u = 0$$ ; confidence 0.993

1362. ; $$\frac { \partial } { \partial x } ( k _ { 1 } \frac { \partial u } { \partial x } ) + \frac { \partial } { \partial y } ( k _ { 2 } \frac { \partial u } { \partial y } ) + \lambda n = 0$$ ; confidence 0.519

1363. ; $$\| \hat { A } - A \| \leq \delta$$ ; confidence 0.245

1364. ; $$\overline { U _ { n } \in N A _ { n } ( B ) }$$ ; confidence 0.452

1365. ; $$\gamma = \left( \begin{array} { l l } { \alpha } & { b } \\ { c } & { d } \end{array} \right) \in GL _ { 2 } ( Q )$$ ; confidence 0.088

1366. ; $$K _ { \infty }$$ ; confidence 0.984

1367. ; $$f ( x _ { 0 } ) < \operatorname { inf } _ { x \in X } f ( x ) + \epsilon$$ ; confidence 0.738

1368. ; $$f = u _ { 1 } + i u _ { 2 }$$ ; confidence 0.994

1369. ; $$0 < \sigma < 0.5$$ ; confidence 0.996

1370. ; $$z _ { k } \in L$$ ; confidence 0.875

1371. ; $$\Delta \Delta w _ { 0 } = 0$$ ; confidence 0.903

1372. ; $$f ^ { em } = q _ { f } E + \frac { 1 } { c } J \times B + ( \nabla E ) P + ( \nabla B ) M +$$ ; confidence 0.640

1373. ; $$f ^ { em } = 0 = \operatorname { div } t ^ { em } f - \frac { \partial G ^ { em f } } { \partial t }$$ ; confidence 0.071

1374. ; $$E ^ { \prime } = 0$$ ; confidence 0.985

1375. ; $$\tau _ { i + 1 } - \tau _ { i }$$ ; confidence 0.970

1376. ; $$\langle P ^ { ( 2 ) } \rangle$$ ; confidence 0.899

1377. ; $$\operatorname { Th } ( K _ { 1 } )$$ ; confidence 0.733

1378. ; $$\Omega _ { * } ^ { SO }$$ ; confidence 0.644

1379. ; $$f ( z _ { 1 } + z _ { 2 } )$$ ; confidence 0.999

1380. ; $$C x ^ { - 1 }$$ ; confidence 0.834

1381. ; $$f ^ { \prime } ( 1 ) = \prod _ { n > 0 } ( \frac { 1 - q ^ { 2 n } } { 1 + q ^ { 2 n } } ) ^ { 2 }$$ ; confidence 0.893

1382. ; $$y ^ { 2 } = R ( x )$$ ; confidence 0.993

1383. ; $$u = - \int _ { z } ^ { \infty } \frac { d z } { w }$$ ; confidence 0.983

1384. ; $$T ^ { * } X \backslash 0$$ ; confidence 0.997

1385. ; $$\int \int _ { \Omega } ( \frac { \partial u } { \partial x } \frac { \partial v } { \partial x } + \frac { \partial u } { \partial y } \frac { \partial v } { \partial y } ) d x d y = - \int _ { \Omega } f v d x d y$$ ; confidence 0.732

1386. ; $$b _ { 2 } = 0$$ ; confidence 1.000

1387. ; $$\alpha ( X ) = \operatorname { tr } \operatorname { deg } M ( X )$$ ; confidence 0.949

1388. ; $$X _ { t } = m F$$ ; confidence 0.993

1389. ; $$y ^ { 2 } = x ^ { 3 } - g x - g$$ ; confidence 0.962

1390. ; $$y ^ { \prime } ( 0 ) = 0$$ ; confidence 0.990

1391. ; $$P _ { n } ( f ) = \int _ { S } f d P _ { n } = \frac { 1 } { n } \sum _ { i = 1 } ^ { n } f ( X _ { i } )$$ ; confidence 0.394

1392. ; $$B \circ F$$ ; confidence 0.974

1393. ; $$c ( n ) \| \mu \| _ { e } = \| U _ { \mu } \|$$ ; confidence 0.789

1394. ; $$U _ { \mu } ( x ) = \int H ( | x - y | ) d \mu ( y )$$ ; confidence 0.999

1395. ; $$U _ { 0 } ( t )$$ ; confidence 0.998

1396. ; $$( \Omega _ { + } - 1 ) ( g - g ) \psi ( t )$$ ; confidence 0.766

1397. ; $$( \Omega _ { + } - 1 ) \psi ( t ) = ( \Omega _ { + } - 1 ) g \psi ( t ) =$$ ; confidence 0.997

1398. ; $$\operatorname { lim } _ { k \rightarrow \infty } | \alpha _ { k } | ^ { 1 / k } = 0$$ ; confidence 0.823

1399. ; $$f : W \rightarrow R$$ ; confidence 0.920

1400. ; $$\sum _ { n } ^ { - 1 }$$ ; confidence 0.820

1401. ; $$\nu ( n ) = \alpha$$ ; confidence 0.430

1402. ; $$\Phi \Psi$$ ; confidence 0.943

1403. ; $$\Psi ( A ) = A$$ ; confidence 0.999

1404. ; $$\frac { D \xi ^ { i } } { d t } = \frac { d \xi ^ { i } } { d t } + \frac { 1 } { 2 } g ^ { i } r \xi ^ { r }$$ ; confidence 0.338

1405. ; $$\lambda _ { 1 } = \lambda _ { 2 }$$ ; confidence 1.000

1406. ; $$P _ { 1 } ^ { 1 } = \frac { 1 } { 4 } p ^ { 2 } + \frac { 1 } { 2 } \dot { p } - q = I$$ ; confidence 0.914

1407. ; $$\tau _ { n } ^ { ( B ) }$$ ; confidence 0.845

1408. ; $$o ( G )$$ ; confidence 0.990

1409. ; $$m ( M )$$ ; confidence 0.999

1410. ; $$2 d \geq n$$ ; confidence 0.758

1411. ; $$R ( \delta ) = 1 - H ( \delta )$$ ; confidence 1.000

1412. ; $$k \geq n - i t$$ ; confidence 0.558

1413. ; $$\sigma \approx s$$ ; confidence 0.994

1414. ; $$l _ { x }$$ ; confidence 0.196

1415. ; $$2 - 2 g - l$$ ; confidence 0.741

1416. ; $$2 - m - 1$$ ; confidence 0.994

1417. ; $$t h$$ ; confidence 0.989

1418. ; $$E ^ { \alpha } ( L ) ( \sigma ^ { 2 } ( x ) ) = 0$$ ; confidence 0.682

1419. ; $$\sigma ^ { k } : M \rightarrow E ^ { k }$$ ; confidence 0.958

1420. ; $$\therefore M \rightarrow F$$ ; confidence 0.313

1421. ; $$M = \overline { U }$$ ; confidence 0.999

1422. ; $$E ( L ) = E ^ { d } ( L ) \omega ^ { \alpha } \bigotimes \Delta$$ ; confidence 0.101

1423. ; $$E ( L )$$ ; confidence 0.960

1424. ; $$E ( L ) = \frac { \partial L } { \partial y } - D ( \frac { \partial L } { \partial y ^ { \prime } } )$$ ; confidence 0.989

1425. ; $$L \mapsto E ( L )$$ ; confidence 0.892

1426. ; $$K ( L )$$ ; confidence 0.907

1427. ; $$Q _ { n - j } ( z ) \equiv 0$$ ; confidence 0.981

1428. ; $$p _ { x } ^ { * } = \lambda \operatorname { exp } ( - \lambda x )$$ ; confidence 0.974

1429. ; $$A + 2$$ ; confidence 0.997

1430. ; $$B = f ( A )$$ ; confidence 0.999

1431. ; $$\phi ^ { - 1 } ( b ) \cong P ^ { \prime } ( C )$$ ; confidence 0.866

1432. ; $$P ^ { \prime } ( C )$$ ; confidence 0.802

1433. ; $$f | _ { A } = \phi$$ ; confidence 0.668

1434. ; $$B _ { \mu } ^ { 1 } \subset B \subset B _ { \mu } ^ { 2 }$$ ; confidence 0.646

1435. ; $$\tau \geq \zeta$$ ; confidence 0.994

1436. ; $$A = \operatorname { lim } _ { n \rightarrow \infty } C _ { n } = ( 1 + \frac { 1 } { 4 } + \frac { 1 } { 16 } + \ldots ) C _ { 1 } = \frac { 4 } { 3 } C _ { 1 }$$ ; confidence 0.919

1437. ; $$K ( B - C _ { N } ) > K ( B - A ) > D$$ ; confidence 0.579

1438. ; $$C _ { n } = C _ { 1 } + \frac { 1 } { 4 } C _ { 1 } + \ldots + \frac { 1 } { 4 ^ { n - 1 } } C _ { 1 }$$ ; confidence 0.974

1439. ; $$\overline { \Pi } _ { k } \subset \Pi _ { k + 1 }$$ ; confidence 0.606

1440. ; $$( L _ { \mu } ) ^ { p }$$ ; confidence 0.998

1441. ; $$z = \operatorname { ln } \alpha = \operatorname { ln } | \alpha | + i \operatorname { Arg } \alpha$$ ; confidence 0.857

1442. ; $$( e ^ { z } 1 ) ^ { z } = e ^ { z } 1 ^ { z _ { 2 } }$$ ; confidence 0.053

1443. ; $$a ^ { X } = e ^ { X \operatorname { ln } \alpha }$$ ; confidence 0.301

1444. ; $$z \in Z$$ ; confidence 0.973

1445. ; $$S = o ( \# A )$$ ; confidence 0.908

1446. ; $$p f$$ ; confidence 0.602

1447. ; $$y _ { j } \delta \theta$$ ; confidence 0.866

1448. ; $$\nu - 1 / 2 \in Z$$ ; confidence 0.954

1449. ; $$y ^ { \prime } + \alpha _ { 1 } y = 0$$ ; confidence 0.639

1450. ; $$\alpha : G \rightarrow \operatorname { Aut } A$$ ; confidence 0.856

1451. ; $$n + = n - = n$$ ; confidence 0.228

1452. ; $$A = A _ { 0 } ^ { * }$$ ; confidence 0.706

1453. ; $$\lambda < \alpha$$ ; confidence 0.600

1454. ; $$r > n$$ ; confidence 0.953

1455. ; $$x _ { i } ^ { 2 } = 0$$ ; confidence 0.840

1456. ; $$\Delta J =$$ ; confidence 0.998

1457. ; $$r < | z | < 1$$ ; confidence 0.987

1458. ; $$\gamma \geq 0$$ ; confidence 0.994

1459. ; $$S h$$ ; confidence 0.739

1460. ; $$V$$ ; confidence 0.996

1461. ; $$R _ { i } = F _ { q } [ x ] / ( f _ { i } )$$ ; confidence 0.671

1462. ; $$G _ { i } = V _ { i } ( E + \Delta - V _ { i } ) ^ { - 1 }$$ ; confidence 0.998

1463. ; $$K _ { X } ^ { - 1 }$$ ; confidence 0.918

1464. ; $$Q \subset P ^ { 4 }$$ ; confidence 0.991

1465. ; $$d _ { k } = \operatorname { det } ( 1 - f _ { t } ^ { \prime } ( x _ { k } ) ) ^ { 1 / 2 }$$ ; confidence 0.976

1466. ; $$q ( 0 ) \neq 0$$ ; confidence 0.997

1467. ; $$w ( x ) = | f ( x ) | ^ { 2 }$$ ; confidence 1.000

1468. ; $$C _ { 0 }$$ ; confidence 0.800

1469. ; $$( + \infty ) - ( + \infty ) = - \infty - ( - \infty ) = - \infty$$ ; confidence 0.999

1470. ; $$\alpha ^ { \lambda } = 1$$ ; confidence 0.972

1471. ; $$q ( m ) = ( m ^ { p - 1 } - 1 ) / p$$ ; confidence 0.963

1472. ; $$\tau _ { 0 } = 0$$ ; confidence 0.955

1473. ; $$\tau _ { k + 1 } = t$$ ; confidence 0.410

1474. ; $$P ( N _ { k } = n ) = p ^ { n } F _ { n + 1 - k } ^ { ( k ) } ( \frac { q } { p } )$$ ; confidence 0.620

1475. ; $$U _ { n } ( x ) = \frac { \alpha ^ { n } ( x ) - \beta ^ { n } ( x ) } { \alpha ( x ) - \beta ( x ) }$$ ; confidence 0.947

1476. ; $$P ^ { * } = \{ P _ { X } ^ { * } : x \in X \}$$ ; confidence 0.505

1477. ; $$F ^ { * } ( \theta | x ) = 1 - F ( x | \theta )$$ ; confidence 0.940

1478. ; $$G = T$$ ; confidence 0.991

1479. ; $$v \in A _ { p } ( G )$$ ; confidence 0.412

1480. ; $$u \in C ^ { G }$$ ; confidence 0.438

1481. ; $$\lambda ^ { p } ( M ^ { 1 } ( G ) )$$ ; confidence 0.996

1482. ; $$V ( x _ { 0 } )$$ ; confidence 0.998

1483. ; $$\phi ( \mathfrak { A } )$$ ; confidence 0.445

1484. ; $$x _ { n } = n$$ ; confidence 0.849

1485. ; $$\Delta ^ { n } f ( x )$$ ; confidence 0.976

1486. ; $$\sum _ { \nu = 1 } ^ { k - 1 } \frac { B _ { \nu } } { \nu ! } \{ f ^ { \langle \nu - 1 \rangle } ( n ) - f ^ { \langle \nu - 1 \rangle } ( 0 ) \} + \frac { B _ { k } } { k ! } \sum _ { x = 0 } ^ { n - 1 } f ^ { ( k ) } ( x + \theta )$$ ; confidence 0.269

1487. ; $$f ^ { - 1 } ( f ( x ) ) \cap U$$ ; confidence 0.998

1488. ; $$G / G 1$$ ; confidence 0.622

1489. ; $$y ^ { i } C _ { i j k } = 0$$ ; confidence 0.942

1490. ; $$\Phi ( \Phi ( x ) ) = x$$ ; confidence 1.000

1491. ; $$| x - x _ { 0 } | \leq b$$ ; confidence 0.990

1492. ; $$| X$$ ; confidence 0.687

1493. ; $$\phi ( p )$$ ; confidence 0.999

1494. ; $$| A | = \int _ { R } | \alpha | 0$$ ; confidence 0.765

1495. ; $$\frac { | \sigma _ { i } | } { ( \operatorname { diam } \sigma _ { i } ) ^ { n } } \geq \eta$$ ; confidence 0.891

1496. ; $$C ^ { b r } ( E ^ { n } )$$ ; confidence 0.943

1497. ; $$\Omega \in ( H ^ { \otimes 0 } ) _ { \alpha } \subset \Gamma ^ { \alpha } ( H )$$ ; confidence 0.995

1498. ; $$\{ \xi _ { f } : f \in H \}$$ ; confidence 0.998

1499. ; $$\alpha _ { \alpha } ^ { * } ( f ) \Omega = f$$ ; confidence 0.962

1500. ; $$t \subset v$$ ; confidence 0.885

1501. ; $$f _ { i } ( X ) = X _ { i } + \ldots$$ ; confidence 0.733

1502. ; $$F ( \overline { m } )$$ ; confidence 0.760

1503. ; $$\omega = \alpha _ { 1 } \ldots \alpha _ { k }$$ ; confidence 0.633

1504. ; $$V _ { 1 } ^ { * }$$ ; confidence 0.750

1505. ; $$\{ \lambda \}$$ ; confidence 1.000

1506. ; $$A \rightarrow w$$ ; confidence 0.934

1507. ; $$\sigma ( \alpha ) = \{ w \}$$ ; confidence 0.997

1508. ; $$I V _ { 2 }$$ ; confidence 0.996

1509. ; $$x ^ { i } \in R$$ ; confidence 0.987

1510. ; $$J _ { \nu }$$ ; confidence 0.556

1511. ; $$F \mu$$ ; confidence 0.813

1512. ; $$P ( x ) = \frac { 1 } { \sqrt { 2 \pi } } F ( x )$$ ; confidence 1.000

1513. ; $$L _ { q } ( X )$$ ; confidence 0.846

1514. ; $$\Lambda _ { G } = 1$$ ; confidence 0.897

1515. ; $$( 8 \times 8 )$$ ; confidence 1.000

1516. ; $$| \varphi ( z ) | ^ { 2 } e ^ { \delta | z | }$$ ; confidence 0.840

1517. ; $$F ( z ) = - \frac { 1 } { 2 \pi i } \int \frac { \operatorname { exp } e ^ { \zeta ^ { 2 } } } { \zeta - z } d \zeta$$ ; confidence 0.622

1518. ; $$f \in L _ { 1 }$$ ; confidence 0.991

1519. ; $$\phi \in C _ { 0 } ^ { \infty } ( \Omega )$$ ; confidence 0.997

1520. ; $$X ^ { \prime } \subset X$$ ; confidence 0.988

1521. ; $$K _ { j } \times R ^ { N j }$$ ; confidence 0.562

1522. ; $$d _ { C } ^ { - 1 } = \operatorname { det } \left\| \begin{array} { c c } { \phi _ { \theta } \theta } & { \phi _ { \theta x } } \\ { \phi _ { y } \theta } & { \phi _ { y x } } \end{array} \right\|$$ ; confidence 0.370

1523. ; $$\alpha = - b$$ ; confidence 0.947

1524. ; $$f * g$$ ; confidence 0.637

1525. ; $$K = D$$ ; confidence 0.998

1526. ; $$F [ \delta ] = 1$$ ; confidence 0.999

1527. ; $$\eta \in \operatorname { ln } t \Gamma ^ { \prime }$$ ; confidence 0.642

1528. ; $$\xi _ { 1 } \neq \infty$$ ; confidence 0.999

1529. ; $$z \rightarrow w = L ( z ) = \frac { a z + b } { c z + d }$$ ; confidence 0.834

1530. ; $$L _ { k } ( z _ { k } )$$ ; confidence 0.991

1531. ; $$\infty \rightarrow \alpha / c$$ ; confidence 0.864

1532. ; $$A / \eta$$ ; confidence 0.702

1533. ; $$D ( B ) \supset D ( A )$$ ; confidence 0.993

1534. ; $$\alpha < \beta < \gamma$$ ; confidence 0.991

1535. ; $$x \in D ( A )$$ ; confidence 0.906

1536. ; $$\Lambda = \frac { \partial } { \partial x } + i \frac { \partial } { \partial y }$$ ; confidence 0.855

1537. ; $$\eta = \frac { ( \alpha ^ { 2 } - \rho ^ { 2 } ) ^ { 1 / 2 } ( \alpha ^ { 2 } - \rho _ { 0 } ^ { 2 } ) ^ { 1 / 2 } } { \alpha }$$ ; confidence 0.628

1538. ; $$v _ { 0 } ^ { k }$$ ; confidence 0.384

1539. ; $$| \Phi ( G )$$ ; confidence 0.956

1540. ; $$\mathfrak { A } \sim _ { l } \mathfrak { B }$$ ; confidence 0.922

1541. ; $$D ( \lambda ) \neq 0$$ ; confidence 0.997

1542. ; $$| \lambda | < B ^ { - 1 }$$ ; confidence 0.997

1543. ; $$\beta ( A ) < \infty$$ ; confidence 0.997

1544. ; $$R ( A )$$ ; confidence 1.000

1545. ; $$\beta ( A - K ) < \infty$$ ; confidence 0.999

1546. ; $$n \| < C$$ ; confidence 0.368

1547. ; $$\beta ( A ) : = \operatorname { codim } R ( A ) < \infty$$ ; confidence 0.981

1548. ; $$( r \geq 1 )$$ ; confidence 1.000

1549. ; $$x _ { 1 } ( t ) + x _ { 2 } ( t ) = A ( t ) \operatorname { cos } ( \omega _ { 1 } t + \phi ( t ) )$$ ; confidence 0.965

1550. ; $$( x M ) ( M ^ { - 1 } y )$$ ; confidence 0.999

1551. ; $$X _ { i } \cap X _ { j } =$$ ; confidence 0.322

1552. ; $$C _ { G } ( n ) \leq N$$ ; confidence 0.972

1553. ; $$N = \{ G \backslash ( \cup _ { x \in G } x ^ { - 1 } H x ) \} \cup \{ 1 \}$$ ; confidence 0.269

1554. ; $$\pi ( \lambda ) = ( \lambda + 2 ) ( \lambda + 1 ) \alpha ^ { 2 } 0 + ( \lambda + 1 ) \alpha ^ { 1 } 0 + a ^ { 0 } =$$ ; confidence 0.071

1555. ; $$| z | < r$$ ; confidence 0.957

1556. ; $$= \frac { ( n _ { 1 } + l ) ! } { ! ! } ( \operatorname { log } z ) ^ { l } z ^ { \lambda _ { 2 } } + \ldots$$ ; confidence 0.665

1557. ; $$\lambda = \lambda _ { j }$$ ; confidence 0.911

1558. ; $$( n ! ) ^ { - 1 } n _ { D }$$ ; confidence 0.991

1559. ; $$\| x \| _ { p } = \int _ { 0 } ^ { 1 } | x ( t ) | ^ { p } d t$$ ; confidence 0.742

1560. ; $$0 < p _ { n } \rightarrow 0$$ ; confidence 0.998

1561. ; $$J : T M \rightarrow T M$$ ; confidence 0.972

1562. ; $$V _ { 0 } ( z )$$ ; confidence 0.971

1563. ; $$x \in R \cup \{ \infty \}$$ ; confidence 0.764

1564. ; $$D = \{ z \in C : | z | < 1 \}$$ ; confidence 0.972

1565. ; $$\chi ( \Delta ) = \chi ( \Gamma ) [ \Gamma : \Delta ]$$ ; confidence 0.999

1566. ; $$L _ { p } ( X )$$ ; confidence 0.970

1567. ; $$S \subset T$$ ; confidence 0.743

1568. ; $$A \in \mathfrak { S }$$ ; confidence 0.285

1569. ; $$f \in N ( \Delta )$$ ; confidence 0.997

1570. ; $$t \mapsto t + T$$ ; confidence 0.520

1571. ; $$T _ { \rightarrow } V ^ { - 1 } T V$$ ; confidence 0.437

1572. ; $$P ( C A )$$ ; confidence 0.999

1573. ; $$f ( - x ) = - f ( x )$$ ; confidence 1.000

1574. ; $$\mathfrak { g } \otimes \mathfrak { g } \rightarrow U \mathfrak { g } \otimes U \mathfrak { g } \otimes U _ { \mathfrak { g } }$$ ; confidence 0.207

1575. ; $$T _ { N } ( t )$$ ; confidence 0.993

1576. ; $$\frac { \partial w } { \partial z } + A ( z ) w + B ( z ) \overline { w } = F ( z )$$ ; confidence 0.777

1577. ; $$\left. \begin{array} { l l } { F _ { 1 } ( A ) } & { \frac { F _ { 1 } ( \alpha ) } { \rightarrow } } & { F _ { 1 } ( B ) } \\ { \phi _ { A } \downarrow } & { \square } & { \downarrow \phi _ { B } } \\ { F _ { 2 } ( A ) } & { \vec { F _ { 2 } ( \alpha ) } } & { F _ { 2 } ( B ) } \end{array} \right.$$ ; confidence 0.308

1578. ; $$\tilde { f } : Y \rightarrow X$$ ; confidence 0.494

1579. ; $$e _ { \lambda } ^ { 1 } \in X$$ ; confidence 0.877

1580. ; $$A ^ { p } \geq ( A ^ { p / 2 } B ^ { p } A ^ { p / 2 } ) ^ { 1 / 2 }$$ ; confidence 0.997

1581. ; $$LOC$$ ; confidence 0.417

1582. ; $$X \times F$$ ; confidence 0.480

1583. ; $$\pi : P \rightarrow G \backslash P$$ ; confidence 0.994

1584. ; $$S ( M ^ { \prime } ) \subset M ^ { \prime }$$ ; confidence 0.989

1585. ; $$H \mapsto C _ { A } ^ { \prime }$$ ; confidence 0.465

1586. ; $$V \oplus \mathfrak { g }$$ ; confidence 0.476

1587. ; $$C ^ { ( 0 ) }$$ ; confidence 0.988

1588. ; $$\delta : G ^ { \prime } \rightarrow W$$ ; confidence 0.965

1589. ; $$\mathfrak { x } \times x$$ ; confidence 0.416

1590. ; $$H _ { i } ( x ^ { \prime } ) > H _ { i } ( x ^ { \prime \prime } )$$ ; confidence 0.924

1591. ; $$\hat { K } _ { i }$$ ; confidence 0.180

1592. ; $$x$$ ; confidence 0.485

1593. ; $$\alpha _ { k } = \frac { \Gamma ( \gamma + k + 1 ) } { \Gamma ( \gamma + 1 ) } \sqrt { \frac { \Gamma ( \alpha _ { 1 } + 1 ) \Gamma ( \alpha _ { 2 } + 1 ) } { \Gamma ( \alpha _ { 1 } + k + 1 ) \Gamma ( \alpha _ { 2 } + k + 1 ) } }$$ ; confidence 0.904

1594. ; $$\nu < \kappa$$ ; confidence 0.992

1595. ; $$\omega = 1 / c ^ { 2 }$$ ; confidence 0.906

1596. ; $$\sum _ { \Sigma } ^ { 3 } \square ^ { i \alpha } \neq 0$$ ; confidence 0.180

1597. ; $$( \partial w / \partial t ) + ( \partial f / \partial x ) = ( h ^ { 2 } / 2 \tau ) ( \partial ^ { 2 } w / \partial x ^ { 2 } )$$ ; confidence 0.582

1598. ; $$\frac { \pi \psi } { Q } = - \theta - \sum _ { n = 1 } ^ { \infty } \frac { 1 } { n } ( \frac { \tau } { \tau _ { 0 } } ) ^ { n } \frac { y _ { n } ( \tau ) } { y _ { n } ( \tau _ { 0 } ) } \operatorname { sin } 2 n \theta$$ ; confidence 0.914

1599. ; $$\beta = \frac { 1 } { \gamma - 1 }$$ ; confidence 0.992

1600. ; $$+ \beta n ( 2 n + 1 ) y _ { n } = 0$$ ; confidence 0.975

1601. ; $$3 n + 2$$ ; confidence 1.000

1602. ; $$= \sum _ { \nu = 1 } ^ { n } \alpha _ { \nu } f ( x _ { \nu } ) + \sum _ { \mu = 1 } ^ { n + 1 } \beta _ { \mu } f ( \xi _ { \mu } )$$ ; confidence 0.992

1603. ; $$\nabla _ { \theta } : H _ { \delta R } ^ { 1 } ( X / K ) \rightarrow H _ { \partial R } ^ { 1 } ( X / K )$$ ; confidence 0.221

1604. ; $$0 \rightarrow \phi ^ { 1 } / \phi ^ { 2 } \rightarrow \phi ^ { 0 } / \phi ^ { 2 } \rightarrow \phi ^ { 0 } / \phi ^ { 1 } \rightarrow 0$$ ; confidence 0.913

1605. ; $$\alpha _ { 31 } / \alpha _ { 11 }$$ ; confidence 0.405

1606. ; $$\quad f j ( x ) - \alpha j = \alpha _ { j 1 } x _ { 1 } + \ldots + \alpha _ { j n } x _ { n } - \alpha _ { j } = 0$$ ; confidence 0.057

1607. ; $$f _ { \zeta } ( \lambda )$$ ; confidence 0.821

1608. ; $$R [ F ( t ) ] = ( 1 - t ^ { 2 } ) F ^ { \prime \prime } - ( 2 \rho - 1 ) t F ^ { \prime \prime }$$ ; confidence 0.876

1609. ; $$K ( y ) = \operatorname { sgn } y . | y | ^ { \alpha }$$ ; confidence 0.655

1610. ; $$\hbar \square ^ { * } ( M )$$ ; confidence 0.620

1611. ; $$T _ { \nu }$$ ; confidence 0.336

1612. ; $$i : A \rightarrow X$$ ; confidence 0.995

1613. ; $$F = p t$$ ; confidence 0.143

1614. ; $$T \xi$$ ; confidence 0.994

1615. ; $$\overline { h } ( X ) = \operatorname { lim } _ { h } h ^ { * } ( X _ { \alpha } )$$ ; confidence 0.185

1616. ; $$C = \text { int } \Gamma$$ ; confidence 0.630

1617. ; $$\overline { O } _ { k }$$ ; confidence 0.968

1618. ; $$\delta ( x ) = \delta ( x _ { 1 } ) \times \ldots \times \delta ( x _ { N } )$$ ; confidence 0.411

1619. ; $$\alpha f \in D ^ { \prime } ( O )$$ ; confidence 0.895

1620. ; $$x u = 0$$ ; confidence 0.979

1621. ; $$I _ { U } = \{ ( u _ { \lambda } ) _ { \lambda \in \Lambda }$$ ; confidence 0.956

1622. ; $$\Gamma \subset \Omega$$ ; confidence 0.987

1623. ; $$w \mapsto ( w ^ { * } \varphi _ { \lambda } ) _ { \lambda \in \Lambda }$$ ; confidence 0.798

1624. ; $$m : A ^ { \prime } \rightarrow A$$ ; confidence 0.997

1625. ; $$v \wedge \wedge \ldots \wedge v _ { m }$$ ; confidence 0.124

1626. ; $$\xi _ { p } \in ( \nu F ^ { m } ) p$$ ; confidence 0.212

1627. ; $$d f ( X )$$ ; confidence 0.998

1628. ; $$\xi \in ( \nu F ^ { m } ) _ { p }$$ ; confidence 0.549

1629. ; $$\alpha ( F ) = 1$$ ; confidence 1.000

1630. ; $$D \Re \subset M$$ ; confidence 0.255

1631. ; $$V ( \Re ) > 2 ^ { n } d ( \Lambda )$$ ; confidence 0.792

1632. ; $$d ( \Lambda ) = \Delta ( \mathfrak { M } )$$ ; confidence 0.934

1633. ; $$p _ { n } ( z ) : = \operatorname { det } \{ z I - A \}$$ ; confidence 0.968

1634. ; $$| \tilde { \varphi } \mathfrak { u } ( \xi ) | \leq c ^ { - 1 } e ^ { - c | \xi | ^ { 1 / s } }$$ ; confidence 0.103

1635. ; $$D _ { x _ { k } } = - i \partial _ { x _ { k } }$$ ; confidence 0.982

1636. ; $$z$$ ; confidence 0.578

1637. ; $$\delta \varepsilon$$ ; confidence 0.600

1638. ; $$d E$$ ; confidence 0.607

1639. ; $$\alpha \equiv f ( x _ { 0 } - ) \leq f ( x _ { 0 } + ) \equiv b$$ ; confidence 0.692

1640. ; $$A < \alpha < b < B$$ ; confidence 0.686

1641. ; $$A = \underbrace { \operatorname { lim } _ { n } \frac { \operatorname { lim } } { x \nmid x _ { 0 } } } s _ { n } ( x )$$ ; confidence 0.055

1642. ; $$\psi \circ \phi = \phi ^ { \prime } \circ \psi$$ ; confidence 0.848

1643. ; $$q ^ { \prime } \in A ^ { \prime }$$ ; confidence 0.966

1644. ; $$a _ { y }$$ ; confidence 0.519

1645. ; $$A _ { 0 } = \mathfrak { A } _ { 0 }$$ ; confidence 0.968

1646. ; $$A = \sum _ { i \geq 0 } A$$ ; confidence 0.975

1647. ; $$\operatorname { grad } ( f g ) = g \operatorname { grad } f + f \operatorname { grad } g$$ ; confidence 0.981

1648. ; $$t \circ \in E$$ ; confidence 0.290

1649. ; $$f _ { B } ( x ) = \frac { \lambda ^ { x } } { x ! } e ^ { - \lambda } \{ 1 + \frac { \mu _ { 2 } - \lambda } { \lambda ^ { 2 } } [ \frac { x ^ { [ 2 ] } } { 2 } - \lambda x ^ { [ 1 ] } + \frac { \lambda ^ { 2 } } { 2 } ] +$$ ; confidence 0.569

1650. ; $$[ \Psi / \Phi ] \Phi$$ ; confidence 0.955

1651. ; $$\mu ( \alpha )$$ ; confidence 0.999

1652. ; $$x \in L ( \Gamma )$$ ; confidence 0.995

1653. ; $$B \rightarrow b B$$ ; confidence 0.994

1654. ; $$V _ { T } ^ { \prime } = \mu ( V _ { T } )$$ ; confidence 0.997

1655. ; $$\sum _ { d ( e ) = Q } f _ { e }$$ ; confidence 0.651

1656. ; $$( n \operatorname { ln } n ) / 2$$ ; confidence 0.978

1657. ; $$E ^ { n } \times R$$ ; confidence 0.937

1658. ; $$f _ { 12 }$$ ; confidence 0.974

1659. ; $$G _ { A B } ^ { ( c ) } ( t - t ^ { \prime } ) = \ll A ( t ) | B ( t ^ { \prime } ) \gg ( c ) \equiv \langle T _ { \eta } A ( t ) B ( t ^ { \prime } ) \rangle$$ ; confidence 0.272

1660. ; $$\psi _ { k } ( \xi )$$ ; confidence 0.998

1661. ; $$y ( \alpha ) = 0$$ ; confidence 0.954

1662. ; $$C = [ p ( \xi ) W ( \xi ) ] ^ { - 1 }$$ ; confidence 0.997

1663. ; $$G _ { A B } ^ { ( n ) } ( E )$$ ; confidence 0.976

1664. ; $$m \equiv 4$$ ; confidence 0.840

1665. ; $$B M$$ ; confidence 0.973

1666. ; $$f ( z ) = e ^ { ( \alpha - i b ) z ^ { \rho } }$$ ; confidence 0.743

1667. ; $$M _ { 2 } \times S ^ { N }$$ ; confidence 0.923

1668. ; $$m \geq 3$$ ; confidence 0.668

1669. ; $$X ^ { ( r ) } \rightarrow V$$ ; confidence 0.950

1670. ; $$g _ { i } \in A$$ ; confidence 0.960

1671. ; $$g \rightarrow g$$ ; confidence 0.987

1672. ; $$| x _ { \mathfrak { j } } | \leq M$$ ; confidence 0.106

1673. ; $$w _ { 2 } = f ( r _ { 1 } ) \ldots f ( r _ { n } )$$ ; confidence 0.851

1674. ; $$\alpha _ { 1 } \ldots \alpha _ { m }$$ ; confidence 0.435

1675. ; $$\frac { d ^ { 2 } y } { d t ^ { 2 } } + P ( t ) y = 0$$ ; confidence 1.000

1676. ; $$x ^ { ( 1 ) } = x ^ { ( 1 ) } ( t )$$ ; confidence 0.898

1677. ; $$X = \| \left. \begin{array} { l l } { U _ { 1 } } & { U _ { 2 } } \\ { V _ { 1 } } & { V _ { 2 } } \end{array} \right. |$$ ; confidence 0.501

1678. ; $$M _ { 0 } \times I$$ ; confidence 0.798

1679. ; $$P _ { n - k }$$ ; confidence 0.990

1680. ; $$P _ { - } \phi \in B _ { p } ^ { 1 / p }$$ ; confidence 0.963

1681. ; $$\hat { \phi } ( j ) = \alpha$$ ; confidence 0.791

1682. ; $$M ( x ) = M _ { f } ( x ) = \operatorname { sup } _ { 0 < k | \leq \pi } \frac { 1 } { t } \int _ { x } ^ { x + t } | f ( u ) | d u$$ ; confidence 0.412

1683. ; $$\int _ { \alpha } ^ { b } \theta ^ { p } ( x ) d x \leq 2 ( \frac { p } { p - 1 } ) ^ { p } \int _ { a } ^ { b } f ^ { p } ( x ) d x$$ ; confidence 0.187

1684. ; $$H ^ { p } ( G )$$ ; confidence 0.998

1685. ; $$M _ { \delta } ( \phi ) \rightarrow 0$$ ; confidence 0.996

1686. ; $$B = B _ { E }$$ ; confidence 0.754

1687. ; $$L _ { \infty } ( \hat { G } )$$ ; confidence 0.973

1688. ; $$F ( \phi ) \in A ( \hat { G } )$$ ; confidence 0.909

1689. ; $$f = f _ { 1 } * f _ { 2 }$$ ; confidence 0.989

1690. ; $$d g = d h d k$$ ; confidence 0.955

1691. ; $$p + q \leq \operatorname { dim } _ { C } M$$ ; confidence 0.688

1692. ; $$d \sigma ( y )$$ ; confidence 0.992

1693. ; $$\operatorname { dim } M = 2$$ ; confidence 0.993

1694. ; $$\{ x : | x - y | < r \}$$ ; confidence 0.915

1695. ; $$F _ { n } ( x ) = ( x _ { 1 } ^ { 2 } + \ldots + x _ { y } ^ { 2 } ) ^ { 1 / 2 }$$ ; confidence 0.316

1696. ; $$\alpha _ { i k } = \overline { a _ { k i } }$$ ; confidence 0.235

1697. ; $$H ( z )$$ ; confidence 0.999

1698. ; $$H ( z ) = \sum _ { i = 1 } ^ { n } \sum _ { j = 1 } ^ { n } a _ { i j } z _ { i } z _ { j }$$ ; confidence 0.374

1699. ; $$C$$ ; confidence 0.952

1700. ; $$X _ { 1 } \cap Y _ { 1 } = \emptyset$$ ; confidence 0.988

1701. ; $$\Sigma _ { n } ^ { 0 }$$ ; confidence 0.998

1702. ; $$\lambda = p ^ { - 1 } + r ^ { - 1 } \leq 1$$ ; confidence 0.999

1703. ; $$\nu \in A$$ ; confidence 0.971

1704. ; $$\sum _ { i } | \alpha _ { i } | ^ { 2 } < \infty$$ ; confidence 0.995

1705. ; $$\sum _ { \nu \in A } \| x _ { \nu } \| ^ { 2 } < \infty$$ ; confidence 0.895

1706. ; $$V = V ^ { + } \oplus V ^ { - }$$ ; confidence 0.953

1707. ; $$\lambda _ { 4 n }$$ ; confidence 0.681

1708. ; $$f ( 0 ) = f ( 1 ) = 0$$ ; confidence 1.000

1709. ; $$\Psi ( y _ { n } ) \subseteq \Psi ( y _ { 0 } )$$ ; confidence 0.934

1710. ; $$F ^ { p }$$ ; confidence 0.768

1711. ; $$h : E ^ { m } \rightarrow R$$ ; confidence 0.941

1712. ; $$\Omega \frac { p } { x }$$ ; confidence 0.447

1713. ; $$f ^ { - 1 } \circ f ( z ) = z$$ ; confidence 0.986

1714. ; $$\mathfrak { M } ( M )$$ ; confidence 0.763

1715. ; $$\mu _ { 1 } < 0 < \lambda _ { 1 }$$ ; confidence 0.999

1716. ; $$n _ { s } + n _ { u } = n$$ ; confidence 0.172

1717. ; $$g x = y$$ ; confidence 0.997

1718. ; $$G = SU ( k )$$ ; confidence 0.645

1719. ; $$\beta ^ { s - k } z ^ { \prime }$$ ; confidence 0.907

1720. ; $$R ) = r . g \operatorname { lowdim } ( R ) = \operatorname { glowdim } ( R )$$ ; confidence 0.142

1721. ; $$0 \rightarrow A ^ { \prime } \rightarrow A \rightarrow A ^ { \prime \prime } \rightarrow 0$$ ; confidence 0.930

1722. ; $$f \phi = 0$$ ; confidence 0.993

1723. ; $$T ( H ( A ) )$$ ; confidence 0.997

1724. ; $$n = r \neq 0$$ ; confidence 0.966

1725. ; $$S X \rightarrow S X$$ ; confidence 0.972

1726. ; $$Z / p$$ ; confidence 0.808

1727. ; $$x = [ u ]$$ ; confidence 0.825

1728. ; $$e _ { i } : O ( \Delta _ { q - 1 } ) \rightarrow O ( \Delta _ { q } )$$ ; confidence 0.793

1729. ; $$\Delta _ { q }$$ ; confidence 0.971

1730. ; $$\eta : \pi _ { N } \otimes \pi _ { N } \rightarrow \pi _ { N } + 1$$ ; confidence 0.085

1731. ; $$\mu ^ { * } : A ^ { * } \rightarrow A ^ { * } \otimes A ^ { * }$$ ; confidence 0.991

1732. ; $$T ^ { \aleph } x \in A$$ ; confidence 0.469

1733. ; $$\Omega \in \Delta ^ { n } S$$ ; confidence 0.506

1734. ; $$\psi ( x ) = \sum x ^ { \prime } \otimes x ^ { \prime \prime }$$ ; confidence 0.991

1735. ; $$n - 1 \geq p$$ ; confidence 0.999

1736. ; $$n \leq s \leq 2 n - 2$$ ; confidence 0.997

1737. ; $$n \neq 0$$ ; confidence 0.999

1738. ; $$\nu = 0$$ ; confidence 0.923

1739. ; $$Z = 1$$ ; confidence 0.980

1740. ; $$| f ( x + y ) - f ( x ) f ( y ) | \leq \varepsilon$$ ; confidence 0.999

1741. ; $$e ^ { i k x }$$ ; confidence 0.648

1742. ; $$O A M$$ ; confidence 0.981

1743. ; $$f : \Omega \rightarrow B$$ ; confidence 0.997

1744. ; $$P _ { m } ( \xi + \tau N )$$ ; confidence 0.978

1745. ; $$\frac { \partial w } { \partial t } = A \frac { \partial w } { \partial x }$$ ; confidence 0.980

1746. ; $$\alpha = a ( x )$$ ; confidence 0.757

1747. ; $$W _ { X } ^ { S }$$ ; confidence 0.678

1748. ; $$E _ { X } ^ { N }$$ ; confidence 0.539

1749. ; $$U ^ { ( 2 ) }$$ ; confidence 0.956

1750. ; $$\int _ { X } | f ( x ) | ^ { 2 } \operatorname { ln } | f ( x ) | d \mu ( x ) \leq$$ ; confidence 0.990

1751. ; $$H _ { 1 } \otimes I + I \otimes H _ { 2 }$$ ; confidence 0.996

1752. ; $$F _ { j } ( z ) = \sum _ { k = 1 } ^ { N } G _ { j k } ( z )$$ ; confidence 0.944

1753. ; $$F _ { + } ( x + i 0 ) - F _ { - } ( x - i 0 )$$ ; confidence 0.881

1754. ; $$\alpha - \beta$$ ; confidence 1.000

1755. ; $$w = z ^ { - \gamma / 2 } ( z - 1 ) ^ { ( \gamma - \alpha - \beta - 1 ) / 2 } u$$ ; confidence 0.892

1756. ; $$z ( 1 - z ) w ^ { \prime \prime } + [ \gamma - ( \alpha + \beta + 1 ) z ] w ^ { \prime } - \alpha \beta w = 0$$ ; confidence 0.996

1757. ; $$| f | = 1$$ ; confidence 0.989

1758. ; $$\operatorname { log } | \phi ( h ) | = \int \operatorname { log } | h | d$$ ; confidence 0.751

1759. ; $$H _ { 1 } ( x ) < H _ { 2 } ( x )$$ ; confidence 0.999

1760. ; $$A = \operatorname { sup } _ { y \in E } A ( y ) < \infty$$ ; confidence 0.997

1761. ; $$I _ { X }$$ ; confidence 0.507

1762. ; $$A \backslash I$$ ; confidence 0.946

1763. ; $$0 = + \infty$$ ; confidence 0.667

1764. ; $$( \lambda \odot \mu ) \odot v = \lambda \odot ( \mu \odot v )$$ ; confidence 0.955

1765. ; $$( A )$$ ; confidence 1.000

1766. ; $$T$$ ; confidence 0.652

1767. ; $$H \equiv L \circ K$$ ; confidence 0.769

1768. ; $$f \in S _ { y } ^ { \prime }$$ ; confidence 0.307

1769. ; $$H _ { p } ^ { r } ( R ^ { n } ) \rightarrow H _ { p ^ { \prime } } ^ { \rho ^ { \prime } } ( R ^ { m } ) \rightarrow H _ { p l ^ { \prime \prime } } ^ { \rho ^ { \prime \prime } } ( R ^ { m ^ { \prime \prime } } )$$ ; confidence 0.143

1770. ; $$1 < m \leq n$$ ; confidence 0.737

1771. ; $$\| f \| _ { \Lambda _ { p } ^ { r } ( R ^ { n } ) } \leq K$$ ; confidence 0.335

1772. ; $$D _ { j } ^ { l } f \in L _ { p } ( R ^ { n } )$$ ; confidence 0.948

1773. ; $$- \infty < r < \infty$$ ; confidence 0.842

1774. ; $$\delta _ { 0 } > 0$$ ; confidence 1.000

1775. ; $$[ t ^ { n } : t ^ { n - 1 } ] = 0$$ ; confidence 0.989

1776. ; $$+ \frac { n } { p _ { 1 } p _ { 2 } } + \ldots + \frac { n } { p _ { k - 1 } p _ { k } } + - \frac { n } { p _ { 1 } p _ { 2 } p _ { 3 } } - \ldots + ( - 1 ) ^ { k } \frac { n } { p _ { 1 } \ldots p _ { k } }$$ ; confidence 0.552

1777. ; $$\gamma = \operatorname { ind } _ { g } a$$ ; confidence 0.608

1778. ; $$D = L _ { 1 } / D ( L _ { 0 } )$$ ; confidence 0.998

1779. ; $$\phi * : H ^ { * } ( B / S ) = H ^ { * } ( T M ) \rightarrow H ^ { * } ( M )$$ ; confidence 0.867

1780. ; $$D$$ ; confidence 0.996

1781. ; $$B ( M )$$ ; confidence 1.000

1782. ; $$\therefore M \rightarrow E$$ ; confidence 0.524

1783. ; $$K ( B / S )$$ ; confidence 0.995

1784. ; $$K ( T M ^ { g } ) \otimes C \rightarrow C$$ ; confidence 0.882

1785. ; $$i _ { \alpha } ( D ) \in K ( Y )$$ ; confidence 0.971

1786. ; $$\Sigma ( M ) = B ^ { + } \cup _ { S ( M ) } B ^ { - }$$ ; confidence 0.500

1787. ; $$h ( [ a ] )$$ ; confidence 0.265

1788. ; $$\pi$$ ; confidence 0.507

1789. ; $$[ T ^ { * } M ]$$ ; confidence 0.990

1790. ; $$\eta : Y \rightarrow B$$ ; confidence 0.984

1791. ; $$\nu _ { S }$$ ; confidence 0.758

1792. ; $$K \subset H$$ ; confidence 0.959

1793. ; $$\chi _ { \pi } ( g ) = \sum _ { \{ \delta : \delta y \in H \delta \} } \chi _ { \rho } ( \delta g \delta ^ { - 1 } )$$ ; confidence 0.903

1794. ; $$\phi _ { \alpha \alpha } = 1 _ { A _ { \alpha } }$$ ; confidence 0.624

1795. ; $$A = \operatorname { lim } _ { \rightarrow } F ( D )$$ ; confidence 0.939

1796. ; $$| \alpha _ { 1 } + \ldots + \alpha _ { n } | \leq | \alpha _ { 1 } | + \ldots + | \alpha _ { n } |$$ ; confidence 0.160

1797. ; $$A < \operatorname { ln } d X$$ ; confidence 0.106

1798. ; $$1 ^ { \circ }$$ ; confidence 0.592

1799. ; $$Y _ { n k }$$ ; confidence 0.813

1800. ; $$= 2 \pi ^ { 3 } a ^ { 2 } \frac { ( n + 1 ) ( 2 n + 1 ) } { 3 n ^ { 2 } }$$ ; confidence 0.781

1801. ; $$S = \frac { K } { 3 }$$ ; confidence 0.850

1802. ; $$F ( M ^ { k } ) \subset \nabla \square ^ { n }$$ ; confidence 0.382

1803. ; $$- \infty < a < + \infty$$ ; confidence 0.959

1804. ; $$3 a$$ ; confidence 0.497

1805. ; $$\overline { \rho } _ { L }$$ ; confidence 0.896

1806. ; $$p ^ { t } ( . )$$ ; confidence 0.817

1807. ; $$c ( I ) = \frac { 1 } { 2 }$$ ; confidence 0.667

1808. ; $$\Theta$$ ; confidence 0.952

1809. ; $$\sum _ { k = 1 } ^ { \infty } b _ { k } \operatorname { sin } k x$$ ; confidence 0.946

1810. ; $$\int f _ { 1 } ( x ) d x \quad \text { and } \quad \int f _ { 2 } ( x ) d x$$ ; confidence 0.921

1811. ; $$\alpha ( \lambda ) = \alpha _ { - } ( \lambda ) \alpha _ { + } ( \lambda )$$ ; confidence 0.598

1812. ; $$0 < \alpha < a$$ ; confidence 0.971

1813. ; $$h ( \lambda )$$ ; confidence 1.000

1814. ; $$| \lambda | < 1 / M ( b - \alpha )$$ ; confidence 0.952

1815. ; $$\hat { \phi } ( x ) = \lambda \sum _ { i = 1 } ^ { n } C _ { i } \alpha _ { i } ( x ) + f ( x )$$ ; confidence 0.810

1816. ; $$\{ \alpha _ { i } ( x ) \}$$ ; confidence 0.971

1817. ; $$| t - \tau |$$ ; confidence 0.984

1818. ; $$\Gamma = \partial D _ { 1 } \times \square \ldots \times \partial D _ { n }$$ ; confidence 0.954

1819. ; $$\Gamma ( z ) = \frac { 1 } { e ^ { 2 i \pi z } - 1 } \int _ { L _ { 1 } } \zeta ^ { z - 1 } e ^ { - \zeta } d \zeta$$ ; confidence 0.895

1820. ; $$\frac { \partial } { \partial z } = \frac { 1 } { 2 } ( \frac { \partial } { \partial x } + i \frac { \partial } { \partial y } )$$ ; confidence 0.997

1821. ; $$\partial D \times D$$ ; confidence 0.998

1822. ; $$g \in E$$ ; confidence 0.988

1823. ; $$T f _ { n } \rightarrow 0$$ ; confidence 0.976

1824. ; $$\psi = \sum \psi _ { i } \partial / \partial x _ { i }$$ ; confidence 0.981

1825. ; $$T _ { W } ^ { 2 k + 1 } ( X )$$ ; confidence 0.984

1826. ; $$\mathfrak { M } \in S _ { 1 }$$ ; confidence 0.842

1827. ; $$Y = C$$ ; confidence 0.871

1828. ; $$\{ f _ { \alpha } : \alpha \in \mathfrak { A } \}$$ ; confidence 0.968

1829. ; $$m \times ( n + 1 )$$ ; confidence 1.000

1830. ; $$\frac { ( x - x _ { k } - 1 ) ( x - x _ { k + 1 } ) } { ( x _ { k } - x _ { k - 1 } ) ( x _ { k } - x _ { k + 1 } ) } f ( x _ { k } ) + \frac { ( x - x _ { k - 1 } ) ( x - x _ { k } ) } { ( x _ { k } + 1 - x _ { k - 1 } ) ( x _ { k + 1 } - x _ { k } ) } f ( x _ { k + 1 } )$$ ; confidence 0.069

1831. ; $$\{ \psi _ { i } ( x ) \} _ { i = 0 } ^ { n }$$ ; confidence 0.981

1832. ; $$\omega _ { n - 1 } ( z ) = ( z - b _ { 0 } ) \ldots ( z - b _ { n } - 1 )$$ ; confidence 0.462

1833. ; $$\Delta ^ { i }$$ ; confidence 0.491

1834. ; $$B = Y \backslash 0$$ ; confidence 0.999

1835. ; $$x < \varrho y$$ ; confidence 0.723

1836. ; $$T \subset R ^ { 1 }$$ ; confidence 0.989

1837. ; $$\forall y \exists z ( \gamma ( y ) + 1 = \alpha ( g * \overline { \beta } ( z ) ) )$$ ; confidence 0.288

1838. ; $$\forall x ( P ( x ) \vee \neg P ( x ) ) \wedge \neg \neg \neg x P ( x ) \supset \exists x P ( x )$$ ; confidence 0.397

1839. ; $$x \leq z \leq y$$ ; confidence 0.995

1840. ; $$Z \in G$$ ; confidence 0.401

1841. ; $$\operatorname { inh } ^ { - 1 } z = - i \operatorname { arcsin } i z$$ ; confidence 0.766

1842. ; $$| r _ { + } ( k ) | \leq 1 - c k ^ { 2 } ( 1 + k ^ { 2 } ) ^ { - 1 }$$ ; confidence 0.554

1843. ; $$s > - \infty$$ ; confidence 0.985

1844. ; $$< 2 a$$ ; confidence 0.500

1845. ; $$y \geq x \geq 0$$ ; confidence 0.999

1846. ; $$q ( x ) \in L ^ { 2 } \operatorname { loc } ( R ^ { 3 } )$$ ; confidence 0.953

1847. ; $$y = Arc$$ ; confidence 0.482

1848. ; $$\operatorname { cos } ^ { - 1 } x$$ ; confidence 1.000

1849. ; $$F [ \phi ( w ) ]$$ ; confidence 0.983

1850. ; $$b = f ( a ) = b _ { 0 }$$ ; confidence 0.455

1851. ; $$P ^ { N } ( k )$$ ; confidence 0.999

1852. ; $$L ^ { \prime }$$ ; confidence 0.256

1853. ; $$O _ { X } ( 1 ) = O ( 1 )$$ ; confidence 0.996

1854. ; $$f ( x ^ { * } x ) \leq f ( 1 ) r ( x ^ { * } x )$$ ; confidence 0.984

1855. ; $$\omega ^ { \beta }$$ ; confidence 0.626

1856. ; $$0 \in R ^ { 3 }$$ ; confidence 0.983

1857. ; $$H = 0$$ ; confidence 0.999

1858. ; $$m s$$ ; confidence 0.683

1859. ; $$\gamma = 7 / 4$$ ; confidence 0.659

1860. ; $$p : G \rightarrow G$$ ; confidence 0.995

1861. ; $$X ^ { \prime \prime } = L _ { 1 } ^ { \prime \prime } \cap L _ { 2 } ^ { \prime \prime } = L _ { 2 } ^ { \prime \prime } \cap L _ { 3 } ^ { \prime \prime } = L _ { 1 } ^ { \prime \prime } \cap L _ { 3 } ^ { \prime \prime }$$ ; confidence 0.831

1862. ; $$x = \{ x ^ { \alpha } ( u ^ { s } ) \}$$ ; confidence 0.775

1863. ; $$E ^ { 2 k + 1 }$$ ; confidence 0.996

1864. ; $$( = 2 / \pi )$$ ; confidence 0.994

1865. ; $$F _ { t } : M ^ { n } \rightarrow M ^ { n }$$ ; confidence 0.989

1866. ; $$Y \times t$$ ; confidence 0.546

1867. ; $$L ^ { \prime } ( T _ { x } M )$$ ; confidence 0.252

1868. ; $$\kappa _ { k } = a _ { n n } ^ { ( k ) }$$ ; confidence 0.556

1869. ; $$\beta _ { k } q _ { k + 1 } = A q _ { k } - \beta _ { k - 1 } q _ { k - 1 } - \alpha _ { k } q _ { k k }$$ ; confidence 0.371

1870. ; $$F _ { 0 }$$ ; confidence 0.994

1871. ; $$k = k _ { 0 } \subset k _ { 1 } \subset \ldots \subset k _ { n } \subset \ldots \subset K = \cup _ { n \geq 0 } k _ { k }$$ ; confidence 0.434

1872. ; $$p < 12000000$$ ; confidence 1.000

1873. ; $$\lambda _ { p } ( K / k ) = \lambda ( X )$$ ; confidence 0.997

1874. ; $$( X ^ { \omega } \chi ^ { - 1 } ) = \pi ^ { \mu _ { \chi } ^ { * } } g _ { \chi } ^ { * } ( T )$$ ; confidence 0.875

1875. ; $$\overline { Q } _ { p }$$ ; confidence 0.689

1876. ; $$\mu _ { m }$$ ; confidence 0.969

1877. ; $$\theta _ { 3 } ( v \pm \frac { 1 } { 2 } \tau ) = e ^ { - i \pi \tau / 4 } \cdot e ^ { - i \pi v } \cdot \theta _ { 2 } ( v )$$ ; confidence 0.312

1878. ; $$dn ^ { 2 } u + k ^ { 2 } sn ^ { 2 } u = 1$$ ; confidence 0.565

1879. ; $$\theta _ { 2 } ( v \pm \tau ) = e ^ { - i \pi \tau } \cdot e ^ { - 2 i \pi v } \cdot \theta _ { 2 } ( v )$$ ; confidence 0.234

1880. ; $$e _ { 1 } = ( 2 - k ^ { 2 } ) / 3$$ ; confidence 0.995

1881. ; $$H _ { 2 } = \prod _ { m = 1 } ^ { \infty } ( 1 + e ^ { ( 2 m - 1 ) i \pi \tau } )$$ ; confidence 0.836

1882. ; $$w _ { 1 } = w _ { 1 } ( z _ { 1 } )$$ ; confidence 0.916

1883. ; $$x = B x + g$$ ; confidence 0.998

1884. ; $$\operatorname { log } F \leq 100$$ ; confidence 0.843

1885. ; $$f _ { 0 } ( \Delta )$$ ; confidence 0.998

1886. ; $$f _ { 0 } ( z _ { j } ) = \left\{ \begin{array} { l l } { \alpha ^ { ( j ) } z _ { j } + \text { non-positive powers of } z _ { j } } & { \text { if } j \leq r } \\ { z _ { j } + \sum _ { s = x _ { j } } ^ { \infty } a _ { s } ^ { ( j ) } z _ { j } ^ { - s } } & { \text { if } j > r } \end{array} \right.$$ ; confidence 0.051

1887. ; $$k _ { \vartheta } ( z ) = \frac { 1 - | z | ^ { 2 } } { | z - e ^ { i \vartheta | ^ { 2 } } }$$ ; confidence 0.753

1888. ; $$B M O$$ ; confidence 0.973

1889. ; $$K ^ { * }$$ ; confidence 0.718

1890. ; $$\operatorname { cr } ( K )$$ ; confidence 0.995

1891. ; $$s ( L ) \geq ( E - e ) / 2$$ ; confidence 0.952

1892. ; $$M ^ { ( 2 ) }$$ ; confidence 0.998

1893. ; $$( n _ { + } - n _ { - } ) - ( s ( D _ { L } ) - 1 ) \leq e \leq E \leq ( n _ { + } - n _ { - } ) + ( s ( D _ { L } ) - 1 )$$ ; confidence 0.972

1894. ; $$J = \left| \begin{array} { c c c c } { J _ { n _ { 1 } } ( \lambda _ { 1 } ) } & { \square } & { \square } & { \square } \\ { \square } & { \ldots } & { \square } & { 0 } \\ { 0 } & { \square } & { \ldots } & { \square } \\ { \square } & { \square } & { \square } & { J _ { n _ { S } } ( \lambda _ { s } ) } \end{array} \right|$$ ; confidence 0.072

1895. ; $$L = \angle \operatorname { lim } _ { z \rightarrow \omega } f ( z )$$ ; confidence 0.923

1896. ; $$\phi _ { \omega } ( F ( z ) ) \leq \phi _ { \omega } ( z )$$ ; confidence 0.994

1897. ; $$t = [ \xi _ { E } ]$$ ; confidence 0.983

1898. ; $$T ( X )$$ ; confidence 0.996

1899. ; $$x _ { 0 } ^ { 4 } + x _ { 1 } ^ { 4 } + x _ { 2 } ^ { 4 } + x _ { 3 } ^ { 4 } = 0$$ ; confidence 0.998

1900. ; $$h = K \eta \leq 1 / 2$$ ; confidence 0.997

1901. ; $$\frac { x ^ { \rho + 1 } f ( x ) } { \int _ { x } ^ { x } t ^ { \sigma } f ( t ) d t } \rightarrow \sigma + \rho + 1 \quad ( x \rightarrow \infty )$$ ; confidence 0.320

1902. ; $$f ( \vec { D } ( A ) ) = ( - A ^ { 3 } ) ^ { - \operatorname { Tait } ( \vec { D } ) } \langle D \rangle$$ ; confidence 0.497

1903. ; $$A | D _ { + } \rangle - A ^ { - 1 } \langle D _ { - } \} = ( A ^ { 2 } - A ^ { - 2 } ) \langle D _ { 0 } \}$$ ; confidence 0.230

1904. ; $$T ( s )$$ ; confidence 1.000

1905. ; $$\overline { 9 } _ { 42 }$$ ; confidence 0.683

1906. ; $$h ^ { 0 } ( K _ { X } \otimes L ^ { * } )$$ ; confidence 0.989

1907. ; $$B = \sum _ { j = 1 } ^ { t } b _ { j } B _ { j }$$ ; confidence 0.961

1908. ; $$m \geq m _ { 0 }$$ ; confidence 0.997

1909. ; $$z ^ { 2 } y ^ { \prime \prime } + z y ^ { \prime } - ( i z ^ { 2 } + \nu ^ { 2 } ) y = 0$$ ; confidence 0.967

1910. ; $$- w _ { 0 } ( \chi )$$ ; confidence 0.944

1911. ; $$W _ { C }$$ ; confidence 0.473

1912. ; $$K _ { p } ( f ) ( p _ { i } ) = f ( p _ { i } )$$ ; confidence 0.995

1913. ; $$K _ { \mu }$$ ; confidence 0.997

1914. ; $$K _ { 0 } ^ { 4 k + 2 }$$ ; confidence 0.990

1915. ; $$\Delta u = - f ( x )$$ ; confidence 0.986

1916. ; $$u | _ { \Sigma } = 0$$ ; confidence 0.837

1917. ; $$R \phi / 6$$ ; confidence 0.994

1918. ; $$\mu = m c / \hbar$$ ; confidence 0.999

1919. ; $$\| g _ { \alpha \beta } \|$$ ; confidence 0.862

1920. ; $$\partial / \partial x ^ { \alpha } \rightarrow ( \partial / \partial x ^ { \alpha } ) - i e A _ { \alpha } / \hbar$$ ; confidence 0.973

1921. ; $$\Omega ( \Gamma )$$ ; confidence 1.000

1922. ; $$\Gamma 20$$ ; confidence 0.310

1923. ; $$D _ { 1 } / \Gamma$$ ; confidence 0.999

1924. ; $$\frac { 1 } { 2 \pi } \{ \text { hyperbolic area of } \Omega \backslash \Gamma \} \leq 2 ( N - 1 )$$ ; confidence 0.926

1925. ; $$\hat { M } _ { 0 }$$ ; confidence 0.537

1926. ; $$Q _ { 1 } : A \rightarrow T ^ { \prime } A T$$ ; confidence 0.990

1927. ; $$| m K _ { V ^ { \prime } } | ^ { J }$$ ; confidence 0.246

1928. ; $$f ( z ) = z + \ldots$$ ; confidence 0.768

1929. ; $$\frac { \partial f } { \partial s } = - A _ { S } f$$ ; confidence 0.702

1930. ; $$I _ { \Gamma } ( x )$$ ; confidence 0.999

1931. ; $$A _ { t } ^ { * }$$ ; confidence 0.985

1932. ; $$= \frac { 2 } { \pi ^ { 2 } x _ { 0 } } \int _ { 0 } ^ { \infty } K _ { i \tau } ( x _ { 0 } ) \tau \operatorname { sinh } ( \pi \tau ) F ( \tau ) d \tau$$ ; confidence 0.890

1933. ; $$( \alpha _ { i } ) _ { i \in I }$$ ; confidence 0.480

1934. ; $$( \partial ^ { 2 } / \partial x \partial t ) u = \operatorname { sin } u$$ ; confidence 0.562

1935. ; $$\square ^ { 1 } S _ { 2 } ( i )$$ ; confidence 0.950

1936. ; $$E ( \Delta ) K \subset D ( A )$$ ; confidence 0.947

1937. ; $$c ( A ) \subset R \cup \{ \infty \}$$ ; confidence 0.588

1938. ; $$C = C ^ { * }$$ ; confidence 0.990

1939. ; $$W _ { \alpha } ( P ) \subseteq ( D _ { \alpha } ) ^ { n }$$ ; confidence 0.991

1940. ; $$D _ { \alpha }$$ ; confidence 0.374

1941. ; $$W _ { \alpha } ( B \supset C ) = T \leftrightarrows$$ ; confidence 0.637

1942. ; $$\sum _ { j = 1 } ^ { n } b _ { j } r j \in Z$$ ; confidence 0.479

1943. ; $$\eta ( \epsilon ) \rightarrow 0$$ ; confidence 0.993

1944. ; $$\frac { d \xi } { d t } = \epsilon X _ { 0 } ( \xi ) + \epsilon ^ { 2 } P _ { 2 } ( \xi ) + \ldots + \epsilon ^ { m } P _ { m } ( \xi )$$ ; confidence 0.966

