Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/40"

Revision as of 17:15, 26 April 2020

List

1. ; $D = \{ z : | z | < 1 \}$ ; confidence 0.812

2. ; $ { i } = 1$ ; confidence 1.000

3. ; $\alpha : X _ { .. } \rightarrow X ^ { \prime }$ ; confidence 1.000

4. ; ${\cal M} _ { 0 } = {\cal M} _ { 1 } \supset \ldots \supset {\cal M}_ { 5 }$ ; confidence 1.000

5. ; $K \supset H$ ; confidence 0.812

6. ; $\operatorname{dens} (X )$ ; confidence 1.000

7. ; $\{ r_+ ( k ) : \forall k > 0 \}$ ; confidence 1.000

8. ; $T _ { g ^ { i } }$ ; confidence 0.812

9. ; $a > 0$ ; confidence 0.812

10. ; $2 ^ { S }$ ; confidence 1.000

11. ; $\operatorname{l}$ ; confidence 1.000

12. ; $\forall ( x , y ) \in R _ { k }$ ; confidence 0.812

13. ; $u \in L ^ { 2 } ( [ 0 , T ] ; H ^ { 2 } ( \Omega ) ) \cap H ^ { 2 } ( [ 0 , T ] ; L ^ { 2 } ( \Omega ) )$ ; confidence 0.811

14. ; $\square _ { H } \cal M$ ; confidence 1.000

15. ; $| L | = 1$ ; confidence 0.811

16. ; $Q _ { 0 } = \{ 1 , \ldots , n \}$ ; confidence 0.811

17. ; $\lambda A : = \{ \lambda a : a \in A \}$ ; confidence 1.000

18. ; $X ^ { * } = \operatorname { sup } _ { t \geq 0 } | X _ { t } |$ ; confidence 0.811

19. ; $v _ { 1 } , v _ { 2 } \in \overline { N E } ( X / S )$ ; confidence 0.811

20. ; $\operatorname { gcd } \{ j : p_j > 0 \} = 1$ ; confidence 1.000

21. ; $\operatorname{SU} ( 2 )$ ; confidence 1.000

22. ; ${\cal R }_ { q ^ { 2 } }$ ; confidence 1.000

23. ; $\langle \rho ^ { \prime } ( \xi ) , \xi - p \rangle ^ { \alpha } = \prod _ { j = 0 } ^ { m } \langle \rho ^ { \prime } ( \xi ) , \xi - p _ { j } \rangle ^ { \alpha_j } $ ; confidence 1.000

24. ; $u _ { i } ^ { n + 1 }$ ; confidence 0.811

25. ; $\overline { \square } = \square$ ; confidence 0.811

26. ; $\operatorname{E} [ W ]$ ; confidence 0.811

27. ; $\beta = \operatorname{P} _ { q } ( S _ { N } = - J )$ ; confidence 1.000

28. ; $Z _ { n } ( x ; \sigma )$ ; confidence 0.810

29. ; $X = Y = Z = \bf R$ ; confidence 1.000

30. ; $B = ( b _ { i j } )$ ; confidence 0.810

31. ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { t ( n ) } { s ( n ) } = 0,$ ; confidence 1.000

32. ; $\operatorname { Eis } ( \omega ) = \sum _ { \gamma \in \Gamma / \Gamma _ { P } } \gamma \,\omega,$ ; confidence 1.000

33. ; $\operatorname{BV}$ ; confidence 1.000

34. ; $z ^ { \prime } + q + z ^ { 2 } / p = 0$ ; confidence 0.810

35. ; ${\cal C} ( X )$ ; confidence 1.000

36. ; $M [ x : = N ]$ ; confidence 0.810

37. ; $| \alpha x _ { 0 } - p | < \rho$ ; confidence 0.810

38. ; $R _ { B }$ ; confidence 0.810

39. ; $\frac { \partial w _ { N } } { \partial t } = \{ H , w _ { N } \} _ { \text{cl.} } \equiv \sum _ { i = 1 } ^ { N } ( \frac { \partial H } { \partial {\bf r} _ { i } } \frac { \partial w _ { N } } { \partial {\bf p} _ { i } } - \frac { \partial w _ { N } } { \partial {\bf r} _ { i } } \frac { \partial H } { \partial {\bf p} _ { i } } ),$ ; confidence 1.000

40. ; $J_2$ ; confidence 1.000

41. ; ${\cal A} ( u , v ) ( \xi , x ) = \int u ( z - \frac { x } { 2 } ) \bar{v} ( z + \frac { x } { 2 } ) e ^ { - 2 i \pi z . \xi } d z.$ ; confidence 0.810

42. ; $m_+ ( \lambda )$ ; confidence 1.000

43. ; $e ^ { - 1 / \varepsilon ^ { \sigma } }$ ; confidence 0.810

44. ; $\Sigma ^ { i } ( g ) = \emptyset$ ; confidence 0.810

45. ; $E ^ { \prime }$ ; confidence 0.810

46. ; $\emptyset \in \cal D$ ; confidence 1.000

47. ; $T : X \rightarrow X$ ; confidence 1.000

48. ; $K ^ { \prime 2 } \searrow K ^ { 2 }$ ; confidence 0.809

49. ; $M ^ { V } ( E + \omega )$ ; confidence 0.809

50. ; $d_Y ^ { \prime }$ ; confidence 1.000

51. ; $r \in \bf N$ ; confidence 1.000

52. ; $- \infty,$ ; confidence 1.000

53. ; $k = 1 , \ldots , K$ ; confidence 0.809

54. ; $V ^ { \pm } \times V ^ { \mp } \times V ^ { \pm } \rightarrow V ^ { \pm }$ ; confidence 1.000

55. ; $b$ ; confidence 0.809

56. ; $X \in \bf K$ ; confidence 1.000

57. ; $f ( z ) = \operatorname { lim } _ { m \rightarrow \infty } \int _ { \Gamma } f ( \zeta ) [ \operatorname{CF} ( \zeta - z , w ) +$ ; confidence 1.000 NOTE: it looks like the end of the formula is missing

58. ; ${\cal L} ( A )$ ; confidence 1.000

59. ; $u | _ { \partial D ^ { 2 } } = x$ ; confidence 0.809

60. ; $L | L ^ { \prime }$ ; confidence 0.809

61. ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { \| x _ { n + 1} - x ^ { * } \| } { \| x _ { n } - x ^ { * } \| } = 0.$ ; confidence 1.000

62. ; $H _ { i } ( t , m ) = H ( \varphi _ { i } ( s , t ) , m )$ ; confidence 1.000

63. ; $\beta_2$ ; confidence 1.000

64. ; $\cal N P$ ; confidence 1.000

65. ; $\operatorname{Fi} _ {\cal D } \bf A$ ; confidence 1.000

66. ; $x = \alpha$ ; confidence 0.808

67. ; $\mu ( a , x ) = \mu _ { 0 } ( a )$ ; confidence 1.000

68. ; $\Lambda ( M , s ) = \varepsilon ( M , s ) \Lambda ( M , i + 1 - s )$ ; confidence 0.808

