Difference between revisions of "User:Maximilian Janisch/latexlist/latex/13"

Revision as of 10:28, 2 September 2019

List

1. ; $D _ { \alpha }$ ; confidence 0.374

2. ; $T ^ { 2 }$ ; confidence 0.373

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

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

5. ; $i = 1 , \dots , r$ ; confidence 0.372

6. ; $\beta _ { k } q _ { k + 1 } = A q _ { k } - \beta _ { k - 1 } q _ { k - 1 } - \alpha _ { k } q _ { k k }$ ; confidence 0.371

7. ; $f _ { h } \in U _ { k }$ ; confidence 0.371

8. ; $d _ { C } ^ { - 1 } = \operatorname { det } \left\| \begin{array} { c c } { \phi _ { \theta } \theta } & { \phi _ { \theta x } } \\ { \phi _ { y } \theta } & { \phi _ { y x } } \end{array} \right\|$ ; confidence 0.370

9. ; $a _ { 1 } b _ { 1 } \ldots a _ { 8 } b _ { 8 }$ ; confidence 0.369

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

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

12. ; $\overline { a } X = \beta a X = \alpha \beta X$ ; confidence 0.369

13. ; $\hat { k } ( \alpha + \beta )$ ; confidence 0.369

14. ; $z \leq | ( \hat { \lambda } I - \Lambda ) ^ { - 1 } | | T ^ { - 1 } | | \delta A | | T | z |$ ; confidence 0.368

15. ; $i = 1 , \ldots , I$ ; confidence 0.368

16. ; $A _ { r } ^ { \alpha }$ ; confidence 0.368

17. ; $\delta b = H . | b$ ; confidence 0.368

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

19. ; $n \| < C$ ; confidence 0.368

20. ; $\partial _ { x } = \partial / \partial x$ ; confidence 0.368

21. ; $E _ { i j }$ ; confidence 0.366

22. ; $m$ ; confidence 0.365

23. ; $f ( z ) = \sum _ { k = 0 } ^ { \infty } \alpha _ { \nu _ { k } } z ^ { \nu _ { k } }$ ; confidence 0.364

24. ; $( \hat { \lambda } B - C ) ^ { - 1 } = P ( \hat { \lambda } I - \Lambda ) ^ { - 1 } Q$ ; confidence 0.363

25. ; $b _ { 0 }$ ; confidence 0.363

26. ; $\frac { 1 } { 4 n } \operatorname { max } \{ \alpha _ { i } : 0 \leq i \leq t \} \leq \Delta _ { 2 } \leq \frac { 1 } { 4 n } ( \sum _ { i = 0 } ^ { t } \alpha _ { i } + 2 )$ ; confidence 0.363

27. ; $c u _ { x t } = u _ { t t } - \frac { 1 } { 2 } c ^ { 2 } u _ { y y }$ ; confidence 0.363

28. ; $\| ( A + \delta A ) ^ { + } \| _ { 2 } \leq \frac { \| A ^ { + } \| _ { 2 } } { 1 - \| A ^ { + } \| _ { 2 } \| ^ { \delta A \| _ { 2 } } }$ ; confidence 0.362

29. ; $u _ { R } ^ { k } ( x ) = \sum _ { i = 1 } ^ { n } u _ { i } a _ { i } ^ { k } ( x )$ ; confidence 0.362

30. ; $j _ { X } ^ { k } ( u )$ ; confidence 0.362

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

32. ; $u _ { m } = u ( M _ { m } )$ ; confidence 0.360

33. ; $\hat { V }$ ; confidence 0.359

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

35. ; $g = d \cdot d ^ { \prime - 1 }$ ; confidence 0.357

36. ; $\alpha = \text { Coker } ( \text { Ker } \alpha ) \theta \text { ker } ( \text { Coker } \alpha )$ ; confidence 0.357

37. ; $v _ { n } \in G$ ; confidence 0.357

38. ; $g _ { 1 } = | d x | ^ { 2 } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } } \leq g = \frac { | d x | ^ { 2 } } { | x | ^ { 2 } } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } }$ ; confidence 0.357

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

40. ; $A = \operatorname { Pic } ^ { 0 } ( A )$ ; confidence 0.355

41. ; $0$ ; confidence 0.355

42. ; $0 \rightarrow A \rightarrow B \stackrel { sp } { \rightarrow } \pi * C \rightarrow 0$ ; confidence 0.355

43. ; $t$ ; confidence 0.354

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

45. ; $\pi _ { 4 n - 1 } ( S ^ { 2 n } ) \rightarrow \pi _ { 4 n } ( S ^ { 2 n + 1 } )$ ; confidence 0.354

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

47. ; $m _ { k } = \dot { k }$ ; confidence 0.352

48. ; $( \alpha \vee ( b . e ) ) : e = ( \alpha : e ) \vee b$ ; confidence 0.351

49. ; $l _ { k } ( A )$ ; confidence 0.348

50. ; $| e ^ { A + \delta A } - e ^ { A } \| \leq k ( T ) \cdot \| W \|$ ; confidence 0.347

51. ; $M$ ; confidence 0.347

52. ; $w _ { 2 }$ ; confidence 0.347

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

54. ; $f _ { h } ( t ) = \frac { 1 } { h } \int _ { t - k / 2 } ^ { t + k / 2 } f ( u ) d u = \frac { 1 } { h } \int _ { - k / 2 } ^ { k / 2 } f ( t + v ) d v$ ; confidence 0.345

55. ; $x _ { 1 } , \ldots , x _ { p }$ ; confidence 0.344

56. ; $y _ { 0 } = A _ { x }$ ; confidence 0.344

57. ; $w$ ; confidence 0.343

58. ; $R = \{ \alpha \in K : \operatorname { mod } _ { K } ( \alpha ) \leq 1 \}$ ; confidence 0.342

59. ; $\left. \begin{array} { c c c } { B _ { i } } & { \stackrel { h _ { i } } { \rightarrow } } & { A _ { i } } \\ { g _ { i } \downarrow } & { \square } & { \downarrow f _ { i } } \\ { B } & { \vec { f } } & { A } \end{array} \right.$ ; confidence 0.342

60. ; $\sigma _ { 1 } \geq \ldots \geq \sigma _ { \zeta }$ ; confidence 0.342

61. ; $( \beta _ { t 0 } , \ldots , \beta _ { i k } )$ ; confidence 0.339

62. ; $x _ { 1 } , \ldots , x _ { x } \in X$ ; confidence 0.338

63. ; $\frac { D \xi ^ { i } } { d t } = \frac { d \xi ^ { i } } { d t } + \frac { 1 } { 2 } g ^ { i } r \xi ^ { r }$ ; confidence 0.338

64. ; $\phi _ { i } / \partial x _ { Y }$ ; confidence 0.338

65. ; $F | X _ { t } | ^ { 2 } + \delta$ ; confidence 0.338

66. ; $\mathfrak { A } = \langle A , C \rangle$ ; confidence 0.337

67. ; $T _ { i j }$ ; confidence 0.337

68. ; $T _ { \nu }$ ; confidence 0.336

69. ; $S _ { x } = X _ { 1 } + \ldots + X _ { x }$ ; confidence 0.335

70. ; $\| f \| _ { \Lambda _ { p } ^ { r } ( R ^ { n } ) } \leq K$ ; confidence 0.335