1945. ; $$\xi = \xi _ { 0 } ( \phi )$$ ; confidence 0.999

1946. ; $$\mu _ { n } ( P \| Q ) =$$ ; confidence 0.972

1947. ; $$P = Q$$ ; confidence 0.998

1948. ; $$E \neq \emptyset$$ ; confidence 0.475

1949. ; $$E = \emptyset$$ ; confidence 0.977

1950. ; $$F _ { M } : G \rightarrow C ^ { * }$$ ; confidence 0.933

1951. ; $$g = \sum g _ { \alpha \overline { \beta } } d z ^ { \alpha } \otimes d z \square ^ { \beta }$$ ; confidence 0.694

1952. ; $$\nu _ { 0 } \in C ^ { n }$$ ; confidence 0.245

1953. ; $$p : X \rightarrow S$$ ; confidence 0.998

1954. ; $$R ^ { k } p \times ( F )$$ ; confidence 0.519

1955. ; $$x \preceq y$$ ; confidence 0.956

1956. ; $$M ( E ) = \vec { X }$$ ; confidence 0.493

1957. ; $$c \rightarrow N$$ ; confidence 0.335

1958. ; $$\overline { B } \rightarrow \overline { B }$$ ; confidence 0.985

1959. ; $$a \rightarrow a b d ^ { 6 }$$ ; confidence 0.569

1960. ; $$n ^ { O ( n ) } M ^ { O ( 1 ) }$$ ; confidence 0.921

1961. ; $$\{ \phi _ { n } \} _ { n = 1 } ^ { \infty }$$ ; confidence 0.817

1962. ; $$1 \leq p < + \infty$$ ; confidence 0.999

1963. ; $$3 N + k + m$$ ; confidence 0.919

1964. ; $$\ddot { x } \square _ { \nu } = d \dot { x } \square _ { \nu } / d t$$ ; confidence 0.944

1965. ; $$\mu$$ ; confidence 0.335

1966. ; $$x g$$ ; confidence 0.734

1967. ; $$T + V = h$$ ; confidence 0.994

1968. ; $$v ( P ) - v ( D )$$ ; confidence 0.999

1969. ; $$x ^ { ( 0 ) } = 1$$ ; confidence 0.976

1970. ; $$M N$$ ; confidence 0.867

1971. ; $$+ ( \lambda x y \cdot y ) : ( \sigma \rightarrow ( \tau \rightarrow \tau ) )$$ ; confidence 0.262

1972. ; $$( M N ) \in \Lambda$$ ; confidence 0.998

1973. ; $$\equiv \lambda x y \cdot x$$ ; confidence 0.709

1974. ; $$( \lambda x M ) \in \Lambda$$ ; confidence 0.756

1975. ; $$k ^ { 2 } ( \tau ) = \lambda$$ ; confidence 0.999

1976. ; $$D = 2 \gamma k T / M$$ ; confidence 0.990

1977. ; $$T _ { F }$$ ; confidence 0.455

1978. ; $$T _ { E } : U \rightarrow U$$ ; confidence 0.704

1979. ; $$v \in C ( \overline { G } )$$ ; confidence 0.795

1980. ; $$\Delta ( \alpha _ { 1 } \ldots i _ { p } d x ^ { i _ { 1 } } \wedge \ldots \wedge d x ^ { i p } ) =$$ ; confidence 0.331

1981. ; $$| t | ^ { - 1 }$$ ; confidence 1.000

1982. ; $$E = \frac { m } { 2 } ( \dot { x } \square _ { 1 } ^ { 2 } + \dot { x } \square _ { 2 } ^ { 2 } + \dot { x } \square _ { 3 } ^ { 2 } ) + \frac { \kappa } { r }$$ ; confidence 0.586

1983. ; $$\sqrt { 2 }$$ ; confidence 0.155

1984. ; $$m < n ^ { ( 1 / 3 ) - \delta }$$ ; confidence 0.883

1985. ; $$U _ { 0 } = 1$$ ; confidence 0.997

1986. ; $$\alpha _ { 1 } + n h _ { 1 }$$ ; confidence 0.738

1987. ; $$E ( \mu _ { n } / n )$$ ; confidence 0.725

1988. ; $$\operatorname { lim } _ { n \rightarrow \infty } \operatorname { sup } \frac { S _ { n } } { c _ { n } } = 1 \quad ( \alpha . s . )$$ ; confidence 0.299

1989. ; $$31$$ ; confidence 0.915

1990. ; $$\mu \approx 18.431$$ ; confidence 0.997

1991. ; $$4.60$$ ; confidence 0.967

1992. ; $$E Y _ { i } = ( \alpha + \beta \overline { t } ) + \beta ( t _ { i } - \overline { t } )$$ ; confidence 0.681

1993. ; $$\alpha _ { 2 } ( t ) = t$$ ; confidence 0.461

1994. ; $$f ( x ) = \operatorname { lim } _ { N \rightarrow \infty } \frac { 4 } { \pi ^ { 2 } } \int _ { 0 } ^ { N } \operatorname { cosh } ( \pi \tau ) \operatorname { Im } K _ { 1 / 2 + i \tau } ( x ) F ( \tau ) d \tau$$ ; confidence 0.580

1995. ; $$\lambda ( I ) = \lambda ^ { * } ( A \cap I ) + \lambda ^ { * } ( I \backslash A )$$ ; confidence 0.776

1996. ; $$H \phi$$ ; confidence 0.878

1997. ; $$\int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle ^ { 2 } } { \lambda } _ { d } \lambda < E _ { 0 }$$ ; confidence 0.248

1998. ; $$\phi \in H$$ ; confidence 0.981

1999. ; $$B \subset X ^ { * }$$ ; confidence 0.699

2000. ; $$v = v ( t )$$ ; confidence 0.987

2001. ; $$s = \int _ { a } ^ { b } \sqrt { 1 + [ f ^ { \prime } ( x ) ] ^ { 2 } } d x$$ ; confidence 0.961

2002. ; $$\{ i _ { k } \}$$ ; confidence 0.773

2003. ; $$\zeta = 0$$ ; confidence 0.999

2004. ; $$- \operatorname { log } | \zeta |$$ ; confidence 0.998

2005. ; $$0 < r < \operatorname { tanh } \pi / 4$$ ; confidence 0.998

2006. ; $$\operatorname { grad } \phi ( \zeta ) \neq 0$$ ; confidence 0.967

2007. ; $$x \# y = x y + y x - \frac { 2 } { n + 1 } ( \operatorname { Tr } x y ) l$$ ; confidence 0.625

2008. ; $$( x y ) x = y ( y x )$$ ; confidence 1.000

2009. ; $$\mathfrak { A } ^ { - }$$ ; confidence 0.906

2010. ; $$S ^ { i j } = \Omega ^ { i j } + T ^ { i j }$$ ; confidence 0.980

2011. ; $$x$$ ; confidence 0.899

2012. ; $$P _ { 8 }$$ ; confidence 0.799

2013. ; $$g ^ { \prime } / ( 1 - u ) g ^ { \prime } = \overline { g }$$ ; confidence 0.215

2014. ; $$\mathfrak { g } = \mathfrak { a } + \mathfrak { n }$$ ; confidence 0.634

2015. ; $$0 \leq p \leq n / 2$$ ; confidence 0.998

2016. ; $$A _ { I l }$$ ; confidence 0.608

2017. ; $$L ( H )$$ ; confidence 0.995

2018. ; $$Q _ { A }$$ ; confidence 0.136

2019. ; $$S \cap R ( G ) = ( e )$$ ; confidence 0.872

2020. ; $$x ( 1 )$$ ; confidence 1.000

2021. ; $$Z \times T$$ ; confidence 0.994

2022. ; $$C ^ { n } / \Gamma _ { 1 }$$ ; confidence 0.708

2023. ; $$G \subset N ( F )$$ ; confidence 0.979

2024. ; $$\pi _ { 1 } ( G ) \cong \Gamma ( G ) / \Gamma _ { 0 }$$ ; confidence 0.992

2025. ; $$l _ { k } ( A )$$ ; confidence 0.348

2026. ; $$\epsilon$$ ; confidence 0.882

2027. ; $$\tilde { y } ( x ) = \operatorname { exp } ( - \epsilon ) f ( x \operatorname { exp } ( - \epsilon ) )$$ ; confidence 0.405

2028. ; $$\operatorname { lm } A _ { * } = \mathfrak { g }$$ ; confidence 0.711

2029. ; $$R ^ { n } \times R ^ { n }$$ ; confidence 0.554

2030. ; $$\left\{ \begin{array} { l l } { \gamma \geq \frac { 1 } { 2 } } & { \text { forn } = 1 } \\ { \gamma > 0 } & { \text { forn } = 2 } \\ { \gamma \geq 0 } & { \text { forn } \geq 3 } \end{array} \right.$$ ; confidence 0.191

2031. ; $$\approx ( 2 \pi ) ^ { - n } \int _ { R ^ { n } \times R ^ { n } } [ p ^ { 2 } + V ( x ) ] _ { - } ^ { \gamma } d p d x =$$ ; confidence 0.680

2032. ; $$\operatorname { lim } _ { x \rightarrow x _ { 0 } } ( f _ { 1 } ( x ) / f _ { 2 } ( x ) )$$ ; confidence 0.857

2033. ; $$\operatorname { lim } _ { x \rightarrow x _ { 0 } } f ( x ) = \alpha$$ ; confidence 0.845

2034. ; $$\tau = \{ t _ { i } \} _ { i = 0 } ^ { i = n }$$ ; confidence 0.875

2035. ; $$- \Delta u + c u$$ ; confidence 0.993

2036. ; $$Z y \rightarrow \infty$$ ; confidence 0.270

2037. ; $$y = \operatorname { sin } ( 1 / x )$$ ; confidence 1.000

2038. ; $$f _ { h } \in F _ { k }$$ ; confidence 0.549

2039. ; $$p i n$$ ; confidence 0.132

2040. ; $$+ \sum _ { i = 1 } ^ { s } \| k _ { i k } [ u ] _ { k } - \{ l _ { i } u \} _ { i k } \| _ { \Phi _ { i k } } + \| p _ { i k } \phi _ { i } - \{ \phi _ { i } \} _ { i k } \| _ { \Phi _ { i k } }$$ ; confidence 0.263

2041. ; $$L _ { h } u _ { k } = f _ { k }$$ ; confidence 0.508

2042. ; $$\{ \phi _ { i } \} _ { i k }$$ ; confidence 0.712

2043. ; $$l _ { 2 } u = \phi _ { 2 } ( t )$$ ; confidence 0.851

2044. ; $$\frac { 1 } { 4 n } \operatorname { max } \{ \alpha _ { i } : 0 \leq i \leq t \} \leq \Delta _ { 2 } \leq \frac { 1 } { 4 n } ( \sum _ { i = 0 } ^ { t } \alpha _ { i } + 2 )$$ ; confidence 0.363

2045. ; $$\nabla _ { Y } ( f X ) = ( Y f ) X + f \nabla _ { Y } X$$ ; confidence 0.681

2046. ; $$T _ { x _ { 1 } } ( M ) \rightarrow T _ { x _ { 0 } } ( M )$$ ; confidence 0.821

2047. ; $$A ^ { ( 0 ) }$$ ; confidence 0.506

2048. ; $$\dot { u } = A _ { n } u$$ ; confidence 0.195

2049. ; $$\operatorname { ln } t$$ ; confidence 0.999

2050. ; $$T _ { \Delta }$$ ; confidence 0.636

2051. ; $$\lambda \geq \gamma$$ ; confidence 0.474

2052. ; $$\Gamma _ { 0 } ( . )$$ ; confidence 0.995

2053. ; $$H ^ { k }$$ ; confidence 0.998

2054. ; $$v \in ( 1 - t ) V$$ ; confidence 0.837

2055. ; $$C _ { 0 } ( R )$$ ; confidence 0.976

2056. ; $$A -$$ ; confidence 0.967

2057. ; $$x ( t ) \equiv 0$$ ; confidence 0.999

2058. ; $$x ^ { ( n ) } + \alpha _ { 1 } ( t ) x ^ { ( n - 1 ) } + \ldots + \alpha _ { n } ( t ) x = 0$$ ; confidence 0.867

2059. ; $$X ( t ) = \operatorname { exp } ( \int _ { t _ { 0 } } ^ { t } A ( \tau ) d \tau )$$ ; confidence 0.977

2060. ; $$Y ( t ) = X ( t ) C$$ ; confidence 0.998

2061. ; $$W ( t ) \neq 0$$ ; confidence 0.995

2062. ; $$x ( 0 ) \in R ^ { n }$$ ; confidence 0.473

2063. ; $$\dot { y } = - A ^ { T } ( t ) y$$ ; confidence 0.993

2064. ; $$Q _ { 3 } ( b )$$ ; confidence 0.962

2065. ; $$x = F ( t ) y$$ ; confidence 0.992

2066. ; $$\rho ^ { ( j ) }$$ ; confidence 0.828

2067. ; $$\alpha ^ { ( 0 ) }$$ ; confidence 0.892

2068. ; $$| \epsilon | < \epsilon$$ ; confidence 0.461

2069. ; $$\frac { d z } { d t } = - A ( t ) ^ { * } Z$$ ; confidence 0.495

2070. ; $$L ( 0 ) = 0$$ ; confidence 1.000

2071. ; $$\frac { d w _ { N } } { d t } = \frac { \partial w _ { N } } { \partial t } + \sum _ { i = 1 } ^ { N } ( \frac { \partial w _ { N } } { \partial r _ { i } } \frac { d r _ { i } } { d t } + \frac { \partial w _ { N } } { \partial p _ { i } } \frac { d p _ { i } } { d t } ) = 0$$ ; confidence 0.716

2072. ; $$f \in H _ { p } ^ { \alpha }$$ ; confidence 0.996

2073. ; $$G ( K _ { p ^ { \prime } } )$$ ; confidence 0.801

2074. ; $$( K _ { p } ) _ { i n s }$$ ; confidence 0.851

2075. ; $$Z _ { \text { tot } S } = Z$$ ; confidence 0.066

2076. ; $$\operatorname { dim } Z \cap \overline { S _ { k + q + 1 } } ( F | _ { X \backslash Z } ) \leq k$$ ; confidence 0.399

2077. ; $$\alpha = E X _ { 1 }$$ ; confidence 0.670

2078. ; $$d ( A )$$ ; confidence 0.998

2079. ; $$\in \Theta$$ ; confidence 0.953

2080. ; $$m = n = 1$$ ; confidence 0.998

2081. ; $$\left. \begin{array} { c c c } { R } & { \stackrel { \pi _ { 2 } \mu } { \rightarrow } } & { B } \\ { \pi _ { 1 } \mu \downarrow } & { \square } & { \downarrow \beta } \\ { A } & { \vec { \alpha } } & { C } \end{array} \right.$$ ; confidence 0.590

2082. ; $$R = \{ \alpha \in K : \operatorname { mod } _ { K } ( \alpha ) \leq 1 \}$$ ; confidence 0.342

2083. ; $$h _ { U } = \phi _ { U } ^ { - 1 }$$ ; confidence 0.912

2084. ; $$w \in T V$$ ; confidence 0.524

2085. ; $$\int \frac { d x } { x } = \operatorname { ln } | x | + C$$ ; confidence 0.986

2086. ; $$\pi < \operatorname { arg } z \leq \pi$$ ; confidence 0.972

2087. ; $$\operatorname { res } _ { \mathscr { d } } \frac { f ^ { \prime } ( z ) } { f ( z ) }$$ ; confidence 0.129

2088. ; $$Q \alpha = Q \beta \gamma$$ ; confidence 0.989

2089. ; $$\operatorname { inv } ( x )$$ ; confidence 0.875

2090. ; $$\Delta ^ { r + 1 } v _ { j } = \Delta ^ { r } v _ { j + 1 } - \Delta ^ { r } v _ { j }$$ ; confidence 0.659

2091. ; $$b \in Q$$ ; confidence 0.934

2092. ; $$Q _ { i - 1 } / Q _ { i }$$ ; confidence 0.640

2093. ; $$( S ^ { 1 } )$$ ; confidence 0.472

2094. ; $$z = e ^ { i \theta }$$ ; confidence 0.999

2095. ; $$\alpha = R \operatorname { ln } \operatorname { tan } ( \frac { \pi } { 4 } + \frac { u } { 2 R } )$$ ; confidence 0.905

2096. ; $$f ^ { \prime } ( x ) = 0$$ ; confidence 1.000

2097. ; $$\| \alpha _ { j } ^ { i } \|$$ ; confidence 0.148

2098. ; $$x = - \sum _ { k = 0 } ^ { \infty } ( A ^ { * } ) ^ { k } C ( A ) ^ { k }$$ ; confidence 0.953

2099. ; $$\lambda _ { j } + \overline { \lambda } _ { k } = 0$$ ; confidence 0.991

2100. ; $$V _ { 0 } \subset E$$ ; confidence 0.979

2101. ; $$x _ { 0 } ( . ) : t _ { 0 } + R ^ { + } \rightarrow U$$ ; confidence 0.802

2102. ; $$E ( T ) = \int \int _ { T } \frac { d x d y } { | x - y | }$$ ; confidence 0.572

2103. ; $$F _ { n } ( - \infty ) \rightarrow F ( - \infty )$$ ; confidence 0.972

2104. ; $$f _ { \theta } ( x )$$ ; confidence 0.998

2105. ; $$\varepsilon ^ { * } ( M A D ) = 1 / 2$$ ; confidence 0.731

2106. ; $$H _ { 2 } \times H _ { 1 }$$ ; confidence 0.537

2107. ; $$f \circ R _ { 1 } = R _ { 2 } \circ f$$ ; confidence 0.984

2108. ; $$F _ { A } = * D _ { A } \phi$$ ; confidence 0.738

2109. ; $$A = ( \frac { 1 } { \operatorname { sinh } r } - \frac { 1 } { r } ) \epsilon _ { i j k } \frac { x _ { j } } { r } \sigma _ { k } d x _ { i }$$ ; confidence 0.768

2110. ; $$f ( z ^ { d } ) = f ( z ) - z$$ ; confidence 0.796

2111. ; $$p < q$$ ; confidence 0.966

2112. ; $$E$$ ; confidence 0.975

2113. ; $$\kappa = \mu ^ { * }$$ ; confidence 0.985

2114. ; $$- i \partial / \partial x _ { j }$$ ; confidence 0.526

2115. ; $$P ^ { * } ( D )$$ ; confidence 0.999

2116. ; $$q ^ { - 1 } = 1 - p ^ { - 1 }$$ ; confidence 1.000

2117. ; $$\Delta \lambda _ { i } ^ { \alpha }$$ ; confidence 0.329

2118. ; $$t ( h ) = T ( h ) \cup \partial T ( k ) \partial F \times D ^ { 2 }$$ ; confidence 0.532

2119. ; $$\pi _ { 1 } ( M ) \neq Z _ { 2 }$$ ; confidence 0.886

2120. ; $$\Phi ( M ) \in Wh ( \pi _ { 1 } ( M ) )$$ ; confidence 0.743

2121. ; $$M _ { \psi } ^ { 0 }$$ ; confidence 0.996

2122. ; $$\mu ^ { - 1 }$$ ; confidence 0.999

2123. ; $$T _ { i j }$$ ; confidence 0.337

2124. ; $$P \{ \xi ( 0 ) = j \} = p _ { j }$$ ; confidence 0.551

2125. ; $$\Lambda \in N ^ { t }$$ ; confidence 0.838

2126. ; $$\Lambda = \{ \omega : x _ { S } \in B \}$$ ; confidence 0.703

2127. ; $$F _ { \infty } ^ { s }$$ ; confidence 0.520

2128. ; $$\alpha _ { \epsilon } ( h ) = o ( h )$$ ; confidence 0.989

2129. ; $$| \theta - \frac { p } { n } | \leq \frac { 1 } { \tau q ^ { 2 } }$$ ; confidence 0.999

2130. ; $$u ( y ) \geq 0$$ ; confidence 0.997

2131. ; $$0 \leq w \leq v$$ ; confidence 0.958

2132. ; $$K _ { y } ^ { \alpha }$$ ; confidence 0.924

2133. ; $$C = Z ( Q )$$ ; confidence 0.941

2134. ; $$\xi _ { k } = + 1$$ ; confidence 0.992

2135. ; $$V _ { [ r ] }$$ ; confidence 0.977

2136. ; $$B = 0$$ ; confidence 0.833

2137. ; $$\alpha = \beta _ { 1 } \vee \ldots \vee \beta _ { r }$$ ; confidence 0.964

2138. ; $$\operatorname { lim } _ { \Delta x \rightarrow 0 } \Delta y = \operatorname { lim } _ { \Delta x \rightarrow 0 } [ f ( x + \Delta x ) - f ( x ) ] = 0$$ ; confidence 0.996

2139. ; $$F ^ { \prime } = f$$ ; confidence 0.997

2140. ; $$\left. \begin{array}{l}{ \frac { d N ^ { 1 } } { d t } = \lambda _ { ( 1 ) } N ^ { 1 } ( 1 - \frac { N ^ { 1 } } { K _ { ( 1 ) } } - \delta _ { ( 1 ) } \frac { N ^ { 2 } } { K _ { ( 1 ) } } ) }\\{ \frac { d N ^ { 2 } } { d t } = \lambda _ { ( 2 ) } N ^ { 2 } ( 1 - \frac { N ^ { 2 } } { K _ { ( 2 ) } } - \delta _ { ( 2 ) } \frac { N ^ { 1 } } { K _ { ( 2 ) } } ) }\end{array} \right.$$ ; confidence 0.089

2141. ; $$= f ( N _ { * } ) + f ^ { \prime } ( N _ { * } ) n + \frac { f ^ { \prime \prime } ( N _ { * } ) } { 2 } n ^ { 2 } + \ldots$$ ; confidence 0.619

2142. ; $$R _ { + } ^ { l }$$ ; confidence 0.977

2143. ; $$b \in R ^ { l - 1 }$$ ; confidence 0.980

2144. ; $$z \square ^ { ( s ) }$$ ; confidence 0.776

2145. ; $$x > y > z$$ ; confidence 0.999

2146. ; $$c ( t ) \geq 0$$ ; confidence 1.000

2147. ; $$\int _ { - \infty } ^ { \infty } x d F ( x )$$ ; confidence 1.000

2148. ; $$k \frac { \partial u } { \partial n } + h u | _ { S } = v ( x )$$ ; confidence 0.973

2149. ; $$\Omega _ { p _ { 1 } n _ { 1 } } ( t ^ { \prime } t ^ { \prime } )$$ ; confidence 0.868

2150. ; $$x _ { i + 1 } = x _ { i } - ( \alpha _ { i } \nabla \nabla f ( x _ { j } ) + \beta _ { i } I ) ^ { - 1 } \nabla f ( x _ { i } )$$ ; confidence 0.559

2151. ; $$r _ { 0 } ^ { * } + \sum _ { j = 1 } ^ { q } \beta _ { j } r _ { j } ^ { * } = \sigma ^ { 2 }$$ ; confidence 0.822

2152. ; $$\hat { \theta } = X$$ ; confidence 0.545

2153. ; $$f ^ { ( m ) } ( x _ { 0 } ) < 0$$ ; confidence 0.978

2154. ; $$x _ { 3 } = z$$ ; confidence 0.989

2155. ; $$- \frac { \partial D } { \partial t } + \operatorname { rot } H = J$$ ; confidence 0.887

2156. ; $$d \sigma ( t )$$ ; confidence 0.999

2157. ; $$\Lambda ( f ) \geq 0$$ ; confidence 0.995

2158. ; $$\mu _ { i } ( X _ { i } ) = 1$$ ; confidence 0.990

2159. ; $$E = E ^ { \prime }$$ ; confidence 0.996

2160. ; $$S _ { 1 } \times S _ { 2 }$$ ; confidence 0.981

2161. ; $$E \in S ( R )$$ ; confidence 0.988

2162. ; $$\prod x$$ ; confidence 0.487

2163. ; $$\int _ { - 1 } ^ { 1 } \frac { 1 } { \sqrt { 1 - x ^ { 2 } } } f ( x ) d x \approx \frac { \pi } { N } \sum _ { k = 1 } ^ { N } f ( \operatorname { cos } \frac { 2 k - 1 } { 2 N } \pi )$$ ; confidence 0.978

2164. ; $$\square _ { q } F _ { p - 1 }$$ ; confidence 0.930

2165. ; $$t = t _ { 0 } > 0$$ ; confidence 0.996

2166. ; $$p \in P \backslash N$$ ; confidence 0.997

2167. ; $$( f ) = D$$ ; confidence 0.999

2168. ; $$D ( z ) \neq 0$$ ; confidence 0.995

2169. ; $$\psi _ { z } \neq 0$$ ; confidence 0.993

2170. ; $$z \in N$$ ; confidence 0.568

2171. ; $$F \mapsto F ( P )$$ ; confidence 0.864

2172. ; $$\int _ { c } ^ { \infty } f ( x ) d x$$ ; confidence 0.991

2173. ; $$n _ { 1 } < n _ { 2 } .$$ ; confidence 0.222

2174. ; $$\beta + \gamma \simeq \alpha . S ( t )$$ ; confidence 0.822

2175. ; $$E S$$ ; confidence 0.930

2176. ; $$0 \rightarrow A \rightarrow B \stackrel { sp } { \rightarrow } \pi * C \rightarrow 0$$ ; confidence 0.355

2177. ; $$\partial W _ { 1 } = M$$ ; confidence 0.996

2178. ; $$\sigma ( W )$$ ; confidence 0.989

2179. ; $$\theta _ { n } ( \partial \pi )$$ ; confidence 0.997

2180. ; $$\{ p _ { \theta } ( \omega ) = \frac { d p } { d \mu } ( \omega ) : \theta \in \Theta \}$$ ; confidence 0.987

2181. ; $$\int \int K d S \leq 2 \pi ( \chi - k )$$ ; confidence 0.858

2182. ; $$n \geq 9$$ ; confidence 0.998

2183. ; $$\int \int K d S$$ ; confidence 0.865

2184. ; $$\| x _ { k } - x ^ { * } \| \leq C q ^ { k }$$ ; confidence 0.985

2185. ; $$A = \pi r ^ { 2 }$$ ; confidence 0.999

2186. ; $$\| u \| _ { H ^ { \prime } } \leq R$$ ; confidence 0.473

2187. ; $$W ( N )$$ ; confidence 0.988

2188. ; $$\epsilon > 0$$ ; confidence 0.971

2189. ; $$F = W _ { 2 } ^ { - 1 } ( \Omega )$$ ; confidence 0.999

2190. ; $$\lambda K + t$$ ; confidence 0.994

2191. ; $$\tau \cup A C \cup B C$$ ; confidence 0.892

2192. ; $$d y / d s \geq 0$$ ; confidence 0.997

2193. ; $$\mathfrak { k } _ { n } | _ { 0 } = 0$$ ; confidence 0.128

2194. ; $$u | _ { \Gamma } = \psi$$ ; confidence 0.930

2195. ; $$k = m / 2$$ ; confidence 0.948

2196. ; $$GL _ { 2 } ( R )$$ ; confidence 0.691

2197. ; $$\operatorname { lm } A ( \tau )$$ ; confidence 0.945

2198. ; $$B O$$ ; confidence 0.877

2199. ; $$w = \lambda ( z )$$ ; confidence 0.985

2200. ; $$c = 0$$ ; confidence 0.874

2201. ; $$J ( F G / I ) = 0$$ ; confidence 0.991

2202. ; $$d ( x + y ) + d ( x y ) = d ( x ) + d ( y )$$ ; confidence 0.999

2203. ; $$m _ { G } = D ( u ) / 2 \pi$$ ; confidence 0.811

2204. ; $$G \rightarrow R _ { + } ^ { * }$$ ; confidence 0.778

2205. ; $$k _ { 1 } + \ldots + k _ { n } = k$$ ; confidence 0.849

2206. ; $$\alpha p$$ ; confidence 0.503

2207. ; $$C _ { \gamma } = C _ { \gamma _ { 1 } } C _ { \gamma _ { 2 } }$$ ; confidence 0.997

2208. ; $$t \in P ^ { 1 }$$ ; confidence 0.984

2209. ; $$\partial V _ { t }$$ ; confidence 0.996

2210. ; $$\alpha = \gamma ( 0 )$$ ; confidence 0.961

2211. ; $$f ( z ) = f ( x + i y )$$ ; confidence 1.000

2212. ; $$f _ { E } ^ { \prime } ( \zeta )$$ ; confidence 0.845

2213. ; $$f ( x ^ { \prime } ) < t$$ ; confidence 1.000

2214. ; $$\xi = x _ { m }$$ ; confidence 0.952

2215. ; $$T$$ ; confidence 0.520

2216. ; $$T _ { e } = j - 744$$ ; confidence 0.742

2217. ; $$Y ( K )$$ ; confidence 0.999

2218. ; $$( ( \partial f ) ^ { - 1 } + t l ) ^ { - 1 }$$ ; confidence 0.971

2219. ; $$- ( K _ { X } + B )$$ ; confidence 0.752

2220. ; $$\phi : X ^ { \prime } \rightarrow Y$$ ; confidence 0.951

2221. ; $$f : M \rightarrow R$$ ; confidence 0.936

2222. ; $$\sum _ { j = 0 } ^ { i } ( - 1 ) ^ { j } m _ { i - j } \geq \sum _ { j = 0 } ^ { i } ( - 1 ) ^ { j } b _ { i - j }$$ ; confidence 0.973

2223. ; $$V _ { 1 } = \emptyset$$ ; confidence 0.731

2224. ; $$\alpha = 4 \pi$$ ; confidence 1.000

2225. ; $$f \in L ^ { p } ( R ^ { n } ) \rightarrow \int _ { R ^ { n } } | x - y | ^ { - \lambda } f ( y ) d y \in L ^ { p ^ { \prime } } ( R ^ { n } )$$ ; confidence 0.413

2226. ; $$\tilde { y } = \alpha _ { 21 } x + \alpha _ { 22 } y + \alpha _ { 23 } z + b$$ ; confidence 0.163

2227. ; $$x = x \operatorname { cos } \phi + y \operatorname { sin } \phi + \alpha$$ ; confidence 0.056

2228. ; $$L C ^ { k - 1 }$$ ; confidence 0.734

2229. ; $$p _ { 1 } + \ldots + p _ { m } = p$$ ; confidence 0.769

2230. ; $$S _ { n }$$ ; confidence 0.963

2231. ; $$\operatorname { ess } \operatorname { sup } _ { X } | f ( x ) | = \operatorname { lim } _ { n \rightarrow \infty } ( \frac { \int | f ( x ) | ^ { n } d M _ { X } } { \int _ { X } d M _ { x } } )$$ ; confidence 0.229

2232. ; $$\alpha : A \rightarrow A _ { 1 }$$ ; confidence 0.999

2233. ; $$\lambda ^ { * } \in R ^ { m }$$ ; confidence 0.957

2234. ; $$G _ { 1 } / N$$ ; confidence 0.991

2235. ; $$\otimes _ { i = 1 } ^ { n } E _ { i } \rightarrow F$$ ; confidence 0.927

2236. ; $$\int | \rho _ { \varepsilon } ( x ) | d x$$ ; confidence 0.965

2237. ; $$s > n / 2$$ ; confidence 0.999

2238. ; $$M _ { 3 } ( R ^ { n } ) = \{$$ ; confidence 0.724

2239. ; $$d _ { é } ^ { l } < \ldots < d _ { e } ^ { 1 } = d$$ ; confidence 0.489

2240. ; $$\Phi _ { t } = id$$ ; confidence 0.507

2241. ; $$E = \{ e \}$$ ; confidence 0.981

2242. ; $$( \alpha \vee ( b . e ) ) : e = ( \alpha : e ) \vee b$$ ; confidence 0.351

2243. ; $$P ( \mathfrak { m } / \mathfrak { m } ^ { 2 } )$$ ; confidence 0.523

2244. ; $$n _ { \Delta } = 1$$ ; confidence 0.532

2245. ; $$x \lambda ( y ) = \rho ( x ) y$$ ; confidence 0.966

2246. ; $$\overline { \alpha } : P \rightarrow X$$ ; confidence 0.421

2247. ; $$\frac { | z | ^ { p } } { ( 1 + | z | ) ^ { 2 p } } \leq | f ( z ) | \leq \frac { | z | ^ { p } } { ( 1 - | z | ) ^ { 2 p } }$$ ; confidence 0.972

2248. ; $$L _ { \cap } \Gamma = 0$$ ; confidence 0.870

2249. ; $$H _ { n - 2 }$$ ; confidence 0.883

2250. ; $$P ( x ) = \sum _ { k = 1 } ^ { n } \alpha _ { k } x ^ { \lambda _ { k } }$$ ; confidence 0.795

2251. ; $$\operatorname { Re } ( \lambda )$$ ; confidence 0.992

2252. ; $$A _ { i \psi }$$ ; confidence 0.179

2253. ; $$f \in L _ { \infty } ( T )$$ ; confidence 0.971

2254. ; $$L _ { \infty } ( T )$$ ; confidence 0.979

2255. ; $$\Sigma _ { n - 1 } ( x )$$ ; confidence 0.905

2256. ; $$x \in V _ { n }$$ ; confidence 0.777

2257. ; $$X _ { i } \subset \Delta _ { 1 } ^ { i }$$ ; confidence 0.988

2258. ; $$\{ x _ { \alpha } \} _ { \alpha \in \Sigma }$$ ; confidence 0.994

2259. ; $$x \in b M$$ ; confidence 0.705

2260. ; $$\overline { \partial } f = \phi$$ ; confidence 0.995

2261. ; $$\sum _ { n = 0 } ^ { \infty } A ^ { n } f$$ ; confidence 0.994

2262. ; $$\phi _ { \alpha } ( f ) = w _ { \alpha }$$ ; confidence 0.945

2263. ; $$f ^ { - 1 } ( \alpha ) \cap \{ z : | z | \leq t \}$$ ; confidence 0.806

2264. ; $$\epsilon < \epsilon ^ { \prime } < \ldots$$ ; confidence 0.860

2265. ; $$A ( u ) = 0$$ ; confidence 1.000

2266. ; $$\Delta _ { k } ^ { k } f ^ { ( s ) }$$ ; confidence 0.968

2267. ; $$M _ { i } ^ { * } = c _ { i } \sum _ { j = 1 } ^ { n } M _ { j }$$ ; confidence 0.662

2268. ; $$0 < r - s < k$$ ; confidence 0.996

2269. ; $$D \cap \{ x ^ { 1 } = c \}$$ ; confidence 0.983

2270. ; $$\{ \psi _ { i } \} _ { 0 } ^ { m }$$ ; confidence 0.581

2271. ; $$v = 1.1 m / sec$$ ; confidence 0.848

2272. ; $$b = 7$$ ; confidence 0.999

2273. ; $$G \rightarrow A$$ ; confidence 0.998

2274. ; $$m ( B ) = 0$$ ; confidence 1.000

2275. ; $$Q ^ { \prime } \subset Q$$ ; confidence 0.984

2276. ; $$y ( 0 ) = y ^ { \prime }$$ ; confidence 0.740

2277. ; $$\left. \begin{array} { c } { B _ { n } ( y _ { n + 1 } ( 0 ) - y _ { n } ( 0 ) ) + B ( y _ { n } ( 0 ) ) = 0 } \\ { D _ { n } ( y _ { n + 1 } ( X ) - y _ { n } ( X ) ) + D ( y _ { n } ( X ) ) = 0 } \end{array} \right\}$$ ; confidence 0.711

2278. ; $$y ^ { * } = \alpha ( g ^ { * } )$$ ; confidence 0.950

2279. ; $$\| z ^ { n } \| \leq q ^ { n } ( 1 - q ) ^ { - 1 } \| u ^ { 0 } - u ^ { 1 } \|$$ ; confidence 0.538

2280. ; $$\phi _ { i } / \partial x _ { Y }$$ ; confidence 0.338

2281. ; $$x + h \in G$$ ; confidence 0.992

2282. ; $$A : G \rightarrow Y$$ ; confidence 0.991

2283. ; $$x \in K$$ ; confidence 0.658

2284. ; $$\xi ( x ) = 1$$ ; confidence 0.999

2285. ; $$\pi / \rho$$ ; confidence 0.416

2286. ; $$y ^ { \prime \prime \prime } = \lambda y$$ ; confidence 0.979

2287. ; $$B O$$ ; confidence 0.799

2288. ; $$\phi ( x ) \geq 0$$ ; confidence 0.999

2289. ; $$U$$ ; confidence 0.698

2290. ; $$\sum _ { k = 1 } ^ { \infty } \| u _ { k } \| = \sum _ { k = 1 } ^ { \infty } 1 / k$$ ; confidence 0.925

2291. ; $$\phi _ { i } ( 0 ) = 0$$ ; confidence 1.000

2292. ; $$j \geq q + 1$$ ; confidence 0.999

2293. ; $$N _ { 2 } = \left| \begin{array} { c c c c c } { . } & { \square } & { \square } & { \square } & { 0 } \\ { \square } & { . } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { L ( e _ { j } ^ { n _ { i j } } ) } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { . } & { \square } \\ { \square } & { \square } & { \square } & { \square } & { \square } \\ { 0 } & { \square } & { \square } & { \square } & { . } \end{array} \right|$$ ; confidence 0.323

2294. ; $$d j \neq 0$$ ; confidence 0.877

2295. ; $$A \simeq K$$ ; confidence 0.550

2296. ; $$N _ { G } ( H )$$ ; confidence 0.982

2297. ; $$( d \nu ) ( x _ { i } ) ( T _ { i } )$$ ; confidence 0.993

2298. ; $$\Omega _ { X }$$ ; confidence 0.976

2299. ; $$N ( A ^ { * } ) = \{ 0 \}$$ ; confidence 0.998

2300. ; $$A \in L _ { \infty } ( H )$$ ; confidence 0.994

2301. ; $$\operatorname { tr } _ { \sigma } A$$ ; confidence 0.814

2302. ; $$u \in E ^ { \prime } \otimes - E$$ ; confidence 0.540

2303. ; $$u = \operatorname { tr } \Gamma ( u )$$ ; confidence 0.766

2304. ; $$V \subset \rho U$$ ; confidence 0.940

2305. ; $$x y = 40$$ ; confidence 1.000

2306. ; $$\alpha + b = b + \alpha$$ ; confidence 0.739

2307. ; $$N > 5$$ ; confidence 0.901

2308. ; $$q 2 = 6$$ ; confidence 0.507

2309. ; $$12$$ ; confidence 0.490

2310. ; $$q 2 = 4$$ ; confidence 0.504

2311. ; $$\left. \begin{array} { l } { \nabla p _ { 1 } = \nabla p _ { 2 } = 0 } \\ { \frac { \partial v _ { 0 } } { \partial t } + [ \nabla v _ { 0 } ] v _ { 0 } = \frac { 1 } { Re } \Delta v _ { 0 } + \operatorname { Re } \nabla p _ { 3 } + \theta _ { 0 } b } \end{array} \right.$$ ; confidence 0.316

2312. ; $$F : L ^ { 2 } ( D ^ { \prime } ) \rightarrow L ^ { 2 } ( R ^ { 3 } )$$ ; confidence 0.936

2313. ; $$I _ { p } ( L )$$ ; confidence 0.985

2314. ; $$K _ { \omega }$$ ; confidence 0.958

2315. ; $$\overline { P _ { 8 } }$$ ; confidence 0.610

2316. ; $$\alpha = 1 / 2$$ ; confidence 0.933

2317. ; $$K _ { 10 }$$ ; confidence 0.993

2318. ; $$K$$ ; confidence 0.967

2319. ; $$T ( t ) x$$ ; confidence 0.794

2320. ; $$X = \sum _ { i } X ^ { i } \partial / \partial x ^ { i }$$ ; confidence 0.987

2321. ; $$\operatorname { lim } _ { x \rightarrow x _ { 0 } } + 0$$ ; confidence 0.628

2322. ; $$e ^ { - \lambda s }$$ ; confidence 0.999

2323. ; $$\phi \in D ( A )$$ ; confidence 0.998

2324. ; $$v \in G$$ ; confidence 0.413

2325. ; $$v _ { n } \in G$$ ; confidence 0.357

2326. ; $$x _ { C }$$ ; confidence 0.256

2327. ; $$( \alpha b ) \sigma = \alpha \sigma b \sigma$$ ; confidence 0.467

2328. ; $$( \sigma _ { 2 } \frac { \partial } { \partial t _ { 1 } } - \sigma _ { 1 } \frac { \partial } { \partial t _ { 2 } } + \gamma ) u = 0$$ ; confidence 0.449

2329. ; $$\frac { 1 } { i } ( A _ { k } - A _ { k } ^ { * } ) = \Phi ^ { * } \sigma _ { k } \Phi$$ ; confidence 0.897

2330. ; $$\overline { \gamma } = \tilde { \gamma } ^ { \prime \prime }$$ ; confidence 0.147

2331. ; $$x ( t _ { 1 } ) = x ^ { 1 } \in R ^ { n }$$ ; confidence 0.985

2332. ; $$2 \leq t \leq 3$$ ; confidence 0.999

2333. ; $$\sigma \leq t \leq \theta$$ ; confidence 0.947

2334. ; $$X = \cup _ { \alpha } X _ { \alpha }$$ ; confidence 0.245

2335. ; $$G / G _ { X }$$ ; confidence 0.936

2336. ; $$G ( x ) = \{ g ( x ) : g \in G \}$$ ; confidence 0.999

2337. ; $$\operatorname { lim } \alpha / \beta = 0$$ ; confidence 0.903

2338. ; $$\beta ( x ) \neq 0$$ ; confidence 0.999

2339. ; $$\{ Z _ { n } \}$$ ; confidence 0.984

2340. ; $$Y _ { n } = \frac { 1 } { 2 } ( X _ { ( n 1 ) } + X _ { ( n n ) } ) \quad \text { and } \quad Z _ { n } = \frac { n + 1 } { 2 } ( n - 1 ) ( X _ { ( n n ) } - X _ { ( n 1 ) } )$$ ; confidence 0.491

2341. ; $$W _ { n } = X _ { ( n n ) } - X _ { ( n 1 ) }$$ ; confidence 0.738

2342. ; $$\alpha ^ { n } < b ^ { n + 1 }$$ ; confidence 0.291

2343. ; $$C _ { \psi }$$ ; confidence 0.409

2344. ; $$C _ { \varphi }$$ ; confidence 0.982

2345. ; $$E$$ ; confidence 0.845

2346. ; $$\int _ { G } x ( t ) y ( t ) d t \leq \| x \| _ { ( M ) } \| y \| _ { ( N ) }$$ ; confidence 0.491

2347. ; $$- \beta V$$ ; confidence 0.966

2348. ; $$6 \pi \eta \alpha$$ ; confidence 0.422

2349. ; $$d W ( t ) / d t = W ^ { \prime } ( t )$$ ; confidence 0.993

2350. ; $$N ( n ) \rightarrow \infty$$ ; confidence 0.992

2351. ; $$A \perp A ^ { T }$$ ; confidence 0.994

2352. ; $$\Delta = \alpha _ { 2 } c ( b ) - \beta _ { 2 } s ( b ) \neq 0$$ ; confidence 0.937

2353. ; $$y = K _ { n } ( x )$$ ; confidence 0.826

2354. ; $$\sum _ { n = 0 } ^ { \infty } a _ { \tilde { m } } ^ { 2 } ( f ) = \int _ { \mathscr { x } } ^ { b } f ^ { 2 } ( x ) d x$$ ; confidence 0.076

2355. ; $$F ^ { k }$$ ; confidence 0.862

2356. ; $$F ( H )$$ ; confidence 0.998

2357. ; $$h > 1$$ ; confidence 0.985

2358. ; $$\overline { \Omega } _ { k } \subset \Omega _ { k + 1 }$$ ; confidence 0.887

2359. ; $$\underline { H } \square _ { f }$$ ; confidence 0.812

2360. ; $$B \operatorname { ccos } ( \omega t + \psi )$$ ; confidence 0.580

2361. ; $$\phi _ { im }$$ ; confidence 0.294

2362. ; $$\epsilon \ll 1$$ ; confidence 0.957

2363. ; $$| V _ { m n } | \ll | E _ { n } ^ { ( 0 ) } - E _ { m } ^ { ( 0 ) } |$$ ; confidence 0.535

2364. ; $$4 x$$ ; confidence 0.375

2365. ; $$E _ { i } ( x )$$ ; confidence 0.976

2366. ; $$\eta ( x ) \in \eta$$ ; confidence 0.999

2367. ; $$A _ { i } = \{ w \in W _ { i } \cap V ^ { s } ( z ) : z \in \Lambda _ { l } \cap U ( x ) \}$$ ; confidence 0.414

2368. ; $$\lambda < \mu$$ ; confidence 1.000

2369. ; $$\operatorname { limsup } _ { n \rightarrow + \infty } \frac { 1 } { n } \operatorname { log } + P _ { N } ( f ) \geq h ( f )$$ ; confidence 0.191

2370. ; $$D _ { 0 } f _ { x } = \left( \begin{array} { c c c } { A _ { 1 } ( x ) } & { \square } & { \square } \\ { \square } & { \ddots } & { \square } \\ { \square } & { \square } & { A _ { \xi } ( x ) ( x ) } \end{array} \right)$$ ; confidence 0.131

2371. ; $$P _ { n } ( f )$$ ; confidence 0.919

2372. ; $$S \square ^ { * }$$ ; confidence 0.590

2373. ; $$T ^ { * } U$$ ; confidence 0.999

2374. ; $$d y _ { 0 } - \sum _ { j = 1 } ^ { p } z _ { j } d y _ { j } = 0$$ ; confidence 0.905

2375. ; $$I ( G _ { p } )$$ ; confidence 0.801

2376. ; $$d f ^ { j }$$ ; confidence 0.726

2377. ; $$p _ { i }$$ ; confidence 0.459

2378. ; $$\operatorname { sch } / S$$ ; confidence 0.616

2379. ; $$f ^ { \prime } ( O _ { X ^ { \prime } } ) = O _ { S ^ { \prime } }$$ ; confidence 0.802

2380. ; $$f ( L )$$ ; confidence 0.999

2381. ; $$t ( P )$$ ; confidence 0.999

2382. ; $$\sigma A = x ^ { * } \partial \sigma ^ { * } \operatorname { lk } _ { A } \sigma + A _ { 1 }$$ ; confidence 0.541

2383. ; $$\theta$$ ; confidence 1.000

2384. ; $$n > 1$$ ; confidence 0.999

2385. ; $$E = E$$ ; confidence 0.907

2386. ; $$E _ { r } = S \cup T$$ ; confidence 0.755

2387. ; $$f ( x ) \mapsto \hat { f } ( y )$$ ; confidence 0.970

2388. ; $$\epsilon _ { i j } ^ { k }$$ ; confidence 0.400

2389. ; $$\sigma _ { i j } ( t )$$ ; confidence 0.998

2390. ; $$X \subset M ^ { n }$$ ; confidence 0.432

2391. ; $$H _ { k } ( M ^ { n } )$$ ; confidence 0.995

2392. ; $$\Omega _ { X } ( k ) \equiv \Omega ( k )$$ ; confidence 0.406

2393. ; $$_ { k }$$ ; confidence 0.179

2394. ; $$\{ z _ { k } \} \subset \Delta$$ ; confidence 0.994

2395. ; $$t _ { \gamma }$$ ; confidence 0.533

2396. ; $$\sigma _ { 2 n } = 2 \pi ^ { n } / ( n - 1 ) !$$ ; confidence 0.994

2397. ; $$u \in C ^ { 2 } ( D )$$ ; confidence 0.987

2398. ; $$p _ { 01 } p _ { 23 } + p _ { 02 } p _ { 31 } + p _ { 03 } p _ { 12 } = 0$$ ; confidence 0.676

2399. ; $$x \preceq y \Rightarrow z x t \preceq x y t$$ ; confidence 0.920

2400. ; $$w ( z ) = \int _ { \gamma } ( t - z ) ^ { \mu + n - 1 } u ( t ) d t$$ ; confidence 0.937

2401. ; $$\beta \in L _ { q }$$ ; confidence 0.972

2402. ; $$\mathfrak { g } = C$$ ; confidence 0.510

2403. ; $$L ( R ) \otimes _ { K } H _ { n } ( R ) = R$$ ; confidence 0.755

2404. ; $$V \cap L$$ ; confidence 0.905

2405. ; $$R \times D$$ ; confidence 0.945

2406. ; $$\mu A = m > 0$$ ; confidence 1.000

2407. ; $$q ^ { ( n ) } = d ^ { n } q / d x ^ { n }$$ ; confidence 0.958

2408. ; $$2 \lambda$$ ; confidence 1.000

2409. ; $$d S _ { n }$$ ; confidence 0.935

2410. ; $$X ( t _ { 2 } ) - X ( t _ { 1 } )$$ ; confidence 0.994

2411. ; $$/ t \rightarrow \lambda$$ ; confidence 0.669

2412. ; $$M ^ { 0 }$$ ; confidence 0.312

2413. ; $$P ^ { \perp } = \cap _ { v \in P } v ^ { \perp } = \emptyset$$ ; confidence 0.185

2414. ; $$W = M + U$$ ; confidence 0.972

2415. ; $$t ^ { i _ { 1 } } \cdots \dot { d p } = \operatorname { det } \| x _ { i } ^ { i _ { k } } \|$$ ; confidence 0.226

2416. ; $$f ( n ) \geq 0$$ ; confidence 1.000

2417. ; $$[ f _ { G } ]$$ ; confidence 0.256

2418. ; $$l _ { n } = \# \{ s \in S : d ( s ) = n \}$$ ; confidence 0.868

2419. ; $$d ( s ) = \operatorname { sup } \{ n : s \in F _ { n } \}$$ ; confidence 0.970

2420. ; $$m / m ^ { 2 }$$ ; confidence 0.612

2421. ; $$( \xi ) _ { R }$$ ; confidence 0.672

2422. ; $$p _ { i } ( \xi ) \in H ^ { 4 i } ( B )$$ ; confidence 0.998

2423. ; $$e ( \xi \otimes C )$$ ; confidence 0.997

2424. ; $$\omega _ { \mathscr { A } } : X ( G ) \rightarrow T$$ ; confidence 0.090

2425. ; $$E \subset X = R ^ { \prime }$$ ; confidence 0.250

2426. ; $$A \supset B$$ ; confidence 0.432

2427. ; $$x _ { 1 } = \ldots = x _ { n } = 0$$ ; confidence 0.697

2428. ; $$A / N _ { f }$$ ; confidence 0.994

2429. ; $$P ( x ) = a _ { 0 } + \alpha _ { 1 } x + \ldots + \alpha _ { n } x ^ { n }$$ ; confidence 0.639

2430. ; $$F \otimes S ^ { m } E$$ ; confidence 0.748

2431. ; $$O _ { 3 } = O _ { 6 } \cap O _ { 7 }$$ ; confidence 0.673

2432. ; $$F _ { 5 } ^ { \mu } = C _ { 4 } \cap F _ { 8 } ^ { \mu }$$ ; confidence 0.951

2433. ; $$\xi : F \rightarrow A$$ ; confidence 0.996

2434. ; $$v _ { i } = \partial f / \partial t ^ { i }$$ ; confidence 0.629

2435. ; $$\phi ^ { + } ( x )$$ ; confidence 0.999

2436. ; $$1 \leq p \leq n / 2$$ ; confidence 0.990

2437. ; $$p > n / 2$$ ; confidence 0.999

2438. ; $$- \infty \leq y < \infty$$ ; confidence 0.999

2439. ; $$\underline { \mathfrak { U } } \square _ { \phi } = - \overline { \mathfrak { U } } _ { \phi }$$ ; confidence 0.680

2440. ; $$f \in C$$ ; confidence 0.990

2441. ; $$\mu _ { 1 } = \mu _ { 2 } = \mu > 0$$ ; confidence 1.000

2442. ; $$\rho = | y |$$ ; confidence 0.958

2443. ; $$\phi ( n ) = n ( 1 - \frac { 1 } { p _ { 1 } } ) \dots ( 1 - \frac { 1 } { p _ { k } } )$$ ; confidence 0.456

2444. ; $$g _ { 0 } g ^ { \prime } \in G$$ ; confidence 0.189

2445. ; $$P \rightarrow e$$ ; confidence 0.910

2446. ; $$\left. \begin{array} { l l } { L - k E } & { M - k F } \\ { M - k F } & { N - k G } \end{array} \right| = 0$$ ; confidence 0.746

2447. ; $$G = G ^ { \prime }$$ ; confidence 1.000

2448. ; $$\pi G ( x ) = b$$ ; confidence 0.845

2449. ; $$\Gamma _ { F }$$ ; confidence 0.663

2450. ; $$\gamma \in G$$ ; confidence 0.994

2451. ; $$q _ { k } R = p _ { j } ^ { n _ { i } } R _ { R }$$ ; confidence 0.083

2452. ; $$q _ { i } R = 0$$ ; confidence 0.743

2453. ; $$0 \leq s _ { 0 } \leq l$$ ; confidence 0.979

2454. ; $$F _ { p q } \neq F _ { p q } ^ { * }$$ ; confidence 0.479

2455. ; $$x \in R ^ { + }$$ ; confidence 0.795

2456. ; $$E X _ { k } = a$$ ; confidence 0.520

2457. ; $$DX _ { k } = \sigma ^ { 2 }$$ ; confidence 0.511

2458. ; $$( K _ { i } / k )$$ ; confidence 0.490

2459. ; $$\alpha _ { 0 } \in A$$ ; confidence 0.998

2460. ; $$E _ { i j }$$ ; confidence 0.366

2461. ; $$x ^ { i } = y ^ { i } \lambda$$ ; confidence 0.985

2462. ; $$\pi _ { D } : X \rightarrow F ( D )$$ ; confidence 0.992

2463. ; $$\lambda _ { 1 } > \ldots > \lambda _ { n } ( \lambda ) > 0$$ ; confidence 0.786

2464. ; $$d ( S )$$ ; confidence 0.993

2465. ; $$q IL$$ ; confidence 0.843

2466. ; $$P _ { n } ( R )$$ ; confidence 0.886

2467. ; $$P _ { s } ^ { l } ( k )$$ ; confidence 0.866

2468. ; $$X = \operatorname { Proj } ( R )$$ ; confidence 0.994

2469. ; $$\operatorname { Proj } ( R )$$ ; confidence 0.995

2470. ; $$F \subset G$$ ; confidence 0.978

2471. ; $$U _ { i j } = \operatorname { Spec } ( A _ { i j } )$$ ; confidence 0.973

2472. ; $$( p \supset ( q \supset r ) ) \supset ( ( p \supset q ) \supset ( p \supset r ) )$$ ; confidence 0.827

2473. ; $$( P . Q ) ! = ( P \times Q ) ! = ( P ! \times Q ! ) !$$ ; confidence 0.823

2474. ; $$P Q = P \times Q$$ ; confidence 0.481

2475. ; $$\square ^ { n - 1 } R _ { n }$$ ; confidence 0.937

2476. ; $$X \cap U = \{ x \in U : \phi ( x ) > 0 \}$$ ; confidence 0.906

2477. ; $$\kappa : \Omega \rightarrow \Omega _ { 1 }$$ ; confidence 0.980

2478. ; $$\partial _ { x } = \partial / \partial x$$ ; confidence 0.368

2479. ; $$A : H ^ { S } ( X ) \rightarrow H ^ { S - m } ( X )$$ ; confidence 0.458

2480. ; $$| \xi | \leq 1 / 2$$ ; confidence 0.995

2481. ; $$q ^ { 1 }$$ ; confidence 0.419

2482. ; $$\gamma \in R$$ ; confidence 0.998

2483. ; $$D \rightarrow \overline { D }$$ ; confidence 0.992

2484. ; $$a \vee b$$ ; confidence 0.827

2485. ; $$I$$ ; confidence 0.923

2486. ; $$P \{ X _ { v + 1 } = k + 1 | X _ { k } = k \} = \frac { b + k c } { b + r + n c } = \frac { p + k \gamma } { 1 + n \gamma }$$ ; confidence 0.303

2487. ; $$\operatorname { arg } \operatorname { lim } _ { q \rightarrow r } Q _ { z } ( z ( q ) ) z ( q ) ^ { 2 }$$ ; confidence 0.802

2488. ; $$\mathfrak { F } \subset \mathfrak { P }$$ ; confidence 0.687

2489. ; $$( n = 4 )$$ ; confidence 1.000

2490. ; $$\alpha = - 1 / 2$$ ; confidence 1.000

2491. ; $$x \in E _ { + } ( s )$$ ; confidence 0.775

2492. ; $$R ^ { 12 } R ^ { 13 } R ^ { 23 } = R ^ { 23 } R ^ { 13 } R ^ { 12 }$$ ; confidence 0.998

2493. ; $$\left( \begin{array} { l } { n } \\ { k } \end{array} \right) _ { q } = \frac { ( q ^ { n } - 1 ) \ldots ( q ^ { n - k + 1 } - 1 ) } { ( q ^ { k } - 1 ) \ldots ( q - 1 ) }$$ ; confidence 0.443

2494. ; $$R ^ { 12 }$$ ; confidence 1.000

2495. ; $$H _ { i } \in \mathfrak { g }$$ ; confidence 0.955

2496. ; $$X ( Y . f ) = ( Y X ) . f$$ ; confidence 0.433

2497. ; $$j _ { X } : F ^ { \prime } \rightarrow F$$ ; confidence 0.809

2498. ; $$3 r ( L _ { 1 } \cap L _ { 2 } ) = 3 _ { r } ( L _ { 1 } ) + 3 r ( L _ { 2 } )$$ ; confidence 0.248

2499. ; $$D ^ { 2 } f ( x ^ { * } ) = D ( D ^ { T } f ( x ^ { * } ) )$$ ; confidence 0.975

2500. ; $$H _ { k + 1 } y ^ { k } = s ^ { k }$$ ; confidence 0.999

2501. ; $$f \in W _ { 2 } ^ { 1 }$$ ; confidence 0.943

2502. ; $$f : R _ { + } ^ { n } \rightarrow R _ { + } ^ { n }$$ ; confidence 0.970

2503. ; $$S _ { 2 m + 1 } ^ { m }$$ ; confidence 0.627

2504. ; $$\square ^ { 01 } S _ { 3 } ^ { 1 }$$ ; confidence 0.621

2505. ; $$x ^ { 1 } = 0$$ ; confidence 0.991

2506. ; $$\beta X = S \square x = \omega _ { \kappa } X$$ ; confidence 0.261

2507. ; $$N _ { A }$$ ; confidence 0.730

2508. ; $$\omega _ { 1 } / \omega _ { 2 }$$ ; confidence 0.996

2509. ; $$K > 1$$ ; confidence 0.997

2510. ; $$J _ { f } ( x ) \leq K l ( f ^ { \prime } ( x ) ) ^ { n }$$ ; confidence 0.794

2511. ; $$R [ x ]$$ ; confidence 0.996

2512. ; $$R _ { q ^ { 2 } }$$ ; confidence 0.811

2513. ; $$X = x _ { 0 } + V$$ ; confidence 0.644

2514. ; $$\alpha > a ^ { * }$$ ; confidence 0.575

2515. ; $$\nu _ { 1 } ^ { S }$$ ; confidence 0.641

2516. ; $$\{ \tau _ { j } ^ { e } \} \in G _ { I }$$ ; confidence 0.146

2517. ; $$\leq \nu _ { i } ^ { s }$$ ; confidence 0.802

2518. ; $$T ^ { S }$$ ; confidence 0.805

2519. ; $$\tau _ { 0 } ^ { e ^ { 3 } }$$ ; confidence 0.252

2520. ; $$\operatorname { lim } _ { t \rightarrow \infty } P \{ q ( t ) < x \sqrt { t } \} = \sqrt { \frac { 2 } { \pi } } \int _ { 0 } ^ { x / \sigma } e ^ { - u ^ { 2 } / 2 } d u$$ ; confidence 0.716

2521. ; $$\operatorname { lim } _ { t \rightarrow \infty } P \{ q ( t ) = k \} = \operatorname { lim } _ { t \rightarrow \infty } P \{ q _ { n } = k \} = \frac { ( \alpha \alpha ) ^ { k } } { k ! } e ^ { - \alpha ^ { \prime } \alpha }$$ ; confidence 0.087

2522. ; $$f ( \xi _ { T } ( t ) )$$ ; confidence 0.925

2523. ; $$E \theta ( t ) \theta ( t + u ) = \int _ { 0 } F ( t + u - v ) ( 1 - G ( t - v ) ) d m ( v )$$ ; confidence 0.887

2524. ; $$\alpha = \operatorname { lim } _ { t \rightarrow 0 } \frac { P ( e ( t ) \geq 1 ) } { t }$$ ; confidence 0.819

2525. ; $$\rho = E m \alpha \tau _ { j } ^ { e }$$ ; confidence 0.537

2526. ; $$p _ { m } = ( \sum _ { j = 0 } ^ { m } A _ { j } ) ^ { - 1 }$$ ; confidence 0.310

2527. ; $$Q _ { 0 } ^ { 0 } = Q ^ { 0 }$$ ; confidence 0.971

2528. ; $$P _ { k } ( x )$$ ; confidence 0.998

2529. ; $$P \{ X _ { n } \in \Delta \} \rightarrow 0$$ ; confidence 0.724

2530. ; $$G _ { l }$$ ; confidence 0.639

2531. ; $$w ^ { S } ( u ) = \operatorname { sup } _ { v \leq u } ( X ( u ) - X ( v ) )$$ ; confidence 0.601

2532. ; $$E [ \tau _ { j } ^ { S } - \tau _ { j } ^ { \dot { e } } ] ^ { 2 + \gamma }$$ ; confidence 0.250

2533. ; $$f _ { X } : V _ { X } \rightarrow V _ { X } ^ { \prime }$$ ; confidence 0.805

2534. ; $$j$$ ; confidence 0.784

2535. ; $$k ( \pi )$$ ; confidence 0.988

2536. ; $$e _ { 3 } = ( \alpha + d ) + ( b + c )$$ ; confidence 0.551

2537. ; $$\Delta u + k ^ { 2 } u = - f$$ ; confidence 0.985

2538. ; $$r _ { 1 } > r _ { 2 }$$ ; confidence 0.966

2539. ; $$\phi < \beta < L < K < J < T < \tau < F$$ ; confidence 0.970

2540. ; $$T w | K v$$ ; confidence 0.987

2541. ; $$( n - \mu _ { 1 } ) / 2$$ ; confidence 1.000

2542. ; $$\zeta _ { 2 n } = \sqrt { - 2 \operatorname { ln } \xi _ { 2 n } } \operatorname { sin } 2 \pi \xi _ { 2 n - 1 }$$ ; confidence 0.840

2543. ; $$P \{ Z _ { n } < x \} - \Phi ( x ) = O ( \frac { 1 } { n } )$$ ; confidence 0.432

2544. ; $$P \{ | \frac { K _ { n } } { n } - \frac { 1 } { 2 } | < \frac { 1 } { 4 } \} = 1 - 2 P \{ \frac { K _ { n } } { n } < \frac { 1 } { 4 } \} \approx 1 - \frac { 4 } { \pi } \frac { \pi } { 6 } = \frac { 1 } { 3 }$$ ; confidence 0.812

2545. ; $$u _ { 0 } = 1$$ ; confidence 0.716

2546. ; $$T = T ( R )$$ ; confidence 1.000

2547. ; $$R ( x )$$ ; confidence 1.000

2548. ; $$\delta _ { \phi }$$ ; confidence 0.541

2549. ; $$D _ { n - 2 }$$ ; confidence 0.996

2550. ; $$u _ { 1 } = | \frac { \partial u } { \partial n } | = 0$$ ; confidence 0.932

2551. ; $$k ^ { 2 } = k _ { c } ^ { 2 } + \frac { 3 } { 8 } \frac { \rho 2 g } { T \lambda _ { 0 } ^ { 2 } } ( 1 - \frac { \rho _ { 1 } } { \rho _ { 2 } } ) \epsilon ^ { 2 } + O ( \epsilon ^ { 3 } )$$ ; confidence 0.807

2552. ; $$P - N \equiv ( \frac { m _ { 1 } } { 2 } ) ^ { 2 } \pm 1 \operatorname { mod } 8$$ ; confidence 0.918