69. ; $p _ { j } ( \lambda )$ ; confidence 0.808

70. ; $\operatorname { lnn } ( F ) = \langle 1 \rangle$ ; confidence 1.000

71. ; $x \in \partial D$ ; confidence 0.808

72. ; $B _ { p }$ ; confidence 1.000

73. ; $\left( \begin{array} { c c } { 0 } & { - 1 } \\ { {\cal A} ( t ) } & { 0 } \end{array} \right), $ ; confidence 1.000

74. ; $\chi \lambda$ ; confidence 0.808

75. ; $= L _ { \gamma , n } ^ { c } \int _ { {\bf R} ^ { n } } V _ { - } ( x ) ^ { \gamma + n / 2 } d x,$ ; confidence 1.000

76. ; $\{ \mu _ { n } \}$ ; confidence 0.808

77. ; $g \in L ^ { 2 } ( {\bf R} ^ { N } )$ ; confidence 1.000

78. ; $D _ { A } : = \sum _ { i = 1 } ^ { n } A _ { i } \otimes E _ { i }$ ; confidence 0.808

79. ; $\lambda _ { m }$ ; confidence 0.808

80. ; $C > 1$ ; confidence 0.808

81. ; $u , v \in V$ ; confidence 0.808

82. ; $g ( \overline { u } _ { 1 } ) \leq v ^ { * } \leq \overline { q }$ ; confidence 0.808

83. ; $m = \operatorname { max } ( m _ { 1 } , m _ { 2 } )$ ; confidence 0.808

84. ; $\hat { H } = H \oplus H$ ; confidence 0.808

85. ; $f _ { j } ( \bar{x} ) \in \tilde{\bf Z} ^ { n }$ ; confidence 1.000

86. ; $L _ { 2 , r }$ ; confidence 0.807

87. ; $0 \rightarrow \square _ { R } \operatorname { Mod } ( ? , A ) \rightarrow \square _ { R } \operatorname { Mod } ( ? , B ) \rightarrow$ ; confidence 0.807

88. ; ${\bf R} ^ { n }$ ; confidence 1.000

89. ; $0 \leq \lambda _ { 0 } \leq \lambda _ { 1 } \leq \ldots$ ; confidence 0.807

90. ; $E _ { c } ^ { * } ( M )$ ; confidence 0.807

91. ; $R _ { 11 }$ ; confidence 0.807

92. ; $\varphi \in D ( {\bf R} ^ { n } ) \}$ ; confidence 1.000

93. ; $| x | + r_j < R$ ; confidence 1.000

94. ; $\bf Y = X B + E$ ; confidence 1.000

95. ; $E ( a _ { 0 } , c _ { 1 } + a _ { 0 } ^ { 2 } m )$ ; confidence 0.807

96. ; $\sum _ { j \geq 0 } \alpha _ { j } z ^ { j } \in \operatorname{VMO}$ ; confidence 1.000

97. ; $\cal E * = \operatorname { Hom } _ { R } ( E , R )$ ; confidence 1.000

98. ; $\Pi ( \phi ) \equiv \phi | _ { E } * \subset E ^ { * * }$ ; confidence 0.806

99. ; $( \lambda | g )$ ; confidence 0.806

100. ; $\in C_i$ ; confidence 1.000

101. ; $V _ { i } = \{ x : \forall j \neq i , d ( x , p _ { i } ) \leq d ( x , p _ { j } ) \},$ ; confidence 1.000

102. ; $\partial \phi / \partial t$ ; confidence 1.000

103. ; $A ^ { 1 }$ ; confidence 0.806

104. ; $T _ { m }$ ; confidence 0.806

105. ; $i > n$ ; confidence 0.806

106. ; $I _ { \alpha } ( x ) = c _ { \alpha } | x | ^ { \alpha - n }$ ; confidence 1.000

107. ; $\Omega \cup {\cal F} = \cup _ { F \in \{\cal F} } \Omega F$ ; confidence 1.000

108. ; $\{ R_{ij} \}$ ; confidence 1.000

109. ; $V ^ { \pm }$ ; confidence 0.806

110. ; $- H M$ ; confidence 0.806

111. ; $p _ { m } ( x , \xi ) = \sum _ { | \alpha | = m } p _ { \alpha } ( x ) \xi ^ { \alpha }$ ; confidence 0.806

112. ; $w ( m , l )$ ; confidence 0.806

113. ; ${\cal A} _ { 2 }$ ; confidence 1.000

114. ; $\operatorname { cov } ( X ) = c \Sigma \otimes \Phi$ ; confidence 0.806

115. ; $\operatorname{add} T$ ; confidence 1.000

116. ; $A _ { 1 } x \leq b _ { 1 }$ ; confidence 0.806

117. ; $\mu ( B ) = \| \mu \| \{ x : ( x , T _ { x } ) \in B \}$ ; confidence 0.806

118. ; $q \geq 3$ ; confidence 0.806

119. ; $= \operatorname{E} _ { \mu _ { X } } [ \psi ( t ) | X ( t ) = x ] p _ { X } ( 0 , x _ { 0 } ; t , x )$ ; confidence 1.000

120. ; ${\cal L} _ { 0 } = \langle e _ { i } : i \geq 0 \rangle$ ; confidence 1.000

121. ; $\[cal C} \rightarrow Z {\cal C}$ ; confidence 1.000

122. ; $\operatorname { Im } \zeta \in \Delta _ { k }$ ; confidence 0.805

123. ; $f ( 2 \pi t ) = \frac { 1 } { \sqrt { 2 \pi } } \int _ { 0 } ^ { 1 } e ^ { - 2 \pi i x t } ( Z \hat { f } ) ( x , t ) d x, $ ; confidence 1.000

124. ; $P ^ { \prime } H$ ; confidence 0.805

125. ; $\theta \in S ^ { 2 }$ ; confidence 0.805

126. ; $x _ { k + 1 } = A x _ { k }$ ; confidence 0.805

127. ; $e\notin S ( x )$ ; confidence 0.805

128. ; $\operatorname{Cl} ( f , \zeta )$ ; confidence 1.000

129. ; ${\bf R} ^ { q }$ ; confidence 1.000

130. ; $\vec { P _ { i } P _ { j } }$ ; confidence 0.805

131. ; $\alpha , b , c , d \in A$ ; confidence 0.805

132. ; $v _ { 0 } = i A ( t ) ^ { 1 / 2 } u$ ; confidence 0.805

133. ; $\left( \begin{array} { c c c c } { 0 } & { 1 } & { \square } & { \square } \\ { \square } & { \ddots } & { \ddots } & { \square } \\ { \square } & { \square } & { 0 } & { 1 } \\ { - a _ { 0 } } & { \cdots } & { \cdots } & { - a _ { n - 1 } } \end{array} \right).$ ; confidence 1.000