71. ; $c \rightarrow N$ ; confidence 0.335

72. ; $\mu$ ; confidence 0.335

73. ; $\frac { \| \delta x \| } { \| x \| } \leq \frac { \| A ^ { - 1 } \delta A \| + \frac { \| A ^ { - 1 } \delta b \| } { | x \| } } { 1 - \| A ^ { - 1 } \delta A \| }$ ; confidence 0.334

74. ; $\eta _ { i } - \eta _ { s }$ ; confidence 0.334

75. ; $\tilde { f } : \Delta ^ { n + 1 } \rightarrow E$ ; confidence 0.333

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

77. ; $F T op$ ; confidence 0.332

78. ; $\| u - P _ { n } u \| _ { A } \rightarrow 0$ ; confidence 0.332

79. ; $n = 1,2 , \dots$ ; confidence 0.331

80. ; $\Delta ( \alpha _ { 1 } \ldots i _ { p } d x ^ { i _ { 1 } } \wedge \ldots \wedge d x ^ { i p } ) =$ ; confidence 0.331

81. ; $p ^ { 4 }$ ; confidence 0.330

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

83. ; $C ^ { \infty } ( \tilde { N } )$ ; confidence 0.330

84. ; $8$ ; confidence 0.330

85. ; $L$ ; confidence 0.330

86. ; $\Delta \lambda _ { i } ^ { \alpha }$ ; confidence 0.329

87. ; $o = e K$ ; confidence 0.327

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

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

90. ; $W _ { 0 }$ ; confidence 0.325

91. ; $p _ { i k } ^ { * } ( t ) = P \{ \xi ^ { * } ( t ) = h | \xi ^ { * } ( 0 ) = i \} =$ ; confidence 0.325

92. ; $N$ ; confidence 0.325

93. ; $c$ ; confidence 0.324

94. ; $C$ ; confidence 0.323

95. ; $N _ { 2 } = \left| \begin{array} { c c c c c } { . } & { \square } & { \square } & { \square } & { 0 } \\ { \square } & { . } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { L ( e _ { j } ^ { n _ { i j } } ) } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { . } & { \square } \\ { \square } & { \square } & { \square } & { \square } & { \square } \\ { 0 } & { \square } & { \square } & { \square } & { . } \end{array} \right|$ ; confidence 0.323

96. ; $\{ x _ { k } , a \}$ ; confidence 0.323

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

98. ; $X _ { i } \cap X _ { j } =$ ; confidence 0.322

99. ; $n ( O _ { x } ) = 0$ ; confidence 0.322

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

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

102. ; $\frac { x ^ { \rho + 1 } f ( x ) } { \int _ { x } ^ { x } t ^ { \sigma } f ( t ) d t } \rightarrow \sigma + \rho + 1 \quad ( x \rightarrow \infty )$ ; confidence 0.320

103. ; $\alpha + b \in C ^ { p }$ ; confidence 0.317

104. ; $F _ { n } ( x ) = ( x _ { 1 } ^ { 2 } + \ldots + x _ { y } ^ { 2 } ) ^ { 1 / 2 }$ ; confidence 0.316

105. ; $\left. \begin{array} { l } { \nabla p _ { 1 } = \nabla p _ { 2 } = 0 } \\ { \frac { \partial v _ { 0 } } { \partial t } + [ \nabla v _ { 0 } ] v _ { 0 } = \frac { 1 } { Re } \Delta v _ { 0 } + \operatorname { Re } \nabla p _ { 3 } + \theta _ { 0 } b } \end{array} \right.$ ; confidence 0.316

106. ; $x \in X ^ { \prime }$ ; confidence 0.315

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

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

109. ; $\partial _ { r }$ ; confidence 0.315

110. ; $\nabla _ { i g j k } = \gamma _ { i } g _ { j k }$ ; confidence 0.315

111. ; $e$ ; confidence 0.314

112. ; $\therefore M \rightarrow F$ ; confidence 0.313

113. ; $\theta _ { 3 } ( v \pm \frac { 1 } { 2 } \tau ) = e ^ { - i \pi \tau / 4 } \cdot e ^ { - i \pi v } \cdot \theta _ { 2 } ( v )$ ; confidence 0.312

114. ; $M ^ { 0 }$ ; confidence 0.312

115. ; $m = 2 ^ { a } 3 ^ { b } u ^ { 2 }$ ; confidence 0.311

116. ; $0$ ; confidence 0.311

117. ; $A _ { 1 } , \ldots , A _ { 8 }$ ; confidence 0.310

118. ; $\Gamma 20$ ; confidence 0.310

119. ; $p _ { m } = ( \sum _ { j = 0 } ^ { m } A _ { j } ) ^ { - 1 }$ ; confidence 0.310

120. ; $A$ ; confidence 0.309

121. ; $k ( T ) = \| T \| T ^ { - 1 } \|$ ; confidence 0.308

122. ; $\left. \begin{array} { l l } { F _ { 1 } ( A ) } & { \frac { F _ { 1 } ( \alpha ) } { \rightarrow } } & { F _ { 1 } ( B ) } \\ { \phi _ { A } \downarrow } & { \square } & { \downarrow \phi _ { B } } \\ { F _ { 2 } ( A ) } & { \vec { F _ { 2 } ( \alpha ) } } & { F _ { 2 } ( B ) } \end{array} \right.$ ; confidence 0.308

123. ; $l \mu \frac { \partial W ^ { k } } { \partial x } + ( 1 - c ) W ^ { k } = c ( \Phi _ { 0 } ^ { k } - \phi _ { 0 } ^ { k } )$ ; confidence 0.308

124. ; $h$ ; confidence 0.307

125. ; $M _ { 1 } = H \cap _ { k \tau _ { S } } H ^ { \prime }$ ; confidence 0.307

126. ; $f \in S _ { y } ^ { \prime }$ ; confidence 0.307

127. ; $\frac { \| \delta X \| } { \| X \| } \leq \frac { \epsilon \cdot k ( A , B ) } { 1 - \epsilon \cdot k ( A , B ) }$ ; confidence 0.305

128. ; $F _ { t } | _ { A } = H _ { t }$ ; confidence 0.304

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

130. ; $\operatorname { Pic } ( F ) \cong p ^ { * } \operatorname { Pic } ( C ) \oplus Z ^ { 5 }$ ; confidence 0.304

131. ; $P \{ X _ { v + 1 } = k + 1 | X _ { k } = k \} = \frac { b + k c } { b + r + n c } = \frac { p + k \gamma } { 1 + n \gamma }$ ; confidence 0.303

132. ; $2 ^ { a + 2 }$ ; confidence 0.302

133. ; $a ^ { X } = e ^ { X \operatorname { ln } \alpha }$ ; confidence 0.301

134. ; $- \infty \leq w \leq + \infty$ ; confidence 0.301

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

136. ; $e \omega ^ { r } f$ ; confidence 0.300

137. ; $\Pi I _ { \lambda }$ ; confidence 0.300

138. ; $\overline { U }$ ; confidence 0.299

139. ; $\operatorname { lim } _ { n \rightarrow \infty } \operatorname { sup } \frac { S _ { n } } { c _ { n } } = 1 \quad ( \alpha . s . )$ ; confidence 0.299

