Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/58"

Revision as of 10:25, 1 May 2020

List

1. ; $X _ { f }$ ; confidence 0.508

2. ; $f \preceq g$ ; confidence 1.000

3. ; $\sigma ( L _ {\bf C } ^ { \infty } ( \hat { G } ) , L _ {\bf C } ^ { 1 } ( \hat { G } ) )$ ; confidence 1.000

4. ; $1 \in \bf C$ ; confidence 0.508

5. ; $Z ( x ( n ) ^ { * } y ( n ) ) = Z ( x ( n ) ) .Z ( y ( n ) ).$ ; confidence 1.000

6. ; $\frac { 1 } { n } \sum _ { j = 1 } ^ { n } \frac { x _ { j } - 1 + p _ { j } } { 2 p _ { j } - 1 }$ ; confidence 0.508

7. ; $\frak N$ ; confidence 1.000

8. ; $\bf Z ^ { * }$ ; confidence 1.000

9. ; $g ( x , k ) = - b ( - k ) f ( x , k ) + a ( k ) f ( x , - k ),$ ; confidence 0.508

10. ; $\langle x \rangle ^ { G }$ ; confidence 1.000

11. ; $v _ { i } \phi _ { , i } = ( {\bf v} . \nabla ) \phi$ ; confidence 1.000

12. ; $( \operatorname{Hom} _ {\frak a } ( D , N ) , \delta ^ { \prime } )$ ; confidence 1.000

13. ; $( {\bf v} . \nabla ) {\bf v} = \frac { 1 } { 2 } \nabla v ^ { 2 } + ( \operatorname { curl } {\bf v} ) \times {\bf v}$ ; confidence 1.000

14. ; $\beta _ { 1 }$ ; confidence 1.000

15. ; $\& , \vee , \supset , \neg$ ; confidence 0.508

16. ; $B _ { n } f$ ; confidence 1.000

17. ; $x \subseteq y$ ; confidence 0.507

18. ; $\langle U _ { \mu } ( x ) , \rho \rangle = \int \langle U _ { t } ( x ) , \rho \rangle d \mu ( t )$ ; confidence 1.000

19. ; $\lambda \int _ { 0 } ^ { \infty } \frac { \int _ { 0 } ^ { x } y [ 1 - B ( y ) ] d y } { [ 1 - \rho ( x ) ] ^ { 2 } } d B ( x ) + \int _ { 0 } ^ { \infty } \frac { 1 - B ( x ) } { 1 - \rho ( x ) } d x,$ ; confidence 0.507

20. ; $\operatorname { lim } _ { N \rightarrow \infty } \operatorname { sup } _ { \varepsilon } | \frac { 1 } { N } \sum _ { n = 1 } ^ { N } f ( T ^ { n } x ) e ^ { 2 \pi i n \varepsilon } | = 0.$ ; confidence 0.507

21. ; $\alpha ^ { N_ 0} \neq 0$ ; confidence 1.000

22. ; $\partial \phi / \partial x _ { i } = \phi _ { ,i }$ ; confidence 1.000

23. ; $h ( x ) \not\equiv 0$ ; confidence 1.000

24. ; $\operatorname{GL}_l$ ; confidence 1.000

25. ; $0 \in {\bf R} ^ { n }$ ; confidence 1.000

26. ; $\hat{\pi}$ ; confidence 1.000

27. ; $\theta > 0$ ; confidence 0.507

28. ; $d _ { \text{in} } < 2$ ; confidence 1.000

29. ; $\operatorname { diag } ( t _ { 1 } , \ldots , t _ { n } ) \mapsto t _ { 1 } ^ { \lambda _ { 1 } } \ldots t _ { n } ^ { \lambda _ { n } } \in K,$ ; confidence 0.507

30. ; $\rho ^ { \prime } = \operatorname { grad } \rho = ( \partial \rho / \partial \zeta _ { 1 } , \dots , \partial \rho / \partial \zeta _ { n } )$ ; confidence 0.507

31. ; $A _ { j_{n _ { k } }} \subset B , \quad k \in \bf N$ ; confidence 1.000

32. ; $\gamma = ( \gamma _ { 1 } , \gamma _ { 2 } , \dots )$ ; confidence 0.506

33. ; $\dot { x } ( t ) = f ( t , x ( t - h _ { 1 } ( t ) ) , \ldots , x ( t - h _ { k } ( t ) ),$ ; confidence 0.506

34. ; $\Pi _ { \kappa }$ ; confidence 1.000

35. ; $Z _ { G } ( - q ^ { - 1 } )$ ; confidence 0.506

36. ; $n \in {\bf N} , \epsilon = \pm 1.$ ; confidence 1.000

37. ; $R _ { n } > \frac { \operatorname { log } 2 } { 1 + \frac { 1 } { 2 } + \ldots + \frac { 1 } { n } }.$ ; confidence 0.506

38. ; $a = B / \overline { u } T$ ; confidence 1.000

39. ; $C _ { m } ^ { 1 } , \ldots$ ; confidence 0.506

40. ; $k_G$ ; confidence 1.000

41. ; $\operatorname{IF} ( x ; T , G )$ ; confidence 1.000

42. ; $F \in \operatorname { Hol } ( \bf B )$ ; confidence 1.000

43. ; $i = 0 , \dots , m$ ; confidence 0.506

44. ; $T _ { \text { vert } } ^ { * } Y$ ; confidence 0.506

45. ; $K [ f _ { 1 } , \ldots , f _ { d } ]$ ; confidence 0.506

46. ; $\langle a b \lanlge c d e \rangle \rangle = \langle \langle a b c \rangle \rangle + \varepsilon \langle c \langle b a d \rangle e \rangle + \langle c d \langle a b e \rangle \rangle,$ ; confidence 1.000

47. ; $\hat { X } = ( A , B )$ ; confidence 1.000

48. ; $m _ { i j } \in \{ 0,1 \}$ ; confidence 0.505

49. ; $U ( g ) \varphi_j ( f ) U ( g ^ { - 1 } )$ ; confidence 1.000

50. ; $T ^ { 2 }$ ; confidence 0.505

51. ; $\mathfrak { n } ^ { + } = [ \mathfrak { b } , \mathfrak { b } ]$ ; confidence 0.505

52. ; $1 = | z _ { 1 } | \geq \ldots \geq | z _ { n } | > 0$ ; confidence 0.505

53. ; $( - ) ^ { * } : \cal C ^ { \text{op} } \rightarrow C$ ; confidence 1.000

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

55. ; $\Lamda M = M \Lambda ^ { t }$ ; confidence 1.000

56. ; $S \subset M ^ { n }$ ; confidence 1.000

57. ; $\left( \begin{array} { c } { [ n ] } \\ { k } \end{array} \right) : = \{ X \subseteq [ n ] : | X | = k \}$ ; confidence 0.505

58. ; $S _ { \text{V} }$ ; confidence 1.000

59. ; $\beta_j > 0$ ; confidence 1.000

60. ; $\{ B x _ { x } \}$ ; confidence 0.505

61. ; $b _ { N } = 0$ ; confidence 0.505

62. ; $B = k [ [ X _ { 1 } , \dots , X _ { d } , Y _ { 1 } , \dots , Y _ { d } ]$ ; confidence 0.505

63. ; $a _ { n + 1 }$ ; confidence 1.000

64. ; $n / 2$ ; confidence 1.000

65. ; $Y , Y _ { 1 } , Y _ { 2 } , \dots$ ; confidence 0.505

66. ; $\{ y _ { n } \}$ ; confidence 1.000

67. ; $d _ { 1 } , \dots , d _ { n }$ ; confidence 0.504

68. ; $\varphi ^ { \prime }$ ; confidence 1.000

69. ; $\sum _ { i } a _ { i } x _ { i } \leq c$ ; confidence 0.504

70. ; $y ( \lambda z z ) \equiv y ( \lambda x x ) \not \equiv w ( \lambda x x )$ ; confidence 0.504

71. ; $Y = [ 0,2 \pi [ ^ { N } $ ; confidence 1.000

72. ; $( \alpha _ { 1 } , \alpha _ { 2 } , \dots , \alpha _ { q } \cup \gamma ^ { d } ) \in {\cal F} ( S ^ { d } ) ^ { q }$ ; confidence 1.000

73. ; $k ^ { \prime } \langle x _ { i } \rangle$ ; confidence 1.000

74. ; $\operatorname{E} [ T _ { p } ] _ {\text{PR} } = \frac { 1 } { 2 ( 1 - \sigma _ { p - 1 } ) ( 1 - \sigma _ { p } ) } \sum _ { k = 1 } ^ { p } \lambda _ { k } b _ { k } ^ { ( 2 ) } + \frac { b _ { p } } { 1 - \sigma _ { p - 1 } }$ ; confidence 1.000

75. ; $\Pi ^ { \text { re } }$ ; confidence 0.504

76. ; $\omega _ { n } = \frac { 2 \pi ^ { n / 2 } } { \Gamma ( \frac { n } { 2 } ) }$ ; confidence 0.504

77. ; $\mu _ { k }$ ; confidence 0.504

78. ; $\square ^ { t } a P a$ ; confidence 0.504

79. ; $f = ( \lambda - a ) ^ { s }$ ; confidence 0.504

80. ; $a_3$ ; confidence 1.000

81. ; $[ \varphi \bigotimes x , \psi \bigotimes Y ] =$ ; confidence 1.000

82. ; $+\frac { - 1 } { k ! ( 1 - 1 ) ! } \times \times \sum _ { \sigma } \operatorname { sign } \sigma \omega ( [ K ( X _ { \sigma 1 } , \ldots , X _ { \sigma k } ) , X _ { \sigma ( k + 1 ) } ] , X _ { \sigma ( k + 2 ) } , \ldots )+$ ; confidence 1.000

83. ; $k$ ; confidence 0.504

84. ; $\cal E$ ; confidence 1.000

85. ; $M _ { 6 } = \operatorname { min } _ { j } | \operatorname { arc } z _ { j } |$ ; confidence 0.504

86. ; $\Delta ( \Lambda , M ) = \text { Det } [ E \bigotimes \Lambda - A \bigotimes M ] =$ ; confidence 1.000

87. ; $\partial S ( \phi ) = S ( d \phi )$ ; confidence 0.504

88. ; $\mu ( A ) = | A |$ ; confidence 0.504

89. ; $\operatorname{GL} _ { s } ( K )$ ; confidence 1.000

90. ; $T$ ; confidence 0.504

91. ; $E _ { 1 } = E _ { 0 } + \int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle | ^ { 2 } } { E _ { 1 } - \lambda } d \lambda < 0.$ ; confidence 0.504

92. ; ${\bf R} _ { x } ^ { 3 N } \times {\bf R} _ { p } ^ { 3 N }$ ; confidence 1.000

93. ; $\operatorname{E} _ { \operatorname{P} _ { n } } ( d ) = \operatorname{E} _ { \operatorname{P}_ { n } } ( d ^ { * } )$ ; confidence 1.000

94. ; $\delta > ( 3 n - 2 ) / 6$ ; confidence 0.503

95. ; $\left( \begin{array} { c c } { L ( a , b ) } & { 0 } \\ { 0 } & { \varepsilon L ( b , a ) } \end{array} \right);$ ; confidence 1.000