2553. ; $$\operatorname { dim } A = n = q - s$$ ; confidence 0.969

2554. ; $$\{ r _ { n } + r _ { n } ^ { \prime } \}$$ ; confidence 0.928

2555. ; $$t _ { k } \in R$$ ; confidence 0.947

2556. ; $$U$$ ; confidence 0.987

2557. ; $$\{ f ^ { t } | \Sigma _ { X } \} _ { t \in R }$$ ; confidence 0.191

2558. ; $$F ( m ) = f _ { m } ( m )$$ ; confidence 0.639

2559. ; $$f ( x ) = x + 1$$ ; confidence 1.000

2560. ; $$E ( Y | x ) = m ( x )$$ ; confidence 0.542

2561. ; $$E ( Y - f ( x ) ) ^ { 2 }$$ ; confidence 0.547

2562. ; $$\beta$$ ; confidence 0.566

2563. ; $$X = \| x _ { i } \|$$ ; confidence 0.794

2564. ; $$y _ { t } = A x _ { t } + \epsilon _ { t }$$ ; confidence 0.979

2565. ; $$x \frac { \operatorname { lim } _ { x \rightarrow D } u ( x ) = f ( y _ { 0 } ) } { x \in D }$$ ; confidence 0.172

2566. ; $$x ( t ) \in D ^ { c }$$ ; confidence 0.992

2567. ; $$x _ { n m _ { n } } \rightarrow ( 0 )$$ ; confidence 0.220

2568. ; $$e \omega ^ { r } f$$ ; confidence 0.300

2569. ; $$\overline { A } z = \overline { u }$$ ; confidence 0.777

2570. ; $$R _ { 0 } \subset F$$ ; confidence 0.991

2571. ; $$\{ \alpha _ { n } ^ { ( e ) } \}$$ ; confidence 0.972

2572. ; $$\{ \alpha _ { n } \} _ { \aleph = 0 } ^ { \infty }$$ ; confidence 0.264

2573. ; $$g 00 = 1 - 2 \phi / c ^ { 2 }$$ ; confidence 0.483

2574. ; $$p \leq \epsilon / 3$$ ; confidence 0.998

2575. ; $$c \approx 3.10 ^ { 10 } cm / se$$ ; confidence 0.741

2576. ; $$c t ^ { \prime } = x ^ { \prime } \operatorname { sinh } \psi + c t \operatorname { cosh } \psi$$ ; confidence 0.906

2577. ; $$\frac { d ^ { 2 } x } { d \tau ^ { 2 } } - \lambda ( 1 - x ^ { 2 } ) \frac { d x } { d \tau } + x = 0$$ ; confidence 0.998

2578. ; $$t + \tau$$ ; confidence 0.811

2579. ; $$B = B _ { 1 } \cup B _ { 2 }$$ ; confidence 0.997

2580. ; $$H ( t ) = E N$$ ; confidence 0.783

2581. ; $$M _ { \gamma _ { i } } M _ { \gamma _ { j } }$$ ; confidence 0.992

2582. ; $$v _ { 2 } \in V _ { 2 }$$ ; confidence 0.962

2583. ; $$s < s ^ { \prime }$$ ; confidence 0.967

2584. ; $$\phi \in E ^ { \prime }$$ ; confidence 0.998

2585. ; $$A = A _ { 1 } \times A _ { 2 }$$ ; confidence 0.989

2586. ; $$e X$$ ; confidence 0.861

2587. ; $$g e = g$$ ; confidence 0.982

2588. ; $$E / E ^ { \prime }$$ ; confidence 0.807

2589. ; $$l _ { i } = \lambda _ { i } + n - i$$ ; confidence 0.990

2590. ; $$V _ { \lambda } ^ { 0 } \subset V _ { \lambda }$$ ; confidence 0.929

2591. ; $$g \mapsto ( \operatorname { det } g ) ^ { k } R ( g )$$ ; confidence 0.974

2592. ; $$\oplus R ( S _ { n } )$$ ; confidence 0.905

2593. ; $$\| f \| = 0$$ ; confidence 0.996

2594. ; $$\{ \phi j ( z ) \}$$ ; confidence 0.543

2595. ; $$\Lambda ^ { 2 } : = \sum _ { j = 1 } ^ { \infty } \lambda _ { j } < \infty$$ ; confidence 0.996

2596. ; $$\psi d z$$ ; confidence 0.981

2597. ; $$R _ { V } = \frac { 1 } { ( 2 \pi i ) ^ { n } } \int _ { \sigma _ { V } } f ( z ) d z$$ ; confidence 0.396

2598. ; $$A = \int _ { - \infty } ^ { \infty } \lambda d E _ { \lambda }$$ ; confidence 1.000

2599. ; $$y _ { 2 } = ( x _ { 1 } + x _ { 3 } ) ( x _ { 2 } + x _ { 4 } )$$ ; confidence 0.881

2600. ; $$x ^ { T } ( t _ { 1 } ) \Phi x ( t _ { 1 } ) + \int _ { t _ { 0 } } ^ { t _ { 1 } } [ x ^ { T } ( t ) M ( t ) x ( t ) + u ^ { T } ( t ) N ( t ) u ( t ) ] d t$$ ; confidence 0.938

2601. ; $$\sum _ { i = 1 } ^ { r } \alpha _ { i } \sigma ( w ^ { i } x + \theta _ { i } )$$ ; confidence 0.982

2602. ; $$D _ { n }$$ ; confidence 0.956

2603. ; $$\operatorname { ch } ( f _ { 1 } ( x ) ) = f * ( \operatorname { ch } ( x ) \operatorname { td } ( T _ { f } ) )$$ ; confidence 0.130

2604. ; $$D \cup \gamma$$ ; confidence 0.997

2605. ; $$G ( K ) \rightarrow G ( Q )$$ ; confidence 0.817

2606. ; $$a _ { 0 } ( z ) \neq 0$$ ; confidence 0.937

2607. ; $$b \in \overline { C }$$ ; confidence 0.690

2608. ; $$AH _ { p }$$ ; confidence 0.775

2609. ; $$\partial \overline { R } _ { \nu }$$ ; confidence 0.821

2610. ; $$2 g - 1$$ ; confidence 0.999

2611. ; $$f ^ { \mu } | _ { K }$$ ; confidence 0.278

2612. ; $$R _ { i l k } ^ { q } = - R _ { k l } ^ { q }$$ ; confidence 0.210

2613. ; $$- \infty \leq \lambda < \mu \leq \infty$$ ; confidence 0.998

2614. ; $$d s ^ { 2 } = g _ { j } \omega ^ { i } \omega ^ { j }$$ ; confidence 0.914

2615. ; $$\partial x ^ { i } / \partial v$$ ; confidence 0.737

2616. ; $$\operatorname { exp } _ { q } X = r$$ ; confidence 0.511

2617. ; $$\gamma : M ^ { n } \rightarrow M ^ { n }$$ ; confidence 0.911

2618. ; $$n < 7$$ ; confidence 0.999

2619. ; $$N = 0$$ ; confidence 0.990

2620. ; $$\{ \operatorname { exp } _ { m } ( \text { Cutval } ( \xi ) \xi ) \} = \text { Cutloc } ( m )$$ ; confidence 0.291

2621. ; $$\gamma _ { \xi } ( t )$$ ; confidence 0.995

2622. ; $$V ^ { \prime } \subset R ^ { \prime }$$ ; confidence 0.979

2623. ; $$\gamma \geq \gamma _ { k }$$ ; confidence 0.999

2624. ; $$V ^ { \prime } = V ^ { \prime \prime } = R ^ { \prime } \cup R ^ { \prime \prime }$$ ; confidence 0.993

2625. ; $$o = e K$$ ; confidence 0.327

2626. ; $$| x _ { i } | \leq 1$$ ; confidence 0.845

2627. ; $$P _ { \sigma } = \frac { 1 } { 2 \pi i } \int _ { \Gamma } ( \lambda - A ) ^ { - 1 } d \lambda$$ ; confidence 0.932

2628. ; $$P _ { \sigma } ^ { 2 } = P _ { \sigma }$$ ; confidence 0.980

2629. ; $$\sigma ( R ) \backslash \lambda$$ ; confidence 0.997

2630. ; $$x + z < y + z$$ ; confidence 0.999

2631. ; $$p _ { \alpha } = e$$ ; confidence 0.518

2632. ; $$U : E \rightarrow M$$ ; confidence 0.994

2633. ; $$y _ { n } \leq x _ { n } \leq z _ { n }$$ ; confidence 0.841

2634. ; $$\operatorname { lim } _ { r \rightarrow 1 } \int _ { E } | f ( r e ^ { i \theta } ) | ^ { \delta } d \theta = \int _ { E } | f ( e ^ { i \theta } ) | ^ { \delta } d \theta$$ ; confidence 0.964

2635. ; $$s : M \rightarrow F ( M )$$ ; confidence 0.983

2636. ; $$\gamma _ { t } ( x + y ) = \sum _ { r = 0 } ^ { t } \gamma _ { r } ( x ) \gamma _ { t - r } ( y )$$ ; confidence 0.991

2637. ; $$I ( A ) = \operatorname { Ker } ( \epsilon )$$ ; confidence 0.898

2638. ; $$( \alpha b ) \alpha = \alpha ( b \alpha )$$ ; confidence 0.731

2639. ; $$( a + b ) \alpha = \alpha \alpha + b \alpha$$ ; confidence 0.463

2640. ; $$\| u - P _ { n } u \| _ { A } \rightarrow 0$$ ; confidence 0.332

2641. ; $$u _ { 0 } = A ^ { - 1 } f$$ ; confidence 0.941

2642. ; $$J ( q ) ^ { T }$$ ; confidence 0.999

2643. ; $$19$$ ; confidence 1.000

2644. ; $$1$$ ; confidence 0.430

2645. ; $$V = 5$$ ; confidence 0.985

2646. ; $$300$$ ; confidence 0.440

2647. ; $$j 2 ^ { - k - l }$$ ; confidence 0.858

2648. ; $$\lambda - \mu$$ ; confidence 1.000

2649. ; $$- 3$$ ; confidence 1.000

2650. ; $$M \dot { y } = f ( y )$$ ; confidence 0.805

2651. ; $$R ^ { \infty } \rightarrow \ldots \rightarrow R ^ { m } \rightarrow \ldots \rightarrow R ^ { 0 }$$ ; confidence 0.522

2652. ; $$c ^ { m } ( \Omega )$$ ; confidence 0.773

2653. ; $$c ^ { \infty } ( \Omega ) ^ { N }$$ ; confidence 0.774

2654. ; $$A _ { k } = U _ { k } ^ { * } A _ { k - 1 } U _ { k }$$ ; confidence 0.993

2655. ; $$| \chi | < \pi$$ ; confidence 0.998

2656. ; $$\operatorname { Pic } ( F ) \cong p ^ { * } \operatorname { Pic } ( C ) \oplus Z ^ { 5 }$$ ; confidence 0.304

2657. ; $$D _ { n } X _ { 1 }$$ ; confidence 0.828

2658. ; $$D _ { n } X \subset S ^ { n } \backslash X$$ ; confidence 0.497

2659. ; $$D _ { n } D _ { n } \theta = \theta$$ ; confidence 0.970

2660. ; $$m _ { i } = 0$$ ; confidence 0.997

2661. ; $$\tilde { D } = E \{ M | m = 0 \} = \frac { ( \sum _ { r = 1 } ^ { N - n } r \frac { C _ { N - r } ^ { n } } { C _ { N } ^ { n } } p _ { r } ) } { P \{ m = 0 \} }$$ ; confidence 0.234

2662. ; $$g _ { t } ( u )$$ ; confidence 0.987

2663. ; $$\phi ( T _ { X } N ) \subset T _ { X } N$$ ; confidence 0.941

2664. ; $$\phi ( D _ { X } ) = D _ { X }$$ ; confidence 0.531

2665. ; $$\overline { D } = \overline { D } _ { S }$$ ; confidence 0.978

2666. ; $$X ^ { * } = \Gamma \backslash D ^ { * }$$ ; confidence 0.822

2667. ; $$\phi _ { \mathscr { A } } ( . )$$ ; confidence 0.193

2668. ; $$d \in C$$ ; confidence 0.487

2669. ; $$\Phi ( r - b + c )$$ ; confidence 1.000

2670. ; $$\phi ( f ( x ) ) = g ( x ) \phi ( x ) + h ( x )$$ ; confidence 0.999

2671. ; $$\pi \Gamma$$ ; confidence 0.616

2672. ; $$\lambda ^ { s _ { \mu } } = \sum _ { \nu } c _ { \lambda \mu } ^ { \nu } s _ { \nu }$$ ; confidence 0.882

2673. ; $$s _ { \lambda } = \sum _ { T } x ^ { T }$$ ; confidence 0.998

2674. ; $$x ^ { T } = x _ { 1 } ^ { 3 } x _ { 2 } x _ { 3 } ^ { 2 } x _ { 4 }$$ ; confidence 0.977

2675. ; $$| \lambda | = \Sigma _ { i } \lambda$$ ; confidence 0.682

2676. ; $$S _ { B B } ( z ) \equiv 0$$ ; confidence 0.476

2677. ; $$\operatorname { Ccm } ( G )$$ ; confidence 0.094

2678. ; $$D ^ { - 1 } \in \pi$$ ; confidence 0.978

2679. ; $$\theta \in \Theta _ { 0 } \subseteq \Theta$$ ; confidence 0.992

2680. ; $$\sum _ { j = 1 } ^ { n } | b _ { j j } | \leq \rho$$ ; confidence 0.569

2681. ; $$q ^ { l } ( q ^ { 2 } - 1 ) \dots ( q ^ { 2 l } - 1 ) / d$$ ; confidence 0.450

2682. ; $$q ^ { 6 } ( q ^ { 2 } - 1 ) ( q ^ { 6 } - 1 )$$ ; confidence 0.814

2683. ; $$\square ^ { 2 } F _ { 4 } ( q ) ^ { \prime }$$ ; confidence 0.889

2684. ; $$c b = c$$ ; confidence 0.994

2685. ; $$18$$ ; confidence 0.479

2686. ; $$s _ { \alpha } \geq 1$$ ; confidence 0.984

2687. ; $$\operatorname { dim } K$$ ; confidence 0.982

2688. ; $$B d K$$ ; confidence 0.567

2689. ; $$s _ { i } : X _ { n } \rightarrow X _ { n } + 1$$ ; confidence 0.593

2690. ; $$X \rightarrow \Delta [ 0 ]$$ ; confidence 0.965

2691. ; $$\tilde { f } : \Delta ^ { n + 1 } \rightarrow E$$ ; confidence 0.333

2692. ; $$x _ { i } \in \pi$$ ; confidence 0.507

2693. ; $$| \sigma ^ { n } |$$ ; confidence 0.923

2694. ; $$M = \frac { a } { a ^ { 2 } - b ^ { 2 } } I - \frac { b } { a ^ { 2 } - b ^ { 2 } } S$$ ; confidence 0.440

2695. ; $$K = \nu - \nu$$ ; confidence 0.596

2696. ; $$\psi ( t ) = a * ( t ) g ( t ) +$$ ; confidence 0.645

2697. ; $$\| x \| = \rho$$ ; confidence 0.826

2698. ; $$x _ { 0 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$$ ; confidence 0.863

2699. ; $$L _ { 2 } : z = \phi _ { 2 } ( t )$$ ; confidence 0.995

2700. ; $$0 < \tau _ { 1 } \leq 1$$ ; confidence 0.993

2701. ; $$f _ { t } = h _ { t } \circ f _ { 0 } \circ k _ { t }$$ ; confidence 0.837

2702. ; $$\int _ { 0 } ^ { t } I _ { \partial D } ( Y _ { s } ) d l _ { s } = 1 _ { t }$$ ; confidence 0.676

2703. ; $$\varphi H G$$ ; confidence 0.652

2704. ; $$\sum _ { l = 1 } ^ { \infty } \frac { \operatorname { ln } q + 1 } { q l }$$ ; confidence 0.755

2705. ; $$\phi : U \rightarrow \sum _ { i \in I } U _ { l }$$ ; confidence 0.895

2706. ; $$b ( x ) < 0$$ ; confidence 1.000

2707. ; $$| w | = \rho < 1$$ ; confidence 0.874

2708. ; $$\overline { D ^ { + } } = D ^ { + } \cup \Gamma$$ ; confidence 0.709

2709. ; $$M = M ^ { \perp \perp }$$ ; confidence 0.970

2710. ; $$J _ { m + n + 1 } ( x ) =$$ ; confidence 0.892

2711. ; $$s \in E ^ { n }$$ ; confidence 0.570

2712. ; $$\| x \| ^ { 2 } = \int _ { \sigma ( A ) } | f _ { \lambda } ( x ) | ^ { 2 } d \rho ( \lambda )$$ ; confidence 0.635

2713. ; $$\sigma _ { d x } ( A )$$ ; confidence 0.138

2714. ; $$A \Phi \subset \Phi$$ ; confidence 0.973

2715. ; $$B ( r ) = \int _ { 0 } ^ { \infty } J _ { 0 } ( \lambda r ) d F ( \lambda )$$ ; confidence 0.998

2716. ; $$s _ { 1 } - t _ { 1 } = s _ { 2 } - t _ { 2 }$$ ; confidence 0.998

2717. ; $$A _ { \delta }$$ ; confidence 0.997

2718. ; $$E | X ( t ) | ^ { n } \leq C < \infty$$ ; confidence 0.578

2719. ; $$d ^ { \prime }$$ ; confidence 0.445

2720. ; $$| T | _ { p }$$ ; confidence 0.714

2721. ; $$\theta _ { T } = \theta$$ ; confidence 0.989

2722. ; $$B _ { N } A ( B _ { N } ( \lambda - \lambda _ { 0 } ) )$$ ; confidence 0.980

2723. ; $$\mathfrak { p } \not p \not \sum _ { n = 1 } ^ { \infty } A _ { n }$$ ; confidence 0.075

2724. ; $$\Sigma ( \Sigma ^ { n } X ) \rightarrow \Sigma ^ { n + 1 } X$$ ; confidence 0.992

2725. ; $$( \pi )$$ ; confidence 1.000

2726. ; $$Z _ { 24 }$$ ; confidence 0.663

2727. ; $$i > 2 n - 1$$ ; confidence 0.989

2728. ; $$e ^ { - k - s | / \mu } / \mu$$ ; confidence 0.763

2729. ; $$V ^ { 3 } = E ^ { 3 }$$ ; confidence 0.992

2730. ; $$K ( d s ) = K$$ ; confidence 0.996

2731. ; $$\pi = n \sqrt { 1 + \sum p ^ { 2 } }$$ ; confidence 0.678

2732. ; $$O ( r )$$ ; confidence 0.866

2733. ; $$\lambda _ { m } ( t )$$ ; confidence 0.691

2734. ; $$5 + 7 n$$ ; confidence 0.141

2735. ; $$f \in W _ { 2 } ^ { 3 } ( \Omega )$$ ; confidence 0.999

2736. ; $$( 2 m - 2 )$$ ; confidence 1.000

2737. ; $$W _ { p } ^ { m } ( I ^ { d } )$$ ; confidence 0.958

2738. ; $$L \subset Z ^ { 0 }$$ ; confidence 0.864

2739. ; $$\Gamma = \Gamma _ { 1 } + \ldots + \Gamma _ { m }$$ ; confidence 0.966

2740. ; $$\gamma ( u ) < \infty$$ ; confidence 0.997

2741. ; $$\operatorname { det } S \neq 0$$ ; confidence 0.896

2742. ; $$- \infty \leq w \leq + \infty$$ ; confidence 0.301

2743. ; $$0 \leq \omega \leq \infty$$ ; confidence 0.754

2744. ; $$\| \eta ( \cdot ) \| ^ { 2 } = \int _ { 0 } ^ { \infty } | \eta ( t ) | ^ { 2 } d t$$ ; confidence 0.669

2745. ; $$\| x _ { 0 } \| \leq \delta$$ ; confidence 0.966

2746. ; $$V < 0$$ ; confidence 0.854

2747. ; $$k \leq p \leq n$$ ; confidence 0.985

2748. ; $$f _ { h } \in U _ { k }$$ ; confidence 0.371

2749. ; $$\operatorname { max } _ { n \atop n } \| u ^ { n } \| _ { H } \leq e ^ { C _ { 1 } T } \{ \| \phi \| _ { H } + C _ { 0 } \sum _ { n } \tau \| f ^ { n + 1 } \| _ { H } \}$$ ; confidence 0.172

2750. ; $$\delta < \alpha$$ ; confidence 0.956

2751. ; $$m < \infty$$ ; confidence 0.973

2752. ; $$\eta _ { 0 } ( i )$$ ; confidence 0.979

2753. ; $$V _ { x } 0 ( \lambda ) \sim \operatorname { exp } [ i \lambda S ( x ^ { 0 } ) ] \sum _ { k = 0 } ^ { \infty } ( \sum _ { l = 0 } ^ { N } \alpha _ { k l } \lambda ^ { - r _ { k } } ( \operatorname { ln } \lambda ) ^ { l } \}$$ ; confidence 0.167

2754. ; $$m = E X ( s )$$ ; confidence 0.808

2755. ; $$Q _ { 1 }$$ ; confidence 0.060

2756. ; $$\Pi ^ { * } \in C$$ ; confidence 0.864

2757. ; $$\mathfrak { R } _ { \mu } ( \Pi _ { 0 } ) = \operatorname { inf } _ { \Pi } \Re _ { \mu } ( \Pi )$$ ; confidence 0.658

2758. ; $$H _ { i } ( \omega )$$ ; confidence 0.983

2759. ; $$I _ { n } ( \theta ) = n I ( \theta )$$ ; confidence 0.870

2760. ; $$P \{ s ^ { 2 } < \frac { \sigma ^ { 2 } x } { n - 1 } \} = G _ { n - 1 } ( x ) = D _ { n - 1 } \int _ { 0 } ^ { x } v ^ { ( n - 3 ) } / 2 e ^ { - v / 2 } d v$$ ; confidence 0.622

2761. ; $$\operatorname { lim } _ { n \rightarrow \infty } P \{ \frac { \alpha - \alpha } { \sigma _ { n } ( \alpha ) } < x \} = \frac { 1 } { \sqrt { 2 \pi } } \int _ { - \infty } ^ { x } e ^ { - t ^ { 2 } / 2 } d t \equiv \Phi ( x )$$ ; confidence 0.827

2762. ; $$\in \Theta _ { 0 } \beta _ { n } ( \theta ) \leq \alpha$$ ; confidence 0.815

2763. ; $$\eta \in R ^ { k }$$ ; confidence 0.999

2764. ; $$H = H _ { V } ( \omega )$$ ; confidence 0.988

2765. ; $$\mathfrak { A } _ { \infty } = \overline { U _ { V \subset R ^ { 3 } } } A ( \mathcal { H } _ { V } )$$ ; confidence 0.216

2766. ; $$\{ f \rangle _ { P } \sim | V |$$ ; confidence 0.071

2767. ; $$\frac { 1 } { 2 \pi } \sum _ { t = - T + 1 } ^ { T - 1 } e ^ { - i t \lambda } r ^ { * } ( t ) c T ( t )$$ ; confidence 0.607

2768. ; $$\xi = \sum b _ { j } x ( t _ { j } )$$ ; confidence 0.942

2769. ; $$\sum b _ { j } \phi _ { l } ( t _ { j } ) = 0$$ ; confidence 0.990

2770. ; $$I _ { T } ( \lambda ) = \frac { 1 } { 2 \pi T } | \int _ { 0 } ^ { T } e ^ { - i t \lambda } x ( t ) d t |$$ ; confidence 0.646

2771. ; $$a T \rightarrow \infty$$ ; confidence 0.506

2772. ; $$\theta _ { T } ^ { * }$$ ; confidence 0.481

2773. ; $$\{ \epsilon _ { t } \}$$ ; confidence 0.993

2774. ; $$h ^ { S * } ( . ) \approx \overline { E } \times ( . )$$ ; confidence 0.489

2775. ; $$\alpha < p b$$ ; confidence 0.578

2776. ; $$\alpha \leq p b$$ ; confidence 0.784

2777. ; $$g \neq 0$$ ; confidence 1.000

2778. ; $$I = \{ f \in O ( X ) : f ( x ) = 0 \}$$ ; confidence 0.993

2779. ; $$I \subset O ( X )$$ ; confidence 0.970

2780. ; $$n ( O _ { x } ) = 0$$ ; confidence 0.322

2781. ; $$f _ { h } ( t ) = \frac { 1 } { h } \int _ { t - k / 2 } ^ { t + k / 2 } f ( u ) d u = \frac { 1 } { h } \int _ { - k / 2 } ^ { k / 2 } f ( t + v ) d v$$ ; confidence 0.345

2782. ; $$\omega ( R )$$ ; confidence 0.999

2783. ; $$\sum _ { i = 1 } ^ { r } \alpha _ { i } \theta ( b _ { i } ) \in Z [ G ]$$ ; confidence 0.947

2784. ; $$RP ^ { \infty }$$ ; confidence 0.165

2785. ; $$V _ { k } ( H ^ { n } ) = \frac { Sp ( n ) } { Sp ( n - k ) }$$ ; confidence 0.259

2786. ; $$x [ M ^ { n } ] = \alpha ( x )$$ ; confidence 0.933

2787. ; $$w ^ { \prime }$$ ; confidence 0.380

2788. ; $$x + C$$ ; confidence 0.988

2789. ; $$| u ( x _ { 1 } ) - u ( x _ { 2 } ) | \leq C | x _ { 1 } - x _ { 2 }$$ ; confidence 0.995

2790. ; $$h _ { n } = \int _ { a } ^ { b } x ^ { n } h ( x ) d x$$ ; confidence 0.183

2791. ; $$| \frac { 1 } { 1 - H \lambda _ { i } } | < 1$$ ; confidence 0.997

2792. ; $$y _ { n + 1 } = y _ { n } + \int _ { 0 } ^ { H / 2 } e ^ { A \tau } d \tau \times$$ ; confidence 0.976

2793. ; $$\alpha _ { 1 } = - 3$$ ; confidence 0.753

2794. ; $$\| y \| = \operatorname { max } _ { i } | y _ { i } |$$ ; confidence 0.800

2795. ; $$H \mapsto \alpha ( H )$$ ; confidence 0.996

2796. ; $$K . ( H X ) = ( K H ) X$$ ; confidence 0.766

2797. ; $$\partial _ { s }$$ ; confidence 0.939

2798. ; $$t / \lambda ^ { 2 } \rightarrow + \infty$$ ; confidence 0.986

2799. ; $$E$$ ; confidence 0.923

2800. ; $$B \in \mathfrak { B } _ { 0 }$$ ; confidence 0.992

2801. ; $$\ldots < t _ { - 1 } < t _ { 0 } \leq 0 < t _ { 1 } < t _ { 2 } <$$ ; confidence 0.500

2802. ; $$\square \ldots < t _ { - 1 } < t _ { 0 } \leq 0 < t _ { 1 } < t _ { 2 } < \ldots$$ ; confidence 0.740

2803. ; $$X ( t _ { 1 } ) = x$$ ; confidence 0.980

2804. ; $$t = Z$$ ; confidence 0.971

2805. ; $$x ( \phi )$$ ; confidence 0.999

2806. ; $$\overline { w }$$ ; confidence 0.553

2807. ; $$d x = A ( t ) x d t + B ( t ) d w ( t )$$ ; confidence 0.986

2808. ; $$d X ( t ) = a ( t ) Z ( t ) d t + d Y ( t )$$ ; confidence 0.505

2809. ; $$\alpha < t < b$$ ; confidence 0.786

2810. ; $$\zeta ^ { \phi } \in C ^ { d }$$ ; confidence 0.837

2811. ; $$W ^ { ( n ) } ( s )$$ ; confidence 0.986

2812. ; $$J ( y ) \leq J ( y )$$ ; confidence 0.683

2813. ; $$\overline { f } : X \rightarrow Y$$ ; confidence 0.998

2814. ; $$\overline { E } * ( X )$$ ; confidence 0.554

2815. ; $$j _ { X } ^ { k } ( u )$$ ; confidence 0.362

2816. ; $$f = 1$$ ; confidence 1.000

2817. ; $$a \neq a _ { 0 }$$ ; confidence 0.773

2818. ; $$p ( \alpha )$$ ; confidence 0.904

2819. ; $$l [ f ] = 0$$ ; confidence 0.979

2820. ; $$L _ { 0 } ^ { * } = L _ { 1 }$$ ; confidence 0.957

2821. ; $$\lambda _ { 1 } < \lambda _ { 2 } < \ldots$$ ; confidence 0.830

2822. ; $$\Phi ^ { \prime \prime } ( + 0 ) = - h$$ ; confidence 0.997

2823. ; $$m _ { 0 } ( \lambda ) = A + \int _ { - \infty } ^ { \infty } ( \frac { 1 } { t - \lambda } - \frac { t } { t ^ { 2 } + 1 } ) d \rho _ { 0 } ( t )$$ ; confidence 0.926

2824. ; $$X ^ { * }$$ ; confidence 0.447

2825. ; $$m : B \rightarrow A$$ ; confidence 0.962

2826. ; $$\xi = \infty \in \partial D$$ ; confidence 0.998

2827. ; $$V = V ( \infty ) = \{ x \in R ^ { n } : | x | > R \}$$ ; confidence 0.624

2828. ; $$c = \operatorname { const } \neq 0$$ ; confidence 0.470

2829. ; $$P _ { \theta } ( A | B )$$ ; confidence 0.963

2830. ; $$\sum _ { n < x } f ( n ) = R ( x ) + O ( x ^ { \{ ( \alpha + 1 ) ( 2 \eta - 1 ) / ( 2 \eta + 1 ) \} + \epsilon } )$$ ; confidence 0.795

2831. ; $$\lambda _ { n } = 1 / ( n + 1 ) ^ { s }$$ ; confidence 0.931

2832. ; $$s _ { n } \rightarrow s$$ ; confidence 0.696

2833. ; $$\sum _ { k = 0 } ^ { \infty } \lambda _ { k } u _ { k }$$ ; confidence 0.542

2834. ; $$\operatorname { psq } ( n ) = \operatorname { sq } ( n ) / \{ c E : c \in C \}$$ ; confidence 0.425

2835. ; $$S ( L )$$ ; confidence 0.980

2836. ; $$x _ { 1 } ^ { 2 } = 0$$ ; confidence 0.997

2837. ; $$\frac { x ^ { 2 } } { p } - \frac { y ^ { 2 } } { q } = 2 z$$ ; confidence 0.932

2838. ; $$T ^ { * } Y \backslash 0$$ ; confidence 0.994

2839. ; $$\Phi ( f ( w ) ) = \sigma ( \Phi ( w ) )$$ ; confidence 0.999

2840. ; $$S ( B _ { n } ^ { m } )$$ ; confidence 0.719

2841. ; $$H ^ { n - k } \cap S ^ { k }$$ ; confidence 0.502

2842. ; $$\alpha _ { H } ( \tilde { x } _ { + } ) - \alpha _ { H } ( \tilde { x } _ { - } ) = 1$$ ; confidence 0.404

2843. ; $$\sim \frac { 2 ^ { n } } { \operatorname { log } _ { 2 } n }$$ ; confidence 0.975

2844. ; $$T _ { i } = C A ^ { i } B ^ { i } B$$ ; confidence 0.233

2845. ; $$- 5 \rightarrow - 14 \rightarrow - 7 \rightarrow - 20 \rightarrow - 10 \rightarrow - 5$$ ; confidence 0.902

2846. ; $$R = \{ \pi ( i ) : \square i \in I \}$$ ; confidence 0.950

2847. ; $$\{ \pi ( i ) : \square i \in I _ { 0 } \}$$ ; confidence 0.752

2848. ; $$L ^ { 1 } ( R ) \cap L ^ { \infty } ( R )$$ ; confidence 0.831

2849. ; $$T ^ { + } = \cap _ { N > 0 } \sigma ( X _ { n } : n \geq N )$$ ; confidence 0.699

2850. ; $$k = R / m$$ ; confidence 0.483

2851. ; $$g ^ { ( i ) }$$ ; confidence 0.484

2852. ; $$( n + 1 ) a _ { n + 1 } + \alpha _ { n } = \tau$$ ; confidence 0.385

2853. ; $$\tau x ^ { n }$$ ; confidence 0.790

2854. ; $$D _ { A } ^ { 2 } = 0$$ ; confidence 0.998

2855. ; $$\sigma ^ { \prime } ( A )$$ ; confidence 0.999

2856. ; $$\psi = \Psi ^ { \prime }$$ ; confidence 0.559

2857. ; $$E _ { 1 } E _ { 2 } E _ { 3 }$$ ; confidence 0.997

2858. ; $$e _ { v } \leq \mathfrak { e } _ { v } + 1$$ ; confidence 0.197

2859. ; $$R _ { T ^ { \prime \prime } }$$ ; confidence 0.675

2860. ; $$M _ { \mathscr { C } } M _ { b } M _ { \alpha ^ { \prime } } M _ { \phi }$$ ; confidence 0.076

2861. ; $$e ^ { \prime }$$ ; confidence 0.559

2862. ; $$( \pi | \tau _ { 1 } | \tau _ { 2 } )$$ ; confidence 0.977

2863. ; $$\theta ( z + \tau ) = \operatorname { exp } ( - 2 \pi i k z ) . \theta ( z )$$ ; confidence 0.660

2864. ; $$\delta = 2$$ ; confidence 0.999

2865. ; $$\operatorname { lm } A = \| \operatorname { lm } \alpha _ { \mu \nu } |$$ ; confidence 0.510

2866. ; $$B = I _ { p }$$ ; confidence 0.852

2867. ; $$d f _ { x } : R ^ { n } \rightarrow R ^ { p }$$ ; confidence 0.932

2868. ; $$f ^ { - 1 } ( S )$$ ; confidence 0.998

2869. ; $$c < 2$$ ; confidence 0.987

2870. ; $$u x + v x ^ { 2 } + w x ^ { 3 } + t x ^ { 4 }$$ ; confidence 0.989

2871. ; $$\{ \partial f \rangle$$ ; confidence 0.295

2872. ; $$x ^ { 3 } + x y ^ { 2 }$$ ; confidence 1.000

2873. ; $$E ^ { Q } ( N )$$ ; confidence 0.962

2874. ; $$N \geq Z$$ ; confidence 0.919

2875. ; $$\Delta _ { i j } = \Delta _ { j i } = \sqrt { ( x _ { i } - x _ { j } ) ^ { 2 } + ( y _ { i } - y _ { j } ) ^ { 2 } + ( z _ { i } - z _ { j } ) ^ { 2 } }$$ ; confidence 0.489

2876. ; $$M = M _ { 1 } \# M _ { 2 }$$ ; confidence 0.954

2877. ; $$O _ { S } ^ { * }$$ ; confidence 0.936

2878. ; $$( 5 \times 10 ^ { 6 } r ) ^ { 3 }$$ ; confidence 0.525

2879. ; $$X _ { ( \tau _ { 1 } + \ldots + \tau _ { j - 1 } + 1 ) } = \ldots = X _ { ( \tau _ { 1 } + \ldots + \tau _ { j } ) }$$ ; confidence 0.575

2880. ; $$B s$$ ; confidence 0.576

2881. ; $$\beta ( M )$$ ; confidence 0.995

2882. ; $$\square _ { H } T$$ ; confidence 0.979

2883. ; $$( Q )$$ ; confidence 0.999

2884. ; $$q R$$ ; confidence 0.245

2885. ; $$q _ { A }$$ ; confidence 0.118

2886. ; $$M = M \Lambda ^ { t }$$ ; confidence 0.505

2887. ; $$C ^ { * } E ( S ) \otimes _ { \delta } C _ { 0 } ( S )$$ ; confidence 0.440

2888. ; $$K ( L ^ { 2 } ( S ) )$$ ; confidence 0.779

2889. ; $$( \Delta ^ { \alpha } \xi ) ^ { \# } = \Delta ^ { - \overline { \alpha } } \xi ^ { \# }$$ ; confidence 0.710

2890. ; $$\eta \in A \mapsto \xi \eta \in A$$ ; confidence 0.962

2891. ; $$f \in S ( R ^ { n } )$$ ; confidence 0.981

2892. ; $$( f _ { i } : B _ { i } \rightarrow B ) _ { i \in l }$$ ; confidence 0.575

2893. ; $$F \in \gamma$$ ; confidence 0.994

2894. ; $$\left. \begin{array} { c c c } { B _ { i } } & { \stackrel { h _ { i } } { \rightarrow } } & { A _ { i } } \\ { g _ { i } \downarrow } & { \square } & { \downarrow f _ { i } } \\ { B } & { \vec { f } } & { A } \end{array} \right.$$ ; confidence 0.342

2895. ; $$A \wedge B$$ ; confidence 0.923

2896. ; $$= C$$ ; confidence 0.931

2897. ; $$\operatorname { sin } 0$$ ; confidence 0.092

2898. ; $$\{ p _ { i } ^ { - 1 } U _ { i } : U _ { i } \in \mu _ { i \square } \text { and } i \in I \}$$ ; confidence 0.601

2899. ; $$A ^ { * } = A \cup \{ \infty _ { A } \}$$ ; confidence 0.980

2900. ; $$p _ { 1 } \otimes \sim p _ { 2 }$$ ; confidence 0.782

2901. ; $$\sum _ { k = 1 } ^ { \infty } p _ { 1 } ( x _ { k } ) p _ { 2 } ( y _ { k } ) \leq p _ { 1 } \overline { Q } p _ { 2 } ( u ) + \epsilon$$ ; confidence 0.229

2902. ; $$D ( R ^ { n + k } )$$ ; confidence 0.995

2903. ; $$H \rightarrow TOP$$ ; confidence 0.688

2904. ; $$\left. \begin{array} { c c c } { \square } & { \square } & { B P L } \\ { \square } & { \square } & { \downarrow } \\ { X } & { \vec { \tau } _ { X } } & { B G } \end{array} \right.$$ ; confidence 0.066

2905. ; $$X \rightarrow P L / O$$ ; confidence 0.928

2906. ; $$d \Phi$$ ; confidence 0.791

2907. ; $$d = 6$$ ; confidence 0.998

2908. ; $$( X ) \in M$$ ; confidence 0.998

2909. ; $$r _ { 2 } \in R$$ ; confidence 0.862

2910. ; $$S _ { j } ^ { k } = \Gamma _ { i j } ^ { k } - \Gamma _ { j i } ^ { k }$$ ; confidence 0.505

2911. ; $$x = \pm \alpha \operatorname { ln } \frac { \alpha + \sqrt { \alpha ^ { 2 } - y ^ { 2 } } } { y } - \sqrt { \alpha ^ { 2 } - y ^ { 2 } }$$ ; confidence 0.391

2912. ; $$r < | w | < 1$$ ; confidence 0.982

2913. ; $$d s _ { é } = \frac { | d z | } { 1 + | z | ^ { 2 } }$$ ; confidence 0.470

2914. ; $$\operatorname { lim } _ { \epsilon \rightarrow 0 } d ( E _ { \epsilon } ) = d ( E )$$ ; confidence 0.993

2915. ; $$x = f ( \alpha )$$ ; confidence 0.993

2916. ; $$\mathfrak { A } f ( x ) = \operatorname { lim } _ { U ! x } [ \frac { E _ { x } f ( x _ { \tau } ) - f ( x ) } { E _ { x } \tau } ]$$ ; confidence 0.104

2917. ; $$\mathfrak { A } f$$ ; confidence 0.742

2918. ; $$R ^ { 0 } f$$ ; confidence 0.999

2919. ; $$g = R ^ { \alpha } f$$ ; confidence 0.864

2920. ; $$P ( S )$$ ; confidence 0.765

2921. ; $$o ( N ) / N \rightarrow 0$$ ; confidence 0.792

2922. ; $$T _ { 23 } n ( \operatorname { cos } \pi \omega )$$ ; confidence 0.946

2923. ; $$g _ { n } ( \Omega )$$ ; confidence 0.875

2924. ; $$l \mu \frac { \partial W ^ { k } } { \partial x } + ( 1 - c ) W ^ { k } = c ( \Phi _ { 0 } ^ { k } - \phi _ { 0 } ^ { k } )$$ ; confidence 0.308

2925. ; $$Q _ { n } W ^ { k } = P _ { n } c ( W ^ { k } + \Phi _ { 0 } ^ { k } - \phi _ { 0 } ^ { k } )$$ ; confidence 0.976

2926. ; $$g _ { k } = ( 1 + y _ { k } ) / 2$$ ; confidence 0.953

2927. ; $$V = f ^ { - 1 } ( X )$$ ; confidence 1.000

2928. ; $$Q _ { 1 } \cup \square \ldots \cup Q _ { m }$$ ; confidence 0.878

2929. ; $$f ( x ) = g ( y )$$ ; confidence 1.000

2930. ; $$2 / ( 3 N / 2 )$$ ; confidence 0.990

2931. ; $$\frac { a _ { 0 } } { 4 } x ^ { 2 } - \sum _ { k = 1 } ^ { \infty } \frac { a _ { k } \operatorname { cos } k x + b _ { k } \operatorname { sin } k x } { k ^ { 2 } }$$ ; confidence 0.667

2932. ; $$\operatorname { Fix } ( T ) \subset \mathfrak { R }$$ ; confidence 0.710

2933. ; $$\left. \begin{array} { c c c } { T A } & { \stackrel { T f } { S } } & { T B } \\ { \alpha \downarrow } & { \square } & { \downarrow \beta } \\ { A } & { \vec { f } } & { B } \end{array} \right.$$ ; confidence 0.204

2934. ; $$\overline { U } / \partial \overline { U }$$ ; confidence 0.976

2935. ; $$u _ { m } = u ( M _ { m } )$$ ; confidence 0.360

2936. ; $$m > - 1$$ ; confidence 0.998

2937. ; $$\operatorname { Re } G _ { 1 } ( r ) \geq B$$ ; confidence 0.984

2938. ; $$\sum ( k _ { i } - 1 )$$ ; confidence 0.930

2939. ; $$\{ \omega _ { n } ^ { + } ( V ) \}$$ ; confidence 0.949

2940. ; $$f _ { 0 } \neq 0$$ ; confidence 0.997

2941. ; $$\alpha \geq A _ { 0 }$$ ; confidence 0.904

2942. ; $$\forall v \phi$$ ; confidence 0.989

2943. ; $$\in M$$ ; confidence 0.717

2944. ; $$( \phi \& \psi )$$ ; confidence 0.997

2945. ; $$\{ f ( z ) \}$$ ; confidence 1.000

2946. ; $$\phi ( z ) = \frac { 1 - z ^ { 2 } } { z } f ( z ) \in C$$ ; confidence 0.993

2947. ; $$T ( X ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } X = 1 } \\ { 0 } & { \text { if } X \geq 2 } \end{array} \right.$$ ; confidence 0.976

2948. ; $$f _ { \alpha } ( x ) \geq - c$$ ; confidence 0.977

2949. ; $$\{ d f _ { n } / d x \}$$ ; confidence 0.954

2950. ; $$t \rightarrow t + w z$$ ; confidence 0.466

2951. ; $$w = \operatorname { sin }$$ ; confidence 0.905

2952. ; $$( g - 1 ) ^ { n } = 0$$ ; confidence 0.996

2953. ; $$U _ { n } ( K )$$ ; confidence 0.987

2954. ; $$g ^ { p } = e$$ ; confidence 0.978

2955. ; $$O ( \epsilon _ { N } )$$ ; confidence 0.478

2956. ; $$U ( \epsilon )$$ ; confidence 0.998

2957. ; $$\sum _ { k = 1 } ^ { \infty } | \alpha _ { k } | ^ { 2 } = \frac { 1 } { 2 \pi } \int _ { 0 } ^ { 2 \pi } | f ( e ^ { i t } ) | ^ { 2 } d t \leq 1$$ ; confidence 0.986

2958. ; $$U : B \rightarrow A$$ ; confidence 0.544

2959. ; $$( n \geq 0 )$$ ; confidence 1.000

2960. ; $$v ( x ) \geq f ( x )$$ ; confidence 0.996

2961. ; $$f ( z ) \in K$$ ; confidence 0.998

2962. ; $$\lambda \leq 0.5$$ ; confidence 0.968

2963. ; $$( f ) \subseteq V ( f )$$ ; confidence 0.998

2964. ; $$s ( r )$$ ; confidence 0.997

2965. ; $$x \in Y ( u )$$ ; confidence 0.570

2966. ; $$( a + b ) + c = a + ( b + c )$$ ; confidence 0.946

2967. ; $$a \perp b$$ ; confidence 0.521

2968. ; $$\left. \begin{array} { l l l } { \alpha _ { 1 } } & { \alpha _ { 2 } } & { \alpha _ { 3 } } \\ { b _ { 1 } } & { b _ { 2 } } & { b _ { 3 } } \\ { c _ { 1 } } & { c _ { 2 } } & { c _ { 3 } } \end{array} \right| = 0$$ ; confidence 0.378

2969. ; $$u ^ { * } ( \pi )$$ ; confidence 0.996

2970. ; $$\pi ^ { \prime } \oplus \theta ^ { \prime }$$ ; confidence 0.992

2971. ; $$G ^ { k } ( V ) \times V$$ ; confidence 0.950

2972. ; $$w : \xi \oplus \zeta \rightarrow \pi$$ ; confidence 0.996

2973. ; $$\pi : B \rightarrow G ^ { k } ( V )$$ ; confidence 0.258

2974. ; $$X ^ { \prime } \cap \pi ^ { - 1 } ( b )$$ ; confidence 0.999

2975. ; $$+ \frac { 1 } { N ! } \int _ { t _ { 0 } } ^ { t } ( t - \tau ) ^ { N _ { r } ( N + 1 ) } ( \tau ) d \tau$$ ; confidence 0.696

2976. ; $$j \in ( 1 / 2 ) Z$$ ; confidence 0.983

2977. ; $$1 _ { n } ( w ) = 0$$ ; confidence 0.957

2978. ; $$f ^ { * } : H ^ { * } ( Y ) \rightarrow H ^ { * } ( X )$$ ; confidence 0.997

2979. ; $$H ^ { n } ( S ^ { n } )$$ ; confidence 0.629

2980. ; $$\delta ^ { * } \circ ( t - r ) ^ { * } \beta _ { 1 } = k ( t ^ { * } \square ^ { - 1 } \beta _ { 3 } )$$ ; confidence 0.259

2981. ; $$F : S ^ { n } \rightarrow K ( E ^ { n + 1 } \backslash \theta )$$ ; confidence 0.783

2982. ; $$t ^ { * } : H ^ { N } ( S ^ { N } ) \rightarrow H ^ { N } ( \Gamma _ { S ^ { n } } )$$ ; confidence 0.119

2983. ; $$d _ { k } = rd _ { Y } M _ { k }$$ ; confidence 0.623

2984. ; $$n \geq 12$$ ; confidence 0.886

2985. ; $$P ^ { 2 r - k }$$ ; confidence 0.936

2986. ; $$v _ { \nu } ( t _ { 0 } ) = 0$$ ; confidence 0.996

2987. ; $$F : \Omega \times R ^ { n } \times R ^ { n } \times S ^ { n } \rightarrow R$$ ; confidence 0.909

2988. ; $$q e ^ { ( - i \theta ) }$$ ; confidence 0.903

2989. ; $$\vec { V }$$ ; confidence 0.987

2990. ; $$\tau _ { j } < 0$$ ; confidence 0.887

2991. ; $$2 i$$ ; confidence 0.747

2992. ; $$\theta = 2 \pi$$ ; confidence 0.999

2993. ; $$U = \frac { \Gamma } { 2 l } \operatorname { tanh } \frac { \pi b } { l } = \frac { \Gamma } { 2 l \sqrt { 2 } }$$ ; confidence 0.768

2994. ; $$\Pi I _ { \lambda }$$ ; confidence 0.300

2995. ; $$\phi ( U T U ^ { - 1 } ) = \phi ( T )$$ ; confidence 0.999

2996. ; $$III _ { 0 }$$ ; confidence 0.560

2997. ; $$P \sim P _ { 1 }$$ ; confidence 0.999

2998. ; $$Q = U U ^ { * }$$ ; confidence 0.977

2999. ; $$P _ { 1 } \in A$$ ; confidence 0.996

3000. ; $$\overline { \sum _ { g } n ( g ) g } = \sum w ( g ) n ( g ) g ^ { - 1 }$$ ; confidence 0.832

3001. ; $$U = \cup _ { i } \operatorname { Im } f$$ ; confidence 0.671

3002. ; $$\int _ { 0 } ^ { \pi / 2 } \operatorname { sin } ^ { 2 m + 1 } x d x$$ ; confidence 0.964

3003. ; $$2 ^ { m } \leq n \leq 2 ^ { m + 1 } - 1$$ ; confidence 0.976

3004. ; $$F ( x )$$ ; confidence 1.000

3005. ; $$\lambda = 2 \pi / | k |$$ ; confidence 0.980

3006. ; $$A _ { n } ( x _ { 0 } )$$ ; confidence 0.499

3007. ; $$\partial ^ { 2 } u / \partial x ^ { 2 } + \partial ^ { 2 } u / \partial y ^ { 2 } + k ^ { 2 } u = 0$$ ; confidence 0.997

3008. ; $$A = N \oplus s$$ ; confidence 0.521

3009. ; $$A = N \oplus S _ { 1 }$$ ; confidence 0.438

3010. ; $$j = g ^ { 3 } / g ^ { 2 }$$ ; confidence 0.799

3011. ; $$= \frac { 1 } { z ^ { 2 } } + c 2 z ^ { 2 } + c _ { 4 } z ^ { 4 } + \ldots$$ ; confidence 0.426

3012. ; $$x ( t _ { i } ) = x _ { 0 } ( t _ { i } )$$ ; confidence 0.980

3013. ; $$K = - ( \frac { 4 | d g | } { ( 1 + | g | ^ { 2 } ) ^ { 2 } | \eta | } \} ^ { 2 }$$ ; confidence 0.571

3014. ; $$m _ { k } = \dot { k }$$ ; confidence 0.352

3015. ; $$q \in T _ { n } ( k )$$ ; confidence 0.977

3016. ; $$D = \langle x ^ { 2 } \} \subset R [ x ]$$ ; confidence 0.413

3017. ; $$D = R [ x ] / D$$ ; confidence 0.968

3018. ; $$H ^ { i } ( X )$$ ; confidence 0.995

3019. ; $$H ^ { 2 n } ( X )$$ ; confidence 0.999

3020. ; $$\beta$$ ; confidence 0.911

3021. ; $$\nabla _ { i g j k } = \gamma _ { i } g _ { j k }$$ ; confidence 0.315

3022. ; $$\operatorname { gr } ( A _ { 1 } ( K ) )$$ ; confidence 0.860

3023. ; $$A _ { k + 1 } ( C )$$ ; confidence 0.634

3024. ; $$\oplus V _ { k } ( M ) / V _ { k - 1 } ( M )$$ ; confidence 0.970

3025. ; $$q$$ ; confidence 0.899

3026. ; $$C ^ { \prime } = 1$$ ; confidence 0.999

3027. ; $$W ( f \times g ) = W ( f ) . W ( g )$$ ; confidence 0.906

3028. ; $$Z _ { \zeta } ( T )$$ ; confidence 0.463

3029. ; $$N _ { G } ( T ) / Z _ { G } ( T )$$ ; confidence 0.990

3030. ; $$N _ { G } ( T )$$ ; confidence 0.970

3031. ; $$f ( x ) = \alpha _ { n } x ^ { n } + \ldots + \alpha _ { 1 } x$$ ; confidence 0.966

3032. ; $$\Delta ( \lambda ) ^ { \mu }$$ ; confidence 1.000

3033. ; $$L ( \mu )$$ ; confidence 0.993

3034. ; $$\left( \begin{array} { c } { h } \\ { i } \end{array} \right) = \frac { h ( h - 1 ) \ldots ( h - i + 1 ) } { i ! }$$ ; confidence 0.487

3035. ; $$S ( R ^ { n } ) \times S ( R ^ { n } )$$ ; confidence 0.944

3036. ; $$\alpha ^ { \psi } = Op ( J ^ { 1 / 2 } \alpha )$$ ; confidence 0.058

3037. ; $$\alpha _ { 2 k + 1 } \in L ^ { 1 } ( \Phi )$$ ; confidence 0.712

3038. ; $$A ^ { * } \sigma A = \sigma$$ ; confidence 0.887

3039. ; $$G = G ^ { \sigma }$$ ; confidence 0.956

3040. ; $$X \in \Phi$$ ; confidence 0.895

3041. ; $$g _ { 1 } = | d x | ^ { 2 } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } } \leq g = \frac { | d x | ^ { 2 } } { | x | ^ { 2 } } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } }$$ ; confidence 0.357

3042. ; $$\pi _ { 4 n - 1 } ( S ^ { 2 n } ) \rightarrow \pi _ { 4 n } ( S ^ { 2 n + 1 } )$$ ; confidence 0.354

3043. ; $$S \square T$$ ; confidence 0.898

3044. ; $$T _ { n }$$ ; confidence 0.602

3045. ; $$N = 2$$ ; confidence 0.996

3046. ; $$S _ { n } = s _ { n } + \theta ^ { 2 } F _ { n }$$ ; confidence 0.942

3047. ; $$T _ { 1 } \sim \Lambda$$ ; confidence 0.998

3048. ; $$\prod _ { \nu } : \prod _ { i \in I _ { \nu } } f _ { i } : = \sum _ { G } \prod _ { e \in G } < f _ { e _ { 1 } } f _ { e _ { 2 } } > : \prod _ { i \notin [ G ] } f _ { i : }$$ ; confidence 0.238

3049. ; $$l \equiv 2 ( \operatorname { mod } 3 )$$ ; confidence 0.997

3050. ; $$B ( \lambda )$$ ; confidence 1.000

3051. ; $$L _ { - } ( \lambda ) C ( \lambda ) / B ( \lambda )$$ ; confidence 0.885

3052. ; $$\Gamma ( H ) = \sum _ { n = 0 } ^ { \infty } H ^ { \otimes n }$$ ; confidence 0.591

3053. ; $$\| \varphi \| _ { L ^ { 2 } ( \mu ) } = \sqrt { n ! } | f | _ { H ^ { \otimes n } }$$ ; confidence 0.909

3054. ; $$( g ) = g ^ { \prime }$$ ; confidence 1.000

3055. ; $$t _ { 1 } \in D ^ { - }$$ ; confidence 0.997

3056. ; $$\| x \| _ { 1 }$$ ; confidence 0.650

3057. ; $$P = - i \hbar \nabla _ { x }$$ ; confidence 0.929

3058. ; $$T _ { W \alpha } = T$$ ; confidence 0.134

3059. ; $$\int _ { a } ^ { b } ( f ^ { ( r ) } ( x ) ) ^ { 2 } d x \leq 1$$ ; confidence 0.515

3060. ; $$B _ { m } = R$$ ; confidence 0.993

3061. ; $$p ( n + 1 ) / 2$$ ; confidence 0.997

3062. ; $$( D ) \leq c \text { length } ( C )$$ ; confidence 0.985

3063. ; $$Y \times X$$ ; confidence 0.869

3064. ; $$\operatorname { Aut } ( R ) / \operatorname { ln } n ( R ) \cong H$$ ; confidence 0.228

3065. ; $$\sigma \in \operatorname { Aut } ( R )$$ ; confidence 0.958

3066. ; $$D ( R )$$ ; confidence 0.960

3067. ; $$J ( \phi )$$ ; confidence 0.976

3068. ; $$\| \phi _ { q } \| _ { q } = 1$$ ; confidence 0.797

3069. ; $$H _ { 1 } \subset L _ { N }$$ ; confidence 0.459

3070. ; $$g ^ { \prime } = \phi ^ { 4 / ( n - 2 ) } g$$ ; confidence 0.828

3071. ; $$R _ { 12 } R _ { 13 } R _ { 23 } = R _ { 23 } R _ { 13 } R _ { 12 }$$ ; confidence 0.996

3072. ; $$R : X \times X \rightarrow \operatorname { End } _ { k } ( V \otimes _ { k } V )$$ ; confidence 0.794

3073. ; $$R _ { V } : V \otimes _ { k } V \rightarrow V \otimes _ { k } V$$ ; confidence 0.786

3074. ; $$\sigma ( M ^ { 4 } )$$ ; confidence 1.000

3075. ; $$\pi _ { 1 } : P _ { 1 } \rightarrow S ^ { 4 }$$ ; confidence 0.998

3076. ; $$t _ { \lambda } ^ { \prime }$$ ; confidence 0.881

3077. ; $$\forall v \exists u ( \forall w \varphi \leftrightarrow u = w )$$ ; confidence 0.569

3078. ; $$\forall y ( \neg y \in x )$$ ; confidence 0.930

3079. ; $$I = ( f )$$ ; confidence 0.997

3080. ; $$( f g f h )$$ ; confidence 0.723

3081. ; $$1.609$$ ; confidence 0.997

3082. ; $$001 c 23 + c 02 c 31 + c 03 c 12 \neq 0$$ ; confidence 0.156

3083. ; $$x _ { 2 } = r \operatorname { sin } \theta$$ ; confidence 0.977

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/1. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/1&oldid=43807

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Difference between revisions of "User:Maximilian Janisch/latexlist/latex/1"