140. ; $F \in Fi _ { D }$ ; confidence 0.298

141. ; $W _ { a }$ ; confidence 0.297

142. ; $C \in | L$ ; confidence 0.296

143. ; $\{ \partial f \rangle$ ; confidence 0.295

144. ; $\alpha = \frac { \| \delta A \| _ { 2 } } { \| A \| _ { 2 } } , \quad \hat { \kappa } = \frac { k ( A ) } { 1 - \alpha k ( A ) }$ ; confidence 0.294

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

146. ; $\phi _ { im }$ ; confidence 0.294

147. ; $n = 0,1 , \ldots$ ; confidence 0.294

148. ; $\alpha ^ { n } < b ^ { n + 1 }$ ; confidence 0.291

149. ; $\{ \operatorname { exp } _ { m } ( \text { Cutval } ( \xi ) \xi ) \} = \text { Cutloc } ( m )$ ; confidence 0.291

150. ; $\sum _ { \mathfrak { D } _ { 1 } ^ { 1 } } ( E \times N ^ { N } )$ ; confidence 0.290

151. ; $t \circ \in E$ ; confidence 0.290

152. ; $\forall y \exists z ( \gamma ( y ) + 1 = \alpha ( g * \overline { \beta } ( z ) ) )$ ; confidence 0.288

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

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

155. ; $A \in \mathfrak { S }$ ; confidence 0.285

156. ; $d _ { 2 }$ ; confidence 0.284

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

158. ; $j = \frac { 1728 g _ { 2 } ^ { 3 } } { g _ { 2 } ^ { 3 } - 27 g _ { 3 } ^ { 2 } }$ ; confidence 0.284

159. ; $\pi _ { p } ( \text { Id } : C ( K ) \rightarrow L _ { p } ( K , \mu ) ) = \mu ( K ) ^ { 1 / p }$ ; confidence 0.283

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

161. ; $1 / S i$ ; confidence 0.280

162. ; $\beta _ { X } ( s ) = \operatorname { sup } _ { t } \beta ( \sigma \{ X _ { z } : u \leq t \} , \sigma \{ X _ { z } : u \geq t + x \} )$ ; confidence 0.279

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

164. ; $f ^ { \mu } | _ { K }$ ; confidence 0.278

165. ; $n = 1,2 , . .$ ; confidence 0.277

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

167. ; $( 4 m ^ { 2 n } \cdot \frac { m ^ { 2 n } - 1 } { m ^ { 2 } - 1 } , m ^ { 2 n - 1 } \cdot ( \frac { 2 ( m ^ { 2 n } - 1 ) } { m + 1 } + 1 )$ ; confidence 0.276

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

169. ; $f = \pi \gamma f _ { \alpha } \pi \overline { x } ^ { 1 }$ ; confidence 0.274

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

171. ; $G _ { A B } ^ { ( c ) } ( t - t ^ { \prime } ) = \ll A ( t ) | B ( t ^ { \prime } ) \gg ( c ) \equiv \langle T _ { \eta } A ( t ) B ( t ^ { \prime } ) \rangle$ ; confidence 0.272

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

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

174. ; $99$ ; confidence 0.271

175. ; $( H _ { 1 } , \ldots , H _ { k + m } ) : C ^ { N } \rightarrow C ^ { k + m }$ ; confidence 0.271

176. ; $Z y \rightarrow \infty$ ; confidence 0.270

177. ; $\sum _ { \nu = 1 } ^ { k - 1 } \frac { B _ { \nu } } { \nu ! } \{ f ^ { \langle \nu - 1 \rangle } ( n ) - f ^ { \langle \nu - 1 \rangle } ( 0 ) \} + \frac { B _ { k } } { k ! } \sum _ { x = 0 } ^ { n - 1 } f ^ { ( k ) } ( x + \theta )$ ; confidence 0.269

178. ; $N = \{ G \backslash ( \cup _ { x \in G } x ^ { - 1 } H x ) \} \cup \{ 1 \}$ ; confidence 0.269

179. ; $q _ { i k } = P \{ \xi ( \tau ( H ) ) = h | \xi ( 0 ) = i \} , \quad i \in S , \quad h \in H$ ; confidence 0.269

180. ; $\chi \pi _ { \alpha }$ ; confidence 0.268

181. ; $21$ ; confidence 0.266

182. ; $\alpha X$ ; confidence 0.266

183. ; $1$ ; confidence 0.266

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

185. ; $h ( [ a ] )$ ; confidence 0.265

186. ; $u _ { t t } = c ^ { 2 } ( u _ { XX } + u _ { y y } )$ ; confidence 0.264

187. ; $\{ \alpha _ { n } \} _ { \aleph = 0 } ^ { \infty }$ ; confidence 0.264

188. ; $\| \alpha _ { j k }$ ; confidence 0.264

189. ; $+ \sum _ { i = 1 } ^ { s } \| k _ { i k } [ u ] _ { k } - \{ l _ { i } u \} _ { i k } \| _ { \Phi _ { i k } } + \| p _ { i k } \phi _ { i } - \{ \phi _ { i } \} _ { i k } \| _ { \Phi _ { i k } }$ ; confidence 0.263

190. ; $\alpha : H ^ { n } ( : Z ) \rightarrow H ^ { n + 3 } ( : Z _ { 2 } )$ ; confidence 0.262

191. ; $+ ( \lambda x y \cdot y ) : ( \sigma \rightarrow ( \tau \rightarrow \tau ) )$ ; confidence 0.262

192. ; $\beta X = S \square x = \omega _ { \kappa } X$ ; confidence 0.261

193. ; $x = T ( \Lambda - \hat { \lambda } I ) ^ { - 1 } T ^ { - 1 } r$ ; confidence 0.261

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

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

196. ; $m$ ; confidence 0.259

197. ; $V _ { k } ( H ^ { n } ) = \frac { Sp ( n ) } { Sp ( n - k ) }$ ; confidence 0.259

198. ; $\delta ^ { * } \circ ( t - r ) ^ { * } \beta _ { 1 } = k ( t ^ { * } \square ^ { - 1 } \beta _ { 3 } )$ ; confidence 0.259

199. ; $\frac { \| \delta x \| _ { 2 } } { \| x \| _ { 2 } } \leq k [ ( 2 + \eta \hat { k } ) \alpha + \beta \gamma ]$ ; confidence 0.259

200. ; $u _ { 1 } = \int _ { c _ { 1 } } ^ { x } d u _ { 1 } , \ldots , u _ { p } = \int _ { \varphi } ^ { x } d u _ { p }$ ; confidence 0.258

201. ; $r = H . | A | . | x$ ; confidence 0.258

202. ; $\pi : B \rightarrow G ^ { k } ( V )$ ; confidence 0.258

203. ; $\operatorname { Ker } \beta \in \mathfrak { A } _ { 1 }$ ; confidence 0.257

204. ; $L ^ { \prime }$ ; confidence 0.256

205. ; $x _ { C }$ ; confidence 0.256

206. ; $[ f _ { G } ]$ ; confidence 0.256

207. ; $D \Re \subset M$ ; confidence 0.255

208. ; $i , j = 1 , \dots , g$ ; confidence 0.255

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

210. ; $7$ ; confidence 0.254

211. ; $( A _ { x } \lambda ^ { x } + A _ { x - 1 } \lambda ^ { x - 1 } + \ldots + A _ { 0 } ) x = 0$ ; confidence 0.253