134. ; $h * ( . ) = \operatorname{E} * ( . )$ ; confidence 1.000

135. ; $\Delta ( {\cal F} ) | \geq \partial _ { k } ( m ).$ ; confidence 1.000

136. ; $\langle A f , g \rangle = \langle f , A g \rangle$ ; confidence 0.805

137. ; $Q _ { \emptyset } ( v , z ) = 1$ ; confidence 0.805

138. ; $a , b \in A$ ; confidence 0.805

139. ; $F \in \operatorname{Hol} ( {\cal D} )$ ; confidence 1.000

140. ; $\operatorname { Im } z > 1$ ; confidence 0.805

141. ; $\operatorname{rank} H _ { \phi } = \operatorname { deg } {\cal P} - \phi$ ; confidence 1.000

142. ; $a _ { 2 } + 2 a_ { 1 } = 0$ ; confidence 1.000

143. ; $t \in {\bf R} ^ { 1 }$ ; confidence 1.000

144. ; $\sum _ { n = 0 } ^ { \infty } D _ { n } ( x , a ) z ^ { n } = \frac { 2 - x z } { 1 - x z + a z ^ { 2 } }.$ ; confidence 1.000

145. ; $v \in T _ { p } M$ ; confidence 0.805

146. ; $Y ( u , x ) v = \sum _ { n \in Z } ( u _ { n } v ) x ^ { - n - 1 }$ ; confidence 0.805

147. ; $g ( x ; m , s ) = \left\{ \begin{array} { l l } { \frac { 1 } { 2 s } \operatorname { exp } ( \frac { x - m } { s } ) } & { \text { for } x \leq m } \\ { \frac { 1 } { 2 s } \operatorname { exp } ( \frac { m - x } { s } ) } & { \text { for } x \geq m } \end{array} \right.$ ; confidence 0.804

148. ; $g ^ { - 1 }$ ; confidence 0.804

149. ; $x _ { m , j } = \alpha _ { j } e ^ { i m \theta } , y _ { m , j } = \beta _ { j } e ^ { i m \theta }$ ; confidence 0.804

150. ; $P G _ { d -1} ( d , q )$ ; confidence 1.000

151. ; $d _ { 1 } ^ { * }$ ; confidence 0.804

152. ; $\{ ., . \}$ ; confidence 1.000

153. ; $t ( \omega )$ ; confidence 0.804

154. ; $\leq B \sum _ { i = 1 } ^ { k } ( t - s ) ^ { \alpha _ { i } } | \lambda | ^ { \beta _ { i } - 1 } , \lambda \in S _ { \theta _ { 0 } } \backslash \{ 0 \} , \quad 0 \leq s \leq t \leq T.$ ; confidence 1.000

155. ; $\delta _ { A , B } : B ( H ) \rightarrow B ( H )$ ; confidence 0.804

156. ; $\operatorname{R}$ ; confidence 1.000

157. ; $\Omega \times [ 0 , T$ ; confidence 0.804 NOTE: the parentesis should probably be closed

158. ; $\varphi ( A ) = \sum _ { i = 0 } ^ { n } a _ { i } A ^ { i } = 0$ ; confidence 0.804

159. ; $\tau _ { \rho }$ ; confidence 0.804

160. ; $p , q \in S$ ; confidence 0.804

161. ; $\Delta \otimes \Delta \cong K _ { X }$ ; confidence 0.804

162. ; $K _ { I } ( f )$ ; confidence 0.804

163. ; ${\cal F} ^ { \# } ( n )$ ; confidence 1.000

164. ; $\frak g$ ; confidence 1.000

165. ; $\tau _ { n } ( t ) = \frac { 1 } { 2 \pi } \frac { 2 ^ { 2 n } ( n ! ) ^ { 2 } } { ( 2 n ) ! } \operatorname { cos } ^ { 2 n } \frac { t } { 2 }$ ; confidence 0.804

166. ; ${\cal E}^l$ ; confidence 1.000

167. ; $\tilde { \cal M } _ { C }$ ; confidence 1.000

168. ; $P_Y \rightarrow Y$ ; confidence 1.000

169. ; $A _ { i } \cap ( - A _ { i } ) \neq \emptyset$ ; confidence 0.804

170. ; $1 + a _ { 1 } ^ { 2 } + \ldots + a _ { k } ^ { 2 }$ ; confidence 0.804

171. ; $\operatorname{Ran}( a )$ ; confidence 1.000

172. ; $3 ^ { 3 } .5 .7,3 ^ { 2 } .5 ^ { 2 } .7,3 ^ { 2 } .5 .7 ^ { 2 }$ ; confidence 0.804

173. ; $f = m \circ e$ ; confidence 0.804

174. ; $T _ { n } ( x _ { n } ) = Q _ { n } f.$ ; confidence 1.000

175. ; $K ( T M )$ ; confidence 0.804

176. ; ${\bf C} ( \mu )$ ; confidence 1.000

177. ; $M u = 0$ ; confidence 0.804

178. ; $( f ( z ^ { n } ) )^ { m / n }$ ; confidence 0.804

179. ; $\|S_{NB}\| /\operatorname { ln } ^ { 2 } N$ ; confidence 1.000

180. ; ${\calA} = Ab$ ; confidence 1.000

181. ; $g = \lambda \mu ( d \rho \otimes d \sigma + d \sigma \otimes d \rho ) / 2$ ; confidence 0.803

182. ; $a ( G )$ ; confidence 0.803

183. ; $\operatorname{rank} ( \Sigma ) = p _ { 1 }$ ; confidence 1.000

184. ; ${\bf E} _ { 6 }$ ; confidence 1.000

185. ; $C _ { 2 }$ ; confidence 0.803

186. ; $C \Gamma : Y \rightarrow V Y \otimes \wedge ^ { 2 } T ^ { * } M$ ; confidence 0.803

187. ; $Q \neq 0$ ; confidence 1.000

188. ; $\operatorname { lim }_\lambda$ ; confidence 1.000

189. ; $\frak p$ ; confidence 1.000 NOTE: it is very hard to read the original image

190. ; $p _ { i k , j } \geq 0$ ; confidence 0.803

191. ; $h = h _ { \beta } \in \frak h$ ; confidence 1.000

192. ; $1.5$ ; confidence 0.803

193. ; $a ( . )$ ; confidence 1.000

194. ; $( f ^ { * } d \mu ) _ { N } ( x )$ ; confidence 0.803

195. ; $| K ( x , y ^ { \prime } ) - K ( x , y ) | \leq C | y ^ { \prime } - y | ^ { \gamma } | x - y | ^ { - n - \gamma }.$ ; confidence 1.000