Revision as of 11:37, 1 September 2019

List

@@ Line 1: / Line 1: @@
-Test
+== List ==
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130010/a13001017.png ; $3 + 5$ ; confidence 0.136
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130010/a1300107.png ; $A , B , C \in C$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130010/a1300103.png ; $( - ) ^ { * } : C ^ { 0 p } \rightarrow C$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130010/a1300109.png ; $s = s ( ( A ^ { * } ) ^ { ( B ^ { * } ) } , ( B ^ { * } ) ^ { ( C ^ { * } ) } )$ ; confidence 0.907
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130010/a13001014.png ; $R el$ ; confidence 0.544
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130010/a1300104.png ; $d ( A , B ) : B ^ { A } \cong A ^ { * } B ^ { * }$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130010/a1300105.png ; $4$ ; confidence 0.531
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130010/a13001015.png ; $S ^ { * } = S$ ; confidence 0.463
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130010/a13001016.png ; $B ^ { A } \cong ( A ^ { * } \otimes B )$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130010/a1300106.png ; $B$ ; confidence 0.895
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130010/a1300102.png ; $C$ ; confidence 0.838
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001048.png ; $( S , g )$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010139.png ; $3$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010117.png ; $D$ ; confidence 0.538
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001030.png ; $5$ ; confidence 0.885
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001056.png ; $F _ { 3 }$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001095.png ; $\operatorname { dim } ( S ) = 4 n + 3$ ; confidence 0.958
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010140.png ; $\geq 7$ ; confidence 0.562
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010134.png ; $( 4 n + 3 )$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001082.png ; $Z = S \nmid F _ { \tau }$ ; confidence 0.763
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001041.png ; $\{ \xi ^ { \alpha } , \eta ^ { \alpha } , \Phi ^ { \alpha } \} \alpha = 1,2,3$ ; confidence 0.761
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010159.png ; $4 n$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010109.png ; $m > 3$ ; confidence 0.916
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010141.png ; $7$ ; confidence 0.937
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001038.png ; $\eta ^ { \alpha } ( Y ) = g ( \xi ^ { \alpha } , Y )$ ; confidence 0.932
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010135.png ; $S ( p )$ ; confidence 0.693
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010148.png ; $T ^ { 2 } \times SO ( 3 )$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001034.png ; $SO ( 3 )$ ; confidence 0.940
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001039.png ; $\Phi ^ { \alpha } ( Y ) = \nabla _ { Y } \xi ^ { \alpha }$ ; confidence 0.798
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010125.png ; $\dot { i } \leq n$ ; confidence 0.190
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001022.png ; $n \geq 1$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001035.png ; $SU ( 2 )$ ; confidence 0.811
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010115.png ; $11$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010128.png ; $b _ { 2 } \neq b _ { 4 }$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010105.png ; $SU ( m ) / S ( U ( m - 2 ) \times U ( 1 ) ) , SO ( k ) / SO ( k - 4 ) \times Sp ( 1 )$ ; confidence 0.164
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001057.png ; $0$ ; confidence 0.311
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001021.png ; $m = 4 n + 3$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001088.png ; $\hat { v } ^ { ( S ) }$ ; confidence 0.182
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010130.png ; $b _ { 2 } \neq b _ { 6 }$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001020.png ; $\operatorname { Sp } ( ( m + 1 ) / 4 )$ ; confidence 0.694
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001072.png ; $\xi ( \tau ) = \tau _ { 1 } \xi ^ { 1 } + \tau _ { 2 } \xi ^ { 2 } + \tau _ { 3 } \xi ^ { 3 }$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001081.png ; $U ( 1 ) _ { \tau } \subset \operatorname { SU } ( 2 )$ ; confidence 0.671
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010123.png ; $\sum _ { k = 1 } ^ { n } k ( n + 1 - k ) ( n + 1 - 2 k ) b _ { 2 k } = 0$ ; confidence 0.782
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001028.png ; $\{ I ^ { 1 } , R ^ { 2 } , \hat { P } \}$ ; confidence 0.143
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001060.png ; $S ^ { 3 } / \Gamma$ ; confidence 0.633
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001098.png ; $k$ ; confidence 0.208
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001070.png ; $\tau = ( \tau _ { 1 } , \tau _ { 2 } , \tau _ { 3 } ) \in R ^ { 3 }$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001029.png ; $C ( S )$ ; confidence 0.946
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200104.png ; $$m$$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001053.png ; $\{ \xi ^ { 1 } , \xi ^ { 2 } , \xi ^ { 3 } \}$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001099.png ; $_ { \nabla } ( G / K )$ ; confidence 0.326
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001094.png ; $$n + 2$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010118.png ; $4 n + 3$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010129.png ; $15$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001014.png ; $5$ ; confidence 0.574
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001075.png ; $s ^ { 2 }$ ; confidence 0.942
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001040.png ; $\alpha = 1,2,3$ ; confidence 0.734
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001046.png ; $\lambda = \operatorname { dim } ( \delta ) - 1$ ; confidence 0.702
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010101.png ; $$Z = G / U ( 1 ) . K$$ ; confidence 0.948
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200109.png ; $$1$$ ; confidence 0.742
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010116.png ; $\operatorname { dim } ( O ) = 4$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010114.png ; $\operatorname { im } ( S ) = 7$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200106.png ; $U ( ( m + 1 ) / 2 )$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001079.png ; $F _ { \tau } \subset F _ { 3 } \subset S$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001026.png ; $\xi ^ { \mathscr { L } } = I ^ { \mathscr { L } } ( \partial _ { r } )$ ; confidence 0.127
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010106.png ; $G _ { 2 } / \operatorname { Sp } ( 1 ) , \quad F _ { 4 } / \operatorname { Sp } ( 3 ) , E _ { 6 } / SU ( 6 ) , \quad E _ { 7 } / \operatorname { Spin } ( 12 ) , \quad E _ { 8 } / E _ { 7 }$ ; confidence 0.614
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001032.png ; $g ( \xi ^ { \alpha } , \xi ^ { b } ) = \delta _ { \alpha b }$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010136.png ; $p = ( p _ { 1 } , \dots , p _ { n } + 2 )$ ; confidence 0.447
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010100.png ; $O = G / \operatorname { Sp } ( 1 ) . K$ ; confidence 0.187
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001091.png ; $z$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010121.png ; $S = SU ( m ) / S ( U ( m - 2 ) \times U ( 1 ) )$ ; confidence 0.541
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010158.png ; $$T ^ { n }$$ ; confidence 0.616
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001019.png ; $( C ( S ) , \overline { g } )$ ; confidence 0.418
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010108.png ; $Sp ( 0 )$ ; confidence 0.378
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001064.png ; $s ^ { 3 }$ ; confidence 0.948
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010138.png ; $D$ ; confidence 0.661
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001011.png ; $$\xi = I ( \partial _ { r } )$$ ; confidence 0.869
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010107.png ; $$n \geq 0$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001061.png ; $\Gamma \subset SU ( 2 )$ ; confidence 0.951
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010124.png ; $b _ { 2 } i + 1 ( S ) = 0$ ; confidence 0.920
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200107.png ; $m = 2 i + 1$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001033.png ; $[ \xi ^ { \alpha } , \xi ^ { b } ] = 2 \epsilon _ { \alpha b c } \xi ^ { c }$ ; confidence 0.322
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001077.png ; $\xi ( \tau )$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010133.png ; $$S ( p ) = U ( 1 ) _ { p } \backslash U ( n + 2 ) / U ( n )$$ ; confidence 0.916
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200108.png ; $1 > 1$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010120.png ; $b _ { 2 } ( s ) \leq 1$ ; confidence 0.580
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001085.png ; $0$ ; confidence 0.355
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001078.png ; $1$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001074.png ; $2$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001071.png ; $\tau _ { 1 } ^ { 2 } + \tau _ { 3 } ^ { 2 } + \tau _ { 3 } ^ { 2 } = 1$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010147.png ; $T ^ { 2 } \times \operatorname { Sp } ( 1 )$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200105.png ; $( C ( S ) , \overline { g } ) = ( R _ { + } \times S , d \nu ^ { 2 } + r ^ { 2 } g )$ ; confidence 0.265
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010110.png ; $k > 7$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010104.png ; $\operatorname { Sp } ( n + 1 ) / \operatorname { Sp } ( n ) , \quad \operatorname { Sp } ( n + 1 ) / \operatorname { Sp } ( n ) \times Z _ { 2 }$ ; confidence 0.901
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001097.png ; $SO ( 4 n + 3 )$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a0100206.png ; $t$ ; confidence 0.637
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a0100205.png ; $P = \cup _ { n _ { 1 } , \ldots , n _ { k } , \ldots } \cap _ { k = 1 } ^ { \infty } E _ { n _ { 1 } } \square \ldots x _ { k }$ ; confidence 0.192
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a0100204.png ; $\{ E _ { n _ { 1 } } \ldots n _ { k } \}$ ; confidence 0.382
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a01002013.png ; $$\sigma \delta$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010080/a01008023.png ; $A _ { x _ { 1 } } ^ { \prime } \ldots x _ { k } = A _ { 1 } \cap \ldots \cap A _ { x _ { 1 } } \ldots x _ { k }$ ; confidence 0.061
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010080/a0100808.png ; $x _ { 1 } , \ldots , A _ { x _ { 1 } } \ldots x _ { k } , \ldots ,$ ; confidence 0.104
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010080/a0100805.png ; $\{ A _ { n _ { 1 } } \ldots n _ { k } \}$ ; confidence 0.200
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010080/a0100807.png ; $A _ { x } _ { 1 } \ldots x _ { k } x _ { k + 1 } \subset A _ { x _ { 1 } } \ldots x _ { k }$ ; confidence 0.139
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010080/a01008024.png ; $M$ ; confidence 0.626
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010080/a0100803.png ; $x$ ; confidence 0.475
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420123.png ; $\pi$ ; confidence 0.772
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420169.png ; $K$ ; confidence 0.738
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420153.png ; $K _ { 0 } ( B ) ^ { + }$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042060.png ; $K _ { 1 }$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420164.png ; $C ( S ^ { 2 n } )$ ; confidence 0.540
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420108.png ; $\tau ( x y ) = \tau ( y x )$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420163.png ; $\theta = 1 - \theta$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420118.png ; $$H$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042090.png ; $n > 0$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042070.png ; $K _ { 0 } ( \varphi ) = \alpha$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042086.png ; $z \in G$ ; confidence 0.715
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420112.png ; $f : G \rightarrow R$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042095.png ; $C ^ { * }$ ; confidence 0.866
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042050.png ; $( K _ { 0 } ( A ) , K _ { 0 } ( A ) ^ { + } , \Sigma ( A ) )$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420127.png ; $D$ ; confidence 0.683
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420138.png ; $I \mapsto I$ ; confidence 0.782
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420149.png ; $K _ { 0 } ( \varphi ) : K _ { 0 } ( A ) \rightarrow K _ { 0 } ( B )$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420113.png ; $f ( G ^ { + } ) \subseteq R ^ { + }$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420128.png ; $h$ ; confidence 0.307
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042064.png ; $( K _ { 0 } ( A ) , K _ { 0 } ( A ) ^ { + } , \Sigma ( A ) )$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042053.png ; $K _ { 0 } ( A )$ ; confidence 0.745
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420117.png ; $H ^ { + } = G ^ { + } \cap H$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042063.png ; $\square ^ { * }$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420150.png ; $K _ { 0 } ( \varphi )$ ; confidence 0.924
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042084.png ; $x _ { 1 } , x _ { 2 } , y _ { 1 } , y _ { 2 } \in G$ ; confidence 0.943
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042088.png ; $( G , G ^ { + } )$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042079.png ; $25$ ; confidence 0.396
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420162.png ; $\theta = \theta ^ { \prime }$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420121.png ; $y \leq x$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042066.png ; $\alpha : K _ { 0 } ( A ) \rightarrow K _ { 0 } ( B )$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042067.png ; $\alpha ( K _ { 0 } ( A ) ^ { + } ) = K _ { 0 } ( B ) ^ { + }$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042055.png ; $K _ { 0 } ( A ) ^ { + }$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042077.png ; $K _ { 0 } ( \varphi ) = K _ { 0 } ( \psi )$ ; confidence 0.842
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420161.png ; $A _ { \theta } \cong A _ { \theta }$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420110.png ; $f$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042089.png ; $\geq 0$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042078.png ; $4$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420166.png ; $2 n$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042068.png ; $\alpha ( \Sigma ( A ) ) = \Sigma ( B )$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042069.png ; $\varphi : A \rightarrow B$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042072.png ; $\alpha ( \Sigma ( A ) ) \subseteq \Sigma ( B )$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042087.png ; $x _ { i } \leq z \leq y _ { j }$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420154.png ; $K _ { 0 }$ ; confidence 0.936
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420137.png ; $\tau \mapsto K _ { 0 } ( \tau )$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042091.png ; $x \in G$ ; confidence 0.737
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420126.png ; $K _ { 0 } ( \tau ) ( [ p ] _ { 0 } - [ q ] _ { 0 } ) = \tau ( p ) - \tau ( q )$ ; confidence 0.889
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420122.png ; $y \in H$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420134.png ; $K _ { 0 } ( I ) \rightarrow K _ { 0 } ( A )$ ; confidence 0.923
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420109.png ; $x , y \in A$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042092.png ; $x > 0$ ; confidence 0.700
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420158.png ; $A _ { \theta }$ ; confidence 0.786
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042065.png ; $( K _ { 0 } ( B ) , K _ { 0 } ( B ) ^ { + } , \Sigma ( B ) )$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420107.png ; $\tau : A \rightarrow C$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420133.png ; $i$ ; confidence 0.450
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042075.png ; $\varphi , \psi : A \rightarrow B$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042056.png ; $\Sigma ( A )$ ; confidence 0.626
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420119.png ; $x \in H ^ { + }$ ; confidence 0.518
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420120.png ; $y \in G ^ { + }$ ; confidence 0.943
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420143.png ; $1$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042085.png ; $x _ { i } \leq y _ { j }$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420160.png ; $K _ { 0 } ( B ) = Z + \theta Z$ ; confidence 0.898
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042098.png ; $K _ { 1 } ( A ) = 0$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420125.png ; $( K _ { 0 } ( A ) , K _ { 0 } ( A ) ^ { + } )$ ; confidence 0.951
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013088.png ; $t$ ; confidence 0.354
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013059.png ; $i$ ; confidence 0.570
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013037.png ; $SL _ { 2 } ( C )$ ; confidence 0.910
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013039.png ; $Q = \sum _ { j = 0 } ^ { \infty } Q _ { j } z ^ { - j } , Q _ { j } = \left( \begin{array} { c c } { h _ { j } } & { e _ { j } } \\ { f _ { j } } & { - h _ { j } } \end{array} \right)$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013075.png ; $( g )$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013023.png ; $$= \operatorname { exp } ( x P _ { 0 } z + \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } ) g ( z ) . . \operatorname { exp } ( - x P _ { 0 } z - \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { \gamma } )$$ ; confidence 0.382
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013026.png ; $( 1 )$ ; confidence 0.515
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013067.png ; $C [ t ] = C [ t _ { 1 } , t _ { 2 } , \ldots$ ; confidence 0.593
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013078.png ; $q ^ { ( l ) } = 2 i \frac { \tau _ { l } + 1 } { \tau _ { l } } , r ^ { ( l ) } = - 2 i \frac { \tau _ { l } - 1 } { \tau _ { l } }$ ; confidence 0.315
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a130130100.png ; $$A K N S$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013025.png ; $C ^ { \infty } ( s ^ { 1 } , SL _ { 2 } ( C ) )$ ; confidence 0.430
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013032.png ; $\phi$ ; confidence 0.476
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013042.png ; $X _ { i } \in \operatorname { sl } _ { 2 } ( C )$ ; confidence 0.209
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013053.png ; $P ^ { ( l ) } = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) z + \left( \begin{array} { c c } { 0 } & { q ^ { ( l ) } } \\ { r ^ { ( l ) } } & { 0 } \end{array} \right)$ ; confidence 0.416
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013021.png ; $$h$$ ; confidence 0.644
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013046.png ; $\frac { \partial } { \partial t _ { k } } F _ { i j } = \frac { \partial } { \partial t _ { i } } F _ { j k }$ ; confidence 0.932
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013010.png ; $t = ( t _ { x } )$ ; confidence 0.458
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013034.png ; $\phi _ { - } ^ { - 1 } \frac { \partial } { \partial t _ { \mu } } - Q _ { 0 } z ^ { \mu } \phi _ { - } = \frac { \partial } { \partial t _ { \mu } } - Q ^ { ( n ) }$ ; confidence 0.140
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013083.png ; $C$ ; confidence 0.175
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013066.png ; $5$ ; confidence 0.571
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013055.png ; $L ( \Lambda _ { 0 } )$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013049.png ; $k$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013022.png ; $\phi ( x , t , z ) =$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301301.png ; $\left. \begin{array} { l } { i \frac { \partial } { \partial t } q ( x , t ) = i q t = - \frac { 1 } { 2 } q x x + q ^ { 2 } r } \\ { i \frac { \partial } { \partial t } r ( x , t ) = i r t = \frac { 1 } { 2 } r x - q r ^ { 2 } } \end{array} \right.$ ; confidence 0.260
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013027.png ; $\phi = \phi _ { - } \phi _ { + }$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301302.png ; $\frac { \partial } { \partial t } P _ { 1 } - \frac { \partial } { \partial x } Q _ { 2 } + [ P _ { 1 } , Q _ { 2 } ] = 0$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013056.png ; $A _ { 1 } ^ { ( 1 ) }$ ; confidence 0.822
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013070.png ; $( \tau _ { l } )$ ; confidence 0.726
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013040.png ; $Q ^ { ( n ) } = \sum _ { j = 0 } ^ { n } Q _ { j } z ^ { n - j }$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301304.png ; $8$ ; confidence 0.857
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013016.png ; $8$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013085.png ; $$L$$ ; confidence 0.550
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013054.png ; $t _ { n }$ ; confidence 0.933
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013079.png ; $F _ { j k } ^ { ( l ) } : = \frac { \partial } { \partial t _ { j } } \frac { \partial } { \partial t _ { k } } \operatorname { log } ( \tau _ { l } )$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013028.png ; $\phi _ { - } ( x , t , z ) = \operatorname { exp } ( \sum _ { i = 1 } ^ { \infty } \chi _ { i } ( x , t ) z ^ { - i } )$ ; confidence 0.963
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a130130103.png ; $K P$ ; confidence 0.846
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013098.png ; $\pi$ ; confidence 0.434
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013029.png ; $\phi _ { + } = \operatorname { exp } ( \sum _ { j = 1 } ^ { \infty } \phi _ { j } ( x , t ) z ^ { j } )$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013031.png ; $( \partial / \partial t _ { x } ) - Q _ { 0 } z ^ { x }$ ; confidence 0.284
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013020.png ; $0.00$ ; confidence 0.237
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013044.png ; $F _ { j k } =$ ; confidence 0.626
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013045.png ; $$= \frac { 1 } { 2 } \operatorname { Tr } ( \sum _ { r = 0 } ^ { j } ( j - r ) Q _ { r } Q _ { k + j - r } + \frac { 1 } { 2 } \sum _ { r = 0 } ^ { j } ( r - k ) Q _ { r } Q _ { k + j - r } )$$ ; confidence 0.240
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013090.png ; $N$ ; confidence 0.183
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013047.png ; $i$ ; confidence 0.889
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013024.png ; $g ( z )$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013069.png ; $\tau ( t ) = ( \tau _ { l } ( t ) ) _ { l \in Z }$ ; confidence 0.585
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013091.png ; $$L : = P _ { 0 } \frac { d } { d x } + P _ { 1 } = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) \frac { d } { d x } + \left( \begin{array} { c c } { 0 } & { q } \\ { r } & { 0 } \end{array} \right)$$ ; confidence 0.711
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013076.png ; $P ^ { ( l ) }$ ; confidence 0.869
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013051.png ; $F _ { j k } = \frac { \partial } { \partial t _ { j } } \frac { \partial } { \partial t _ { k } } \operatorname { log } ( \tau )$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013052.png ; $q ^ { ( l + 1 ) } = - ( q ^ { ( l ) } ) ^ { 2 } r ^ { ( l ) } + q ^ { ( l ) } \operatorname { log } ( q ^ { ( l ) } ) , r ^ { ( l + 1 ) } = \frac { 1 } { q ^ { ( l ) } }$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301306.png ; $Q ^ { ( n ) } : = Q _ { 0 } z ^ { n } + Q _ { 1 } z ^ { n - 1 } \ldots Q _ { n }$ ; confidence 0.716
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013036.png ; $\partial / \partial x = \partial / \partial t _ { 1 }$ ; confidence 0.401
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013014.png ; $\Leftrightarrow [ \frac { \partial } { \partial x } - P , \frac { \partial } { \partial t _ { n } } - Q ^ { ( n ) } ] = 0$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301305.png ; $P = P _ { 0 } z + P _ { 1 } : = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) z + \left( \begin{array} { l l } { 0 } & { q } \\ { r } & { 0 } \end{array} \right)$ ; confidence 0.374
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013041.png ; $\sum _ { i = 0 } ^ { \infty } X _ { i } z ^ { - i }$ ; confidence 0.831
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013096.png ; $P _ { 1 }$ ; confidence 0.674
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013097.png ; $L ( \psi ) = z \psi$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301303.png ; $P _ { 1 } = \left( \begin{array} { c c c } { 0 } & { \square } & { q } \\ { r } & { \square } & { 0 } \end{array} \right) , Q _ { 2 } = \left( \begin{array} { c c } { - \frac { i } { 2 } q r } & { \frac { i } { 2 } q x } \\ { - \frac { i } { 2 } r _ { x } } & { \frac { i } { 2 } q r } \end{array} \right)$ ; confidence 0.352
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301307.png ; $Q$ ; confidence 0.380
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013058.png ; $s = \sum _ { i > 0 } C \lambda ^ { i } \left( \begin{array} { c c } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) \oplus \sum _ { i > 0 } C \lambda ^ { - i } \left( \begin{array} { c c } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) \oplus C _ { i }$ ; confidence 0.161
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013095.png ; $12$ ; confidence 0.590
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013035.png ; $Q _ { 0 } = P _ { 0 }$ ; confidence 0.896
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013073.png ; $Q$ ; confidence 0.095
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013099.png ; $z \in C$ ; confidence 0.369
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013033.png ; $\phi - ^ { 1 } ( \frac { \partial } { \partial x } - P _ { 0 z } ) \phi _ { - } = \frac { \partial } { \partial x } - P$ ; confidence 0.173
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013013.png ; $\frac { \partial } { \partial t _ { m } } P - \frac { \partial } { \partial x } Q ^ { ( m ) } + [ P , Q ^ { ( r ) } ] = 0 \Leftrightarrow$ ; confidence 0.156
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013012.png ; $Q _ { 1 } = P _ { 1 }$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013030.png ; $( \partial / \partial x ) - P _ { 0 } z$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013048.png ; $i$ ; confidence 0.474
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013043.png ; $F _ { j k }$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013093.png ; $P _ { n + 1 } = \sum _ { i = 0 } ^ { n + 1 } u _ { i } ( \frac { d } { d x } ) ^ { i }$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301308.png ; $s l _ { 2 }$ ; confidence 0.247
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013092.png ; $( 2 \times 2 )$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013017.png ; $P$ ; confidence 0.462
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013038.png ; $\frac { \partial } { \partial t _ { n } } Q = [ Q ^ { ( n ) } , Q ] , n \geq 1$ ; confidence 0.137
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013074.png ; $T$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022026.png ; $L ^ { Y } ( X , Y )$ ; confidence 0.431
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022034.png ; $0 \leq S \leq T \in L ( X )$ ; confidence 0.657
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a1202206.png ; $\varepsilon \in X$ ; confidence 0.430
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022022.png ; $Y$ ; confidence 0.894
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022037.png ; $r _ { ess } ( T )$ ; confidence 0.259
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022013.png ; $$T : X \rightarrow Y$$ ; confidence 0.863
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022011.png ; $X = 1 ^ { p }$ ; confidence 0.914
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022021.png ; $T$ ; confidence 0.750
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a1202209.png ; $x | < e$ ; confidence 0.841
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a1202207.png ; $| e | | < 1$ ; confidence 0.271
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022039.png ; $S < T$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022042.png ; $r _ { e . s s } ( T ) \in \sigma _ { ess } ( T )$ ; confidence 0.088
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022025.png ; $Y = L ^ { 1 } ( \mu )$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022033.png ; $5$ ; confidence 0.396
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022038.png ; $S , T \in L ( X )$ ; confidence 0.814
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022035.png ; $r ( S ) \leq r ( T )$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022036.png ; $\sigma _ { ess } ( T )$ ; confidence 0.490
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022012.png ; $1 \leq p < \infty$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022031.png ; $0 \leq S \leq T$ ; confidence 0.838
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022010.png ; $X = c 0$ ; confidence 0.759
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a1202208.png ; $| x | | \leq 1$ ; confidence 0.929
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240286.png ; $1 - \alpha$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240135.png ; $A$ ; confidence 0.952
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240204.png ; $74$ ; confidence 0.550
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024051.png ; $3$ ; confidence 0.891
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240441.png ; $\beta _ { 1 } , \ldots , \beta _ { p }$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240336.png ; $Z = X \Gamma + F$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240339.png ; $\Sigma _ { 1 } = X _ { 4 } ^ { \prime } \Sigma X _ { 4 }$ ; confidence 0.322
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240101.png ; $x$ ; confidence 0.751
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240218.png ; $z = \Gamma y$ ; confidence 0.946
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024048.png ; $s \times p$ ; confidence 0.642
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024059.png ; $( i , j )$ ; confidence 0.935
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240137.png ; $B$ ; confidence 0.651
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240478.png ; $0$ ; confidence 0.969
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240397.png ; $M _ { E }$ ; confidence 0.680
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240527.png ; $( n$ ; confidence 0.239
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240519.png ; $Z _ { 13 }$ ; confidence 0.481
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240539.png ; $T _ { 1 }$ ; confidence 0.446
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240452.png ; $P$ ; confidence 0.403
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240446.png ; $j = 1 , \ldots , p$ ; confidence 0.616
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240545.png ; $2$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240141.png ; $$c$$ ; confidence 0.324
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240308.png ; $\hat { \eta } _ { \Omega } = X \hat { \beta }$ ; confidence 0.485
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240106.png ; $t$ ; confidence 0.895
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240516.png ; $R = V _ { 33 } ^ { - 1 } V _ { 32 }$ ; confidence 0.628
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240276.png ; $\leq F _ { \alpha ; q , x - \gamma }$ ; confidence 0.345
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240431.png ; $a ^ { \prime } \Theta$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240449.png ; $y _ { 1 } , \dots , y _ { j }$ ; confidence 0.424
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240196.png ; $\sqrt { 3 }$ ; confidence 0.281
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240399.png ; $X _ { 3 }$ ; confidence 0.593
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240238.png ; $MS _ { e } = SS _ { e } / ( n - r )$ ; confidence 0.793
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240152.png ; $X \beta$ ; confidence 0.414
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240309.png ; $\sum _ { i j k } ( y _ { i j k } - \eta _ { i j } ) ^ { 2 }$ ; confidence 0.779
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240444.png ; $N$ ; confidence 0.740
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240371.png ; $Z _ { 1 } M _ { E } ^ { - 1 } Z _ { 1 } ^ { \prime }$ ; confidence 0.548
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240500.png ; $2$ ; confidence 0.672
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240342.png ; $Y , B , E$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240194.png ; $8$ ; confidence 0.593
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240509.png ; $E [ Z _ { 32 } , Z _ { 33 } ] = 0$ ; confidence 0.584
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240343.png ; $2$ ; confidence 0.473
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024029.png ; $1$ ; confidence 0.458
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240122.png ; $t _ { 1 } , t _ { 2 } , \ldots$ ; confidence 0.731
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240407.png ; $$M _ { E } = \sum _ { i j k } ( y _ { i j k } - y _ { i j . } ) ^ { \prime } ( y _ { i j k } - y _ { i j } )$$ ; confidence 0.159
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240518.png ; $Z _ { 12 }$ ; confidence 0.917
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024039.png ; $p \times p$ ; confidence 0.711
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240383.png ; $H ^ { \prime }$ ; confidence 0.219
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024067.png ; $e _ { j k }$ ; confidence 0.169
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240506.png ; $Z _ { 32 } , Z _ { 33 }$ ; confidence 0.917
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240430.png ; $a ^ { \prime } \Theta$ ; confidence 0.275
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240110.png ; $x$ ; confidence 0.968
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240248.png ; $( q , n - r )$ ; confidence 0.777
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240348.png ; $( r - q ) \times p$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240213.png ; $7$ ; confidence 0.945
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240472.png ; $i = 1 , \ldots , m$ ; confidence 0.480
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240453.png ; $q = 1$ ; confidence 0.790
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240338.png ; $N ( 0 , \Sigma _ { 1 } )$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240373.png ; $z _ { 1 }$ ; confidence 0.669
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024025.png ; $y , \beta , e$ ; confidence 0.936
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240244.png ; $= \operatorname { sin } \gamma q$ ; confidence 0.055
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240162.png ; $c ^ { \prime } \beta = \eta$ ; confidence 0.492
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240424.png ; $( 1 \times p )$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240485.png ; $B$ ; confidence 0.738
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240302.png ; $\hat { \eta } \omega$ ; confidence 0.852
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240236.png ; $n - r$ ; confidence 0.377
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240142.png ; $m \times 1$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240191.png ; $X ^ { \prime } X \hat { \beta } = X ^ { \prime } y$ ; confidence 0.277
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240254.png ; $6$ ; confidence 0.612
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240524.png ; $Z _ { 12 } - Z _ { 13 } \Sigma _ { 33 } ^ { - 1 } \Sigma _ { 32 }$ ; confidence 0.727
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240289.png ; $\hat { \psi } \pm S \cdot \hat { \sigma } \hat { \psi }$ ; confidence 0.134
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240285.png ; $\psi \in L$ ; confidence 0.533
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240177.png ; $\alpha$ ; confidence 0.905
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240334.png ; $\Gamma = B X$ ; confidence 0.884
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240443.png ; $H _ { j } : X _ { 3 } \beta _ { j } = 0$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240301.png ; $\hat { \eta } \Omega$ ; confidence 0.902
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240515.png ; $Z _ { 0 } = Z _ { 12 } - Z _ { 13 } R$ ; confidence 0.674
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240414.png ; $f ( Z _ { 1 } )$ ; confidence 0.795
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240429.png ; $\Theta$ ; confidence 0.834
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240261.png ; $\psi = \sum _ { i = 1 } ^ { q } d _ { i } \zeta _ { i }$ ; confidence 0.961
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024019.png ; $y$ ; confidence 0.478
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240396.png ; $M _ { H }$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240408.png ; $y _ { i j k }$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240353.png ; $E ( Z _ { 3 } ) = 0$ ; confidence 0.631
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240109.png ; $( \alpha , \beta , \gamma ) ^ { \prime } = \beta$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240367.png ; $M _ { E } = Z _ { 3 } ^ { \prime } Z _ { 3 }$ ; confidence 0.783
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240493.png ; $( 1 , t _ { j } , \ldots , t _ { j } ^ { k } ) ^ { \prime }$ ; confidence 0.604
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024046.png ; $m \times s$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240242.png ; $SS _ { H } = \sum _ { i = 1 } ^ { \Psi } z _ { i } ^ { 2 }$ ; confidence 0.251
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240423.png ; $$q \times 1$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240216.png ; $\operatorname { dim } ( \Omega ) = r$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240354.png ; $E ( Z _ { 2 } )$ ; confidence 0.857
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240330.png ; $( p \times p _ { 1 } )$ ; confidence 0.958
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240362.png ; $22$ ; confidence 0.710
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240240.png ; $\sigma ^ { 2 }$ ; confidence 0.864
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240281.png ; $\| d \| ^ { 2 } \sigma ^ { 2 }$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024015.png ; $n > m$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240209.png ; $S$ ; confidence 0.868
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240219.png ; $$I$$ ; confidence 0.738
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240231.png ; $a$ ; confidence 0.607
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240220.png ; $$n \times n$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240147.png ; $\mu$ ; confidence 0.780
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240239.png ; $$MS _ { e }$$ ; confidence 0.884
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240375.png ; $$( n - r ) F$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240328.png ; $$H : X _ { 3 } B X _ { 4 } = 0$$ ; confidence 0.914
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240508.png ; $$E ( Z _ { 13 } ) = 0$$ ; confidence 0.388
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120310/a120310159.png ; $\Omega$ ; confidence 0.783
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010249.png ; $$( A + \delta A ) \hat { x } = \hat { \lambda } \hat { x }$$ ; confidence 0.467
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010186.png ; $$A + \delta A$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010124.png ; $$A A ^ { + } A = A$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010282.png ; $$A _ { i } \in R ^ { n \times n }$$ ; confidence 0.952
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a11001016.png ; $$x + \delta x$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010117.png ; $$A x = b$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010138.png ; $$\sigma _ { i } ( A ) - \sigma _ { 1 } ( \delta A ) \leq \sigma _ { i } ( A + \delta A ) \leq \sigma _ { i } ( A ) + \sigma _ { i } ( \delta A )$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010250.png ; $$A x - \hat { \lambda } x = - \delta A x$$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010217.png ; $$1 / | y ^ { i } _ { x ^ { i } } ^ { * }$$ ; confidence 0.245
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010278.png ; $$X$$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010144.png ; $$\frac { \| ( A + \delta A ) ^ { + } - A ^ { + } \| } { \| ( A + \delta A ) ^ { + } \| _ { 2 } } \leq \mu \| A ^ { + } \| _ { 2 } \| \delta A _ { 2 }$$ ; confidence 0.551
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a11001037.png ; $$\| \delta b \| \leq \epsilon \| b \|$$ ; confidence 0.440
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020027.png ; $$3$$ ; confidence 0.899
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020080.png ; $6$ ; confidence 0.907
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020025.png ; $$D : \mathfrak { D } \rightarrow A$$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110020/a11002020.png ; $$D _ { 2 }$$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a01021067.png ; $$( 1 / z ) d z$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a010210119.png ; $$d [ ( \omega ) ] = 2 g - 2$$ ; confidence 0.588
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010220/a01022081.png ; $$\alpha _ { j k } = \alpha _ { k l }$$ ; confidence 0.439
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010240/a01024027.png ; $2$ ; confidence 0.729
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010240/a01024055.png ; $$L \subset F$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010240/a01024062.png ; $$B i$$ ; confidence 0.539
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010240/a01024073.png ; $$\omega P _ { i } P _ { j }$$ ; confidence 0.938
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040185.png ; $$p | D _ { i }$$ ; confidence 0.587
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a11004020.png ; $a$ ; confidence 0.856
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040170.png ; $$A$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040106.png ; $$L ] = \lambda$$ ; confidence 0.859
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040196.png ; $$\varphi _ { L } : A \rightarrow P ^ { 4 }$$ ; confidence 0.936
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a0101207.png ; $$\sum _ { n = 0 } ^ { \infty } f ^ { ( n ) } ( \lambda _ { n } ) P _ { n } ( z )$$ ; confidence 0.754
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012049.png ; $$A _ { 1 } ^ { * }$$ ; confidence 0.975
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012050.png ; $$z | > 1$$ ; confidence 0.823
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120020/a12002022.png ; $$F _ { 0 } = f$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120020/a1200203.png ; $$A \subset Y$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110060/a11006029.png ; $$B _ { j } \in B$$ ; confidence 0.414
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010430/a01043023.png ; $$t \rightarrow \infty$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a13004067.png ; $$\psi \in \Gamma$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040149.png ; $$\Lambda _ { S 5 } T$$ ; confidence 0.591
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040397.png ; $$\operatorname { Mod } ^ { * } S = \operatorname { Mod } ^ { * } L _ { D }$$ ; confidence 0.117
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a13004089.png ; $$D$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040367.png ; $$\tilde { \Omega }$$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040685.png ; $X \in X$ ; confidence 0.278
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040442.png ; $$h ^ { - 1 } ( F _ { 0 } )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050230.png ; $$A ^ { \# }$$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050246.png ; $$Z _ { G } ( - q ^ { - 1 } ) \neq 0$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110100/a11010055.png ; $$C _ { W } ( X )$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110100/a1101003.png ; $$V$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a120050110.png ; $$M$$ ; confidence 0.455
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005085.png ; $$0 \leq t _ { 1 } \leq \ldots \leq t _ { k } \leq T$$ ; confidence 0.863
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a1200608.png ; $$c ( x )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060150.png ; $$P _ { V } ^ { \# } ( n )$$ ; confidence 0.472
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a13006083.png ; $$\overline { H }$$ ; confidence 0.950
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a130070121.png ; $$n \equiv a ( \operatorname { mod } b )$$ ; confidence 0.605
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007057.png ; $$A _ { \alpha } ( x ) = o ( \frac { x } { \operatorname { log } x } )$$ ; confidence 0.911
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007080.png ; $$\sigma ( n ) > \sigma ( m )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007033.png ; $$< 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007083.png ; $$H ( x ) > ( 1 - \varepsilon ) ( \operatorname { log } x ) ^ { 2 }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110160/a11016019.png ; $$x _ { k + 1 } = M ^ { - 1 } ( N x _ { k } + b )$$ ; confidence 0.894
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110160/a11016079.png ; $$[ M ^ { - 1 } A ] x = [ M ^ { - 1 } b ]$$ ; confidence 0.783
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110160/a11016027.png ; $$A = L + D + U$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110170/a1101706.png ; $$\phi : \Omega \rightarrow \Omega _ { t }$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008083.png ; $$X \leftarrow ( U - 1 / 2 ) / ( \sqrt { ( U - U ^ { 2 } ) } / 2 )$$ ; confidence 0.910
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008058.png ; $$X \leftarrow m + s ( U _ { 1 } + U _ { 2 } - 1 )$$ ; confidence 0.929
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110220/a110220101.png ; $$R ( f )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110220/a110220112.png ; $$\int _ { H } f d m = \int _ { \Omega } R _ { 1 } f d P _ { 1 } = \int _ { \Omega } R _ { 2 } f d P _ { 2 }$$ ; confidence 0.794
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a1201008.png ; $$y ( 0 ) = x$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010079.png ; $$( I + \lambda A )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010550/a01055060.png ; $$\partial X ^ { \prime \prime }$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012069.png ; $$p ^ { * } y \leq \lambda ^ { * } p ^ { * } x$$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012024.png ; $$7$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012049.png ; $$x ^ { \prime } > x$$ ; confidence 0.689
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110280/a11028017.png ; $$l ( D ) \geq \chi ( G ) - 1$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110280/a11028064.png ; $$\chi ( G ) < \operatorname { girth } ( G )$$ ; confidence 0.791
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110320/a11032019.png ; $$z \rightarrow 0$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a1201308.png ; $$m$$ ; confidence 0.259
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110330/a11033016.png ; $$N p$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010600/a01060019.png ; $H _ { \hat { j } }$ ; confidence 0.205
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010640/a01064020.png ; $$d ( m )$$ ; confidence 0.930
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010640/a01064015.png ; $$k _ { 1 } = 2$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010700/a01070020.png ; $$\beta : S \rightarrow B / L$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110360/a11036013.png ; $$n > 1$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010710/a01071024.png ; $$A = A _ { 1 } \cap \ldots \cap A _ { n }$$ ; confidence 0.254
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110380/a11038041.png ; $$\approx 3$$ ; confidence 0.590
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110380/a11038040.png ; $$\sim 2$$ ; confidence 0.512
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120150/a12015047.png ; $$\operatorname { ad } X$$ ; confidence 0.415
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120150/a12015069.png ; $$\mathfrak { a } / W$$ ; confidence 0.438
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120150/a12015019.png ; $$( g )$$ ; confidence 0.376
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010810/a01081095.png ; $$\lambda \neq \mu$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010810/a01081069.png ; $$U _ { j } ^ { * } ( \xi )$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010820/a01082073.png ; $$X \in Ob \odot$$ ; confidence 0.251
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010840/a01084029.png ; $$l \mapsto ( . l )$$ ; confidence 0.425
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110400/a11040023.png ; $$T ^ { * }$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110410/a11041070.png ; $$K _ { X } ^ { v } \otimes L ^ { i }$$ ; confidence 0.368
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016064.png ; $$\lambda < 1$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a120160130.png ; $$W E = R . F . I$$ ; confidence 0.845
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016079.png ; $$1 / ( 1 - \lambda )$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010950/a01095099.png ; $$X = \xi ^ { i }$$ ; confidence 0.662
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011050/a01105018.png ; $$f \times ( O _ { X } )$$ ; confidence 0.620
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a12017016.png ; $$b ( t ) = F ( t ) + \int _ { 0 } ^ { t } K ( t - s ) b ( s ) d s$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011210/a0112107.png ; $$\operatorname { Ai } ( x )$$ ; confidence 0.619
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011210/a011210114.png ; $$w ^ { \prime \prime } ( z ) = z w ( z )$$ ; confidence 0.701
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018084.png ; $$10 ^ { 16 }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011300/a01130060.png ; $$\gamma m$$ ; confidence 0.719
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011370/a01137073.png ; $$\{ U _ { i } \}$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011370/a011370171.png ; $$f ( \psi ( z ) )$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011370/a01137088.png ; $$\int _ { - \infty } ^ { + \infty } \operatorname { ln } \| \operatorname { exp } ( i t f _ { \alpha } ) \| \frac { d t } { 1 + t ^ { 2 } } < \infty$$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011390/a01139015.png ; $$\mu _ { f } ( E ) = \int _ { E } f d x$$ ; confidence 0.622
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110490/a1104901.png ; $$D = d / d t$$ ; confidence 0.954
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450195.png ; $$C / \Omega$$ ; confidence 0.538
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a0114501.png ; $$A _ { k } ^ { 2 }$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011460/a01146020.png ; $$( 2 n - 2 p )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011460/a011460108.png ; $$x \in A ^ { p } ( X ) = A ^ { * } ( X ) \cap H ^ { 2 p } ( X )$$ ; confidence 0.669
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011460/a01146029.png ; $$p = n - 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011490/a01149058.png ; $$D ( x _ { 0 } ) = 0$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150079.png ; $$x _ { 0 } ^ { 3 } x _ { 1 } + x _ { 1 } ^ { 3 } x _ { 2 } + x _ { 2 } ^ { 3 } x _ { 0 } = 0$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011520/a01152034.png ; $$\tau : G \times V \rightarrow V$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011520/a01152028.png ; $$G _ { X } = \{ g \in G : g x = x \}$$ ; confidence 0.901
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011520/a01152036.png ; $$V ^ { 1 }$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018015.png ; $$\tau \in V o c$$ ; confidence 0.532
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a011600189.png ; $$( K / k )$$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a011600128.png ; $$f _ { 1 } = \ldots = f _ { m }$$ ; confidence 0.889
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a011600249.png ; $$L / K$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a011600198.png ; $$N _ { 0 }$$ ; confidence 0.151
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a011600163.png ; $$1 \leq h _ { m } \leq h . \phi ( m )$$ ; confidence 0.774
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011620/a01162010.png ; $$f ( x ) - P _ { n } ^ { 0 } ( x )$$ ; confidence 0.810
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164040.png ; $$q ( V )$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164014.png ; $$| K _ { i } | = | i K _ { V ^ { J } } |$$ ; confidence 0.620
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640127.png ; $$M = 10 p _ { t x } - p _ { g } - 2 p ^ { ( 1 ) } + 12 + \theta$$ ; confidence 0.369
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640155.png ; $$p _ { g } \neq 1$$ ; confidence 0.708
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011650/a01165079.png ; $$H$$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011650/a011650288.png ; $$m = \nu ( P )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011650/a01165078.png ; $$H \times H \rightarrow H$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011650/a011650412.png ; $$A _ { \alpha } \subseteq A$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011650/a011650252.png ; $$\forall x _ { k }$$ ; confidence 0.834
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011650/a011650408.png ; $$\Omega _ { p } ^ { * } = \Omega _ { p } \cup \{ F _ { i } ^ { * } : F _ { i } \in \Omega _ { f } \}$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011690/a01169071.png ; $$L _ { \Omega }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011720/a01172012.png ; $$\operatorname { Red } : X ( K ) \rightarrow X _ { 0 } ( k )$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011780/a01178066.png ; $$p \in C$$ ; confidence 0.958
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011780/a01178016.png ; $$b a P$$ ; confidence 0.779
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011820/a011820124.png ; $$M \times N$$ ; confidence 0.757
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011970/a01197046.png ; $$U - \text { a.p. } \subset S ^ { p } - \text { a.p. } \subset W ^ { p } - \text { a.p. } \subset B ^ { p } - \text { a.p. } \quad p \geq 1$$ ; confidence 0.179
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011980/a01198058.png ; $$\{ f ( x ) \overline { \phi } _ { \lambda } ( x ) \}$$ ; confidence 0.564
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011990/a0119906.png ; $$\pi _ { k } ( x )$$ ; confidence 0.899
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130220/a13022025.png ; $$i : A \rightarrow X$$ ; confidence 0.601
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110540/a11054026.png ; $$O ( n ^ { 2 } \operatorname { log } n )$$ ; confidence 0.568
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130230/a13023028.png ; $$f _ { 1 } = ( P _ { n } \ldots P _ { 1 } ) ^ { 1 } f$$ ; confidence 0.568
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130230/a13023034.png ; $$\| f _ { 1 } - P _ { U \cap V ^ { J } } f \| \leq c ^ { 2 l - 1 } \| f \|$$ ; confidence 0.287
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130230/a13023032.png ; $$1 \rightarrow \infty$$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012040/a01204016.png ; $$\partial M ^ { n + 1 } = K ^ { n }$$ ; confidence 0.516
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012040/a01204017.png ; $$X \subset Y$$ ; confidence 0.590
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012090/a0120907.png ; $$\alpha \neq 0$$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012090/a01209091.png ; $$N ( R ) \neq 0$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012090/a01209097.png ; $$Z ( A ) = A \cap Z ( R )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012100/a01210023.png ; $$| \alpha | = \sqrt { \overline { \alpha } \alpha }$$ ; confidence 0.964
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012120/a01212040.png ; $$\alpha _ { i } + 1$$ ; confidence 0.659
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012160/a0121604.png ; $$\phi = \operatorname { am } z$$ ; confidence 0.783
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110580/a11058047.png ; $$= v : q$$ ; confidence 0.846
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023068.png ; $$c _ { q }$$ ; confidence 0.425
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a1202303.png ; $$f \in C ( \partial D )$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012210/a01221035.png ; $$f ( t ) = \psi ( \phi ( t ) )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012250/a01225011.png ; $$R > 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012330/a01233050.png ; $$x <$$ ; confidence 0.424
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012340/a01234035.png ; $$a \in V$$ ; confidence 0.699
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012410/a012410135.png ; $$f ( S )$$ ; confidence 0.968
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012410/a01241063.png ; $$s = s ^ { * } \cup ( s \backslash s ^ { * } ) ^ { * } U \ldots$$ ; confidence 0.271
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012410/a012410141.png ; $$R ^ { n } \subset C ^ { k }$$ ; confidence 0.407
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012430/a01243088.png ; $$f$$ ; confidence 0.816
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012430/a012430100.png ; $$I Y \subset O$$ ; confidence 0.739
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012460/a012460130.png ; $$X \equiv 0$$ ; confidence 0.220
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110600/a11060013.png ; $$0.96$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012550/a01255032.png ; $$\Gamma _ { n } ^ { \alpha } ( H ) _ { \alpha } ^ { 8 }$$ ; confidence 0.595
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110610/a110610171.png ; $$h \in \operatorname { Diff } ^ { + } ( M )$$ ; confidence 0.591
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110610/a110610104.png ; $$Z = \int _ { A } D A \sqrt { \operatorname { det } ( / \partial _ { A } ^ { * } / \partial _ { A } ) } \operatorname { exp } [ - \| F \| ^ { 2 } ]$$ ; confidence 0.921
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110630/a11063032.png ; $$\rho _ { 0 n + } = \operatorname { sin } A$$ ; confidence 0.354
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012800/a01280065.png ; $$\times \frac { \partial ^ { m + n } } { \partial x ^ { m } \partial y ^ { n } } [ x ^ { \gamma + m - 1 } y ^ { \prime } + n - 1 _ { ( 1 - x - y ) } \alpha + w + n - \gamma - \gamma ^ { \prime } ]$$ ; confidence 0.072
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012930/a01293027.png ; $$L u \equiv \frac { \partial u } { \partial t } - \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = 0$$ ; confidence 0.607
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012940/a01294080.png ; $$F _ { b }$$ ; confidence 0.450
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012940/a01294081.png ; $$f \in F$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012950/a012950197.png ; $$( L _ { 2 } )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012960/a01296094.png ; $$n > r$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012970/a012970198.png ; $$\hat { W } \square _ { \infty } ^ { \gamma }$$ ; confidence 0.199
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012970/a012970176.png ; $$d _ { 2 n - 1 } = d _ { 2 n }$$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012970/a012970129.png ; $$S _ { 2 } ^ { \gamma }$$ ; confidence 0.562
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012970/a012970196.png ; $$m \geq r$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012970/a01297077.png ; $$\operatorname { inf } _ { u \in \mathfrak { N } } \| x - u \| = \operatorname { sup } _ { F \in X ^ { * } } [ F ( x ) - \operatorname { sup } _ { u \in \mathfrak { N } } F ( u ) ]$$ ; confidence 0.144
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012970/a012970244.png ; $$L ( f )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012980/a01298030.png ; $$\phi _ { k } ( t _ { k } ) = 1$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012980/a01298033.png ; $$X = H$$ ; confidence 0.599
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013000/a01300068.png ; $$P _ { 0 } ( z )$$ ; confidence 0.963
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013000/a01300057.png ; $$L _ { p } ( E )$$ ; confidence 0.872
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013000/a01300016.png ; $$\operatorname { deg } P \leq n$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013010/a01301081.png ; $$D ^ { 0 } f = f$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027051.png ; $$\{ x _ { n j } ^ { \prime } \}$$ ; confidence 0.273
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013030/a01303027.png ; $$\operatorname { sup } _ { x \in \mathfrak { M } } \| x - A x \|$$ ; confidence 0.679
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013170/a01317026.png ; $$y _ { t } = t - S _ { \eta _ { t } }$$ ; confidence 0.968
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013180/a013180116.png ; $$H _ { k + 1 } ( f ( M ) )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013180/a013180158.png ; $$\| T _ { M } \|$$ ; confidence 0.918
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013220/a0132202.png ; $$F ( z ) = z + \alpha _ { 0 } + \frac { \alpha _ { 1 } } { z } + \ldots$$ ; confidence 0.619
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013220/a01322017.png ; $$\overline { B } = C F ( \Delta ^ { \prime } )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110660/a11066057.png ; $$1 ^ { 1 } = 1 ^ { 1 } ( N )$$ ; confidence 0.689
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110680/a11068093.png ; $$L f \theta$$ ; confidence 0.169
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110680/a110680125.png ; $$p / p$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110680/a110680195.png ; $$b _ { i } = \alpha _ { i } \alpha _ { 1 }$$ ; confidence 0.437
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110680/a11068053.png ; $$r ^ { \prime } < r$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110680/a11068076.png ; $$\alpha \geq b$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110680/a110680200.png ; $$r$$ ; confidence 0.805
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110680/a110680179.png ; $$\phi _ { x y } a \leq b$$ ; confidence 0.847
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013250/a01325016.png ; $$\operatorname { Arg } f$$ ; confidence 0.692
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013250/a01325046.png ; $$0 \notin f ( \partial D )$$ ; confidence 0.904
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013250/a01325015.png ; $$\operatorname { arg } f$$ ; confidence 0.862
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110700/a11070050.png ; $$\beta ( A )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110700/a11070056.png ; $$M ( A ) = V \backslash N ( A )$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110700/a11070080.png ; $$\Omega ^ { p } [ V ]$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120280/a120280141.png ; $$S _ { E } = \{ \omega \in \hat { G } : E + \omega \subseteq E \}$$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013570/a01357020.png ; $$g ( u ) d u$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013590/a01359029.png ; $$\Phi ^ { ( 3 ) } ( x )$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013670/a01367016.png ; $$J _ { \nu } ( x ) \sim \sqrt { \frac { 2 } { \pi x } } [ \operatorname { cos } ( x - \frac { \pi \nu } { 2 } - \frac { \pi } { 4 } ) \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \alpha _ { 2 n } x ^ { - 2 n }$$ ; confidence 0.755
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013670/a0136709.png ; $$f ( x ) \sim \sum _ { n = 0 } ^ { \infty } a _ { n } \phi _ { n } ( x ) \quad ( x \rightarrow x _ { 0 } )$$ ; confidence 0.754
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110790/a11079027.png ; $$M \subset G$$ ; confidence 0.949
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130290/a13029066.png ; $$Y$$ ; confidence 0.441
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130290/a13029031.png ; $$P \rightarrow \Sigma$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013980/a01398016.png ; $$f ( \lambda ) = ( \frac { \sigma ^ { 2 } } { 2 \pi } ) | \phi ( e ^ { i \lambda } ) | ^ { - 2 }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014060/a01406076.png ; $$\mathfrak { A } _ { s _ { 1 } }$$ ; confidence 0.833
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014060/a014060256.png ; $$A = S ^ { \prime }$$ ; confidence 0.502
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014060/a01406028.png ; $$20$$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014060/a014060135.png ; $$W _ { N } \rightarrow W _ { n }$$ ; confidence 0.076
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014090/a01409051.png ; $$\psi ( t _ { i } )$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014090/a014090219.png ; $$L ( \Sigma )$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014140/a014140121.png ; $$\sigma ( 1 ) = s$$ ; confidence 0.805
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014190/a01419058.png ; $$\phi ( t ) \equiv$$ ; confidence 0.467
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014190/a014190112.png ; $$\dot { x } = A x$$ ; confidence 0.608
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014190/a0141905.png ; $$x _ { y } + 1 = t$$ ; confidence 0.287
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014190/a01419047.png ; $$t _ { + } < + \infty$$ ; confidence 0.793
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032031.png ; $$p < .5$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032030.png ; $$Y _ { i } = 2 X _ { i } - 1$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014230/a0142305.png ; $$\{ A \rangle$$ ; confidence 0.294
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014300/a0143001.png ; $$\epsilon - \delta$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014310/a01431097.png ; $$| x$$ ; confidence 0.207
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014310/a0143102.png ; $$e$$ ; confidence 0.314
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014310/a01431093.png ; $$A ( \iota X A ( x ) )$$ ; confidence 0.456
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014310/a01431027.png ; $$\exists x A$$ ; confidence 0.894
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110190/b11019019.png ; $$x ^ { * } ( x ^ { * } y ) = x \wedge y$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110190/b11019030.png ; $$( x ^ { * } y ) ^ { * } z = ( x ^ { * } z ) ^ { * } ( y ^ { * } z )$$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b120210148.png ; $$\mathfrak { p } \supset b$$ ; confidence 0.356
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021067.png ; $$( L ( \lambda ) )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b120210104.png ; $$\rho = ( 1 / 2 ) \sum _ { \alpha \in \Delta ^ { + } } \alpha$$ ; confidence 0.628
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b120210102.png ; $$\{ \mu _ { i } \} _ { i = 1 } ^ { s - 1 } = \{ w . \lambda \} _ { w \in W ^ { ( k ) } }$$ ; confidence 0.489
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021075.png ; $$\mathfrak { F } _ { \lambda }$$ ; confidence 0.661
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110660/b11066023.png ; $$L _ { p } ( R )$$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130010/b13001099.png ; $$\left( \begin{array} { l l } { A } & { B } \\ { C } & { D } \end{array} \right)$$ ; confidence 0.965
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130010/b13001094.png ; $$V ^ { * } - V$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130010/b130010103.png ; $$V _ { n } = H _ { n } / \Gamma$$ ; confidence 0.724
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015110/b01511064.png ; $$\mu = \delta _ { X }$$ ; confidence 0.951
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015110/b01511035.png ; $$U ( y ) = \int _ { \Gamma } f ( x ) d \beta _ { Y } ( x )$$ ; confidence 0.820
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130020/b13002056.png ; $$x \in J$$ ; confidence 0.908
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b1300303.png ; $$V ^ { \pm } \times V ^ { - } \times V ^ { \pm } \rightarrow V ^ { \pm }$$ ; confidence 0.809
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110100/b110100392.png ; $$T _ { K } ( K )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110100/b110100377.png ; $$\frac { c _ { 1 } } { n } \leq ( | K | | K ^ { \circlearrowright } | ) ^ { 1 / n } \leq \frac { c _ { 2 } } { n }$$ ; confidence 0.421
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110100/b11010099.png ; $$\| T \| T ^ { - 1 } \| \geq c n$$ ; confidence 0.835
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b12004080.png ; $$T : L _ { \infty } \rightarrow L _ { \infty }$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b12004018.png ; $$| x _ { y } \| \rightarrow 0$$ ; confidence 0.611
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110090/b1100902.png ; $$l ^ { \infty } ( N )$$ ; confidence 0.759
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110130/b110130207.png ; $$\left( \begin{array} { c } { y - p } \\ { \vdots } \\ { y - 1 } \\ { y _ { 0 } } \end{array} \right) = \Gamma ^ { - 1 } \left( \begin{array} { c } { 0 } \\ { \vdots } \\ { 0 } \\ { 1 } \end{array} \right)$$ ; confidence 0.427
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110130/b110130197.png ; $$f ( \zeta ) > 0$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110130/b11013099.png ; $$m _ { 1 } \in M _ { 1 }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110130/b11013012.png ; $$M _ { d } ^ { * } = M _ { d }$$ ; confidence 0.900
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110130/b110130209.png ; $$v ( \lambda ) = ( y _ { 0 } + \lambda ^ { - 1 } y _ { - 1 } + \ldots + \lambda ^ { - p } y - p ) y _ { 0 } ^ { - 1 / 2 }$$ ; confidence 0.241
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110130/b1101309.png ; $$E _ { 2 }$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015210/b01521049.png ; $$\alpha \in S _ { \alpha }$$ ; confidence 0.784
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015260/b0152609.png ; $$D \cup \Gamma$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015280/b0152808.png ; $$\lambda _ { 0 } + \ldots + \lambda _ { n } = 1$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015310/b01531023.png ; $$X _ { s } = X \times s s$$ ; confidence 0.533
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015350/b01535027.png ; $$\alpha _ { i } \in \Omega$$ ; confidence 0.833
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015350/b015350372.png ; $$\{ \xi _ { t } \}$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015350/b015350251.png ; $$\{ \xi _ { t } ( s ) \}$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015350/b015350300.png ; $$\delta _ { i k } = 0$$ ; confidence 0.900
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110160/b11016019.png ; $$f ( x ) = a x + b$$ ; confidence 0.931
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110160/b11016013.png ; $$f ( n ) \equiv 0 ( \operatorname { mod } p )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130060/b13006022.png ; $$\| A \| _ { \infty }$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130060/b13006060.png ; $$b _ { i }$$ ; confidence 0.854
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130070/b13007015.png ; $$\pi ( m )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015380/b0153803.png ; $$A _ { i } \Gamma \cap A _ { j } = \emptyset$$ ; confidence 0.946
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539034.png ; $\operatorname { inf } _ { d } \int _ { \Theta } L ( \theta , d ) \frac { p ( x | \theta ) \pi ( \theta ) } { p ( x ) } d \nu ( \theta )$ ; confidence 0.420
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539050.png ; $\theta = \theta _ { i }$ ; confidence 0.949
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539042.png ; $D = \{ d _ { 1 } , d _ { 2 } \}$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539023.png ; $P _ { \theta } ( d x ) = p ( x | \theta ) d \mu ( x )$ ; confidence 0.550
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539013.png ; $\delta ( x ) \in D$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539045.png ; $\pi ( \theta _ { 1 } ) = \pi _ { 1 }$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539046.png ; $\pi ( \theta _ { 2 } ) = \pi _ { 2 }$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b0153901.png ; $( X , B X )$ ; confidence 0.566
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539056.png ; $\delta ^ { * } ( x ) = \left\{ \begin{array} { l l } { d _ { 1 } , } & { \text { if } \frac { p ( x | \theta _ { 2 } ) } { p ( x | \theta _ { 1 } ) } \leq \frac { \pi _ { 1 } } { \pi _ { 2 } } \frac { L _ { 12 } - L _ { 11 } } { L _ { 21 } - L _ { 22 } } } \\ { d _ { 2 } , } & { \text { if } \frac { p ( x | \theta _ { 2 } ) } { p ( x | \theta _ { 1 } ) } \geq \frac { \pi _ { 1 } } { \pi _ { 2 } } \frac { L _ { 12 } - L _ { 11 } } { L _ { 21 } - L _ { 22 } } } \end{array} \right.$ ; confidence 0.853
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539036.png ; $\int _ { \Theta } L ( \theta , d ) \frac { p ( x | \theta ) \pi ( \theta ) } { p ( x ) } d \nu ( \theta ) = E [ L ( \theta , d ) | x ]$ ; confidence 0.885
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539019.png ; $\rho ( \pi , \delta ) = \int _ { \Theta } \rho ( \theta , \delta ) \pi ( d \theta )$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539022.png ; $\delta ^ { * } = \delta ^ { * } ( x )$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539030.png ; $= \int _ { X } d \mu ( x ) [ \int _ { \Theta } L ( \theta , \delta ( x ) ) p ( x | \theta ) \pi ( \theta ) d \nu ( \theta ) ]$ ; confidence 0.736
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b0153903.png ; $( \Theta , B _ { \Theta } )$ ; confidence 0.937
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539032.png ; $d ^ { x }$ ; confidence 0.785
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539028.png ; $\int \int _ { \Theta } L ( \theta , \delta ( x ) ) P _ { \theta } ( d x ) \pi ( d \theta ) =$ ; confidence 0.604
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539043.png ; $L _ { i j } = L = ( \theta _ { i } , d _ { j } )$ ; confidence 0.694
