Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/35"

Revision as of 13:34, 8 April 2020

List

1. ; $q ( x ) \in C _ { 0 } ^ { \infty } ( \mathbf{R} + )$ ; confidence 0.883

2. ; $x , y \in \mathbf{R} ^ { n }$ ; confidence 0.883

3. ; $F \mathbf{c} _ { k } = \mathbf{c} _ { f } ( k )$ ; confidence 0.883

4. ; $a < 1$ ; confidence 0.883

5. ; $\sigma ( \mathbf{w}.\mathbf{v} + \theta )$ ; confidence 0.883

6. ; $H _ { n - 2 }$ ; confidence 0.883

7. ; $K _ { 0 } > 1$ ; confidence 0.883

8. ; $\lambda _ { k } ( t ) = \alpha ( t ) e ^ { Z _ { k } ^ { T } ( t ) \beta } I _ { k } ( t ),$ ; confidence 0.883

9. ; $\tilde{\pi}$ ; confidence 0.883

10. ; $\rho : \operatorname{GL} _ { l } \rightarrow \operatorname{GL} _ { m }$ ; confidence 0.883

11. ; $\operatorname{Wh} ^ { * } ( \pi ) \subseteq \operatorname{Wh} ( \pi )$ ; confidence 0.883

12. ; $\phi _ { f } \phi _ { g } = \phi _ { f g }$ ; confidence 0.883

13. ; $= \oint _ { z = \infty } \tau _ { n + 1 } ( x , y - [ z ] ) \tau _ { m } ( x ^ { \prime } , y ^ { \prime } + [ z ] ) \times$ ; confidence 0.883

14. ; $( \mathfrak { E } , M )$ ; confidence 0.883

15. ; $\pi _ { k } ( \mathcal{X} , * ) \rightarrow \pi _ { k } ( \mathcal{Y} , * )$ ; confidence 0.883

16. ; $\mathcal{D} _ { g , n } = \overline { \mathcal{M} _ { g , n } } - \mathcal{M} _ { g , n }$ ; confidence 0.883

17. ; $\| u \| : = ( u , u ) ^ { 1 / 2 }_ { - }$ ; confidence 0.883

18. ; $( S _ { n } )$ ; confidence 0.882

19. ; $\overline { U } _ { 1 }$ ; confidence 0.882

20. ; $\theta = .5$ ; confidence 0.882

21. ; $| K ( x , y ) | = O ( | x - y | ^ { - x } )$ ; confidence 0.882

22. ; $| d \varphi | ^ { 2 } ( x ) = g ^ { i j } ( x ) h _ { \alpha \beta } ( \varphi ( x ) ) \cdot \frac { \partial \varphi ^ { \alpha } } { \partial x ^ { i } } \frac { \partial \varphi ^ { \beta } } { \partial x ^ { j } },$ ; confidence 0.882

23. ; $\Sigma ^ { i } ( f )$ ; confidence 0.882

24. ; $C _ { U }$ ; confidence 0.882

25. ; $\{ T ^ { t } \}$ ; confidence 0.882

26. ; $U _ { a }$ ; confidence 0.882

27. ; $( T f ) ( z ) = f ( - z )$ ; confidence 0.882

28. ; $\xi ( t ) = \frac { 1 } { \sqrt { \omega _ { N + 1 } } } \int _ { \mathbf{R} ^ { N } } \frac { e ^ { i ( t , \lambda ) } - 1 } { | \lambda | ^ { ( N + 1 ) / 2 } } W ( d \lambda ),$ ; confidence 0.882

29. ; $\lambda ^ { s _ { \mu } } = \sum _ { \nu } c _ { \lambda \mu } ^ { \nu } s _ { \nu },$ ; confidence 0.882

30. ; $x = x ( t , u , v )$ ; confidence 0.882

31. ; $\operatorname{ Soc } ( V )$ ; confidence 0.882

32. ; $f _ { 0 } ^ { \prime \prime } ( \overline{c} ) > 0$ ; confidence 0.882

33. ; $g ^ { \prime } = \phi g$ ; confidence 0.882

34. ; $\mathbf{A}, \mathbf{B} \in \textsf{K}$ ; confidence 0.882

35. ; $4$ ; confidence 0.882

36. ; $\operatorname{GCD} ( h ( n ) , q ) = 1$ ; confidence 0.882

37. ; $\hat { f } ( x _ { i } ) = c ( x _ { i } )$ ; confidence 0.882

38. ; $\alpha f = \alpha q$ ; confidence 0.882

39. ; $L y + p ( x ) y = 0$ ; confidence 0.882

40. ; $\mathfrak { n } ^ { + } = \sum ^{ \oplus }_{ \alpha \in \Phi ^ { + } } \mathfrak { g } _ { \alpha }$ ; confidence 0.882

41. ; $S _ { i } = + 1$ ; confidence 0.881

42. ; $\mathbf{P} ( \wedge ^ { k } \mathbf{C} ^ { n } )$ ; confidence 0.881

43. ; $M _ { C }$ ; confidence 0.881

44. ; $A _ { 1 } = I$ ; confidence 0.881

45. ; $\tau _ { A }$ ; confidence 0.881

46. ; $\textsf{P}$ ; confidence 0.881

47. ; $\gamma : \mathbf{R} ^ { n } \rightarrow \mathbf{R} ^ { k }$ ; confidence 0.881

48. ; $G _ { p , n } ( x ) = \sum _ { i = 1 } ^ { N } 1 _ { \{ n p _ { i n } \geq x \} }.$ ; confidence 0.881

49. ; $= \frac { \rho } { 2 ( 1 - \rho ) } \sum _ { p = 1 } ^ { P } \lambda _ { p } b _ { p } ^ { ( 2 ) } + \rho \frac { \Delta ^ { 2 } } { 2 R } +$ ; confidence 0.881

50. ; $( X , \| \, .\, \| )$ ; confidence 0.881

51. ; $\operatorname{deg}_{B} [ l , \Omega , y ] = 1$ ; confidence 0.881

52. ; $\sigma ( T ) \backslash \sigma _ { d } ( T )$ ; confidence 0.881

53. ; $1 \leq i \leq l$ ; confidence 0.881

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

55. ; $H _ { \text{new} } = H _ { k + 1 }$ ; confidence 0.881

56. ; $G ( x ) = 0$ ; confidence 0.881

57. ; $\operatorname { Deg } ( F , \overline { D } \square ^ { n + 1 } , \theta )$ ; confidence 0.881

58. ; $| S _ { k } ( 0 ) | = 1$ ; confidence 0.881

59. ; $f \in J _ { E }$ ; confidence 0.881

60. ; $p _ { j } \geq 0$ ; confidence 0.881

61. ; $d _ { - 1 } - d _ { 1 } = - c , d _ { - 1 } + d _ { 1 } = c ^ { 2 }.$ ; confidence 0.881

62. ; $R ^ { * } N$ ; confidence 0.881

63. ; $\mathcal{X} _ { t }$ ; confidence 0.881

64. ; $y( n )$ ; confidence 0.881

65. ; $\int _ { 0 } ^ { t } f ( W _ { s } ) d s = \int \operatorname{l}( t , x ) f ( x ) d x,$ ; confidence 0.880

66. ; $S ( k )$ ; confidence 0.880

67. ; $K ^ { ( j ) _{i} }( X ) \subset K _ { i } ( X ) \otimes \mathbf{Q}$ ; confidence 0.880

68. ; $M _ { K } = K \otimes _ { Z } M$ ; confidence 0.880

69. ; $x _ { i } \neq 0$ ; confidence 0.880

70. ; $( u , v ) _ { + } : = ( A ^ { - 1 / 2 } u , A ^ { - 1 / 2 } v ) _ { 0 },$ ; confidence 0.880

71. ; $f _ { 1 } ( T ) = W ^ { ( n - k ) / 2 } f ( T )$ ; confidence 0.880

72. ; $g : B [ R ] \rightarrow \mathbf{R} ^ { n }$ ; confidence 0.880

73. ; $\mathbf{F} _ { q }$ ; confidence 0.880

74. ; $P < Q$ ; confidence 0.880

75. ; $d w [ k ] = d w _ { 1 } \wedge \ldots \wedge d w _ { k - 1 } \wedge d w _ { k + 1 } \wedge \ldots \wedge d w _ { n }$ ; confidence 0.880

76. ; $\sum _ { j = m } ^ { \infty } f _ { j } ( x ) \varepsilon ^ { j }$ ; confidence 0.880

77. ; $\angle \operatorname { lim } _ { z \rightarrow \omega } F ( z )$ ; confidence 0.880

78. ; $D _ { K _ { \rho } } = \left\{ F ( \xi ) : \int _ { - \infty } ^ { + \infty } \xi ^ { 2 } | F ( \xi ) | ^ { 2 } d \rho ( \xi ) < \infty \right\}.$ ; confidence 0.880

79. ; $n \alpha ( \operatorname { mod } 1 )$ ; confidence 0.880

80. ; $n \in \mathcal{O} $ ; confidence 0.880

81. ; $m \geq m _ { 0 } > 0$ ; confidence 0.880

82. ; $n \in \mathbf{Z} _ { 3 }$ ; confidence 0.880

83. ; $l _ { V } : V \rightarrow \underline { 1 } \otimes V$ ; confidence 0.880

84. ; $\frac { a _ { 0 } } { 2 } + \sum _ { k = 1 } ^ { \infty } ( a _ { k } \operatorname { cos } k x + b _ { k } \operatorname { sin } k x ),$ ; confidence 0.880

85. ; $N / Q$ ; confidence 0.880

86. ; $\mathcal{K} = \{ B _ { r _ { 1 } } , B _ { r _ { 2 } } \}$ ; confidence 0.879

87. ; $\textsf{PK}$ ; confidence 0.879

88. ; $\| u - h \| _ { L } \infty < 1$ ; confidence 0.879

89. ; $\langle y _ { 1 } - y _ { 2 } , x _ { 1 } - x _ { 2 } \rangle \geq 0,$ ; confidence 0.879

90. ; $\mathcal{Q} = \mathcal{H} _ { D ^ { n } } ( \tilde { \mathcal{O} } )$ ; confidence 0.879

91. ; $Q = [ \xi _ { l } ^ { 0 } ] ^ { 2 } - [ \xi _ { r } ^ { 0 } ] ^ { 2 },$ ; confidence 0.879

92. ; $945 = 3 ^ { 3 } .5 .7$ ; confidence 0.879

93. ; $\mathcal{R} = q ^ { - 1 / 2 } \left( \begin{array} { c c c c } { q } & { 0 } & { 0 } & { 1 } \\ { 0 } & { 0 } & { q - q ^ { - 1 } } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 0 } & { q } \end{array} \right)$ ; confidence 0.879