196. ; $e ^ { i \eta . y}$ ; confidence 1.000

197. ; $| \mu ( 0,1 ) |$ ; confidence 0.802

198. ; $\alpha , b \in F ^ { * }$ ; confidence 0.802

199. ; $\epsilon > r$ ; confidence 0.802

200. ; $\operatorname{ch} : R \rightarrow \Lambda$ ; confidence 1.000

201. ; $a \in L ^ { 1 } ( {\bf T} )$ ; confidence 1.000

202. ; $( \Omega f ) _ { W } = f$ ; confidence 0.802

203. ; $B ( t , \omega ) = \omega ( t )$ ; confidence 0.802

204. ; $X \in U ( a )$ ; confidence 0.802

205. ; $\Omega A _ { W } = A$ ; confidence 0.802

206. ; ${\cal D} = ( G , \{ D g : g \in G \} , \in )$ ; confidence 1.000

207. ; $F _ { n } ( x ; \lambda ) = \sum _ { m = 0 } ^ { \infty } \sum _ { k = m + n / 2 } ^ { \infty } \frac { ( \lambda / 2 ) ^ { m } ( x / 2 ) ^ { k } } { m ! k ! } e ^ { - ( \lambda + x ) / 2 }.$ ; confidence 0.801

208. ; $Z _ { n } ( x ; \sigma ) = ( 1 + \sigma ) ^ { n } T _ { n } ( \frac { x - \sigma } { 1 + \sigma } )$ ; confidence 0.801

209. ; $l = 1,2$ ; confidence 0.801

210. ; $D^{( i )}$ ; confidence 1.000

211. ; $\{ 0,1 , \vee , \wedge \}$ ; confidence 0.801

212. ; $\dot { x } \square ^ { i }$ ; confidence 1.000

213. ; $\hat { f } ( \omega ) = \int _ { - \infty } ^ { \infty } e ^ { - i \omega t } f ( t ) d t$ ; confidence 0.801

214. ; $[ a ]$ ; confidence 0.801

215. ; $G ( K _ { p ^ { \prime } } )$ ; confidence 0.801

216. ; $K ( . , . )$ ; confidence 0.801

217. ; ${\cal P M} ^ { * }$ ; confidence 1.000

218. ; $\operatorname{VMO}(\bf R )$ ; confidence 1.000

219. ; $a ( z ) : = \prod _ { j = 1 } ^ { J } \frac { z - i k _ { j } } { z + i k _ { j } } \operatorname { exp } \{ - \frac { 1 } { 2 \pi i } \int _ { - \infty } ^ { \infty } \frac { \operatorname { ln } ( 1 - | r _ { + } ( k ) | ^ { 2 } ) } { k - z } d k \}.$ ; confidence 1.000

220. ; ${\cal D} ^ { \prime }$ ; confidence 1.000

221. ; ${\bf Z} ^ { 0 }$ ; confidence 1.000

222. ; $A = \left[ \begin{array} { l } { A _ { 1 } } \\ { A _ { 2 } } \end{array} \right] \in C ^ { ( m n + p ) \times m }$ ; confidence 0.801

223. ; $\overline { U M } = U M$ ; confidence 0.801

224. ; $L : {\cal H} \rightarrow H$ ; confidence 1.000

225. ; $F ( f ) = F _ { g } ( f ) = \int _ { \partial D _ { m } } f g,$ ; confidence 1.000

226. ; $f : [ 0,1 ] ^ { d } \rightarrow \bf R$ ; confidence 1.000

227. ; $a_n ( g )$ ; confidence 1.000

228. ; $u \in T x , v \in T y$ ; confidence 0.800

229. ; ${\cal T} ^ { + }$ ; confidence 1.000

230. ; $u - \Delta u = f$ ; confidence 0.800

231. ; $M ^ { \perp } \Bigcap N ^ { \perp } = ( M \Bigcup N ) ^ { \perp }$ ; confidence 1.000

232. ; $\xi ^ { * \prime } : X \rightarrow B _ { n }$ ; confidence 0.800

233. ; $\operatorname { Ric } \geq - ( n - 1 ) \delta ^ { 2 } , \quad \delta \geq 0$ ; confidence 0.800

234. ; $X = \{ X _ { 1 } , \dots , X _ { n } \}$ ; confidence 0.800

235. ; $\times | I _ { p } + \Sigma ^ { - 1 } ( X - M ) \Omega ^ { - 1 } ( X - M ) ^ { \prime } | ^ { - ( n + m + p - 1 ) / 2 } , X \in {\bf R} ^ { p \times n } , M \in {\bf R} ^ { p \times n } , \Sigma > 0 , \Omega > 0.$ ; confidence 1.000

236. ; $a \neq b$ ; confidence 0.800

237. ; $\operatorname { Re } \mu _ { j } ( k , R ) < \operatorname { Re } \mu _ { 0 } ( k , R )$ ; confidence 0.800

238. ; $Z_n$ ; confidence 1.000

239. ; $\lfloor x \rfloor$ ; confidence 1.000

240. ; $\{ x y \{ z u v \} \} = \{ x y z \} u v \} + \{ z \{ x y u \} v \} + \{ z u \{ x y v \} \}$ ; confidence 0.800

241. ; $w_i$ ; confidence 1.000

242. ; $T \approx f _ { y } ( t _ { m } , u _ { m } )$ ; confidence 0.800

243. ; $y \in E$ ; confidence 0.800

244. ; $\sim_l$ ; confidence 1.000

245. ; $[ \alpha ] = ( \alpha , \alpha ^ { 2 } / 2 , \alpha ^ { 2 } / 3 , \ldots )$ ; confidence 0.800

246. ; $f : X \times Y \rightarrow \bf R$ ; confidence 1.000

247. ; $F ( z ) = ( 1 / k ! ) \int _ { i } ^ { z } f ( \tau ) ( z - \tau ) ^ { k } d \tau$ ; confidence 0.799

248. ; $\xi \in \Xi$ ; confidence 1.000

249. ; $\operatorname { gcd } ( a ^ { ( q ^ { i } - 1 ) / 2 } - 1 , f _ { i } )$ ; confidence 1.000

250. ; $x ^ { 1 } = \operatorname { sinh } u ^ { 1 } \operatorname { cosh } u ^ { 2 } \ldots \operatorname { cosh } u ^ { n }$ ; confidence 0.799

251. ; $( \alpha \supset ^ { * } b ) \in D$ ; confidence 0.799

252. ; $= \sum _ { \alpha \in Z _ { f } } \varphi ( \alpha )$ ; confidence 0.799

253. ; $\operatorname { dim } ( {\cal S} ) = 7$ ; confidence 1.000

254. ; $P _ { 8 }$ ; confidence 0.799

255. ; $n/100$ ; confidence 1.000

256. ; ${\bf D} \in \operatorname{K}$ ; confidence 1.000

257. ; $\{ ( x _ { j } , t _ { n } ) : x _ { j } = j h , t _ { n } = n k , 0 \leq j \leq J , 0 \leq n \leq N \},$ ; confidence 0.799