212. ; $\sum _ { i = 1 } ^ { n } S _ { i } S _ { i } ^ { * } < I$ ; confidence 0.253

213. ; $L ^ { \prime } ( T _ { x } M )$ ; confidence 0.252

214. ; $\tau _ { 0 } ^ { e ^ { 3 } }$ ; confidence 0.252

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

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

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

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

219. ; $E \subset X = R ^ { \prime }$ ; confidence 0.250

220. ; $E [ \tau _ { j } ^ { S } - \tau _ { j } ^ { \dot { e } } ] ^ { 2 + \gamma }$ ; confidence 0.250

221. ; $97$ ; confidence 0.250

222. ; $t _ { 8 } + 1 / 2 = t _ { n } + \tau / 2$ ; confidence 0.248

223. ; $\int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle ^ { 2 } } { \lambda } _ { d } \lambda < E _ { 0 }$ ; confidence 0.248

224. ; $3 r ( L _ { 1 } \cap L _ { 2 } ) = 3 _ { r } ( L _ { 1 } ) + 3 r ( L _ { 2 } )$ ; confidence 0.248

225. ; $\| \delta x \| f \| x \| \approx \epsilon . k ( A )$ ; confidence 0.247

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

227. ; $| m K _ { V ^ { \prime } } | ^ { J }$ ; confidence 0.246

228. ; $1 / | y ^ { i } _ { x ^ { i } } ^ { * }$ ; confidence 0.245

229. ; $\| \hat { A } - A \| \leq \delta$ ; confidence 0.245

230. ; $\nu _ { 0 } \in C ^ { n }$ ; confidence 0.245

231. ; $X = \cup _ { \alpha } X _ { \alpha }$ ; confidence 0.245

232. ; $q R$ ; confidence 0.245

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

234. ; $\| v \| = \| A x - \hat { \lambda } x \| _ { 2 } \leq \epsilon \| A \| _ { 2 } \| x \| _ { 2 }$ ; confidence 0.243

235. ; $\operatorname { min } _ { i } | \hat { \lambda } - \lambda _ { i } | \leq \rho ( | T ^ { - 1 } | | \delta A | | T | )$ ; confidence 0.242

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

237. ; $A N = \operatorname { max } _ { 1 } \leq i _ { j } \leq n | \alpha _ { \xi } j |$ ; confidence 0.241

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

239. ; $( n$ ; confidence 0.239

240. ; $\nu _ { n } = \sum _ { k = 0 } ^ { n - 1 } \mu _ { k } / n$ ; confidence 0.239

241. ; $\prod _ { \nu } : \prod _ { i \in I _ { \nu } } f _ { i } : = \sum _ { G } \prod _ { e \in G } < f _ { e _ { 1 } } f _ { e _ { 2 } } > : \prod _ { i \notin [ G ] } f _ { i : }$ ; confidence 0.238

242. ; $0.00$ ; confidence 0.237

243. ; $X _ { 1 }$ ; confidence 0.237

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

245. ; $2$ ; confidence 0.235

246. ; $\alpha _ { i k } = \overline { a _ { k i } }$ ; confidence 0.235

247. ; $\langle A , F \rangle$ ; confidence 0.234

248. ; $\theta _ { 2 } ( v \pm \tau ) = e ^ { - i \pi \tau } \cdot e ^ { - 2 i \pi v } \cdot \theta _ { 2 } ( v )$ ; confidence 0.234

249. ; $\tilde { D } = E \{ M | m = 0 \} = \frac { ( \sum _ { r = 1 } ^ { N - n } r \frac { C _ { N - r } ^ { n } } { C _ { N } ^ { n } } p _ { r } ) } { P \{ m = 0 \} }$ ; confidence 0.234

250. ; $= 0 \text { as. } \cdot P _ { \theta _ { 0 } } ]$ ; confidence 0.233

251. ; $T _ { i } = C A ^ { i } B ^ { i } B$ ; confidence 0.233

252. ; $\frac { \| x ^ { 2 } - x ^ { i } \| } { \| x ^ { i } \| } \leq \frac { \psi } { \operatorname { min } _ { j \neq i } | \lambda _ { i } - \lambda _ { j } | - 2 \psi }$ ; confidence 0.233

253. ; $C A$ ; confidence 0.232

254. ; $\Pi \stackrel { D } { 3 } = F _ { \sigma \delta }$ ; confidence 0.232

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

256. ; $im ( \Omega _ { S C } \rightarrow \Omega _ { O } )$ ; confidence 0.230

257. ; $A | D _ { + } \rangle - A ^ { - 1 } \langle D _ { - } \} = ( A ^ { 2 } - A ^ { - 2 } ) \langle D _ { 0 } \}$ ; confidence 0.230

258. ; $\operatorname { ess } \operatorname { sup } _ { X } | f ( x ) | = \operatorname { lim } _ { n \rightarrow \infty } ( \frac { \int | f ( x ) | ^ { n } d M _ { X } } { \int _ { X } d M _ { x } } )$ ; confidence 0.229

259. ; $\sum _ { k = 1 } ^ { \infty } p _ { 1 } ( x _ { k } ) p _ { 2 } ( y _ { k } ) \leq p _ { 1 } \overline { Q } p _ { 2 } ( u ) + \epsilon$ ; confidence 0.229

260. ; $( \omega ) = P _ { 1 } ^ { \alpha _ { 1 } } 1 ^ { \square } \ldots P _ { n } ^ { \alpha _ { R } }$ ; confidence 0.228

261. ; $Z _ { 23 }$ ; confidence 0.228

262. ; $n + = n - = n$ ; confidence 0.228

263. ; $\operatorname { Aut } ( R ) / \operatorname { ln } n ( R ) \cong H$ ; confidence 0.228

264. ; $C X Y$ ; confidence 0.226

265. ; $t ^ { i _ { 1 } } \cdots \dot { d p } = \operatorname { det } \| x _ { i } ^ { i _ { k } } \|$ ; confidence 0.226

266. ; $P _ { X } ( z ) = \frac { 1 } { n ! } ( z - \alpha ) ( z - \alpha - n h ) ^ { \gamma - 1 }$ ; confidence 0.226

267. ; $20$ ; confidence 0.225

268. ; $I \rightarrow \cup _ { i \in l } J _ { i }$ ; confidence 0.225

269. ; $\sum _ { K \in \mathscr { K } } \lambda _ { K } \chi _ { K } ( i ) = \chi _ { I } ( i ) \quad \text { for all } i \in I$ ; confidence 0.223

270. ; $x - a | < b - a$ ; confidence 0.223

271. ; $n _ { 1 } < n _ { 2 } .$ ; confidence 0.222

272. ; $\{ \lambda _ { n } \} \in \Lambda _ { \alpha }$ ; confidence 0.221

273. ; $\nabla _ { \theta } : H _ { \delta R } ^ { 1 } ( X / K ) \rightarrow H _ { \partial R } ^ { 1 } ( X / K )$ ; confidence 0.221