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539035.png ; $p ( x ) = \int _ { \Theta } p ( x | \theta ) \pi ( \theta ) d \nu ( \theta )$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539020.png ; $\rho ( \theta , \delta ) = \int _ { Y } L ( \theta , \delta ( x ) ) P _ { \theta } ( d x )$ ; confidence 0.192
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539052.png ; $L _ { 22 } < L _ { 21 }$ ; confidence 0.945
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539053.png ; $\rho ( \pi , \delta ) = \int _ { X } [ \pi _ { 1 } p ( x | \theta _ { 1 } ) L ( \theta _ { 1 } , \delta ( x ) ) +$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539057.png ; $\rho ( \theta , \delta )$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539047.png ; $\pi _ { 1 } + \pi _ { 2 } = 1$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539029.png ; $= \int \int _ { \Theta } L ( \theta , \delta ( x ) ) p ( x | \theta ) \pi ( \theta ) d \mu ( x ) d \nu ( \theta ) =$ ; confidence 0.774
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539040.png ; $E [ L ( \theta , d ) | x ]$ ; confidence 0.361
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539018.png ; $\delta \rho ( \pi , \delta )$ ; confidence 0.650
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b0153907.png ; $( D , B _ { D } )$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539061.png ; $\rho ( \pi , \delta _ { \epsilon } ^ { * } ) \leq \operatorname { inf } _ { \delta } \rho ( \pi , \delta ) + \epsilon$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539015.png ; $\pi = \pi ( d \theta )$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539011.png ; $\delta = \delta ( x )$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539021.png ; $\rho ( \pi , \delta ^ { * } ) = \operatorname { inf } _ { \delta } \int _ { \Theta } \int _ { X } L ( \theta , \delta ( x ) ) P _ { \theta } ( d x ) \pi ( d \theta )$ ; confidence 0.586
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539063.png ; $( \epsilon > 0 )$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539054.png ; $+ \pi _ { 2 } p ( x | \theta _ { 2 } ) L ( \theta _ { 2 } , \delta ( x ) ) ] d \mu ( x )$ ; confidence 0.612
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b0153905.png ; $\{ P _ { \theta } : \theta \in \Theta \}$ ; confidence 0.633
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539058.png ; $\rho ( \pi , \delta )$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539044.png ; $i , j = 1,2$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539024.png ; $\pi ( d \theta ) = \pi ( \theta ) d \nu ( \theta )$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539041.png ; $= \{ \theta _ { 1 } , \theta _ { 2 } \}$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539038.png ; $\delta ^ { * } ( x )$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539031.png ; $x \in X , \delta ^ { * } ( x )$ ; confidence 0.710
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539060.png ; $\delta _ { \epsilon } ^ { * }$ ; confidence 0.648
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b0153908.png ; $L ( \theta , d )$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539051.png ; $L _ { 11 } < L _ { 12 }$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015400/b01540062.png ; $$s ( z ) = q ( z )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015400/b01540048.png ; $$s ( z )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015400/b01540091.png ; $$\Psi _ { 1 } ( Y ) / \hat { q } ( Y ) \leq \psi ( Y ) \leq \Psi _ { 2 } ( Y ) / \hat { q } ( Y )$$ ; confidence 0.236
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015420/b01542034.png ; $$x = ( x _ { 1 } + \ldots + x _ { n } ) / n$$ ; confidence 0.514
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009080.png ; $$| f ( z ) | < 1$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009092.png ; $$f \in B ( m / n )$$ ; confidence 0.956
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009082.png ; $$L ( r ) = \int _ { 0 } ^ { 2 \pi } | z f ^ { \prime } ( z ) | d \theta = O ( \operatorname { log } \frac { 1 } { 1 - r } )$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015440/b0154406.png ; $$E X _ { 2 j } = \mu _ { 2 }$$ ; confidence 0.517
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015440/b01544026.png ; $$X _ { 1 }$$ ; confidence 0.637
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110250/b11025093.png ; $$L ( t )$$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015540/b01554027.png ; $$\phi = \Pi ^ { \prime } \Pi ^ { - 1 }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110270/b11027042.png ; $$P ( s S ) = P ( S )$$ ; confidence 0.219
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130100/b13010015.png ; $$k _ { z } = K _ { z } / \| K _ { z } \|$$ ; confidence 0.674
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015560/b01556018.png ; $$D \times D \in \Gamma ^ { 2 }$$ ; confidence 0.230
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120140/b12014039.png ; $$a ( z )$$ ; confidence 0.948
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015580/b0155806.png ; $$p _ { i } = \nu ( \alpha _ { i } )$$ ; confidence 0.832
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150110.png ; $$d : N \cup \{ 0 \} \rightarrow R$$ ; confidence 0.953
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015024.png ; $$x = \frac { 1 } { n } \sum _ { j = 1 } ^ { n } x$$ ; confidence 0.315
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110330/b1103309.png ; $$\Omega = S ^ { D } = \{ \omega _ { i } \} _ { i \in D }$$ ; confidence 0.591
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110330/b11033038.png ; $$P ^ { \prime }$$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015630/b01563017.png ; $$p \leq 2$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015650/b01565010.png ; $$B _ { n } ( x + 1 ) - B _ { n } ( x ) = n x ^ { n - 1 }$$ ; confidence 0.672
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015660/b01566078.png ; $$/ N = T$$ ; confidence 0.692
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015660/b01566054.png ; $$\alpha = ( k + 1 / 2 )$$ ; confidence 0.643
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015660/b01566081.png ; $$1 - \frac { 2 } { \sqrt { 2 \pi } } \int _ { 0 } ^ { \alpha / T } e ^ { - z ^ { 2 } / 2 } d z = \frac { 2 } { \sqrt { 2 \pi } } \int _ { \alpha / \sqrt { T } } ^ { \infty } e ^ { - z ^ { 2 } / 2 } d z$$ ; confidence 0.722
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015660/b01566071.png ; $$\nu = a + x + 2 [ \frac { n - t - x - \alpha } { 2 } ] + 1$$ ; confidence 0.213
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015680/b01568021.png ; $$2 \operatorname { exp } \{ - \frac { 1 } { 2 } n \epsilon ^ { 2 } \}$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110370/b11037053.png ; $$K ( t ) \equiv 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110370/b11037052.png ; $$= 0 \text { as. } \cdot P _ { \theta _ { 0 } } ]$$ ; confidence 0.233
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110370/b11037025.png ; $$0 < \epsilon < i ( \theta _ { 0 } )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110340/b11034032.png ; $$\omega ( x y ) = \omega ( x ) \omega ( y )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015720/b01572032.png ; $$+ \frac { \alpha } { u } [ \alpha ( \frac { \partial u } { \partial x } ) ^ { 2 } + 2 b \frac { \partial u } { \partial x } \frac { \partial u } { \partial y } + c ( \frac { \partial u } { \partial y } ) ^ { 2 } ] +$$ ; confidence 0.828
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120160/b12016030.png ; $$x _ { i } ^ { \prime \prime } = x _ { i } ^ { \prime }$$ ; confidence 0.895
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110380/b11038019.png ; $$w = \pi ( z )$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110380/b11038070.png ; $$\Theta f$$ ; confidence 0.864
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110390/b110390108.png ; $$K > 0$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110400/b11040029.png ; $$F ^ { 2 } = \beta ^ { 2 } \operatorname { exp } \{ \frac { I \gamma } { \beta } \}$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110400/b11040017.png ; $$F . C _ { i j k } = I m$$ ; confidence 0.621
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015870/b01587024.png ; $$( 1 - \Delta ) ^ { m } P _ { \alpha } ( x ) = P _ { \alpha - 2 m } ( x )$$ ; confidence 0.951
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110420/b11042025.png ; $$V _ { k } \varphi ( x ) = \varphi ( x - h )$$ ; confidence 0.922
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110420/b11042055.png ; $$\mu \in R$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110420/b11042087.png ; $$\overline { B } ^ { \nu }$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110420/b11042014.png ; $$( Id - \Delta ) ^ { \nu }$$ ; confidence 0.560
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110440/b1104407.png ; $$\overline { \Xi } \epsilon = 0$$ ; confidence 0.326
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110490/b1104909.png ; $$P _ { 1 }$$ ; confidence 0.928
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016050/b0160507.png ; $$E _ { \theta } \{ T \}$$ ; confidence 0.560
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016050/b01605010.png ; $$b ( \theta ) \equiv 0$$ ; confidence 0.580
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016160/b01616031.png ; $$\hat { R } ( c )$$ ; confidence 0.613
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016160/b01616036.png ; $$0 < c < 1$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016150/b01615033.png ; $$\operatorname { Re } _ { c _ { N } } = n$$ ; confidence 0.069
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016170/b01617015.png ; $$F _ { n } ( z _ { 0 } ) = 0$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016170/b0161704.png ; $$| w | < r _ { 0 }$$ ; confidence 0.478
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016170/b01617013.png ; $$F _ { n } ( z )$$ ; confidence 0.855
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110520/b1105203.png ; $$\sum _ { n = 1 } ^ { \infty } l _ { k } ^ { 2 } \operatorname { exp } ( l _ { 1 } + \ldots + l _ { n } ) = \infty$$ ; confidence 0.545
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110520/b11052027.png ; $$x \in G _ { n }$$ ; confidence 0.415
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016470/b0164707.png ; $$( \tau = \text { const } )$$ ; confidence 0.589
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110560/b11056013.png ; $$w _ { 2 } ( F )$$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016540/b0165404.png ; $$B = \{ b _ { i } : i \in I \}$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110570/b11057061.png ; $$H _ { m }$$ ; confidence 0.869
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110570/b11057039.png ; $$H _ { k } \circ \operatorname { exp } ( X _ { F } ) = \operatorname { exp } ( X _ { F } ) ( H _ { k } )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016550/b01655023.png ; $$\mu _ { n } ( t ) = 0$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016550/b01655040.png ; $$\lambda _ { n } ( t ) = v$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110590/b11059067.png ; $$u = q ( x ) \text { on } g$$ ; confidence 0.462
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016610/b01661046.png ; $$\vec { u } = A _ { j } ^ { i } u ^ { j }$$ ; confidence 0.648
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016610/b01661030.png ; $$R _ { y } ^ { t }$$ ; confidence 0.060
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130170/b13017045.png ; $$S _ { T }$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027050.png ; $$U ( t ) = \sum _ { 1 } ^ { \infty } P ( S _ { k } \leq t ) = \sum _ { 1 } ^ { \infty } F ^ { ( k ) } ( t )$$ ; confidence 0.917
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110610/b11061011.png ; $$K ^ { * }$$ ; confidence 0.777
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016650/b0166503.png ; $$2 \int \int _ { G } ( x \frac { \partial y } { \partial u } \frac { \partial y } { \partial v } ) d u d v = \oint _ { \partial G } ( x y d y )$$ ; confidence 0.204
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030013.png ; $$q \in Z ^ { N }$$ ; confidence 0.950
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030060.png ; $$0 \leq \lambda _ { 1 } ( \eta ) \leq \ldots \leq \lambda _ { m } ( \eta ) \leq \ldots \rightarrow \infty$$ ; confidence 0.714
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016670/b01667088.png ; $$A A ^ { T } = ( r - \lambda ) E + \lambda J$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016670/b01667071.png ; $$n _ { 1 } = 9$$ ; confidence 0.822
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110640/b11064038.png ; $$X _ { 1 } \times X _ { 2 }$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031032.png ; $$0 \leq \delta \leq ( n - 1 ) / 2 ( n + 1 )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031064.png ; $$\tau ^ { n }$$ ; confidence 0.408
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016730/b01673033.png ; $$r ^ { 3 } / v \ll 1$$ ; confidence 0.747
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016740/b0167404.png ; $$\leq \frac { 1 } { N } \langle U _ { 1 } - U _ { 2 } \} _ { U _ { 2 } }$$ ; confidence 0.419
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110690/b11069080.png ; $$M _ { A g }$$ ; confidence 0.870
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110690/b11069063.png ; $$P T ( C ) \in G$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032011.png ; $$\| x + y \| _ { p } = \| u + v \| _ { p }$$ ; confidence 0.572
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016810/b01681038.png ; $$n ( z ) = n _ { 0 } e ^ { - m g z / k T }$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016810/b01681021.png ; $$H = \sum _ { i } \frac { p _ { i } ^ { 2 } } { 2 m } + \sum _ { i } U ( r _ { i } )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016850/b01685023.png ; $$E = \sum _ { i = 1 } ^ { M } \epsilon _ { i } N _ { i }$$ ; confidence 0.900
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016850/b01685022.png ; $$N = \sum _ { i = 1 } ^ { M } N$$ ; confidence 0.965
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120360/b12036013.png ; $$E$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130190/b1301906.png ; $$F ( x ) = f ( M x )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016900/b0169001.png ; $$d s ^ { 2 } = \frac { d u ^ { 2 } + d v ^ { 2 } } { ( U + V ) ^ { 2 } }$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016990/b0169909.png ; $$\Omega _ { M } ( \rho ) \in V _ { M } ^ { V ^ { n } }$$ ; confidence 0.820
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016920/b01692023.png ; $$( x \vee C x ) \wedge y = y$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016920/b016920121.png ; $$( M )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120370/b12037030.png ; $$h \in \Omega$$ ; confidence 0.914
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120370/b12037092.png ; $$\sum \frac { 1 } { 1 }$$ ; confidence 0.251
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110760/b11076042.png ; $$\partial ^ { k } f / \partial x : B ^ { m } \rightarrow B$$ ; confidence 0.717
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016960/b016960150.png ; $$99$$ ; confidence 0.271
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016960/b016960167.png ; $$\tilde { \mathfrak { N } } = \mathfrak { N } \backslash ( V _ { j = 1 } ^ { t } \mathfrak { A } ^ { \prime \prime } )$$ ; confidence 0.082
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016960/b016960126.png ; $$\omega _ { i } = 1$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016960/b016960175.png ; $$M _ { 1 } \cup M _ { 2 }$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016970/b0169702.png ; $$x ^ { \sigma } = x$$ ; confidence 0.948
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016970/b01697035.png ; $$t _ { f } ( n )$$ ; confidence 0.917
+. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016970/b01697056.png ; $$\frac { 2 ^ { n } } { \operatorname { log } _ { 2 } n \cdot \operatorname { log } _ { 2 } \operatorname { log } _ { 2 } n } < l _ { f } ( n ) < \frac { 2 ^ { n } } { \operatorname { log } _ { 2 } n }$$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b130200102.png ; $$\beta \neq - \alpha$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020088.png ; $$\Delta _ { - } = - \Delta _ { + }$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020036.png ; $$[ e _ { i } f _ { j } ] = h _ { i }$$ ; confidence 0.684
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020048.png ; $$\alpha _ { i j } \neq 0$$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020023.png ; $$\alpha _ { i } \in R$$ ; confidence 0.443
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b130200163.png ; $$\operatorname { lim } \mathfrak { g } ^ { \alpha } = 1$$ ; confidence 0.737
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020073.png ; $$9 -$$ ; confidence 0.467
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017010/b01701014.png ; $$\alpha _ { k } = a _ { k k } - v _ { k } A _ { k - 1 } ^ { - 1 } u _ { k }$$ ; confidence 0.522
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017030/b01703046.png ; $$\mathfrak { M } _ { n }$$ ; confidence 0.373
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b12040052.png ; $$\mathfrak { h } \subset \mathfrak { g }$$ ; confidence 0.959
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017290/b01729088.png ; $$A = R ( X )$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017290/b01729042.png ; $$\partial M _ { A } \subset X \subset M _ { A }$$ ; confidence 0.891
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017290/b0172908.png ; $$\Gamma \subset M _ { A }$$ ; confidence 0.920
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017290/b01729066.png ; $$| \hat { \alpha } ( \xi ) | > | \hat { \alpha } ( \eta ) |$$ ; confidence 0.745
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017280/b01728011.png ; $$\hat { G } \backslash G$$ ; confidence 0.582
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017330/b01733030.png ; $$f ( e ^ { i \theta } ) = \operatorname { lim } _ { r \rightarrow 1 - 0 } f ( r e ^ { i \theta } )$$ ; confidence 0.451
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017330/b01733087.png ; $$N ^ { * } ( D )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017330/b017330215.png ; $$F ^ { \prime } ( w )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017330/b017330250.png ; $$U ^ { N }$$ ; confidence 0.743
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017330/b017330260.png ; $$N ^ { * } ( \Omega )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017330/b017330155.png ; $$\Phi ( \theta )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017330/b017330242.png ; $$f ^ { * } ( z ) = \operatorname { lim } _ { r \rightarrow 1 - 0 } f ( r z )$$ ; confidence 0.445
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017330/b017330240.png ; $$B = H ^ { \infty } \subset H _ { \psi } \subset N ^ { * }$$ ; confidence 0.752
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017340/b017340100.png ; $$n ^ { \prime } = - n + m - 1$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017340/b01734046.png ; $$t _ { 0 } \in \partial S$$ ; confidence 0.816
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017340/b01734029.png ; $$C _ { \alpha }$$ ; confidence 0.664
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017350/b01735065.png ; $$K$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017350/b01735056.png ; $$K ^ { + }$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017380/b01738057.png ; $$L u = \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } - \frac { \partial u } { \partial t } = 0$$ ; confidence 0.466
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017380/b01738068.png ; $$t \in S$$ ; confidence 0.474
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017400/b01740070.png ; $$k ^ { \prime } = 1$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110820/b11082017.png ; $$\pi _ { i } / ( \pi _ { i } + \pi _ { j } )$$ ; confidence 0.304
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b01747076.png ; $$1 \rightarrow K ( n ) \rightarrow B ( n ) \rightarrow S ( n ) \rightarrow 1$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b01747034.png ; $$( i i + 1 )$$ ; confidence 0.886
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b01747053.png ; $$\Pi ^ { \prime \prime }$$ ; confidence 0.914
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b01747069.png ; $$P _ { 1 / 2 }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b01747067.png ; $$\omega ^ { - 1 }$$ ; confidence 0.909
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b017470190.png ; $$H ^ { * } ( O ( n ) ) \rightarrow H ^ { * } ( B ( n ) )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b120420145.png ; $$\sum h _ { ( 1 ) } \otimes h _ { ( 2 ) }$$ ; confidence 0.516
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b120420159.png ; $$\lambda _ { W } : V \otimes W \rightarrow W \otimes V$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b120420115.png ; $$U _ { q } ( \mathfrak { g } )$$ ; confidence 0.626
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022030.png ; $$L _ { p } ( T )$$ ; confidence 0.938
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110840/b11084049.png ; $$X$$ ; confidence 0.601
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130230/b13023050.png ; $$G ( u )$$ ; confidence 0.489
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017530/b0175307.png ; $$P \{ \mu ( t + t _ { 0 } ) = j | \mu ( t _ { 0 } ) = i \}$$ ; confidence 0.724
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017550/b0175508.png ; $$t _ { 1 } + t$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017560/b01756018.png ; $$P \{ \xi _ { t } \equiv 0 \} = 1$$ ; confidence 0.670
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017580/b01758025.png ; $$\int _ { 0 } ^ { 1 } \frac { 1 - G ( s ) } { F ( s ) - s } d s < \infty$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017620/b0176209.png ; $$P _ { C } ^ { 1 }$$ ; confidence 0.433
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017620/b01762024.png ; $$r ^ { 2 }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110850/b11085036.png ; $$\operatorname { dim } ( V / K ) = 1$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120440/b120440103.png ; $$R [ H \times H$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120460/b12046037.png ; $$( \oplus _ { b } G _ { E B } b )$$ ; confidence 0.179
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110880/b11088033.png ; $$P _ { I } ^ { f } : C ^ { \infty } \rightarrow L$$ ; confidence 0.321
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110890/b11089088.png ; $$\alpha ^ { i }$$ ; confidence 0.739
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110890/b11089054.png ; $$f ( x ) = x ^ { t } M x$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110910/b11091027.png ; $$\frac { \partial N _ { i } } { \partial t } + u _ { i } \nabla N _ { i } = G _ { i } - L _ { i }$$ ; confidence 0.250
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130270/b13027070.png ; $$B \otimes K ( H )$$ ; confidence 0.796
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130270/b1302706.png ; $$Q ( H ) = B ( H ) / K ( H )$$ ; confidence 0.959
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120500/b12050014.png ; $$M _ { t } : = \operatorname { sup } _ { s \leq t } W _ { s }$$ ; confidence 0.396
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120510/b12051029.png ; $$\operatorname { lim } _ { n \rightarrow \infty } \nabla f ( x _ { n } ) = 0$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120510/b12051051.png ; $$x _ { + } = x _ { c } + \lambda d$$ ; confidence 0.719
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110960/b11096026.png ; $$\nu : Z ( K ) \rightarrow V \subset \operatorname { Aff } ( A )$$ ; confidence 0.915
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b130290121.png ; $$\operatorname { dim } A = 2$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b130290203.png ; $$0 \leq i \leq d - 1$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b1302903.png ; $$d = \operatorname { dim } A$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110990/b11099015.png ; $$P _ { \alpha }$$ ; confidence 0.384
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110990/b11099011.png ; $$V _ { Q }$$ ; confidence 0.244
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b130300113.png ; $$A$$ ; confidence 0.535
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b130300112.png ; $$F _ { m }$$ ; confidence 0.945
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030089.png ; $$n \geq 2 ^ { 13 }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017800/b01780053.png ; $$n = p$$ ; confidence 0.858
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017800/b01780036.png ; $$d \geq n$$ ; confidence 0.956
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017800/b01780019.png ; $$2 ^ { 12 }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001032.png ; $$\frac { \partial v } { \partial t } - 6 v ^ { 2 } \frac { \partial v } { \partial x } + \frac { \partial ^ { 3 } v } { \partial x ^ { 3 } } = 0$$ ; confidence 0.944
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c12001098.png ; $$\rho _ { j \overline { k } } = \partial ^ { 2 } \rho / \partial z _ { j } \partial z _ { k }$$ ; confidence 0.185
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110470/c11047054.png ; $$h : H \rightarrow ( C \bigotimes T M ) / ( H \oplus \overline { H } )$$ ; confidence 0.332
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110480/c11048046.png ; $$D ^ { \perp }$$ ; confidence 0.893
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110010/c1100106.png ; $$T : A _ { j } \rightarrow A$$ ; confidence 0.526
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110030/c11003017.png ; $$v = u ^ { 2 } +$$ ; confidence 0.633
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110050/c11005025.png ; $$X _ { t } = 2.632 + 1.492 X _ { t - 1 } - 1.324 X _ { t - 2 } + \epsilon _ { t } ^ { ( 2 ) }$$ ; confidence 0.949
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110050/c11005010.png ; $$CW ( 9.63 )$$ ; confidence 0.827
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020140/c02014016.png ; $$\Sigma _ { 12 } = \Sigma _ { 2 } ^ { T }$$ ; confidence 0.747
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020160/c02016022.png ; $$K _ { X } K _ { X }$$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020190/c02019023.png ; $$C A$$ ; confidence 0.232
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020230/c02023043.png ; $$X \backslash K _ { X }$$ ; confidence 0.934
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020280/c020280124.png ; $$E ( \lambda )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020280/c020280177.png ; $$\underline { C } ( E ) = \operatorname { sup } C ( K )$$ ; confidence 0.963
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110080/c11008041.png ; $$f$$ ; confidence 0.647
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110060/c11006048.png ; $$0 \leq j < k$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004012.png ; $$( f \in H _ { C } ( D ) )$$ ; confidence 0.513
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004049.png ; $$f \in H _ { c } ( D )$$ ; confidence 0.898
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004038.png ; $$\rho \in C ^ { 2 } ( \overline { \Omega } )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020420/c0204203.png ; $$E \times E$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020540/c020540218.png ; $$\nabla ^ { \prime } = \nabla$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020540/c020540105.png ; $$s _ { m } = r - s - \operatorname { rank } M _ { m } - 1$$ ; confidence 0.443
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020540/c020540177.png ; $$\epsilon ( \sigma ) = 1$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020550/c02055049.png ; $$1$$ ; confidence 0.897
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020550/c02055058.png ; $$t \otimes _ { k } K$$ ; confidence 0.618
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020640/c02064012.png ; $$\mu = \beta \nu$$ ; confidence 0.406
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020640/c02064013.png ; $$\lambda : V \rightarrow P$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020650/c0206506.png ; $$1 / \mu = d S / d \sigma$$ ; confidence 0.936
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130040/c1300406.png ; $$\psi ( z ) : = \frac { d } { d z } \{ \operatorname { log } \Gamma ( z ) \} = \frac { \Gamma ^ { \prime } ( z ) } { \Gamma ( z ) }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130040/c1300407.png ; $$\operatorname { log } \Gamma ( z ) = \int _ { 1 } ^ { z } \psi ( t ) d t$$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020740/c020740168.png ; $$F ( 1 _ { A } ) = 1 _ { F A }$$ ; confidence 0.901
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020740/c020740394.png ; $$( \alpha \circ \beta ) ( c ) _ { d x } = \sum _ { b } \alpha ( b ) _ { a } \beta ( c ) _ { b }$$ ; confidence 0.330
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020740/c020740146.png ; $$\alpha \rightarrow \dot { b }$$ ; confidence 0.200
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020740/c020740328.png ; $$e \in E$$ ; confidence 0.839
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020740/c020740324.png ; $$( \alpha _ { e } ) _ { é \in E }$$ ; confidence 0.403
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020740/c020740318.png ; $$Z [ X _ { é } : e \in E$$ ; confidence 0.114
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007011.png ; $$1 \leq i \leq n - 1$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007055.png ; $$Ab ^ { Z C } \approx Ab ^ { C }$$ ; confidence 0.662
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020920/c02092013.png ; $$\Omega _ { 0 } \times \{ x _ { 0 }$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020920/c02092043.png ; $$x = x ^ { 0 }$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020890/c020890175.png ; $$F ^ { - } ( \zeta _ { 0 } )$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020890/c020890110.png ; $$\psi = \psi ( s )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020950/c0209509.png ; $$u ( x _ { 0 } ) = u _ { 0 }$$ ; confidence 0.932
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020950/c02095032.png ; $$L u = \sum _ { | \alpha | \leq m } \alpha _ { \alpha } ( x ) \frac { \partial ^ { \alpha } u } { \partial x ^ { \alpha } } = f ( x )$$ ; confidence 0.358
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020960/c02096032.png ; $$y _ { n + 1 } = y _ { n } + \frac { h } { 2 } ( f _ { n + 1 } + f _ { n } )$$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021040/c02104082.png ; $$- w$$ ; confidence 0.598
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021040/c02104057.png ; $$- u _ { 3 }$$ ; confidence 0.803
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008028.png ; $$A _ { j } A _ { k l } = A _ { k l } A _ { j }$$ ; confidence 0.372
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021060/c02106028.png ; $$V ( t ) = - V ( s )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130050/c13005021.png ; $$\Gamma$$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021100/c02110012.png ; $$x \in \operatorname { Dom } A$$ ; confidence 0.300
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021130/c02113024.png ; $$\partial I ^ { p }$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021180/c021180110.png ; $$E \| X _ { k } \| ^ { 3 + \alpha } < \infty$$ ; confidence 0.604
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110130/c11013026.png ; $$f \in C ^ { k }$$ ; confidence 0.918
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110160/c11016063.png ; $$( a b \alpha ) ^ { \alpha } = \alpha ^ { \alpha } b ^ { \alpha } \alpha ^ { \alpha }$$ ; confidence 0.173
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110170/c1101705.png ; $$D _ { p }$$ ; confidence 0.949
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110170/c11017044.png ; $$C \rho _ { p } C ^ { \prime }$$ ; confidence 0.884
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021470/c02147033.png ; $$\tilde { Y } \square _ { j } ^ { ( k ) } \in Y _ { j }$$ ; confidence 0.172
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021480/c02148045.png ; $$b \neq 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021500/c02150017.png ; $$y ^ { \prime \prime } - y > f ( x )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021520/c02152013.png ; $$V ( \Lambda ^ { \prime } ) \otimes V ( \Lambda ^ { \prime \prime } )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021550/c0215505.png ; $$\phi : \mathfrak { g } \rightarrow \mathfrak { g } ( V )$$ ; confidence 0.515
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021570/c02157044.png ; $$\chi \pi _ { \alpha }$$ ; confidence 0.268
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021570/c02157034.png ; $$\pi _ { 0 }$$ ; confidence 0.537
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021600/c02160021.png ; $$A$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021610/c02161069.png ; $$\alpha _ { \nu } ( x ) \rightarrow b _ { \nu } ( x ^ { \prime } )$$ ; confidence 0.798
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021620/c02162068.png ; $$\pi _ { \mathscr { q } } ( F )$$ ; confidence 0.437
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021620/c02162091.png ; $$c _ { q } ( \xi ) = \kappa ( \eta ^ { q } )$$ ; confidence 0.820
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021620/c021620209.png ; $$B G$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021620/c02162087.png ; $$\kappa ( \eta ^ { q } ) \in H ^ { 2 q } ( B )$$ ; confidence 0.856
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021650/c02165039.png ; $$E X ^ { 2 n } < \infty$$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021650/c02165011.png ; $$t _ { k } \in R ^ { 1 }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021720/c02172031.png ; $$b _ { k } ^ { \prime } = ( - 1 ) ^ { k + 1 } b _ { k }$$ ; confidence 0.930
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021760/c02176012.png ; $$X = \frac { 1 } { n } \sum _ { j = 1 } ^ { n } X$$ ; confidence 0.670
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021760/c0217608.png ; $$p ( x ) = \frac { 1 } { ( 2 \pi ) ^ { 3 / 2 } \sigma ^ { 2 } } \operatorname { exp } \{ - \frac { 1 } { 2 \sigma ^ { 2 } } ( x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } + x _ { 3 } ^ { 2 } ) \}$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c130070146.png ; $$k ( C ^ { * } )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007063.png ; $$g = 0 \Rightarrow c$$ ; confidence 0.793
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021850/c0218501.png ; $$\tau = \tau ( E )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130090/c13009010.png ; $$x _ { j } = \operatorname { cos } ( \pi j / N )$$ ; confidence 0.826
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022030/c02203033.png ; $$C _ { \omega }$$ ; confidence 0.073
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022040/c02204033.png ; $$h ^ { * } ( pt )$$ ; confidence 0.903
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022040/c02204098.png ; $$\Omega _ { 2 n } ^ { 2 } \rightarrow Z$$ ; confidence 0.476
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022110/c02211060.png ; $$\xi _ { 1 } ^ { 2 } + \ldots + \xi _ { k - m - 1 } ^ { 2 } + \mu _ { 1 } \xi _ { k - m } ^ { 2 } + \ldots + \mu _ { m } \xi _ { k - 1 } ^ { 2 }$$ ; confidence 0.818
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120160/c12016016.png ; $$j = 1 : n$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110210/c11021043.png ; $$T ( 0 ) = 0$$ ; confidence 0.574
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110200/c11020072.png ; $$\lambda \in \Lambda$$ ; confidence 0.954
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130100/c13010015.png ; $$f = \sum _ { i = 1 } ^ { n } \alpha _ { i } \chi _ { i }$$ ; confidence 0.422
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022290/c02229022.png ; $$+ \frac { 1 } { 2 } \sum _ { 0 < u \leq \sqrt { x / 3 } } ( [ \sqrt { x - 2 u ^ { 2 } } ] - u ) + O ( \sqrt { x } )$$ ; confidence 0.498
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022290/c0222907.png ; $$\theta \leq 1 / 2$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022330/c0223301.png ; $$a ( r )$$ ; confidence 0.924
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022370/c02237023.png ; $$N = L . L$$ ; confidence 0.482
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022370/c02237063.png ; $$Q / Z$$ ; confidence 0.664
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022400/c02240053.png ; $$( k \times n )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022420/c02242028.png ; $$\phi ( x ) = [ ( 1 - x ) ( 1 + x ) ] ^ { 1 / 2 }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022420/c02242026.png ; $$\phi ( x ) \equiv 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022420/c02242019.png ; $$\phi ( x ) = ( 1 - x ) ^ { \alpha } ( 1 + x ) ^ { \beta }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022450/c0224501.png ; $$x ( t ) : R \rightarrow R ^ { n }$$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110250/c1102508.png ; $$20$$ ; confidence 0.225
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022500/c02250014.png ; $$j \leq n$$ ; confidence 0.544
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022530/c02253039.png ; $$[ \gamma ]$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022570/c0225705.png ; $$x \in D _ { A }$$ ; confidence 0.542
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022570/c0225702.png ; $$x _ { n } \in D _ { A }$$ ; confidence 0.553
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022660/c022660300.png ; $$K ( f )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022660/c022660241.png ; $$C = C ( f )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022660/c022660281.png ; $$f : D \rightarrow \Omega$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022660/c02266075.png ; $$\mu ( E ) = \mu _ { 1 } ( E ) = 0$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022660/c02266091.png ; $$\mu _ { 2 } ( C R ) = 0$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022660/c022660219.png ; $$F = \{ f ( z ) \}$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022690/c02269052.png ; $$\Delta = \tilde { A } + \hat { B } - \hat { C }$$ ; confidence 0.152
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022700/c02270026.png ; $$g : Y \rightarrow Z$$ ; confidence 0.951
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110290/c11029014.png ; $$Q ( t ) : S ^ { \prime } \rightarrow S ^ { \prime }$$ ; confidence 0.764
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780429.png ; $$\phi ^ { h } ( pt )$$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780377.png ; $$1 B S G$$ ; confidence 0.389
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c02278052.png ; $$N \gg n$$ ; confidence 0.849
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c02278060.png ; $$B O _ { m } \times B O _ { n } \rightarrow B O _ { m } + n$$ ; confidence 0.775
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780545.png ; $$B P \square ^ { * } ( B P )$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780129.png ; $$\Omega _ { f r } ^ { i }$$ ; confidence 0.443
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c02278058.png ; $$O ( X ) = \oplus _ { n = - \infty } ^ { + \infty } O ^ { n } ( X )$$ ; confidence 0.863
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780210.png ; $$x _ { i } / ( e ^ { x _ { i } } - 1 )$$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780302.png ; $$( S _ { \omega } ^ { c } ( e ) T ) [ M ] \in Z$$ ; confidence 0.570
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780356.png ; $$\Omega$$ ; confidence 0.892
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780445.png ; $$M U ^ { * } ( X )$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780177.png ; $$( n )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780128.png ; $$\Omega _ { fr } ^ { - i } = \Omega _ { i } ^ { fr } = \pi _ { i + N } ( S ^ { N } )$$ ; confidence 0.922
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780207.png ; $$e ^ { x _ { i } } - 1$$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780328.png ; $$im ( \Omega _ { S C } \rightarrow \Omega _ { O } )$$ ; confidence 0.230
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022800/c022800161.png ; $$\partial N$$ ; confidence 0.677
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022860/c02286015.png ; $$b _ { i + 1 } \ldots b _ { j }$$ ; confidence 0.553
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022890/c02289075.png ; $$l _ { i } ( P ) \leq l _ { i } < l _ { i } ( P ) + 1$$ ; confidence 0.413
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022920/c02292048.png ; $$V _ { 3 }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022920/c02292049.png ; $$\operatorname { lm } c _ { 3 } = 0$$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022930/c0229306.png ; $$\{ x _ { n } > 0 \}$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022930/c02293015.png ; $$u ( x ) = w ( x _ { n } ) \operatorname { exp } i ( x _ { 1 } \xi _ { 1 } + \ldots + x _ { n - 1 } \xi _ { n - 1 } )$$ ; confidence 0.744
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022940/c02294010.png ; $$M$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023050/c023050103.png ; $$\operatorname { cd } _ { p } ( X ) \leq \operatorname { cohcd } ( X ) + 1$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023050/c02305060.png ; $$( U ) = n - 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023050/c02305085.png ; $$cd _ { l } ( Spec A )$$ ; confidence 0.637
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023120/c02312031.png ; $$x g = \lambda x$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023140/c023140243.png ; $$u \mapsto \rho ( u ) - \operatorname { Tr } ( \text { ad } u ) \in \operatorname { End } _ { K } ( M )$$ ; confidence 0.830
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023110/c02311056.png ; $$A ^ { G } = \{ \alpha \in A : g \alpha = \alpha \text { for all } g \in G \}$$ ; confidence 0.750
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023110/c023110101.png ; $$Z G$$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023150/c02315041.png ; $$f : S ^ { m } \rightarrow S ^ { n }$$ ; confidence 0.195
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023150/c023150291.png ; $$\pi _ { n } ( E ) = \pi$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023150/c02315068.png ; $$\square ^ { 1 } P ^ { i } = P$$ ; confidence 0.776
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023150/c023150156.png ; $$i ^ { * } ( \phi ) = 0$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023150/c023150259.png ; $$\beta \circ \beta = 0$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023150/c023150187.png ; $$\alpha : H ^ { n } ( : Z ) \rightarrow H ^ { n + 3 } ( : Z _ { 2 } )$$ ; confidence 0.262
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023180/c0231806.png ; $$\pi ^ { 1 } ( X )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130150/c1301504.png ; $$C ^ { \infty } ( D ( \Omega ) )$$ ; confidence 0.935
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023250/c023250173.png ; $$\beta _ { 0 }$$ ; confidence 0.851
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023250/c023250187.png ; $$[ \sigma ] = [ \alpha _ { 1 } ^ { \alpha _ { 1 } } \ldots a _ { n } ^ { \alpha _ { n } } ]$$ ; confidence 0.729
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023270/c0232708.png ; $$\overline { \overline { A } } = \vec { A }$$ ; confidence 0.649
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023380/c02338015.png ; $$\phi \in \Phi$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023380/c023380197.png ; $$F \subset U$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023380/c02338044.png ; $$x 0$$ ; confidence 0.689
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023380/c023380172.png ; $$C ( S ^ { n } )$$ ; confidence 0.498
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023380/c02338039.png ; $$f \in L _ { 1 } ( G )$$ ; confidence 0.969
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023530/c023530133.png ; $$\Pi ^ { N } \tau$$ ; confidence 0.183
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023550/c023550235.png ; $$\beta Y \backslash Y$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023550/c023550175.png ; $$X = 0$$ ; confidence 0.554
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023550/c023550172.png ; $$\overline { f } : \mu X \rightarrow \mu Y$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023620/c0236203.png ; $$| \alpha ( z ) |$$ ; confidence 0.916
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023890/c02389043.png ; $$\{ d F _ { i } \} _ { 1 } ^ { m }$$ ; confidence 0.930
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024100/c024100277.png ; $$\partial _ { r }$$ ; confidence 0.315
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024100/c024100241.png ; $$f : K \rightarrow K$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024110/c02411026.png ; $$d = ( d _ { n } )$$ ; confidence 0.939
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024120/c02412032.png ; $$\pi J ( s ) = \operatorname { sin } \pi s \int _ { r } ^ { \infty } \delta ^ { s - 1 } f ( - \delta ) d \delta + \frac { r ^ { s } } { 2 } \int _ { - \pi } ^ { \pi } e ^ { i \theta s } f ( r e ^ { i \theta } ) d \theta$$ ; confidence 0.764
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024120/c02412084.png ; $$\int _ { - \infty } ^ { \infty } ( P ( x ) / Q ( x ) ) d x$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024120/c02412065.png ; $$J ( s ) = \operatorname { lim } J _ { N } ( s ) = 2 ( 2 \pi ) ^ { s - 1 } \zeta ( 1 - s ) \operatorname { sin } \frac { \pi s } { 2 }$$ ; confidence 0.964
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024120/c02412030.png ; $$f ( z ) = 1 / ( e ^ { z } - 1 )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024160/c02416048.png ; $$O _ { A } = O _ { D } / J | _ { A }$$ ; confidence 0.748
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110330/c1103302.png ; $$DT ( S )$$ ; confidence 0.583
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110330/c1103309.png ; $$p _ { i } \in S$$ ; confidence 0.931
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024450/c0244507.png ; $$U ( A ) \subset Y$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024510/c0245107.png ; $$P ( A | B ) = \frac { P ( A \cap B ) } { P ( B ) }$$ ; confidence 0.724
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024520/c02452065.png ; $$x _ { 0 } \in V ^ { n }$$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024540/c0245407.png ; $$\dot { \phi } = \omega$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024670/c02467021.png ; $$A _ { 3 }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024730/c02473061.png ; $$\Omega ^ { \prime } = \| \Omega _ { \alpha } ^ { \prime \beta } \|$$ ; confidence 0.913
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024730/c024730113.png ; $$P _ { i j } = \frac { 1 } { n - 2 } R _ { j } - \delta _ { j } ^ { i } \frac { R } { 2 ( n - 1 ) ( n - 2 ) }$$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180209.png ; $$\varepsilon$$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180501.png ; $$g \in S ^ { 2 } \varepsilon$$ ; confidence 0.445
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180506.png ; $$N = N \times \{ 1 \} \times \{ 0 \}$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180420.png ; $$C ^ { \infty } ( \tilde { N } )$$ ; confidence 0.330
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180152.png ; $$\gamma$$ ; confidence 0.764
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180182.png ; $$\tau _ { 2 } \Theta = - \Theta$$ ; confidence 0.618
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024780/c02478054.png ; $$f ^ { \prime } ( z _ { 0 } )$$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024780/c024780240.png ; $$0 < \beta \leq 2 \pi$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024780/c024780261.png ; $$( x ^ { 2 } / a ^ { 2 } ) + ( y ^ { 2 } / b ^ { 2 } ) = 1$$ ; confidence 0.891
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024780/c024780245.png ; $$\operatorname { arg } z = c$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024790/c02479065.png ; $$f ( \zeta )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024800/c02480058.png ; $$D \subset D _ { 1 }$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024820/c02482046.png ; $$\leq ( n + 1 ) ( n + 2 ) / 2$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024850/c024850206.png ; $$f ^ { \prime } ( x _ { 1 } ) \equiv 0$$ ; confidence 0.424
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024850/c02485065.png ; $$A . B$$ ; confidence 0.944
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024850/c024850182.png ; $$m = p _ { 1 } ^ { \alpha _ { 1 } } \ldots p _ { s } ^ { \alpha _ { S } }$$ ; confidence 0.462
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024890/c02489056.png ; $$\mu ( d )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024890/c0248905.png ; $$\alpha ( x ) - b ( x ) = f ( x ) g ( x ) + p h ( x )$$ ; confidence 0.849
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024900/c02490030.png ; $$q = p ^ { r }$$ ; confidence 0.892
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024990/c02499018.png ; $$\int _ { - \pi } ^ { \pi } f ( x ) d x = 0$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025020/c02502055.png ; $$r \uparrow 1$$ ; confidence 0.659
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130190/c13019046.png ; $$X = R ^ { n }$$ ; confidence 0.975
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025130/c0251306.png ; $$f _ { i } : D ^ { n } \rightarrow M _ { i }$$ ; confidence 0.449
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025130/c02513010.png ; $$f _ { 2 } \circ f _ { 1 } ^ { - 1 }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025140/c025140162.png ; $$X \in V ( B )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025140/c025140160.png ; $$E = T B$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025140/c025140196.png ; $$X : B \rightarrow T B$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025150/c02515011.png ; $$Y \in T _ { y } ( P )$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025170/c02517037.png ; $$\omega ^ { k } = d x ^ { k }$$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025180/c02518080.png ; $$f _ { x } ^ { - 1 }$$ ; confidence 0.443
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025180/c02518044.png ; $$X _ { X } \in T _ { X } ( M )$$ ; confidence 0.414
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025180/c02518096.png ; $$T _ { s ( x ) } ( E ) = \Delta _ { s ( x ) } \oplus T _ { s ( x ) } ( F _ { x } )$$ ; confidence 0.402
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120190/c12019044.png ; $$T ( M )$$ ; confidence 0.884
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025350/c025350104.png ; $$B \rightarrow H$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025350/c025350101.png ; $$E _ { 1 } \rightarrow E _ { 1 }$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025420/c025420100.png ; $$\neg \neg \exists x R \supset \exists x R$$ ; confidence 0.760
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025440/c0254401.png ; $$\int _ { \alpha } ^ { b } p ( t ) \operatorname { ln } | t - t _ { 0 } | d t = f ( t _ { 0 } ) + C$$ ; confidence 0.687
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025440/c02544025.png ; $$D ^ { + } = \cup _ { k = 1 } ^ { m } D _ { k }$$ ; confidence 0.835
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025440/c02544057.png ; $$\forall x \in D _ { k } : \mu _ { k } \Delta u + ( \lambda _ { k } + \mu _ { k } ) \text { grad div } u = 0$$ ; confidence 0.915
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025450/c02545035.png ; $$T ^ { * }$$ ; confidence 0.527
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025470/c02547051.png ; $$\alpha \wedge ( d \alpha ) ^ { n }$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025470/c02547063.png ; $$\alpha = d t + \sum p _ { i } d q _ { i }$$ ; confidence 0.858
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025470/c02547031.png ; $$\alpha \wedge ( d \alpha ) ^ { s } ( x ) \neq 0$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120200/c12020014.png ; $$W ^ { m + 1 }$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c120210117.png ; $$\Lambda _ { n } ( \theta ) - h ^ { \prime } \Delta _ { n } ( \theta ) \rightarrow - \frac { 1 } { 2 } h ^ { \prime } \Gamma ( \theta ) h$$ ; confidence 0.843
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025600/c02560048.png ; $$u ^ { k } = u ^ { k - 1 } - \Delta \lambda _ { k } \phi ^ { \prime } ( u ^ { k - 1 } ) ^ { - 1 } \phi ( u ^ { 0 } )$$ ; confidence 0.687
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025600/c02560042.png ; $$\frac { d u } { d \lambda } = - \phi ^ { \prime } ( u ) ^ { - 1 } \phi ( u ^ { 0 } )$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025640/c0256402.png ; $$\{ \alpha _ { n } \} _ { n = 0 } ^ { \omega } \quad \text { and } \quad \{ b _ { n } \} _ { n = 1 } ^ { \omega }$$ ; confidence 0.788
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025650/c02565066.png ; $$D \subset R$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025700/c02570021.png ; $$I \rightarrow \cup _ { i \in l } J _ { i }$$ ; confidence 0.225
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025710/c02571015.png ; $$f ^ { - 1 } ( F )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025710/c0257107.png ; $$U = U ( x _ { 0 } )$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025720/c02572034.png ; $$y _ { 0 } = A _ { x }$$ ; confidence 0.344
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025720/c02572035.png ; $$B \circ A$$ ; confidence 0.963
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025720/c02572060.png ; $$x - y \in U$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025830/c02583071.png ; $$i B _ { 0 }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025890/c02589013.png ; $$( T ^ { * } ( t ) = T ( t ) )$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025920/c02592019.png ; $$631$$ ; confidence 0.381
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025970/c02597042.png ; $$e ^ { i } ( e _ { j } ) = \delta _ { j } ^ { s }$$ ; confidence 0.182
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026010/c026010134.png ; $$\mathfrak { A } _ { E }$$ ; confidence 0.121
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026010/c026010308.png ; $$v _ { ( E ) } = v$$ ; confidence 0.188
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026010/c026010417.png ; $$\rho < 1$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026010/c026010468.png ; $$P s$$ ; confidence 0.529
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026010/c026010588.png ; $$J ( \alpha )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026010/c02601042.png ; $$N = N _ { 0 }$$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026010/c026010556.png ; $$d y _ { t } = h ( x _ { t } ) d t + d w _ { t } ^ { 0 }$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026040/c02604071.png ; $$A _ { n } x _ { n } = y _ { n }$$ ; confidence 0.869
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026040/c02604027.png ; $$P Q$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026040/c02604025.png ; $$A _ { n } : E _ { n } \rightarrow F _ { n }$$ ; confidence 0.561
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026230/c02623020.png ; $$c _ { 1 } = f ^ { \prime } ( 0 ) = 1$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026230/c02623013.png ; $$\int _ { - \pi } ^ { \pi } d \mu ( \theta ) = 1$$ ; confidence 0.969
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026250/c0262508.png ; $$( f _ { 1 } + f _ { 2 } ) ( x ) = f _ { 1 } ( x ) + f _ { 2 } ( x )$$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110400/c110400102.png ; $$M ^ { \perp } = \{ x \in G$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026390/c026390117.png ; $$r _ { u } \times r _ { v } \neq 0$$ ; confidence 0.643
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026430/c02643058.png ; $$F [ f ^ { * } g ] = \sqrt { 2 \pi } F [ f ] F [ g ]$$ ; confidence 0.818
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026430/c02643025.png ; $$F [ f ] = \frac { F [ g ] } { 1 - \sqrt { 2 \pi } F [ K ] }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026450/c02645091.png ; $$X _ { 1 }$$ ; confidence 0.237
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026450/c02645033.png ; $$\sum _ { K \in \mathscr { K } } \lambda _ { K } \chi _ { K } ( i ) = \chi _ { I } ( i ) \quad \text { for all } i \in I$$ ; confidence 0.223
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026460/c02646046.png ; $$\{ x _ { k } \}$$ ; confidence 0.963
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026460/c02646028.png ; $$x _ { k + 1 } = x _ { k } - \alpha _ { k } p _ { k }$$ ; confidence 0.819
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026460/c0264605.png ; $$\alpha _ { i } < b _ { i }$$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026460/c02646017.png ; $$i _ { k } = k - n [ k / n ] + 1$$ ; confidence 0.964
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026480/c0264808.png ; $$\alpha _ { i } : A _ { i } \rightarrow X$$ ; confidence 0.918
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026480/c02648027.png ; $$\pi _ { i } : S \rightarrow A$$ ; confidence 0.579
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026480/c02648015.png ; $$\prod _ { i \in l } ^ { * } A _ { i }$$ ; confidence 0.474
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110410/c11041079.png ; $$A ^ { * } B$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110410/c11041043.png ; $$C X Y$$ ; confidence 0.226
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110410/c11041077.png ; $$B _ { 1 }$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110410/c11041081.png ; $$\{ X _ { t } : t \in T \}$$ ; confidence 0.835
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110430/c11043040.png ; $$m ( S ) ^ { 2 } > ( 2 k + 1 ) ( n - k ) + \frac { k ( k + 1 ) } { 2 } - \frac { 2 ^ { k } n ^ { 2 k + 1 } } { m ( 2 k ) ! \left( \begin{array} { l } { n } \\ { k } \end{array} \right) }$$ ; confidence 0.753
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026580/c0265803.png ; $$\eta _ { Y | X } ^ { 2 } = 1 - E [ \frac { D ( Y | X ) } { D Y } ]$$ ; confidence 0.635
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026600/c026600121.png ; $$\operatorname { lm } z ( x ) = 1$$ ; confidence 0.908
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110440/c11044082.png ; $$C ( n ) = 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026830/c02683020.png ; $$\sum _ { 2 } = \sum _ { \nu \in \langle \nu \rangle } U _ { 2 } ( n - D \nu )$$ ; confidence 0.960
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026870/c02687095.png ; $$D U$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026870/c026870129.png ; $$( \nabla _ { X } U ) _ { p }$$ ; confidence 0.933
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026870/c026870106.png ; $$e _ { i } = \partial / \partial x ^ { i } | _ { p }$$ ; confidence 0.599
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026910/c02691013.png ; $$\Gamma ( C ) = V$$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026970/c02697049.png ; $$| w | < 1 / 16$$ ; confidence 0.877
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130250/c13025017.png ; $$Y _ { j } = i$$ ; confidence 0.850
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026980/c02698053.png ; $$E _ { 8 }$$ ; confidence 0.860
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027000/c02700011.png ; $$\frac { F _ { n } ( - x ) } { \Phi ( - x ) } = \operatorname { exp } \{ - \frac { x ^ { 3 } } { \sqrt { n } } \lambda ( - \frac { x } { \sqrt { n } } ) \} [ 1 + O ( \frac { x } { \sqrt { n } } ) ]$$ ; confidence 0.444
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027000/c0270004.png ; $$E _ { e } ^ { t X } 1$$ ; confidence 0.078
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026044.png ; $$1 \leq n \leq N$$ ; confidence 0.763
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026032.png ; $$V _ { 0 } ^ { n } = V _ { j } ^ { n } = 0$$ ; confidence 0.626
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110490/c1104902.png ; $$\sqrt { 2 }$$ ; confidence 0.191
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120270/c1202706.png ; $$t \mapsto \gamma ( t ) = \operatorname { exp } _ { p } ( t v )$$ ; confidence 0.936
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c1202805.png ; $$X *$$ ; confidence 0.383
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c1202808.png ; $$F T op$$ ; confidence 0.332
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027170/c02717082.png ; $$q = 59$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027180/c027180124.png ; $$7$$ ; confidence 0.254
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027180/c027180172.png ; $$M _ { k } = C _ { k }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027180/c027180181.png ; $$E _ { x } ( s )$$ ; confidence 0.467
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027180/c02718064.png ; $$H ( K )$$ ; confidence 0.395
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027210/c02721080.png ; $$N = \mu / ( n + 1 )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027210/c02721040.png ; $$P ( x ) = \sum _ { j = 1 } ^ { \mu } L j ( x ) f ( x ^ { ( j ) } )$$ ; confidence 0.718
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027240/c02724015.png ; $$x ^ { 3 } + y ^ { 3 } - 3 a x y = 0$$ ; confidence 0.887
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027270/c02727013.png ; $$j = \frac { 1728 g _ { 2 } ^ { 3 } } { g _ { 2 } ^ { 3 } - 27 g _ { 3 } ^ { 2 } }$$ ; confidence 0.284
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030053.png ; $$\sum _ { i = 1 } ^ { n } S _ { i } S _ { i } ^ { * } < I$$ ; confidence 0.253
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030069.png ; $$n = \infty$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030087.png ; $$T _ { 1 } ( H )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030042.png ; $$u : H \rightarrow H ^ { \prime }$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120310/c12031028.png ; $$| \alpha | = \sum _ { l = 1 } ^ { d ^ { 2 } } \alpha _ { l }$$ ; confidence 0.447
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027320/c027320130.png ; $$C = R _ { k m m } ^ { i } R _ { k } ^ { k k m }$$ ; confidence 0.081
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027480/c027480106.png ; $$\Sigma _ { S }$$ ; confidence 0.760
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027480/c027480102.png ; $$( \sigma ^ { t } f ) ( t ^ { \prime } ) = f ( t + t ^ { \prime } )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110500/c11050032.png ; $$H C ^ { 0 } ( A )$$ ; confidence 0.945
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027570/c02757085.png ; $$z$$ ; confidence 0.525
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027600/c02760032.png ; $$( u = const )$$ ; confidence 0.538
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027600/c0276008.png ; $$- \infty < z < \infty$$ ; confidence 0.577
+. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027620/c0276205.png ; $$F \in L ^ { * }$$ ; confidence 0.961
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030060/d03006013.png ; $$+ \frac { 1 } { 2 \alpha } \int _ { x - w t } ^ { x + c t } \psi ( \xi ) d \xi + \frac { 1 } { 2 } [ \phi ( x + a t ) + \phi ( x - a t ) ]$$ ; confidence 0.187
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030020/d03002056.png ; $$D x$$ ; confidence 0.713
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030020/d030020144.png ; $$\operatorname { gr } D _ { X }$$ ; confidence 0.395
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030020/d03002094.png ; $$f ^ { * } N = O _ { X } \otimes _ { f } - 1 _ { O _ { Y } } f ^ { - 1 } N$$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002092.png ; $$V _ { V }$$ ; confidence 0.082
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020131.png ; $$= g ( \overline { u } _ { 1 } ) - \overline { q } = g ( \overline { u } _ { 1 } ) - v _ { M }$$ ; confidence 0.711
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020174.png ; $$( US )$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002050.png ; $$( L )$$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002046.png ; $$= \operatorname { min } _ { k \in P } c ^ { T } x ^ { ( k ) } + u _ { 1 } ^ { T } ( A _ { 1 } x ^ { ( k ) } - b _ { 1 } )$$ ; confidence 0.488
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130020/d13002017.png ; $$0 \leq k < 1$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030210/d03021016.png ; $$2$$ ; confidence 0.110
+. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110020/d11002099.png ; $$f : S \rightarrow C$$ ; confidence 0.674
+. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110040/d1100407.png ; $$S _ { p } ^ { n + p } ( c ) = \{ x \in R _ { p } ^ { n + p + 1 }$$ ; confidence 0.809
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030250/d03025016.png ; $$u _ { n } + 1 - k$$ ; confidence 0.616
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030280/d0302808.png ; $$\tau _ { n } ( t ) = \frac { 1 } { 2 \pi } \frac { 2 ^ { 2 n } ( n ! ) ^ { 2 } } { ( 2 n ) ! } \operatorname { cos } ^ { 2 n } \frac { t } { 2 }$$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110080/d11008067.png ; $$= d ( w ^ { H _ { i } } | v ^ { H _ { i } } ) \cdot e ( w ^ { H _ { i } } | v ^ { H _ { i } } ) . f ( w ^ { H _ { i } } | v ^ { H _ { i } } )$$ ; confidence 0.435
+. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110090/d11009089.png ; $$D \subseteq g H g ^ { - 1 }$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030620/d03062019.png ; $$\alpha \in C \cup \{ \infty \}$$ ; confidence 0.176
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070037.png ; $$\pi ^ { \prime } : X ^ { \prime } \rightarrow S ^ { \prime }$$ ; confidence 0.952
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700139.png ; $$\kappa ^ { \prime } \cong \kappa \otimes O \Lambda$$ ; confidence 0.541
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030790/d0307909.png ; $$\lambda ^ { m }$$ ; confidence 0.955
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030870/d03087032.png ; $$\pi ( \chi )$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030870/d03087020.png ; $$C ^ { \infty } ( G )$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110110/d11011084.png ; $$L \cup O$$ ; confidence 0.130
+. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110110/d11011051.png ; $$M _ { 1 } = H \cap _ { k \tau _ { S } } H ^ { \prime }$$ ; confidence 0.307
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130050/d13005022.png ; $$m - 2 r$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d130060103.png ; $$Z \in X$$ ; confidence 0.820
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d13006091.png ; $$m _ { B } ( A ) = 0$$ ; confidence 0.968
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d13006089.png ; $$m B$$ ; confidence 0.535
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031010/d03101088.png ; $$S ^ { 4 k - 1 }$$ ; confidence 0.950
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d13008069.png ; $$H = C ^ { n }$$ ; confidence 0.847
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d130080108.png ; $$F \in Hol ( D )$$ ; confidence 0.805
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031100/d0311001.png ; $$\zeta ( s ) = \sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { s } }$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031250/d03125086.png ; $$\Omega _ { X / Y } ^ { 1 }$$ ; confidence 0.919
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031250/d03125044.png ; $$\phi : A \rightarrow A$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031280/d03128063.png ; $$s ^ { \prime } : Y ^ { \prime } \rightarrow X ^ { \prime }$$ ; confidence 0.953
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031280/d031280173.png ; $$R ^ { i } F = H ^ { i } \circ R ^ { * } F$$ ; confidence 0.941
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031280/d03128077.png ; $$f t = g t$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031280/d031280129.png ; $$f : X ^ { \cdot } \rightarrow Y$$ ; confidence 0.209
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031380/d031380303.png ; $$\Pi \stackrel { D } { 3 } = F _ { \sigma \delta }$$ ; confidence 0.232
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031380/d031380332.png ; $$E = N$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031380/d031380384.png ; $$\sum _ { \mathfrak { D } _ { 1 } ^ { 1 } } ( E \times N ^ { N } )$$ ; confidence 0.290
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031380/d031380296.png ; $$\sum _ { \sim } D _ { n + 1 } ^ { 0 }$$ ; confidence 0.204
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031420/d0314205.png ; $$k [ ( T _ { i j } ) _ { 1 \leq i \leq d } ]$$ ; confidence 0.679
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031470/d0314706.png ; $$| \hat { b } _ { n } | = 1$$ ; confidence 0.209
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031540/d03154015.png ; $$G r$$ ; confidence 0.809
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130090/d13009046.png ; $$1 \leq u \leq \operatorname { exp } ( \operatorname { log } ( 3 / 5 ) - \epsilon _ { y } )$$ ; confidence 0.512
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130090/d13009024.png ; $$1 \leq u \leq 2$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130090/d13009051.png ; $$u > 1$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031680/d03168056.png ; $$q _ { 2 } \neq q _ { 1 }$$ ; confidence 0.828
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031680/d0316809.png ; $$\Delta ^ { m } y _ { n } = \sum _ { k = 0 } ^ { m } ( - 1 ) ^ { m - k } \left( \begin{array} { c } { m } \\ { k } \end{array} \right) y _ { n + k }$$ ; confidence 0.786
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031730/d03173088.png ; $$| u - v | \leq \operatorname { inf } _ { w ^ { \prime } \in K } | u - w |$$ ; confidence 0.210
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031750/d03175051.png ; $$Z _ { h }$$ ; confidence 0.217
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031750/d03175013.png ; $$\overline { G } = G + \Gamma$$ ; confidence 0.752
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031770/d03177042.png ; $$t = t _ { 0 } = x _ { 0 } ( 0 )$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830278.png ; $$u \leq \theta u$$ ; confidence 0.794
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830344.png ; $$\operatorname { rank } ( A _ { i } ) = \operatorname { rank } ( B _ { i } )$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830290.png ; $$A = \sum _ { i = 0 } ^ { d } A _ { i } u _ { A } ^ { i }$$ ; confidence 0.523
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830239.png ; $$G ( G / F _ { 1 } ) = G _ { 1 }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830269.png ; $$\operatorname { ord } ( \theta ) = \sum e$$ ; confidence 0.833
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830152.png ; $$G \neq 0$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830116.png ; $$\{ A \}$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830267.png ; $$\theta = \Pi _ { i } \partial _ { i } ^ { e _ { i } ^ { e _ { i } } }$$ ; confidence 0.142
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031850/d03185095.png ; $$x \neq \pm 1$$ ; confidence 0.956
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031850/d03185088.png ; $$( \operatorname { sin } x ) ^ { \prime } = \operatorname { cos } x$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031850/d031850109.png ; $$( \frac { u } { v } ) ^ { \prime } = \frac { u ^ { \prime } v - u v ^ { \prime } } { v ^ { 2 } }$$ ; confidence 0.958
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031850/d03185094.png ; $$( \operatorname { arccos } x ) ^ { \prime } = - 1 / \sqrt { 1 - x ^ { 2 } }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031890/d03189028.png ; $$\Delta \rightarrow 0$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031910/d03191048.png ; $$x _ { 2 } ( t )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031910/d0319107.png ; $$\dot { x } = f ( t )$$ ; confidence 0.623
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031910/d03191051.png ; $$x _ { 1 } ( t _ { 0 } ) = x _ { 2 } ( t _ { 0 } )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031920/d03192079.png ; $$0 < l < n$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031930/d031930232.png ; $$= \Phi ( z ) \operatorname { exp } \{ \frac { z - t } { \pi } \int \int _ { S } \frac { A ( \zeta ) w ( \zeta ) + B ( \zeta ) \overline { w ( \zeta ) } } { ( \zeta - z ) ( \zeta - t ) w } d \xi d \eta \}$$ ; confidence 0.918
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031950/d03195029.png ; $$W _ { 2 } ^ { p }$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031950/d03195033.png ; $$L u = \operatorname { div } ( p ( x ) \operatorname { grad } u ) + q ( x ) u$$ ; confidence 0.840
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031990/d031990131.png ; $$R _ { L } = H ( V )$$ ; confidence 0.569
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032010/d03201064.png ; $$( x - x _ { 0 } ) / ( t - t _ { 0 } ) = u _ { 0 }$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032010/d03201093.png ; $$n - m$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032010/d03201062.png ; $$\partial x / u = \partial t / 1$$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032060/d03206019.png ; $$\sum _ { n = 1 } ^ { \infty } | x _ { n } ( t ) |$$ ; confidence 0.933
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032060/d03206068.png ; $$| x ( t ( t ) ) \| \leq \rho$$ ; confidence 0.117
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032100/d032100109.png ; $$\dot { x } ( t ) = A x ( t - h ) - D x ( t )$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032070/d03207031.png ; $$2 \pi \alpha$$ ; confidence 0.461
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032110/d03211024.png ; $$z = \phi _ { i }$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032130/d032130352.png ; $$s ^ { \prime } ( \Omega ^ { r } ( X ) )$$ ; confidence 0.911
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032130/d032130227.png ; $$\int _ { S } \omega$$ ; confidence 0.561
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032130/d032130311.png ; $$\omega \in \Omega ^ { d } [ X ]$$ ; confidence 0.948
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032150/d032150132.png ; $$\hat { V }$$ ; confidence 0.359
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032240/d03224071.png ; $$d \omega = d \square ^ { * } \omega = 0$$ ; confidence 0.954
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032250/d03225022.png ; $$\partial M$$ ; confidence 0.831
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032320/d03232015.png ; $$u _ { R } ^ { k } ( x ) = \sum _ { i = 1 } ^ { n } u _ { i } a _ { i } ^ { k } ( x )$$ ; confidence 0.362
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032320/d03232034.png ; $$u ( x _ { i } )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032330/d03233032.png ; $$r \in F$$ ; confidence 0.671
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032330/d03233040.png ; $$b _ { 0 }$$ ; confidence 0.363
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032330/d03233041.png ; $$r : h \rightarrow f ( x _ { 0 } + h ) - f ( x _ { 0 } ) - h _ { 0 } ( h )$$ ; confidence 0.388
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032360/d03236035.png ; $$\frac { \partial u } { \partial t } + u \frac { \partial u } { \partial x } = D \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } }$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032450/d032450444.png ; $$X _ { 1 } \cup X _ { 2 } = X$$ ; confidence 0.917
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032450/d032450146.png ; $$\operatorname { dim } X \times Y < \operatorname { dim } X + \operatorname { dim } Y$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032450/d032450371.png ; $$\{ fd ( M )$$ ; confidence 0.531
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032450/d032450404.png ; $$[ V ] = \operatorname { limsup } ( \operatorname { log } d _ { V } ( n ) \operatorname { log } ( n ) ^ { - 1 } )$$ ; confidence 0.618
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032450/d032450327.png ; $$< \operatorname { Gdim } L < 1 +$$ ; confidence 0.485