258. ; $u [ 1 ] = u - 2 ( \operatorname { log } \varphi ) _ { x y } = - u + \frac { \varphi _ { x } \varphi_y } { \varphi ^ { 2 } };$ ; confidence 1.000

259. ; $U _ { n } ^ { ( k ) }$ ; confidence 0.799

260. ; $m _ { i } : \Sigma \rightarrow X$ ; confidence 0.799

261. ; $X _ { 0 }$ ; confidence 0.798

262. ; $I = [ \xi _ { l } ^ { 0 } ] ^ { 2 } + [ \xi _ { r } ^ { 0 } ] ^ { 2 }$ ; confidence 0.798

263. ; $\pi ( \lambda ) = \sum _ { n = 0 } ^ { N } ( \lambda + n ) ( \lambda + n - 1 ) \ldots ( \lambda + 1 ) a ^ { n _0} =$ ; confidence 1.000

264. ; $M ( 1 )$ ; confidence 0.798

265. ; $\bf r \times l$ ; confidence 1.000

266. ; $\operatorname{QS} ( T ) \subset M$ ; confidence 1.000

267. ; $\varphi = \sum _ { n = 0 } ^ { \infty } \theta _ { n } ( f _ { n } ),$ ; confidence 1.000

268. ; $f \in L _ { 1 } ( R _ { + } ; e ^ { - x } / \sqrt { x } )$ ; confidence 0.798

269. ; $c _ { N } = c _ { - N } = 1 , c _ { j } = 2 \text{ otherwise}$ ; confidence 1.000

270. ; $S , Y , Z \rightarrow U , V , W$ ; confidence 0.798

271. ; $\tau _ { n } ( x , y + [ z ] )$ ; confidence 1.000

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

273. ; $w \mapsto ( w ^ { * } \varphi _ { \lambda } ) _ { \lambda \in \Lambda }$ ; confidence 0.798

274. ; $H _ { \phi } = H _ { \phi + \psi }$ ; confidence 0.798

275. ; $S _ { B }$ ; confidence 0.798

276. ; $M _ { p }$ ; confidence 0.798

277. ; $\operatorname { deg } r _ { j } = 2 k _ { j }$ ; confidence 0.798

278. ; $C _ { D }$ ; confidence 0.798

279. ; $1 \leq m \leq l$ ; confidence 0.798

280. ; $( v _ { i } , u _ { i } )$ ; confidence 0.797

281. ; $\bf A \in Q$ ; confidence 1.000

282. ; $d ( P _ { N } u ) / d x = \sum _ { n = 0 } ^ { N } b _ { n } T _ { N } ( x )$ ; confidence 0.797

283. ; $\operatorname{WC} ( A , k ) = 0$ ; confidence 1.000

284. ; $.d Y _ { 1 } \ldots d Y _ { 2 k }$ ; confidence 1.000

285. ; $\tilde{\bf E} _ { 6 }$ ; confidence 1.000

286. ; $\tau ^ { 2 } = \operatorname{id}$ ; confidence 1.000

287. ; $E ( \varphi ) = \frac { 1 } { 2 } \int _ { M } | d \varphi | ^ { 2 } v _ { g }$ ; confidence 0.797

288. ; $\operatorname{min}_j | z _ { j } | = \operatorname { min } _ { j } | w _ { j } | = 1$ ; confidence 1.000

289. ; $\sum _ { j \geq 1 } | e | ^ { \gamma } \approx$ ; confidence 0.797

290. ; $( \bar{x} )$ ; confidence 1.000

291. ; $( \phi _ { 1 } \& \ldots \& \phi _ { n } )$ ; confidence 0.797

292. ; $\alpha _ { i i } \neq 0$ ; confidence 1.000

293. ; $a b = 1$ ; confidence 0.797

294. ; $\tilde { \gamma } = \gamma _ { \tilde{\omega} }$ ; confidence 1.000

295. ; $\bf Z (\cal C )$ ; confidence 1.000

296. ; $r _ { N } ( \alpha , b ) \in S ( m _ { 1 } m _ { 2 } H ^ { N } , G )$ ; confidence 0.797

297. ; $S _ { i } ( t | \{ u _ { i } ( t ) \} , \{ C _ { i j } ( t ) \} )$ ; confidence 0.797

298. ; $\{ \xi_r\}$ ; confidence 1.000

299. ; $h ^ { I I } ( z ) ^ { - 1 }$ ; confidence 0.797

300. ; $a _ { X } : = \operatorname { inf } \{ s : \operatorname{l} ( s , 0 ) > x \}$ ; confidence 1.000

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/40. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/40&oldid=45569

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Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/40"