94. ; $\mathcal{L} ^ { \perp } = \{ x : [ x , \mathcal{L} ] = \{ 0 \} \}$ ; confidence 0.879

95. ; $\mathcal{L} _ { p }$ ; confidence 0.879

96. ; $A _ { 1 } , A _ { 2 } : \mathcal{H} \rightarrow \mathcal{H}$ ; confidence 0.879

97. ; $H _ { N }$ ; confidence 0.879

98. ; $z$ ; confidence 0.879

99. ; $\alpha ^ { \prime } , \alpha \in S ^ { 2 }$ ; confidence 0.879

100. ; $n = p ^ { \text{l} }$ ; confidence 0.879

101. ; $P _ { q }$ ; confidence 0.879

102. ; $f _ { k } ( z )$ ; confidence 0.878

103. ; $f ( x , k ) = b ( k ) g ( x , k ) + a ( k ) g ( x , - k ),$ ; confidence 0.878

104. ; $c _ { 1 } ( L ) ^ { \operatorname { dim } X } > 0$ ; confidence 0.878

105. ; $g ( n ) = \sum _ { d | n } f ( d ) \Leftrightarrow f ( n ) = \sum _ { d | n } g ( d ) \mu \left( \frac { n } { d } \right).$ ; confidence 0.878

106. ; $d s _ { N } ^ { 2 }$ ; confidence 0.878

107. ; $K _ { 0 } = K _ { \text{BN} }$ ; confidence 0.878

108. ; $S \cup T$ ; confidence 0.878

109. ; $M _ { 4 } = \operatorname { min } _ { 1 \leq j < k \leq n } | z _ { j } - z _ { k } |$ ; confidence 0.878

110. ; $-n$ ; confidence 0.878

111. ; $x \notin \overline { D } \subset \mathbf{R} ^ { 2 }$ ; confidence 0.878

112. ; $H \phi$ ; confidence 0.878

113. ; $\Theta _ { \Delta } ( z ) = H + z G ( I - z T ) ^ { - 1 } F,$ ; confidence 0.878

114. ; $\forall x _ { i } \in D ( A ),$ ; confidence 0.878

115. ; $y \in V ^ { \mp }$ ; confidence 0.878

116. ; $M ( n )$ ; confidence 0.878

117. ; $( N _ { * } ^ { 1 } , N _ { * } ^ { 2 } )$ ; confidence 0.878

118. ; $\sum s _ { j } x _ { j }$ ; confidence 0.878

119. ; $\gamma ^ { d } \cap \alpha _ { 1 } = \ldots = \gamma ^ { d } \cap \alpha _ { q } = \emptyset$ ; confidence 0.878

120. ; $\mathcal{T} ^ { \# } ( n )$ ; confidence 0.878

121. ; $z _ { 1 } = \ldots = z _ { m } = 1$ ; confidence 0.878

122. ; $N > 0$ ; confidence 0.878

123. ; $z = m l$ ; confidence 0.878

124. ; $E ^ { * }$ ; confidence 0.878

125. ; $K ^ { \prime }$ ; confidence 0.878

126. ; $x \preceq z \preceq y \Rightarrow z \in H.$ ; confidence 0.878

127. ; $D ^ { - }$ ; confidence 0.877

128. ; $( x , \xi ) \in \mathbf{R} ^ { x } \times S ^ { x - 1 }$ ; confidence 0.877

129. ; $w ( x , y )$ ; confidence 0.877

130. ; $\operatorname { Idim } ( P ) = \operatorname { dim } ( Q )$ ; confidence 0.877

131. ; $F \circ f \in \mathcal{A} ^ { * }$ ; confidence 0.877

132. ; $\{ a _ { k } \}$ ; confidence 0.877

133. ; $Z _ { q } ( y ) = \sum _ { n = 0 } ^ { \infty } q ^ { n } y ^ { n } = ( 1 - q y ) ^ { - 1 },$ ; confidence 0.877

134. ; $F ( u ) = \{ v \in V : ( u , v ) \in E \}$ ; confidence 0.877

135. ; $K _ { i } \in \Omega ^ { k _ { i } } ( M ; T M )$ ; confidence 0.877

136. ; $Q _ { x _ { 0 } } ^ { T }$ ; confidence 0.877

137. ; $\Delta \subset \subset \Gamma$ ; confidence 0.877

138. ; $d j \neq 0$ ; confidence 0.877

139. ; $( \xi \oplus \sigma , \eta \oplus \sigma , \zeta \oplus \text { id } \sigma )$ ; confidence 0.877

140. ; $\theta ( a _ { 0 } , a _ { 1 } )$ ; confidence 0.877

141. ; $\nu ( t ) : = ( 1 / ( 1 - t ) , 0 )$ ; confidence 0.877

142. ; $\nabla . \mathbf{B} = 0 ;$ ; confidence 0.877

143. ; $\{ p _ { M } \in P ( k ) : M \in \Gamma \}$ ; confidence 0.877

144. ; $M ( n + 2 ) , M ( n + 3 ) , \ldots$ ; confidence 0.877

145. ; $2$ ; confidence 0.876

146. ; $1 / 2 < \gamma < 3 / 2$ ; confidence 0.876

147. ; $\operatorname{dim}_{A} M = \operatorname{dim} A $ ; confidence 0.876

148. ; $C _ { f }$ ; confidence 0.876

149. ; $R ( \nabla ) : \mathcal{E} \rightarrow \otimes ^ { 3 } \mathcal{E}$ ; confidence 0.876

150. ; $\| \lambda \| = \operatorname { sup } _ { 0 \leq s < t \leq 1 } | \operatorname { log } \{ ( t - s ) ^ { - 1 } ( \lambda ( t ) - \lambda ( s ) ) \} |.$ ; confidence 0.876

151. ; $d w [ k ] = d w _ { 1 } \wedge \ldots \wedge d w _ { k - 1 } \wedge d w _ { k + 1 } \wedge \ldots \wedge d w _ { n }$ ; confidence 0.876

152. ; $\int _ { T } | u ( x ) | ^ { p } d x$ ; confidence 0.876

153. ; $P = \{ p _ { 1 } , \dots , p _ { n } \} \subset \mathbf{R} ^ { k }$ ; confidence 0.876

154. ; $Q ^ { \pm }$ ; confidence 0.876

155. ; $N _ { A } = \left( \# \frac { A } { n } + o ( 1 ) \right) x \operatorname { log } x,$ ; confidence 0.876

156. ; $( \lambda x M ) x = M$ ; confidence 0.876

157. ; $\tilde { \gamma } - \gamma = i ( \sigma _ { 1 } \Phi \Phi ^ { * } \sigma _ { 2 } - \sigma _ { 2 } \Phi \Phi ^ { * } \sigma _ { 1 } ).$ ; confidence 0.876

158. ; $\alpha \in S ^ { n - 1 }$ ; confidence 0.876

159. ; $[ H , \rho ] = H \rho - \rho H$ ; confidence 0.876

160. ; $R _ { t } ( x )$ ; confidence 0.876

161. ; $\mathcal{N} = \{ X \in \mathfrak { g } : \operatorname{ad}X \, \text{is a nilpotent endomorphism of} \, \mathfrak { g } \}$ ; confidence 0.876

162. ; $Y _ { n } \subset Y _ { n + 1 }$ ; confidence 0.876

163. ; $\mathcal{R} _ { \text{nd} } ( \Omega ) = \mathcal{B} / \mathcal{I} _ { \text{nd} }$ ; confidence 0.876

164. ; $[ L ^ { 1 } ( \mu ) ]$ ; confidence 0.875

165. ; $\sigma _ { p } ( T )$ ; confidence 0.875

166. ; $P _ { - } \psi ( t )$ ; confidence 0.875

167. ; $\| x ( t ) \| \leq c \| x _ { 0 } \| \text { for all } \, t \in [ 0 , \tau ],$ ; confidence 0.875

168. ; $P^3$ ; confidence 0.875

169. ; $K _ { E } ( V )$ ; confidence 0.875

170. ; $n \times 1$ ; confidence 0.875

171. ; $f \in L ^ { 2 } ( \mathbf{R} )$ ; confidence 0.875

172. ; $A \langle X \rangle $ ; confidence 0.875

173. ; $| x - x _ { x } | < y _ { x }$ ; confidence 0.875

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

175. ; $\operatorname{char}( X ^ { \omega \chi ^ { - 1 }} ) = \pi ^ { \mu _ { \chi } ^ { * } } g _ { \chi } ^ { * } ( T ).$ ; confidence 0.875

176. ; $D f ( x _ { 0 } , h ) = \frac { d } { d t } f ( x _ { 0 } + t h ) | _ { t = 0 } =$ ; confidence 0.875

177. ; $S \left( \begin{array} { c c } { \alpha } & { \beta } \\ { \gamma } & { \delta } \end{array} \right) = \left( \begin{array} { c c } { q ^ { 2 } \delta + ( 1 - q ^ { 2 } ) \alpha } & { - q ^ { 2 } \beta } \\ { - q ^ { 2 } \gamma } & { \alpha } \end{array} \right).$ ; confidence 0.875

178. ; $m _ { \nu } w _ { \nu }$ ; confidence 0.875

179. ; $C ^ { K }$ ; confidence 0.875

180. ; $k = 4$ ; confidence 0.875

181. ; $\{ m , a \} \equiv \{ m , b \}$ ; confidence 0.875

182. ; $\operatorname{BMO}( \mathbf{R} ^ { n } )$ ; confidence 0.875

183. ; $\operatorname{Wh} ( \pi )$ ; confidence 0.875

184. ; $D ( 2 n _ { 1 } )$ ; confidence 0.875

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

186. ; $\Phi _ { \alpha }$ ; confidence 0.875

187. ; $\operatorname{l} ( A )$ ; confidence 0.875

188. ; $\mathbf{R} ^ { N }$ ; confidence 0.875

189. ; $( - 1 ) ^ { n }$ ; confidence 0.874

190. ; $\lambda _ { 1 } > \ldots > \lambda _ { 2 m } \geq 0$ ; confidence 0.874

191. ; $b = v$ ; confidence 0.874

192. ; $| x | \leq | y |$ ; confidence 0.874

193. ; $F | _ { l } : l \rightarrow \mathbf{C} ^ { 2 }$ ; confidence 0.874

194. ; $m_{i}$ ; confidence 0.874

195. ; $u$ ; confidence 0.874

196. ; $x ^ { q ^ { d } } - x$ ; confidence 0.874

197. ; $\tau = \operatorname { inf } \{ t > 0 : | B _ { t } | = 1 \}$ ; confidence 0.874

198. ; $| x | = | x _ { 0 } | ^ { 1 - \theta } | x _ { 1 } | ^ { \theta }$ ; confidence 0.874