96. ; $M _ { 5 } = \operatorname { max } _ { j } | b _ { j } |$ ; confidence 0.503

97. ; $P _ { + } T P _ { - }$ ; confidence 0.503

98. ; $= - J - k _ { B }T \operatorname { ln } \{ \operatorname { cosh } ( \frac { H } { k _ { B } T } ) + + [ \operatorname { sinh } ^ { 2 } ( \frac { H } { k _ { B } T } ) + \operatorname { exp } ( - \frac { 4 J } { k _ { B } T } ) ] ^ { 1 / 2 }\],$ ; confidence 0.503

99. ; $\tilde { h } : Z \rightarrow B$ ; confidence 0.503

100. ; $\lambda_j$ ; confidence 1.000

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

102. ; $R _ { L }$ ; confidence 1.000

103. ; $a \in B$ ; confidence 0.503

104. ; $g \in \operatorname { Gal } ( k _ { \infty } ^ { \prime } / k )$ ; confidence 0.503

105. ; $( \epsilon \bigotimes \operatorname{id} _ { A } ) \circ L = \operatorname{id} _ { A }$ ; confidence 1.000

106. ; $u . v$ ; confidence 1.000

107. ; $q _ { A_ { 2 } } \circ \mu = q _ { A _ { 1 } }$ ; confidence 1.000

108. ; $P .P \subseteq P$ ; confidence 1.000

109. ; $D _ { \xi } = ( 1 , \xi _ { 1 } , \dots , \xi _ { N } , | \xi | ^ { 2 } / 2 )\bf R _ { + }$ ; confidence 1.000

110. ; $\xi : X \rightarrow B O _ { n }$ ; confidence 1.000

111. ; $\times \int _ { 0 } ^ { \alpha } [ K _ { i \tau } ( \alpha ) I _ { i \tau } ( x ) - I _ { i \tau } ( \alpha ) K _ { i \tau } ( x ) ] f ( x ) \frac { d x } { x }$ ; confidence 0.502

112. ; $O ( | V |+ | E | )$ ; confidence 1.000

113. ; $h _ { \lambda _ { i } }$ ; confidence 0.502

114. ; $\int _ { \operatorname{SO} ( n ) } d \gamma \int _ { 0 } ^ { \infty } \frac { f ^ { * } \mu _ { \gamma , t } } { t } d t = c _ { \mu } f.$ ; confidence 1.000

115. ; $\operatorname{Wh} ^ { * }$ ; confidence 1.000

116. ; $m _ { n } : {\cal A} \rightarrow [ 0 , + \infty )$ ; confidence 1.000

117. ; $j = 1 , \dots , k$ ; confidence 0.502

118. ; $n _ { + }$ ; confidence 0.502

119. ; $X = C ( S \times T )$ ; confidence 0.502

120. ; $\operatorname{E} X$ ; confidence 1.000

121. ; ${\cal C} = \operatorname { co }\cal C$ ; confidence 1.000

122. ; $x \in U$ ; confidence 0.502

123. ; $f \in \operatorname { Lip } 1$ ; confidence 0.502

124. ; $\lambda _ { 1 } ( \Omega ) \geq \frac { a } { r _ { \Omega } ^ { 2 } }$ ; confidence 0.502

125. ; $\operatorname{Sp} ( n )$ ; confidence 1.000

126. ; $K _ { 1 } ( {\cal O} _ { n } ) = 0$ ; confidence 1.000

127. ; $e ^ { \pi z }$ ; confidence 0.502

128. ; $\tilde { \Omega } _ { S 5 } T$ ; confidence 0.501

129. ; $\{ f_j \}$ ; confidence 1.000

130. ; $q \in L ^ { 1 } ( 0 , \infty )$ ; confidence 0.501 NOTE: should the bracket be also closed?

131. ; $\operatorname { GCD } ( a , b ) = 1$ ; confidence 1.000

132. ; $m$ ; confidence 0.501

133. ; $\operatorname { size } ( x ) = n$ ; confidence 0.501

134. ; $d _ { i + 1 }$ ; confidence 1.000

135. ; $q \in k$ ; confidence 0.501

136. ; $Z \subset X$ ; confidence 0.501

137. ; $\gamma \rho ^ { 2 / 3 } = \Phi$ ; confidence 1.000

138. ; $\frac { \partial c } { \partial t } = \operatorname { div } \{ M \operatorname { grad } [ f _ { 0 } ^ { \prime } ( c ) - 2 \kappa \Delta c ] \} \text { in } V,$ ; confidence 0.501

139. ; $K ( ., s ) \in L ^ { 1 } ( \mu )$ ; confidence 1.000

140. ; $\varphi ( a , b , 1 ) = a. b$ ; confidence 1.000

141. ; $K = e ^ { - \beta h } \in T _ { 1 } ( H )$ ; confidence 0.501

142. ; $p \in \bf R$ ; confidence 1.000

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

144. ; $( 1 + a ) ^ { - 1 } = 1 - a + a ^ { 2 } - a ^ { 3 } +\dots$ ; confidence 1.000

145. ; $F ( 2,2 n ) = \pi _ { 1 } ( M _ { n } )$ ; confidence 0.501

146. ; $\lambda _ { 1 } + j , \ldots , \lambda _ { \nu } + j$ ; confidence 0.501

147. ; $\pi _ { n } ( X ; A , B , x _ { 0 } )$ ; confidence 1.000

148. ; ${\bf l} _ { A } ( M / q M )$ ; confidence 0.501

149. ; $\delta _ { \text{BRST} } ^ { 2 } = 0$ ; confidence 1.000

150. ; $0 < m \leq n$ ; confidence 0.500

151. ; $\tilde {\cal P }$ ; confidence 1.000

152. ; $V _ { 1 } \bigotimes \ldots \bigotimes V _ { n } \rightarrow V _ { \sigma ( 1 ) } \bigotimes \ldots \bigotimes V _ { \sigma ( n ) }$ ; confidence 1.000

153. ; $W _ { \text{loc} } ^ { 1 , n } ( G )$ ; confidence 1.000

154. ; $x _ { 1 } , \dots , x _ { r }$ ; confidence 0.500

155. ; ${\bf Z} + 2 {\bf Z}$ ; confidence 1.000

156. ; $\psi _ { n } ( z ) = \frac { 1 } { 2 \pi } \int _ { - \pi } ^ { \pi } R ( e ^ { i \theta } , z ) [ \phi _ { n } ( e ^ { i \theta } ) - \phi _ { n } ( z ) ] d \mu ( \theta ).$ ; confidence 0.500

157. ; $\wedge ^ { k } (\frak a )$ ; confidence 1.000

158. ; $\bf Z = X \Gamma + F$ ; confidence 1.000

159. ; $< 2 a$ ; confidence 0.500

160. ; $\operatorname{Vec}_n$ ; confidence 1.000

161. ; $\operatorname{E} ( Z _ { 1 } ) = 0$ ; confidence 1.000

162. ; $q ^ { - 1 } \sum _ { i = 1 } ^ { q } ( z _ { i } - \zeta _ { i } ) ^ { 2 } / \operatorname{MS} _ { e }$ ; confidence 1.000

163. ; $TT'$ ; confidence 1.000

164. ; $\{ D ^ { \lambda } : \lambda \text { a $p\square$ regular partition of } n\}$ ; confidence 1.000

165. ; $( x _ { 0 } , x _ { 1 } ] , \ldots , ( x _ { k } - 1 , x _ { k } )$ ; confidence 0.500

166. ; $\operatorname { prin } K I$ ; confidence 1.000

167. ; $\operatorname { sup } _ { z _ { 1 } , \ldots , z _ { n } \in U } \operatorname { min } _ { k \in S } \frac { | \sum _ { j = 1 } ^ { n } b _ { j } z _ { j } ^ { k } | } { M _ { d } ( k ) }$ ; confidence 1.000

168. ; $I + ( P _ { 1 } , \dots , P _ { m } )$ ; confidence 0.499

169. ; ${\bf l} ( w )$ ; confidence 1.000

170. ; $\Delta ( \lambda ) = K \operatorname{GL} _ { n } ( K ) z _ { \lambda },$ ; confidence 1.000

171. ; $x,x_0$ ; confidence 1.000

172. ; $V _ { \text { simp } } ( O _ { K , p } ) \neq \emptyset$ ; confidence 1.000

173. ; $t \in {\bf R}_ +$ ; confidence 1.000

174. ; $\pi '$ ; confidence 1.000

175. ; $m$ ; confidence 0.499

176. ; $P ( E _ { l } ) = \frac { \operatorname { exp } ( - E _ { l } / k _ { B } T ) } { \sum _ { l } \operatorname { exp } ( - E _ { l } / k _ { B } T ) }.$ ; confidence 0.499

177. ; $\bf C A$ ; confidence 1.000

178. ; $x _ { i } \in \cal X$ ; confidence 1.000

179. ; $x _ { j } ^ { \prime } = \sum _ { i , k } c _ { i k } f _ { i } f _ { k }$ ; confidence 0.499

180. ; $X : = U \Lambda V,$ ; confidence 1.000

181. ; $k ( 0 ) = I$ ; confidence 1.000

182. ; $G = \operatorname{SL} ( 2 , {\bf C} ) \rtimes {\bf R} ^ { 4 }$ ; confidence 1.000

183. ; $a \neq b \in {\bf C} ^ { n }$ ; confidence 1.000

184. ; $\operatorname{ Mp } ( n )$ ; confidence 1.000

185. ; $C_{abcd}$ ; confidence 1.000

186. ; $\sum _ { n \leq x } G _ { K } ( n ) = A _ { K } x + O ( x ^ { \eta_K} ) \text { as } x \rightarrow \infty,$ ; confidence 1.000

187. ; $q _ { m } \in L _ { 1,1 }$ ; confidence 0.498

188. ; $\operatorname{GL} _ { n } ( {\bf Z} A )$ ; confidence 1.000

189. ; $M : \sigma$ ; confidence 0.498

190. ; $A _ { i } : = M _ { z _ { i } }$ ; confidence 0.498

191. ; $\overline { T G }$ ; confidence 0.498

192. ; $f \in L ^ { 1 } ( {\bf R} ^ { 2 n } )$ ; confidence 1.000

193. ; $K _ { Z } \in H$ ; confidence 0.498

194. ; $E ( \Gamma , \Delta ) \dashv _ {\cal D } \epsilon _ { i } ( \varphi , \psi )$ ; confidence 1.000

195. ; $O _ { s + 2,2} (\bf R )$ ; confidence 1.000

196. ; $I _ { \epsilon } ( X )$ ; confidence 0.498

197. ; $\chi _ { K I } : K _ { 0 } ( \operatorname { prin } K I ) \rightarrow \bf Z$ ; confidence 1.000

198. ; $\operatorname{P} _ { K _ { + } } ( v , z ) - \operatorname{P} _ { K _ { - } } ( v , z ) \equiv \operatorname { lk } ( K _ { 0 } ) \operatorname { mod } ( v ^ { 2 } - 1 , z )$ ; confidence 1.000