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

275. ; $x _ { n m _ { n } } \rightarrow ( 0 )$ ; confidence 0.220

276. ; $f ( z ) = \sum _ { n = 0 } ^ { \infty } ( n ! ) ^ { - \alpha } a _ { n } z ^ { n } , \quad \underset { n \rightarrow \infty } { \operatorname { lim } } | \alpha _ { n } | ^ { 1 / n } \leq r$ ; confidence 0.220

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

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

279. ; $3$ ; confidence 0.218

280. ; $Z _ { h }$ ; confidence 0.217

281. ; $\mathfrak { A } _ { \infty } = \overline { U _ { V \subset R ^ { 3 } } } A ( \mathcal { H } _ { V } )$ ; confidence 0.216

282. ; $S _ { a }$ ; confidence 0.216

283. ; $g ^ { \prime } / ( 1 - u ) g ^ { \prime } = \overline { g }$ ; confidence 0.215

284. ; $^ { * } L D S$ ; confidence 0.214

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

286. ; $21 / 21$ ; confidence 0.212

287. ; $\xi _ { p } \in ( \nu F ^ { m } ) p$ ; confidence 0.212

288. ; $= \{ M e _ { S _ { i } }$ ; confidence 0.212

289. ; $\{ 21 , n \}$ ; confidence 0.211

290. ; $x _ { k } \in X$ ; confidence 0.211

291. ; $| u - v | \leq \operatorname { inf } _ { w ^ { \prime } \in K } | u - w |$ ; confidence 0.210

292. ; $R _ { i l k } ^ { q } = - R _ { k l } ^ { q }$ ; confidence 0.210

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

294. ; $f : X ^ { \cdot } \rightarrow Y$ ; confidence 0.209

295. ; $| \hat { b } _ { n } | = 1$ ; confidence 0.209

296. ; $B \in Ob \mathfrak { A } _ { 1 }$ ; confidence 0.209

297. ; $Z _ { i j }$ ; confidence 0.208

298. ; $k$ ; confidence 0.208

299. ; $A , C \in Ob A _ { 1 }$ ; confidence 0.207

300. ; $| x$ ; confidence 0.207

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/13. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/13&oldid=43874

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Difference between revisions of "User:Maximilian Janisch/latexlist/latex/13"