199. ; $\Leftrightarrow$ ; confidence 0.874

200. ; $\{ f _ { n } \} _ { n = 0 } ^ { \infty }$ ; confidence 0.874

201. ; $( \mathcal{C} , U )$ ; confidence 0.874

202. ; $S N = \pi ^ { - 1 } ( N ) \subset U M$ ; confidence 0.874

203. ; $\operatorname{SH} ^ { * } ( M , \omega ) = \operatorname{SH} ^ { * } ( M , \omega , \phi )$ ; confidence 0.874

204. ; $q _ { 1 } = x _ { 1 } + x _ { 3 } , \quad q _ { 2 } = x _ { 2 } + x _ { 4 }.$ ; confidence 0.874

205. ; $m \geq 2$ ; confidence 0.874

206. ; $C ^ { 0 , \sigma _ { 1 } ( t ) } ( \Omega )$ ; confidence 0.874

207. ; $D _ { n }$ ; confidence 0.874

208. ; $W _ { 1 } = S _ { 1 } e ^ { \sum _ { 1 } ^ { \infty } x _ { k } \Lambda ^ { k } },$ ; confidence 0.873

209. ; $\sum _ { j = 1 } ^ { n } \xi _ { j } d x _ { j }$ ; confidence 0.873

210. ; $\operatorname { Map } ( X \times Z , Y ) \rightarrow \operatorname { Map } ( X , \operatorname { Map } ( Z , Y ) )$ ; confidence 0.873

211. ; $\mathbf{Z}H$ ; confidence 0.873

212. ; $\rho ( x , y ) = \langle x - y , x - y \rangle ^ { 1 / 2 }$ ; confidence 0.873

213. ; $\operatorname{so}( 1,3 ) \oplus \mathbf{R} ^ { 1,3 }$ ; confidence 0.873

214. ; $\overline{\Delta}$ ; confidence 0.873

215. ; $\operatorname { cosh } \delta = | - X _ { 0 } Y _ { 0 } + \sum X _ { t } Y _ { t } |.$ ; confidence 0.873

216. ; $X : = K \backslash G ( \mathbf{R} )$ ; confidence 0.873

217. ; $E ^ { 3 }$ ; confidence 0.873

218. ; $u | _ { \partial \Omega } \in H _ { 2 } ^ { \rho } ( \partial \Omega )$ ; confidence 0.873

219. ; $\mathcal{S} : = \left\{ r _ { + } ( k ) , i k _ { j } , ( m _ { j } ^ { + } ) ^ { 2 } : 1 \leq j \leq J , k _ { j } > 0 , m _ { j } ^ { + } > 0 , k > 0 \right\}$ ; confidence 0.873

220. ; $R ^ { \prime }$ ; confidence 0.873

221. ; $\mathbf{y} _ { i j k }$ ; confidence 0.873

222. ; $w \in A$ ; confidence 0.873

223. ; $q = v ^ { * }$ ; confidence 0.873

224. ; $x ( t ) \in \mathbf{R} ^ { n }$ ; confidence 0.873

225. ; $A = L D L ^ { T }$ ; confidence 0.873

226. ; $\operatorname { sup } _ { i \in I } \mu _ { i } \in \mathcal{D}$ ; confidence 0.873

227. ; $\alpha \leq k$ ; confidence 0.873

228. ; $B ( \mathcal{H} )$ ; confidence 0.873

229. ; $j _ { e } ( z ) = J ( z )$ ; confidence 0.873

230. ; $\| \Delta ( \mathbf{U} ^ { n } - \mathbf{u} ^ { n } ) \| \leq \| \Delta ( \mathbf{U} ^ { 0 } - \mathbf{u} ^ { 0 } ) \| + O ( h ^ { 2 } + k ^ { 2 } ),$ ; confidence 0.873

231. ; $\{ s _ { k } , y _ { k } \} _ { k = 0 } ^ { n - 1 }$ ; confidence 0.873

232. ; $\tilde{z}$ ; confidence 0.873

233. ; $c M$ ; confidence 0.873

234. ; $g = 0 \Leftrightarrow C$ ; confidence 0.873

235. ; $w = \phi + i \psi$ ; confidence 0.873

236. ; $|S|$ ; confidence 0.873

237. ; $\{ A _ { j n _ { k } } \}$ ; confidence 0.872

238. ; $A ( D ) ^ { * } \simeq A ( \tilde { D } ),$ ; confidence 0.872

239. ; $F ^ { ( k + 1 ) } \in \{ \Gamma , k + 2 , \mathbf{v} \}$ ; confidence 0.872

240. ; $\Phi ^ { ( 3 ) } = O ( | Z | ^ { 2 } )$ ; confidence 0.872

241. ; $[ \omega \wedge D _ { 1 } , D _ { 2 } ] =$ ; confidence 0.872

242. ; $W = \operatorname { lin } ( w )$ ; confidence 0.872

243. ; $N ( . )$ ; confidence 0.872

244. ; $f _ { j } ( \overline{x} ) \in \mathbf{Z} _ { p } ^ { n }$ ; confidence 0.872

245. ; $T V _ { X }$ ; confidence 0.872

246. ; $v _ { \varepsilon } ( \alpha , \theta )$ ; confidence 0.872

247. ; $n > \delta$ ; confidence 0.872

248. ; $b ( x ) = \sum _ { j = 1 } ^ { m } n _ { j } ( x ) a _ { j } ( x )$ ; confidence 0.872

249. ; $\nu ( \lambda )$ ; confidence 0.872

250. ; $\lim \inf \rightarrow \omega ( 1 - | F ( z ) | ) / ( 1 - | z | ) = d ( \omega ) < \infty$ ; confidence 0.872

251. ; $[ a , b ] \subseteq T$ ; confidence 0.872

252. ; $T ( \square _ { \alpha } \varphi ) = \square _ { \alpha } ( T ( \varphi ) )$ ; confidence 0.872

253. ; $G_{x}$ ; confidence 0.872

254. ; $\chi _ { \lambda I - T } < 0$ ; confidence 0.872

255. ; $p \notin \overline { I \backslash p }$ ; confidence 0.872

256. ; $H _ { \phi } : H ^ { 2 } \rightarrow H _ { - } ^ { 2 }$ ; confidence 0.872

257. ; $\operatorname{ Wh} ^ { * } ( \pi )$ ; confidence 0.872

258. ; $K _ { 0 } \in \mathcal{K}$ ; confidence 0.872

259. ; $\mathfrak { g } _ { \pm } = \oplus _ { \alpha \in \Delta _ { \pm } } \mathfrak { g } ^ { \alpha }$ ; confidence 0.871

260. ; $\psi _ { i - 1 } : F _ { m } \rightarrow B ( m , n , i - 1 )$ ; confidence 0.871

261. ; $x = x ^ { x }$ ; confidence 0.871

262. ; $\nabla . H = 0$ ; confidence 0.871

263. ; $( 2 \pi ) ^ { - 2 n } \int _ { \mathbf{R} ^ { 2 n } } \rho ( p , q , 0 ) \hat { \sigma } ( p , q ) d p d q =$ ; confidence 0.871

264. ; $d s ^ { 2 } = \frac { 1 } { 4 } ( 1 + | g | ^ { 2 } ) ^ { 2 } | \eta | ^ { 2 } = \frac { 1 } { 2 } \sum _ { j = 1 } ^ { 3 } | \omega _ { j } | ^ { 2 },$ ; confidence 0.871

265. ; $\operatorname{ind} T _ { \phi } = \operatorname { dim } \operatorname { Ker } T _ { \phi } - \operatorname { dim } \operatorname { Ker } T _ { \phi } ^ { * } = 0$ ; confidence 0.871

266. ; $\psi = \sum _ { i = 1 } ^ { r } d _ { i } \zeta _ { i }$ ; confidence 0.871

267. ; $C ( 4 )$ ; confidence 0.871

268. ; $W ^ { 1 } L _ { \Phi } ( \Omega )$ ; confidence 0.871

269. ; $u , v \in T M$ ; confidence 0.871

270. ; $S : L ^ { 1 } \rightarrow Y$ ; confidence 0.871

271. ; $X ^ { n } + A _ { 1 } X ^ { n - 1 } + \ldots + A _ { n - 1 } X + A _ { n } = 0,$ ; confidence 0.871

272. ; $F ( s , t ) = \| t x + s y \| \text { for all } s , t \geq 0,$ ; confidence 0.871

273. ; $\operatorname { deg } ( F , \overline { D } \square ^ { n + 1 } , \theta ) = k$ ; confidence 0.871

274. ; $m = 2l + 1$ ; confidence 0.871

275. ; $N L$ ; confidence 0.871

276. ; $x ( \alpha ) = x _ { 12 } ( \alpha )$ ; confidence 0.871

277. ; $\mathbf{G} = G _ { 1 } + \ldots + G _ { m }$ ; confidence 0.871

278. ; $\mu ( E , F ) = ( - 1 ) ^ { d }$ ; confidence 0.871

279. ; $\overline{z}$ ; confidence 0.871

280. ; $P ( f \otimes g ) = f * g$ ; confidence 0.871

281. ; $( \# A ) ^ { 1 / 2 }$ ; confidence 0.871

282. ; $N = k$ ; confidence 0.871

283. ; $a _ { 1 } \sigma _ { 1 } ( u ) + \ldots + a _ { t } \sigma _ { t } ( u ) \neq 0.$ ; confidence 0.871

284. ; $\langle \tilde { \gamma } ( X ) , Y \rangle = g ( X \otimes Y ) \in \mathcal{R}$ ; confidence 0.871

285. ; $\frac { \overline { \Omega \Omega ^ { \prime } } } { 2 \operatorname { sin } \omega } = \overline { O \Omega } = \overline { O \Omega ^ { \prime } } = R \sqrt { 1 - 4 \operatorname { sin } ^ { 2 } \omega }.$ ; confidence 0.871

286. ; $U _ { q } ( n _ { + } )$ ; confidence 0.871

287. ; $( f , g ) : = \left( \sum _ { j = 1 } ^ { J } K ( x , y _ { j } ) c _ { j } , \sum _ { m = 1 } ^ { M } K ( x , z _ { m } ) \beta _ { m } \right) =$ ; confidence 0.871

288. ; $v ( x , \alpha , k ) = \frac { e ^ { i k r } } { r } A ( \alpha ^ { \prime } , \alpha , k ) + o ( \frac { 1 } { r } ),$ ; confidence 0.871

289. ; $d S _ { t } / d u _ { t } = c _ { 1 }$ ; confidence 0.870

290. ; $\sum _ { j = 1 } ^ { M } \sum _ { t = 1 } ^ { T } c _ { j t } x _ { j t } \leq B,$ ; confidence 0.870