199. ; $[ P , ] _ { A }$ ; confidence 0.497

200. ; $P = \cap _ { i \in I } P _ { i }$ ; confidence 0.497

201. ; $| X | ^ { r }$ ; confidence 1.000

202. ; $\left. \begin{cases} { U _ { 0 } ( x ) = 0 } \\ { U _ { 1 } ( x ) = 1 } \\ { U _ { n } ( x ) = x U _ { n - 1 } ( x ) + U _ { n - 2 } ( x ) , \quad n = 2,3 } \end{cases} \right.$ ; confidence 1.000

203. ; $[ .,. ] : \cal K \times K \rightarrow \bf C$ ; confidence 1.000

204. ; $\| F \| _ { \infty } = \operatorname { esssup } _ { \omega } | F ( i \omega ) |$ ; confidence 0.497

205. ; $\operatorname { lim } _ { N \rightarrow \infty } \| f - f _ { N } \| _ { \cal A ^ { * } }= 0.$ ; confidence 1.000

206. ; $( E _ { n } : n \in {\bf Z} ^ { + } )$ ; confidence 1.000

207. ; ${\cal T} _ { A } \xi = \kappa _ { M } \circ T _ { A } \xi.$ ; confidence 1.000

208. ; $f ( \overset{\rightharpoonup}{ D } ( A ) ) = ( - A ^ { 3 } ) ^ { - \operatorname { Tait } ( \overset{\rightharpoonup}{ D } ) } ( D )$ ; confidence 1.000

209. ; $a _ { 1 } , \dots , a _ { r }$ ; confidence 0.497

210. ; $\operatorname{E} ( Y ) = 2 \theta - 1$ ; confidence 1.000

211. ; $u \in Q _ { 1 } ( R )$ ; confidence 0.497

212. ; ${\cal P} = ( P _ { s s ^ { \prime } } ) = ( \langle S | {\cal P} | S ^ { \prime } \rangle )$ ; confidence 1.000

213. ; $\psi _ { n } \in L ^ { 2 } ( - \infty , \infty )$ ; confidence 1.000

214. ; ${\bf y} _ { 1 } , \dots , {\bf y} _ { p }$ ; confidence 1.000

215. ; $L _ { p } ( 1 - n , \chi ) = L ( 1 - n , \chi \omega ^ { - n } ) \prod _ { {\frak p} | p } ( 1 - \chi \omega ^ { - n } ( {\frak p} ) N {\frak p} ^ { n - 1 } )$ ; confidence 1.000

216. ; $\rho \in \mathfrak { h } ^ { * }$ ; confidence 0.496

217. ; $E ( a ) = \operatorname { exp } ( \int _ { 0 } ^ { \infty } t \hat{s} ( t ) \hat{s} ( - t ) d t ).$ ; confidence 1.000

218. ; $\rho _ { d }$ ; confidence 0.496

219. ; $S ^ { n - 1 }$ ; confidence 0.496

220. ; $x \mu _ { x } ( x )$ ; confidence 0.496

221. ; $\sum _ { i = 1 } ^ { k } \lambda _ { i } \geq \frac { n } { n + 2 } \frac { 4 \pi ^ { 2 } k ^ { 1 + 2 / n } } { ( C _ { n } | \Omega | ) ^ { 2 / n } } k = 1,2 , \ldots$ ; confidence 0.496

222. ; $\psi _ { x y } + u ( x , y ) \psi = 0$ ; confidence 1.000

223. ; $a, b , x , y , z \in E$ ; confidence 1.000

224. ; ${\cal M} _ { n } = \operatorname { det } M _ { n }$ ; confidence 1.000

225. ; $\Phi : ( \otimes ) \otimes \rightarrow \otimes ( \otimes )$ ; confidence 1.000

226. ; ${\cal H} *$ ; confidence 1.000

227. ; ${\cal Q}_2$ ; confidence 1.000

228. ; $D ^ { \alpha } = D _ { 1 } ^ { \alpha _ { 1 } } \ldots D _ { N } ^ { \alpha _ { N } }$ ; confidence 0.496

229. ; $r \equiv \operatorname { rank } M ( n )$ ; confidence 0.496

230. ; $E$ ; confidence 1.000

231. ; $p \in \hat{K}$ ; confidence 1.000

232. ; $P _ { M } ( v ) \neq 0$ ; confidence 0.496

233. ; $( \lambda x y . y x ) A B = B A$ ; confidence 1.000

234. ; $F ( 2,2 n ) \subset \operatorname { PSL } _ { 2 } ( {\bf C} )$ ; confidence 1.000

235. ; $\| X \| { * } \leq 1$ ; confidence 1.000

236. ; $\operatorname { Th } \cal D$ ; confidence 1.000

237. ; $\| t g ( t ) \| _ { 2 } \| \gamma \tilde{g} ( \gamma ) \| _ { 2 } = \infty$ ; confidence 1.000

238. ; $U ^ { ( n )_ t} = \sum _ { k = 0 } ^ { n } \frac { ( - 1 ) ^ { k } } { k ! ( n - k ) ! } S ^ { s + n - k } ( - t , x _ { 1 } , \dots , x _ { s + n - k} )$ ; confidence 1.000

239. ; $( F ^ { n } , h : F \rightarrow F ) \rightarrow T ( h )$ ; confidence 1.000

240. ; $s _ { i } ( z )$ ; confidence 0.496

241. ; $S ^ { n } \times S ^ { m }$ ; confidence 0.496

242. ; $\{ t = t_j \} \cup K$ ; confidence 1.000

243. ; $X \sim N _ { p , n } ( 0 , \Sigma \otimes I _ { n } )$ ; confidence 0.495

244. ; $\operatorname{lim\,sup}_R S _ { R } ^ { ( n - 1 ) / 2 } f ( 0 ) = + \infty$ ; confidence 1.000

245. ; ${\cal X} _ { t } \sim {\cal X}_{ - t }$ ; confidence 1.000

246. ; $a _2$ ; confidence 1.000

247. ; $\tilde{\omega}$ ; confidence 1.000

248. ; $X ^ { 2 } = \sum _ { i = 1 } ^ { k } \frac { ( \nu _ { i } - n p _ { i } ) ^ { 2 } } { n p _ { i } } = \frac { 1 } { n } \sum \frac { \nu _ { i } ^ { 2 } } { p _ { i } } - n , \quad n = \nu _ { 1 } + \ldots + \nu _ { k }$ ; confidence 0.495

249. ; $\varphi_j ( f )$ ; confidence 1.000

250. ; $a _ { 1 } , \dots , a _ { t }$ ; confidence 0.495

251. ; $f \in A _ { s } ^ { + }$ ; confidence 0.495

252. ; $\operatorname{lbl} ( D )$ ; confidence 1.000

253. ; $- ( \text {const} ) \int _ { {\bf R} ^ { 3 } } \rho ( x ) ^ { 4 / 3 } d x$ ; confidence 1.000

254. ; $h \in \cal H$ ; confidence 1.000

255. ; $( G m _ { i } ) \circ f = ( G f _ { i } ) \circ e$ ; confidence 0.495

256. ; $K \subset D ^ { n }$ ; confidence 1.000

257. ; $S _ { m } [ f ] = \sum _ { v = 1 } ^ { m } b _ { v , m } f ( y_{v , m} )$ ; confidence 1.000

258. ; $\overset{\rightharpoonup} { \Delta }$ ; confidence 1.000

259. ; $\theta _ { n } ^ { * }$ ; confidence 0.495

260. ; $M = \int ( \partial / \partial e ) \eta ( \overset{\rightharpoonup} { x } , e ) \overset{\rightharpoonup} { x } \overset{\rightharpoonup} {X } ^ { t } d H _ { \overset{\rightharpoonup} { \theta } } ( \overset{\rightharpoonup} { x } , y )$ ; confidence 1.000

261. ; $\frac { d \operatorname { ln } g ( L ; m , s ) } { d m } \frac { d \operatorname { ln } g ( R ; m , s ) } { d s }$ ; confidence 0.495

262. ; $H ^ { N - 1 - k } ( S ^ { n } \backslash X )$ ; confidence 1.000

263. ; $i = 0 , \ldots , n - 1$ ; confidence 0.495

264. ; $\int _ { \partial D } \operatorname { exp } ( \varepsilon | \varphi ( e ^ { i \vartheta } ) - \varphi _ { I } | ) d \vartheta$ ; confidence 0.495

265. ; $s _ { A } : A \times L A \rightarrow L A$ ; confidence 1.000

266. ; $( X _ { n } ) _ { n \geq 0}$ ; confidence 1.000

267. ; $\varphi ( q )$ ; confidence 0.494

268. ; $X = {\bf P} ^ { d }$ ; confidence 1.000

269. ; $u ( x , k ) = e ^ { i \delta } \operatorname { sin } ( k x + \delta ) + o ( 1 ) , \quad \text { as } x \rightarrow \infty.$ ; confidence 0.494

270. ; $\operatorname{Re} \lambda _ { i } < 0$ ; confidence 1.000

271. ; $\Omega \subset {\bf C} ^ { n }$ ; confidence 1.000

272. ; ${\cal F} _ { k }$ ; confidence 1.000

273. ; $l \neq p$ ; confidence 1.000

274. ; $\{ e _ { i } : - 1 \leq i \leq p ^ { m } - 2 \}$ ; confidence 0.494

275. ; $\tilde{i} ( \nu ) = \operatorname { lim } _ { j \rightarrow \infty } I ( u _ { j } )$ ; confidence 1.000

276. ; $V ^ { 1 } , V ^ { 2 } , \dots,$ ; confidence 0.494

277. ; $V _ { f } = \{ f ( a ) : a \in {\bf F} _ { q } \}$ ; confidence 1.000

278. ; $\operatorname{coh} \bf X$ ; confidence 1.000

279. ; $\frac { \mu _ { n } ( x ) } { \mu _ { n } } \stackrel { \operatorname{P} } { \rightarrow } \alpha ( x ) = - \int _ { 0 } ^ { \infty } \frac { \lambda ^ { x } e ^ { - \lambda } } { x ! } R ( d \lambda )$ ; confidence 0.493

280. ; $x = 1 , \dots , f_{( 1 , n )}$ ; confidence 1.000

281. ; $r_j > 0$ ; confidence 1.000

282. ; $\sigma _ { T } ( A , {\cal X} ) : = \{ \lambda \in {\bf C} ^ { n } : A - \lambda \text { is singular } \}$ ; confidence 1.000

283. ; $\pi _ { v , p } ( d \theta ) P ( \theta , \mu ) ( d x )$ ; confidence 0.493

284. ; $P ( t ) = \prod _ { m = 1 } ^ { n } ( t - t _ { m } ) ^ { \gamma _ { m } }$ ; confidence 0.493

285. ; ${\bf R} ^ { n } \backslash K _ { 2 }$ ; confidence 1.000

286. ; $A X \sim \operatorname { RS } _ { q , n } ( \psi )$ ; confidence 0.493

287. ; $\Sigma n _ { j } = n$ ; confidence 0.493

288. ; $M ( {\cal E} ) = \dot { X }$ ; confidence 1.000

289. ; $A _ { 0 } , \ldots , A _ { n }$ ; confidence 1.000

290. ; $\in {\bf A} ^ { 2 } {\cal E} \bigotimes {\bf A} ^ { 2 } {\cal E}$ ; confidence 1.000

291. ; $x \otimes y \rightarrow x . y$ ; confidence 0.493

292. ; $\lambda x x \equiv \lambda x x \not \equiv \lambda x y$ ; confidence 0.493