Revision as of 10:28, 2 September 2019

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 == List ==
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240422.png ; $1$ ; confidence 0.077
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055850/k055850103.png ; $D _ { \alpha }$ ; confidence 0.374
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a01021072.png ; $\mathfrak { C } 1 , \ldots , \mathfrak { C } _ { x }$ ; confidence 0.076
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240377.png ; $T ^ { 2 }$ ; confidence 0.373
-. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014060/a014060135.png ; $W _ { N } \rightarrow W _ { n }$ ; confidence 0.076
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017030/b01703046.png ; $\mathfrak { M } _ { n }$ ; confidence 0.373
-. 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/c/c120/c120080/c12008028.png ; $A _ { j } A _ { k l } = A _ { k l } A _ { j }$ ; confidence 0.372
-. 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/a/a110/a110010/a110010139.png ; $i = 1 , \dots , r$ ; confidence 0.372
-. 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/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/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/s087/s087030/s0870309.png ; $f _ { h } \in U _ { k }$ ; confidence 0.371
-. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022030/c02203033.png ; $C _ { \omega }$ ; confidence 0.073
+. 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/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/a010/a010210/a0102104.png ; $a _ { 1 } b _ { 1 } \ldots a _ { 8 } b _ { 8 }$ ; confidence 0.369
-. 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/a/a130/a130130/a13013099.png ; $z \in C$ ; confidence 0.369
-. 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/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/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/a/a010/a010290/a01029055.png ; $\overline { a } X = \beta a X = \alpha \beta X$ ; confidence 0.369
-. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087420/s08742067.png ; $\{ f \rangle _ { P } \sim | V |$ ; confidence 0.071
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010168.png ; $\hat { k } ( \alpha + \beta )$ ; confidence 0.369
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010180/a01018019.png ; $z \frac { \operatorname { lim } } { z \rightarrow z _ { 0 } } \quad S ( z ) = S ( z 0 )$ ; confidence 0.069
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010206.png ; $z \leq | ( \hat { \lambda } I - \Lambda ) ^ { - 1 } | | T ^ { - 1 } | | \delta A | | T | z |$ ; confidence 0.368
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010198.png ; $\leq \| T \| ^ { T ^ { - 1 } } \| \| \delta A \| \frac { 1 } { \operatorname { min } } | \hat { \lambda } - \lambda _ { i } |$ ; confidence 0.069
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024056.png ; $i = 1 , \ldots , I$ ; confidence 0.368
-. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016150/b01615033.png ; $\operatorname { Re } _ { c _ { N } } = n$ ; confidence 0.069
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012023.png ; $A _ { r } ^ { \alpha }$ ; confidence 0.368
-. 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/a/a110/a110010/a110010113.png ; $\delta b = H . | b$ ; confidence 0.368
-. 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/a/a110/a110410/a11041070.png ; $K _ { X } ^ { v } \otimes L ^ { i }$ ; confidence 0.368
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l12012087.png ; $Z _ { \text { tot } S } = Z$ ; confidence 0.066
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f120150202.png ; $n \| < C$ ; confidence 0.368
-. 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/p/p075/p075660/p07566043.png ; $\partial _ { x } = \partial / \partial x$ ; confidence 0.368
-. 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/p/p075/p075190/p07519074.png ; $E _ { i j }$ ; confidence 0.366
-. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016610/b01661030.png ; $R _ { y } ^ { t }$ ; confidence 0.060
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010220/a01022067.png ; $m$ ; confidence 0.365
-. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087300/s08730040.png ; $Q _ { 1 }$ ; confidence 0.060
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012076.png ; $f ( z ) = \sum _ { k = 0 } ^ { \infty } \alpha _ { \nu _ { k } } z ^ { \nu _ { k } }$ ; confidence 0.364
-. 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/a/a110/a110010/a110010286.png ; $( \hat { \lambda } B - C ) ^ { - 1 } = P ( \hat { \lambda } I - \Lambda ) ^ { - 1 } Q$ ; confidence 0.363
-. 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/d/d032/d032330/d03233040.png ; $b _ { 0 }$ ; confidence 0.363
-. 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/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/a/a130/a130240/a130240244.png ; $= \operatorname { sin } \gamma q$ ; confidence 0.055
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110080/a11008029.png ; $c u _ { x t } = u _ { t t } - \frac { 1 } { 2 } c ^ { 2 } u _ { y y }$ ; confidence 0.363
-. 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/a/a110/a110010/a110010135.png ; $\| ( A + \delta A ) ^ { + } \| _ { 2 } \leq \frac { \| A ^ { + } \| _ { 2 } } { 1 - \| A ^ { + } \| _ { 2 } \| ^ { \delta A \| _ { 2 } } }$ ; confidence 0.362
-. 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/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/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/s/s090/s090670/s09067035.png ; $j _ { X } ^ { k } ( u )$ ; confidence 0.362
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539040.png ; $E [ L ( \theta , d ) | x ]$ ; confidence 0.361
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094440/t09444040.png ; $u _ { m } = u ( M _ { m } )$ ; confidence 0.360
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032150/d032150132.png ; $\hat { V }$ ; confidence 0.359
+. 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/a/a110/a110020/a11002013.png ; $g = d \cdot d ^ { \prime - 1 }$ ; confidence 0.357
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020079.png ; $\alpha = \text { Coker } ( \text { Ker } \alpha ) \theta \text { ker } ( \text { Coker } \alpha )$ ; confidence 0.357
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005087.png ; $v _ { n } \in G$ ; confidence 0.357
+. 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/b/b120/b120210/b120210148.png ; $\mathfrak { p } \supset b$ ; confidence 0.356
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a1100408.png ; $A = \operatorname { Pic } ^ { 0 } ( A )$ ; confidence 0.355
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001085.png ; $0$ ; confidence 0.355
+. 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/a/a130/a130130/a13013088.png ; $t$ ; confidence 0.354
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110630/a11063032.png ; $\rho _ { 0 n + } = \operatorname { sin } A$ ; confidence 0.354
+. 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/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/w/w097/w097510/w09751010.png ; $m _ { k } = \dot { k }$ ; confidence 0.352
+. 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/l/l058/l058720/l05872090.png ; $l _ { k } ( A )$ ; confidence 0.348
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010288.png ; $| e ^ { A + \delta A } - e ^ { A } \| \leq k ( T ) \cdot \| W \|$ ; confidence 0.347
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020036.png ; $M$ ; confidence 0.347
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a01021080.png ; $w _ { 2 }$ ; confidence 0.347
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240276.png ; $\leq F _ { \alpha ; q , x - \gamma }$ ; confidence 0.345
+. 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/a/a010/a010220/a01022034.png ; $x _ { 1 } , \ldots , x _ { p }$ ; confidence 0.344
+. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025720/c02572034.png ; $y _ { 0 } = A _ { x }$ ; confidence 0.344
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a010210142.png ; $w$ ; confidence 0.343
+. 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/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/a/a110/a110010/a110010140.png ; $\sigma _ { 1 } \geq \ldots \geq \sigma _ { \zeta }$ ; confidence 0.342
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240488.png ; $( \beta _ { t 0 } , \ldots , \beta _ { i k } )$ ; confidence 0.339
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110070/a11007010.png ; $x _ { 1 } , \ldots , x _ { x } \in X$ ; confidence 0.338
+. 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/n/n067/n067110/n06711048.png ; $\phi _ { i } / \partial x _ { Y }$ ; confidence 0.338
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110060/a11006044.png ; $F | X _ { t } | ^ { 2 } + \delta$ ; confidence 0.338
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040515.png ; $\mathfrak { A } = \langle A , C \rangle$ ; confidence 0.337
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062360/m06236012.png ; $T _ { i j }$ ; confidence 0.337
+. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043780/g043780168.png ; $T _ { \nu }$ ; confidence 0.336
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010420/a0104204.png ; $S _ { x } = X _ { 1 } + \ldots + X _ { x }$ ; confidence 0.335
+. 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/l/l057/l057050/l057050123.png ; $c \rightarrow N$ ; confidence 0.335
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057150/l05715031.png ; $\mu$ ; confidence 0.335
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a11001027.png ; $\frac { \| \delta x \| } { \| x \| } \leq \frac { \| A ^ { - 1 } \delta A \| + \frac { \| A ^ { - 1 } \delta b \| } { | x \| } } { 1 - \| A ^ { - 1 } \delta A \| }$ ; confidence 0.334
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240184.png ; $\eta _ { i } - \eta _ { s }$ ; confidence 0.334
+. 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/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/c120/c120280/c1202808.png ; $F T op$ ; confidence 0.332
+. 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/a/a010/a010420/a0104207.png ; $n = 1,2 , \dots$ ; confidence 0.331
+. 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/a/a110/a110040/a110040271.png ; $p ^ { 4 }$ ; confidence 0.330