291. ; $t _ { i } ( z )$ ; confidence 0.870

292. ; $p = n$ ; confidence 0.870

293. ; $( n \times m )$ ; confidence 0.870

294. ; $= ( m - n ) L ( m + n ) + \frac { 1 } { 12 } ( m ^ { 3 } - m ) \delta _ { n + m , 0 } c,$ ; confidence 0.870

295. ; $\{ 1 ^ { \prime } < 1 < 2 ^ { \prime } < 2 < \ldots \}$ ; confidence 0.870

296. ; $\hat { \theta } = \psi _ { \mu } ( X )$ ; confidence 0.870

297. ; $\mathcal{O} ( U )$ ; confidence 0.870

298. ; $\Theta = \textsf{E} ( \mathbf{Z} _ { 12 } )$ ; confidence 0.870

299. ; $\mathcal{L} _ { Y } P = 0$ ; confidence 0.870

300. ; $\{ D _ { N } ( x , 1 ) \}$ ; confidence 0.870

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/35. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/35&oldid=45303

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Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/35"

Revision as of 13:34, 8 April 2020

List

@@ Line 1: / Line 1: @@
 == List ==
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i130060148.png ; $q ( x ) \in C _ { 0 } ^ { \infty } ( R + )$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i130060148.png ; $q ( x ) \in C _ { 0 } ^ { \infty } ( \mathbf{R} + )$ ; confidence 0.883
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120020/c12002085.png ; $x , y \in R ^ { n }$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120020/c12002085.png ; $x , y \in \mathbf{R} ^ { n }$ ; confidence 0.883
-. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700086.png ; $F c _ { k } = c _ { f } ( k )$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700086.png ; $F \mathbf{c} _ { k } = \mathbf{c} _ { f } ( k )$ ; confidence 0.883
 . https://www.encyclopediaofmath.org/legacyimages/l/l057/l057320/l05732010.png ; $a < 1$ ; confidence 0.883
-. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130090/r13009022.png ; $\sigma ( w x + \theta )$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130090/r13009022.png ; $\sigma ( \mathbf{w}.\mathbf{v}  + \theta )$ ; confidence 0.883
 . https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m130180141.png ; $H _ { n - 2 }$ ; confidence 0.883
@@ Line 14: / Line 14: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060134.png ; $K _ { 0 } > 1$ ; confidence 0.883
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130250/c13025040.png ; $\lambda _ { k } ( t ) = \alpha ( t ) e ^ { Z _ { k } ^ { T } ( t ) \beta } I _ { k } ( t )$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130250/c13025040.png ; $\lambda _ { k } ( t ) = \alpha ( t ) e ^ { Z _ { k } ^ { T } ( t ) \beta } I _ { k } ( t ),$ ; confidence 0.883
-. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047080/h04708061.png ; $\pi$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047080/h04708061.png ; $\tilde{\pi}$ ; confidence 0.883
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004079.png ; $\rho : GL _ { l } \rightarrow GL _ { m }$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004079.png ; $\rho : \operatorname{GL} _ { l } \rightarrow \operatorname{GL} _ { m }$ ; confidence 0.883
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170184.png ; $Wh ^ { * } ( \pi ) \subseteq Wh ( \pi )$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170184.png ; $\operatorname{Wh} ^ { * } ( \pi ) \subseteq \operatorname{Wh} ( \pi )$ ; confidence 0.883
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120050/f12005035.png ; $\phi _ { f } \phi _ { g } = \phi _ { f g }$ ; confidence 0.883
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013030.png ; $= \oint _ { z = \infty } \tau _ { n + 1 } ( x , y - [ z ] ) \tau _ { m } ( x ^ { \prime } , y ^ { \prime } + [ z ] ) x$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013030.png ; $= \oint _ { z = \infty } \tau _ { n + 1 } ( x , y - [ z ] ) \tau _ { m } ( x ^ { \prime } , y ^ { \prime } + [ z ] ) \times$ ; confidence 0.883
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120010/e12001084.png ; $( \mathfrak { E } , M )$ ; confidence 0.883
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120250/m12025022.png ; $\pi _ { k } ( X , * ) \rightarrow \pi _ { k } ( Y , * )$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120250/m12025022.png ; $\pi _ { k } ( \mathcal{X} , * ) \rightarrow \pi _ { k } ( \mathcal{Y} , * )$ ; confidence 0.883
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130060/w13006016.png ; $D _ { g , n } = \overline { M _ { g , n } } - M _ { g , n }$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130060/w13006016.png ; $\mathcal{D} _ { g , n } = \overline { \mathcal{M} _ { g , n } } - \mathcal{M} _ { g , n }$ ; confidence 0.883
-. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007035.png ; $\| u \| : = ( u , u ) ^ { 1 / 2 }$ ; confidence 0.883
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007035.png ; $\| u \| : = ( u , u ) ^ { 1 / 2 }_ { - }$ ; confidence 0.883
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018054.png ; $( S _ { n } )$ ; confidence 0.882
@@ Line 42: / Line 42: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b110/b110660/b11066054.png ; $| K ( x , y ) | = O ( | x - y | ^ { - x } )$ ; confidence 0.882
-. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120030/h12003017.png ; $| d \varphi | ^ { 2 } ( x ) = g ^ { i j } ( x ) h _ { \alpha \beta } ( \varphi ( x ) ) \cdot \frac { \partial \varphi ^ { \alpha } } { \partial x ^ { i } } \frac { \partial \varphi ^ { \beta } } { \partial x ^ { j } }$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120030/h12003017.png ; $| d \varphi | ^ { 2 } ( x ) = g ^ { i j } ( x ) h _ { \alpha \beta } ( \varphi ( x ) ) \cdot \frac { \partial \varphi ^ { \alpha } } { \partial x ^ { i } } \frac { \partial \varphi ^ { \beta } } { \partial x ^ { j } },$ ; confidence 0.882
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120050/t12005038.png ; $\Sigma ^ { i } ( f )$ ; confidence 0.882
@@ Line 54: / Line 54: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130100/b13010068.png ; $( T f ) ( z ) = f ( - z )$ ; confidence 0.882
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018081.png ; $\xi ( t ) = \frac { 1 } { \sqrt { \omega _ { N + 1 } } } \int _ { R ^ { N } } \frac { e ^ { i ( t , \lambda ) } - 1 } { | \lambda | ^ { ( N + 1 ) / 2 } } W ( d \lambda )$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018081.png ; $\xi ( t ) = \frac { 1 } { \sqrt { \omega _ { N + 1 } } } \int _ { \mathbf{R} ^ { N } } \frac { e ^ { i ( t , \lambda ) } - 1 } { | \lambda | ^ { ( N + 1 ) / 2 } } W ( d \lambda ),$ ; confidence 0.882
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s120040132.png ; $\lambda ^ { s _ { \mu } } = \sum _ { \nu } c _ { \lambda \mu } ^ { \nu } s _ { \nu }$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s120040132.png ; $\lambda ^ { s _ { \mu } } = \sum _ { \nu } c _ { \lambda \mu } ^ { \nu } s _ { \nu },$ ; confidence 0.882
 . https://www.encyclopediaofmath.org/legacyimages/m/m062/m062220/m06222073.png ; $x = x ( t , u , v )$ ; confidence 0.882
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b13003054.png ; $( V )$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b13003054.png ; $\operatorname{ Soc } ( V )$ ; confidence 0.882
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130010/c13001026.png ; $f _ { 0 } ^ { \prime \prime } ( c ) > 0$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130010/c13001026.png ; $f _ { 0 } ^ { \prime \prime } ( \overline{c} ) > 0$ ; confidence 0.882
 . https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p1201208.png ; $g ^ { \prime } = \phi g$ ; confidence 0.882
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040786.png ; $A , B \in K$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040786.png ; $\mathbf{A}, \mathbf{B} \in \textsf{K}$ ; confidence 0.882
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040126.png ; $4$ ; confidence 0.882
-. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e13007013.png ; $GCD ( h ( n ) , q ) = 1$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e13007013.png ; $\operatorname{GCD} ( h ( n ) , q ) = 1$ ; confidence 0.882
 . https://www.encyclopediaofmath.org/legacyimages/m/m130/m130010/m13001027.png ; $\hat { f } ( x _ { i } ) = c ( x _ { i } )$ ; confidence 0.882
@@ Line 78: / Line 78: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d110/d110220/d11022062.png ; $L y + p ( x ) y = 0$ ; confidence 0.882
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090295.png ; $\mathfrak { n } ^ { + } = \sum _ { \alpha \in \Phi ^ { + } } \mathfrak { g } _ { \alpha }$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090295.png ; $\mathfrak { n } ^ { + } = \sum ^{ \oplus }_{ \alpha \in \Phi ^ { + } } \mathfrak { g } _ { \alpha }$ ; confidence 0.882
 . https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008062.png ; $S _ { i } = + 1$ ; confidence 0.881
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120020/q12002012.png ; $P ( \wedge ^ { k } C ^ { n } )$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120020/q12002012.png ; $\mathbf{P} ( \wedge ^ { k } \mathbf{C} ^ { n } )$ ; confidence 0.881
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120210/t12021068.png ; $M _ { C }$ ; confidence 0.881
@@ Line 90: / Line 90: @@
 . https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010017.png ; $\tau _ { A }$ ; confidence 0.881
-. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110210/c11021038.png ; $P$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110210/c11021038.png ; $\textsf{P}$ ; confidence 0.881
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d12030025.png ; $\gamma : R ^ { n } \rightarrow R ^ { k }$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d12030025.png ; $\gamma : \mathbf{R} ^ { n } \rightarrow \mathbf{R} ^ { k }$ ; confidence 0.881
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011055.png ; $G _ { p , n } ( x ) = \sum _ { i = 1 } ^ { N } 1 _ { \{ n p _ { i n } \geq x \} }$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011055.png ; $G _ { p , n } ( x ) = \sum _ { i = 1 } ^ { N } 1 _ { \{ n p _ { i n } \geq x \} }.$ ; confidence 0.881
 . https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008063.png ; $= \frac { \rho } { 2 ( 1 - \rho ) } \sum _ { p = 1 } ^ { P } \lambda _ { p } b _ { p } ^ { ( 2 ) } + \rho \frac { \Delta ^ { 2 } } { 2 R } +$ ; confidence 0.881
-. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110030/e11003043.png ; $( X , \| \| )$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110030/e11003043.png ; $( X , \| \, .\,  \| )$ ; confidence 0.881
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026055.png ; $[ l , \Omega , y ] = 1$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026055.png ; $\operatorname{deg}_{B} [ l , \Omega , y ] = 1$ ; confidence 0.881
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120130/w12013011.png ; $\sigma ( T ) \backslash \sigma _ { d } ( T )$ ; confidence 0.881
@@ Line 108: / Line 108: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120280/a120280141.png ; $S _ { E } = \{ \omega \in \hat { G } : E + \omega \subseteq E \}$ ; confidence 0.881