293. ; $i = 0 , \ldots , N$ ; confidence 0.492

294. ; $l _ { i } = \delta _ { i } ^ { * } G _ { i } \Theta _ { i } \left( \begin{array} { c } { 1 } \\ { 0 } \end{array} \right) , d _ { i } = | \delta _ { i } | ^ { 2 }.$ ; confidence 0.492

295. ; $a _ { 2 } = 1 , \dots , a _ { k - 1 } = k - 2$ ; confidence 1.000

296. ; $M [ z ^ { n } ] = c _ { n } , n = 0 , \pm 1 , \pm 2 , \dots,$ ; confidence 0.492

297. ; $G \times ^ { R } V$ ; confidence 0.492

298. ; $P = \{ ( z _ { 1 } , \dots , z _ { n } ) : | z _ { j } - a _ { j } | < r _ { j } , j = 1 , \dots , n \}$ ; confidence 0.492

299. ; $( g, f ( z ) )$ ; confidence 1.000

300. ; $f_{ t _ { 1 } \ldots t _ { \rho } ( f )} \in T$ ; confidence 1.000

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/58. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/58&oldid=45626

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Revision as of 10:25, 1 May 2020

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@@ Line 2: / Line 2: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f041/f041940/f04194061.png ; $X _ { f }$ ; confidence 0.508
-. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110010/l11001032.png ; $f \leq g$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110010/l11001032.png ; $f \preceq g$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f130100127.png ; $\sigma ( L _ { C } ^ { \infty } ( \hat { G } ) , L _ { C } ^ { 1 } ( \hat { G } ) )$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f130100127.png ; $\sigma ( L _ {\bf C } ^ { \infty } ( \hat { G } ) , L _ {\bf C } ^ { 1 } ( \hat { G } ) )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120050/g12005049.png ; $1 \in C$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120050/g12005049.png ; $1 \in \bf C$ ; confidence 0.508
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001031.png ; $Z ( x ( n ) ^ { * } y ( n ) ) = Z ( x ( n ) ) Z ( y ( n ) )$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001031.png ; $Z ( x ( n ) ^ { * } y ( n ) ) = Z ( x ( n ) ) .Z ( y ( n ) ).$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150159.png ; $\frac { 1 } { n } \sum _ { j = 1 } ^ { n } \frac { x _ { j } - 1 + p _ { j } } { 2 p _ { j } - 1 }$ ; confidence 0.508
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130060/c13006045.png ; $27$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130060/c13006045.png ; $\frak N$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023076.png ; $Z ^ { * }$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023076.png ; $\bf Z ^ { * }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005035.png ; $g ( x , k ) = - b ( - k ) f ( x , k ) + a ( k ) f ( x , - k )$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005035.png ; $g ( x , k ) = - b ( - k ) f ( x , k ) + a ( k ) f ( x , - k ),$ ; confidence 0.508
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120090/c1200903.png ; $\{ x \} ^ { G }$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120090/c1200903.png ; $\langle x \rangle ^ { G }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m130110125.png ; $v _ { i } \phi _ { , i } = ( v . \nabla ) \phi$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m130110125.png ; $v _ { i } \phi _ { , i } = ( {\bf v} . \nabla ) \phi$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b120210110.png ; $( Hom _ { a } ( D , N ) , \delta ^ { \prime } )$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b120210110.png ; $( \operatorname{Hom} _ {\frak a } ( D , N ) , \delta ^ { \prime } )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m130110138.png ; $( v . \nabla ) v = \frac { 1 } { 2 } \nabla v ^ { 2 } + ( \operatorname { curl } v ) \times v$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m130110138.png ; $( {\bf v} . \nabla ) {\bf v} = \frac { 1 } { 2 } \nabla v ^ { 2 } + ( \operatorname { curl } {\bf v} ) \times {\bf v}$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022860/c02286044.png ; $B _ { 1 }$ ; confidence 0.508
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022860/c02286044.png ; $\beta _ { 1 }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/l/l060/l060740/l0607408.png ; $\& , \vee , \supset , \neg$ ; confidence 0.508
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130110/b13011010.png ; $B _ { N } f$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130110/b13011010.png ; $B _ { n } f$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z13010028.png ; $x \subseteq y$ ; confidence 0.507
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120280/a12028064.png ; $\langle U _ { \mu } ( x ) , \rho \rangle = \int \{ U _ { t } ( x ) , \rho \rangle d \mu ( t )$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120280/a12028064.png ; $\langle U _ { \mu } ( x ) , \rho \rangle = \int \langle U _ { t } ( x ) , \rho \rangle d \mu ( t )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008087.png ; $\lambda \int _ { 0 } ^ { \infty } \frac { \int _ { 0 } ^ { x } y [ 1 - B ( y ) ] d y } { [ 1 - \rho ( x ) ] ^ { 2 } } d B ( x ) + \int _ { 0 } ^ { \infty } \frac { 1 - B ( x ) } { 1 - \rho ( x ) } d x$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008087.png ; $\lambda \int _ { 0 } ^ { \infty } \frac { \int _ { 0 } ^ { x } y [ 1 - B ( y ) ] d y } { [ 1 - \rho ( x ) ] ^ { 2 } } d B ( x ) + \int _ { 0 } ^ { \infty } \frac { 1 - B ( x ) } { 1 - \rho ( x ) } d x,$ ; confidence 0.507
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130110/w13011019.png ; $\operatorname { lim } _ { N \rightarrow \infty } \operatorname { sup } _ { \varepsilon } | \frac { 1 } { N } \sum _ { n = 1 } ^ { N } f ( T ^ { n } x ) e ^ { 2 \pi i n \varepsilon } | = 0$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130110/w13011019.png ; $\operatorname { lim } _ { N \rightarrow \infty } \operatorname { sup } _ { \varepsilon } | \frac { 1 } { N } \sum _ { n = 1 } ^ { N } f ( T ^ { n } x ) e ^ { 2 \pi i n \varepsilon } | = 0.$ ; confidence 0.507
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f1202106.png ; $\alpha ^ { N } 0 \neq 0$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f1202106.png ; $\alpha ^ { N_ 0} \neq 0$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m130110115.png ; $\partial \phi / \partial x _ { i } = \phi _ { i }$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m130110115.png ; $\partial \phi / \partial x _ { i } = \phi _ { ,i }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o13008037.png ; $h ( x ) \equiv 0$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o13008037.png ; $h ( x ) \not\equiv 0$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004083.png ; $GL$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004083.png ; $\operatorname{GL}_l$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040340/f04034080.png ; $0 \in R ^ { x }$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040340/f04034080.png ; $0 \in {\bf R} ^ { n }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i130030142.png ; $\pi$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i130030142.png ; $\hat{\pi}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/h/h130/h130120/h13012025.png ; $\theta > 0$ ; confidence 0.507
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510159.png ; $d _ { i n } < 2$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510159.png ; $d _ { \text{in} } < 2$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090122.png ; $\operatorname { diag } ( t _ { 1 } , \ldots , t _ { n } ) \mapsto t _ { 1 } ^ { \lambda _ { 1 } } \ldots t _ { n } ^ { \lambda _ { n } } \in K$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090122.png ; $\operatorname { diag } ( t _ { 1 } , \ldots , t _ { n } ) \mapsto t _ { 1 } ^ { \lambda _ { 1 } } \ldots t _ { n } ^ { \lambda _ { n } } \in K,$ ; confidence 0.507
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004048.png ; $\rho ^ { \prime } = \operatorname { grad } \rho = ( \partial \rho / \partial \zeta _ { 1 } , \dots , \partial \rho / \partial \zeta _ { n } )$ ; confidence 0.507
-. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120070/n12007023.png ; $A _ { j n _ { k } } \subset B , \quad k \in N$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120070/n12007023.png ; $A _ { j_{n _ { k } }} \subset B , \quad k \in \bf N$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130140/s13014030.png ; $\gamma = ( \gamma _ { 1 } , \gamma _ { 2 } , \dots )$ ; confidence 0.506
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120240/f12024027.png ; $\dot { x } ( t ) = f ( t , x ( t - h _ { 1 } ( t ) ) , \ldots , x ( t - h _ { k } ( t ) )$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120240/f12024027.png ; $\dot { x } ( t ) = f ( t , x ( t - h _ { 1 } ( t ) ) , \ldots , x ( t - h _ { k } ( t ) ),$ ; confidence 0.506
-. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047390/h047390141.png ; $\Pi _ { r }$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047390/h047390141.png ; $\Pi _ { \kappa }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050252.png ; $Z _ { G } ( - q ^ { - 1 } )$ ; confidence 0.506
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120060/b1200606.png ; $n \in N , \epsilon = \pm 1$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120060/b1200606.png ; $n \in {\bf N} , \epsilon = \pm 1.$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020065.png ; $R _ { n } > \frac { \operatorname { log } 2 } { 1 + \frac { 1 } { 2 } + \ldots + \frac { 1 } { n } }$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020065.png ; $R _ { n } > \frac { \operatorname { log } 2 } { 1 + \frac { 1 } { 2 } + \ldots + \frac { 1 } { n } }.$ ; confidence 0.506
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016023.png ; $\alpha = B / \overline { u } T$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016023.png ; $a = B / \overline { u } T$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030035.png ; $C _ { m } ^ { 1 } , \ldots$ ; confidence 0.506
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120160/f12016030.png ; $k$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120160/f12016030.png ; $k_G$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003032.png ; $IF ( x ; T , G )$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003032.png ; $\operatorname{IF} ( x ; T , G )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d13008073.png ; $F \in \operatorname { Hol } ( B )$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d13008073.png ; $F \in \operatorname { Hol } ( \bf B )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b015/b015940/b01594030.png ; $i = 0 , \dots , m$ ; confidence 0.506
@@ Line 90: / Line 90: @@
 . https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002030.png ; $K [ f _ { 1 } , \ldots , f _ { d } ]$ ; confidence 0.506
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f1302409.png ; $\langle a b | c d e \rangle \rangle = \langle \langle a b c \rangle \rangle + \varepsilon \langle c | b a d \rangle e \rangle + \langle c d \langle a b e \rangle \rangle$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f1302409.png ; $\langle a b \lanlge c d e \rangle \rangle = \langle \langle a b c \rangle \rangle + \varepsilon \langle c \langle b a d \rangle e \rangle + \langle c d \langle a b e \rangle \rangle,$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p12017019.png ; $\overline { X } = ( A , B )$ ; confidence 0.506
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p12017019.png ; $\hat { X } = ( A , B )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/m/m130/m130130/m13013090.png ; $m _ { i j } \in \{ 0,1 \}$ ; confidence 0.505
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001010.png ; $U ( g ) \varphi ; ( f ) U ( g ^ { - 1 } )$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001010.png ; $U ( g ) \varphi_j ( f ) U ( g ^ { - 1 } )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240547.png ; $T ^ { 2 }$ ; confidence 0.505
@@ Line 104: / Line 104: @@
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200234.png ; $1 = | z _ { 1 } | \geq \ldots \geq | z _ { n } | > 0$ ; confidence 0.505
-. 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/a1300103.png ; $( - ) ^ { * } : \cal C ^ { \text{op} } \rightarrow C$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040367.png ; $\tilde { \Omega }$ ; confidence 0.505