Revision as of 17:15, 26 April 2020

List

@@ Line 302: / Line 302: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015053.png ; $d _ { 1 } ^ { * }$ ; confidence 0.804
-. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110170/p11017040.png ; $\{ . . \}$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110170/p11017040.png ; $\{ ., . \}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e12026064.png ; $t ( \omega )$ ; confidence 0.804
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005049.png ; $\leq B \sum _ { i = 1 } ^ { k } ( t - s ) ^ { \alpha _ { i } } | \lambda | ^ { \beta _ { i } - 1 } , \lambda \in S _ { \theta _ { 0 } } \backslash \{ 0 \} , \quad 0 \leq s \leq t \leq T$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005049.png ; $\leq B \sum _ { i = 1 } ^ { k } ( t - s ) ^ { \alpha _ { i } } | \lambda | ^ { \beta _ { i } - 1 } , \lambda \in S _ { \theta _ { 0 } } \backslash \{ 0 \} , \quad 0 \leq s \leq t \leq T.$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p1201704.png ; $\delta _ { A , B } : B ( H ) \rightarrow B ( H )$ ; confidence 0.804
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014099.png ; $R$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014099.png ; $\operatorname{R}$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130090/b13009028.png ; $\Omega \times [ 0 , T$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130090/b13009028.png ; $\Omega \times [ 0 , T$ ; confidence 0.804 NOTE: the parentesis should probably be closed
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c1200808.png ; $\varphi ( A ) = \sum _ { i = 0 } ^ { n } a _ { i } A ^ { i } = 0$ ; confidence 0.804
@@ Line 324: / Line 324: @@
 . https://www.encyclopediaofmath.org/legacyimages/q/q130/q130040/q13004024.png ; $K _ { I } ( f )$ ; confidence 0.804
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060131.png ; $F ^ { \# } ( n )$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060131.png ; ${\cal F} ^ { \# } ( n )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013016.png ; $8$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013016.png ; $\frak g$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/d/d030/d030280/d0302808.png ; $\tau _ { n } ( t ) = \frac { 1 } { 2 \pi } \frac { 2 ^ { 2 n } ( n ! ) ^ { 2 } } { ( 2 n ) ! } \operatorname { cos } ^ { 2 n } \frac { t } { 2 }$ ; confidence 0.804
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090273.png ; $\varepsilon$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090273.png ; ${\cal E}^l$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003024.png ; $\tilde { M } _ { C }$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003024.png ; $\tilde { \cal M } _ { C }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130290/a1302907.png ; $P Y \rightarrow Y$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130290/a1302907.png ; $P_Y \rightarrow Y$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120200/l1202004.png ; $A _ { i } \cap ( - A _ { i } ) \neq \emptyset$ ; confidence 0.804
@@ Line 340: / Line 340: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120050/w1200509.png ; $1 + a _ { 1 } ^ { 2 } + \ldots + a _ { k } ^ { 2 }$ ; confidence 0.804
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064029.png ; $( a )$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064029.png ; $\operatorname{Ran}( a )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007036.png ; $3 ^ { 3 } .5 .7,3 ^ { 2 } .5 ^ { 2 } .7,3 ^ { 2 } .5 .7 ^ { 2 }$ ; confidence 0.804
@@ Line 346: / Line 346: @@
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120010/e12001035.png ; $f = m \circ e$ ; confidence 0.804
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027023.png ; $T _ { n } ( x _ { n } ) = Q _ { n } f$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027023.png ; $T _ { n } ( x _ { n } ) = Q _ { n } f.$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120190/c12019047.png ; $K ( T M )$ ; confidence 0.804
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021079.png ; $C ( \mu )$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021079.png ; ${\bf C} ( \mu )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p13007049.png ; $M u = 0$ ; confidence 0.804
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009093.png ; $( f ( z ^ { n } ) ) ^ { m / n }$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009093.png ; $( f ( z ^ { n } ) )^ { m / n }$ ; confidence 0.804
-. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130010/l13001069.png ; $\operatorname { ln } ^ { 2 } N$ ; confidence 0.804
+. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130010/l13001069.png ; $\|S_{NB}\| /\operatorname { ln } ^ { 2 } N$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007073.png ; $A = Ab$ ; confidence 0.803
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007073.png ; ${\calA} = Ab$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c12018076.png ; $g = \lambda \mu ( d \rho \otimes d \sigma + d \sigma \otimes d \rho ) / 2$ ; confidence 0.803
@@ Line 364: / Line 364: @@
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120210/t12021050.png ; $a ( G )$ ; confidence 0.803
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016053.png ; $k ( \Sigma ) = p _ { 1 }$ ; confidence 0.803
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016053.png ; $\operatorname{rank} ( \Sigma ) = p _ { 1 }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010093.png ; $E _ { 6 }$ ; confidence 0.803
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010093.png ; ${\bf E} _ { 6 }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c130070228.png ; $C _ { 2 }$ ; confidence 0.803
@@ Line 372: / Line 372: @@
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e12006050.png ; $C \Gamma : Y \rightarrow V Y \otimes \wedge ^ { 2 } T ^ { * } M$ ; confidence 0.803
-. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064250/m06425028.png ; $2 \neq 0$ ; confidence 0.803
+. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064250/m06425028.png ; $Q \neq 0$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007097.png ; $\operatorname { lim } x$ ; confidence 0.803
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007097.png ; $\operatorname { lim }_\lambda$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003027.png ; $3$ ; confidence 0.803
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003027.png ; $\frak p$ ; confidence 1.000 NOTE: it is very hard to read the original image
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120160/b1201604.png ; $p _ { i k , j } \geq 0$ ; confidence 0.803
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090343.png ; $h = h _ { \beta } \in h$ ; confidence 0.803
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090343.png ; $h = h _ { \beta } \in \frak h$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120200/e12020020.png ; $1.5$ ; confidence 0.803
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027066.png ; $\alpha ( . )$ ; confidence 0.803
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027066.png ; $a ( . )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012038.png ; $( f ^ { * } d \mu ) _ { N } ( x )$ ; confidence 0.803
-. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110660/b11066062.png ; $| K ( x , y ^ { \prime } ) - K ( x , y ) | \leq C | y ^ { \prime } - y | ^ { \gamma } | x - y | ^ { - n - \gamma }$ ; confidence 0.802
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110660/b11066062.png ; $| K ( x , y ^ { \prime } ) - K ( x , y ) | \leq C | y ^ { \prime } - y | ^ { \gamma } | x - y | ^ { - n - \gamma }.$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030024.png ; $e ^ { i \eta } \cdot y$ ; confidence 0.802
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030024.png ; $e ^ { i \eta . y}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m130180160.png ; $| \mu ( 0,1 ) |$ ; confidence 0.802
@@ Line 398: / Line 398: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021014.png ; $\epsilon > r$ ; confidence 0.802
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s120040104.png ; $ch : R \rightarrow \Lambda$ ; confidence 0.802
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s120040104.png ; $\operatorname{ch} : R \rightarrow \Lambda$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064021.png ; $a \in L ^ { 1 } ( T )$ ; confidence 0.802