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032480/d03248013.png ; $$d ( I ^ { n } ) = n$$ ; confidence 0.754
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032490/d03249024.png ; $$s \in Z$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032490/d03249026.png ; $$G$$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032600/d032600176.png ; $$w _ { N } ( \alpha ) \geq n$$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032610/d03261012.png ; $$y = y _ { 0 } - a n$$ ; confidence 0.836
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032610/d0326107.png ; $$a x + b y = 1$$ ; confidence 0.602
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130130/d1301309.png ; $$z = r \operatorname { cos } \theta$$ ; confidence 0.866
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032890/d032890165.png ; $$\operatorname { li } x / \phi ( d )$$ ; confidence 0.594
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032890/d03289066.png ; $$s = - 2 \nu - \delta$$ ; confidence 0.945
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120190/d1201904.png ; $$C _ { 0 } ^ { \infty } ( \Omega ) \subset L _ { 2 } ( \Omega )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120180/d12018028.png ; $$H ^ { p } ( d \theta / 2 \pi )$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120180/d12018084.png ; $$C ( G )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130170/d13017013.png ; $$0 < \lambda _ { 1 } ( \Omega ) \leq \lambda _ { 2 } ( \Omega ) \leq$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032920/d03292042.png ; $$\sigma > h$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032920/d03292035.png ; $$s = 0$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110220/d11022035.png ; $$L y = g$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110230/d11023041.png ; $$K = \overline { K } \cap L _ { m } ( G )$$ ; confidence 0.866
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033110/d03311036.png ; $$| \{ Z \} _ { n } | \rightarrow \infty$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033160/d03316011.png ; $$\sigma _ { i } ^ { z }$$ ; confidence 0.702
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033180/d03318044.png ; $$e ( B / A ) f ( B / A ) = n$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033180/d03318055.png ; $$f ( B / A ) = 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033190/d03319041.png ; $$t _ { 8 } + 1 / 2 = t _ { n } + \tau / 2$$ ; confidence 0.248
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033210/d03321058.png ; $$R _ { 2 } : x ^ { \prime } \Sigma ^ { - 1 } ( \mu ^ { ( 1 ) } - \mu ^ { ( 2 ) } ) +$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033280/d03328018.png ; $$x d y$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033340/d033340103.png ; $$\gamma$$ ; confidence 0.589
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033340/d03334050.png ; $$c * x = \frac { 1 } { I J } \sum _ { i j } c _ { j } = \frac { 1 } { I } \sum _ { i } c _ { i } x = \frac { 1 } { J } \sum _ { j } c * j$$ ; confidence 0.068
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033340/d033340195.png ; $$\lambda _ { 3 } = K \sum _ { i j } \frac { \delta _ { i j } ^ { 2 } } { \sigma ^ { 2 } }$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023063.png ; $$R = \sum _ { i = 0 } ^ { n - 1 } Z ^ { i } G J G ^ { * } Z ^ { * i } =$$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230125.png ; $$T _ { 1 } T _ { 2 } ^ { - 1 } T _ { 3 }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023076.png ; $$Z ^ { * }$$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023093.png ; $$| f _ { i } | < 1$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023095.png ; $$R - F R F ^ { * } = G J G ^ { * }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033420/d03342015.png ; $$\sigma _ { k }$$ ; confidence 0.198
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033430/d03343022.png ; $$x \in D _ { B }$$ ; confidence 0.620
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033460/d03346020.png ; $$| w - \beta _ { 0 } | = | \zeta _ { 0 } |$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033460/d033460124.png ; $$| F _ { 0 } ^ { \prime } ( \zeta _ { 0 } ) | \leq | F ^ { \prime } ( \zeta _ { 0 } ) | \leq | F _ { \pi / 2 } ^ { \prime } ( \zeta _ { 0 } ) |$$ ; confidence 0.854
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033460/d03346022.png ; $$\operatorname { ln } F ^ { \prime } ( \zeta _ { 0 } ) | \leq - \operatorname { ln } ( 1 - \frac { 1 } { | \zeta _ { 0 } | ^ { 2 } } )$$ ; confidence 0.488
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033530/d033530372.png ; $$d _ { n } \ll p _ { n } ^ { \theta }$$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033530/d03353095.png ; $$\psi ( x ) = x - \sum _ { | \gamma | \leq T } \frac { x ^ { \rho } } { \rho } + O ( \frac { X } { T } \operatorname { log } ^ { 2 } x T + \operatorname { log } 2 x )$$ ; confidence 0.429
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033530/d03353048.png ; $$\pi ( y ) - \operatorname { li } y > - M y \operatorname { log } ^ { - m } y$$ ; confidence 0.899
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033530/d033530133.png ; $$\zeta ( \sigma + i t ) \neq 0$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033570/d0335708.png ; $$\sum _ { i \in I } \prod _ { j \in J ( i ) } \alpha _ { i j } = \prod _ { \phi \in \Phi } \sum _ { i \in I } \alpha _ { i \phi ( i ) }$$ ; confidence 0.170
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033570/d0335707.png ; $$\prod _ { i \in I } \sum _ { j \in J ( i ) } \alpha _ { i j } = \sum _ { \phi \in \Phi } \prod _ { i \in I } \alpha _ { i \phi ( i ) }$$ ; confidence 0.076
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033570/d0335705.png ; $$\alpha \sum _ { i \in I } b _ { i } = \sum _ { i \in I } a b _ { i }$$ ; confidence 0.661
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d13018035.png ; $$\| \hat { f } \| = \| f \| _ { 1 }$$ ; confidence 0.870
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d13018075.png ; $$A ( \vec { G } )$$ ; confidence 0.484
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d13018088.png ; $$\operatorname { lim } _ { n \rightarrow \infty } f g _ { n } = f$$ ; confidence 0.784
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033630/d03363020.png ; $$\operatorname { lim } _ { x \rightarrow \infty } e ^ { - x } \sum _ { n = 0 } ^ { \infty } \frac { s _ { n } x ^ { n } } { n ! }$$ ; confidence 0.659
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033680/d03368022.png ; $$[ A : F ] = [ L : F ] ^ { 2 }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033720/d03372075.png ; $$\sigma > 1 / 2$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033720/d03372050.png ; $$\gamma _ { k } < \sigma < 1$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033790/d03379044.png ; $$\Delta _ { D } ( z )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033790/d03379012.png ; $$D \backslash K$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033850/d0338502.png ; $$x \square ^ { j }$$ ; confidence 0.818
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033930/d0339309.png ; $$p _ { 1 } / p _ { 2 }$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033990/d03399055.png ; $$y ^ { \prime } ( b ) + v ( b ) y ( b ) = \gamma ( b )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033990/d03399034.png ; $$y ^ { \prime } ( b ) + \psi y ( b ) = \beta$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033980/d03398025.png ; $$\sum _ { m = 1 } ^ { \infty } u _ { m n n }$$ ; confidence 0.852
+. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120342.png ; $$O \subset A _ { R }$$ ; confidence 0.132
+. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120272.png ; $$A _ { 0 } ( G )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120271.png ; $$\infty \in G$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d120280147.png ; $$\overline { U }$$ ; confidence 0.299
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d120280152.png ; $$A ( D ) ^ { * } \simeq A / B$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029018.png ; $$f ( q ) = 1 / ( \sqrt { 5 } q ^ { 2 } )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d1203009.png ; $$Y ( t ) \in R ^ { m }$$ ; confidence 0.934
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120320/d1203201.png ; $$T : L ^ { 1 } \rightarrow X$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034260/d03426025.png ; $$\delta ( t )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034280/d03428088.png ; $$S _ { g } ( w _ { 0 } )$$ ; confidence 0.921
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120010/e1200103.png ; $$A \stackrel { f } { \rightarrow } B = A \stackrel { é } { \rightarrow } f [ A ] \stackrel { m } { \rightarrow } B$$ ; confidence 0.193
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012065.png ; $$\propto \| \Sigma \| ^ { - 1 / 2 } [ \nu + ( y - \mu ) ^ { T } \Sigma ^ { - 1 } ( y - \mu ) ] ^ { - ( \nu + p ) / 2 }$$ ; confidence 0.904
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120020/e12002045.png ; $$T$$ ; confidence 0.914
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120020/e12002093.png ; $$\Sigma \Omega X \rightarrow X$$ ; confidence 0.748
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120020/e12002023.png ; $$74$$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120020/e120020102.png ; $$V \not \equiv W$$ ; confidence 0.489
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130020/e13002010.png ; $$\varphi$$ ; confidence 0.858
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035110/e03511022.png ; $$\Sigma - 1$$ ; confidence 0.852
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120050/e12005039.png ; $$h ^ { i } ( w ) = g ^ { i } ( w )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e12006018.png ; $$T p ( A _ { y } ) = A$$ ; confidence 0.900
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e12006038.png ; $$Y \rightarrow J ^ { 1 } Y$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e12007012.png ; $$\Gamma _ { q }$$ ; confidence 0.846
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035160/e0351605.png ; $$L ( u ) + \lambda u = 0$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035160/e03516059.png ; $$\frac { \partial } { \partial x } ( k _ { 1 } \frac { \partial u } { \partial x } ) + \frac { \partial } { \partial y } ( k _ { 2 } \frac { \partial u } { \partial y } ) + \lambda n = 0$$ ; confidence 0.519
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035170/e03517056.png ; $$\| \hat { A } - A \| \leq \delta$$ ; confidence 0.245
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035170/e03517077.png ; $$\overline { U _ { n } \in N A _ { n } ( B ) }$$ ; confidence 0.452
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e1300308.png ; $$\gamma = \left( \begin{array} { l l } { \alpha } & { b } \\ { c } & { d } \end{array} \right) \in GL _ { 2 } ( Q )$$ ; confidence 0.088
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003029.png ; $$K _ { \infty }$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110030/e11003020.png ; $$f ( x _ { 0 } ) < \operatorname { inf } _ { x \in X } f ( x ) + \epsilon$$ ; confidence 0.738
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035250/e035250110.png ; $$f = u _ { 1 } + i u _ { 2 }$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035250/e03525048.png ; $$0 < \sigma < 0.5$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035250/e03525091.png ; $$z _ { k } \in L$$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035250/e035250143.png ; $$\Delta \Delta w _ { 0 } = 0$$ ; confidence 0.903
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120100/e12010015.png ; $$f ^ { em } = q _ { f } E + \frac { 1 } { c } J \times B + ( \nabla E ) P + ( \nabla B ) M +$$ ; confidence 0.640
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120100/e12010035.png ; $$f ^ { em } = 0 = \operatorname { div } t ^ { em } f - \frac { \partial G ^ { em f } } { \partial t }$$ ; confidence 0.071
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120100/e12010055.png ; $$E ^ { \prime } = 0$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035320/e0353202.png ; $$\tau _ { i + 1 } - \tau _ { i }$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035360/e03536067.png ; $$\langle P ^ { ( 2 ) } \rangle$$ ; confidence 0.899
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035360/e03536090.png ; $$\operatorname { Th } ( K _ { 1 } )$$ ; confidence 0.733
+. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110060/e11006015.png ; $$\Omega _ { * } ^ { SO }$$ ; confidence 0.644
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035470/e03547029.png ; $$f ( z _ { 1 } + z _ { 2 } )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110070/e11007046.png ; $$C x ^ { - 1 }$$ ; confidence 0.834
+. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110070/e110070191.png ; $$f ^ { \prime } ( 1 ) = \prod _ { n > 0 } ( \frac { 1 - q ^ { 2 n } } { 1 + q ^ { 2 n } } ) ^ { 2 }$$ ; confidence 0.893
+. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110070/e11007067.png ; $$y ^ { 2 } = R ( x )$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035490/e03549042.png ; $$u = - \int _ { z } ^ { \infty } \frac { d z } { w }$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035500/e03550031.png ; $$T ^ { * } X \backslash 0$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035530/e0355309.png ; $$\int \int _ { \Omega } ( \frac { \partial u } { \partial x } \frac { \partial v } { \partial x } + \frac { \partial u } { \partial y } \frac { \partial v } { \partial y } ) d x d y = - \int _ { \Omega } f v d x d y$$ ; confidence 0.732
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035550/e035550163.png ; $$b _ { 2 } = 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035550/e035550128.png ; $$\alpha ( X ) = \operatorname { tr } \operatorname { deg } M ( X )$$ ; confidence 0.949
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035550/e03555010.png ; $$X _ { t } = m F$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035550/e03555028.png ; $$y ^ { 2 } = x ^ { 3 } - g x - g$$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035560/e03556014.png ; $$y ^ { \prime } ( 0 ) = 0$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110080/e11008028.png ; $$P _ { n } ( f ) = \int _ { S } f d P _ { n } = \frac { 1 } { n } \sum _ { i = 1 } ^ { n } f ( X _ { i } )$$ ; confidence 0.394
+. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110080/e11008048.png ; $$B \circ F$$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035660/e03566053.png ; $$c ( n ) \| \mu \| _ { e } = \| U _ { \mu } \|$$ ; confidence 0.789
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035660/e0356605.png ; $$U _ { \mu } ( x ) = \int H ( | x - y | ) d \mu ( y )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130040/e1300407.png ; $$U _ { 0 } ( t )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130040/e13004044.png ; $$( \Omega _ { + } - 1 ) ( g - g ) \psi ( t )$$ ; confidence 0.766
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130040/e13004035.png ; $$( \Omega _ { + } - 1 ) \psi ( t ) = ( \Omega _ { + } - 1 ) g \psi ( t ) =$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035720/e0357202.png ; $$\operatorname { lim } _ { k \rightarrow \infty } | \alpha _ { k } | ^ { 1 / k } = 0$$ ; confidence 0.823
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035760/e0357604.png ; $$f : W \rightarrow R$$ ; confidence 0.920
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035790/e03579057.png ; $$\sum _ { n } ^ { - 1 }$$ ; confidence 0.820
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035800/e0358008.png ; $$\nu ( n ) = \alpha$$ ; confidence 0.430
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035810/e03581038.png ; $$\Phi \Psi$$ ; confidence 0.943
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035810/e03581047.png ; $$\Psi ( A ) = A$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015019.png ; $$\frac { D \xi ^ { i } } { d t } = \frac { d \xi ^ { i } } { d t } + \frac { 1 } { 2 } g ^ { i } r \xi ^ { r }$$ ; confidence 0.338
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015070.png ; $$\lambda _ { 1 } = \lambda _ { 2 }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015064.png ; $$P _ { 1 } ^ { 1 } = \frac { 1 } { 4 } p ^ { 2 } + \frac { 1 } { 2 } \dot { p } - q = I$$ ; confidence 0.914
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036070/e03607020.png ; $$\tau _ { n } ^ { ( B ) }$$ ; confidence 0.845
+. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110100/e11010022.png ; $$o ( G )$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036120/e03612012.png ; $$m ( M )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036230/e03623076.png ; $$2 d \geq n$$ ; confidence 0.758
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036230/e036230210.png ; $$R ( \delta ) = 1 - H ( \delta )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036230/e036230124.png ; $$k \geq n - i t$$ ; confidence 0.558
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036240/e03624043.png ; $$\sigma \approx s$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120190/e12019037.png ; $$l _ { x }$$ ; confidence 0.196
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036400/e03640030.png ; $$2 - 2 g - l$$ ; confidence 0.741
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036400/e03640033.png ; $$2 - m - 1$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036530/e03653023.png ; $$t h$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023072.png ; $$E ^ { \alpha } ( L ) ( \sigma ^ { 2 } ( x ) ) = 0$$ ; confidence 0.682
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023094.png ; $$\sigma ^ { k } : M \rightarrow E ^ { k }$$ ; confidence 0.958
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023045.png ; $$\therefore M \rightarrow F$$ ; confidence 0.313
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e1202308.png ; $$M = \overline { U }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230115.png ; $$E ( L ) = E ^ { d } ( L ) \omega ^ { \alpha } \bigotimes \Delta$$ ; confidence 0.101
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230111.png ; $$E ( L )$$ ; confidence 0.960
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023058.png ; $$E ( L ) = \frac { \partial L } { \partial y } - D ( \frac { \partial L } { \partial y ^ { \prime } } )$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023061.png ; $$L \mapsto E ( L )$$ ; confidence 0.892
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120240/e12024025.png ; $$K ( L )$$ ; confidence 0.907
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036620/e03662025.png ; $$Q _ { n - j } ( z ) \equiv 0$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110130/e11013060.png ; $$p _ { x } ^ { * } = \lambda \operatorname { exp } ( - \lambda x )$$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036770/e03677085.png ; $$A + 2$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036770/e03677073.png ; $$B = f ( A )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036770/e03677067.png ; $$\phi ^ { - 1 } ( b ) \cong P ^ { \prime } ( C )$$ ; confidence 0.866
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036770/e03677058.png ; $$P ^ { \prime } ( C )$$ ; confidence 0.802
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036770/e03677051.png ; $$f | _ { A } = \phi$$ ; confidence 0.668
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036820/e03682019.png ; $$B _ { \mu } ^ { 1 } \subset B \subset B _ { \mu } ^ { 2 }$$ ; confidence 0.646
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036820/e03682038.png ; $$\tau \geq \zeta$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036840/e03684025.png ; $$A = \operatorname { lim } _ { n \rightarrow \infty } C _ { n } = ( 1 + \frac { 1 } { 4 } + \frac { 1 } { 16 } + \ldots ) C _ { 1 } = \frac { 4 } { 3 } C _ { 1 }$$ ; confidence 0.919
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036840/e03684018.png ; $$K ( B - C _ { N } ) > K ( B - A ) > D$$ ; confidence 0.579
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036840/e03684024.png ; $$C _ { n } = C _ { 1 } + \frac { 1 } { 4 } C _ { 1 } + \ldots + \frac { 1 } { 4 ^ { n - 1 } } C _ { 1 }$$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036850/e03685016.png ; $$\overline { \Pi } _ { k } \subset \Pi _ { k + 1 }$$ ; confidence 0.606
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e12026092.png ; $$( L _ { \mu } ) ^ { p }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036910/e03691052.png ; $$z = \operatorname { ln } \alpha = \operatorname { ln } | \alpha | + i \operatorname { Arg } \alpha$$ ; confidence 0.857
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036910/e03691064.png ; $$( e ^ { z } 1 ) ^ { z } = e ^ { z } 1 ^ { z _ { 2 } }$$ ; confidence 0.053
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036910/e03691017.png ; $$a ^ { X } = e ^ { X \operatorname { ln } \alpha }$$ ; confidence 0.301
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130060/e13006023.png ; $$z \in Z$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e1300704.png ; $$S = o ( \# A )$$ ; confidence 0.908
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036940/e03694044.png ; $$p f$$ ; confidence 0.602
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696065.png ; $$y _ { j } \delta \theta$$ ; confidence 0.866
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960205.png ; $$\nu - 1 / 2 \in Z$$ ; confidence 0.954
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960198.png ; $$y ^ { \prime } + \alpha _ { 1 } y = 0$$ ; confidence 0.639
+. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036980/e03698026.png ; $$\alpha : G \rightarrow \operatorname { Aut } A$$ ; confidence 0.856
+. https://www.encyclopediaofmath.org/legacyimages/e/e037/e037040/e03704050.png ; $$n + = n - = n$$ ; confidence 0.228
+. https://www.encyclopediaofmath.org/legacyimages/e/e037/e037040/e037040161.png ; $$A = A _ { 0 } ^ { * }$$ ; confidence 0.706
+. https://www.encyclopediaofmath.org/legacyimages/e/e037/e037040/e03704077.png ; $$\lambda < \alpha$$ ; confidence 0.600
+. https://www.encyclopediaofmath.org/legacyimages/e/e037/e037080/e03708021.png ; $$r > n$$ ; confidence 0.953
+. https://www.encyclopediaofmath.org/legacyimages/e/e037/e037080/e03708073.png ; $$x _ { i } ^ { 2 } = 0$$ ; confidence 0.840
+. https://www.encyclopediaofmath.org/legacyimages/e/e037/e037160/e03716049.png ; $$\Delta J =$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/e/e037/e037170/e03717072.png ; $$r < | z | < 1$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/e/e037/e037200/e037200118.png ; $$\gamma \geq 0$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120010/f1200101.png ; $$S h$$ ; confidence 0.739
+. https://www.encyclopediaofmath.org/legacyimages/f/f038/f038060/f03806015.png ; $$V$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130010/f13001030.png ; $$R _ { i } = F _ { q } [ x ] / ( f _ { i } )$$ ; confidence 0.671
+. https://www.encyclopediaofmath.org/legacyimages/f/f038/f038130/f0381302.png ; $$G _ { i } = V _ { i } ( E + \Delta - V _ { i } ) ^ { - 1 }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/f/f038/f038220/f0382203.png ; $$K _ { X } ^ { - 1 }$$ ; confidence 0.918
+. https://www.encyclopediaofmath.org/legacyimages/f/f038/f038220/f03822036.png ; $$Q \subset P ^ { 4 }$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130040/f13004017.png ; $$d _ { k } = \operatorname { det } ( 1 - f _ { t } ^ { \prime } ( x _ { k } ) ) ^ { 1 / 2 }$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110050/f11005019.png ; $$q ( 0 ) \neq 0$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110050/f11005048.png ; $$w ( x ) = | f ( x ) | ^ { 2 }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/f/f038/f038380/f03838022.png ; $$C _ { 0 }$$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120040/f1200408.png ; $$( + \infty ) - ( + \infty ) = - \infty - ( - \infty ) = - \infty$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/f/f038/f038390/f038390152.png ; $$\alpha ^ { \lambda } = 1$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/f/f038/f038390/f038390108.png ; $$q ( m ) = ( m ^ { p - 1 } - 1 ) / p$$ ; confidence 0.963
+. https://www.encyclopediaofmath.org/legacyimages/f/f038/f038470/f03847048.png ; $$\tau _ { 0 } = 0$$ ; confidence 0.955
+. https://www.encyclopediaofmath.org/legacyimages/f/f038/f038470/f03847049.png ; $$\tau _ { k + 1 } = t$$ ; confidence 0.410
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f13009060.png ; $$P ( N _ { k } = n ) = p ^ { n } F _ { n + 1 - k } ^ { ( k ) } ( \frac { q } { p } )$$ ; confidence 0.620
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f1300908.png ; $$U _ { n } ( x ) = \frac { \alpha ^ { n } ( x ) - \beta ^ { n } ( x ) } { \alpha ( x ) - \beta ( x ) }$$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040080/f04008051.png ; $$P ^ { * } = \{ P _ { X } ^ { * } : x \in X \}$$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040080/f04008010.png ; $$F ^ { * } ( \theta | x ) = 1 - F ( x | \theta )$$ ; confidence 0.940
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f130100140.png ; $$G = T$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f130100152.png ; $$v \in A _ { p } ( G )$$ ; confidence 0.412
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f13010016.png ; $$u \in C ^ { G }$$ ; confidence 0.438
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f13010077.png ; $$\lambda ^ { p } ( M ^ { 1 } ( G ) )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040190/f04019037.png ; $$V ( x _ { 0 } )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040210/f04021064.png ; $$\phi ( \mathfrak { A } )$$ ; confidence 0.445
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040230/f040230100.png ; $$x _ { n } = n$$ ; confidence 0.849
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040230/f040230157.png ; $$\Delta ^ { n } f ( x )$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040230/f040230147.png ; $$\sum _ { \nu = 1 } ^ { k - 1 } \frac { B _ { \nu } } { \nu ! } \{ f ^ { \langle \nu - 1 \rangle } ( n ) - f ^ { \langle \nu - 1 \rangle } ( 0 ) \} + \frac { B _ { k } } { k ! } \sum _ { x = 0 } ^ { n - 1 } f ^ { ( k ) } ( x + \theta )$$ ; confidence 0.269
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040330/f04033018.png ; $$f ^ { - 1 } ( f ( x ) ) \cap U$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040290/f04029031.png ; $$G / G 1$$ ; confidence 0.622
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040390/f04039064.png ; $$y ^ { i } C _ { i j k } = 0$$ ; confidence 0.942
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040420/f04042034.png ; $$\Phi ( \Phi ( x ) ) = x$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040520/f04052043.png ; $$| x - x _ { 0 } | \leq b$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040580/f04058030.png ; $$| X$$ ; confidence 0.687
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040580/f04058044.png ; $$\phi ( p )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040580/f04058066.png ; $$| A | = \int _ { R } | \alpha | 0$$ ; confidence 0.765
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040580/f04058050.png ; $$\frac { | \sigma _ { i } | } { ( \operatorname { diam } \sigma _ { i } ) ^ { n } } \geq \eta$$ ; confidence 0.891
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040610/f04061036.png ; $$C ^ { b r } ( E ^ { n } )$$ ; confidence 0.943
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040690/f04069050.png ; $$\Omega \in ( H ^ { \otimes 0 } ) _ { \alpha } \subset \Gamma ^ { \alpha } ( H )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040690/f04069087.png ; $$\{ \xi _ { f } : f \in H \}$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040690/f04069072.png ; $$\alpha _ { \alpha } ^ { * } ( f ) \Omega = f$$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110150/f11015067.png ; $$t \subset v$$ ; confidence 0.885
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820110.png ; $$f _ { i } ( X ) = X _ { i } + \ldots$$ ; confidence 0.733
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820173.png ; $$F ( \overline { m } )$$ ; confidence 0.760
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040830/f0408302.png ; $$\omega = \alpha _ { 1 } \ldots \alpha _ { k }$$ ; confidence 0.633
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040850/f040850279.png ; $$V _ { 1 } ^ { * }$$ ; confidence 0.750
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040850/f040850143.png ; $$\{ \lambda \}$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040850/f040850122.png ; $$A \rightarrow w$$ ; confidence 0.934
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040850/f04085058.png ; $$\sigma ( \alpha ) = \{ w \}$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040960/f04096043.png ; $$I V _ { 2 }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040960/f04096055.png ; $$x ^ { i } \in R$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041000/f0410005.png ; $$J _ { \nu }$$ ; confidence 0.556
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120090/f12009069.png ; $$F \mu$$ ; confidence 0.813
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041140/f04114018.png ; $$P ( x ) = \frac { 1 } { \sqrt { 2 \pi } } F ( x )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f120080162.png ; $$L _ { q } ( X )$$ ; confidence 0.846
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f120080135.png ; $$\Lambda _ { G } = 1$$ ; confidence 0.897
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120100/f12010041.png ; $$( 8 \times 8 )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011010.png ; $$| \varphi ( z ) | ^ { 2 } e ^ { \delta | z | }$$ ; confidence 0.840
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f120110126.png ; $$F ( z ) = - \frac { 1 } { 2 \pi i } \int \frac { \operatorname { exp } e ^ { \zeta ^ { 2 } } } { \zeta - z } d \zeta$$ ; confidence 0.622
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041050/f04105039.png ; $$f \in L _ { 1 }$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041060/f04106025.png ; $$\phi \in C _ { 0 } ^ { \infty } ( \Omega )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041060/f041060172.png ; $$X ^ { \prime } \subset X$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041060/f041060187.png ; $$K _ { j } \times R ^ { N j }$$ ; confidence 0.562
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041060/f041060205.png ; $$d _ { C } ^ { - 1 } = \operatorname { det } \left\| \begin{array} { c c } { \phi _ { \theta } \theta } & { \phi _ { \theta x } } \\ { \phi _ { y } \theta } & { \phi _ { y x } } \end{array} \right\|$$ ; confidence 0.370
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041160/f04116031.png ; $$\alpha = - b$$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041170/f04117079.png ; $$f * g$$ ; confidence 0.637
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041170/f04117026.png ; $$K = D$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041170/f04117046.png ; $$F [ \delta ] = 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041170/f041170108.png ; $$\eta \in \operatorname { ln } t \Gamma ^ { \prime }$$ ; confidence 0.642
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041250/f04125082.png ; $$\xi _ { 1 } \neq \infty$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041250/f0412503.png ; $$z \rightarrow w = L ( z ) = \frac { a z + b } { c z + d }$$ ; confidence 0.834
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041250/f041250105.png ; $$L _ { k } ( z _ { k } )$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041250/f0412506.png ; $$\infty \rightarrow \alpha / c$$ ; confidence 0.864
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041210/f0412109.png ; $$A / \eta$$ ; confidence 0.702
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041270/f04127048.png ; $$D ( B ) \supset D ( A )$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041270/f04127030.png ; $$\alpha < \beta < \gamma$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041270/f04127050.png ; $$x \in D ( A )$$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041310/f04131029.png ; $$\Lambda = \frac { \partial } { \partial x } + i \frac { \partial } { \partial y }$$ ; confidence 0.855
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041310/f04131016.png ; $$\eta = \frac { ( \alpha ^ { 2 } - \rho ^ { 2 } ) ^ { 1 / 2 } ( \alpha ^ { 2 } - \rho _ { 0 } ^ { 2 } ) ^ { 1 / 2 } } { \alpha }$$ ; confidence 0.628
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041320/f04132023.png ; $$v _ { 0 } ^ { k }$$ ; confidence 0.384
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120130/f12013083.png ; $$| \Phi ( G )$$ ; confidence 0.956
+. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110160/f110160161.png ; $$\mathfrak { A } \sim _ { l } \mathfrak { B }$$ ; confidence 0.922
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041420/f04142082.png ; $$D ( \lambda ) \neq 0$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041420/f041420175.png ; $$| \lambda | < B ^ { - 1 }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f12015043.png ; $$\beta ( A ) < \infty$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f12015010.png ; $$R ( A )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f120150156.png ; $$\beta ( A - K ) < \infty$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f120150202.png ; $$n \| < C$$ ; confidence 0.368
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f12015012.png ; $$\beta ( A ) : = \operatorname { codim } R ( A ) < \infty$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041510/f04151086.png ; $$( r \geq 1 )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041570/f04157048.png ; $$x _ { 1 } ( t ) + x _ { 2 } ( t ) = A ( t ) \operatorname { cos } ( \omega _ { 1 } t + \phi ( t ) )$$ ; confidence 0.965
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041580/f04158014.png ; $$( x M ) ( M ^ { - 1 } y )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041620/f04162020.png ; $$X _ { i } \cap X _ { j } =$$ ; confidence 0.322
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120190/f12019028.png ; $$C _ { G } ( n ) \leq N$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120190/f12019010.png ; $$N = \{ G \backslash ( \cup _ { x \in G } x ^ { - 1 } H x ) \} \cup \{ 1 \}$$ ; confidence 0.269
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021089.png ; $$\pi ( \lambda ) = ( \lambda + 2 ) ( \lambda + 1 ) \alpha ^ { 2 } 0 + ( \lambda + 1 ) \alpha ^ { 1 } 0 + a ^ { 0 } =$$ ; confidence 0.071
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f1202105.png ; $$| z | < r$$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021069.png ; $$= \frac { ( n _ { 1 } + l ) ! } { ! ! } ( \operatorname { log } z ) ^ { l } z ^ { \lambda _ { 2 } } + \ldots$$ ; confidence 0.665
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021085.png ; $$\lambda = \lambda _ { j }$$ ; confidence 0.911
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041790/f04179028.png ; $$( n ! ) ^ { - 1 } n _ { D }$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110180/f11018097.png ; $$\| x \| _ { p } = \int _ { 0 } ^ { 1 } | x ( t ) | ^ { p } d t$$ ; confidence 0.742
+. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110180/f110180102.png ; $$0 < p _ { n } \rightarrow 0$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230136.png ; $$J : T M \rightarrow T M$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041880/f04188062.png ; $$V _ { 0 } ( z )$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041890/f041890119.png ; $$x \in R \cup \{ \infty \}$$ ; confidence 0.764
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041890/f0418904.png ; $$D = \{ z \in C : | z | < 1 \}$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041890/f04189063.png ; $$\chi ( \Delta ) = \chi ( \Gamma ) [ \Gamma : \Delta ]$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041940/f041940314.png ; $$L _ { p } ( X )$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041940/f041940175.png ; $$S \subset T$$ ; confidence 0.743
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041940/f041940310.png ; $$A \in \mathfrak { S }$$ ; confidence 0.285
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041950/f041950110.png ; $$f \in N ( \Delta )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120240/f1202409.png ; $$t \mapsto t + T$$ ; confidence 0.520
+. https://www.encyclopediaofmath.org/legacyimages/f/f042/f042030/f04203082.png ; $$T _ { \rightarrow } V ^ { - 1 } T V$$ ; confidence 0.437
+. https://www.encyclopediaofmath.org/legacyimages/f/f042/f042060/f04206038.png ; $$P ( C A )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/f/f042/f042060/f04206074.png ; $$f ( - x ) = - f ( x )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/f/f042/f042060/f042060121.png ; $$\mathfrak { g } \otimes \mathfrak { g } \rightarrow U \mathfrak { g } \otimes U \mathfrak { g } \otimes U _ { \mathfrak { g } }$$ ; confidence 0.207
+. https://www.encyclopediaofmath.org/legacyimages/f/f042/f042070/f04207074.png ; $$T _ { N } ( t )$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/f/f042/f042120/f04212073.png ; $$\frac { \partial w } { \partial z } + A ( z ) w + B ( z ) \overline { w } = F ( z )$$ ; confidence 0.777
+. https://www.encyclopediaofmath.org/legacyimages/f/f042/f042150/f04215011.png ; $$\left. \begin{array} { l l } { F _ { 1 } ( A ) } & { \frac { F _ { 1 } ( \alpha ) } { \rightarrow } } & { F _ { 1 } ( B ) } \\ { \phi _ { A } \downarrow } & { \square } & { \downarrow \phi _ { B } } \\ { F _ { 2 } ( A ) } & { \vec { F _ { 2 } ( \alpha ) } } & { F _ { 2 } ( B ) } \end{array} \right.$$ ; confidence 0.308
+. https://www.encyclopediaofmath.org/legacyimages/f/f042/f042210/f04221073.png ; $$\tilde { f } : Y \rightarrow X$$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/f/f042/f042210/f04221056.png ; $$e _ { \lambda } ^ { 1 } \in X$$ ; confidence 0.877
+. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110220/f11022029.png ; $$A ^ { p } \geq ( A ^ { p / 2 } B ^ { p } A ^ { p / 2 } ) ^ { 1 / 2 }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130290/f130290181.png ; $$LOC$$ ; confidence 0.417
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043010/g04301029.png ; $$X \times F$$ ; confidence 0.480
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043020/g043020138.png ; $$\pi : P \rightarrow G \backslash P$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043020/g043020283.png ; $$S ( M ^ { \prime } ) \subset M ^ { \prime }$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043020/g043020169.png ; $$H \mapsto C _ { A } ^ { \prime }$$ ; confidence 0.465
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043020/g043020155.png ; $$V \oplus \mathfrak { g }$$ ; confidence 0.476
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043020/g043020256.png ; $$C ^ { ( 0 ) }$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043020/g043020187.png ; $$\delta : G ^ { \prime } \rightarrow W$$ ; confidence 0.965
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043280/g0432806.png ; $$\mathfrak { x } \times x$$ ; confidence 0.416
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043280/g04328069.png ; $$H _ { i } ( x ^ { \prime } ) > H _ { i } ( x ^ { \prime \prime } )$$ ; confidence 0.924
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043280/g0432804.png ; $$\hat { K } _ { i }$$ ; confidence 0.180
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043280/g0432802.png ; $$x$$ ; confidence 0.485
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043290/g0432908.png ; $$\alpha _ { k } = \frac { \Gamma ( \gamma + k + 1 ) } { \Gamma ( \gamma + 1 ) } \sqrt { \frac { \Gamma ( \alpha _ { 1 } + 1 ) \Gamma ( \alpha _ { 2 } + 1 ) } { \Gamma ( \alpha _ { 1 } + k + 1 ) \Gamma ( \alpha _ { 2 } + k + 1 ) } }$$ ; confidence 0.904
+. https://www.encyclopediaofmath.org/legacyimages/g/g110/g110050/g11005015.png ; $$\nu < \kappa$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043330/g04333080.png ; $$\omega = 1 / c ^ { 2 }$$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043340/g04334048.png ; $$\sum _ { \Sigma } ^ { 3 } \square ^ { i \alpha } \neq 0$$ ; confidence 0.180
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043340/g04334058.png ; $$( \partial w / \partial t ) + ( \partial f / \partial x ) = ( h ^ { 2 } / 2 \tau ) ( \partial ^ { 2 } w / \partial x ^ { 2 } )$$ ; confidence 0.582
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043350/g04335040.png ; $$\frac { \pi \psi } { Q } = - \theta - \sum _ { n = 1 } ^ { \infty } \frac { 1 } { n } ( \frac { \tau } { \tau _ { 0 } } ) ^ { n } \frac { y _ { n } ( \tau ) } { y _ { n } ( \tau _ { 0 } ) } \operatorname { sin } 2 n \theta$$ ; confidence 0.914
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043350/g04335015.png ; $$\beta = \frac { 1 } { \gamma - 1 }$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043350/g04335037.png ; $$+ \beta n ( 2 n + 1 ) y _ { n } = 0$$ ; confidence 0.975
+. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120030/g12003011.png ; $$3 n + 2$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120030/g1200302.png ; $$= \sum _ { \nu = 1 } ^ { n } \alpha _ { \nu } f ( x _ { \nu } ) + \sum _ { \mu = 1 } ^ { n + 1 } \beta _ { \mu } f ( \xi _ { \mu } )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043470/g0434707.png ; $$\nabla _ { \theta } : H _ { \delta R } ^ { 1 } ( X / K ) \rightarrow H _ { \partial R } ^ { 1 } ( X / K )$$ ; confidence 0.221
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043470/g04347036.png ; $$0 \rightarrow \phi ^ { 1 } / \phi ^ { 2 } \rightarrow \phi ^ { 0 } / \phi ^ { 2 } \rightarrow \phi ^ { 0 } / \phi ^ { 1 } \rightarrow 0$$ ; confidence 0.913
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043480/g0434807.png ; $$\alpha _ { 31 } / \alpha _ { 11 }$$ ; confidence 0.405
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043480/g0434801.png ; $$\quad f j ( x ) - \alpha j = \alpha _ { j 1 } x _ { 1 } + \ldots + \alpha _ { j n } x _ { n } - \alpha _ { j } = 0$$ ; confidence 0.057
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043580/g04358023.png ; $$f _ { \zeta } ( \lambda )$$ ; confidence 0.821
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043620/g0436207.png ; $$R [ F ( t ) ] = ( 1 - t ^ { 2 } ) F ^ { \prime \prime } - ( 2 \rho - 1 ) t F ^ { \prime \prime }$$ ; confidence 0.876
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043640/g04364030.png ; $$K ( y ) = \operatorname { sgn } y . | y | ^ { \alpha }$$ ; confidence 0.655
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043780/g043780250.png ; $$\hbar \square ^ { * } ( M )$$ ; confidence 0.620
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043780/g043780168.png ; $$T _ { \nu }$$ ; confidence 0.336
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043780/g04378073.png ; $$i : A \rightarrow X$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043780/g043780134.png ; $$F = p t$$ ; confidence 0.143
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043780/g043780157.png ; $$T \xi$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043780/g043780231.png ; $$\overline { h } ( X ) = \operatorname { lim } _ { h } h ^ { * } ( X _ { \alpha } )$$ ; confidence 0.185
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043810/g043810381.png ; $$C = \text { int } \Gamma$$ ; confidence 0.630
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043810/g04381012.png ; $$\overline { O } _ { k }$$ ; confidence 0.968
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043810/g043810261.png ; $$\delta ( x ) = \delta ( x _ { 1 } ) \times \ldots \times \delta ( x _ { N } )$$ ; confidence 0.411
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043810/g043810179.png ; $$\alpha f \in D ^ { \prime } ( O )$$ ; confidence 0.895
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043810/g043810238.png ; $$x u = 0$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130030/g13003048.png ; $$I _ { U } = \{ ( u _ { \lambda } ) _ { \lambda \in \Lambda }$$ ; confidence 0.956
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130030/g13003082.png ; $$\Gamma \subset \Omega$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130030/g13003022.png ; $$w \mapsto ( w ^ { * } \varphi _ { \lambda } ) _ { \lambda \in \Lambda }$$ ; confidence 0.798
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043930/g0439304.png ; $$m : A ^ { \prime } \rightarrow A$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g130040116.png ; $$v \wedge \wedge \ldots \wedge v _ { m }$$ ; confidence 0.124
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044340/g044340202.png ; $$\xi _ { p } \in ( \nu F ^ { m } ) p$$ ; confidence 0.212
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044340/g04434018.png ; $$d f ( X )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044340/g044340228.png ; $$\xi \in ( \nu F ^ { m } ) _ { p }$$ ; confidence 0.549
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044350/g044350167.png ; $$\alpha ( F ) = 1$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044350/g044350101.png ; $$D \Re \subset M$$ ; confidence 0.255
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044350/g044350116.png ; $$V ( \Re ) > 2 ^ { n } d ( \Lambda )$$ ; confidence 0.792
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044350/g04435074.png ; $$d ( \Lambda ) = \Delta ( \mathfrak { M } )$$ ; confidence 0.934
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g1300606.png ; $$p _ { n } ( z ) : = \operatorname { det } \{ z I - A \}$$ ; confidence 0.968
+. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g12004053.png ; $$| \tilde { \varphi } \mathfrak { u } ( \xi ) | \leq c ^ { - 1 } e ^ { - c | \xi | ^ { 1 / s } }$$ ; confidence 0.103
+. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g12004074.png ; $$D _ { x _ { k } } = - i \partial _ { x _ { k } }$$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044400/g04440061.png ; $$z$$ ; confidence 0.578
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044400/g04440029.png ; $$\delta \varepsilon$$ ; confidence 0.600
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044400/g04440032.png ; $$d E$$ ; confidence 0.607
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044410/g0444106.png ; $$\alpha \equiv f ( x _ { 0 } - ) \leq f ( x _ { 0 } + ) \equiv b$$ ; confidence 0.692
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044410/g0444109.png ; $$A < \alpha < b < B$$ ; confidence 0.686
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044410/g04441010.png ; $$A = \underbrace { \operatorname { lim } _ { n } \frac { \operatorname { lim } } { x \nmid x _ { 0 } } } s _ { n } ( x )$$ ; confidence 0.055
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044470/g044470103.png ; $$\psi \circ \phi = \phi ^ { \prime } \circ \psi$$ ; confidence 0.848
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044470/g04447072.png ; $$q ^ { \prime } \in A ^ { \prime }$$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044650/g04465025.png ; $$a _ { y }$$ ; confidence 0.519
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044660/g04466023.png ; $$A _ { 0 } = \mathfrak { A } _ { 0 }$$ ; confidence 0.968
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044660/g04466018.png ; $$A = \sum _ { i \geq 0 } A$$ ; confidence 0.975
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044680/g04468042.png ; $$\operatorname { grad } ( f g ) = g \operatorname { grad } f + f \operatorname { grad } g$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044680/g04468049.png ; $$t \circ \in E$$ ; confidence 0.290
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044730/g04473023.png ; $$f _ { B } ( x ) = \frac { \lambda ^ { x } } { x ! } e ^ { - \lambda } \{ 1 + \frac { \mu _ { 2 } - \lambda } { \lambda ^ { 2 } } [ \frac { x ^ { [ 2 ] } } { 2 } - \lambda x ^ { [ 1 ] } + \frac { \lambda ^ { 2 } } { 2 } ] +$$ ; confidence 0.569
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044770/g04477022.png ; $$[ \Psi / \Phi ] \Phi$$ ; confidence 0.955
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044780/g04478033.png ; $$\mu ( \alpha )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044820/g04482057.png ; $$x \in L ( \Gamma )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044840/g04484023.png ; $$B \rightarrow b B$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/g/g110/g110180/g11018025.png ; $$V _ { T } ^ { \prime } = \mu ( V _ { T } )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044910/g04491070.png ; $$\sum _ { d ( e ) = Q } f _ { e }$$ ; confidence 0.651
+. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045000/g04500031.png ; $$( n \operatorname { ln } n ) / 2$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044970/g04497028.png ; $$E ^ { n } \times R$$ ; confidence 0.937
+. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045040/g0450402.png ; $$f _ { 12 }$$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045090/g045090279.png ; $$G _ { A B } ^ { ( c ) } ( t - t ^ { \prime } ) = \ll A ( t ) | B ( t ^ { \prime } ) \gg ( c ) \equiv \langle T _ { \eta } A ( t ) B ( t ^ { \prime } ) \rangle$$ ; confidence 0.272
+. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045090/g045090122.png ; $$\psi _ { k } ( \xi )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045090/g04509046.png ; $$y ( \alpha ) = 0$$ ; confidence 0.954
+. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045090/g04509054.png ; $$C = [ p ( \xi ) W ( \xi ) ] ^ { - 1 }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045090/g045090287.png ; $$G _ { A B } ^ { ( n ) } ( E )$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120070/g12007022.png ; $$m \equiv 4$$ ; confidence 0.840
+. https://www.encyclopediaofmath.org/legacyimages/g/g110/g110260/g1102602.png ; $$B M$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045370/g0453708.png ; $$f ( z ) = e ^ { ( \alpha - i b ) z ^ { \rho } }$$ ; confidence 0.743
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046010/h046010125.png ; $$M _ { 2 } \times S ^ { N }$$ ; confidence 0.923
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046010/h046010104.png ; $$m \geq 3$$ ; confidence 0.668
+. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120010/h12001013.png ; $$X ^ { ( r ) } \rightarrow V$$ ; confidence 0.950
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130090/h13009043.png ; $$g _ { i } \in A$$ ; confidence 0.960
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130090/h13009035.png ; $$g \rightarrow g$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046080/h04608018.png ; $$| x _ { \mathfrak { j } } | \leq M$$ ; confidence 0.106
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110050/h11005031.png ; $$w _ { 2 } = f ( r _ { 1 } ) \ldots f ( r _ { n } )$$ ; confidence 0.851
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110050/h1100503.png ; $$\alpha _ { 1 } \ldots \alpha _ { m }$$ ; confidence 0.435
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046280/h04628046.png ; $$\frac { d ^ { 2 } y } { d t ^ { 2 } } + P ( t ) y = 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046280/h04628059.png ; $$x ^ { ( 1 ) } = x ^ { ( 1 ) } ( t )$$ ; confidence 0.898
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046280/h046280124.png ; $$X = \| \left. \begin{array} { l l } { U _ { 1 } } & { U _ { 2 } } \\ { V _ { 1 } } & { V _ { 2 } } \end{array} \right. |$$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046300/h04630075.png ; $$M _ { 0 } \times I$$ ; confidence 0.798
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046300/h046300124.png ; $$P _ { n - k }$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120020/h120020104.png ; $$P _ { - } \phi \in B _ { p } ^ { 1 / p }$$ ; confidence 0.963
+. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120020/h1200207.png ; $$\hat { \phi } ( j ) = \alpha$$ ; confidence 0.791
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046370/h04637024.png ; $$M ( x ) = M _ { f } ( x ) = \operatorname { sup } _ { 0 < k | \leq \pi } \frac { 1 } { t } \int _ { x } ^ { x + t } | f ( u ) | d u$$ ; confidence 0.412
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046370/h04637012.png ; $$\int _ { \alpha } ^ { b } \theta ^ { p } ( x ) d x \leq 2 ( \frac { p } { p - 1 } ) ^ { p } \int _ { a } ^ { b } f ^ { p } ( x ) d x$$ ; confidence 0.187
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046320/h046320114.png ; $$H ^ { p } ( G )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046320/h046320200.png ; $$M _ { \delta } ( \phi ) \rightarrow 0$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046420/h046420330.png ; $$B = B _ { E }$$ ; confidence 0.754
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046420/h04642087.png ; $$L _ { \infty } ( \hat { G } )$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046420/h046420200.png ; $$F ( \phi ) \in A ( \hat { G } )$$ ; confidence 0.909
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046420/h046420189.png ; $$f = f _ { 1 } * f _ { 2 }$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046420/h046420157.png ; $$d g = d h d k$$ ; confidence 0.955
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046460/h04646046.png ; $$p + q \leq \operatorname { dim } _ { C } M$$ ; confidence 0.688
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046470/h046470224.png ; $$d \sigma ( y )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120030/h12003026.png ; $$\operatorname { dim } M = 2$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046600/h0466006.png ; $$\{ x : | x - y | < r \}$$ ; confidence 0.915
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047020/h04702011.png ; $$F _ { n } ( x ) = ( x _ { 1 } ^ { 2 } + \ldots + x _ { y } ^ { 2 } ) ^ { 1 / 2 }$$ ; confidence 0.316
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047070/h0470704.png ; $$\alpha _ { i k } = \overline { a _ { k i } }$$ ; confidence 0.235
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047160/h04716013.png ; $$H ( z )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047160/h0471603.png ; $$H ( z ) = \sum _ { i = 1 } ^ { n } \sum _ { j = 1 } ^ { n } a _ { i j } z _ { i } z _ { j }$$ ; confidence 0.374
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047210/h0472103.png ; $$C$$ ; confidence 0.952
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047210/h04721080.png ; $$X _ { 1 } \cap Y _ { 1 } = \emptyset$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047210/h04721043.png ; $$\Sigma _ { n } ^ { 0 }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047270/h04727012.png ; $$\lambda = p ^ { - 1 } + r ^ { - 1 } \leq 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047380/h047380203.png ; $$\nu \in A$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047380/h047380120.png ; $$\sum _ { i } | \alpha _ { i } | ^ { 2 } < \infty$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047380/h047380204.png ; $$\sum _ { \nu \in A } \| x _ { \nu } \| ^ { 2 } < \infty$$ ; confidence 0.895
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047390/h047390181.png ; $$V = V ^ { + } \oplus V ^ { - }$$ ; confidence 0.953
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047440/h04744011.png ; $$\lambda _ { 4 n }$$ ; confidence 0.681
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047440/h04744030.png ; $$f ( 0 ) = f ( 1 ) = 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110200/h11020058.png ; $$\Psi ( y _ { n } ) \subseteq \Psi ( y _ { 0 } )$$ ; confidence 0.934
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047470/h04747031.png ; $$F ^ { p }$$ ; confidence 0.768
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110220/h1102204.png ; $$h : E ^ { m } \rightarrow R$$ ; confidence 0.941
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047540/h04754045.png ; $$\Omega \frac { p } { x }$$ ; confidence 0.447
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047560/h04756028.png ; $$f ^ { - 1 } \circ f ( z ) = z$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047610/h04761062.png ; $$\mathfrak { M } ( M )$$ ; confidence 0.763
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110240/h11024037.png ; $$\mu _ { 1 } < 0 < \lambda _ { 1 }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110240/h11024025.png ; $$n _ { s } + n _ { u } = n$$ ; confidence 0.172
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h04769040.png ; $$g x = y$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h047690116.png ; $$G = SU ( k )$$ ; confidence 0.645
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047730/h04773077.png ; $$\beta ^ { s - k } z ^ { \prime }$$ ; confidence 0.907
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047740/h047740112.png ; $$R ) = r . g \operatorname { lowdim } ( R ) = \operatorname { glowdim } ( R )$$ ; confidence 0.142
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047740/h04774059.png ; $$0 \rightarrow A ^ { \prime } \rightarrow A \rightarrow A ^ { \prime \prime } \rightarrow 0$$ ; confidence 0.930
+. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120120/h12012026.png ; $$f \phi = 0$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120120/h120120117.png ; $$T ( H ( A ) )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047860/h047860136.png ; $$n = r \neq 0$$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047930/h047930317.png ; $$S X \rightarrow S X$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047930/h047930299.png ; $$Z / p$$ ; confidence 0.808
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047930/h04793027.png ; $$x = [ u ]$$ ; confidence 0.825
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047940/h04794088.png ; $$e _ { i } : O ( \Delta _ { q - 1 } ) \rightarrow O ( \Delta _ { q } )$$ ; confidence 0.793
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047940/h047940245.png ; $$\Delta _ { q }$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047940/h047940319.png ; $$\eta : \pi _ { N } \otimes \pi _ { N } \rightarrow \pi _ { N } + 1$$ ; confidence 0.085
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797023.png ; $$\mu ^ { * } : A ^ { * } \rightarrow A ^ { * } \otimes A ^ { * }$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110250/h11025012.png ; $$T ^ { \aleph } x \in A$$ ; confidence 0.469
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048000/h04800018.png ; $$\Omega \in \Delta ^ { n } S$$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110300/h1103003.png ; $$\psi ( x ) = \sum x ^ { \prime } \otimes x ^ { \prime \prime }$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048080/h04808011.png ; $$n - 1 \geq p$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110330/h11033039.png ; $$n \leq s \leq 2 n - 2$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110370/h11037062.png ; $$n \neq 0$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048190/h0481908.png ; $$\nu = 0$$ ; confidence 0.923
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048200/h0482005.png ; $$Z = 1$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130120/h13012038.png ; $$| f ( x + y ) - f ( x ) f ( y ) | \leq \varepsilon$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130130/h13013015.png ; $$e ^ { i k x }$$ ; confidence 0.648
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048250/h04825025.png ; $$O A M$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048270/h04827072.png ; $$f : \Omega \rightarrow B$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048300/h04830032.png ; $$P _ { m } ( \xi + \tau N )$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048310/h0483101.png ; $$\frac { \partial w } { \partial t } = A \frac { \partial w } { \partial x }$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048310/h04831085.png ; $$\alpha = a ( x )$$ ; confidence 0.757
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048330/h04833042.png ; $$W _ { X } ^ { S }$$ ; confidence 0.678
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048330/h04833033.png ; $$E _ { X } ^ { N }$$ ; confidence 0.539
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048390/h04839015.png ; $$U ^ { ( 2 ) }$$ ; confidence 0.956
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110400/h11040046.png ; $$\int _ { X } | f ( x ) | ^ { 2 } \operatorname { ln } | f ( x ) | d \mu ( x ) \leq$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110400/h11040065.png ; $$H _ { 1 } \otimes I + I \otimes H _ { 2 }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048420/h048420118.png ; $$F _ { j } ( z ) = \sum _ { k = 1 } ^ { N } G _ { j k } ( z )$$ ; confidence 0.944
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048420/h0484203.png ; $$F _ { + } ( x + i 0 ) - F _ { - } ( x - i 0 )$$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048440/h04844022.png ; $$\alpha - \beta$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048440/h0484406.png ; $$w = z ^ { - \gamma / 2 } ( z - 1 ) ^ { ( \gamma - \alpha - \beta - 1 ) / 2 } u$$ ; confidence 0.892
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048450/h0484501.png ; $$z ( 1 - z ) w ^ { \prime \prime } + [ \gamma - ( \alpha + \beta + 1 ) z ] w ^ { \prime } - \alpha \beta w = 0$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048520/h04852064.png ; $$| f | = 1$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120150/h12015024.png ; $$\operatorname { log } | \phi ( h ) | = \int \operatorname { log } | h | d$$ ; confidence 0.751
+. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110430/h1104304.png ; $$H _ { 1 } ( x ) < H _ { 2 } ( x )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047512/h04751218.png ; $$A = \operatorname { sup } _ { y \in E } A ( y ) < \infty$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050030/i05003048.png ; $$I _ { X }$$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050030/i050030120.png ; $$A \backslash I$$ ; confidence 0.946
+. https://www.encyclopediaofmath.org/legacyimages/i/i110/i110020/i11002022.png ; $$0 = + \infty$$ ; confidence 0.667
+. https://www.encyclopediaofmath.org/legacyimages/i/i110/i110020/i11002068.png ; $$( \lambda \odot \mu ) \odot v = \lambda \odot ( \mu \odot v )$$ ; confidence 0.955
+. https://www.encyclopediaofmath.org/legacyimages/i/i110/i110020/i11002080.png ; $$( A )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/i/i110/i110060/i11006080.png ; $$T$$ ; confidence 0.652
+. https://www.encyclopediaofmath.org/legacyimages/i/i110/i110060/i11006083.png ; $$H \equiv L \circ K$$ ; confidence 0.769
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050230/i050230319.png ; $$f \in S _ { y } ^ { \prime }$$ ; confidence 0.307
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050230/i050230164.png ; $$H _ { p } ^ { r } ( R ^ { n } ) \rightarrow H _ { p ^ { \prime } } ^ { \rho ^ { \prime } } ( R ^ { m } ) \rightarrow H _ { p l ^ { \prime \prime } } ^ { \rho ^ { \prime \prime } } ( R ^ { m ^ { \prime \prime } } )$$ ; confidence 0.143
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050230/i05023059.png ; $$1 < m \leq n$$ ; confidence 0.737
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050230/i050230379.png ; $$\| f \| _ { \Lambda _ { p } ^ { r } ( R ^ { n } ) } \leq K$$ ; confidence 0.335
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050230/i050230228.png ; $$D _ { j } ^ { l } f \in L _ { p } ( R ^ { n } )$$ ; confidence 0.948
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050230/i050230312.png ; $$- \infty < r < \infty$$ ; confidence 0.842
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050310/i05031036.png ; $$\delta _ { 0 } > 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050400/i05040021.png ; $$[ t ^ { n } : t ^ { n - 1 } ] = 0$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002074.png ; $$+ \frac { n } { p _ { 1 } p _ { 2 } } + \ldots + \frac { n } { p _ { k - 1 } p _ { k } } + - \frac { n } { p _ { 1 } p _ { 2 } p _ { 3 } } - \ldots + ( - 1 ) ^ { k } \frac { n } { p _ { 1 } \ldots p _ { k } }$$ ; confidence 0.552
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050640/i05064012.png ; $$\gamma = \operatorname { ind } _ { g } a$$ ; confidence 0.608
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050650/i0506506.png ; $$D = L _ { 1 } / D ( L _ { 0 } )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050650/i050650145.png ; $$\phi * : H ^ { * } ( B / S ) = H ^ { * } ( T M ) \rightarrow H ^ { * } ( M )$$ ; confidence 0.867
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050650/i050650302.png ; $$D$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050650/i05065016.png ; $$B ( M )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050650/i050650148.png ; $$\therefore M \rightarrow E$$ ; confidence 0.524
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050650/i050650137.png ; $$K ( B / S )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050650/i050650262.png ; $$K ( T M ^ { g } ) \otimes C \rightarrow C$$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050650/i050650350.png ; $$i _ { \alpha } ( D ) \in K ( Y )$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050650/i050650103.png ; $$\Sigma ( M ) = B ^ { + } \cup _ { S ( M ) } B ^ { - }$$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i130030178.png ; $$h ( [ a ] )$$ ; confidence 0.265
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i130030142.png ; $$\pi$$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i13003026.png ; $$[ T ^ { * } M ]$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050720/i05072015.png ; $$\eta : Y \rightarrow B$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050730/i050730155.png ; $$\nu _ { S }$$ ; confidence 0.758
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050730/i05073063.png ; $$K \subset H$$ ; confidence 0.959
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050730/i05073087.png ; $$\chi _ { \pi } ( g ) = \sum _ { \{ \delta : \delta y \in H \delta \} } \chi _ { \rho } ( \delta g \delta ^ { - 1 } )$$ ; confidence 0.903
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050770/i05077013.png ; $$\phi _ { \alpha \alpha } = 1 _ { A _ { \alpha } }$$ ; confidence 0.624
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050770/i05077064.png ; $$A = \operatorname { lim } _ { \rightarrow } F ( D )$$ ; confidence 0.939
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050790/i05079039.png ; $$| \alpha _ { 1 } + \ldots + \alpha _ { n } | \leq | \alpha _ { 1 } | + \ldots + | \alpha _ { n } |$$ ; confidence 0.160
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050850/i05085060.png ; $$A < \operatorname { ln } d X$$ ; confidence 0.106
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050850/i05085011.png ; $$1 ^ { \circ }$$ ; confidence 0.592
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050910/i05091079.png ; $$Y _ { n k }$$ ; confidence 0.813
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050950/i05095025.png ; $$= 2 \pi ^ { 3 } a ^ { 2 } \frac { ( n + 1 ) ( 2 n + 1 ) } { 3 n ^ { 2 } }$$ ; confidence 0.781
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050950/i05095033.png ; $$S = \frac { K } { 3 }$$ ; confidence 0.850
+. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050970/i05097047.png ; $$F ( M ^ { k } ) \subset \nabla \square ^ { n }$$ ; confidence 0.382
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051000/i05100028.png ; $$- \infty < a < + \infty$$ ; confidence 0.959
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051040/i05104010.png ; $$3 a$$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051130/i05113068.png ; $$\overline { \rho } _ { L }$$ ; confidence 0.896
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051150/i051150191.png ; $$p ^ { t } ( . )$$ ; confidence 0.817
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051070/i05107042.png ; $$c ( I ) = \frac { 1 } { 2 }$$ ; confidence 0.667
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051090/i05109035.png ; $$\Theta$$ ; confidence 0.952
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i1300404.png ; $$\sum _ { k = 1 } ^ { \infty } b _ { k } \operatorname { sin } k x$$ ; confidence 0.946
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051360/i0513609.png ; $$\int f _ { 1 } ( x ) d x \quad \text { and } \quad \int f _ { 2 } ( x ) d x$$ ; confidence 0.921
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051410/i051410114.png ; $$\alpha ( \lambda ) = \alpha _ { - } ( \lambda ) \alpha _ { + } ( \lambda )$$ ; confidence 0.598
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051410/i05141058.png ; $$0 < \alpha < a$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051410/i05141060.png ; $$h ( \lambda )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051430/i05143058.png ; $$| \lambda | < 1 / M ( b - \alpha )$$ ; confidence 0.952
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051430/i05143039.png ; $$\hat { \phi } ( x ) = \lambda \sum _ { i = 1 } ^ { n } C _ { i } \alpha _ { i } ( x ) + f ( x )$$ ; confidence 0.810
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051430/i05143036.png ; $$\{ \alpha _ { i } ( x ) \}$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051560/i05156047.png ; $$| t - \tau |$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051620/i051620138.png ; $$\Gamma = \partial D _ { 1 } \times \square \ldots \times \partial D _ { n }$$ ; confidence 0.954
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051620/i05162045.png ; $$\Gamma ( z ) = \frac { 1 } { e ^ { 2 i \pi z } - 1 } \int _ { L _ { 1 } } \zeta ^ { z - 1 } e ^ { - \zeta } d \zeta$$ ; confidence 0.895
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051620/i05162064.png ; $$\frac { \partial } { \partial z } = \frac { 1 } { 2 } ( \frac { \partial } { \partial x } + i \frac { \partial } { \partial y } )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i12004046.png ; $$\partial D \times D$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/i/i110/i110080/i11008014.png ; $$g \in E$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/i/i110/i110080/i11008077.png ; $$T f _ { n } \rightarrow 0$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051770/i05177061.png ; $$\psi = \sum \psi _ { i } \partial / \partial x _ { i }$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051870/i05187033.png ; $$T _ { W } ^ { 2 k + 1 } ( X )$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051880/i05188051.png ; $$\mathfrak { M } \in S _ { 1 }$$ ; confidence 0.842
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051930/i051930181.png ; $$Y = C$$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051930/i051930154.png ; $$\{ f _ { \alpha } : \alpha \in \mathfrak { A } \}$$ ; confidence 0.968
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051940/i05194058.png ; $$m \times ( n + 1 )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051950/i05195031.png ; $$\frac { ( x - x _ { k } - 1 ) ( x - x _ { k + 1 } ) } { ( x _ { k } - x _ { k - 1 } ) ( x _ { k } - x _ { k + 1 } ) } f ( x _ { k } ) + \frac { ( x - x _ { k - 1 } ) ( x - x _ { k } ) } { ( x _ { k } + 1 - x _ { k - 1 } ) ( x _ { k + 1 } - x _ { k } ) } f ( x _ { k + 1 } )$$ ; confidence 0.069
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051950/i051950193.png ; $$\{ \psi _ { i } ( x ) \} _ { i = 0 } ^ { n }$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051970/i051970120.png ; $$\omega _ { n - 1 } ( z ) = ( z - b _ { 0 } ) \ldots ( z - b _ { n } - 1 )$$ ; confidence 0.462
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052000/i05200039.png ; $$\Delta ^ { i }$$ ; confidence 0.491
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052020/i05202038.png ; $$B = Y \backslash 0$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006014.png ; $$x < \varrho y$$ ; confidence 0.723
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052110/i05211013.png ; $$T \subset R ^ { 1 }$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052130/i05213037.png ; $$\forall y \exists z ( \gamma ( y ) + 1 = \alpha ( g * \overline { \beta } ( z ) ) )$$ ; confidence 0.288
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052150/i0521507.png ; $$\forall x ( P ( x ) \vee \neg P ( x ) ) \wedge \neg \neg \neg x P ( x ) \supset \exists x P ( x )$$ ; confidence 0.397
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052230/i0522303.png ; $$x \leq z \leq y$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052260/i05226072.png ; $$Z \in G$$ ; confidence 0.401
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052370/i05237019.png ; $$\operatorname { inh } ^ { - 1 } z = - i \operatorname { arcsin } i z$$ ; confidence 0.766
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005074.png ; $$| r _ { + } ( k ) | \leq 1 - c k ^ { 2 } ( 1 + k ^ { 2 } ) ^ { - 1 }$$ ; confidence 0.554
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005080.png ; $$s > - \infty$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i130060185.png ; $$< 2 a$$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006049.png ; $$y \geq x \geq 0$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007010.png ; $$q ( x ) \in L ^ { 2 } \operatorname { loc } ( R ^ { 3 } )$$ ; confidence 0.953
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052410/i05241032.png ; $$y = Arc$$ ; confidence 0.482
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052410/i05241017.png ; $$\operatorname { cos } ^ { - 1 } x$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052450/i0524507.png ; $$F [ \phi ( w ) ]$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052450/i0524504.png ; $$b = f ( a ) = b _ { 0 }$$ ; confidence 0.455
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052500/i05250047.png ; $$P ^ { N } ( k )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052500/i05250054.png ; $$L ^ { \prime }$$ ; confidence 0.256
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052500/i05250023.png ; $$O _ { X } ( 1 ) = O ( 1 )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052520/i05252091.png ; $$f ( x ^ { * } x ) \leq f ( 1 ) r ( x ^ { * } x )$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052550/i05255041.png ; $$\omega ^ { \beta }$$ ; confidence 0.626
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052660/i05266017.png ; $$0 \in R ^ { 3 }$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008061.png ; $$H = 0$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008047.png ; $$m s$$ ; confidence 0.683
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i120080116.png ; $$\gamma = 7 / 4$$ ; confidence 0.659
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052730/i05273034.png ; $$p : G \rightarrow G$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130080/i13008028.png ; $$X ^ { \prime \prime } = L _ { 1 } ^ { \prime \prime } \cap L _ { 2 } ^ { \prime \prime } = L _ { 2 } ^ { \prime \prime } \cap L _ { 3 } ^ { \prime \prime } = L _ { 1 } ^ { \prime \prime } \cap L _ { 3 } ^ { \prime \prime }$$ ; confidence 0.831
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052800/i05280027.png ; $$x = \{ x ^ { \alpha } ( u ^ { s } ) \}$$ ; confidence 0.775
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052800/i052800127.png ; $$E ^ { 2 k + 1 }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052860/i052860119.png ; $$( = 2 / \pi )$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052940/i05294039.png ; $$F _ { t } : M ^ { n } \rightarrow M ^ { n }$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052940/i05294012.png ; $$Y \times t$$ ; confidence 0.546
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052980/i05298049.png ; $$L ^ { \prime } ( T _ { x } M )$$ ; confidence 0.252
+. https://www.encyclopediaofmath.org/legacyimages/i/i053/i053020/i05302031.png ; $$\kappa _ { k } = a _ { n n } ^ { ( k ) }$$ ; confidence 0.556
+. https://www.encyclopediaofmath.org/legacyimages/i/i053/i053020/i05302096.png ; $$\beta _ { k } q _ { k + 1 } = A q _ { k } - \beta _ { k - 1 } q _ { k - 1 } - \alpha _ { k } q _ { k k }$$ ; confidence 0.371
+. https://www.encyclopediaofmath.org/legacyimages/i/i053/i053040/i05304033.png ; $$F _ { 0 }$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009013.png ; $$k = k _ { 0 } \subset k _ { 1 } \subset \ldots \subset k _ { n } \subset \ldots \subset K = \cup _ { n \geq 0 } k _ { k }$$ ; confidence 0.434
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090151.png ; $$p < 12000000$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090126.png ; $$\lambda _ { p } ( K / k ) = \lambda ( X )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090231.png ; $$( X ^ { \omega } \chi ^ { - 1 } ) = \pi ^ { \mu _ { \chi } ^ { * } } g _ { \chi } ^ { * } ( T )$$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090155.png ; $$\overline { Q } _ { p }$$ ; confidence 0.689
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009026.png ; $$\mu _ { m }$$ ; confidence 0.969
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054050/j05405048.png ; $$\theta _ { 3 } ( v \pm \frac { 1 } { 2 } \tau ) = e ^ { - i \pi \tau / 4 } \cdot e ^ { - i \pi v } \cdot \theta _ { 2 } ( v )$$ ; confidence 0.312
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054050/j054050109.png ; $$dn ^ { 2 } u + k ^ { 2 } sn ^ { 2 } u = 1$$ ; confidence 0.565
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054050/j05405038.png ; $$\theta _ { 2 } ( v \pm \tau ) = e ^ { - i \pi \tau } \cdot e ^ { - 2 i \pi v } \cdot \theta _ { 2 } ( v )$$ ; confidence 0.234