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005065.png ; $H _ { new } = H _ { k + 1 }$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005065.png ; $H _ { \text{new} } = H _ { k + 1 }$ ; confidence 0.881
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120520/b12052065.png ; $G ( x ) = 0$ ; confidence 0.881
@@ Line 120: / Line 120: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027061.png ; $p _ { j } \geq 0$ ; confidence 0.881
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004053.png ; $d _ { - 1 } - d _ { 1 } = - c , d _ { - 1 } + d _ { 1 } = c ^ { 2 }$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004053.png ; $d _ { - 1 } - d _ { 1 } = - c , d _ { - 1 } + d _ { 1 } = c ^ { 2 }.$ ; confidence 0.881
 . https://www.encyclopediaofmath.org/legacyimages/x/x120/x120010/x12001089.png ; $R ^ { * } N$ ; confidence 0.881
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001023.png ; $X _ { t }$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001023.png ; $\mathcal{X} _ { t }$ ; confidence 0.881
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001029.png ; $y ^ { \prime } ( n )$ ; confidence 0.881
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001029.png ; $y( n )$ ; confidence 0.881
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120500/b12050027.png ; $\int _ { 0 } ^ { t } f ( W _ { s } ) d s = \int 1 ( t , x ) f ( x ) d x$ ; confidence 0.880
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120500/b12050027.png ; $\int _ { 0 } ^ { t } f ( W _ { s } ) d s = \int \operatorname{l}( t , x ) f ( x ) d x,$ ; confidence 0.880
 . https://www.encyclopediaofmath.org/legacyimages/k/k130/k130070/k13007056.png ; $S ( k )$ ; confidence 0.880
-. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b11022047.png ; $K ^ { ( j ) } i ( X ) \subset K _ { i } ( X ) \otimes Q$ ; confidence 0.880
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b11022047.png ; $K ^ { ( j ) _{i} }( X ) \subset K _ { i } ( X ) \otimes \mathbf{Q}$ ; confidence 0.880
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090355.png ; $M _ { K } = K \otimes _ { Z } M$ ; confidence 0.880
@@ Line 138: / Line 138: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021077.png ; $x _ { i } \neq 0$ ; confidence 0.880
-. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007040.png ; $( u , v ) _ { + } : = ( A ^ { - 1 / 2 } u , A ^ { - 1 / 2 } v ) _ { 0 }$ ; confidence 0.880
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007040.png ; $( u , v ) _ { + } : = ( A ^ { - 1 / 2 } u , A ^ { - 1 / 2 } v ) _ { 0 },$ ; confidence 0.880
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230148.png ; $f _ { 1 } ( T ) = W ^ { ( n - k ) / 2 } f ( T )$ ; confidence 0.880
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026082.png ; $g : B [ R ] \rightarrow R ^ { n }$ ; confidence 0.880
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026082.png ; $g : B [ R ] \rightarrow \mathbf{R} ^ { n }$ ; confidence 0.880
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050176.png ; $F _ { q }$ ; confidence 0.880
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050176.png ; $\mathbf{F} _ { q }$ ; confidence 0.880
 . https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900123.png ; $P < Q$ ; confidence 0.880
@@ Line 154: / Line 154: @@
 . https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007054.png ; $\angle \operatorname { lim } _ { z \rightarrow \omega } F ( z )$ ; confidence 0.880
-. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520286.png ; $D _ { K _ { \rho } } = \{ F ( \xi ) : \int _ { - \infty } ^ { + \infty } \xi ^ { 2 } | F ( \xi ) | ^ { 2 } d \rho ( \xi ) < \infty \}$ ; confidence 0.880
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520286.png ; $D _ { K _ { \rho } } = \left\{ F ( \xi ) : \int _ { - \infty } ^ { + \infty } \xi ^ { 2 } | F ( \xi ) | ^ { 2 } d \rho ( \xi ) < \infty \right\}.$ ; confidence 0.880
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029093.png ; $( \operatorname { mod } 1 )$ ; confidence 0.880
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029093.png ; $n \alpha ( \operatorname { mod } 1 )$ ; confidence 0.880
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051050.png ; $n \in O$ ; confidence 0.880
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051050.png ; $n \in \mathcal{O} $ ; confidence 0.880
 . https://www.encyclopediaofmath.org/legacyimages/m/m130/m130070/m13007019.png ; $m \geq m _ { 0 } > 0$ ; confidence 0.880
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120060/d12006028.png ; $n \in Z _ { 3 }$ ; confidence 0.880
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120060/d12006028.png ; $n \in \mathbf{Z} _ { 3 }$ ; confidence 0.880
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042026.png ; $l _ { V } : V \rightarrow \underline { 1 } \otimes V$ ; confidence 0.880
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i1300401.png ; $\frac { a _ { 0 } } { 2 } + \sum _ { k = 1 } ^ { \infty } ( a _ { k } \operatorname { cos } k x + b _ { k } \operatorname { sin } k x )$ ; confidence 0.880
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i1300401.png ; $\frac { a _ { 0 } } { 2 } + \sum _ { k = 1 } ^ { \infty } ( a _ { k } \operatorname { cos } k x + b _ { k } \operatorname { sin } k x ),$ ; confidence 0.880
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120270/a120270128.png ; $N + Q$ ; confidence 0.880
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120270/a120270128.png ; $N / Q$ ; confidence 0.880
-. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015026.png ; $K = \{ B _ { r _ { 1 } } , B _ { r _ { 2 } } \}$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015026.png ; $\mathcal{K} = \{ B _ { r _ { 1 } } , B _ { r _ { 2 } } \}$ ; confidence 0.879
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040403.png ; $P K$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040403.png ; $\textsf{PK}$ ; confidence 0.879
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t12014082.png ; $\| u - h \| _ { L } \infty < 1$ ; confidence 0.879
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010033.png ; $\langle y _ { 1 } - y _ { 2 } , x _ { 1 } - x _ { 2 } \rangle \geq 0$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010033.png ; $\langle y _ { 1 } - y _ { 2 } , x _ { 1 } - x _ { 2 } \rangle \geq 0,$ ; confidence 0.879
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011072.png ; $Q = H _ { D ^ { n } } ( \tilde { O } )$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011072.png ; $\mathcal{Q} = \mathcal{H} _ { D ^ { n } } ( \tilde { \mathcal{O} } )$ ; confidence 0.879
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130580/s13058015.png ; $Q = [ \xi _ { l } ^ { 0 } ] ^ { 2 } - [ \xi _ { r } ^ { 0 } ] ^ { 2 }$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130580/s13058015.png ; $Q = [ \xi _ { l } ^ { 0 } ] ^ { 2 } - [ \xi _ { r } ^ { 0 } ] ^ { 2 },$ ; confidence 0.879
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007020.png ; $945 = 3 ^ { 3 } .5 .7$ ; confidence 0.879
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q120070119.png ; $R = q ^ { - 1 / 2 } \left( \begin{array} { c c c c } { q } & { 0 } & { 0 } & { 1 } \\ { 0 } & { 0 } & { q - q ^ { - 1 } } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 0 } & { q } \end{array} \right)$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q120070119.png ; $\mathcal{R} = q ^ { - 1 / 2 } \left( \begin{array} { c c c c } { q } & { 0 } & { 0 } & { 1 } \\ { 0 } & { 0 } & { q - q ^ { - 1 } } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 0 } & { q } \end{array} \right)$ ; confidence 0.879
-. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840120.png ; $L ^ { \perp } = \{ x : [ x , L ] = \{ 0 \} \}$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840120.png ; $\mathcal{L} ^ { \perp } = \{ x : [ x , \mathcal{L} ] = \{ 0 \} \}$ ; confidence 0.879
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040201.png ; $L _ { p }$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040201.png ; $\mathcal{L} _ { p }$ ; confidence 0.879
-. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006040.png ; $A _ { 1 } , A _ { 2 } : H \rightarrow H$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006040.png ; $A _ { 1 } , A _ { 2 } : \mathcal{H} \rightarrow \mathcal{H}$ ; confidence 0.879
 . https://www.encyclopediaofmath.org/legacyimages/d/d110/d110020/d11002048.png ; $H _ { N }$ ; confidence 0.879
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240222.png ; $r$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240222.png ; $z$ ; confidence 0.879
 . https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007021.png ; $\alpha ^ { \prime } , \alpha \in S ^ { 2 }$ ; confidence 0.879
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030056.png ; $n = p ^ { 1 }$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030056.png ; $n = p ^ { \text{l} }$ ; confidence 0.879
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a13006042.png ; $P _ { q }$ ; confidence 0.879
@@ Line 204: / Line 204: @@
 . https://www.encyclopediaofmath.org/legacyimages/l/l060/l060040/l06004011.png ; $f _ { k } ( z )$ ; confidence 0.878
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005034.png ; $f ( x , k ) = b ( k ) g ( x , k ) + a ( k ) g ( x , - k )$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005034.png ; $f ( x , k ) = b ( k ) g ( x , k ) + a ( k ) g ( x , - k ),$ ; confidence 0.878
 . https://www.encyclopediaofmath.org/legacyimages/k/k120/k120060/k12006013.png ; $c _ { 1 } ( L ) ^ { \operatorname { dim } X } > 0$ ; confidence 0.878
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m13018035.png ; $g ( n ) = \sum _ { d | n } f ( d ) \Leftrightarrow f ( n ) = \sum _ { d | n } g ( d ) \mu ( \frac { n } { d } )$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m13018035.png ; $g ( n ) = \sum _ { d | n } f ( d ) \Leftrightarrow f ( n ) = \sum _ { d | n } g ( d ) \mu \left( \frac { n } { d } \right).$ ; confidence 0.878
 . https://www.encyclopediaofmath.org/legacyimages/i/i120/i120100/i12010021.png ; $d s _ { N } ^ { 2 }$ ; confidence 0.878
-. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i12004094.png ; $K _ { 0 } = K _ { BN }$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i12004094.png ; $K _ { 0 } = K _ { \text{BN} }$ ; confidence 0.878
 . https://www.encyclopediaofmath.org/legacyimages/p/p120/p120130/p12013047.png ; $S \cup T$ ; confidence 0.878
@@ Line 218: / Line 218: @@
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t1202008.png ; $M _ { 4 } = \operatorname { min } _ { 1 \leq j < k \leq n } | z _ { j } - z _ { k } |$ ; confidence 0.878
-. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020070/c0200706.png ; $- 12$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020070/c0200706.png ; $-n$ ; confidence 0.878
-. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130100/l1301003.png ; $x \notin \overline { D } \subset R ^ { 2 }$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130100/l1301003.png ; $x \notin \overline { D } \subset \mathbf{R} ^ { 2 }$ ; confidence 0.878
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006098.png ; $H \phi$ ; confidence 0.878
-. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005073.png ; $\Theta _ { \Delta } ( z ) = H + z G ( I - z T ) ^ { - 1 } F$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005073.png ; $\Theta _ { \Delta } ( z ) = H + z G ( I - z T ) ^ { - 1 } F,$ ; confidence 0.878
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010039.png ; $\forall x _ { i } \in D ( A )$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010039.png ; $\forall x _ { i } \in D ( A ),$ ; confidence 0.878
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b13003011.png ; $y \in V ^ { - }$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b13003011.png ; $y \in V ^ { \mp }$ ; confidence 0.878
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c120170159.png ; $M ( n )$ ; confidence 0.878
@@ Line 238: / Line 238: @@
 . https://www.encyclopediaofmath.org/legacyimages/h/h130/h130020/h13002075.png ; $\gamma ^ { d } \cap \alpha _ { 1 } = \ldots = \gamma ^ { d } \cap \alpha _ { q } = \emptyset$ ; confidence 0.878
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060125.png ; $T ^ { \# } ( n )$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060125.png ; $\mathcal{T} ^ { \# } ( n )$ ; confidence 0.878
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020069.png ; $z _ { 1 } = \ldots = z _ { m } = 1$ ; confidence 0.878
@@ Line 250: / Line 250: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110500/a11050058.png ; $K ^ { \prime }$ ; confidence 0.878
-. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110020/l110020102.png ; $x \preceq z \preceq y \Rightarrow z \in H$ ; confidence 0.878
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110020/l110020102.png ; $x \preceq z \preceq y \Rightarrow z \in H.$ ; confidence 0.878
 . https://www.encyclopediaofmath.org/legacyimages/c/c025/c025440/c02544032.png ; $D ^ { - }$ ; confidence 0.877
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m13025051.png ; $( x , \xi ) \in R ^ { x } \times S ^ { x - 1 }$ ; confidence 0.877
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m13025051.png ; $( x , \xi ) \in \mathbf{R} ^ { x } \times S ^ { x - 1 }$ ; confidence 0.877
 . https://www.encyclopediaofmath.org/legacyimages/v/v110/v110060/v11006021.png ; $w ( x , y )$ ; confidence 0.877
-. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006039.png ; $\operatorname { ldim } ( P ) = \operatorname { dim } ( Q )$ ; confidence 0.877
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006039.png ; $\operatorname { Idim } ( P ) = \operatorname { dim } ( Q )$ ; confidence 0.877
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012053.png ; $F \circ f \in A ^ { * }$ ; confidence 0.877
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012053.png ; $F \circ f \in \mathcal{A} ^ { * }$ ; confidence 0.877
 . https://www.encyclopediaofmath.org/legacyimages/b/b015/b015170/b01517023.png ; $\{ a _ { k } \}$ ; confidence 0.877
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050177.png ; $Z _ { q } ( y ) = \sum _ { n = 0 } ^ { \infty } q ^ { n } y ^ { n } = ( 1 - q y ) ^ { - 1 }$ ; confidence 0.877
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050177.png ; $Z _ { q } ( y ) = \sum _ { n = 0 } ^ { \infty } q ^ { n } y ^ { n } = ( 1 - q y ) ^ { - 1 },$ ; confidence 0.877
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051010.png ; $F ( u ) = \{ v \in V : ( u , v ) \in E \}$ ; confidence 0.877
@@ Line 282: / Line 282: @@
 . https://www.encyclopediaofmath.org/legacyimages/n/n120/n120010/n1200105.png ; $\nu ( t ) : = ( 1 / ( 1 - t ) , 0 )$ ; confidence 0.877
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120110/e1201103.png ; $\nabla B = 0$ ; confidence 0.877
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120110/e1201103.png ; $\nabla . \mathbf{B} = 0 ;$ ; confidence 0.877
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e12007080.png ; $\{ p _ { M } \in P ( k ) : M \in \Gamma \}$ ; confidence 0.877
@@ Line 288: / Line 288: @@
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c12017097.png ; $M ( n + 2 ) , M ( n + 3 ) , \ldots$ ; confidence 0.877
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110020/a11002062.png ; $3$ ; confidence 0.876
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110020/a11002062.png ; $2$ ; confidence 0.876
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010047.png ; $1 / 2 < \gamma < 3 / 2$ ; confidence 0.876
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b130290144.png ; $M = dim$ ; confidence 0.876
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b130290144.png ; $\operatorname{dim}_{A} M = \operatorname{dim} A $ ; confidence 0.876
 . https://www.encyclopediaofmath.org/legacyimages/b/b110/b110620/b11062013.png ; $C _ { f }$ ; confidence 0.876
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180302.png ; $R ( \nabla ) : E \rightarrow \otimes ^ { 3 } E$ ; confidence 0.876
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180302.png ; $R ( \nabla ) : \mathcal{E} \rightarrow \otimes ^ { 3 } \mathcal{E}$ ; confidence 0.876
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130370/s13037014.png ; $\| \lambda \| = \operatorname { sup } _ { 0 \leq s < t \leq 1 } | \operatorname { log } \{ ( t - s ) ^ { - 1 } ( \lambda ( t ) - \lambda ( s ) ) \} |$ ; confidence 0.876
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130370/s13037014.png ; $\| \lambda \| = \operatorname { sup } _ { 0 \leq s < t \leq 1 } | \operatorname { log } \{ ( t - s ) ^ { - 1 } ( \lambda ( t ) - \lambda ( s ) ) \} |.$ ; confidence 0.876
 . https://www.encyclopediaofmath.org/legacyimages/m/m120/m120270/m12027020.png ; $d w [ k ] = d w _ { 1 } \wedge \ldots \wedge d w _ { k - 1 } \wedge d w _ { k + 1 } \wedge \ldots \wedge d w _ { n }$ ; confidence 0.876
@@ Line 304: / Line 304: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022024.png ; $\int _ { T } | u ( x ) | ^ { p } d x$ ; confidence 0.876
-. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130050/g13005084.png ; $P = \{ p _ { 1 } , \dots , p _ { n } \} \subset R ^ { k }$ ; confidence 0.876
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130050/g13005084.png ; $P = \{ p _ { 1 } , \dots , p _ { n } \} \subset \mathbf{R} ^ { k }$ ; confidence 0.876
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120060/d12006024.png ; $Q ^ { \pm }$ ; confidence 0.876
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130080/c13008032.png ; $N _ { A } = ( \# \frac { A } { n } + o ( 1 ) ) x \operatorname { log } x$ ; confidence 0.876
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130080/c13008032.png ; $N _ { A } = \left( \# \frac { A } { n } + o ( 1 ) \right) x \operatorname { log } x,$ ; confidence 0.876
 . https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700044.png ; $( \lambda x M ) x = M$ ; confidence 0.876
-. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006017.png ; $\tilde { \gamma } - \gamma = i ( \sigma _ { 1 } \Phi \Phi ^ { * } \sigma _ { 2 } - \sigma _ { 2 } \Phi \Phi ^ { * } \sigma _ { 1 } )$ ; confidence 0.876
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006017.png ; $\tilde { \gamma } - \gamma = i ( \sigma _ { 1 } \Phi \Phi ^ { * } \sigma _ { 2 } - \sigma _ { 2 } \Phi \Phi ^ { * } \sigma _ { 1 } ).$ ; confidence 0.876
 . https://www.encyclopediaofmath.org/legacyimages/l/l130/l130100/l13010074.png ; $\alpha \in S ^ { n - 1 }$ ; confidence 0.876
@@ Line 320: / Line 320: @@
 . https://www.encyclopediaofmath.org/legacyimages/m/m120/m120230/m12023039.png ; $R _ { t } ( x )$ ; confidence 0.876
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120150/a12015049.png ; $N = \{ X \in \mathfrak { g } :$ ; confidence 0.876
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120150/a12015049.png ; $\mathcal{N} = \{ X \in \mathfrak { g } : \operatorname{ad}X \, \text{is a nilpotent endomorphism of} \, \mathfrak { g } \}$ ; confidence 0.876
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027081.png ; $Y _ { n } \subset Y _ { n + 1 }$ ; confidence 0.876
-. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130030/g13003089.png ; $R _ { nd } ( \Omega ) = B / I _ { nd }$ ; confidence 0.876
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130030/g13003089.png ; $\mathcal{R} _ { \text{nd} } ( \Omega ) = \mathcal{B} / \mathcal{I} _ { \text{nd} }$ ; confidence 0.876
 . https://www.encyclopediaofmath.org/legacyimages/l/l110/l110030/l11003093.png ; $[ L ^ { 1 } ( \mu ) ]$ ; confidence 0.875
@@ Line 332: / Line 332: @@
 . https://www.encyclopediaofmath.org/legacyimages/e/e130/e130040/e13004051.png ; $P _ { - } \psi ( t )$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120040/a12004024.png ; $| x ( t ) \| \leq c \| x _ { 0 } \| \text { for all } t \in [ 0 , \tau ]$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120040/a12004024.png ; $\| x ( t ) \| \leq c \| x _ { 0 } \| \text { for all } \, t \in [ 0 , \tau ],$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145024.png ; $p 3$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145024.png ; $P^3$ ; confidence 0.875
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l120100112.png ; $K _ { E } ( V )$ ; confidence 0.875
@@ Line 340: / Line 340: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a1302403.png ; $n \times 1$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120030/b1200305.png ; $f \in L ^ { 2 } ( R )$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120030/b1200305.png ; $f \in L ^ { 2 } ( \mathbf{R} )$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120260/a120260113.png ; $A ( X )$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120260/a120260113.png ; $A \langle  X \rangle $ ; confidence 0.875
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029085.png ; $| x - x _ { x } | < y _ { x }$ ; confidence 0.875
@@ Line 348: / Line 348: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012069.png ; $p ^ { * } y \leq \lambda ^ { * } p ^ { * } x$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090231.png ; $( X ^ { \omega } \chi ^ { - 1 } ) = \pi ^ { \mu _ { \chi } ^ { * } } g _ { \chi } ^ { * } ( T )$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090231.png ; $\operatorname{char}( X ^ { \omega  \chi ^ { - 1 }} ) = \pi ^ { \mu _ { \chi } ^ { * } } g _ { \chi } ^ { * } ( T ).$ ; confidence 0.875
 . https://www.encyclopediaofmath.org/legacyimages/g/g043/g043370/g0433705.png ; $D f ( x _ { 0 } , h ) = \frac { d } { d t } f ( x _ { 0 } + t h ) | _ { t = 0 } =$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430117.png ; $S \left( \begin{array} { c c } { \alpha } & { \beta } \\ { \gamma } & { \delta } \end{array} \right) = \left( \begin{array} { c c } { q ^ { 2 } \delta + ( 1 - q ^ { 2 } ) \alpha } & { - q ^ { 2 } \beta } \\ { - q ^ { 2 } \gamma } & { \alpha } \end{array} \right)$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430117.png ; $S \left( \begin{array} { c c } { \alpha } & { \beta } \\ { \gamma } & { \delta } \end{array} \right) = \left( \begin{array} { c c } { q ^ { 2 } \delta + ( 1 - q ^ { 2 } ) \alpha } & { - q ^ { 2 } \beta } \\ { - q ^ { 2 } \gamma } & { \alpha } \end{array} \right).$ ; confidence 0.875