+. 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/c120/c120180/c120180420.png ; $C ^ { \infty } ( \tilde { N } )$ ; confidence 0.330
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040349.png ; $8$ ; confidence 0.330
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a01021095.png ; $L$ ; confidence 0.330
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062220/m06222011.png ; $\Delta \lambda _ { i } ^ { \alpha }$ ; confidence 0.329
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082210/r08221030.png ; $o = e K$ ; confidence 0.327
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001099.png ; $_ { \nabla } ( G / K )$ ; confidence 0.326
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110440/b1104407.png ; $\overline { \Xi } \epsilon = 0$ ; confidence 0.326
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012043.png ; $W _ { 0 }$ ; confidence 0.325
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010430/a01043017.png ; $p _ { i k } ^ { * } ( t ) = P \{ \xi ^ { * } ( t ) = h | \xi ^ { * } ( 0 ) = i \} =$ ; confidence 0.325
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120310/a12031010.png ; $N$ ; confidence 0.325
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240141.png ; $c$ ; confidence 0.324
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a01021085.png ; $C$ ; confidence 0.323
+. 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/a/a110/a110070/a11007012.png ; $\{ x _ { k } , a \}$ ; confidence 0.323
+. 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/f/f041/f041620/f04162020.png ; $X _ { i } \cap X _ { j } =$ ; confidence 0.322
+. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087640/s08764086.png ; $n ( O _ { x } ) = 0$ ; confidence 0.322
+. 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/b/b110/b110880/b11088033.png ; $P _ { I } ^ { f } : C ^ { \infty } \rightarrow L$ ; confidence 0.321
+. 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/a/a010/a010220/a01022097.png ; $\alpha + b \in C ^ { p }$ ; confidence 0.317
+. 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/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/a/a110/a110070/a11007013.png ; $x \in X ^ { \prime }$ ; confidence 0.315
+. 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/b/b120/b120150/b12015024.png ; $x = \frac { 1 } { n } \sum _ { j = 1 } ^ { n } x$ ; confidence 0.315
+. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024100/c024100277.png ; $\partial _ { r }$ ; confidence 0.315
+. 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/a/a014/a014310/a0143102.png ; $e$ ; confidence 0.314
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023045.png ; $\therefore M \rightarrow F$ ; confidence 0.313
+. 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/p/p073/p073400/p07340055.png ; $M ^ { 0 }$ ; confidence 0.312
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110020/a11002049.png ; $m = 2 ^ { a } 3 ^ { b } u ^ { 2 }$ ; confidence 0.311
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001057.png ; $0$ ; confidence 0.311
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a01021060.png ; $A _ { 1 } , \ldots , A _ { 8 }$ ; confidence 0.310
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055520/k05552082.png ; $\Gamma 20$ ; confidence 0.310
+. 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/a/a120/a120310/a120310136.png ; $A$ ; confidence 0.309
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010199.png ; $k ( T ) = \| T \| T ^ { - 1 } \|$ ; confidence 0.308
+. 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/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/a/a110/a110420/a110420128.png ; $h$ ; confidence 0.307
+. 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/i/i050/i050230/i050230319.png ; $f \in S _ { y } ^ { \prime }$ ; confidence 0.307
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010279.png ; $\frac { \| \delta X \| } { \| X \| } \leq \frac { \epsilon \cdot k ( A , B ) } { 1 - \epsilon \cdot k ( A , B ) }$ ; confidence 0.305
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120020/a12002024.png ; $F _ { t } | _ { A } = H _ { t }$ ; confidence 0.304
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110820/b11082017.png ; $\pi _ { i } / ( \pi _ { i } + \pi _ { j } )$ ; confidence 0.304
+. 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/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/a/a110/a110020/a11002053.png ; $2 ^ { a + 2 }$ ; confidence 0.302
+. 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/s/s086/s086940/s086940100.png ; $- \infty \leq w \leq + \infty$ ; confidence 0.301
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021100/c02110012.png ; $x \in \operatorname { Dom } A$ ; confidence 0.300
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080850/r08085028.png ; $e \omega ^ { r } f$ ; confidence 0.300
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900234.png ; $\Pi I _ { \lambda }$ ; confidence 0.300
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d120280147.png ; $\overline { U }$ ; confidence 0.299
+. 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/a/a130/a130040/a130040382.png ; $F \in Fi _ { D }$ ; confidence 0.298
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012035.png ; $W _ { a }$ ; confidence 0.297
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040152.png ; $C \in | L$ ; confidence 0.296
+. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092650/t09265033.png ; $\{ \partial f \rangle$ ; confidence 0.295
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010159.png ; $\alpha = \frac { \| \delta A \| _ { 2 } } { \| A \| _ { 2 } } , \quad \hat { \kappa } = \frac { k ( A ) } { 1 - \alpha k ( A ) }$ ; confidence 0.294
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014230/a0142305.png ; $\{ A \rangle$ ; confidence 0.294
+. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072430/p072430105.png ; $\phi _ { im }$ ; confidence 0.294
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012040.png ; $n = 0,1 , \ldots$ ; confidence 0.294
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070150/o07015054.png ; $\alpha ^ { n } < b ^ { n + 1 }$ ; confidence 0.291
+. 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/d/d031/d031380/d031380384.png ; $\sum _ { \mathfrak { D } _ { 1 } ^ { 1 } } ( E \times N ^ { N } )$ ; confidence 0.290
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044680/g04468049.png ; $t \circ \in E$ ; confidence 0.290
+. 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/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/a014/a014190/a0141905.png ; $x _ { y } + 1 = t$ ; confidence 0.287
+. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041940/f041940310.png ; $A \in \mathfrak { S }$ ; confidence 0.285
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a11004048.png ; $d _ { 2 }$ ; confidence 0.284
+. 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/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/a/a110/a110070/a11007026.png ; $\pi _ { p } ( \text { Id } : C ( K ) \rightarrow L _ { p } ( K , \mu ) ) = \mu ( K ) ^ { 1 / p }$ ; confidence 0.283
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240196.png ; $\sqrt { 3 }$ ; confidence 0.281
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010211.png ; $1 / S i$ ; confidence 0.280
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110060/a11006033.png ; $\beta _ { X } ( s ) = \operatorname { sup } _ { t } \beta ( \sigma \{ X _ { z } : u \leq t \} , \sigma \{ X _ { z } : u \geq t + x \} )$ ; confidence 0.279
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040685.png ; $X \in X$ ; confidence 0.278
+. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082060/r082060102.png ; $f ^ { \mu } | _ { K }$ ; confidence 0.278
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010420/a0104203.png ; $n = 1,2 , . .$ ; confidence 0.277
+. 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/a110/a110020/a11002054.png ; $( 4 m ^ { 2 n } \cdot \frac { m ^ { 2 n } - 1 } { m ^ { 2 } - 1 } , m ^ { 2 n - 1 } \cdot ( \frac { 2 ( m ^ { 2 n } - 1 ) } { m + 1 } + 1 )$ ; confidence 0.276
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240430.png ; $a ^ { \prime } \Theta$ ; confidence 0.275
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010290/a01029014.png ; $f = \pi \gamma f _ { \alpha } \pi \overline { x } ^ { 1 }$ ; confidence 0.274
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027051.png ; $\{ x _ { n j } ^ { \prime } \}$ ; confidence 0.273
+. 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/a/a120/a120220/a1202207.png ; $| e | | < 1$ ; confidence 0.271
+. 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/b/b016/b016960/b016960150.png ; $99$ ; confidence 0.271
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040257.png ; $( H _ { 1 } , \ldots , H _ { k + m } ) : C ^ { N } \rightarrow C ^ { k + m }$ ; confidence 0.271
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058920/l05892067.png ; $Z y \rightarrow \infty$ ; confidence 0.270
+. 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/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/a/a010/a010430/a0104309.png ; $q _ { i k } = P \{ \xi ( \tau ( H ) ) = h | \xi ( 0 ) = i \} , \quad i \in S , \quad h \in H$ ; confidence 0.269
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021570/c02157044.png ; $\chi \pi _ { \alpha }$ ; confidence 0.268
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040573.png ; $21$ ; confidence 0.266
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010290/a01029051.png ; $\alpha X$ ; confidence 0.266
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040583.png ; $1$ ; confidence 0.266
+. 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/i/i130/i130030/i130030178.png ; $h ( [ a ] )$ ; confidence 0.265
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110080/a1100801.png ; $u _ { t t } = c ^ { 2 } ( u _ { XX } + u _ { y y } )$ ; confidence 0.264
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080940/r08094048.png ; $\{ \alpha _ { n } \} _ { \aleph = 0 } ^ { \infty }$ ; confidence 0.264
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010220/a01022079.png ; $\| \alpha _ { j k }$ ; confidence 0.264
+. 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/c/c023/c023150/c023150187.png ; $\alpha : H ^ { n } ( : Z ) \rightarrow H ^ { n + 3 } ( : Z _ { 2 } )$ ; confidence 0.262