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013055.png ; $M = M \Lambda ^ { t }$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013055.png ; $\Lamda M = M \Lambda ^ { t }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130050/f13005048.png ; $S \subset M ^ { x }$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130050/f13005048.png ; $S \subset M ^ { n }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/k/k130/k130060/k1300602.png ; $\left( \begin{array} { c } { [ n ] } \\ { k } \end{array} \right) : = \{ X \subseteq [ n ] : | X | = k \}$ ; confidence 0.505
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060159.png ; $S _ { Y }$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060159.png ; $S _ { \text{V} }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012028.png ; $\beta j > 0$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012028.png ; $\beta_j > 0$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f120150203.png ; $\{ B x _ { x } \}$ ; confidence 0.505
@@ Line 124: / Line 124: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b13029038.png ; $B = k [ [ X _ { 1 } , \dots , X _ { d } , Y _ { 1 } , \dots , Y _ { d } ]$ ; confidence 0.505
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130040/t13004016.png ; $a _ { x } + 1$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130040/t13004016.png ; $a _ { n + 1 }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030780/d03078032.png ; $n + 2$ ; confidence 0.505
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030780/d03078032.png ; $n / 2$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032015.png ; $Y , Y _ { 1 } , Y _ { 2 } , \dots$ ; confidence 0.505
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120030/d1200304.png ; $\{ y _ { N } \}$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120030/d1200304.png ; $\{ y _ { n } \}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/i/i052/i052040/i052040102.png ; $d _ { 1 } , \dots , d _ { n }$ ; confidence 0.504
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040128.png ; $\phi ^ { \prime }$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040128.png ; $\varphi ^ { \prime }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/k/k130/k130040/k1300409.png ; $\sum _ { i } a _ { i } x _ { i } \leq c$ ; confidence 0.504
@@ Line 140: / Line 140: @@
 . https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700041.png ; $y ( \lambda z z ) \equiv y ( \lambda x x ) \not \equiv w ( \lambda x x )$ ; confidence 0.504
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b1203009.png ; $Y = [ 0,2 \pi [ ^ { N } ]$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b1203009.png ; $Y = [ 0,2 \pi [ ^ { N } $ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130020/h13002080.png ; $( \alpha _ { 1 } , \alpha _ { 2 } , \dots , \alpha _ { q } \cup \gamma ^ { d } ) \in F ( S ^ { d } ) ^ { q }$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130020/h13002080.png ; $( \alpha _ { 1 } , \alpha _ { 2 } , \dots , \alpha _ { q } \cup \gamma ^ { d } ) \in {\cal F} ( S ^ { d } ) ^ { q }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043075.png ; $k ^ { \prime } ( x _ { i } )$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043075.png ; $k ^ { \prime } \langle x _ { i } \rangle$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008051.png ; $E [ T _ { p } ] _ { p R } = \frac { 1 } { 2 ( 1 - \sigma _ { p - 1 } ) ( 1 - \sigma _ { p } ) } \sum _ { k = 1 } ^ { p } \lambda _ { k } b _ { k } ^ { ( 2 ) } + \frac { b _ { p } } { 1 - \sigma _ { p - 1 } }$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008051.png ; $\operatorname{E} [ T _ { p } ] _ {\text{PR} } = \frac { 1 } { 2 ( 1 - \sigma _ { p - 1 } ) ( 1 - \sigma _ { p } ) } \sum _ { k = 1 } ^ { p } \lambda _ { k } b _ { k } ^ { ( 2 ) } + \frac { b _ { p } } { 1 - \sigma _ { p - 1 } }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b130200152.png ; $\Pi ^ { \text { re } }$ ; confidence 0.504
@@ Line 158: / Line 158: @@
 . https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520164.png ; $f = ( \lambda - a ) ^ { s }$ ; confidence 0.504
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120190/e12019071.png ; $a \geq$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120190/e12019071.png ; $a_3$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f12023010.png ; $[ \varphi \otimes x , \psi \otimes Y ] =$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f12023010.png ; $[ \varphi \bigotimes x , \psi \bigotimes Y ] =$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230125.png ; $\frac { - 1 } { k ! ( 1 - 1 ) ! } \times \times \sum _ { \sigma } \operatorname { sign } \sigma \omega ( [ K ( X _ { \sigma 1 } , \ldots , X _ { \sigma k } ) , X _ { \sigma ( k + 1 ) } ] , X _ { \sigma ( k + 2 ) } , \ldots )$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230125.png ; $+\frac { - 1 } { k ! ( 1 - 1 ) ! } \times \times \sum _ { \sigma } \operatorname { sign } \sigma \omega ( [ K ( X _ { \sigma 1 } , \ldots , X _ { \sigma k } ) , X _ { \sigma ( k + 1 ) } ] , X _ { \sigma ( k + 2 ) } , \ldots )+$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013049.png ; $k$ ; confidence 0.504
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180209.png ; $\varepsilon$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180209.png ; $\cal E$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020010.png ; $M _ { 6 } = \operatorname { min } _ { j } | \operatorname { arc } z _ { j } |$ ; confidence 0.504
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008068.png ; $\Delta ( \Lambda , M ) = \text { Det } [ E \otimes \Lambda - A \otimes M ] =$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008068.png ; $\Delta ( \Lambda , M ) = \text { Det } [ E \bigotimes \Lambda - A \bigotimes M ] =$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g130040104.png ; $\partial S ( \phi ) = S ( d \phi )$ ; confidence 0.504
@@ Line 176: / Line 176: @@
 . https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002067.png ; $\mu ( A ) = | A |$ ; confidence 0.504
-. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520213.png ; $GL _ { S } ( K )$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520213.png ; $\operatorname{GL} _ { s } ( K )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/p/p120/p120130/p12013045.png ; $T$ ; confidence 0.504
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006039.png ; $E _ { 1 } = E _ { 0 } + \int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle | ^ { 2 } } { E _ { 1 } - \lambda } d \lambda < 0$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006039.png ; $E _ { 1 } = E _ { 0 } + \int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle | ^ { 2 } } { E _ { 1 } - \lambda } d \lambda < 0.$ ; confidence 0.504
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120190/w12019036.png ; $R _ { x } ^ { 3 N } \times R _ { p } ^ { 3 N }$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120190/w12019036.png ; ${\bf R} _ { x } ^ { 3 N } \times {\bf R} _ { p } ^ { 3 N }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150111.png ; $E _ { P _ { n } } ( d ) = E _ { P _ { n } } ( d ^ { * } )$ ; confidence 0.504
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150111.png ; $\operatorname{E} _ { \operatorname{P} _ { n } } ( d ) = \operatorname{E} _ { \operatorname{P}_ { n } } ( d ^ { * } )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b120310100.png ; $\delta > ( 3 n - 2 ) / 6$ ; confidence 0.503
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f13024043.png ; $\left( \begin{array} { c c } { L ( \alpha , b ) } & { 0 } \\ { 0 } & { \varepsilon L ( b , \alpha ) } \end{array} \right)$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f13024043.png ; $\left( \begin{array} { c c } { L ( a , b ) } & { 0 } \\ { 0 } & { \varepsilon L ( b , a ) } \end{array} \right);$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t1202009.png ; $M _ { 5 } = \operatorname { max } _ { j } | b _ { j } |$ ; confidence 0.503
@@ Line 194: / Line 194: @@
 . https://www.encyclopediaofmath.org/legacyimages/h/h047/h047390/h047390136.png ; $P _ { + } T P _ { - }$ ; confidence 0.503
-. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008092.png ; $= - J - k _ { B } \operatorname { Tn } \{ \operatorname { cosh } ( \frac { H } { k _ { B } T } ) + + [ \operatorname { sinh } ^ { 2 } ( \frac { H } { k _ { B } T } ) + \operatorname { exp } ( - \frac { 4 J } { k _ { B } T } ) ] ^ { 1 / 2 }$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008092.png ; $= - J - k _ { B }T \operatorname { ln } \{ \operatorname { cosh } ( \frac { H } { k _ { B } T } ) + + [ \operatorname { sinh } ^ { 2 } ( \frac { H } { k _ { B } T } ) + \operatorname { exp } ( - \frac { 4 J } { k _ { B } T } ) ] ^ { 1 / 2 }\],$ ; confidence 0.503
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130220/a13022022.png ; $\tilde { h } : Z \rightarrow B$ ; confidence 0.503
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010233.png ; $\lambda$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010233.png ; $\lambda_j$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420122.png ; $y \in H$ ; confidence 0.503
-. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031990/d03199091.png ; $R _ { 1 }$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031990/d03199091.png ; $R _ { L }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c110/c110420/c11042010.png ; $a \in B$ ; confidence 0.503
@@ Line 208: / Line 208: @@
 . https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090218.png ; $g \in \operatorname { Gal } ( k _ { \infty } ^ { \prime } / k )$ ; confidence 0.503
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120030/q12003016.png ; $( \epsilon \otimes id _ { A } ) \circ L = id _ { A }$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120030/q12003016.png ; $( \epsilon \bigotimes \operatorname{id} _ { A } ) \circ L = \operatorname{id} _ { A }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130060/h13006042.png ; $u _ { N }$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130060/h13006042.png ; $u . v$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120090/l120090115.png ; $q _ { H _ { 2 } } \circ \mu = q _ { A _ { 1 } }$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120090/l120090115.png ; $q _ { A_ { 2 } } \circ \mu = q _ { A _ { 1 } }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110010/l11001070.png ; $P P \subseteq P$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110010/l11001070.png ; $P .P \subseteq P$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022081.png ; $D _ { \xi } = ( 1 , \xi _ { 1 } , \dots , \xi _ { N } , | \xi | ^ { 2 } / 2 ) R _ { + }$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022081.png ; $D _ { \xi } = ( 1 , \xi _ { 1 } , \dots , \xi _ { N } , | \xi | ^ { 2 } / 2 )\bf R _ { + }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015010/b0150106.png ; $\xi : X \rightarrow B O _ { N }$ ; confidence 0.503
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015010/b0150106.png ; $\xi : X \rightarrow B O _ { n }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/k/k055/k055780/k05578014.png ; $\times \int _ { 0 } ^ { \alpha } [ K _ { i \tau } ( \alpha ) I _ { i \tau } ( x ) - I _ { i \tau } ( \alpha ) K _ { i \tau } ( x ) ] f ( x ) \frac { d x } { x }$ ; confidence 0.502
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051092.png ; $O ( | M + | E | )$ ; confidence 0.502
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051092.png ; $O ( | V |+ | E | )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004046.png ; $h _ { \lambda _ { i } }$ ; confidence 0.502
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120020/c12002063.png ; $\int _ { S O ( n ) } d \gamma \int _ { 0 } ^ { \infty } \frac { f ^ { * } \mu _ { \gamma , t } } { t } d t = c _ { \mu } f$ ; confidence 0.502
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120020/c12002063.png ; $\int _ { \operatorname{SO} ( n ) } d \gamma \int _ { 0 } ^ { \infty } \frac { f ^ { * } \mu _ { \gamma , t } } { t } d t = c _ { \mu } f.$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170177.png ; $W h ^ { x }$ ; confidence 0.502
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170177.png ; $\operatorname{Wh} ^ { * }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120490/b12049048.png ; $m _ { N } : A \rightarrow [ 0 , + \infty )$ ; confidence 0.502
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120490/b12049048.png ; $m _ { n } : {\cal A} \rightarrow [ 0 , + \infty )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f130090105.png ; $j = 1 , \dots , k$ ; confidence 0.502
@@ Line 238: / Line 238: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130230/a13023062.png ; $X = C ( S \times T )$ ; confidence 0.502
-. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013990/a0139904.png ; $= X$ ; confidence 0.502
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013990/a0139904.png ; $\operatorname{E} X$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c13016081.png ; $C = \operatorname { coc }$ ; confidence 0.502
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c13016081.png ; ${\cal C} = \operatorname { co }\cal C$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a014/a014190/a01419091.png ; $x \in U$ ; confidence 0.502
@@ Line 248: / Line 248: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d130/d130170/d13017067.png ; $\lambda _ { 1 } ( \Omega ) \geq \frac { a } { r _ { \Omega } ^ { 2 } }$ ; confidence 0.502
-. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861058.png ; $Sp ( n )$ ; confidence 0.502
+. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861058.png ; $\operatorname{Sp} ( n )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030072.png ; $K _ { 1 } ( O _ { N } ) = 0$ ; confidence 0.502
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030072.png ; $K _ { 1 } ( {\cal O} _ { n } ) = 0$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002010.png ; $e ^ { \pi z }$ ; confidence 0.502
@@ Line 256: / Line 256: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040153.png ; $\tilde { \Omega } _ { S 5 } T$ ; confidence 0.501
-. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046280/h046280183.png ; $\{ f , \}$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046280/h046280183.png ; $\{ f_j \}$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s13062098.png ; $q \in L ^ { 1 } ( 0 , \infty )$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s13062098.png ; $q \in L ^ { 1 } ( 0 , \infty )$ ; confidence 0.501 NOTE: should the bracket be also closed?
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007049.png ; $\operatorname { GCD } ( \alpha , b ) = 1$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007049.png ; $\operatorname { GCD } ( a , b ) = 1$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/p/p120/p120140/p12014053.png ; $m$ ; confidence 0.501
@@ Line 266: / Line 266: @@
 . https://www.encyclopediaofmath.org/legacyimages/n/n120/n120120/n12012016.png ; $\operatorname { size } ( x ) = n$ ; confidence 0.501
-. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n06752038.png ; $a _ { i + 1 }$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n06752038.png ; $d _ { i + 1 }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042083.png ; $q \in k$ ; confidence 0.501
@@ Line 272: / Line 272: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d030/d030020/d030020252.png ; $Z \subset X$ ; confidence 0.501
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006062.png ; $\rho ^ { 2 / 3 } = \Phi$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006062.png ; $\gamma \rho ^ { 2 / 3 } = \Phi$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130010/c13001041.png ; $\frac { \partial c } { \partial t } = \operatorname { div } \{ M \operatorname { grad } [ f _ { 0 } ^ { \prime } ( c ) - 2 \kappa \Delta c ] \} \text { in } V$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130010/c13001041.png ; $\frac { \partial c } { \partial t } = \operatorname { div } \{ M \operatorname { grad } [ f _ { 0 } ^ { \prime } ( c ) - 2 \kappa \Delta c ] \} \text { in } V,$ ; confidence 0.501
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120530/b1205304.png ; $K ( , s ) \in L ^ { 1 } ( \mu )$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120530/b1205304.png ; $K ( ., s ) \in L ^ { 1 } ( \mu )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120110/a1201107.png ; $\varphi ( \alpha , b , 1 ) = \alpha b$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120110/a1201107.png ; $\varphi ( a , b , 1 ) = a. b$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c120300105.png ; $K = e ^ { - \beta h } \in T _ { 1 } ( H )$ ; confidence 0.501
-. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130100/l13010012.png ; $p \in R$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130100/l13010012.png ; $p \in \bf R$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240441.png ; $\beta _ { 1 } , \ldots , \beta _ { p }$ ; confidence 0.501
-. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120100/k12010069.png ; $( 1 + a ) ^ { - 1 } = 1 - a + a ^ { 2 } - a ^ { 3 } +$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120100/k12010069.png ; $( 1 + a ) ^ { - 1 } = 1 - a + a ^ { 2 } - a ^ { 3 } +\dots$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/f/f130/f130070/f13007014.png ; $F ( 2,2 n ) = \pi _ { 1 } ( M _ { n } )$ ; confidence 0.501
@@ Line 292: / Line 292: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021046.png ; $\lambda _ { 1 } + j , \ldots , \lambda _ { \nu } + j$ ; confidence 0.501
-. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t0940807.png ; $\pi _ { N } ( X ; A , B , x _ { 0 } )$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t0940807.png ; $\pi _ { n } ( X ; A , B , x _ { 0 } )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b13029013.png ; $1 _ { A } ( M / q M )$ ; confidence 0.501
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b13029013.png ; ${\bf l} _ { A } ( M / q M )$ ; confidence 0.501
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130020/f13002017.png ; $\delta _ { BDST } ^ { 2 } = 0$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130020/f13002017.png ; $\delta _ { \text{BRST} } ^ { 2 } = 0$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/h/h120/h120070/h12007056.png ; $0 < m \leq n$ ; confidence 0.500
-. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054420/j05442077.png ; $\overline { P }$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054420/j05442077.png ; $\tilde {\cal  P }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042039.png ; $V _ { 1 } \otimes \ldots \otimes V _ { n } \rightarrow V _ { \sigma ( 1 ) } \otimes \ldots \otimes V _ { \sigma ( n ) }$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042039.png ; $V _ { 1 } \bigotimes \ldots \bigotimes V _ { n } \rightarrow V _ { \sigma ( 1 ) } \bigotimes \ldots \bigotimes V _ { \sigma ( n ) }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130040/q1300405.png ; $W _ { loc } ^ { 1 , n } ( G )$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130040/q1300405.png ; $W _ { \text{loc} } ^ { 1 , n } ( G )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a011/a011670/a01167078.png ; $x _ { 1 } , \dots , x _ { r }$ ; confidence 0.500
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042097.png ; $2 + 2 z$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042097.png ; ${\bf Z} + 2 {\bf Z}$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065043.png ; $\psi _ { n } ( z ) = \frac { 1 } { 2 \pi } \int _ { - \pi } ^ { \pi } R ( e ^ { i \theta } , z ) [ \phi _ { n } ( e ^ { i \theta } ) - \phi _ { n } ( z ) ] d \mu ( \theta )$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065043.png ; $\psi _ { n } ( z ) = \frac { 1 } { 2 \pi } \int _ { - \pi } ^ { \pi } R ( e ^ { i \theta } , z ) [ \phi _ { n } ( e ^ { i \theta } ) - \phi _ { n } ( z ) ] d \mu ( \theta ).$ ; confidence 0.500
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021027.png ; $\wedge ^ { k } ( a )$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021027.png ; $\wedge ^ { k } (\frak a )$ ; confidence 1.000
-. 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/a130240336.png ; $\bf Z = X \Gamma + F$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i130060185.png ; $< 2 a$ ; confidence 0.500
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042085.png ; $\theta$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042085.png ; $\operatorname{Vec}_n$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240356.png ; $E ( Z _ { 1 } ) = 0$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240356.png ; $\operatorname{E} ( Z _ { 1 } ) = 0$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240272.png ; $q ^ { - 1 } \sum _ { i = 1 } ^ { q } ( z _ { i } - \zeta _ { i } ) ^ { 2 } / MS _ { e }$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240272.png ; $q ^ { - 1 } \sum _ { i = 1 } ^ { q } ( z _ { i } - \zeta _ { i } ) ^ { 2 } / \operatorname{MS} _ { e }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230117.png ; $\pi r$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230117.png ; $TT'$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020093.png ; $\{ D ^ { \lambda } : \lambda \text { ap\square regular partition of } n$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020093.png ; $\{ D ^ { \lambda } : \lambda \text { a $p\square$  regular partition of } n\}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c022/c022110/c02211027.png ; $( x _ { 0 } , x _ { 1 } ] , \ldots , ( x _ { k } - 1 , x _ { k } )$ ; confidence 0.500
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140151.png ; $\operatorname { prin } K l$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140151.png ; $\operatorname { prin } K I$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020025.png ; $\operatorname { sup } _ { z _ { 1 } , \ldots , z _ { n } \in U } \operatorname { min } _ { k \in S } \frac { | \sum _ { j = 1 } ^ { n } b _ { j } z _ { j } ^ { k } | } { M _ { \phi } ( k ) }$ ; confidence 0.500
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020025.png ; $\operatorname { sup } _ { z _ { 1 } , \ldots , z _ { n } \in U } \operatorname { min } _ { k \in S } \frac { | \sum _ { j = 1 } ^ { n } b _ { j } z _ { j } ^ { k } | } { M _ { d } ( k ) }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l13008030.png ; $I + ( P _ { 1 } , \dots , P _ { m } )$ ; confidence 0.499
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130110/s13011018.png ; $I ( w )$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130110/s13011018.png ; ${\bf l} ( w )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090116.png ; $\Delta ( \lambda ) = K GL _ { n } ( K ) z _ { \lambda }$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090116.png ; $\Delta ( \lambda ) = K \operatorname{GL} _ { n } ( K ) z _ { \lambda },$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005032.png ; $X , X D$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005032.png ; $x,x_0$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l12012093.png ; $V _ { \operatorname { sin } p } ( O _ { K , p } ) \neq \emptyset$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l12012093.png ; $V _ { \text { simp } } ( O _ { K , p } ) \neq \emptyset$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067170/n06717077.png ; $t \in R +$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067170/n06717077.png ; $t \in {\bf R}_ +$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051320/i05132021.png ; $\pi$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051320/i05132021.png ; $\pi '$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200104.png ; $m$ ; confidence 0.499
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120360/b12036014.png ; $P ( E _ { l } ) = \frac { \operatorname { exp } ( - E _ { l } / k _ { B } T ) } { \sum _ { l } \operatorname { exp } ( - E _ { l } / k _ { B } T ) }$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120360/b12036014.png ; $P ( E _ { l } ) = \frac { \operatorname { exp } ( - E _ { l } / k _ { B } T ) } { \sum _ { l } \operatorname { exp } ( - E _ { l } / k _ { B } T ) }.$ ; confidence 0.499
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180190.png ; $C A$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180190.png ; $\bf C A$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130010/m13001023.png ; $x _ { i } \in X$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130010/m13001023.png ; $x _ { i } \in \cal X$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120160/b12016044.png ; $x _ { j } ^ { \prime } = \sum _ { i , k } c _ { i k } f _ { i } f _ { k }$ ; confidence 0.499
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230108.png ; $X : = U \wedge V$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230108.png ; $X : = U \Lambda V,$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017067.png ; $k ( 0 ) = 1$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017067.png ; $k ( 0 ) = I$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q1200102.png ; $G = SL ( 2 , C ) \times R ^ { 4 }$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q1200102.png ; $G = \operatorname{SL} ( 2 , {\bf C} ) \rtimes {\bf R} ^ { 4 }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120010/j12001061.png ; $a \neq b \in C ^ { n }$ ; confidence 0.499
+. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120010/j12001061.png ; $a \neq b \in {\bf C} ^ { n }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011098.png ; $p ( n )$ ; confidence 0.498
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011098.png ; $\operatorname{ Mp } ( n )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120120/w12012029.png ; $F$ ; confidence 0.498
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120120/w12012029.png ; $C_{abcd}$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050206.png ; $\sum _ { n \leq x } G _ { K } ( n ) = A _ { K } x + O ( x ^ { \eta } K ) \text { as } x \rightarrow \infty$ ; confidence 0.498
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050206.png ; $\sum _ { n \leq x } G _ { K } ( n ) = A _ { K } x + O ( x ^ { \eta_K} ) \text { as } x \rightarrow \infty,$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o13008029.png ; $q _ { m } \in L _ { 1,1 }$ ; confidence 0.498
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007051.png ; $GL _ { n } ( Z A )$ ; confidence 0.498
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007051.png ; $\operatorname{GL} _ { n } ( {\bf Z} A )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l057000130.png ; $M : \sigma$ ; confidence 0.498
@@ Line 382: / Line 382: @@
 . https://www.encyclopediaofmath.org/legacyimages/m/m120/m120010/m12001047.png ; $\overline { T G }$ ; confidence 0.498
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007045.png ; $f \in L ^ { 1 } ( R ^ { 2 n } )$ ; confidence 0.498
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007045.png ; $f \in L ^ { 1 } ( {\bf R} ^ { 2 n } )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130100/b1301008.png ; $K _ { Z } \in H$ ; confidence 0.498
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040234.png ; $E ( \Gamma , \Delta ) \dagger _ { D } \epsilon _ { i } ( \varphi , \psi )$ ; confidence 0.498
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040234.png ; $E ( \Gamma , \Delta ) \dashv _ {\cal  D } \epsilon _ { i } ( \varphi , \psi )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b130200204.png ; $O _ { s } + 2,2 ( R )$ ; confidence 0.498
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b130200204.png ; $O _ { s + 2,2} (\bf R )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e035000111.png ; $I _ { \epsilon } ( X )$ ; confidence 0.498
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140157.png ; $\chi _ { K I } : K _ { 0 } ( \operatorname { prin } K l ) \rightarrow Z$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140157.png ; $\chi _ { K I } : K _ { 0 } ( \operatorname { prin } K I ) \rightarrow \bf Z$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004098.png ; $P _ { K _ { + } } ( v , z ) - P _ { K _ { - } } ( v , z ) \equiv \operatorname { lk } ( K _ { 0 } ) \operatorname { mod } ( v ^ { 2 } - 1 , z )$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004098.png ; $\operatorname{P} _ { K _ { + } } ( v , z ) - \operatorname{P} _ { K _ { - } } ( v , z ) \equiv \operatorname { lk } ( K _ { 0 } ) \operatorname { mod } ( v ^ { 2 } - 1 , z )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120090/l12009094.png ; $[ P , ] _ { A }$ ; confidence 0.497
@@ Line 400: / Line 400: @@
 . https://www.encyclopediaofmath.org/legacyimages/l/l110/l110010/l110010105.png ; $P = \cap _ { i \in I } P _ { i }$ ; confidence 0.497
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010330/a0103302.png ; $| X | ^ { \prime }$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010330/a0103302.png ; $| X | ^ { r }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f1300902.png ; $\left. \begin{array} { l } { U _ { 0 } ( x ) = 0 } \\ { U _ { 1 } ( x ) = 1 } \\ { U _ { n } ( x ) = x U _ { n - 1 } ( x ) + U _ { n - 2 } ( x ) , \quad n = 2,3 } \end{array} \right.$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f1300902.png ; $\left. \begin{cases} { U _ { 0 } ( x ) = 0 } \\ { U _ { 1 } ( x ) = 1 } \\ { U _ { n } ( x ) = x U _ { n - 1 } ( x ) + U _ { n - 2 } ( x ) , \quad n = 2,3 } \end{cases} \right.$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k0558403.png ; $[ , ] : K \times K \rightarrow C$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k0558403.png ; $[ .,. ] : \cal K \times K \rightarrow \bf C$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/h/h046/h046020/h0460208.png ; $\| F \| _ { \infty } = \operatorname { esssup } _ { \omega } | F ( i \omega ) |$ ; confidence 0.497
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012072.png ; $\operatorname { lim } _ { N \rightarrow \infty } \| f - f _ { N } \| _ { A } ^ { * } = 0$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012072.png ; $\operatorname { lim } _ { N \rightarrow \infty } \| f - f _ { N } \| _ { \cal A ^ { * } }= 0.$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130300/a13030052.png ; $( E _ { n } : n \in Z ^ { + } )$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130300/a13030052.png ; $( E _ { n } : n \in {\bf Z} ^ { + } )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120060/w12006086.png ; $T _ { A } \xi = \kappa _ { M } \circ T _ { A } \xi$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120060/w12006086.png ; ${\cal T} _ { A } \xi = \kappa _ { M } \circ T _ { A } \xi.$ ; confidence 1.000
-. 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/k13001035.png ; $f ( \overset{\rightharpoonup}{ D } ( A ) ) = ( - A ^ { 3 } ) ^ { - \operatorname { Tait } ( \overset{\rightharpoonup}{ D } ) } ( D )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/i/i050/i050430/i0504302.png ; $a _ { 1 } , \dots , a _ { r }$ ; confidence 0.497
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032040.png ; $E ( Y ) = 2 \theta - 1$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032040.png ; $\operatorname{E} ( Y ) = 2 \theta - 1$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/m/m120/m120120/m120120102.png ; $u \in Q _ { 1 } ( R )$ ; confidence 0.497
-. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008075.png ; $P = ( P _ { s s ^ { \prime } } ) = ( \langle S | P | S ^ { \prime } \rangle )$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008075.png ; ${\cal P} = ( P _ { s s ^ { \prime } } ) = ( \langle S | {\cal P} | S ^ { \prime } \rangle )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130050/h13005020.png ; $\psi _ { N } \in L ^ { 2 } ( - \infty , \infty )$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130050/h13005020.png ; $\psi _ { n } \in L ^ { 2 } ( - \infty , \infty )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240445.png ; $y _ { 1 } , \dots , y _ { p }$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240445.png ; ${\bf y} _ { 1 } , \dots , {\bf y} _ { p }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090183.png ; $L _ { p } ( 1 - n , \chi ) = L ( 1 - n , \chi \omega ^ { - n } ) \prod _ { p | p } ( 1 - \chi \omega ^ { - n } ( p ) N p ^ { n - 1 } )$ ; confidence 0.497
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090183.png ; $L _ { p } ( 1 - n , \chi ) = L ( 1 - n , \chi \omega ^ { - n } ) \prod _ { {\frak p} | p } ( 1 - \chi \omega ^ { - n } ( {\frak p} ) N {\frak p} ^ { n - 1 } )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b130200186.png ; $\rho \in \mathfrak { h } ^ { * }$ ; confidence 0.496
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064074.png ; $E ( a ) = \operatorname { exp } ( \int _ { 0 } ^ { \infty } t s ( t ) s ( - t ) d t )$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064074.png ; $E ( a ) = \operatorname { exp } ( \int _ { 0 } ^ { \infty } t \hat{s} ( t ) \hat{s} ( - t ) d t ).$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/m/m130/m130220/m13022032.png ; $\rho _ { d }$ ; confidence 0.496
@@ Line 442: / Line 442: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d130/d130170/d13017046.png ; $\sum _ { i = 1 } ^ { k } \lambda _ { i } \geq \frac { n } { n + 2 } \frac { 4 \pi ^ { 2 } k ^ { 1 + 2 / n } } { ( C _ { n } | \Omega | ) ^ { 2 / n } } k = 1,2 , \ldots$ ; confidence 0.496
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120240/m1202401.png ; $\psi _ { X y } + u ( x , y ) \psi = 0$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120240/m1202401.png ; $\psi _ { x y } + u ( x , y ) \psi = 0$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130030/j13003023.png ; $x , b , x , y , z \in E$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130030/j13003023.png ; $a, b , x , y , z \in E$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130190/m13019047.png ; $M _ { n } = \operatorname { det } M _ { n }$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130190/m13019047.png ; ${\cal M} _ { n } = \operatorname { det } M _ { n }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042013.png ; $\Phi : ( \otimes ) \otimes \rightarrow \otimes ( \varnothing )$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042013.png ; $\Phi : ( \otimes ) \otimes \rightarrow \otimes ( \otimes )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120020/e12002023.png ; $74$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120020/e12002023.png ; ${\cal H} *$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130310/a13031041.png ; $22$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130310/a13031041.png ; ${\cal Q}_2$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022020.png ; $D ^ { \alpha } = D _ { 1 } ^ { \alpha _ { 1 } } \ldots D _ { N } ^ { \alpha _ { N } }$ ; confidence 0.496
@@ Line 458: / Line 458: @@
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c12017084.png ; $r \equiv \operatorname { rank } M ( n )$ ; confidence 0.496
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120310/a12031042.png ; $k$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120310/a12031042.png ; $E$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130100/p13010092.png ; $p \in R$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130100/p13010092.png ; $p \in \hat{K}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004051.png ; $P _ { M } ( v ) \neq 0$ ; confidence 0.496
-. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700064.png ; $( \lambda x y \cdot y x ) A B = B A$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700064.png ; $( \lambda x y . y x ) A B = B A$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130070/f13007027.png ; $F ( 2,2 n ) \subset \operatorname { PSL } _ { 2 } ( C )$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130070/f13007027.png ; $F ( 2,2 n ) \subset \operatorname { PSL } _ { 2 } ( {\bf C} )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020110.png ; $\| X \| _ { * } \leq 1$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020110.png ; $\| X \|  { * } \leq 1$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a13004042.png ; $\operatorname { Th } D$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a13004042.png ; $\operatorname { Th } \cal D$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120030/b12003049.png ; $\| t g ( t ) \| _ { 2 } \| \gamma g ( \gamma ) \| _ { 2 } = \infty$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120030/b12003049.png ; $\| t g ( t ) \| _ { 2 } \| \gamma \tilde{g} ( \gamma ) \| _ { 2 } = \infty$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120100/b12010036.png ; $U ^ { ( n ) } t = \sum _ { k = 0 } ^ { n } \frac { ( - 1 ) ^ { k } } { k ! ( n - k ) ! } S ^ { s + n - k } ( - t , x _ { 1 } , \dots , x _ { s } + x - k )$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120100/b12010036.png ; $U ^ { ( n )_ t} = \sum _ { k = 0 } ^ { n } \frac { ( - 1 ) ^ { k } } { k ! ( n - k ) ! } S ^ { s + n - k } ( - t , x _ { 1 } , \dots , x _ { s  + n - k} )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120110/m12011070.png ; $( F ^ { x } , h : F \rightarrow F ) \rightarrow T ( h )$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120110/m12011070.png ; $( F ^ { n } , h : F \rightarrow F ) \rightarrow T ( h )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120140/b12014042.png ; $s _ { i } ( z )$ ; confidence 0.496
@@ Line 482: / Line 482: @@
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120200/c12020067.png ; $S ^ { n } \times S ^ { m }$ ; confidence 0.496
-. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120100/k12010025.png ; $\{ t = t ; \} \cup K$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120100/k12010025.png ; $\{ t = t_j \} \cup K$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023042.png ; $X \sim N _ { p , n } ( 0 , \Sigma \otimes I _ { n } )$ ; confidence 0.495