 . https://www.encyclopediaofmath.org/legacyimages/d/d030/d030090/d0300906.png ; $m _ { \nu } w _ { \nu }$ ; confidence 0.875
@@ Line 362: / Line 362: @@
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120190/e12019067.png ; $\{ m , a \} \equiv \{ m , b \}$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/v/v110/v110050/v1100504.png ; $( R ^ { n } )$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/v/v110/v110050/v1100504.png ; $\operatorname{BMO}( \mathbf{R} ^ { n } )$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170182.png ; $Wh ( \pi )$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170182.png ; $\operatorname{Wh} ( \pi )$ ; confidence 0.875
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b130300163.png ; $D ( 2 n _ { 1 } )$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013039.png ; $Q = \sum _ { j = 0 } ^ { \infty } Q _ { j } z ^ { - j } , Q _ { j } = \left( \begin{array} { c c } { h _ { j } } & { e _ { j } } \\ { f _ { j } } & { - h _ { j } } \end{array} \right)$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013039.png ; $Q = \sum _ { j = 0 } ^ { \infty } Q _ { j } z ^ { - j } , Q _ { j } = \left( \begin{array} { c c } { h _ { j } } & { e _ { j } } \\ { f _ { j } } & { - h _ { j } } \end{array} \right),$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110030/d11003021.png ; $\Phi _ { Q }$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110030/d11003021.png ; $\Phi _ { \alpha }$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130120/f13012024.png ; $1 ( A )$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130120/f13012024.png ; $\operatorname{l} ( A )$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a120050132.png ; $R ^ { N }$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a120050132.png ; $\mathbf{R} ^ { N }$ ; confidence 0.875
-. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021720/c02172025.png ; $( - 1 ) ^ { x }$ ; confidence 0.874
+. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021720/c02172025.png ; $( - 1 ) ^ { n }$ ; confidence 0.874
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130140/s13014013.png ; $\lambda _ { 1 } > \ldots > \lambda _ { 2 m } \geq 0$ ; confidence 0.874
@@ Line 384: / Line 384: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b12004016.png ; $| x | \leq | y |$ ; confidence 0.874
-. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120010/j12001041.png ; $F | _ { l } : l \rightarrow C ^ { 2 }$ ; confidence 0.874
+. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120010/j12001041.png ; $F | _ { l } : l \rightarrow \mathbf{C} ^ { 2 }$ ; confidence 0.874
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010299.png ; $m$ ; confidence 0.874
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010299.png ; $m_{i}$ ; confidence 0.874
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022079.png ; $2$ ; confidence 0.874
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022079.png ; $u$ ; confidence 0.874
 . https://www.encyclopediaofmath.org/legacyimages/f/f130/f130010/f13001018.png ; $x ^ { q ^ { d } } - x$ ; confidence 0.874
@@ Line 400: / Line 400: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009055.png ; $\{ f _ { n } \} _ { n = 0 } ^ { \infty }$ ; confidence 0.874
-. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090670/s0906701.png ; $( C , U )$ ; confidence 0.874
+. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090670/s0906701.png ; $( \mathcal{C} , U )$ ; confidence 0.874
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130020/s13002021.png ; $S N = \pi ^ { - 1 } ( N ) \subset U M$ ; confidence 0.874
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s12034018.png ; $SH ^ { * } ( M , \omega ) = SH ^ { * } ( M , \omega , \phi )$ ; confidence 0.874
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s12034018.png ; $\operatorname{SH} ^ { * } ( M , \omega ) = \operatorname{SH} ^ { * } ( M , \omega , \phi )$ ; confidence 0.874
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120160/b12016049.png ; $q _ { 1 } = x _ { 1 } + x _ { 3 } , \quad q _ { 2 } = x _ { 2 } + x _ { 4 }$ ; confidence 0.874
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120160/b12016049.png ; $q _ { 1 } = x _ { 1 } + x _ { 3 } , \quad q _ { 2 } = x _ { 2 } + x _ { 4 }.$ ; confidence 0.874
-. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011620/a01162016.png ; $m > 2$ ; confidence 0.874
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011620/a01162016.png ; $m \geq 2$ ; confidence 0.874
 . https://www.encyclopediaofmath.org/legacyimages/i/i120/i120010/i12001041.png ; $C ^ { 0 , \sigma _ { 1 } ( t ) } ( \Omega )$ ; confidence 0.874
@@ Line 414: / Line 414: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b110/b110100/b110100235.png ; $D _ { n }$ ; confidence 0.874
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013025.png ; $W _ { 1 } = S _ { 1 } e ^ { \sum _ { 1 } ^ { \infty } x _ { k } \Lambda ^ { k } }$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013025.png ; $W _ { 1 } = S _ { 1 } e ^ { \sum _ { 1 } ^ { \infty } x _ { k } \Lambda ^ { k } },$ ; confidence 0.873
 . https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g12004099.png ; $\sum _ { j = 1 } ^ { n } \xi _ { j } d x _ { j }$ ; confidence 0.873
@@ Line 420: / Line 420: @@
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120030/l12003035.png ; $\operatorname { Map } ( X \times Z , Y ) \rightarrow \operatorname { Map } ( X , \operatorname { Map } ( Z , Y ) )$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007031.png ; $Z H$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007031.png ; $\mathbf{Z}H$ ; confidence 0.873
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120180/s12018067.png ; $\rho ( x , y ) = \langle x - y , x - y \rangle ^ { 1 / 2 }$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s12032018.png ; $( 1,3 ) \oplus R ^ { 1,3 }$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s12032018.png ; $\operatorname{so}( 1,3 ) \oplus \mathbf{R} ^ { 1,3 }$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d13008011.png ; $\Delta$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d13008011.png ; $\overline{\Delta}$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060050/l06005072.png ; $\operatorname { cosh } \delta = | - X _ { 0 } Y _ { 0 } + \sum X _ { t } Y _ { t } |$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060050/l06005072.png ; $\operatorname { cosh } \delta = | - X _ { 0 } Y _ { 0 } + \sum X _ { t } Y _ { t } |.$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130010/b13001012.png ; $X : = K \backslash G ( R )$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130010/b13001012.png ; $X : = K \backslash G ( \mathbf{R} )$ ; confidence 0.873
 . https://www.encyclopediaofmath.org/legacyimages/c/c022/c022360/c02236032.png ; $E ^ { 3 }$ ; confidence 0.873
@@ Line 436: / Line 436: @@
 . https://www.encyclopediaofmath.org/legacyimages/n/n066/n066630/n066630124.png ; $u | _ { \partial \Omega } \in H _ { 2 } ^ { \rho } ( \partial \Omega )$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005068.png ; $S : = \{ r _ { + } ( k ) , i k _ { j } , ( m _ { j } ^ { + } ) ^ { 2 } : 1 \leq j \leq J , k _ { j } > 0 , m _ { j } ^ { + } > 0 , k > 0 \}$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005068.png ; $\mathcal{S} : = \left\{ r _ { + } ( k ) , i k _ { j } , ( m _ { j } ^ { + } ) ^ { 2 } : 1 \leq j \leq J , k _ { j } > 0 , m _ { j } ^ { + } > 0 , k > 0 \right\}$ ; confidence 0.873
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040741.png ; $R ^ { \prime }$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240408.png ; $y _ { i j k }$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240408.png ; $\mathbf{y} _ { i j k }$ ; confidence 0.873
 . https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c130160100.png ; $w \in A$ ; confidence 0.873
@@ Line 446: / Line 446: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002051.png ; $q = v ^ { * }$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120240/f12024049.png ; $x ( t ) \in R ^ { n }$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120240/f12024049.png ; $x ( t ) \in \mathbf{R} ^ { n }$ ; confidence 0.873
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120160/c12016032.png ; $A = L D L ^ { T }$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110030/l11003029.png ; $\operatorname { sup } _ { i \in I } \mu _ { i } \in D$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110030/l11003029.png ; $\operatorname { sup } _ { i \in I } \mu _ { i } \in \mathcal{D}$ ; confidence 0.873
 . https://www.encyclopediaofmath.org/legacyimages/o/o120/o120060/o12006027.png ; $\alpha \leq k$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130260/m13026051.png ; $B ( H )$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130260/m13026051.png ; $B ( \mathcal{H} )$ ; confidence 0.873
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t12007053.png ; $j _ { e } ( z ) = J ( z )$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026052.png ; $\| \Delta ( U ^ { n } - u ^ { n } ) \| \leq \| \Delta ( U ^ { 0 } - u ^ { 0 } ) \| + O ( h ^ { 2 } + k ^ { 2 } )$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026052.png ; $\| \Delta ( \mathbf{U} ^ { n } - \mathbf{u} ^ { n } ) \| \leq \| \Delta ( \mathbf{U} ^ { 0 } - \mathbf{u} ^ { 0 } ) \| + O ( h ^ { 2 } + k ^ { 2 } ),$ ; confidence 0.873
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120510/b12051087.png ; $\{ s _ { k } , y _ { k } \} _ { k = 0 } ^ { n - 1 }$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006080.png ; $2$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006080.png ; $\tilde{z}$ ; confidence 0.873
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007078.png ; $c M$ ; confidence 0.873
@@ Line 470: / Line 470: @@
 . https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v13007032.png ; $w = \phi + i \psi$ ; confidence 0.873
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130050/c13005014.png ; $15$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130050/c13005014.png ; $|S|$ ; confidence 0.873
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120490/b12049041.png ; $\{ A _ { j n _ { k } } \}$ ; confidence 0.872
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d12028062.png ; $A ( D ) ^ { * } \simeq A ( \tilde { D } )$ ; confidence 0.872
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d12028062.png ; $A ( D ) ^ { * } \simeq A ( \tilde { D } ),$ ; confidence 0.872
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e12007058.png ; $F ^ { ( k + 1 ) } \in \{ \Gamma , k + 2 , v \}$ ; confidence 0.872