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064021.png ; $a \in L ^ { 1 } ( {\bf T} )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120190/w12019048.png ; $( \Omega f ) _ { W } = f$ ; confidence 0.802
@@ Line 410: / Line 410: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120190/w12019049.png ; $\Omega A _ { W } = A$ ; confidence 0.802
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120330/s12033061.png ; $D = ( G , \{ D g : g \in G \} , \in )$ ; confidence 0.802
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120330/s12033061.png ; ${\cal D} = ( G , \{ D g : g \in G \} , \in )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066960/n06696021.png ; $F _ { n } ( x ; \lambda ) = \sum _ { m = 0 } ^ { \infty } \sum _ { k = m + n / 2 } ^ { \infty } \frac { ( \lambda / 2 ) ^ { m } ( x / 2 ) ^ { k } } { m ! k ! } e ^ { - ( \lambda + x ) / 2 }$ ; confidence 0.801
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066960/n06696021.png ; $F _ { n } ( x ; \lambda ) = \sum _ { m = 0 } ^ { \infty } \sum _ { k = m + n / 2 } ^ { \infty } \frac { ( \lambda / 2 ) ^ { m } ( x / 2 ) ^ { k } } { m ! k ! } e ^ { - ( \lambda + x ) / 2 }.$ ; confidence 0.801
 . https://www.encyclopediaofmath.org/legacyimages/z/z130/z130120/z13012024.png ; $Z _ { n } ( x ; \sigma ) = ( 1 + \sigma ) ^ { n } T _ { n } ( \frac { x - \sigma } { 1 + \sigma } )$ ; confidence 0.801
@@ Line 418: / Line 418: @@
 . https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006083.png ; $l = 1,2$ ; confidence 0.801
-. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v130050101.png ; $D ( i )$ ; confidence 0.801
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v130050101.png ; $D^{( i )}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120370/b12037084.png ; $\{ 0,1 , \vee , \wedge \}$ ; confidence 0.801
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015051.png ; $\dot { X } \square ^ { i }$ ; confidence 0.801
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015051.png ; $\dot { x } \square ^ { i }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/g/g120/g120010/g1200103.png ; $\hat { f } ( \omega ) = \int _ { - \infty } ^ { \infty } e ^ { - i \omega t } f ( t ) d t$ ; confidence 0.801
@@ Line 432: / Line 432: @@
 . https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e035000126.png ; $K ( . , . )$ ; confidence 0.801
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012060.png ; $P M ^ { * }$ ; confidence 0.801
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012060.png ; ${\cal P M} ^ { * }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/v/v110/v110050/v11005020.png ; $( R )$ ; confidence 0.801
+. https://www.encyclopediaofmath.org/legacyimages/v/v110/v110050/v11005020.png ; $\operatorname{VMO}(\bf R )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005081.png ; $\alpha ( z ) : = \prod _ { j = 1 } ^ { J } \frac { z - i k _ { j } } { z + i k _ { j } } \operatorname { exp } \{ - \frac { 1 } { 2 \pi i } \int _ { - \infty } ^ { \infty } \frac { \operatorname { ln } ( 1 - | r _ { + } ( k ) | ^ { 2 } ) } { k - z } d k \}$ ; confidence 0.801
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005081.png ; $a ( z ) : = \prod _ { j = 1 } ^ { J } \frac { z - i k _ { j } } { z + i k _ { j } } \operatorname { exp } \{ - \frac { 1 } { 2 \pi i } \int _ { - \infty } ^ { \infty } \frac { \operatorname { ln } ( 1 - | r _ { + } ( k ) | ^ { 2 } ) } { k - z } d k \}.$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130260/c13026017.png ; $D ^ { \prime }$ ; confidence 0.801
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130260/c13026017.png ; ${\cal D} ^ { \prime }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s1305104.png ; $z ^ { 0 }$ ; confidence 0.801
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s1305104.png ; ${\bf Z} ^ { 0 }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008044.png ; $A = \left[ \begin{array} { l } { A _ { 1 } } \\ { A _ { 2 } } \end{array} \right] \in C ^ { ( m n + p ) \times m }$ ; confidence 0.801
@@ Line 446: / Line 446: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130020/s13002050.png ; $\overline { U M } = U M$ ; confidence 0.801
-. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070110.png ; $L : H \rightarrow H$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070110.png ; $L : {\cal H} \rightarrow H$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d120280124.png ; $F ( f ) = F _ { g } ( f ) = \int _ { \partial D _ { m } } f g$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d120280124.png ; $F ( f ) = F _ { g } ( f ) = \int _ { \partial D _ { m } } f g,$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120310/c12031034.png ; $f : [ 0,1 ] ^ { d } \rightarrow R$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120310/c12031034.png ; $f : [ 0,1 ] ^ { d } \rightarrow \bf R$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t12007071.png ; $\operatorname { ln } ( g )$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t12007071.png ; $a_n ( g )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/m/m120/m120010/m1200107.png ; $u \in T x , v \in T y$ ; confidence 0.800
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120020/t12002019.png ; $\tau ^ { + }$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120020/t12002019.png ; ${\cal T} ^ { + }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010068.png ; $u - \Delta u = f$ ; confidence 0.800
-. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110020/l110020131.png ; $M ^ { \perp } \cap N ^ { \perp } = ( M \cup N ) ^ { \perp }$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110020/l110020131.png ; $M ^ { \perp } \Bigcap N ^ { \perp } = ( M \Bigcup N ) ^ { \perp }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b015/b015010/b01501014.png ; $\xi ^ { * \prime } : X \rightarrow B _ { n }$ ; confidence 0.800
@@ Line 468: / Line 468: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d13006061.png ; $X = \{ X _ { 1 } , \dots , X _ { n } \}$ ; confidence 0.800
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015064.png ; $\times | I _ { p } + \Sigma ^ { - 1 } ( X - M ) \Omega ^ { - 1 } ( X - M ) ^ { \prime } | ^ { - ( n + m + p - 1 ) / 2 } , X \in R ^ { p \times n } , M \in R ^ { p \times n } , \Sigma > 0 , \Omega > 0$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015064.png ; $\times | I _ { p } + \Sigma ^ { - 1 } ( X - M ) \Omega ^ { - 1 } ( X - M ) ^ { \prime } | ^ { - ( n + m + p - 1 ) / 2 } , X \in {\bf R} ^ { p \times n } , M \in {\bf R} ^ { p \times n } , \Sigma > 0 , \Omega > 0.$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c024/c024780/c024780251.png ; $a \neq b$ ; confidence 0.800
@@ Line 474: / Line 474: @@
 . https://www.encyclopediaofmath.org/legacyimages/g/g120/g120050/g12005016.png ; $\operatorname { Re } \mu _ { j } ( k , R ) < \operatorname { Re } \mu _ { 0 } ( k , R )$ ; confidence 0.800
-. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015030.png ; $z$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015030.png ; $Z_n$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l13006065.png ; $\lfloor x$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l13006065.png ; $\lfloor x \rfloor$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130250/a1302508.png ; $\{ x y \{ z u v \} \} = \{ x y z \} u v \} + \{ z \{ x y u \} v \} + \{ z u \{ x y v \} \}$ ; confidence 0.800
-. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014060/a014060130.png ; $w$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014060/a014060130.png ; $w_i$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110320/a11032013.png ; $T \approx f _ { y } ( t _ { m } , u _ { m } )$ ; confidence 0.800
@@ Line 486: / Line 486: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b110/b110920/b11092021.png ; $y \in E$ ; confidence 0.800
-. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110160/f110160195.png ; $\sim$ ; confidence 0.800
+. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110160/f110160195.png ; $\sim_l$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013017.png ; $[ \alpha ] = ( \alpha , \alpha ^ { 2 } / 2 , \alpha ^ { 2 } / 3 , \ldots )$ ; confidence 0.800
-. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130020/n13002033.png ; $f : X \times Y \rightarrow R$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130020/n13002033.png ; $f : X \times Y \rightarrow \bf R$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e12007061.png ; $F ( z ) = ( 1 / k ! ) \int _ { i } ^ { z } f ( \tau ) ( z - \tau ) ^ { k } d \tau$ ; confidence 0.799