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054050/j054050155.png ; $$e _ { 1 } = ( 2 - k ^ { 2 } ) / 3$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054050/j05405060.png ; $$H _ { 2 } = \prod _ { m = 1 } ^ { \infty } ( 1 + e ^ { ( 2 m - 1 ) i \pi \tau } )$$ ; confidence 0.836
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054070/j05407010.png ; $$w _ { 1 } = w _ { 1 } ( z _ { 1 } )$$ ; confidence 0.916
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054090/j05409038.png ; $$x = B x + g$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120010/j12001037.png ; $$\operatorname { log } F \leq 100$$ ; confidence 0.843
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054200/j05420048.png ; $$f _ { 0 } ( \Delta )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054200/j05420029.png ; $$f _ { 0 } ( z _ { j } ) = \left\{ \begin{array} { l l } { \alpha ^ { ( j ) } z _ { j } + \text { non-positive powers of } z _ { j } } & { \text { if } j \leq r } \\ { z _ { j } + \sum _ { s = x _ { j } } ^ { \infty } a _ { s } ^ { ( j ) } z _ { j } ^ { - s } } & { \text { if } j > r } \end{array} \right.$$ ; confidence 0.051
+. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020198.png ; $$k _ { \vartheta } ( z ) = \frac { 1 - | z | ^ { 2 } } { | z - e ^ { i \vartheta | ^ { 2 } } }$$ ; confidence 0.753
+. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020240.png ; $$B M O$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054250/j05425028.png ; $$K ^ { * }$$ ; confidence 0.718
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004062.png ; $$\operatorname { cr } ( K )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004079.png ; $$s ( L ) \geq ( E - e ) / 2$$ ; confidence 0.952
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j130040145.png ; $$M ^ { ( 2 ) }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004075.png ; $$( n _ { + } - n _ { - } ) - ( s ( D _ { L } ) - 1 ) \leq e \leq E \leq ( n _ { + } - n _ { - } ) + ( s ( D _ { L } ) - 1 )$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054340/j0543403.png ; $$J = \left| \begin{array} { c c c c } { J _ { n _ { 1 } } ( \lambda _ { 1 } ) } & { \square } & { \square } & { \square } \\ { \square } & { \ldots } & { \square } & { 0 } \\ { 0 } & { \square } & { \ldots } & { \square } \\ { \square } & { \square } & { \square } & { J _ { n _ { S } } ( \lambda _ { s } ) } \end{array} \right|$$ ; confidence 0.072
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007031.png ; $$L = \angle \operatorname { lim } _ { z \rightarrow \omega } f ( z )$$ ; confidence 0.923
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007082.png ; $$\phi _ { \omega } ( F ( z ) ) \leq \phi _ { \omega } ( z )$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055030/k055030100.png ; $$t = [ \xi _ { E } ]$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055030/k05503063.png ; $$T ( X )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055040/k05504059.png ; $$x _ { 0 } ^ { 4 } + x _ { 1 } ^ { 4 } + x _ { 2 } ^ { 4 } + x _ { 3 } ^ { 4 } = 0$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055100/k05510011.png ; $$h = K \eta \leq 1 / 2$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110030/k11003029.png ; $$\frac { x ^ { \rho + 1 } f ( x ) } { \int _ { x } ^ { x } t ^ { \sigma } f ( t ) d t } \rightarrow \sigma + \rho + 1 \quad ( x \rightarrow \infty )$$ ; confidence 0.320
+. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130010/k13001035.png ; $$f ( \vec { D } ( A ) ) = ( - A ^ { 3 } ) ^ { - \operatorname { Tait } ( \vec { D } ) } \langle D \rangle$$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130010/k13001041.png ; $$A | D _ { + } \rangle - A ^ { - 1 } \langle D _ { - } \} = ( A ^ { 2 } - A ^ { - 2 } ) \langle D _ { 0 } \}$$ ; confidence 0.230
+. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130010/k13001019.png ; $$T ( s )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120040/k12004019.png ; $$\overline { 9 } _ { 42 }$$ ; confidence 0.683
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120060/k12006031.png ; $$h ^ { 0 } ( K _ { X } \otimes L ^ { * } )$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120050/k1200504.png ; $$B = \sum _ { j = 1 } ^ { t } b _ { j } B _ { j }$$ ; confidence 0.961
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120050/k12005074.png ; $$m \geq m _ { 0 }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055180/k05518015.png ; $$z ^ { 2 } y ^ { \prime \prime } + z y ^ { \prime } - ( i z ^ { 2 } + \nu ^ { 2 } ) y = 0$$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110070/k11007019.png ; $$- w _ { 0 } ( \chi )$$ ; confidence 0.944
+. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110080/k1100801.png ; $$W _ { C }$$ ; confidence 0.473
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120080/k12008015.png ; $$K _ { p } ( f ) ( p _ { i } ) = f ( p _ { i } )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055340/k0553405.png ; $$K _ { \mu }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055350/k05535065.png ; $$K _ { 0 } ^ { 4 k + 2 }$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055440/k05544031.png ; $$\Delta u = - f ( x )$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055450/k0554502.png ; $$u | _ { \Sigma } = 0$$ ; confidence 0.837
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055480/k05548037.png ; $$R \phi / 6$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055480/k0554806.png ; $$\mu = m c / \hbar$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055480/k05548036.png ; $$\| g _ { \alpha \beta } \|$$ ; confidence 0.862
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055480/k05548012.png ; $$\partial / \partial x ^ { \alpha } \rightarrow ( \partial / \partial x ^ { \alpha } ) - i e A _ { \alpha } / \hbar$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055520/k05552076.png ; $$\Omega ( \Gamma )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055520/k05552082.png ; $$\Gamma 20$$ ; confidence 0.310
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055520/k05552062.png ; $$D _ { 1 } / \Gamma$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055520/k055520124.png ; $$\frac { 1 } { 2 \pi } \{ \text { hyperbolic area of } \Omega \backslash \Gamma \} \leq 2 ( N - 1 )$$ ; confidence 0.926
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055580/k055580126.png ; $$\hat { M } _ { 0 }$$ ; confidence 0.537
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055610/k055610105.png ; $$Q _ { 1 } : A \rightarrow T ^ { \prime } A T$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055630/k0556303.png ; $$| m K _ { V ^ { \prime } } | ^ { J }$$ ; confidence 0.246
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055660/k0556604.png ; $$f ( z ) = z + \ldots$$ ; confidence 0.768
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055700/k0557001.png ; $$\frac { \partial f } { \partial s } = - A _ { S } f$$ ; confidence 0.702
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055700/k05570014.png ; $$I _ { \Gamma } ( x )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055700/k05570017.png ; $$A _ { t } ^ { * }$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120090/k12009012.png ; $$= \frac { 2 } { \pi ^ { 2 } x _ { 0 } } \int _ { 0 } ^ { \infty } K _ { i \tau } ( x _ { 0 } ) \tau \operatorname { sinh } ( \pi \tau ) F ( \tau ) d \tau$$ ; confidence 0.890
+. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110130/k11013020.png ; $$( \alpha _ { i } ) _ { i \in I }$$ ; confidence 0.480
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055800/k05580079.png ; $$( \partial ^ { 2 } / \partial x \partial t ) u = \operatorname { sin } u$$ ; confidence 0.562
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055820/k0558203.png ; $$\square ^ { 1 } S _ { 2 } ( i )$$ ; confidence 0.950
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840272.png ; $$E ( \Delta ) K \subset D ( A )$$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840256.png ; $$c ( A ) \subset R \cup \{ \infty \}$$ ; confidence 0.588
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840354.png ; $$C = C ^ { * }$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055850/k05585032.png ; $$W _ { \alpha } ( P ) \subseteq ( D _ { \alpha } ) ^ { n }$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055850/k055850103.png ; $$D _ { \alpha }$$ ; confidence 0.374
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055850/k05585059.png ; $$W _ { \alpha } ( B \supset C ) = T \leftrightarrows$$ ; confidence 0.637
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055910/k05591019.png ; $$\sum _ { j = 1 } ^ { n } b _ { j } r j \in Z$$ ; confidence 0.479
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055940/k05594036.png ; $$\eta ( \epsilon ) \rightarrow 0$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055940/k05594016.png ; $$\frac { d \xi } { d t } = \epsilon X _ { 0 } ( \xi ) + \epsilon ^ { 2 } P _ { 2 } ( \xi ) + \ldots + \epsilon ^ { m } P _ { m } ( \xi )$$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055940/k05594047.png ; $$\xi = \xi _ { 0 } ( \phi )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110190/k11019034.png ; $$\mu _ { n } ( P \| Q ) =$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110190/k11019069.png ; $$P = Q$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k12003033.png ; $$E \neq \emptyset$$ ; confidence 0.475
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k12003040.png ; $$E = \emptyset$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k12003036.png ; $$F _ { M } : G \rightarrow C ^ { * }$$ ; confidence 0.933
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055070/k05507045.png ; $$g = \sum g _ { \alpha \overline { \beta } } d z ^ { \alpha } \otimes d z \square ^ { \beta }$$ ; confidence 0.694
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055080/k05508019.png ; $$\nu _ { 0 } \in C ^ { n }$$ ; confidence 0.245
+. https://www.encyclopediaofmath.org/legacyimages/k/k056/k056010/k056010135.png ; $$p : X \rightarrow S$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/k/k056/k056010/k056010160.png ; $$R ^ { k } p \times ( F )$$ ; confidence 0.519
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110020/l11002085.png ; $$x \preceq y$$ ; confidence 0.956
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110030/l11003082.png ; $$M ( E ) = \vec { X }$$ ; confidence 0.493
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057050/l057050123.png ; $$c \rightarrow N$$ ; confidence 0.335
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057050/l057050113.png ; $$\overline { B } \rightarrow \overline { B }$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057050/l057050165.png ; $$a \rightarrow a b d ^ { 6 }$$ ; confidence 0.569
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110160/l11016049.png ; $$n ^ { O ( n ) } M ^ { O ( 1 ) }$$ ; confidence 0.921
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057110/l0571105.png ; $$\{ \phi _ { n } \} _ { n = 1 } ^ { \infty }$$ ; confidence 0.817
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057120/l0571208.png ; $$1 \leq p < + \infty$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057150/l05715028.png ; $$3 N + k + m$$ ; confidence 0.919
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057150/l05715026.png ; $$\ddot { x } \square _ { \nu } = d \dot { x } \square _ { \nu } / d t$$ ; confidence 0.944
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057150/l05715031.png ; $$\mu$$ ; confidence 0.335
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057180/l05718018.png ; $$x g$$ ; confidence 0.734
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057200/l0572001.png ; $$T + V = h$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110050/l11005048.png ; $$v ( P ) - v ( D )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110060/l1100603.png ; $$x ^ { ( 0 ) } = 1$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700011.png ; $$M N$$ ; confidence 0.867
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l057000153.png ; $$+ ( \lambda x y \cdot y ) : ( \sigma \rightarrow ( \tau \rightarrow \tau ) )$$ ; confidence 0.262
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l0570007.png ; $$( M N ) \in \Lambda$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700094.png ; $$\equiv \lambda x y \cdot x$$ ; confidence 0.709
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700010.png ; $$( \lambda x M ) \in \Lambda$$ ; confidence 0.756
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057430/l05743029.png ; $$k ^ { 2 } ( \tau ) = \lambda$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057440/l05744010.png ; $$D = 2 \gamma k T / M$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120030/l12003069.png ; $$T _ { F }$$ ; confidence 0.455
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120030/l12003046.png ; $$T _ { E } : U \rightarrow U$$ ; confidence 0.704
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057450/l05745021.png ; $$v \in C ( \overline { G } )$$ ; confidence 0.795
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057510/l05751032.png ; $$\Delta ( \alpha _ { 1 } \ldots i _ { p } d x ^ { i _ { 1 } } \wedge \ldots \wedge d x ^ { i p } ) =$$ ; confidence 0.331
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057540/l05754082.png ; $$| t | ^ { - 1 }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057560/l05756010.png ; $$E = \frac { m } { 2 } ( \dot { x } \square _ { 1 } ^ { 2 } + \dot { x } \square _ { 2 } ^ { 2 } + \dot { x } \square _ { 3 } ^ { 2 } ) + \frac { \kappa } { r }$$ ; confidence 0.586
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057590/l05759015.png ; $$\sqrt { 2 }$$ ; confidence 0.155
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057610/l05761045.png ; $$m < n ^ { ( 1 / 3 ) - \delta }$$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057610/l05761040.png ; $$U _ { 0 } = 1$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057640/l0576408.png ; $$\alpha _ { 1 } + n h _ { 1 }$$ ; confidence 0.738
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057720/l05772024.png ; $$E ( \mu _ { n } / n )$$ ; confidence 0.725
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057740/l05774010.png ; $$\operatorname { lim } _ { n \rightarrow \infty } \operatorname { sup } \frac { S _ { n } } { c _ { n } } = 1 \quad ( \alpha . s . )$$ ; confidence 0.299
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057780/l057780212.png ; $$31$$ ; confidence 0.915
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057780/l057780113.png ; $$\mu \approx 18.431$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057780/l05778086.png ; $$4.60$$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057780/l057780230.png ; $$E Y _ { i } = ( \alpha + \beta \overline { t } ) + \beta ( t _ { i } - \overline { t } )$$ ; confidence 0.681
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057780/l057780185.png ; $$\alpha _ { 2 } ( t ) = t$$ ; confidence 0.461
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120050/l12005018.png ; $$f ( x ) = \operatorname { lim } _ { N \rightarrow \infty } \frac { 4 } { \pi ^ { 2 } } \int _ { 0 } ^ { N } \operatorname { cosh } ( \pi \tau ) \operatorname { Im } K _ { 1 / 2 + i \tau } ( x ) F ( \tau ) d \tau$$ ; confidence 0.580
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057870/l05787021.png ; $$\lambda ( I ) = \lambda ^ { * } ( A \cap I ) + \lambda ^ { * } ( I \backslash A )$$ ; confidence 0.776
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006098.png ; $$H \phi$$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006043.png ; $$\int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle ^ { 2 } } { \lambda } _ { d } \lambda < E _ { 0 }$$ ; confidence 0.248
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006027.png ; $$\phi \in H$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058080/l0580808.png ; $$B \subset X ^ { * }$$ ; confidence 0.699
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058140/l05814017.png ; $$v = v ( t )$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058140/l0581405.png ; $$s = \int _ { a } ^ { b } \sqrt { 1 + [ f ^ { \prime } ( x ) ] ^ { 2 } } d x$$ ; confidence 0.961
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058170/l05817023.png ; $$\{ i _ { k } \}$$ ; confidence 0.773
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058210/l05821011.png ; $$\zeta = 0$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058210/l05821012.png ; $$- \operatorname { log } | \zeta |$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058210/l05821045.png ; $$0 < r < \operatorname { tanh } \pi / 4$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058240/l0582408.png ; $$\operatorname { grad } \phi ( \zeta ) \neq 0$$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058360/l05836041.png ; $$x \# y = x y + y x - \frac { 2 } { n + 1 } ( \operatorname { Tr } x y ) l$$ ; confidence 0.625
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058360/l05836011.png ; $$( x y ) x = y ( y x )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058360/l058360172.png ; $$\mathfrak { A } ^ { - }$$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058360/l05836089.png ; $$S ^ { i j } = \Omega ^ { i j } + T ^ { i j }$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058360/l058360168.png ; $$x$$ ; confidence 0.899
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058360/l058360142.png ; $$P _ { 8 }$$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058430/l058430107.png ; $$g ^ { \prime } / ( 1 - u ) g ^ { \prime } = \overline { g }$$ ; confidence 0.215
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058470/l05847082.png ; $$\mathfrak { g } = \mathfrak { a } + \mathfrak { n }$$ ; confidence 0.634
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510198.png ; $$0 \leq p \leq n / 2$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510173.png ; $$A _ { I l }$$ ; confidence 0.608
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058480/l05848075.png ; $$L ( H )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120090/l12009013.png ; $$Q _ { A }$$ ; confidence 0.136
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590134.png ; $$S \cap R ( G ) = ( e )$$ ; confidence 0.872
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859076.png ; $$x ( 1 )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861031.png ; $$Z \times T$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861083.png ; $$C ^ { n } / \Gamma _ { 1 }$$ ; confidence 0.708
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058660/l05866027.png ; $$G \subset N ( F )$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868041.png ; $$\pi _ { 1 } ( G ) \cong \Gamma ( G ) / \Gamma _ { 0 }$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872090.png ; $$l _ { k } ( A )$$ ; confidence 0.348
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110140/l11014038.png ; $$\epsilon$$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110140/l11014014.png ; $$\tilde { y } ( x ) = \operatorname { exp } ( - \epsilon ) f ( x \operatorname { exp } ( - \epsilon ) )$$ ; confidence 0.405
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058770/l05877073.png ; $$\operatorname { lm } A _ { * } = \mathfrak { g }$$ ; confidence 0.711
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l120100122.png ; $$R ^ { n } \times R ^ { n }$$ ; confidence 0.554
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010011.png ; $$\left\{ \begin{array} { l l } { \gamma \geq \frac { 1 } { 2 } } & { \text { forn } = 1 } \\ { \gamma > 0 } & { \text { forn } = 2 } \\ { \gamma \geq 0 } & { \text { forn } \geq 3 } \end{array} \right.$$ ; confidence 0.191
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010023.png ; $$\approx ( 2 \pi ) ^ { - n } \int _ { R ^ { n } \times R ^ { n } } [ p ^ { 2 } + V ( x ) ] _ { - } ^ { \gamma } d p d x =$$ ; confidence 0.680
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058820/l058820245.png ; $$\operatorname { lim } _ { x \rightarrow x _ { 0 } } ( f _ { 1 } ( x ) / f _ { 2 } ( x ) )$$ ; confidence 0.857
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058820/l058820138.png ; $$\operatorname { lim } _ { x \rightarrow x _ { 0 } } f ( x ) = \alpha$$ ; confidence 0.845
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058820/l058820374.png ; $$\tau = \{ t _ { i } \} _ { i = 0 } ^ { i = n }$$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058830/l05883068.png ; $$- \Delta u + c u$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058920/l05892067.png ; $$Z y \rightarrow \infty$$ ; confidence 0.270
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059020/l05902046.png ; $$y = \operatorname { sin } ( 1 / x )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059110/l059110158.png ; $$f _ { h } \in F _ { k }$$ ; confidence 0.549
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059110/l05911037.png ; $$p i n$$ ; confidence 0.132
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059110/l05911071.png ; $$+ \sum _ { i = 1 } ^ { s } \| k _ { i k } [ u ] _ { k } - \{ l _ { i } u \} _ { i k } \| _ { \Phi _ { i k } } + \| p _ { i k } \phi _ { i } - \{ \phi _ { i } \} _ { i k } \| _ { \Phi _ { i k } }$$ ; confidence 0.263
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059110/l059110155.png ; $$L _ { h } u _ { k } = f _ { k }$$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059110/l05911046.png ; $$\{ \phi _ { i } \} _ { i k }$$ ; confidence 0.712
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059110/l05911087.png ; $$l _ { 2 } u = \phi _ { 2 } ( t )$$ ; confidence 0.851
+. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l13006070.png ; $$\frac { 1 } { 4 n } \operatorname { max } \{ \alpha _ { i } : 0 \leq i \leq t \} \leq \Delta _ { 2 } \leq \frac { 1 } { 4 n } ( \sum _ { i = 0 } ^ { t } \alpha _ { i } + 2 )$$ ; confidence 0.363
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059140/l05914024.png ; $$\nabla _ { Y } ( f X ) = ( Y f ) X + f \nabla _ { Y } X$$ ; confidence 0.681
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059140/l0591406.png ; $$T _ { x _ { 1 } } ( M ) \rightarrow T _ { x _ { 0 } } ( M )$$ ; confidence 0.821
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059160/l05916065.png ; $$A ^ { ( 0 ) }$$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059160/l059160187.png ; $$\dot { u } = A _ { n } u$$ ; confidence 0.195
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059160/l05916072.png ; $$\operatorname { ln } t$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059160/l059160335.png ; $$T _ { \Delta }$$ ; confidence 0.636
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059160/l059160231.png ; $$\lambda \geq \gamma$$ ; confidence 0.474
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059170/l05917055.png ; $$\Gamma _ { 0 } ( . )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059170/l059170161.png ; $$H ^ { k }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059250/l05925090.png ; $$v \in ( 1 - t ) V$$ ; confidence 0.837
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059340/l059340144.png ; $$C _ { 0 } ( R )$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059340/l059340213.png ; $$A -$$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059350/l05935016.png ; $$x ( t ) \equiv 0$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059350/l05935013.png ; $$x ^ { ( n ) } + \alpha _ { 1 } ( t ) x ^ { ( n - 1 ) } + \ldots + \alpha _ { n } ( t ) x = 0$$ ; confidence 0.867
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059350/l059350101.png ; $$X ( t ) = \operatorname { exp } ( \int _ { t _ { 0 } } ^ { t } A ( \tau ) d \tau )$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059350/l05935092.png ; $$Y ( t ) = X ( t ) C$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059350/l05935079.png ; $$W ( t ) \neq 0$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059350/l059350157.png ; $$x ( 0 ) \in R ^ { n }$$ ; confidence 0.473
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059350/l059350126.png ; $$\dot { y } = - A ^ { T } ( t ) y$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059410/l05941048.png ; $$Q _ { 3 } ( b )$$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059490/l05949079.png ; $$x = F ( t ) y$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059490/l059490217.png ; $$\rho ^ { ( j ) }$$ ; confidence 0.828
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059490/l05949032.png ; $$\alpha ^ { ( 0 ) }$$ ; confidence 0.892
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059490/l059490155.png ; $$| \epsilon | < \epsilon$$ ; confidence 0.461
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059490/l059490127.png ; $$\frac { d z } { d t } = - A ( t ) ^ { * } Z$$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059540/l0595404.png ; $$L ( 0 ) = 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059610/l05961011.png ; $$\frac { d w _ { N } } { d t } = \frac { \partial w _ { N } } { \partial t } + \sum _ { i = 1 } ^ { N } ( \frac { \partial w _ { N } } { \partial r _ { i } } \frac { d r _ { i } } { d t } + \frac { \partial w _ { N } } { \partial p _ { i } } \frac { d p _ { i } } { d t } ) = 0$$ ; confidence 0.716
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059710/l05971012.png ; $$f \in H _ { p } ^ { \alpha }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l120120208.png ; $$G ( K _ { p ^ { \prime } } )$$ ; confidence 0.801
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l120120133.png ; $$( K _ { p } ) _ { i n s }$$ ; confidence 0.851
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l12012087.png ; $$Z _ { \text { tot } S } = Z$$ ; confidence 0.066
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060090/l060090100.png ; $$\operatorname { dim } Z \cap \overline { S _ { k + q + 1 } } ( F | _ { X \backslash Z } ) \leq k$$ ; confidence 0.399
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060160/l06016034.png ; $$\alpha = E X _ { 1 }$$ ; confidence 0.670
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060190/l06019071.png ; $$d ( A )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060220/l0602207.png ; $$\in \Theta$$ ; confidence 0.953
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060250/l06025052.png ; $$m = n = 1$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060290/l06029012.png ; $$\left. \begin{array} { c c c } { R } & { \stackrel { \pi _ { 2 } \mu } { \rightarrow } } & { B } \\ { \pi _ { 1 } \mu \downarrow } & { \square } & { \downarrow \beta } \\ { A } & { \vec { \alpha } } & { C } \end{array} \right.$$ ; confidence 0.590
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060310/l06031040.png ; $$R = \{ \alpha \in K : \operatorname { mod } _ { K } ( \alpha ) \leq 1 \}$$ ; confidence 0.342
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060530/l0605309.png ; $$h _ { U } = \phi _ { U } ^ { - 1 }$$ ; confidence 0.912
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120150/l12015025.png ; $$w \in T V$$ ; confidence 0.524
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060600/l06060022.png ; $$\int \frac { d x } { x } = \operatorname { ln } | x | + C$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060600/l06060030.png ; $$\pi < \operatorname { arg } z \leq \pi$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060640/l0606404.png ; $$\operatorname { res } _ { \mathscr { d } } \frac { f ^ { \prime } ( z ) } { f ( z ) }$$ ; confidence 0.129
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110170/l110170115.png ; $$Q \alpha = Q \beta \gamma$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060770/l0607706.png ; $$\operatorname { inv } ( x )$$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060820/l06082028.png ; $$\Delta ^ { r + 1 } v _ { j } = \Delta ^ { r } v _ { j + 1 } - \Delta ^ { r } v _ { j }$$ ; confidence 0.659
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060830/l06083045.png ; $$b \in Q$$ ; confidence 0.934
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060830/l06083024.png ; $$Q _ { i - 1 } / Q _ { i }$$ ; confidence 0.640
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120160/l12016033.png ; $$( S ^ { 1 } )$$ ; confidence 0.472
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120160/l1201604.png ; $$z = e ^ { i \theta }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060970/l0609706.png ; $$\alpha = R \operatorname { ln } \operatorname { tan } ( \frac { \pi } { 4 } + \frac { u } { 2 R } )$$ ; confidence 0.905
+. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061050/l0610509.png ; $$f ^ { \prime } ( x ) = 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061130/l06113042.png ; $$\| \alpha _ { j } ^ { i } \|$$ ; confidence 0.148
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120190/l12019039.png ; $$x = - \sum _ { k = 0 } ^ { \infty } ( A ^ { * } ) ^ { k } C ( A ) ^ { k }$$ ; confidence 0.953
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120190/l12019010.png ; $$\lambda _ { j } + \overline { \lambda } _ { k } = 0$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061160/l06116099.png ; $$V _ { 0 } \subset E$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061160/l061160114.png ; $$x _ { 0 } ( . ) : t _ { 0 } + R ^ { + } \rightarrow U$$ ; confidence 0.802
+. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061200/l06120026.png ; $$E ( T ) = \int \int _ { T } \frac { d x d y } { | x - y | }$$ ; confidence 0.572
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058310/l05831065.png ; $$F _ { n } ( - \infty ) \rightarrow F ( - \infty )$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m1200304.png ; $$f _ { \theta } ( x )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003057.png ; $$\varepsilon ^ { * } ( M A D ) = 1 / 2$$ ; confidence 0.731
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062070/m06207013.png ; $$H _ { 2 } \times H _ { 1 }$$ ; confidence 0.537
+. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110020/m11002071.png ; $$f \circ R _ { 1 } = R _ { 2 } \circ f$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130020/m13002013.png ; $$F _ { A } = * D _ { A } \phi$$ ; confidence 0.738
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130020/m13002029.png ; $$A = ( \frac { 1 } { \operatorname { sinh } r } - \frac { 1 } { r } ) \epsilon _ { i j k } \frac { x _ { j } } { r } \sigma _ { k } d x _ { i }$$ ; confidence 0.768
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130030/m1300307.png ; $$f ( z ^ { d } ) = f ( z ) - z$$ ; confidence 0.796
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062160/m06216027.png ; $$p < q$$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062160/m062160173.png ; $$E$$ ; confidence 0.975
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062160/m062160147.png ; $$\kappa = \mu ^ { * }$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120090/m12009011.png ; $$- i \partial / \partial x _ { j }$$ ; confidence 0.526
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120090/m12009064.png ; $$P ^ { * } ( D )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110050/m11005068.png ; $$q ^ { - 1 } = 1 - p ^ { - 1 }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062220/m06222011.png ; $$\Delta \lambda _ { i } ^ { \alpha }$$ ; confidence 0.329
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120110/m12011020.png ; $$t ( h ) = T ( h ) \cup \partial T ( k ) \partial F \times D ^ { 2 }$$ ; confidence 0.532
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120110/m12011054.png ; $$\pi _ { 1 } ( M ) \neq Z _ { 2 }$$ ; confidence 0.886
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120110/m12011082.png ; $$\Phi ( M ) \in Wh ( \pi _ { 1 } ( M ) )$$ ; confidence 0.743
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062330/m06233049.png ; $$M _ { \psi } ^ { 0 }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062350/m06235096.png ; $$\mu ^ { - 1 }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062360/m06236012.png ; $$T _ { i j }$$ ; confidence 0.337
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062390/m0623907.png ; $$P \{ \xi ( 0 ) = j \} = p _ { j }$$ ; confidence 0.551
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062490/m06249026.png ; $$\Lambda \in N ^ { t }$$ ; confidence 0.838
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062490/m062490165.png ; $$\Lambda = \{ \omega : x _ { S } \in B \}$$ ; confidence 0.703
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062490/m06249054.png ; $$F _ { \infty } ^ { s }$$ ; confidence 0.520
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062490/m06249090.png ; $$\alpha _ { \epsilon } ( h ) = o ( h )$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062540/m06254054.png ; $$| \theta - \frac { p } { n } | \leq \frac { 1 } { \tau q ^ { 2 } }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062550/m06255040.png ; $$u ( y ) \geq 0$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062550/m06255050.png ; $$0 \leq w \leq v$$ ; confidence 0.958
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062560/m06256075.png ; $$K _ { y } ^ { \alpha }$$ ; confidence 0.924
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120120/m120120128.png ; $$C = Z ( Q )$$ ; confidence 0.941
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062570/m06257039.png ; $$\xi _ { k } = + 1$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062590/m06259044.png ; $$V _ { [ r ] }$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062590/m06259032.png ; $$B = 0$$ ; confidence 0.833
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062590/m06259061.png ; $$\alpha = \beta _ { 1 } \vee \ldots \vee \beta _ { r }$$ ; confidence 0.964
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062610/m06261017.png ; $$\operatorname { lim } _ { \Delta x \rightarrow 0 } \Delta y = \operatorname { lim } _ { \Delta x \rightarrow 0 } [ f ( x + \Delta x ) - f ( x ) ] = 0$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062610/m06261090.png ; $$F ^ { \prime } = f$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013051.png ; $$\left. \begin{array}{l}{ \frac { d N ^ { 1 } } { d t } = \lambda _ { ( 1 ) } N ^ { 1 } ( 1 - \frac { N ^ { 1 } } { K _ { ( 1 ) } } - \delta _ { ( 1 ) } \frac { N ^ { 2 } } { K _ { ( 1 ) } } ) }\\{ \frac { d N ^ { 2 } } { d t } = \lambda _ { ( 2 ) } N ^ { 2 } ( 1 - \frac { N ^ { 2 } } { K _ { ( 2 ) } } - \delta _ { ( 2 ) } \frac { N ^ { 1 } } { K _ { ( 2 ) } } ) }\end{array} \right.$$ ; confidence 0.089
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013029.png ; $$= f ( N _ { * } ) + f ^ { \prime } ( N _ { * } ) n + \frac { f ^ { \prime \prime } ( N _ { * } ) } { 2 } n ^ { 2 } + \ldots$$ ; confidence 0.619
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062620/m062620207.png ; $$R _ { + } ^ { l }$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062620/m06262012.png ; $$b \in R ^ { l - 1 }$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062620/m062620198.png ; $$z \square ^ { ( s ) }$$ ; confidence 0.776
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062620/m062620248.png ; $$x > y > z$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062620/m06262048.png ; $$c ( t ) \geq 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062630/m06263022.png ; $$\int _ { - \infty } ^ { \infty } x d F ( x )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062690/m06269073.png ; $$k \frac { \partial u } { \partial n } + h u | _ { S } = v ( x )$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016065.png ; $$\Omega _ { p _ { 1 } n _ { 1 } } ( t ^ { \prime } t ^ { \prime } )$$ ; confidence 0.868
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063060/m06306029.png ; $$x _ { i + 1 } = x _ { i } - ( \alpha _ { i } \nabla \nabla f ( x _ { j } ) + \beta _ { i } I ) ^ { - 1 } \nabla f ( x _ { i } )$$ ; confidence 0.559
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063090/m06309023.png ; $$r _ { 0 } ^ { * } + \sum _ { j = 1 } ^ { q } \beta _ { j } r _ { j } ^ { * } = \sigma ^ { 2 }$$ ; confidence 0.822
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063100/m06310035.png ; $$\hat { \theta } = X$$ ; confidence 0.545
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063080/m06308045.png ; $$f ^ { ( m ) } ( x _ { 0 } ) < 0$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063140/m06314076.png ; $$x _ { 3 } = z$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063140/m06314012.png ; $$- \frac { \partial D } { \partial t } + \operatorname { rot } H = J$$ ; confidence 0.887
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063170/m0631709.png ; $$d \sigma ( t )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063240/m063240572.png ; $$\Lambda ( f ) \geq 0$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063240/m063240457.png ; $$\mu _ { i } ( X _ { i } ) = 1$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063240/m063240678.png ; $$E = E ^ { \prime }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063240/m063240428.png ; $$S _ { 1 } \times S _ { 2 }$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063240/m063240221.png ; $$E \in S ( R )$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063240/m063240749.png ; $$\prod x$$ ; confidence 0.487
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063350/m0633503.png ; $$\int _ { - 1 } ^ { 1 } \frac { 1 } { \sqrt { 1 - x ^ { 2 } } } f ( x ) d x \approx \frac { \pi } { N } \sum _ { k = 1 } ^ { N } f ( \operatorname { cos } \frac { 2 k - 1 } { 2 N } \pi )$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110110/m11011038.png ; $$\square _ { q } F _ { p - 1 }$$ ; confidence 0.930
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063370/m06337017.png ; $$t = t _ { 0 } > 0$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063460/m063460143.png ; $$p \in P \backslash N$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063460/m063460237.png ; $$( f ) = D$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063460/m06346056.png ; $$D ( z ) \neq 0$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063460/m063460176.png ; $$\psi _ { z } \neq 0$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063460/m063460182.png ; $$z \in N$$ ; confidence 0.568
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063590/m06359074.png ; $$F \mapsto F ( P )$$ ; confidence 0.864
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063710/m06371076.png ; $$\int _ { c } ^ { \infty } f ( x ) d x$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063710/m06371091.png ; $$n _ { 1 } < n _ { 2 } .$$ ; confidence 0.222
+. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110130/m11013041.png ; $$\beta + \gamma \simeq \alpha . S ( t )$$ ; confidence 0.822
+. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110130/m11013015.png ; $$E S$$ ; confidence 0.930
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063760/m063760111.png ; $$0 \rightarrow A \rightarrow B \stackrel { sp } { \rightarrow } \pi * C \rightarrow 0$$ ; confidence 0.355
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063800/m06380058.png ; $$\partial W _ { 1 } = M$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063800/m06380081.png ; $$\sigma ( W )$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063800/m06380038.png ; $$\theta _ { n } ( \partial \pi )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063910/m06391025.png ; $$\{ p _ { \theta } ( \omega ) = \frac { d p } { d \mu } ( \omega ) : \theta \in \Theta \}$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063920/m063920117.png ; $$\int \int K d S \leq 2 \pi ( \chi - k )$$ ; confidence 0.858
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063920/m06392082.png ; $$n \geq 9$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063920/m063920116.png ; $$\int \int K d S$$ ; confidence 0.865
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063980/m06398045.png ; $$\| x _ { k } - x ^ { * } \| \leq C q ^ { k }$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063990/m06399032.png ; $$A = \pi r ^ { 2 }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064000/m064000100.png ; $$\| u \| _ { H ^ { \prime } } \leq R$$ ; confidence 0.473
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064000/m06400065.png ; $$W ( N )$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064000/m0640004.png ; $$\epsilon > 0$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064000/m064000127.png ; $$F = W _ { 2 } ^ { - 1 } ( \Omega )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120210/m12021026.png ; $$\lambda K + t$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064250/m064250151.png ; $$\tau \cup A C \cup B C$$ ; confidence 0.892
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064250/m064250142.png ; $$d y / d s \geq 0$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064180/m064180110.png ; $$\mathfrak { k } _ { n } | _ { 0 } = 0$$ ; confidence 0.128
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064190/m064190102.png ; $$u | _ { \Gamma } = \psi$$ ; confidence 0.930
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064420/m06442050.png ; $$k = m / 2$$ ; confidence 0.948
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064430/m064430169.png ; $$GL _ { 2 } ( R )$$ ; confidence 0.691
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064430/m064430225.png ; $$\operatorname { lm } A ( \tau )$$ ; confidence 0.945
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064430/m06443090.png ; $$B O$$ ; confidence 0.877
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064430/m064430134.png ; $$w = \lambda ( z )$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064440/m06444056.png ; $$c = 0$$ ; confidence 0.874
+. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110180/m11018050.png ; $$J ( F G / I ) = 0$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064460/m0644606.png ; $$d ( x + y ) + d ( x y ) = d ( x ) + d ( y )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064540/m0645406.png ; $$m _ { G } = D ( u ) / 2 \pi$$ ; confidence 0.811
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064550/m06455029.png ; $$G \rightarrow R _ { + } ^ { * }$$ ; confidence 0.778
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064580/m06458025.png ; $$k _ { 1 } + \ldots + k _ { n } = k$$ ; confidence 0.849
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064590/m064590192.png ; $$\alpha p$$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064660/m06466019.png ; $$C _ { \gamma } = C _ { \gamma _ { 1 } } C _ { \gamma _ { 2 } }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064700/m064700127.png ; $$t \in P ^ { 1 }$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064700/m06470068.png ; $$\partial V _ { t }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064700/m0647004.png ; $$\alpha = \gamma ( 0 )$$ ; confidence 0.961
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064710/m06471081.png ; $$f ( z ) = f ( x + i y )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064720/m0647206.png ; $$f _ { E } ^ { \prime } ( \zeta )$$ ; confidence 0.845
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064830/m06483029.png ; $$f ( x ^ { \prime } ) < t$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064870/m06487010.png ; $$\xi = x _ { m }$$ ; confidence 0.952
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130220/m13022071.png ; $$T$$ ; confidence 0.520
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130220/m13022026.png ; $$T _ { e } = j - 744$$ ; confidence 0.742
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064910/m06491014.png ; $$Y ( K )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120230/m12023042.png ; $$( ( \partial f ) ^ { - 1 } + t l ) ^ { - 1 }$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130230/m130230103.png ; $$- ( K _ { X } + B )$$ ; confidence 0.752
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130230/m130230127.png ; $$\phi : X ^ { \prime } \rightarrow Y$$ ; confidence 0.951
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064990/m06499012.png ; $$f : M \rightarrow R$$ ; confidence 0.936
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064990/m06499028.png ; $$\sum _ { j = 0 } ^ { i } ( - 1 ) ^ { j } m _ { i - j } \geq \sum _ { j = 0 } ^ { i } ( - 1 ) ^ { j } b _ { i - j }$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064950/m06495010.png ; $$V _ { 1 } = \emptyset$$ ; confidence 0.731
+. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110210/m11021026.png ; $$\alpha = 4 \pi$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110210/m11021064.png ; $$f \in L ^ { p } ( R ^ { n } ) \rightarrow \int _ { R ^ { n } } | x - y | ^ { - \lambda } f ( y ) d y \in L ^ { p ^ { \prime } } ( R ^ { n } )$$ ; confidence 0.413
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065030/m06503013.png ; $$\tilde { y } = \alpha _ { 21 } x + \alpha _ { 22 } y + \alpha _ { 23 } z + b$$ ; confidence 0.163
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065030/m0650309.png ; $$x = x \operatorname { cos } \phi + y \operatorname { sin } \phi + \alpha$$ ; confidence 0.056
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120250/m12025047.png ; $$L C ^ { k - 1 }$$ ; confidence 0.734
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065140/m065140117.png ; $$p _ { 1 } + \ldots + p _ { m } = p$$ ; confidence 0.769
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065140/m06514041.png ; $$S _ { n }$$ ; confidence 0.963
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065160/m06516021.png ; $$\operatorname { ess } \operatorname { sup } _ { X } | f ( x ) | = \operatorname { lim } _ { n \rightarrow \infty } ( \frac { \int | f ( x ) | ^ { n } d M _ { X } } { \int _ { X } d M _ { x } } )$$ ; confidence 0.229
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065180/m06518046.png ; $$\alpha : A \rightarrow A _ { 1 }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110220/m11022016.png ; $$\lambda ^ { * } \in R ^ { m }$$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065250/m06525013.png ; $$G _ { 1 } / N$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065300/m06530022.png ; $$\otimes _ { i = 1 } ^ { n } E _ { i } \rightarrow F$$ ; confidence 0.927
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m13025061.png ; $$\int | \rho _ { \varepsilon } ( x ) | d x$$ ; confidence 0.965
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m130250103.png ; $$s > n / 2$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m13025065.png ; $$M _ { 3 } ( R ^ { n } ) = \{$$ ; confidence 0.724
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065440/m06544062.png ; $$d _ { é } ^ { l } < \ldots < d _ { e } ^ { 1 } = d$$ ; confidence 0.489
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065440/m06544031.png ; $$\Phi _ { t } = id$$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065440/m06544030.png ; $$E = \{ e \}$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065460/m06546014.png ; $$( \alpha \vee ( b . e ) ) : e = ( \alpha : e ) \vee b$$ ; confidence 0.351
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065500/m06550014.png ; $$P ( \mathfrak { m } / \mathfrak { m } ^ { 2 } )$$ ; confidence 0.523
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065510/m06551020.png ; $$n _ { \Delta } = 1$$ ; confidence 0.532
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130260/m13026036.png ; $$x \lambda ( y ) = \rho ( x ) y$$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130260/m130260171.png ; $$\overline { \alpha } : P \rightarrow X$$ ; confidence 0.421
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065560/m06556075.png ; $$\frac { | z | ^ { p } } { ( 1 + | z | ) ^ { 2 p } } \leq | f ( z ) | \leq \frac { | z | ^ { p } } { ( 1 - | z | ) ^ { 2 p } }$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065570/m06557014.png ; $$L _ { \cap } \Gamma = 0$$ ; confidence 0.870
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m130180141.png ; $$H _ { n - 2 }$$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065580/m0655809.png ; $$P ( x ) = \sum _ { k = 1 } ^ { n } \alpha _ { k } x ^ { \lambda _ { k } }$$ ; confidence 0.795
+. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130030/n13003066.png ; $$\operatorname { Re } ( \lambda )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120040/n1200405.png ; $$A _ { i \psi }$$ ; confidence 0.179
+. https://www.encyclopediaofmath.org/legacyimages/n/n110/n110010/n1100102.png ; $$f \in L _ { \infty } ( T )$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/n/n110/n110010/n11001011.png ; $$L _ { \infty } ( T )$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066340/n06634043.png ; $$\Sigma _ { n - 1 } ( x )$$ ; confidence 0.905
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066340/n06634090.png ; $$x \in V _ { n }$$ ; confidence 0.777
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066340/n06634047.png ; $$X _ { i } \subset \Delta _ { 1 } ^ { i }$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066360/n06636034.png ; $$\{ x _ { \alpha } \} _ { \alpha \in \Sigma }$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066410/n06641020.png ; $$x \in b M$$ ; confidence 0.705
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066410/n06641023.png ; $$\overline { \partial } f = \phi$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066440/n06644040.png ; $$\sum _ { n = 0 } ^ { \infty } A ^ { n } f$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066480/n06648031.png ; $$\phi _ { \alpha } ( f ) = w _ { \alpha }$$ ; confidence 0.945
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066490/n06649018.png ; $$f ^ { - 1 } ( \alpha ) \cap \{ z : | z | \leq t \}$$ ; confidence 0.806
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066520/n06652019.png ; $$\epsilon < \epsilon ^ { \prime } < \ldots$$ ; confidence 0.860
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066560/n06656013.png ; $$A ( u ) = 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066630/n06663069.png ; $$\Delta _ { k } ^ { k } f ^ { ( s ) }$$ ; confidence 0.968
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066630/n066630108.png ; $$M _ { i } ^ { * } = c _ { i } \sum _ { j = 1 } ^ { n } M _ { j }$$ ; confidence 0.662
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066630/n06663062.png ; $$0 < r - s < k$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066790/n06679025.png ; $$D \cap \{ x ^ { 1 } = c \}$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066840/n06684017.png ; $$\{ \psi _ { i } \} _ { 0 } ^ { m }$$ ; confidence 0.581
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066890/n06689067.png ; $$v = 1.1 m / sec$$ ; confidence 0.848
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066890/n06689035.png ; $$b = 7$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690064.png ; $$G \rightarrow A$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130070/n13007025.png ; $$m ( B ) = 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066980/n06698028.png ; $$Q ^ { \prime } \subset Q$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067080/n06708019.png ; $$y ( 0 ) = y ^ { \prime }$$ ; confidence 0.740
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067080/n06708029.png ; $$\left. \begin{array} { c } { B _ { n } ( y _ { n + 1 } ( 0 ) - y _ { n } ( 0 ) ) + B ( y _ { n } ( 0 ) ) = 0 } \\ { D _ { n } ( y _ { n + 1 } ( X ) - y _ { n } ( X ) ) + D ( y _ { n } ( X ) ) = 0 } \end{array} \right\}$$ ; confidence 0.711
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067080/n06708018.png ; $$y ^ { * } = \alpha ( g ^ { * } )$$ ; confidence 0.950
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067110/n06711026.png ; $$\| z ^ { n } \| \leq q ^ { n } ( 1 - q ) ^ { - 1 } \| u ^ { 0 } - u ^ { 1 } \|$$ ; confidence 0.538
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067110/n06711048.png ; $$\phi _ { i } / \partial x _ { Y }$$ ; confidence 0.338
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067150/n067150173.png ; $$x + h \in G$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067150/n067150152.png ; $$A : G \rightarrow Y$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120110/n12011031.png ; $$x \in K$$ ; confidence 0.658
+. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120110/n12011011.png ; $$\xi ( x ) = 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067280/n06728058.png ; $$\pi / \rho$$ ; confidence 0.416
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067280/n06728084.png ; $$y ^ { \prime \prime \prime } = \lambda y$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067310/n06731043.png ; $$B O$$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067360/n0673605.png ; $$\phi ( x ) \geq 0$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067400/n06740041.png ; $$U$$ ; confidence 0.698
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067430/n06743015.png ; $$\sum _ { k = 1 } ^ { \infty } \| u _ { k } \| = \sum _ { k = 1 } ^ { \infty } 1 / k$$ ; confidence 0.925
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520368.png ; $$\phi _ { i } ( 0 ) = 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520122.png ; $$j \geq q + 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520141.png ; $$N _ { 2 } = \left| \begin{array} { c c c c c } { . } & { \square } & { \square } & { \square } & { 0 } \\ { \square } & { . } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { L ( e _ { j } ^ { n _ { i j } } ) } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { . } & { \square } \\ { \square } & { \square } & { \square } & { \square } & { \square } \\ { 0 } & { \square } & { \square } & { \square } & { . } \end{array} \right|$$ ; confidence 0.323
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520250.png ; $$d j \neq 0$$ ; confidence 0.877
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520303.png ; $$A \simeq K$$ ; confidence 0.550
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067580/n06758032.png ; $$N _ { G } ( H )$$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067610/n06761056.png ; $$( d \nu ) ( x _ { i } ) ( T _ { i } )$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067640/n06764043.png ; $$\Omega _ { X }$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067760/n06776016.png ; $$N ( A ^ { * } ) = \{ 0 \}$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067840/n06784093.png ; $$A \in L _ { \infty } ( H )$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067850/n067850200.png ; $$\operatorname { tr } _ { \sigma } A$$ ; confidence 0.814
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067850/n067850111.png ; $$u \in E ^ { \prime } \otimes - E$$ ; confidence 0.540
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067850/n067850131.png ; $$u = \operatorname { tr } \Gamma ( u )$$ ; confidence 0.766
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067860/n067860258.png ; $$V \subset \rho U$$ ; confidence 0.940
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067900/n0679002.png ; $$x y = 40$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067900/n06790027.png ; $$\alpha + b = b + \alpha$$ ; confidence 0.739
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067940/n06794014.png ; $$N > 5$$ ; confidence 0.901
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067960/n06796016.png ; $$q 2 = 6$$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067960/n0679601.png ; $$12$$ ; confidence 0.490
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067960/n06796020.png ; $$q 2 = 4$$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120010/o12001037.png ; $$\left. \begin{array} { l } { \nabla p _ { 1 } = \nabla p _ { 2 } = 0 } \\ { \frac { \partial v _ { 0 } } { \partial t } + [ \nabla v _ { 0 } ] v _ { 0 } = \frac { 1 } { Re } \Delta v _ { 0 } + \operatorname { Re } \nabla p _ { 3 } + \theta _ { 0 } b } \end{array} \right.$$ ; confidence 0.316
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001044.png ; $$F : L ^ { 2 } ( D ^ { \prime } ) \rightarrow L ^ { 2 } ( R ^ { 3 } )$$ ; confidence 0.936
+. https://www.encyclopediaofmath.org/legacyimages/o/o110/o110030/o11003071.png ; $$I _ { p } ( L )$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/o/o110/o110030/o11003037.png ; $$K _ { \omega }$$ ; confidence 0.958
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130030/o13003024.png ; $$\overline { P _ { 8 } }$$ ; confidence 0.610
+. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120020/o1200204.png ; $$\alpha = 1 / 2$$ ; confidence 0.933
+. https://www.encyclopediaofmath.org/legacyimages/o/o110/o110070/o11007085.png ; $$K _ { 10 }$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/o/o110/o110070/o11007062.png ; $$K$$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068190/o0681907.png ; $$T ( t ) x$$ ; confidence 0.794
+. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068210/o06821028.png ; $$X = \sum _ { i } X ^ { i } \partial / \partial x ^ { i }$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068250/o06825018.png ; $$\operatorname { lim } _ { x \rightarrow x _ { 0 } } + 0$$ ; confidence 0.628
+. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068330/o06833067.png ; $$e ^ { - \lambda s }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068350/o068350148.png ; $$\phi \in D ( A )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005095.png ; $$v \in G$$ ; confidence 0.413
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005087.png ; $$v _ { n } \in G$$ ; confidence 0.357
+. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068370/o06837057.png ; $$x _ { C }$$ ; confidence 0.256
+. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068370/o06837017.png ; $$( \alpha b ) \sigma = \alpha \sigma b \sigma$$ ; confidence 0.467
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060187.png ; $$( \sigma _ { 2 } \frac { \partial } { \partial t _ { 1 } } - \sigma _ { 1 } \frac { \partial } { \partial t _ { 2 } } + \gamma ) u = 0$$ ; confidence 0.449
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006047.png ; $$\frac { 1 } { i } ( A _ { k } - A _ { k } ^ { * } ) = \Phi ^ { * } \sigma _ { k } \Phi$$ ; confidence 0.897
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006052.png ; $$\overline { \gamma } = \tilde { \gamma } ^ { \prime \prime }$$ ; confidence 0.147
+. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068460/o0684606.png ; $$x ( t _ { 1 } ) = x ^ { 1 } \in R ^ { n }$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068490/o06849072.png ; $$2 \leq t \leq 3$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068500/o06850051.png ; $$\sigma \leq t \leq \theta$$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o070010110.png ; $$X = \cup _ { \alpha } X _ { \alpha }$$ ; confidence 0.245
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o07001011.png ; $$G / G _ { X }$$ ; confidence 0.936
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o0700104.png ; $$G ( x ) = \{ g ( x ) : g \in G \}$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070040/o07004017.png ; $$\operatorname { lim } \alpha / \beta = 0$$ ; confidence 0.903
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070060/o07006030.png ; $$\beta ( x ) \neq 0$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070070/o070070117.png ; $$\{ Z _ { n } \}$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070070/o070070118.png ; $$Y _ { n } = \frac { 1 } { 2 } ( X _ { ( n 1 ) } + X _ { ( n n ) } ) \quad \text { and } \quad Z _ { n } = \frac { n + 1 } { 2 } ( n - 1 ) ( X _ { ( n n ) } - X _ { ( n 1 ) } )$$ ; confidence 0.491
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070070/o07007051.png ; $$W _ { n } = X _ { ( n n ) } - X _ { ( n 1 ) }$$ ; confidence 0.738
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070150/o07015054.png ; $$\alpha ^ { n } < b ^ { n + 1 }$$ ; confidence 0.291
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o13008026.png ; $$C _ { \psi }$$ ; confidence 0.409
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o13008035.png ; $$C _ { \varphi }$$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070220/o07022036.png ; $$E$$ ; confidence 0.845
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070220/o07022045.png ; $$\int _ { G } x ( t ) y ( t ) d t \leq \| x \| _ { ( M ) } \| y \| _ { ( N ) }$$ ; confidence 0.491
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070240/o07024025.png ; $$- \beta V$$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070240/o07024014.png ; $$6 \pi \eta \alpha$$ ; confidence 0.422
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070240/o0702405.png ; $$d W ( t ) / d t = W ^ { \prime } ( t )$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070310/o07031053.png ; $$N ( n ) \rightarrow \infty$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070310/o070310119.png ; $$A \perp A ^ { T }$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070290/o07029017.png ; $$\Delta = \alpha _ { 2 } c ( b ) - \beta _ { 2 } s ( b ) \neq 0$$ ; confidence 0.937
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070340/o07034097.png ; $$y = K _ { n } ( x )$$ ; confidence 0.826
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070370/o07037028.png ; $$\sum _ { n = 0 } ^ { \infty } a _ { \tilde { m } } ^ { 2 } ( f ) = \int _ { \mathscr { x } } ^ { b } f ^ { 2 } ( x ) d x$$ ; confidence 0.076
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072210/p07221037.png ; $$F ^ { k }$$ ; confidence 0.862
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072300/p0723004.png ; $$F ( H )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072350/p07235016.png ; $$h > 1$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072370/p07237060.png ; $$\overline { \Omega } _ { k } \subset \Omega _ { k + 1 }$$ ; confidence 0.887
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072370/p07237025.png ; $$\underline { H } \square _ { f }$$ ; confidence 0.812
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072430/p0724304.png ; $$B \operatorname { ccos } ( \omega t + \psi )$$ ; confidence 0.580
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072430/p072430105.png ; $$\phi _ { im }$$ ; confidence 0.294
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072430/p0724307.png ; $$\epsilon \ll 1$$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072430/p07243078.png ; $$| V _ { m n } | \ll | E _ { n } ^ { ( 0 ) } - E _ { m } ^ { ( 0 ) } |$$ ; confidence 0.535
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110120/p110120321.png ; $$4 x$$ ; confidence 0.375
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110120/p110120376.png ; $$E _ { i } ( x )$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110120/p110120339.png ; $$\eta ( x ) \in \eta$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110120/p110120247.png ; $$A _ { i } = \{ w \in W _ { i } \cap V ^ { s } ( z ) : z \in \Lambda _ { l } \cap U ( x ) \}$$ ; confidence 0.414
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110120/p11012025.png ; $$\lambda < \mu$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110120/p110120432.png ; $$\operatorname { limsup } _ { n \rightarrow + \infty } \frac { 1 } { n } \operatorname { log } + P _ { N } ( f ) \geq h ( f )$$ ; confidence 0.191
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110120/p110120214.png ; $$D _ { 0 } f _ { x } = \left( \begin{array} { c c c } { A _ { 1 } ( x ) } & { \square } & { \square } \\ { \square } & { \ddots } & { \square } \\ { \square } & { \square } & { A _ { \xi } ( x ) ( x ) } \end{array} \right)$$ ; confidence 0.131
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110120/p110120428.png ; $$P _ { n } ( f )$$ ; confidence 0.919
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072460/p07246025.png ; $$S \square ^ { * }$$ ; confidence 0.590
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072510/p07251086.png ; $$T ^ { * } U$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072510/p07251047.png ; $$d y _ { 0 } - \sum _ { j = 1 } ^ { p } z _ { j } d y _ { j } = 0$$ ; confidence 0.905
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072530/p072530183.png ; $$I ( G _ { p } )$$ ; confidence 0.801
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072530/p07253081.png ; $$d f ^ { j }$$ ; confidence 0.726
+. https://www.encyclopediaofmath.org/legacyimages/p/p071/p071010/p07101037.png ; $$p _ { i }$$ ; confidence 0.459
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p0726706.png ; $$\operatorname { sch } / S$$ ; confidence 0.616
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267050.png ; $$f ^ { \prime } ( O _ { X ^ { \prime } } ) = O _ { S ^ { \prime } }$$ ; confidence 0.802
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072700/p07270029.png ; $$f ( L )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072710/p07271076.png ; $$t ( P )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072710/p072710140.png ; $$\sigma A = x ^ { * } \partial \sigma ^ { * } \operatorname { lk } _ { A } \sigma + A _ { 1 }$$ ; confidence 0.541
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120130/p1201308.png ; $$\theta$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120130/p12013011.png ; $$n > 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120140/p12014048.png ; $$E = E$$ ; confidence 0.907
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120140/p12014039.png ; $$E _ { r } = S \cup T$$ ; confidence 0.755
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072760/p0727608.png ; $$f ( x ) \mapsto \hat { f } ( y )$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072830/p07283021.png ; $$\epsilon _ { i j } ^ { k }$$ ; confidence 0.400
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072830/p072830109.png ; $$\sigma _ { i j } ( t )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072850/p072850130.png ; $$X \subset M ^ { n }$$ ; confidence 0.432
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072850/p072850146.png ; $$H _ { k } ( M ^ { n } )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072850/p072850150.png ; $$\Omega _ { X } ( k ) \equiv \Omega ( k )$$ ; confidence 0.406
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072850/p0728502.png ; $$_ { k }$$ ; confidence 0.179
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072880/p07288011.png ; $$\{ z _ { k } \} \subset \Delta$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072930/p072930169.png ; $$t _ { \gamma }$$ ; confidence 0.533
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072930/p07293055.png ; $$\sigma _ { 2 n } = 2 \pi ^ { n } / ( n - 1 ) !$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072930/p072930108.png ; $$u \in C ^ { 2 } ( D )$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072890/p07289041.png ; $$p _ { 01 } p _ { 23 } + p _ { 02 } p _ { 31 } + p _ { 03 } p _ { 12 } = 0$$ ; confidence 0.676
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110150/p1101505.png ; $$x \preceq y \Rightarrow z x t \preceq x y t$$ ; confidence 0.920
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072950/p07295010.png ; $$w ( z ) = \int _ { \gamma } ( t - z ) ^ { \mu + n - 1 } u ( t ) d t$$ ; confidence 0.937
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072980/p07298015.png ; $$\beta \in L _ { q }$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073030/p07303077.png ; $$\mathfrak { g } = C$$ ; confidence 0.510
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073020/p07302077.png ; $$L ( R ) \otimes _ { K } H _ { n } ( R ) = R$$ ; confidence 0.755
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073090/p07309030.png ; $$V \cap L$$ ; confidence 0.905
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073090/p07309060.png ; $$R \times D$$ ; confidence 0.945
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073100/p07310032.png ; $$\mu A = m > 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073270/p07327037.png ; $$q ^ { ( n ) } = d ^ { n } q / d x ^ { n }$$ ; confidence 0.958
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073280/p07328015.png ; $$2 \lambda$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073330/p07333012.png ; $$d S _ { n }$$ ; confidence 0.935
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073340/p0733402.png ; $$X ( t _ { 2 } ) - X ( t _ { 1 } )$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073340/p07334022.png ; $$/ t \rightarrow \lambda$$ ; confidence 0.669
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073400/p07340055.png ; $$M ^ { 0 }$$ ; confidence 0.312
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073460/p07346086.png ; $$P ^ { \perp } = \cap _ { v \in P } v ^ { \perp } = \emptyset$$ ; confidence 0.185
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073460/p07346048.png ; $$W = M + U$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073530/p07353041.png ; $$t ^ { i _ { 1 } } \cdots \dot { d p } = \operatorname { det } \| x _ { i } ^ { i _ { k } } \|$$ ; confidence 0.226
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073700/p07370015.png ; $$f ( n ) \geq 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073700/p07370045.png ; $$[ f _ { G } ]$$ ; confidence 0.256
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073700/p073700205.png ; $$l _ { n } = \# \{ s \in S : d ( s ) = n \}$$ ; confidence 0.868
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073700/p073700202.png ; $$d ( s ) = \operatorname { sup } \{ n : s \in F _ { n } \}$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073700/p073700127.png ; $$m / m ^ { 2 }$$ ; confidence 0.612
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073740/p07374027.png ; $$( \xi ) _ { R }$$ ; confidence 0.672
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073750/p0737503.png ; $$p _ { i } ( \xi ) \in H ^ { 4 i } ( B )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073750/p073750105.png ; $$e ( \xi \otimes C )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073760/p0737605.png ; $$\omega _ { \mathscr { A } } : X ( G ) \rightarrow T$$ ; confidence 0.090
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073830/p07383050.png ; $$E \subset X = R ^ { \prime }$$ ; confidence 0.250
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073840/p0738407.png ; $$A \supset B$$ ; confidence 0.432
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073880/p0738804.png ; $$x _ { 1 } = \ldots = x _ { n } = 0$$ ; confidence 0.697
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073930/p07393024.png ; $$A / N _ { f }$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073960/p0739603.png ; $$P ( x ) = a _ { 0 } + \alpha _ { 1 } x + \ldots + \alpha _ { n } x ^ { n }$$ ; confidence 0.639
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073980/p07398067.png ; $$F \otimes S ^ { m } E$$ ; confidence 0.748
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074010/p07401048.png ; $$O _ { 3 } = O _ { 6 } \cap O _ { 7 }$$ ; confidence 0.673
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074010/p07401072.png ; $$F _ { 5 } ^ { \mu } = C _ { 4 } \cap F _ { 8 } ^ { \mu }$$ ; confidence 0.951
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074070/p0740707.png ; $$\xi : F \rightarrow A$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074100/p07410035.png ; $$v _ { i } = \partial f / \partial t ^ { i }$$ ; confidence 0.629
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074140/p074140226.png ; $$\phi ^ { + } ( x )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074140/p074140115.png ; $$1 \leq p \leq n / 2$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074140/p074140120.png ; $$p > n / 2$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074150/p074150271.png ; $$- \infty \leq y < \infty$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074150/p07415079.png ; $$\underline { \mathfrak { U } } \square _ { \phi } = - \overline { \mathfrak { U } } _ { \phi }$$ ; confidence 0.680
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074150/p074150292.png ; $$f \in C$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074160/p07416038.png ; $$\mu _ { 1 } = \mu _ { 2 } = \mu > 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074160/p07416055.png ; $$\rho = | y |$$ ; confidence 0.958
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074530/p07453019.png ; $$\phi ( n ) = n ( 1 - \frac { 1 } { p _ { 1 } } ) \dots ( 1 - \frac { 1 } { p _ { k } } )$$ ; confidence 0.456
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074710/p07471055.png ; $$g _ { 0 } g ^ { \prime } \in G$$ ; confidence 0.189
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074710/p074710106.png ; $$P \rightarrow e$$ ; confidence 0.910
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074660/p0746603.png ; $$\left. \begin{array} { l l } { L - k E } & { M - k F } \\ { M - k F } & { N - k G } \end{array} \right| = 0$$ ; confidence 0.746
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074690/p07469036.png ; $$G = G ^ { \prime }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074690/p07469030.png ; $$\pi G ( x ) = b$$ ; confidence 0.845
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472020.png ; $$\Gamma _ { F }$$ ; confidence 0.663
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472076.png ; $$\gamma \in G$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074740/p07474069.png ; $$q _ { k } R = p _ { j } ^ { n _ { i } } R _ { R }$$ ; confidence 0.083
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074740/p07474068.png ; $$q _ { i } R = 0$$ ; confidence 0.743
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074860/p07486040.png ; $$0 \leq s _ { 0 } \leq l$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110230/p110230174.png ; $$F _ { p q } \neq F _ { p q } ^ { * }$$ ; confidence 0.479
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110230/p11023076.png ; $$x \in R ^ { + }$$ ; confidence 0.795
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074970/p074970164.png ; $$E X _ { k } = a$$ ; confidence 0.520
+. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074970/p074970165.png ; $$DX _ { k } = \sigma ^ { 2 }$$ ; confidence 0.511
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075050/p07505047.png ; $$( K _ { i } / k )$$ ; confidence 0.490
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075150/p07515035.png ; $$\alpha _ { 0 } \in A$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075190/p07519074.png ; $$E _ { i j }$$ ; confidence 0.366
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075190/p07519013.png ; $$x ^ { i } = y ^ { i } \lambda$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075260/p07526038.png ; $$\pi _ { D } : X \rightarrow F ( D )$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130130/p13013032.png ; $$\lambda _ { 1 } > \ldots > \lambda _ { n } ( \lambda ) > 0$$ ; confidence 0.786
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075350/p07535038.png ; $$d ( S )$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075350/p07535017.png ; $$q IL$$ ; confidence 0.843
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075350/p075350108.png ; $$P _ { n } ( R )$$ ; confidence 0.886
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075350/p07535088.png ; $$P _ { s } ^ { l } ( k )$$ ; confidence 0.866
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075360/p0753601.png ; $$X = \operatorname { Proj } ( R )$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075360/p07536031.png ; $$\operatorname { Proj } ( R )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075400/p07540018.png ; $$F \subset G$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075450/p07545043.png ; $$U _ { i j } = \operatorname { Spec } ( A _ { i j } )$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075480/p0754802.png ; $$( p \supset ( q \supset r ) ) \supset ( ( p \supset q ) \supset ( p \supset r ) )$$ ; confidence 0.827
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075560/p075560134.png ; $$( P . Q ) ! = ( P \times Q ) ! = ( P ! \times Q ! ) !$$ ; confidence 0.823
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075560/p075560136.png ; $$P Q = P \times Q$$ ; confidence 0.481
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075800/p07580013.png ; $$\square ^ { n - 1 } R _ { n }$$ ; confidence 0.937
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075650/p07565068.png ; $$X \cap U = \{ x \in U : \phi ( x ) > 0 \}$$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075660/p075660207.png ; $$\kappa : \Omega \rightarrow \Omega _ { 1 }$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075660/p07566043.png ; $$\partial _ { x } = \partial / \partial x$$ ; confidence 0.368
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075660/p075660284.png ; $$A : H ^ { S } ( X ) \rightarrow H ^ { S - m } ( X )$$ ; confidence 0.458
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075660/p075660113.png ; $$| \xi | \leq 1 / 2$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075700/p075700100.png ; $$q ^ { 1 }$$ ; confidence 0.419
+. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p13014049.png ; $$\gamma \in R$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075780/p07578019.png ; $$D \rightarrow \overline { D }$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075830/p0758301.png ; $$a \vee b$$ ; confidence 0.827
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p12017067.png ; $$I$$ ; confidence 0.923
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073540/p07354050.png ; $$P \{ X _ { v + 1 } = k + 1 | X _ { k } = k \} = \frac { b + k c } { b + r + n c } = \frac { p + k \gamma } { 1 + n \gamma }$$ ; confidence 0.303