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e12007058.png ; $F ^ { ( k + 1 ) } \in \{ \Gamma , k + 2 , \mathbf{v} \}$ ; confidence 0.872
 . https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520488.png ; $\Phi ^ { ( 3 ) } = O ( | Z | ^ { 2 } )$ ; confidence 0.872
@@ Line 486: / Line 486: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016053.png ; $N ( . )$ ; confidence 0.872
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120130/l12013029.png ; $f _ { j } ( x ) \in Z _ { p } ^ { n }$ ; confidence 0.872
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120130/l12013029.png ; $f _ { j } ( \overline{x} ) \in \mathbf{Z} _ { p } ^ { n }$ ; confidence 0.872
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120050/t12005023.png ; $T V _ { X }$ ; confidence 0.872
@@ Line 498: / Line 498: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130470/s1304709.png ; $\nu ( \lambda )$ ; confidence 0.872
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007059.png ; $\rightarrow \omega ( 1 - | F ( z ) | ) / ( 1 - | z | ) = d ( \omega ) < \infty$ ; confidence 0.872
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007059.png ; $\lim \inf \rightarrow \omega ( 1 - | F ( z ) | ) / ( 1 - | z | ) = d ( \omega ) < \infty$ ; confidence 0.872
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120190/e120190130.png ; $[ a , b ] \subseteq T$ ; confidence 0.872
@@ Line 504: / Line 504: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f13010051.png ; $T ( \square _ { \alpha } \varphi ) = \square _ { \alpha } ( T ( \varphi ) )$ ; confidence 0.872
-. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130210/d13021013.png ; $G$ ; confidence 0.872
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130210/d13021013.png ; $G_{x}$ ; confidence 0.872
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120160/f12016057.png ; $\chi _ { \lambda I - T } < 0$ ; confidence 0.872
@@ Line 512: / Line 512: @@
 . https://www.encyclopediaofmath.org/legacyimages/h/h120/h120020/h12002043.png ; $H _ { \phi } : H ^ { 2 } \rightarrow H _ { - } ^ { 2 }$ ; confidence 0.872
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170190.png ; $Wh ^ { * } ( \pi )$ ; confidence 0.872
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170190.png ; $\operatorname{ Wh} ^ { * } ( \pi )$ ; confidence 0.872
-. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015061.png ; $K _ { 0 } \in K$ ; confidence 0.872
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015061.png ; $K _ { 0 } \in \mathcal{K}$ ; confidence 0.872
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020086.png ; $\mathfrak { g } _ { \pm } = \oplus _ { \alpha \in \Delta _ { \pm } } \mathfrak { g } ^ { \alpha }$ ; confidence 0.871
@@ Line 522: / Line 522: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002021.png ; $x = x ^ { x }$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120090/e1200904.png ; $\nabla \cdot H = 0$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120090/e1200904.png ; $\nabla . H = 0$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007054.png ; $( 2 \pi ) ^ { - 2 n } \int _ { R ^ { 2 n } } \rho ( p , q , 0 ) \hat { \sigma } ( p , q ) d p d q =$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007054.png ; $( 2 \pi ) ^ { - 2 n } \int _ { \mathbf{R} ^ { 2 n } } \rho ( p , q , 0 ) \hat { \sigma } ( p , q ) d p d q =$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130040/w13004042.png ; $d s ^ { 2 } = \frac { 1 } { 4 } ( 1 + | g | ^ { 2 } ) ^ { 2 } | \eta | ^ { 2 } = \frac { 1 } { 2 } \sum _ { j = 1 } ^ { 3 } | \omega _ { j } | ^ { 2 }$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130040/w13004042.png ; $d s ^ { 2 } = \frac { 1 } { 4 } ( 1 + | g | ^ { 2 } ) ^ { 2 } | \eta | ^ { 2 } = \frac { 1 } { 2 } \sum _ { j = 1 } ^ { 3 } | \omega _ { j } | ^ { 2 },$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t12014044.png ; $T _ { \phi } = \operatorname { dim } \operatorname { Ker } T _ { \phi } - \operatorname { dim } \operatorname { Ker } T _ { \phi } ^ { * } = 0$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t12014044.png ; $\operatorname{ind} T _ { \phi } = \operatorname { dim } \operatorname { Ker } T _ { \phi } - \operatorname { dim } \operatorname { Ker } T _ { \phi } ^ { * } = 0$ ; confidence 0.871
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240230.png ; $\psi = \sum _ { i = 1 } ^ { r } d _ { i } \zeta _ { i }$ ; confidence 0.871
@@ Line 540: / Line 540: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120320/d1203205.png ; $S : L ^ { 1 } \rightarrow Y$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120170/m1201705.png ; $X ^ { n } + A _ { 1 } X ^ { n - 1 } + \ldots + A _ { n - 1 } X + A _ { n } = 0$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120170/m1201705.png ; $X ^ { n } + A _ { 1 } X ^ { n - 1 } + \ldots + A _ { n - 1 } X + A _ { n } = 0,$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032053.png ; $F ( s , t ) = \| t x + s y \| \text { for all } s , t \geq 0$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032053.png ; $F ( s , t ) = \| t x + s y \| \text { for all } s , t \geq 0,$ ; confidence 0.871
 . https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020191.png ; $\operatorname { deg } ( F , \overline { D } \square ^ { n + 1 } , \theta ) = k$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200107.png ; $m = 2 i + 1$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200107.png ; $m = 2l + 1$ ; confidence 0.871
 . https://www.encyclopediaofmath.org/legacyimages/k/k120/k120060/k12006041.png ; $N L$ ; confidence 0.871
@@ Line 552: / Line 552: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054032.png ; $x ( \alpha ) = x _ { 12 } ( \alpha )$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051070.png ; $G = G _ { 1 } + \ldots + G _ { m }$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051070.png ; $\mathbf{G} = G _ { 1 } + \ldots + G _ { m }$ ; confidence 0.871
 . https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m130180132.png ; $\mu ( E , F ) = ( - 1 ) ^ { d }$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023380/c023380240.png ; $2$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023380/c023380240.png ; $\overline{z}$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f120080153.png ; $P ( f \otimes g ) = f ^ { * } g$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f120080153.png ; $P ( f \otimes g ) = f  *  g$ ; confidence 0.871
 . https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e1300707.png ; $( \# A ) ^ { 1 / 2 }$ ; confidence 0.871
@@ Line 564: / Line 564: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032017.png ; $N = k$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120070/d1200709.png ; $a _ { 1 } \sigma _ { 1 } ( u ) + \ldots + a _ { t } \sigma _ { t } ( u ) \neq 0$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120070/d1200709.png ; $a _ { 1 } \sigma _ { 1 } ( u ) + \ldots + a _ { t } \sigma _ { t } ( u ) \neq 0.$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180149.png ; $\langle \tilde { \gamma } ( X ) , Y \rangle = g ( X \otimes Y ) \in R$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180149.png ; $\langle \tilde { \gamma } ( X ) , Y \rangle = g ( X \otimes Y ) \in \mathcal{R}$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130250/b13025055.png ; $\frac { \overline { \Omega } \Omega ^ { \prime } } { 2 \operatorname { sin } \omega } = \overline { O \Omega } = \overline { O \Omega ^ { \prime } } = R \sqrt { 1 - 4 \operatorname { sin } ^ { 2 } \omega }$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130250/b13025055.png ; $\frac { \overline { \Omega  \Omega ^ { \prime } }  } { 2 \operatorname { sin } \omega } = \overline { O \Omega } = \overline { O \Omega ^ { \prime } } = R \sqrt { 1 - 4 \operatorname { sin } ^ { 2 } \omega }.$ ; confidence 0.871
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043082.png ; $U _ { q } ( n _ { + } )$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007068.png ; $( f , g ) : = ( \sum _ { j = 1 } ^ { J } K ( x , y _ { j } ) c _ { j } , \sum _ { m = 1 } ^ { M } K ( x , z _ { m } ) \beta _ { m } ) =$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007068.png ; $( f , g ) : = \left( \sum _ { j = 1 } ^ { J } K ( x , y _ { j } ) c _ { j } , \sum _ { m = 1 } ^ { M } K ( x , z _ { m } ) \beta _ { m } \right) =$ ; confidence 0.871
-. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001020.png ; $v ( x , \alpha , k ) = \frac { e ^ { i k r } } { r } A ( \alpha ^ { \prime } , \alpha , k ) + o ( \frac { 1 } { r } )$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001020.png ; $v ( x , \alpha , k ) = \frac { e ^ { i k r } } { r } A ( \alpha ^ { \prime } , \alpha , k ) + o ( \frac { 1 } { r } ),$ ; confidence 0.871
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016071.png ; $d S _ { t } / d u _ { t } = c _ { 1 }$ ; confidence 0.870
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a120160163.png ; $\sum _ { j = 1 } ^ { M } \sum _ { t = 1 } ^ { T } c _ { j t } x _ { j t } \leq B$ ; confidence 0.870
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a120160163.png ; $\sum _ { j = 1 } ^ { M } \sum _ { t = 1 } ^ { T } c _ { j t } x _ { j t } \leq B,$ ; confidence 0.870
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120140/b12014043.png ; $t _ { i } ( z )$ ; confidence 0.870
@@ Line 586: / Line 586: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a1302405.png ; $( n \times m )$ ; confidence 0.870
-. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005084.png ; $= ( m - n ) L ( m + n ) + \frac { 1 } { 12 } ( m ^ { 3 } - m ) \delta _ { n + m , 0 } c$ ; confidence 0.870
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005084.png ; $= ( m - n ) L ( m + n ) + \frac { 1 } { 12 } ( m ^ { 3 } - m ) \delta _ { n + m , 0 } c,$ ; confidence 0.870
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130140/s13014020.png ; $\{ 1 ^ { \prime } < 1 < 2 ^ { \prime } < 2 < \ldots \}$ ; confidence 0.870
@@ Line 592: / Line 592: @@
 . https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n12002055.png ; $\hat { \theta } = \psi _ { \mu } ( X )$ ; confidence 0.870
-. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048420/h048420160.png ; $O ( U )$ ; confidence 0.870
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048420/h048420160.png ; $\mathcal{O} ( U )$ ; confidence 0.870
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240510.png ; $\Theta = E ( Z _ { 12 } )$ ; confidence 0.870
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240510.png ; $\Theta = \textsf{E} ( \mathbf{Z} _ { 12 } )$ ; confidence 0.870
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130200/m1302009.png ; $L _ { Y } P = 0$ ; confidence 0.870
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130200/m1302009.png ; $\mathcal{L} _ { Y } P = 0$ ; confidence 0.870
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120140/d12014077.png ; $\{ D _ { N } ( x , 1 ) \}$ ; confidence 0.870