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022042.png ; $\xi \in E$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022042.png ; $\xi \in \Xi$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130010/f13001036.png ; $\operatorname { gcd } ( \alpha ^ { ( q ^ { i } - 1 ) / 2 } - 1 , f _ { i } )$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130010/f13001036.png ; $\operatorname { gcd } ( a ^ { ( q ^ { i } - 1 ) / 2 } - 1 , f _ { i } )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/l/l060/l060050/l06005055.png ; $x ^ { 1 } = \operatorname { sinh } u ^ { 1 } \operatorname { cosh } u ^ { 2 } \ldots \operatorname { cosh } u ^ { n }$ ; confidence 0.799
@@ Line 504: / Line 504: @@
 . https://www.encyclopediaofmath.org/legacyimages/m/m120/m120270/m12027017.png ; $= \sum _ { \alpha \in Z _ { f } } \varphi ( \alpha )$ ; confidence 0.799
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010114.png ; $\operatorname { im } ( S ) = 7$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010114.png ; $\operatorname { dim } ( {\cal S} ) = 7$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/l/l058/l058360/l058360142.png ; $P _ { 8 }$ ; confidence 0.799
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130020/j13002054.png ; $1100$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130020/j13002054.png ; $n/100$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040799.png ; $D \in K$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040799.png ; ${\bf D} \in \operatorname{K}$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c1202604.png ; $\{ ( x _ { j } , t _ { n } ) : x _ { j } = j h , t _ { n } = n k , 0 \leq j \leq J , 0 \leq n \leq N \}$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c1202604.png ; $\{ ( x _ { j } , t _ { n } ) : x _ { j } = j h , t _ { n } = n k , 0 \leq j \leq J , 0 \leq n \leq N \},$ ; confidence 0.799
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120240/m1202408.png ; $u [ 1 ] = u - 2 ( \operatorname { log } \varphi ) _ { x y } = - u + \frac { \varphi _ { x } \varphi y } { \varphi ^ { 2 } }$ ; confidence 0.799
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120240/m1202408.png ; $u [ 1 ] = u - 2 ( \operatorname { log } \varphi ) _ { x y } = - u + \frac { \varphi _ { x } \varphi_y } { \varphi ^ { 2 } };$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f13009040.png ; $U _ { n } ^ { ( k ) }$ ; confidence 0.799
@@ Line 524: / Line 524: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130580/s13058014.png ; $I = [ \xi _ { l } ^ { 0 } ] ^ { 2 } + [ \xi _ { r } ^ { 0 } ] ^ { 2 }$ ; confidence 0.798
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021022.png ; $\pi ( \lambda ) = \sum _ { n = 0 } ^ { N } ( \lambda + n ) ( \lambda + n - 1 ) \ldots ( \lambda + 1 ) a ^ { n } 0 =$ ; confidence 0.798
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021022.png ; $\pi ( \lambda ) = \sum _ { n = 0 } ^ { N } ( \lambda + n ) ( \lambda + n - 1 ) \ldots ( \lambda + 1 ) a ^ { n _0} =$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c120170146.png ; $M ( 1 )$ ; confidence 0.798
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130580/s1305807.png ; $r \times l$ ; confidence 0.798
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130580/s1305807.png ; $\bf r \times l$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130050/q13005094.png ; $QS ( T ) \subset M$ ; confidence 0.798
+. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130050/q13005094.png ; $\operatorname{QS} ( T ) \subset M$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009057.png ; $\varphi = \sum _ { n = 0 } ^ { \infty } \theta _ { n } ( f _ { n } )$ ; confidence 0.798
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009057.png ; $\varphi = \sum _ { n = 0 } ^ { \infty } \theta _ { n } ( f _ { n } ),$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120050/l12005013.png ; $f \in L _ { 1 } ( R _ { + } ; e ^ { - x } / \sqrt { x } )$ ; confidence 0.798
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130190/f13019016.png ; $c _ { N } = c _ { - N } = 1 , c _ { j } = 2$ ; confidence 0.798
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130190/f13019016.png ; $c _ { N } = c _ { - N } = 1 , c _ { j } = 2 \text{ otherwise}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520493.png ; $S , Y , Z \rightarrow U , V , W$ ; confidence 0.798
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013051.png ; $\tau _ { N } ( x , y + [ z ] )$ ; confidence 0.798
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013051.png ; $\tau _ { n } ( x , y + [ z ] )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001039.png ; $\Phi ^ { \alpha } ( Y ) = \nabla _ { Y } \xi ^ { \alpha }$ ; confidence 0.798
@@ Line 560: / Line 560: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080185.png ; $( v _ { i } , u _ { i } )$ ; confidence 0.797
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040298.png ; $A \in Q$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040298.png ; $\bf A \in Q$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c130/c130090/c13009033.png ; $d ( P _ { N } u ) / d x = \sum _ { n = 0 } ^ { N } b _ { n } T _ { N } ( x )$ ; confidence 0.797
-. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097590/w0975909.png ; $WC ( A , k ) = 0$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097590/w0975909.png ; $\operatorname{WC} ( A , k ) = 0$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110152.png ; $d Y _ { 1 } \ldots d Y _ { 2 k }$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110152.png ; $.d Y _ { 1 } \ldots d Y _ { 2 k }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014039.png ; $E _ { 6 }$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014039.png ; $\tilde{\bf E} _ { 6 }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001069.png ; $\tau ^ { 2 } = id$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001069.png ; $\tau ^ { 2 } = \operatorname{id}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/h/h120/h120030/h1200302.png ; $E ( \varphi ) = \frac { 1 } { 2 } \int _ { M } | d \varphi | ^ { 2 } v _ { g }$ ; confidence 0.797
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200236.png ; $j | z _ { j } | = \operatorname { min } _ { j } | w _ { j } | = 1$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200236.png ; $\operatorname{min}_j | z _ { j } | = \operatorname { min } _ { j } | w _ { j } | = 1$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010022.png ; $\sum _ { j \geq 1 } | e | ^ { \gamma } \approx$ ; confidence 0.797
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015045.png ; $( x )$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015045.png ; $( \bar{x} )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/f/f110/f110160/f110160111.png ; $( \phi _ { 1 } \& \ldots \& \phi _ { n } )$ ; confidence 0.797
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020048.png ; $\alpha _ { i j } \neq 0$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020048.png ; $\alpha _ { i i } \neq 0$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c020/c020660/c020660157.png ; $a b = 1$ ; confidence 0.797
-. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055070/k05507064.png ; $\tilde { \gamma } = \gamma _ { \varpi }$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055070/k05507064.png ; $\tilde { \gamma } = \gamma _ { \tilde{\omega} }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b120420155.png ; $Z ( C )$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b120420155.png ; $\bf Z (\cal C )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110237.png ; $r _ { N } ( \alpha , b ) \in S ( m _ { 1 } m _ { 2 } H ^ { N } , G )$ ; confidence 0.797
@@ Line 594: / Line 594: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a1201607.png ; $S _ { i } ( t | \{ u _ { i } ( t ) \} , \{ C _ { i j } ( t ) \} )$ ; confidence 0.797
-. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015010/b01501024.png ; $\{ \xi , \}$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015010/b01501024.png ; $\{ \xi_r\}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006066.png ; $h ^ { I I } ( z ) ^ { - 1 }$ ; confidence 0.797
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120500/b12050044.png ; $\alpha _ { X } : = \operatorname { inf } \{ s : 1 ( s , 0 ) > x \}$ ; confidence 0.797
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120500/b12050044.png ; $a _ { X } : = \operatorname { inf } \{ s : \operatorname{l} ( s , 0 ) > x \}$ ; confidence 1.000