+. 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/q/q076/q076610/q07661044.png ; $\beta X = S \square x = \omega _ { \kappa } X$ ; confidence 0.261
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010241.png ; $x = T ( \Lambda - \hat { \lambda } I ) ^ { - 1 } T ^ { - 1 } r$ ; confidence 0.261
+. 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/a120/a120220/a12022037.png ; $r _ { ess } ( T )$ ; confidence 0.259
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a1201308.png ; $m$ ; confidence 0.259
+. 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/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/a/a110/a110010/a110010158.png ; $\frac { \| \delta x \| _ { 2 } } { \| x \| _ { 2 } } \leq k [ ( 2 + \eta \hat { k } ) \alpha + \beta \gamma ]$ ; confidence 0.259
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010220/a01022029.png ; $u _ { 1 } = \int _ { c _ { 1 } } ^ { x } d u _ { 1 } , \ldots , u _ { p } = \int _ { \varphi } ^ { x } d u _ { p }$ ; confidence 0.258
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010258.png ; $r = H . | A | . | x$ ; confidence 0.258
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v09638089.png ; $\pi : B \rightarrow G ^ { k } ( V )$ ; confidence 0.258
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020058.png ; $\operatorname { Ker } \beta \in \mathfrak { A } _ { 1 }$ ; confidence 0.257
+. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052500/i05250054.png ; $L ^ { \prime }$ ; confidence 0.256
+. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068370/o06837057.png ; $x _ { C }$ ; confidence 0.256
+. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073700/p07370045.png ; $[ f _ { G } ]$ ; confidence 0.256
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044350/g044350101.png ; $D \Re \subset M$ ; confidence 0.255
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a01021042.png ; $i , j = 1 , \dots , g$ ; confidence 0.255
+. 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/c/c027/c027180/c027180124.png ; $7$ ; confidence 0.254
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010281.png ; $( A _ { x } \lambda ^ { x } + A _ { x - 1 } \lambda ^ { x - 1 } + \ldots + A _ { 0 } ) x = 0$ ; confidence 0.253
+. 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/i/i052/i052980/i05298049.png ; $L ^ { \prime } ( T _ { x } M )$ ; confidence 0.252
+. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076800/q07680094.png ; $\tau _ { 0 } ^ { e ^ { 3 } }$ ; confidence 0.252
+. 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/a010/a010820/a01082073.png ; $X \in Ob \odot$ ; confidence 0.251
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120370/b12037092.png ; $\sum \frac { 1 } { 1 }$ ; confidence 0.251
+. 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/p/p073/p073830/p07383050.png ; $E \subset X = R ^ { \prime }$ ; confidence 0.250
+. 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/a/a130/a130040/a130040612.png ; $97$ ; confidence 0.250
+. 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/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/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/a/a110/a110010/a11001043.png ; $\| \delta x \| f \| x \| \approx \epsilon . k ( A )$ ; confidence 0.247
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301308.png ; $s l _ { 2 }$ ; confidence 0.247
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055630/k0556303.png ; $| m K _ { V ^ { \prime } } | ^ { J }$ ; confidence 0.246
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010217.png ; $1 / | y ^ { i } _ { x ^ { i } } ^ { * }$ ; confidence 0.245
+. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035170/e03517056.png ; $\| \hat { A } - A \| \leq \delta$ ; confidence 0.245
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055080/k05508019.png ; $\nu _ { 0 } \in C ^ { n }$ ; confidence 0.245
+. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o070010110.png ; $X = \cup _ { \alpha } X _ { \alpha }$ ; confidence 0.245
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140116.png ; $q R$ ; confidence 0.245
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110990/b11099011.png ; $V _ { Q }$ ; confidence 0.244
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010251.png ; $\| v \| = \| A x - \hat { \lambda } x \| _ { 2 } \leq \epsilon \| A \| _ { 2 } \| x \| _ { 2 }$ ; confidence 0.243
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010207.png ; $\operatorname { min } _ { i } | \hat { \lambda } - \lambda _ { i } | \leq \rho ( | T ^ { - 1 } | | \delta A | | T | )$ ; confidence 0.242
+. 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/a/a110/a110010/a110010110.png ; $A N = \operatorname { max } _ { 1 } \leq i _ { j } \leq n | \alpha _ { \xi } j |$ ; confidence 0.241
+. 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/a130240/a130240527.png ; $( n$ ; confidence 0.239
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130020/a13002011.png ; $\nu _ { n } = \sum _ { k = 0 } ^ { n - 1 } \mu _ { k } / n$ ; confidence 0.239
+. 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/a/a130/a130130/a13013020.png ; $0.00$ ; confidence 0.237
+. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026450/c02645091.png ; $X _ { 1 }$ ; confidence 0.237
+. 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/a/a130/a130240/a130240370.png ; $2$ ; confidence 0.235
+. 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/a/a130/a130040/a130040163.png ; $\langle A , F \rangle$ ; confidence 0.234
+. 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/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/b/b110/b110370/b11037052.png ; $= 0 \text { as. } \cdot P _ { \theta _ { 0 } } ]$ ; confidence 0.233
+. 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/a/a110/a110010/a110010229.png ; $\frac { \| x ^ { 2 } - x ^ { i } \| } { \| x ^ { i } \| } \leq \frac { \psi } { \operatorname { min } _ { j \neq i } | \lambda _ { i } - \lambda _ { j } | - 2 \psi }$ ; confidence 0.233
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020190/c02019023.png ; $C A$ ; confidence 0.232
+. 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/b/b015/b015560/b01556018.png ; $D \times D \in \Gamma ^ { 2 }$ ; confidence 0.230
+. 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/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/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/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/a/a010/a010210/a010210112.png ; $( \omega ) = P _ { 1 } ^ { \alpha _ { 1 } } 1 ^ { \square } \ldots P _ { n } ^ { \alpha _ { R } }$ ; confidence 0.228
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240536.png ; $Z _ { 23 }$ ; confidence 0.228
+. https://www.encyclopediaofmath.org/legacyimages/e/e037/e037040/e03704050.png ; $n + = n - = n$ ; confidence 0.228
+. 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/c/c110/c110410/c11041043.png ; $C X Y$ ; confidence 0.226
+. 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/a/a010/a010120/a01012015.png ; $P _ { X } ( z ) = \frac { 1 } { n ! } ( z - \alpha ) ( z - \alpha - n h ) ^ { \gamma - 1 }$ ; confidence 0.226
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110250/c1102508.png ; $20$ ; confidence 0.225
+. 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/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/a/a120/a120030/a12003012.png ; $x - a | < b - a$ ; confidence 0.223
+. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063710/m06371091.png ; $n _ { 1 } < n _ { 2 } .$ ; confidence 0.222
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012038.png ; $\{ \lambda _ { n } \} \in \Lambda _ { \alpha }$ ; confidence 0.221
+. 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/a/a012/a012460/a012460130.png ; $X \equiv 0$ ; confidence 0.220
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080740/r0807408.png ; $x _ { n m _ { n } } \rightarrow ( 0 )$ ; confidence 0.220
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012025.png ; $f ( z ) = \sum _ { n = 0 } ^ { \infty } ( n ! ) ^ { - \alpha } a _ { n } z ^ { n } , \quad \underset { n \rightarrow \infty } { \operatorname { lim } } | \alpha _ { n } | ^ { 1 / n } \leq r$ ; confidence 0.220
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240383.png ; $H ^ { \prime }$ ; confidence 0.219
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110270/b11027042.png ; $P ( s S ) = P ( S )$ ; confidence 0.219
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020082.png ; $3$ ; confidence 0.218
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031750/d03175051.png ; $Z _ { h }$ ; confidence 0.217
+. 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/a/a010/a010120/a01012032.png ; $S _ { a }$ ; confidence 0.216
+. 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/a/a130/a130040/a130040808.png ; $^ { * } L D S$ ; confidence 0.214
+. 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/a/a010/a010200/a01020063.png ; $21 / 21$ ; confidence 0.212
+. 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/a/a130/a130040/a130040661.png ; $= \{ M e _ { S _ { i } }$ ; confidence 0.212
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a13004085.png ; $\{ 21 , n \}$ ; confidence 0.211
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110070/a11007015.png ; $x _ { k } \in X$ ; confidence 0.211
+. 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/r/r082/r082070/r08207022.png ; $R _ { i l k } ^ { q } = - R _ { k l } ^ { q }$ ; confidence 0.210
+. 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/d/d031/d031280/d031280129.png ; $f : X ^ { \cdot } \rightarrow Y$ ; confidence 0.209
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031470/d0314706.png ; $| \hat { b } _ { n } | = 1$ ; confidence 0.209
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020048.png ; $B \in Ob \mathfrak { A } _ { 1 }$ ; confidence 0.209
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240502.png ; $Z _ { i j }$ ; confidence 0.208
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001098.png ; $k$ ; confidence 0.208
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020049.png ; $A , C \in Ob A _ { 1 }$ ; confidence 0.207
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014310/a01431097.png ; $| x$ ; confidence 0.207