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076040/q07604075.png ; $$\operatorname { arg } \operatorname { lim } _ { q \rightarrow r } Q _ { z } ( z ( q ) ) z ( q ) ^ { 2 }$$ ; confidence 0.802
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076080/q076080314.png ; $$\mathfrak { F } \subset \mathfrak { P }$$ ; confidence 0.687
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076090/q07609018.png ; $$( n = 4 )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076190/q07619068.png ; $$\alpha = - 1 / 2$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076250/q076250144.png ; $$x \in E _ { + } ( s )$$ ; confidence 0.775
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310127.png ; $$R ^ { 12 } R ^ { 13 } R ^ { 23 } = R ^ { 23 } R ^ { 13 } R ^ { 12 }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631095.png ; $$\left( \begin{array} { l } { n } \\ { k } \end{array} \right) _ { q } = \frac { ( q ^ { n } - 1 ) \ldots ( q ^ { n - k + 1 } - 1 ) } { ( q ^ { k } - 1 ) \ldots ( q - 1 ) }$$ ; confidence 0.443
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310117.png ; $$R ^ { 12 }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631081.png ; $$H _ { i } \in \mathfrak { g }$$ ; confidence 0.955
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120030/q12003027.png ; $$X ( Y . f ) = ( Y X ) . f$$ ; confidence 0.433
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076320/q07632017.png ; $$j _ { X } : F ^ { \prime } \rightarrow F$$ ; confidence 0.809
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076500/q07650033.png ; $$3 r ( L _ { 1 } \cap L _ { 2 } ) = 3 _ { r } ( L _ { 1 } ) + 3 r ( L _ { 2 } )$$ ; confidence 0.248
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005015.png ; $$D ^ { 2 } f ( x ^ { * } ) = D ( D ^ { T } f ( x ^ { * } ) )$$ ; confidence 0.975
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005052.png ; $$H _ { k + 1 } y ^ { k } = s ^ { k }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076430/q07643044.png ; $$f \in W _ { 2 } ^ { 1 }$$ ; confidence 0.943
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076430/q076430127.png ; $$f : R _ { + } ^ { n } \rightarrow R _ { + } ^ { n }$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076470/q07647062.png ; $$S _ { 2 m + 1 } ^ { m }$$ ; confidence 0.627
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076530/q07653094.png ; $$\square ^ { 01 } S _ { 3 } ^ { 1 }$$ ; confidence 0.621
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076530/q07653051.png ; $$x ^ { 1 } = 0$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076610/q07661044.png ; $$\beta X = S \square x = \omega _ { \kappa } X$$ ; confidence 0.261
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076610/q07661012.png ; $$N _ { A }$$ ; confidence 0.730
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076630/q07663014.png ; $$\omega _ { 1 } / \omega _ { 2 }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130040/q13004038.png ; $$K > 1$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130040/q13004026.png ; $$J _ { f } ( x ) \leq K l ( f ^ { \prime } ( x ) ) ^ { n }$$ ; confidence 0.794
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076670/q07667033.png ; $$R [ x ]$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q12007060.png ; $$R _ { q ^ { 2 } }$$ ; confidence 0.811
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076770/q07677043.png ; $$X = x _ { 0 } + V$$ ; confidence 0.644
+. https://www.encyclopediaofmath.org/legacyimages/q/q110/q110030/q11003019.png ; $$\alpha > a ^ { * }$$ ; confidence 0.575
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076800/q07680042.png ; $$\nu _ { 1 } ^ { S }$$ ; confidence 0.641
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076800/q07680082.png ; $$\{ \tau _ { j } ^ { e } \} \in G _ { I }$$ ; confidence 0.146
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076800/q07680048.png ; $$\leq \nu _ { i } ^ { s }$$ ; confidence 0.802
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076800/q07680012.png ; $$T ^ { S }$$ ; confidence 0.805
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076800/q07680094.png ; $$\tau _ { 0 } ^ { e ^ { 3 } }$$ ; confidence 0.252
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076820/q076820110.png ; $$\operatorname { lim } _ { t \rightarrow \infty } P \{ q ( t ) < x \sqrt { t } \} = \sqrt { \frac { 2 } { \pi } } \int _ { 0 } ^ { x / \sigma } e ^ { - u ^ { 2 } / 2 } d u$$ ; confidence 0.716
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076820/q076820155.png ; $$\operatorname { lim } _ { t \rightarrow \infty } P \{ q ( t ) = k \} = \operatorname { lim } _ { t \rightarrow \infty } P \{ q _ { n } = k \} = \frac { ( \alpha \alpha ) ^ { k } } { k ! } e ^ { - \alpha ^ { \prime } \alpha }$$ ; confidence 0.087
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076820/q076820199.png ; $$f ( \xi _ { T } ( t ) )$$ ; confidence 0.925
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076820/q076820220.png ; $$E \theta ( t ) \theta ( t + u ) = \int _ { 0 } F ( t + u - v ) ( 1 - G ( t - v ) ) d m ( v )$$ ; confidence 0.887
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076810/q07681026.png ; $$\alpha = \operatorname { lim } _ { t \rightarrow 0 } \frac { P ( e ( t ) \geq 1 ) } { t }$$ ; confidence 0.819
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076830/q07683079.png ; $$\rho = E m \alpha \tau _ { j } ^ { e }$$ ; confidence 0.537
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076830/q07683071.png ; $$p _ { m } = ( \sum _ { j = 0 } ^ { m } A _ { j } ) ^ { - 1 }$$ ; confidence 0.310
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076830/q07683018.png ; $$Q _ { 0 } ^ { 0 } = Q ^ { 0 }$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076840/q076840162.png ; $$P _ { k } ( x )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076840/q07684029.png ; $$P \{ X _ { n } \in \Delta \} \rightarrow 0$$ ; confidence 0.724
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076840/q076840293.png ; $$G _ { l }$$ ; confidence 0.639
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076840/q07684072.png ; $$w ^ { S } ( u ) = \operatorname { sup } _ { v \leq u } ( X ( u ) - X ( v ) )$$ ; confidence 0.601
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076850/q07685043.png ; $$E [ \tau _ { j } ^ { S } - \tau _ { j } ^ { \dot { e } } ] ^ { 2 + \gamma }$$ ; confidence 0.250
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076860/q07686069.png ; $$f _ { X } : V _ { X } \rightarrow V _ { X } ^ { \prime }$$ ; confidence 0.805
+. https://www.encyclopediaofmath.org/legacyimages/r/r110/r110010/r110010322.png ; $$j$$ ; confidence 0.784
+. https://www.encyclopediaofmath.org/legacyimages/r/r110/r110010/r110010167.png ; $$k ( \pi )$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/r/r110/r110010/r110010273.png ; $$e _ { 3 } = ( \alpha + d ) + ( b + c )$$ ; confidence 0.551
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077060/r0770601.png ; $$\Delta u + k ^ { 2 } u = - f$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077130/r07713084.png ; $$r _ { 1 } > r _ { 2 }$$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077130/r077130114.png ; $$\phi < \beta < L < K < J < T < \tau < F$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/r/r110/r110020/r11002077.png ; $$T w | K v$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077250/r07725048.png ; $$( n - \mu _ { 1 } ) / 2$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077260/r07726020.png ; $$\zeta _ { 2 n } = \sqrt { - 2 \operatorname { ln } \xi _ { 2 n } } \operatorname { sin } 2 \pi \xi _ { 2 n - 1 }$$ ; confidence 0.840
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077370/r07737019.png ; $$P \{ Z _ { n } < x \} - \Phi ( x ) = O ( \frac { 1 } { n } )$$ ; confidence 0.432
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077380/r07738071.png ; $$P \{ | \frac { K _ { n } } { n } - \frac { 1 } { 2 } | < \frac { 1 } { 4 } \} = 1 - 2 P \{ \frac { K _ { n } } { n } < \frac { 1 } { 4 } \} \approx 1 - \frac { 4 } { \pi } \frac { \pi } { 6 } = \frac { 1 } { 3 }$$ ; confidence 0.812
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077380/r07738036.png ; $$u _ { 0 } = 1$$ ; confidence 0.716
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077510/r0775103.png ; $$T = T ( R )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077590/r07759075.png ; $$R ( x )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763050.png ; $$\delta _ { \phi }$$ ; confidence 0.541
+. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764046.png ; $$D _ { n - 2 }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130040/r13004063.png ; $$u _ { 1 } = | \frac { \partial u } { \partial n } | = 0$$ ; confidence 0.932
+. https://www.encyclopediaofmath.org/legacyimages/r/r110/r110040/r11004022.png ; $$k ^ { 2 } = k _ { c } ^ { 2 } + \frac { 3 } { 8 } \frac { \rho 2 g } { T \lambda _ { 0 } ^ { 2 } } ( 1 - \frac { \rho _ { 1 } } { \rho _ { 2 } } ) \epsilon ^ { 2 } + O ( \epsilon ^ { 3 } )$$ ; confidence 0.807
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080020/r080020171.png ; $$P - N \equiv ( \frac { m _ { 1 } } { 2 } ) ^ { 2 } \pm 1 \operatorname { mod } 8$$ ; confidence 0.918
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080020/r08002019.png ; $$\operatorname { dim } A = n = q - s$$ ; confidence 0.969
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080060/r080060177.png ; $$\{ r _ { n } + r _ { n } ^ { \prime } \}$$ ; confidence 0.928
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080180/r0801808.png ; $$t _ { k } \in R$$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080190/r08019033.png ; $$U$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080190/r08019038.png ; $$\{ f ^ { t } | \Sigma _ { X } \} _ { t \in R }$$ ; confidence 0.191
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080210/r08021055.png ; $$F ( m ) = f _ { m } ( m )$$ ; confidence 0.639
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080210/r08021025.png ; $$f ( x ) = x + 1$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080610/r08061012.png ; $$E ( Y | x ) = m ( x )$$ ; confidence 0.542
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080610/r08061050.png ; $$E ( Y - f ( x ) ) ^ { 2 }$$ ; confidence 0.547
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080620/r08062076.png ; $$\beta$$ ; confidence 0.566
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080620/r08062044.png ; $$X = \| x _ { i } \|$$ ; confidence 0.794
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080640/r08064034.png ; $$y _ { t } = A x _ { t } + \epsilon _ { t }$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080680/r08068010.png ; $$x \frac { \operatorname { lim } _ { x \rightarrow D } u ( x ) = f ( y _ { 0 } ) } { x \in D }$$ ; confidence 0.172
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080680/r08068055.png ; $$x ( t ) \in D ^ { c }$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080740/r0807408.png ; $$x _ { n m _ { n } } \rightarrow ( 0 )$$ ; confidence 0.220
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080850/r08085028.png ; $$e \omega ^ { r } f$$ ; confidence 0.300
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080930/r08093013.png ; $$\overline { A } z = \overline { u }$$ ; confidence 0.777
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080930/r08093022.png ; $$R _ { 0 } \subset F$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080940/r08094028.png ; $$\{ \alpha _ { n } ^ { ( e ) } \}$$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080940/r08094048.png ; $$\{ \alpha _ { n } \} _ { \aleph = 0 } ^ { \infty }$$ ; confidence 0.264
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081110/r08111018.png ; $$g 00 = 1 - 2 \phi / c ^ { 2 }$$ ; confidence 0.483
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081110/r08111011.png ; $$p \leq \epsilon / 3$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081130/r0811301.png ; $$c \approx 3.10 ^ { 10 } cm / se$$ ; confidence 0.741
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081130/r08113085.png ; $$c t ^ { \prime } = x ^ { \prime } \operatorname { sinh } \psi + c t \operatorname { cosh } \psi$$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081150/r0811504.png ; $$\frac { d ^ { 2 } x } { d \tau ^ { 2 } } - \lambda ( 1 - x ^ { 2 } ) \frac { d x } { d \tau } + x = 0$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081160/r08116074.png ; $$t + \tau$$ ; confidence 0.811
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081170/r08117020.png ; $$B = B _ { 1 } \cup B _ { 2 }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081250/r08125011.png ; $$H ( t ) = E N$$ ; confidence 0.783
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081260/r08126015.png ; $$M _ { \gamma _ { i } } M _ { \gamma _ { j } }$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081390/r08139031.png ; $$v _ { 2 } \in V _ { 2 }$$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081400/r08140012.png ; $$s < s ^ { \prime }$$ ; confidence 0.967
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081420/r08142047.png ; $$\phi \in E ^ { \prime }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081430/r08143084.png ; $$A = A _ { 1 } \times A _ { 2 }$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081430/r08143081.png ; $$e X$$ ; confidence 0.861
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081430/r081430150.png ; $$g e = g$$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081430/r08143031.png ; $$E / E ^ { \prime }$$ ; confidence 0.807
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081460/r08146090.png ; $$l _ { i } = \lambda _ { i } + n - i$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081460/r081460129.png ; $$V _ { \lambda } ^ { 0 } \subset V _ { \lambda }$$ ; confidence 0.929
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081460/r08146017.png ; $$g \mapsto ( \operatorname { det } g ) ^ { k } R ( g )$$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081470/r081470221.png ; $$\oplus R ( S _ { n } )$$ ; confidence 0.905
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007076.png ; $$\| f \| = 0$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r13008048.png ; $$\{ \phi j ( z ) \}$$ ; confidence 0.543
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r130080102.png ; $$\Lambda ^ { 2 } : = \sum _ { j = 1 } ^ { \infty } \lambda _ { j } < \infty$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081550/r08155085.png ; $$\psi d z$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081560/r081560116.png ; $$R _ { V } = \frac { 1 } { ( 2 \pi i ) ^ { n } } \int _ { \sigma _ { V } } f ( z ) d z$$ ; confidence 0.396
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081590/r08159047.png ; $$A = \int _ { - \infty } ^ { \infty } \lambda d E _ { \lambda }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081600/r08160033.png ; $$y _ { 2 } = ( x _ { 1 } + x _ { 3 } ) ( x _ { 2 } + x _ { 4 } )$$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081770/r08177046.png ; $$x ^ { T } ( t _ { 1 } ) \Phi x ( t _ { 1 } ) + \int _ { t _ { 0 } } ^ { t _ { 1 } } [ x ^ { T } ( t ) M ( t ) x ( t ) + u ^ { T } ( t ) N ( t ) u ( t ) ] d t$$ ; confidence 0.938
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130090/r13009016.png ; $$\sum _ { i = 1 } ^ { r } \alpha _ { i } \sigma ( w ^ { i } x + \theta _ { i } )$$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010034.png ; $$D _ { n }$$ ; confidence 0.956
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081980/r08198090.png ; $$\operatorname { ch } ( f _ { 1 } ( x ) ) = f * ( \operatorname { ch } ( x ) \operatorname { td } ( T _ { f } ) )$$ ; confidence 0.130
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081990/r08199034.png ; $$D \cup \gamma$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081940/r08194033.png ; $$G ( K ) \rightarrow G ( Q )$$ ; confidence 0.817
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082040/r08204012.png ; $$a _ { 0 } ( z ) \neq 0$$ ; confidence 0.937
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082040/r08204062.png ; $$b \in \overline { C }$$ ; confidence 0.690
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082050/r082050121.png ; $$AH _ { p }$$ ; confidence 0.775
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082050/r08205056.png ; $$\partial \overline { R } _ { \nu }$$ ; confidence 0.821
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082060/r082060128.png ; $$2 g - 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082060/r082060102.png ; $$f ^ { \mu } | _ { K }$$ ; confidence 0.278
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082070/r08207022.png ; $$R _ { i l k } ^ { q } = - R _ { k l } ^ { q }$$ ; confidence 0.210
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082080/r08208036.png ; $$- \infty \leq \lambda < \mu \leq \infty$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082110/r0821106.png ; $$d s ^ { 2 } = g _ { j } \omega ^ { i } \omega ^ { j }$$ ; confidence 0.914
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082130/r08213015.png ; $$\partial x ^ { i } / \partial v$$ ; confidence 0.737
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082150/r082150142.png ; $$\operatorname { exp } _ { q } X = r$$ ; confidence 0.511
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082160/r082160280.png ; $$\gamma : M ^ { n } \rightarrow M ^ { n }$$ ; confidence 0.911
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082160/r08216030.png ; $$n < 7$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082160/r08216057.png ; $$N = 0$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082160/r082160299.png ; $$\{ \operatorname { exp } _ { m } ( \text { Cutval } ( \xi ) \xi ) \} = \text { Cutloc } ( m )$$ ; confidence 0.291
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082160/r082160294.png ; $$\gamma _ { \xi } ( t )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082200/r082200143.png ; $$V ^ { \prime } \subset R ^ { \prime }$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082200/r082200111.png ; $$\gamma \geq \gamma _ { k }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082200/r082200148.png ; $$V ^ { \prime } = V ^ { \prime \prime } = R ^ { \prime } \cup R ^ { \prime \prime }$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082210/r08221030.png ; $$o = e K$$ ; confidence 0.327
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082230/r0822307.png ; $$| x _ { i } | \leq 1$$ ; confidence 0.845
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130130/r13013012.png ; $$P _ { \sigma } = \frac { 1 } { 2 \pi i } \int _ { \Gamma } ( \lambda - A ) ^ { - 1 } d \lambda$$ ; confidence 0.932
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130130/r13013019.png ; $$P _ { \sigma } ^ { 2 } = P _ { \sigma }$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130140/r1301406.png ; $$\sigma ( R ) \backslash \lambda$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082290/r0822904.png ; $$x + z < y + z$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082290/r082290200.png ; $$p _ { \alpha } = e$$ ; confidence 0.518
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082290/r082290135.png ; $$U : E \rightarrow M$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082290/r08229026.png ; $$y _ { n } \leq x _ { n } \leq z _ { n }$$ ; confidence 0.841
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082320/r08232050.png ; $$\operatorname { lim } _ { r \rightarrow 1 } \int _ { E } | f ( r e ^ { i \theta } ) | ^ { \delta } d \theta = \int _ { E } | f ( e ^ { i \theta } ) | ^ { \delta } d \theta$$ ; confidence 0.964
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082350/r08235027.png ; $$s : M \rightarrow F ( M )$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082430/r08243011.png ; $$\gamma _ { t } ( x + y ) = \sum _ { r = 0 } ^ { t } \gamma _ { r } ( x ) \gamma _ { t - r } ( y )$$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082430/r0824307.png ; $$I ( A ) = \operatorname { Ker } ( \epsilon )$$ ; confidence 0.898
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082450/r08245049.png ; $$( \alpha b ) \alpha = \alpha ( b \alpha )$$ ; confidence 0.731
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082450/r0824503.png ; $$( a + b ) \alpha = \alpha \alpha + b \alpha$$ ; confidence 0.463
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082500/r08250032.png ; $$\| u - P _ { n } u \| _ { A } \rightarrow 0$$ ; confidence 0.332
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082500/r08250029.png ; $$u _ { 0 } = A ^ { - 1 } f$$ ; confidence 0.941
+. https://www.encyclopediaofmath.org/legacyimages/r/r120/r120020/r12002013.png ; $$J ( q ) ^ { T }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256054.png ; $$19$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256016.png ; $$1$$ ; confidence 0.430
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r0825605.png ; $$V = 5$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256041.png ; $$300$$ ; confidence 0.440
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082570/r08257030.png ; $$j 2 ^ { - k - l }$$ ; confidence 0.858
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082590/r082590243.png ; $$\lambda - \mu$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082590/r082590135.png ; $$- 3$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/r/r110/r110150/r11015028.png ; $$M \dot { y } = f ( y )$$ ; confidence 0.805
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130160/r13016036.png ; $$R ^ { \infty } \rightarrow \ldots \rightarrow R ^ { m } \rightarrow \ldots \rightarrow R ^ { 0 }$$ ; confidence 0.522
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130160/r13016037.png ; $$c ^ { m } ( \Omega )$$ ; confidence 0.773
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130160/r1301601.png ; $$c ^ { \infty } ( \Omega ) ^ { N }$$ ; confidence 0.774
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082640/r0826403.png ; $$A _ { k } = U _ { k } ^ { * } A _ { k - 1 } U _ { k }$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082690/r08269033.png ; $$| \chi | < \pi$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082790/r08279064.png ; $$\operatorname { Pic } ( F ) \cong p ^ { * } \operatorname { Pic } ( C ) \oplus Z ^ { 5 }$$ ; confidence 0.304
+. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083000/s08300044.png ; $$D _ { n } X _ { 1 }$$ ; confidence 0.828
+. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083000/s08300037.png ; $$D _ { n } X \subset S ^ { n } \backslash X$$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083000/s08300055.png ; $$D _ { n } D _ { n } \theta = \theta$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083170/s08317053.png ; $$m _ { i } = 0$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083170/s08317062.png ; $$\tilde { D } = E \{ M | m = 0 \} = \frac { ( \sum _ { r = 1 } ^ { N - n } r \frac { C _ { N - r } ^ { n } } { C _ { N } ^ { n } } p _ { r } ) } { P \{ m = 0 \} }$$ ; confidence 0.234
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130020/s13002040.png ; $$g _ { t } ( u )$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110040/s11004082.png ; $$\phi ( T _ { X } N ) \subset T _ { X } N$$ ; confidence 0.941
+. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110040/s110040107.png ; $$\phi ( D _ { X } ) = D _ { X }$$ ; confidence 0.531
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004056.png ; $$\overline { D } = \overline { D } _ { S }$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004069.png ; $$X ^ { * } = \Gamma \backslash D ^ { * }$$ ; confidence 0.822
+. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083330/s0833306.png ; $$\phi _ { \mathscr { A } } ( . )$$ ; confidence 0.193
+. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083380/s08338085.png ; $$d \in C$$ ; confidence 0.487
+. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083380/s08338074.png ; $$\Phi ( r - b + c )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130070/s1300707.png ; $$\phi ( f ( x ) ) = g ( x ) \phi ( x ) + h ( x )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s120040125.png ; $$\pi \Gamma$$ ; confidence 0.616
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s120040132.png ; $$\lambda ^ { s _ { \mu } } = \sum _ { \nu } c _ { \lambda \mu } ^ { \nu } s _ { \nu }$$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004027.png ; $$s _ { \lambda } = \sum _ { T } x ^ { T }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004026.png ; $$x ^ { T } = x _ { 1 } ^ { 3 } x _ { 2 } x _ { 3 } ^ { 2 } x _ { 4 }$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004016.png ; $$| \lambda | = \Sigma _ { i } \lambda$$ ; confidence 0.682
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120050/s12005011.png ; $$S _ { B B } ( z ) \equiv 0$$ ; confidence 0.476
+. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083460/s08346028.png ; $$\operatorname { Ccm } ( G )$$ ; confidence 0.094
+. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083470/s08347010.png ; $$D ^ { - 1 } \in \pi$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085140/s0851406.png ; $$\theta \in \Theta _ { 0 } \subseteq \Theta$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085250/s08525014.png ; $$\sum _ { j = 1 } ^ { n } | b _ { j j } | \leq \rho$$ ; confidence 0.569
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085210/s08521029.png ; $$q ^ { l } ( q ^ { 2 } - 1 ) \dots ( q ^ { 2 l } - 1 ) / d$$ ; confidence 0.450
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085210/s08521047.png ; $$q ^ { 6 } ( q ^ { 2 } - 1 ) ( q ^ { 6 } - 1 )$$ ; confidence 0.814
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085210/s08521071.png ; $$\square ^ { 2 } F _ { 4 } ( q ) ^ { \prime }$$ ; confidence 0.889
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085300/s08530020.png ; $$c b = c$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085330/s08533026.png ; $$18$$ ; confidence 0.479
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085340/s0853408.png ; $$s _ { \alpha } \geq 1$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085360/s0853606.png ; $$\operatorname { dim } K$$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085360/s085360140.png ; $$B d K$$ ; confidence 0.567
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085380/s08538041.png ; $$s _ { i } : X _ { n } \rightarrow X _ { n } + 1$$ ; confidence 0.593
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085400/s085400446.png ; $$X \rightarrow \Delta [ 0 ]$$ ; confidence 0.965
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085400/s085400325.png ; $$\tilde { f } : \Delta ^ { n + 1 } \rightarrow E$$ ; confidence 0.333
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085400/s08540076.png ; $$x _ { i } \in \pi$$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085560/s0855608.png ; $$| \sigma ^ { n } |$$ ; confidence 0.923
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085580/s085580244.png ; $$M = \frac { a } { a ^ { 2 } - b ^ { 2 } } I - \frac { b } { a ^ { 2 } - b ^ { 2 } } S$$ ; confidence 0.440
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085580/s085580113.png ; $$K = \nu - \nu$$ ; confidence 0.596
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085580/s08558099.png ; $$\psi ( t ) = a * ( t ) g ( t ) +$$ ; confidence 0.645
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590585.png ; $$\| x \| = \rho$$ ; confidence 0.826
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590370.png ; $$x _ { 0 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$$ ; confidence 0.863
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559028.png ; $$L _ { 2 } : z = \phi _ { 2 } ( t )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559026.png ; $$0 < \tau _ { 1 } \leq 1$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085620/s085620184.png ; $$f _ { t } = h _ { t } \circ f _ { 0 } \circ k _ { t }$$ ; confidence 0.837
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130360/s13036039.png ; $$\int _ { 0 } ^ { t } I _ { \partial D } ( Y _ { s } ) d l _ { s } = 1 _ { t }$$ ; confidence 0.676
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120150/s120150139.png ; $$\varphi H G$$ ; confidence 0.652
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085790/s08579085.png ; $$\sum _ { l = 1 } ^ { \infty } \frac { \operatorname { ln } q + 1 } { q l }$$ ; confidence 0.755
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085810/s0858103.png ; $$\phi : U \rightarrow \sum _ { i \in I } U _ { l }$$ ; confidence 0.895
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085820/s085820238.png ; $$b ( x ) < 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085830/s08583016.png ; $$| w | = \rho < 1$$ ; confidence 0.874
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086020/s08602026.png ; $$\overline { D ^ { + } } = D ^ { + } \cup \Gamma$$ ; confidence 0.709
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120180/s12018056.png ; $$M = M ^ { \perp \perp }$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086160/s0861605.png ; $$J _ { m + n + 1 } ( x ) =$$ ; confidence 0.892
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086190/s086190182.png ; $$s \in E ^ { n }$$ ; confidence 0.570
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086330/s086330106.png ; $$\| x \| ^ { 2 } = \int _ { \sigma ( A ) } | f _ { \lambda } ( x ) | ^ { 2 } d \rho ( \lambda )$$ ; confidence 0.635
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086330/s08633021.png ; $$\sigma _ { d x } ( A )$$ ; confidence 0.138
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086330/s08633098.png ; $$A \Phi \subset \Phi$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086360/s086360102.png ; $$B ( r ) = \int _ { 0 } ^ { \infty } J _ { 0 } ( \lambda r ) d F ( \lambda )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086380/s0863808.png ; $$s _ { 1 } - t _ { 1 } = s _ { 2 } - t _ { 2 }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086450/s08645013.png ; $$A _ { \delta }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086480/s0864803.png ; $$E | X ( t ) | ^ { n } \leq C < \infty$$ ; confidence 0.578
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086490/s086490118.png ; $$d ^ { \prime }$$ ; confidence 0.445
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086520/s08652091.png ; $$| T | _ { p }$$ ; confidence 0.714
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086520/s086520138.png ; $$\theta _ { T } = \theta$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086550/s0865507.png ; $$B _ { N } A ( B _ { N } ( \lambda - \lambda _ { 0 } ) )$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086590/s08659060.png ; $$\mathfrak { p } \not p \not \sum _ { n = 1 } ^ { \infty } A _ { n }$$ ; confidence 0.075
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086620/s08662027.png ; $$\Sigma ( \Sigma ^ { n } X ) \rightarrow \Sigma ^ { n + 1 } X$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086620/s08662031.png ; $$( \pi )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086650/s086650167.png ; $$Z _ { 24 }$$ ; confidence 0.663
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086650/s08665020.png ; $$i > 2 n - 1$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086700/s08670044.png ; $$e ^ { - k - s | / \mu } / \mu$$ ; confidence 0.763
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086720/s086720108.png ; $$V ^ { 3 } = E ^ { 3 }$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086720/s086720109.png ; $$K ( d s ) = K$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086720/s08672038.png ; $$\pi = n \sqrt { 1 + \sum p ^ { 2 } }$$ ; confidence 0.678
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s1202309.png ; $$O ( r )$$ ; confidence 0.866
+. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110240/s11024022.png ; $$\lambda _ { m } ( t )$$ ; confidence 0.691
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086770/s08677096.png ; $$5 + 7 n$$ ; confidence 0.141
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086810/s086810102.png ; $$f \in W _ { 2 } ^ { 3 } ( \Omega )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086810/s08681080.png ; $$( 2 m - 2 )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086810/s086810108.png ; $$W _ { p } ^ { m } ( I ^ { d } )$$ ; confidence 0.958
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510139.png ; $$L \subset Z ^ { 0 }$$ ; confidence 0.864
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051063.png ; $$\Gamma = \Gamma _ { 1 } + \ldots + \Gamma _ { m }$$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510126.png ; $$\gamma ( u ) < \infty$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086940/s086940114.png ; $$\operatorname { det } S \neq 0$$ ; confidence 0.896
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086940/s086940100.png ; $$- \infty \leq w \leq + \infty$$ ; confidence 0.301
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086940/s086940134.png ; $$0 \leq \omega \leq \infty$$ ; confidence 0.754
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086940/s08694070.png ; $$\| \eta ( \cdot ) \| ^ { 2 } = \int _ { 0 } ^ { \infty } | \eta ( t ) | ^ { 2 } d t$$ ; confidence 0.669
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086960/s08696030.png ; $$\| x _ { 0 } \| \leq \delta$$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086960/s08696076.png ; $$V < 0$$ ; confidence 0.854
+. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086960/s08696095.png ; $$k \leq p \leq n$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087030/s0870309.png ; $$f _ { h } \in U _ { k }$$ ; confidence 0.371
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087030/s08703096.png ; $$\operatorname { max } _ { n \atop n } \| u ^ { n } \| _ { H } \leq e ^ { C _ { 1 } T } \{ \| \phi \| _ { H } + C _ { 0 } \sum _ { n } \tau \| f ^ { n + 1 } \| _ { H } \}$$ ; confidence 0.172
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087110/s08711028.png ; $$\delta < \alpha$$ ; confidence 0.956
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087130/s08713053.png ; $$m < \infty$$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087260/s08726044.png ; $$\eta _ { 0 } ( i )$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087270/s08727063.png ; $$V _ { x } 0 ( \lambda ) \sim \operatorname { exp } [ i \lambda S ( x ^ { 0 } ) ] \sum _ { k = 0 } ^ { \infty } ( \sum _ { l = 0 } ^ { N } \alpha _ { k l } \lambda ^ { - r _ { k } } ( \operatorname { ln } \lambda ) ^ { l } \}$$ ; confidence 0.167
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087280/s087280193.png ; $$m = E X ( s )$$ ; confidence 0.808
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087300/s08730040.png ; $$Q _ { 1 }$$ ; confidence 0.060
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087320/s08732031.png ; $$\Pi ^ { * } \in C$$ ; confidence 0.864
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087320/s08732041.png ; $$\mathfrak { R } _ { \mu } ( \Pi _ { 0 } ) = \operatorname { inf } _ { \Pi } \Re _ { \mu } ( \Pi )$$ ; confidence 0.658
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087330/s08733032.png ; $$H _ { i } ( \omega )$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087350/s08735095.png ; $$I _ { n } ( \theta ) = n I ( \theta )$$ ; confidence 0.870
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087360/s087360228.png ; $$P \{ s ^ { 2 } < \frac { \sigma ^ { 2 } x } { n - 1 } \} = G _ { n - 1 } ( x ) = D _ { n - 1 } \int _ { 0 } ^ { x } v ^ { ( n - 3 ) } / 2 e ^ { - v / 2 } d v$$ ; confidence 0.622
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087360/s087360105.png ; $$\operatorname { lim } _ { n \rightarrow \infty } P \{ \frac { \alpha - \alpha } { \sigma _ { n } ( \alpha ) } < x \} = \frac { 1 } { \sqrt { 2 \pi } } \int _ { - \infty } ^ { x } e ^ { - t ^ { 2 } / 2 } d t \equiv \Phi ( x )$$ ; confidence 0.827
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087400/s087400105.png ; $$\in \Theta _ { 0 } \beta _ { n } ( \theta ) \leq \alpha$$ ; confidence 0.815
+. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110260/s11026022.png ; $$\eta \in R ^ { k }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087420/s08742011.png ; $$H = H _ { V } ( \omega )$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087420/s087420178.png ; $$\mathfrak { A } _ { \infty } = \overline { U _ { V \subset R ^ { 3 } } } A ( \mathcal { H } _ { V } )$$ ; confidence 0.216
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087420/s08742067.png ; $$\{ f \rangle _ { P } \sim | V |$$ ; confidence 0.071
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450224.png ; $$\frac { 1 } { 2 \pi } \sum _ { t = - T + 1 } ^ { T - 1 } e ^ { - i t \lambda } r ^ { * } ( t ) c T ( t )$$ ; confidence 0.607
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450112.png ; $$\xi = \sum b _ { j } x ( t _ { j } )$$ ; confidence 0.942
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450113.png ; $$\sum b _ { j } \phi _ { l } ( t _ { j } ) = 0$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450208.png ; $$I _ { T } ( \lambda ) = \frac { 1 } { 2 \pi T } | \int _ { 0 } ^ { T } e ^ { - i t \lambda } x ( t ) d t |$$ ; confidence 0.646
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450221.png ; $$a T \rightarrow \infty$$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450204.png ; $$\theta _ { T } ^ { * }$$ ; confidence 0.481
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087460/s08746026.png ; $$\{ \epsilon _ { t } \}$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120240/s12024033.png ; $$h ^ { S * } ( . ) \approx \overline { E } \times ( . )$$ ; confidence 0.489
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087550/s08755019.png ; $$\alpha < p b$$ ; confidence 0.578
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087550/s08755022.png ; $$\alpha \leq p b$$ ; confidence 0.784
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087640/s08764034.png ; $$g \neq 0$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087640/s08764060.png ; $$I = \{ f \in O ( X ) : f ( x ) = 0 \}$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087640/s08764057.png ; $$I \subset O ( X )$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087640/s08764086.png ; $$n ( O _ { x } ) = 0$$ ; confidence 0.322
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087690/s0876903.png ; $$f _ { h } ( t ) = \frac { 1 } { h } \int _ { t - k / 2 } ^ { t + k / 2 } f ( u ) d u = \frac { 1 } { h } \int _ { - k / 2 } ^ { k / 2 } f ( t + v ) d v$$ ; confidence 0.345
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087710/s08771037.png ; $$\omega ( R )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110280/s11028060.png ; $$\sum _ { i = 1 } ^ { r } \alpha _ { i } \theta ( b _ { i } ) \in Z [ G ]$$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087790/s08779013.png ; $$RP ^ { \infty }$$ ; confidence 0.165
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087770/s08777049.png ; $$V _ { k } ( H ^ { n } ) = \frac { Sp ( n ) } { Sp ( n - k ) }$$ ; confidence 0.259
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087780/s08778069.png ; $$x [ M ^ { n } ] = \alpha ( x )$$ ; confidence 0.933
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087780/s08778021.png ; $$w ^ { \prime }$$ ; confidence 0.380
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087800/s08780026.png ; $$x + C$$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087800/s08780044.png ; $$| u ( x _ { 1 } ) - u ( x _ { 2 } ) | \leq C | x _ { 1 } - x _ { 2 }$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120250/s1202506.png ; $$h _ { n } = \int _ { a } ^ { b } x ^ { n } h ( x ) d x$$ ; confidence 0.183
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087820/s08782077.png ; $$| \frac { 1 } { 1 - H \lambda _ { i } } | < 1$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087820/s087820210.png ; $$y _ { n + 1 } = y _ { n } + \int _ { 0 } ^ { H / 2 } e ^ { A \tau } d \tau \times$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087820/s08782061.png ; $$\alpha _ { 1 } = - 3$$ ; confidence 0.753
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087820/s087820182.png ; $$\| y \| = \operatorname { max } _ { i } | y _ { i } |$$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090130/s09013024.png ; $$H \mapsto \alpha ( H )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090130/s09013055.png ; $$K . ( H X ) = ( K H ) X$$ ; confidence 0.766
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026061.png ; $$\partial _ { s }$$ ; confidence 0.939
+. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110290/s11029032.png ; $$t / \lambda ^ { 2 } \rightarrow + \infty$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090170/s09017045.png ; $$E$$ ; confidence 0.923
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090170/s09017090.png ; $$B \in \mathfrak { B } _ { 0 }$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090170/s0901702.png ; $$\ldots < t _ { - 1 } < t _ { 0 } \leq 0 < t _ { 1 } < t _ { 2 } <$$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090180/s0901802.png ; $$\square \ldots < t _ { - 1 } < t _ { 0 } \leq 0 < t _ { 1 } < t _ { 2 } < \ldots$$ ; confidence 0.740
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090190/s090190160.png ; $$X ( t _ { 1 } ) = x$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090190/s09019043.png ; $$t = Z$$ ; confidence 0.971
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090220/s09022010.png ; $$x ( \phi )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090230/s09023035.png ; $$\overline { w }$$ ; confidence 0.553
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090260/s09026037.png ; $$d x = A ( t ) x d t + B ( t ) d w ( t )$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090260/s09026014.png ; $$d X ( t ) = a ( t ) Z ( t ) d t + d Y ( t )$$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090270/s0902702.png ; $$\alpha < t < b$$ ; confidence 0.786
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090450/s09045062.png ; $$\zeta ^ { \phi } \in C ^ { d }$$ ; confidence 0.837
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090450/s09045037.png ; $$W ^ { ( n ) } ( s )$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090590/s0905905.png ; $$J ( y ) \leq J ( y )$$ ; confidence 0.683
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120280/s1202804.png ; $$\overline { f } : X \rightarrow Y$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120280/s12028015.png ; $$\overline { E } * ( X )$$ ; confidence 0.554
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090670/s09067035.png ; $$j _ { X } ^ { k } ( u )$$ ; confidence 0.362
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090710/s09071014.png ; $$f = 1$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090720/s09072010.png ; $$a \neq a _ { 0 }$$ ; confidence 0.773
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090760/s09076059.png ; $$p ( \alpha )$$ ; confidence 0.904
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090760/s09076071.png ; $$l [ f ] = 0$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090760/s09076026.png ; $$L _ { 0 } ^ { * } = L _ { 1 }$$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090770/s090770137.png ; $$\lambda _ { 1 } < \lambda _ { 2 } < \ldots$$ ; confidence 0.830
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090780/s09078074.png ; $$\Phi ^ { \prime \prime } ( + 0 ) = - h$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s13062062.png ; $$m _ { 0 } ( \lambda ) = A + \int _ { - \infty } ^ { \infty } ( \frac { 1 } { t - \lambda } - \frac { t } { t ^ { 2 } + 1 } ) d \rho _ { 0 } ( t )$$ ; confidence 0.926
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090820/s0908209.png ; $$X ^ { * }$$ ; confidence 0.447
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090830/s0908308.png ; $$m : B \rightarrow A$$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090900/s09090088.png ; $$\xi = \infty \in \partial D$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090900/s09090090.png ; $$V = V ( \infty ) = \{ x \in R ^ { n } : | x | > R \}$$ ; confidence 0.624
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091010/s09101020.png ; $$c = \operatorname { const } \neq 0$$ ; confidence 0.470
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091070/s09107089.png ; $$P _ { \theta } ( A | B )$$ ; confidence 0.963
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091080/s09108054.png ; $$\sum _ { n < x } f ( n ) = R ( x ) + O ( x ^ { \{ ( \alpha + 1 ) ( 2 \eta - 1 ) / ( 2 \eta + 1 ) \} + \epsilon } )$$ ; confidence 0.795
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091100/s0911009.png ; $$\lambda _ { n } = 1 / ( n + 1 ) ^ { s }$$ ; confidence 0.931
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091140/s09114035.png ; $$s _ { n } \rightarrow s$$ ; confidence 0.696
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091140/s09114030.png ; $$\sum _ { k = 0 } ^ { \infty } \lambda _ { k } u _ { k }$$ ; confidence 0.542
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091200/s09120056.png ; $$\operatorname { psq } ( n ) = \operatorname { sq } ( n ) / \{ c E : c \in C \}$$ ; confidence 0.425
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s12032058.png ; $$S ( L )$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091390/s09139063.png ; $$x _ { 1 } ^ { 2 } = 0$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091390/s0913909.png ; $$\frac { x ^ { 2 } } { p } - \frac { y ^ { 2 } } { q } = 2 z$$ ; confidence 0.932
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091570/s09157097.png ; $$T ^ { * } Y \backslash 0$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091580/s09158080.png ; $$\Phi ( f ( w ) ) = \sigma ( \Phi ( w ) )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091670/s09167062.png ; $$S ( B _ { n } ^ { m } )$$ ; confidence 0.719
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091730/s09173026.png ; $$H ^ { n - k } \cap S ^ { k }$$ ; confidence 0.502
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s120340135.png ; $$\alpha _ { H } ( \tilde { x } _ { + } ) - \alpha _ { H } ( \tilde { x } _ { - } ) = 1$$ ; confidence 0.404
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091910/s09191051.png ; $$\sim \frac { 2 ^ { n } } { \operatorname { log } _ { 2 } n }$$ ; confidence 0.975
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091910/s091910121.png ; $$T _ { i } = C A ^ { i } B ^ { i } B$$ ; confidence 0.233
+. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110330/s11033016.png ; $$- 5 \rightarrow - 14 \rightarrow - 7 \rightarrow - 20 \rightarrow - 10 \rightarrow - 5$$ ; confidence 0.902
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091960/s0919603.png ; $$R = \{ \pi ( i ) : \square i \in I \}$$ ; confidence 0.950
+. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091960/s09196011.png ; $$\{ \pi ( i ) : \square i \in I _ { 0 } \}$$ ; confidence 0.752
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064057.png ; $$L ^ { 1 } ( R ) \cap L ^ { \infty } ( R )$$ ; confidence 0.831
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120020/t12002014.png ; $$T ^ { + } = \cap _ { N > 0 } \sigma ( X _ { n } : n \geq N )$$ ; confidence 0.699
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092240/t0922406.png ; $$k = R / m$$ ; confidence 0.483
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092250/t09225012.png ; $$g ^ { ( i ) }$$ ; confidence 0.484
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130040/t13004015.png ; $$( n + 1 ) a _ { n + 1 } + \alpha _ { n } = \tau$$ ; confidence 0.385
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130040/t13004014.png ; $$\tau x ^ { n }$$ ; confidence 0.790
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005033.png ; $$D _ { A } ^ { 2 } = 0$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005053.png ; $$\sigma ^ { \prime } ( A )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120030/t12003042.png ; $$\psi = \Psi ^ { \prime }$$ ; confidence 0.559
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092470/t09247071.png ; $$E _ { 1 } E _ { 2 } E _ { 3 }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092470/t092470182.png ; $$e _ { v } \leq \mathfrak { e } _ { v } + 1$$ ; confidence 0.197
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092470/t092470133.png ; $$R _ { T ^ { \prime \prime } }$$ ; confidence 0.675
+. https://www.encyclopediaofmath.org/legacyimages/t/t110/t110020/t11002078.png ; $$M _ { \mathscr { C } } M _ { b } M _ { \alpha ^ { \prime } } M _ { \phi }$$ ; confidence 0.076
+. https://www.encyclopediaofmath.org/legacyimages/t/t110/t110020/t11002049.png ; $$e ^ { \prime }$$ ; confidence 0.559
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092530/t09253011.png ; $$( \pi | \tau _ { 1 } | \tau _ { 2 } )$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092600/t09260017.png ; $$\theta ( z + \tau ) = \operatorname { exp } ( - 2 \pi i k z ) . \theta ( z )$$ ; confidence 0.660
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092600/t09260081.png ; $$\delta = 2$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092600/t09260032.png ; $$\operatorname { lm } A = \| \operatorname { lm } \alpha _ { \mu \nu } |$$ ; confidence 0.510
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092600/t092600123.png ; $$B = I _ { p }$$ ; confidence 0.852
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120050/t12005046.png ; $$d f _ { x } : R ^ { n } \rightarrow R ^ { p }$$ ; confidence 0.932
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130090/t13009023.png ; $$f ^ { - 1 } ( S )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092650/t09265044.png ; $$c < 2$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092650/t09265019.png ; $$u x + v x ^ { 2 } + w x ^ { 3 } + t x ^ { 4 }$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092650/t09265033.png ; $$\{ \partial f \rangle$$ ; confidence 0.295
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092650/t09265012.png ; $$x ^ { 3 } + x y ^ { 2 }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t120060116.png ; $$E ^ { Q } ( N )$$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006058.png ; $$N \geq Z$$ ; confidence 0.919
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092720/t09272013.png ; $$\Delta _ { i j } = \Delta _ { j i } = \sqrt { ( x _ { i } - x _ { j } ) ^ { 2 } + ( y _ { i } - y _ { j } ) ^ { 2 } + ( z _ { i } - z _ { j } ) ^ { 2 } }$$ ; confidence 0.489
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092730/t09273032.png ; $$M = M _ { 1 } \# M _ { 2 }$$ ; confidence 0.954
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120080/t12008015.png ; $$O _ { S } ^ { * }$$ ; confidence 0.936
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120080/t12008049.png ; $$( 5 \times 10 ^ { 6 } r ) ^ { 3 }$$ ; confidence 0.525
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092800/t09280017.png ; $$X _ { ( \tau _ { 1 } + \ldots + \tau _ { j - 1 } + 1 ) } = \ldots = X _ { ( \tau _ { 1 } + \ldots + \tau _ { j } ) }$$ ; confidence 0.575
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092810/t092810186.png ; $$B s$$ ; confidence 0.576
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092810/t092810205.png ; $$\beta ( M )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130100/t1301005.png ; $$\square _ { H } T$$ ; confidence 0.979
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014052.png ; $$( Q )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140116.png ; $$q R$$ ; confidence 0.245
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140169.png ; $$q _ { A }$$ ; confidence 0.118
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013055.png ; $$M = M \Lambda ^ { t }$$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130150/t13015070.png ; $$C ^ { * } E ( S ) \otimes _ { \delta } C _ { 0 } ( S )$$ ; confidence 0.440
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130150/t13015064.png ; $$K ( L ^ { 2 } ( S ) )$$ ; confidence 0.779
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120150/t12015061.png ; $$( \Delta ^ { \alpha } \xi ) ^ { \# } = \Delta ^ { - \overline { \alpha } } \xi ^ { \# }$$ ; confidence 0.710
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120150/t1201505.png ; $$\eta \in A \mapsto \xi \eta \in A$$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092980/t09298063.png ; $$f \in S ( R ^ { n } )$$ ; confidence 0.981
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150622.png ; $$( f _ { i } : B _ { i } \rightarrow B ) _ { i \in l }$$ ; confidence 0.575
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150169.png ; $$F \in \gamma$$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150743.png ; $$\left. \begin{array} { c c c } { B _ { i } } & { \stackrel { h _ { i } } { \rightarrow } } & { A _ { i } } \\ { g _ { i } \downarrow } & { \square } & { \downarrow f _ { i } } \\ { B } & { \vec { f } } & { A } \end{array} \right.$$ ; confidence 0.342
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150395.png ; $$A \wedge B$$ ; confidence 0.923
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150306.png ; $$= C$$ ; confidence 0.931
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150450.png ; $$\operatorname { sin } 0$$ ; confidence 0.092
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150393.png ; $$\{ p _ { i } ^ { - 1 } U _ { i } : U _ { i } \in \mu _ { i \square } \text { and } i \in I \}$$ ; confidence 0.601
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150728.png ; $$A ^ { * } = A \cup \{ \infty _ { A } \}$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093160/t09316047.png ; $$p _ { 1 } \otimes \sim p _ { 2 }$$ ; confidence 0.782
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093160/t09316053.png ; $$\sum _ { k = 1 } ^ { \infty } p _ { 1 } ( x _ { k } ) p _ { 2 } ( y _ { k } ) \leq p _ { 1 } \overline { Q } p _ { 2 } ( u ) + \epsilon$$ ; confidence 0.229
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093180/t093180434.png ; $$D ( R ^ { n + k } )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093230/t09323048.png ; $$H \rightarrow TOP$$ ; confidence 0.688
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093230/t093230103.png ; $$\left. \begin{array} { c c c } { \square } & { \square } & { B P L } \\ { \square } & { \square } & { \downarrow } \\ { X } & { \vec { \tau } _ { X } } & { B G } \end{array} \right.$$ ; confidence 0.066
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093230/t09323071.png ; $$X \rightarrow P L / O$$ ; confidence 0.928
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093260/t09326056.png ; $$d \Phi$$ ; confidence 0.791
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093260/t09326078.png ; $$d = 6$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093260/t09326038.png ; $$( X ) \in M$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093330/t09333059.png ; $$r _ { 2 } \in R$$ ; confidence 0.862
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093340/t0933407.png ; $$S _ { j } ^ { k } = \Gamma _ { i j } ^ { k } - \Gamma _ { j i } ^ { k }$$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093570/t0935701.png ; $$x = \pm \alpha \operatorname { ln } \frac { \alpha + \sqrt { \alpha ^ { 2 } - y ^ { 2 } } } { y } - \sqrt { \alpha ^ { 2 } - y ^ { 2 } }$$ ; confidence 0.391
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093670/t09367085.png ; $$r < | w | < 1$$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093670/t09367092.png ; $$d s _ { é } = \frac { | d z | } { 1 + | z | ^ { 2 } }$$ ; confidence 0.470
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093670/t09367039.png ; $$\operatorname { lim } _ { \epsilon \rightarrow 0 } d ( E _ { \epsilon } ) = d ( E )$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093710/t0937107.png ; $$x = f ( \alpha )$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093770/t09377057.png ; $$\mathfrak { A } f ( x ) = \operatorname { lim } _ { U ! x } [ \frac { E _ { x } f ( x _ { \tau } ) - f ( x ) } { E _ { x } \tau } ]$$ ; confidence 0.104
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093770/t09377067.png ; $$\mathfrak { A } f$$ ; confidence 0.742
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093770/t09377043.png ; $$R ^ { 0 } f$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093770/t09377039.png ; $$g = R ^ { \alpha } f$$ ; confidence 0.864
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093860/t09386023.png ; $$P ( S )$$ ; confidence 0.765
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093890/t09389045.png ; $$o ( N ) / N \rightarrow 0$$ ; confidence 0.792
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093900/t093900196.png ; $$T _ { 23 } n ( \operatorname { cos } \pi \omega )$$ ; confidence 0.946
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093900/t09390073.png ; $$g _ { n } ( \Omega )$$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093900/t093900115.png ; $$l \mu \frac { \partial W ^ { k } } { \partial x } + ( 1 - c ) W ^ { k } = c ( \Phi _ { 0 } ^ { k } - \phi _ { 0 } ^ { k } )$$ ; confidence 0.308
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093900/t093900146.png ; $$Q _ { n } W ^ { k } = P _ { n } c ( W ^ { k } + \Phi _ { 0 } ^ { k } - \phi _ { 0 } ^ { k } )$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093900/t093900154.png ; $$g _ { k } = ( 1 + y _ { k } ) / 2$$ ; confidence 0.953
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093980/t0939808.png ; $$V = f ^ { - 1 } ( X )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093990/t09399044.png ; $$Q _ { 1 } \cup \square \ldots \cup Q _ { m }$$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094000/t09400030.png ; $$f ( x ) = g ( y )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130210/t13021052.png ; $$2 / ( 3 N / 2 )$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094240/t09424015.png ; $$\frac { a _ { 0 } } { 4 } x ^ { 2 } - \sum _ { k = 1 } ^ { \infty } \frac { a _ { k } \operatorname { cos } k x + b _ { k } \operatorname { sin } k x } { k ^ { 2 } }$$ ; confidence 0.667
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094300/t094300134.png ; $$\operatorname { Fix } ( T ) \subset \mathfrak { R }$$ ; confidence 0.710
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094300/t09430077.png ; $$\left. \begin{array} { c c c } { T A } & { \stackrel { T f } { S } } & { T B } \\ { \alpha \downarrow } & { \square } & { \downarrow \beta } \\ { A } & { \vec { f } } & { B } \end{array} \right.$$ ; confidence 0.204
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094420/t09442025.png ; $$\overline { U } / \partial \overline { U }$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094440/t09444040.png ; $$u _ { m } = u ( M _ { m } )$$ ; confidence 0.360
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200142.png ; $$m > - 1$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200179.png ; $$\operatorname { Re } G _ { 1 } ( r ) \geq B$$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094530/t094530109.png ; $$\sum ( k _ { i } - 1 )$$ ; confidence 0.930
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094540/t09454051.png ; $$\{ \omega _ { n } ^ { + } ( V ) \}$$ ; confidence 0.949
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094600/t09460022.png ; $$f _ { 0 } \neq 0$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094600/t0946003.png ; $$\alpha \geq A _ { 0 }$$ ; confidence 0.904
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094650/t09465038.png ; $$\forall v \phi$$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094650/t09465066.png ; $$\in M$$ ; confidence 0.717
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094650/t09465036.png ; $$( \phi \& \psi )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094660/t09466060.png ; $$\{ f ( z ) \}$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094660/t09466020.png ; $$\phi ( z ) = \frac { 1 - z ^ { 2 } } { z } f ( z ) \in C$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095070/u09507044.png ; $$T ( X ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } X = 1 } \\ { 0 } & { \text { if } X \geq 2 } \end{array} \right.$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095210/u0952109.png ; $$f _ { \alpha } ( x ) \geq - c$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095230/u09523081.png ; $$\{ d f _ { n } / d x \}$$ ; confidence 0.954
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095290/u09529039.png ; $$t \rightarrow t + w z$$ ; confidence 0.466
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095290/u09529022.png ; $$w = \operatorname { sin }$$ ; confidence 0.905
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095400/u09540011.png ; $$( g - 1 ) ^ { n } = 0$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095410/u09541013.png ; $$U _ { n } ( K )$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095410/u09541052.png ; $$g ^ { p } = e$$ ; confidence 0.978
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095440/u09544022.png ; $$O ( \epsilon _ { N } )$$ ; confidence 0.478
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095440/u09544020.png ; $$U ( \epsilon )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095620/u09562096.png ; $$\sum _ { k = 1 } ^ { \infty } | \alpha _ { k } | ^ { 2 } = \frac { 1 } { 2 \pi } \int _ { 0 } ^ { 2 \pi } | f ( e ^ { i t } ) | ^ { 2 } d t \leq 1$$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095630/u09563071.png ; $$U : B \rightarrow A$$ ; confidence 0.544
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095680/u09568015.png ; $$( n \geq 0 )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095820/u09582023.png ; $$v ( x ) \geq f ( x )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096020/v096020116.png ; $$f ( z ) \in K$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096020/v096020108.png ; $$\lambda \leq 0.5$$ ; confidence 0.968
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096020/v096020147.png ; $$( f ) \subseteq V ( f )$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096040/v0960408.png ; $$s ( r )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/v/v110/v110020/v11002046.png ; $$x \in Y ( u )$$ ; confidence 0.570
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096350/v0963509.png ; $$( a + b ) + c = a + ( b + c )$$ ; confidence 0.946
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096350/v09635084.png ; $$a \perp b$$ ; confidence 0.521
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096350/v09635060.png ; $$\left. \begin{array} { l l l } { \alpha _ { 1 } } & { \alpha _ { 2 } } & { \alpha _ { 3 } } \\ { b _ { 1 } } & { b _ { 2 } } & { b _ { 3 } } \\ { c _ { 1 } } & { c _ { 2 } } & { c _ { 3 } } \end{array} \right| = 0$$ ; confidence 0.378
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v09638081.png ; $$u ^ { * } ( \pi )$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v096380113.png ; $$\pi ^ { \prime } \oplus \theta ^ { \prime }$$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v09638042.png ; $$G ^ { k } ( V ) \times V$$ ; confidence 0.950
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v096380128.png ; $$w : \xi \oplus \zeta \rightarrow \pi$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v09638089.png ; $$\pi : B \rightarrow G ^ { k } ( V )$$ ; confidence 0.258
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v09638020.png ; $$X ^ { \prime } \cap \pi ^ { - 1 } ( b )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096450/v09645016.png ; $$+ \frac { 1 } { N ! } \int _ { t _ { 0 } } ^ { t } ( t - \tau ) ^ { N _ { r } ( N + 1 ) } ( \tau ) d \tau$$ ; confidence 0.696
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130060/v13006019.png ; $$j \in ( 1 / 2 ) Z$$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v130050114.png ; $$1 _ { n } ( w ) = 0$$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v1200207.png ; $$f ^ { * } : H ^ { * } ( Y ) \rightarrow H ^ { * } ( X )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020197.png ; $$H ^ { n } ( S ^ { n } )$$ ; confidence 0.629
+. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020220.png ; $$\delta ^ { * } \circ ( t - r ) ^ { * } \beta _ { 1 } = k ( t ^ { * } \square ^ { - 1 } \beta _ { 3 } )$$ ; confidence 0.259
+. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020184.png ; $$F : S ^ { n } \rightarrow K ( E ^ { n + 1 } \backslash \theta )$$ ; confidence 0.783
+. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020188.png ; $$t ^ { * } : H ^ { N } ( S ^ { N } ) \rightarrow H ^ { N } ( \Gamma _ { S ^ { n } } )$$ ; confidence 0.119
+. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v12002064.png ; $$d _ { k } = rd _ { Y } M _ { k }$$ ; confidence 0.623
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096650/v0966506.png ; $$n \geq 12$$ ; confidence 0.886
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096670/v09667018.png ; $$P ^ { 2 r - k }$$ ; confidence 0.936
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096740/v0967406.png ; $$v _ { \nu } ( t _ { 0 } ) = 0$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096770/v0967704.png ; $$F : \Omega \times R ^ { n } \times R ^ { n } \times S ^ { n } \rightarrow R$$ ; confidence 0.909
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v13007046.png ; $$q e ^ { ( - i \theta ) }$$ ; confidence 0.903
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v1300709.png ; $$\vec { V }$$ ; confidence 0.987
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096870/v09687032.png ; $$\tau _ { j } < 0$$ ; confidence 0.887
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011059.png ; $$2 i$$ ; confidence 0.747
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011069.png ; $$\theta = 2 \pi$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011064.png ; $$U = \frac { \Gamma } { 2 l } \operatorname { tanh } \frac { \pi b } { l } = \frac { \Gamma } { 2 l \sqrt { 2 } }$$ ; confidence 0.768
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900234.png ; $$\Pi I _ { \lambda }$$ ; confidence 0.300
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v09690074.png ; $$\phi ( U T U ^ { - 1 } ) = \phi ( T )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900232.png ; $$III _ { 0 }$$ ; confidence 0.560
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900125.png ; $$P \sim P _ { 1 }$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900122.png ; $$Q = U U ^ { * }$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900124.png ; $$P _ { 1 } \in A$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097030/w09703012.png ; $$\overline { \sum _ { g } n ( g ) g } = \sum w ( g ) n ( g ) g ^ { - 1 }$$ ; confidence 0.832
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097030/w09703029.png ; $$U = \cup _ { i } \operatorname { Im } f$$ ; confidence 0.671
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097040/w0970409.png ; $$\int _ { 0 } ^ { \pi / 2 } \operatorname { sin } ^ { 2 m + 1 } x d x$$ ; confidence 0.964
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097060/w09706017.png ; $$2 ^ { m } \leq n \leq 2 ^ { m + 1 } - 1$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097090/w0970903.png ; $$F ( x )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097150/w0971508.png ; $$\lambda = 2 \pi / | k |$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097290/w09729017.png ; $$A _ { n } ( x _ { 0 } )$$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097310/w09731010.png ; $$\partial ^ { 2 } u / \partial x ^ { 2 } + \partial ^ { 2 } u / \partial y ^ { 2 } + k ^ { 2 } u = 0$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097350/w0973508.png ; $$A = N \oplus s$$ ; confidence 0.521
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097350/w0973509.png ; $$A = N \oplus S _ { 1 }$$ ; confidence 0.438
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097450/w09745039.png ; $$j = g ^ { 3 } / g ^ { 2 }$$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097450/w09745010.png ; $$= \frac { 1 } { z ^ { 2 } } + c 2 z ^ { 2 } + c _ { 4 } z ^ { 4 } + \ldots$$ ; confidence 0.426
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097470/w09747012.png ; $$x ( t _ { i } ) = x _ { 0 } ( t _ { i } )$$ ; confidence 0.980
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130040/w13004043.png ; $$K = - ( \frac { 4 | d g | } { ( 1 + | g | ^ { 2 } ) ^ { 2 } | \eta | } \} ^ { 2 }$$ ; confidence 0.571
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097510/w09751010.png ; $$m _ { k } = \dot { k }$$ ; confidence 0.352
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097510/w097510202.png ; $$q \in T _ { n } ( k )$$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120050/w12005030.png ; $$D = \langle x ^ { 2 } \} \subset R [ x ]$$ ; confidence 0.413
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120050/w12005029.png ; $$D = R [ x ] / D$$ ; confidence 0.968
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097600/w09760044.png ; $$H ^ { i } ( X )$$ ; confidence 0.995
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097600/w0976009.png ; $$H ^ { 2 n } ( X )$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130070/w13007023.png ; $$\beta$$ ; confidence 0.911
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120100/w12010028.png ; $$\nabla _ { i g j k } = \gamma _ { i } g _ { j k }$$ ; confidence 0.315
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097670/w097670169.png ; $$\operatorname { gr } ( A _ { 1 } ( K ) )$$ ; confidence 0.860
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097670/w097670151.png ; $$A _ { k + 1 } ( C )$$ ; confidence 0.634
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097670/w097670153.png ; $$\oplus V _ { k } ( M ) / V _ { k - 1 } ( M )$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007015.png ; $$q$$ ; confidence 0.899
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w120070106.png ; $$C ^ { \prime } = 1$$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120080/w12008025.png ; $$W ( f \times g ) = W ( f ) . W ( g )$$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097710/w09771010.png ; $$Z _ { \zeta } ( T )$$ ; confidence 0.463
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097710/w09771067.png ; $$N _ { G } ( T ) / Z _ { G } ( T )$$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097710/w0977109.png ; $$N _ { G } ( T )$$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097720/w0977202.png ; $$f ( x ) = \alpha _ { n } x ^ { n } + \ldots + \alpha _ { 1 } x$$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090131.png ; $$\Delta ( \lambda ) ^ { \mu }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090399.png ; $$L ( \mu )$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090342.png ; $$\left( \begin{array} { c } { h } \\ { i } \end{array} \right) = \frac { h ( h - 1 ) \ldots ( h - i + 1 ) } { i ! }$$ ; confidence 0.487
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011033.png ; $$S ( R ^ { n } ) \times S ( R ^ { n } )$$ ; confidence 0.944
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011024.png ; $$\alpha ^ { \psi } = Op ( J ^ { 1 / 2 } \alpha )$$ ; confidence 0.058
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110153.png ; $$\alpha _ { 2 k + 1 } \in L ^ { 1 } ( \Phi )$$ ; confidence 0.712
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011079.png ; $$A ^ { * } \sigma A = \sigma$$ ; confidence 0.887
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110210.png ; $$G = G ^ { \sigma }$$ ; confidence 0.956
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110192.png ; $$X \in \Phi$$ ; confidence 0.895
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110269.png ; $$g _ { 1 } = | d x | ^ { 2 } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } } \leq g = \frac { | d x | ^ { 2 } } { | x | ^ { 2 } } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } }$$ ; confidence 0.357
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097790/w09779041.png ; $$\pi _ { 4 n - 1 } ( S ^ { 2 n } ) \rightarrow \pi _ { 4 n } ( S ^ { 2 n + 1 } )$$ ; confidence 0.354
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120140/w12014036.png ; $$S \square T$$ ; confidence 0.898
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080142.png ; $$T _ { n }$$ ; confidence 0.602
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008076.png ; $$N = 2$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080127.png ; $$S _ { n } = s _ { n } + \theta ^ { 2 } F _ { n }$$ ; confidence 0.942
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080124.png ; $$T _ { 1 } \sim \Lambda$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097870/w09787060.png ; $$\prod _ { \nu } : \prod _ { i \in I _ { \nu } } f _ { i } : = \sum _ { G } \prod _ { e \in G } < f _ { e _ { 1 } } f _ { e _ { 2 } } > : \prod _ { i \notin [ G ] } f _ { i : }$$ ; confidence 0.238
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120170/w12017064.png ; $$l \equiv 2 ( \operatorname { mod } 3 )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097910/w0979106.png ; $$B ( \lambda )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097910/w09791036.png ; $$L _ { - } ( \lambda ) C ( \lambda ) / B ( \lambda )$$ ; confidence 0.885
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009059.png ; $$\Gamma ( H ) = \sum _ { n = 0 } ^ { \infty } H ^ { \otimes n }$$ ; confidence 0.591
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009053.png ; $$\| \varphi \| _ { L ^ { 2 } ( \mu ) } = \sqrt { n ! } | f | _ { H ^ { \otimes n } }$$ ; confidence 0.909
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009083.png ; $$( g ) = g ^ { \prime }$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018046.png ; $$t _ { 1 } \in D ^ { - }$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/w/w110/w110070/w11007022.png ; $$\| x \| _ { 1 }$$ ; confidence 0.650
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120190/w12019047.png ; $$P = - i \hbar \nabla _ { x }$$ ; confidence 0.929
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130120/w13012027.png ; $$T _ { W \alpha } = T$$ ; confidence 0.134
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120200/w12020038.png ; $$\int _ { a } ^ { b } ( f ^ { ( r ) } ( x ) ) ^ { 2 } d x \leq 1$$ ; confidence 0.515
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021059.png ; $$B _ { m } = R$$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098040/w09804013.png ; $$p ( n + 1 ) / 2$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/w/w110/w110120/w11012047.png ; $$( D ) \leq c \text { length } ( C )$$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098160/w09816057.png ; $$Y \times X$$ ; confidence 0.869
+. https://www.encyclopediaofmath.org/legacyimages/x/x120/x120010/x120010101.png ; $$\operatorname { Aut } ( R ) / \operatorname { ln } n ( R ) \cong H$$ ; confidence 0.228
+. https://www.encyclopediaofmath.org/legacyimages/x/x120/x120010/x12001022.png ; $$\sigma \in \operatorname { Aut } ( R )$$ ; confidence 0.958
+. https://www.encyclopediaofmath.org/legacyimages/x/x120/x120020/x12002033.png ; $$D ( R )$$ ; confidence 0.960
+. https://www.encyclopediaofmath.org/legacyimages/y/y110/y110010/y11001021.png ; $$J ( \phi )$$ ; confidence 0.976
+. https://www.encyclopediaofmath.org/legacyimages/y/y110/y110010/y11001038.png ; $$\| \phi _ { q } \| _ { q } = 1$$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/y/y110/y110010/y11001031.png ; $$H _ { 1 } \subset L _ { N }$$ ; confidence 0.459
+. https://www.encyclopediaofmath.org/legacyimages/y/y110/y110010/y11001011.png ; $$g ^ { \prime } = \phi ^ { 4 / ( n - 2 ) } g$$ ; confidence 0.828
+. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120010/y12001017.png ; $$R _ { 12 } R _ { 13 } R _ { 23 } = R _ { 23 } R _ { 13 } R _ { 12 }$$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120010/y120010139.png ; $$R : X \times X \rightarrow \operatorname { End } _ { k } ( V \otimes _ { k } V )$$ ; confidence 0.794
+. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120010/y12001036.png ; $$R _ { V } : V \otimes _ { k } V \rightarrow V \otimes _ { k } V$$ ; confidence 0.786
+. https://www.encyclopediaofmath.org/legacyimages/y/y099/y099030/y09903095.png ; $$\sigma ( M ^ { 4 } )$$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/y/y099/y099030/y099030101.png ; $$\pi _ { 1 } : P _ { 1 } \rightarrow S ^ { 4 }$$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/y/y099/y099070/y09907014.png ; $$t _ { \lambda } ^ { \prime }$$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z130100102.png ; $$\forall v \exists u ( \forall w \varphi \leftrightarrow u = w )$$ ; confidence 0.569
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z13010033.png ; $$\forall y ( \neg y \in x )$$ ; confidence 0.930
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130050/z13005046.png ; $$I = ( f )$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/z/z110/z110010/z11001018.png ; $$( f g f h )$$ ; confidence 0.723
+. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120020/z12002043.png ; $$1.609$$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/z/z099/z099250/z09925023.png ; $$001 c 23 + c 02 c 31 + c 03 c 12 \neq 0$$ ; confidence 0.156
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130130/z1301303.png ; $$x _ { 2 } = r \operatorname { sin } \theta$$ ; confidence 0.977