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031082.png ; $R S _ { R } ^ { ( n - 1 ) / 2 } f ( 0 ) = + \infty$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031082.png ; $\operatorname{lim\,sup}_R S _ { R } ^ { ( n - 1 ) / 2 } f ( 0 ) = + \infty$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001024.png ; $X _ { t } \sim X - t$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001024.png ; ${\cal X} _ { t } \sim {\cal X}_{ - t }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014060/a014060109.png ; $a \geq$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014060/a014060109.png ; $a _2$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b017470223.png ; $\pi$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b017470223.png ; $\tilde{\omega}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c022/c022110/c0221105.png ; $X ^ { 2 } = \sum _ { i = 1 } ^ { k } \frac { ( \nu _ { i } - n p _ { i } ) ^ { 2 } } { n p _ { i } } = \frac { 1 } { n } \sum \frac { \nu _ { i } ^ { 2 } } { p _ { i } } - n , \quad n = \nu _ { 1 } + \ldots + \nu _ { k }$ ; confidence 0.495
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001018.png ; $\varphi ; ( f )$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001018.png ; $\varphi_j ( f )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120070/d1200706.png ; $a _ { 1 } , \dots , a _ { t }$ ; confidence 0.495
@@ Line 502: / Line 502: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120270/s12027035.png ; $f \in A _ { s } ^ { + }$ ; confidence 0.495
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130010/j13001017.png ; $( D )$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130010/j13001017.png ; $\operatorname{lbl} ( D )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t120060128.png ; $- ( \text { const } ) \int _ { R ^ { 3 } } \rho ( x ) ^ { 4 / 3 } d x$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t120060128.png ; $- ( \text {const} ) \int _ { {\bf R} ^ { 3 } } \rho ( x ) ^ { 4 / 3 } d x$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520275.png ; $h \in H$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520275.png ; $h \in \cal  H$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120010/e120010124.png ; $( G m _ { i } ) \circ f = ( G f _ { i } ) \circ e$ ; confidence 0.495
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011095.png ; $K \subset D ^ { \gamma }$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011095.png ; $K \subset D ^ { n }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120270/s12027018.png ; $S _ { m } [ f ] = \sum _ { v = 1 } ^ { m } b _ { v , m } f ( y v , m )$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120270/s12027018.png ; $S _ { m } [ f ] = \sum _ { v = 1 } ^ { m } b _ { v , m } f ( y_{v , m} )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010050.png ; $\hat { \Delta }$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010050.png ; $\overset{\rightharpoonup} { \Delta }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a12013064.png ; $\theta _ { n } ^ { * }$ ; confidence 0.495
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003098.png ; $M = \int ( \partial / \partial e ) \eta ( \vec { x } , e ) \vec { x X } ^ { t } d H _ { \vec { \theta } } ( \vec { x } , y )$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003098.png ; $M = \int ( \partial / \partial e ) \eta ( \overset{\rightharpoonup}  { x } , e ) \overset{\rightharpoonup}  { x } \overset{\rightharpoonup} {X } ^ { t } d H _ { \overset{\rightharpoonup} { \theta } } ( \overset{\rightharpoonup}  { x } , y )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008050.png ; $\frac { d \operatorname { ln } g ( L ; m , s ) } { d m } \frac { d \operatorname { ln } g ( R ; m , s ) } { d s }$ ; confidence 0.495
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130440/s13044027.png ; $H ^ { N - 1 - k } ( S ^ { x } \backslash X )$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130440/s13044027.png ; $H ^ { N - 1 - k } ( S ^ { n } \backslash X )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010283.png ; $i = 0 , \ldots , n - 1$ ; confidence 0.495
@@ Line 528: / Line 528: @@
 . https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020119.png ; $\int _ { \partial D } \operatorname { exp } ( \varepsilon | \varphi ( e ^ { i \vartheta } ) - \varphi _ { I } | ) d \vartheta$ ; confidence 0.495
-. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120030/n12003030.png ; $S _ { A } : A \times L A \rightarrow L A$ ; confidence 0.495
+. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120030/n12003030.png ; $s _ { A } : A \times L A \rightarrow L A$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c1202806.png ; $( X _ { n } ) _ { n } > 0$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c1202806.png ; $( X _ { n } ) _ { n \geq 0}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d1202902.png ; $\varphi ( q )$ ; confidence 0.494
-. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120050/k12005058.png ; $X = P ^ { d }$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120050/k12005058.png ; $X = {\bf P} ^ { d }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i1300604.png ; $u ( x , k ) = e ^ { i \delta } \operatorname { sin } ( k x + \delta ) + o ( 1 ) , \quad \text { as } x \rightarrow \infty$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i1300604.png ; $u ( x , k ) = e ^ { i \delta } \operatorname { sin } ( k x + \delta ) + o ( 1 ) , \quad \text { as } x \rightarrow \infty.$ ; confidence 0.494
-. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520451.png ; $\lambda _ { i } < 0$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520451.png ; $\operatorname{Re} \lambda _ { i } < 0$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023081.png ; $\Omega \subset C ^ { x }$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023081.png ; $\Omega \subset {\bf C} ^ { n }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s12032055.png ; $F _ { k }$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s12032055.png ; ${\cal F} _ { k }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057020/l05702080.png ; $i \neq p$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057020/l05702080.png ; $l \neq p$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/z/z120/z120010/z1200106.png ; $\{ e _ { i } : - 1 \leq i \leq p ^ { m } - 2 \}$ ; confidence 0.494
-. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120040/y12004016.png ; $T ( \nu ) = \operatorname { lim } _ { j \rightarrow \infty } I ( u _ { j } )$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120040/y12004016.png ; $\tilde{i} ( \nu ) = \operatorname { lim } _ { j \rightarrow \infty } I ( u _ { j } )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020030/c02003032.png ; $V ^ { 1 } , V ^ { 2 } , \dots$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020030/c02003032.png ; $V ^ { 1 } , V ^ { 2 } , \dots,$ ; confidence 0.494
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120140/d12014071.png ; $V _ { f } = \{ f ( a ) : a \in F _ { q } \}$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120140/d12014071.png ; $V _ { f } = \{ f ( a ) : a \in {\bf F} _ { q } \}$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013098.png ; $x$ ; confidence 0.494
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013098.png ; $\operatorname{coh} \bf X$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011060.png ; $\frac { \mu _ { n } ( x ) } { \mu _ { n } } \stackrel { P } { \rightarrow } \alpha ( x ) = - \int _ { 0 } ^ { \infty } \frac { \lambda ^ { x } e ^ { - \lambda } } { x ! } R ( d \lambda )$ ; confidence 0.493
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011060.png ; $\frac { \mu _ { n } ( x ) } { \mu _ { n } } \stackrel { \operatorname{P} } { \rightarrow } \alpha ( x ) = - \int _ { 0 } ^ { \infty } \frac { \lambda ^ { x } e ^ { - \lambda } } { x ! } R ( d \lambda )$ ; confidence 0.493
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011039.png ; $x = 1 , \dots , f ( 1 , n )$ ; confidence 0.493
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011039.png ; $x = 1 , \dots , f_{( 1 , n )}$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130130/h13013010.png ; $r j > 0$ ; confidence 0.493
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130130/h13013010.png ; $r_j > 0$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005041.png ; $\sigma _ { T } ( A , X ) : = \{ \lambda \in C ^ { n } : A - \lambda \text { is singular } \}$ ; confidence 0.493
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005041.png ; $\sigma _ { T } ( A , {\cal X} ) : = \{ \lambda \in {\bf C} ^ { n } : A - \lambda \text { is singular } \}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e120260135.png ; $\pi _ { v , p } ( d \theta ) P ( \theta , \mu ) ( d x )$ ; confidence 0.493
@@ Line 568: / Line 568: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020052.png ; $P ( t ) = \prod _ { m = 1 } ^ { n } ( t - t _ { m } ) ^ { \gamma _ { m } }$ ; confidence 0.493
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026078.png ; $R ^ { n } \backslash K _ { 2 }$ ; confidence 0.493
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026078.png ; ${\bf R} ^ { n } \backslash K _ { 2 }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023025.png ; $A X \sim \operatorname { RS } _ { q , n } ( \psi )$ ; confidence 0.493
@@ Line 574: / Line 574: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w110/w110060/w11006050.png ; $\Sigma n _ { j } = n$ ; confidence 0.493
-. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110030/l11003082.png ; $M ( E ) = \vec { X }$ ; confidence 0.493
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110030/l11003082.png ; $M ( {\cal E} ) = \dot { X }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015280/b01528024.png ; $A _ { 0 } , \ldots , A _ { N }$ ; confidence 0.493
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015280/b01528024.png ; $A _ { 0 } , \ldots , A _ { n }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180223.png ; $\in A ^ { 2 } \varepsilon \otimes A ^ { 2 } \varepsilon$ ; confidence 0.493
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180223.png ; $\in {\bf A} ^ { 2 } {\cal E} \bigotimes {\bf A} ^ { 2 } {\cal E}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s12032011.png ; $x \otimes y \rightarrow x . y$ ; confidence 0.493
@@ Line 586: / Line 586: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d032/d032150/d03215060.png ; $i = 0 , \ldots , N$ ; confidence 0.492
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230172.png ; $l _ { i } = \delta _ { i } ^ { * } G _ { i } \Theta _ { i } \left( \begin{array} { c } { 1 } \\ { 0 } \end{array} \right) , d _ { i } = | \delta _ { i } | ^ { 2 }$ ; confidence 0.492
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230172.png ; $l _ { i } = \delta _ { i } ^ { * } G _ { i } \Theta _ { i } \left( \begin{array} { c } { 1 } \\ { 0 } \end{array} \right) , d _ { i } = | \delta _ { i } | ^ { 2 }.$ ; confidence 0.492
-. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130060/k13006026.png ; $\alpha _ { 2 } = 1 , \dots , \alpha _ { k - 1 } = k - 2$ ; confidence 0.492
+. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130060/k13006026.png ; $a _ { 2 } = 1 , \dots , a _ { k - 1 } = k - 2$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059018.png ; $M [ z ^ { n } ] = c _ { n } , n = 0 , \pm 1 , \pm 2 , \dots$ ; confidence 0.492
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059018.png ; $M [ z ^ { n } ] = c _ { n } , n = 0 , \pm 1 , \pm 2 , \dots,$ ; confidence 0.492
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b120400101.png ; $G \times ^ { R } V$ ; confidence 0.492
@@ Line 596: / Line 596: @@
 . https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i1200401.png ; $P = \{ ( z _ { 1 } , \dots , z _ { n } ) : | z _ { j } - a _ { j } | < r _ { j } , j = 1 , \dots , n \}$ ; confidence 0.492
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006081.png ; $( g f ( z ) )$ ; confidence 0.492
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006081.png ; $( g, f ( z ) )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120140/e12014029.png ; $f t _ { 1 } \ldots t _ { \rho } ( f ) \in T$ ; confidence 0.492
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120140/e12014029.png ; $f_{ t _ { 1 } \ldots t _ { \rho } ( f )} \in T$ ; confidence 1.000