Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/50"

Revision as of 14:55, 10 May 2020

List

1. ; $f , g \in C [ \mathbf{R} ]$ ; confidence 0.643

2. ; $o : 1 \rightarrow N$ ; confidence 0.643

3. ; $r ( K _ { X } + B )$ ; confidence 0.643

4. ; $\mathbf{1}$ ; confidence 0.643

5. ; $\widetilde { F B }$ ; confidence 0.643

6. ; $\pi _ { 0 } : N _ { 0 } \rightarrow N$ ; confidence 0.643

7. ; $x \in A ^ { + }$ ; confidence 0.643

8. ; $\{ A _ { i } \} _ { i = 1 } ^ { k }$ ; confidence 0.642

9. ; $\operatorname{cat}_{\mathbf{R} P ^ { n }} \mathbf{R}P^n \geq n + 1$ ; confidence 0.642

10. ; $\sigma _ { 1 } , \ldots , \sigma _ { t }$ ; confidence 0.642

11. ; $C ( S \times T )$ ; confidence 0.642

12. ; $F ( x , y ) = a p _ { 1 } ^ { z _ { 1 } } \dots p _ { s } ^ { z _ { s } }$ ; confidence 0.642

13. ; $\sqrt { 1 - x ^ { 2 } } w ( x ) > 0$ ; confidence 0.642

14. ; $S = \frac { 1 } { n - 1 } \sum _ { i = 1 } ^ { n } ( X _ { i } - \overline{X} ) ( X _ { i } - \overline{X} ) ^ { \prime },$ ; confidence 0.642

15. ; $\phi_j$ ; confidence 0.642

16. ; $\langle [ A ] , \phi \rangle = \int _ { \operatorname { reg } A } \phi.$ ; confidence 0.642

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

18. ; $l_2$ ; confidence 0.642

19. ; $F _ { \sigma } \in \widetilde { \mathcal{O} } ( ( \Omega + \Gamma _ { \sigma } ) \cap U ).$ ; confidence 0.642

20. ; $N _ { \epsilon } ( C )$ ; confidence 0.642

21. ; $X \times Y$ ; confidence 0.642

22. ; $Q \in [ \alpha , b ]$ ; confidence 0.642

23. ; $f _ { 1 } : = x _ { 1 } ^ { d },$ ; confidence 0.642

24. ; $t \searrow 0$ ; confidence 0.641

25. ; $E ^ { \text{TF} } ( N ) = \operatorname { inf } \{ \mathcal{E} ( \rho ) : \rho \in L ^ { 5 / 3 } , \int \rho = N , \rho \geq 0 \},$ ; confidence 0.641

26. ; $L _ { \text{C} } ^ { p } ( G )$ ; confidence 0.641

27. ; $\pi _ { n } ( X ; A , B , * ) = \pi _ { n - 1 } ( \Omega ( X ; A , B ) , * ).$ ; confidence 0.641

28. ; $\mathfrak{p} \subset \mathfrak{a}$ ; confidence 0.641

29. ; $h = 1$ ; confidence 0.641

30. ; $f \rightarrow \frac { 1 } { 2 \pi } \int _ { 0 } ^ { 2 \pi } \operatorname { Re } \frac { e ^ { i t } + z } { e ^ { t t } - z } f ( e ^ { i t } ) d t,$ ; confidence 0.641

31. ; $e \leq x$ ; confidence 0.641

32. ; $x \in \Lambda$ ; confidence 0.641

33. ; $\| u_f \| \leq \| f \| / c$ ; confidence 0.641

34. ; $E ^ { k } = M \times F \times F ^ { ( 1 ) } \times \ldots F ^ { ( k ) }$ ; confidence 0.641

35. ; $\mathsf{E} _ { \theta } ( N ) = \frac { \mathsf{P} _ { \theta } ( S _ { N } = K ) K - \mathsf{P} _ { \theta } ( S _ { N } = - J ) J } { 2 \theta - 1 }.$ ; confidence 0.641

36. ; $U : \mathcal{C} \rightarrow \operatorname{Set}$ ; confidence 0.641

37. ; $s = 1 + p _ { 1 } / r + \ldots + p _ { 1 } \ldots p _ { k - 1 } / r ^ { k - 1 }$ ; confidence 0.641

38. ; $y _ { 0 } = g ( x _ { 0 } )$ ; confidence 0.641

39. ; $A = \operatorname { diag } ( \lambda _ { 1 } , \dots , \lambda _ { n } )$ ; confidence 0.641

40. ; $d _ { 2 } ( e _ { 2 } ^ { j } )$ ; confidence 0.640

41. ; $a \leftrightarrow b a b ^ { - 1 }$ ; confidence 0.640

42. ; $\phi _ { p }$ ; confidence 0.640

43. ; $( \mathbf{R} _ { + } \backslash \{ 0 \} , \times , \leq )$ ; confidence 0.640

44. ; $\in \bigotimes \square ^ { p + q + 1 } \mathcal{E}$ ; confidence 0.640

45. ; $R \subseteq A ^ { n }$ ; confidence 0.640

46. ; $\text{E} _ { \mathsf{P} } ( d _ { 0 } ) = 0$ ; confidence 0.640

47. ; $( C ) \int _ { A } f d m = ( C ) \int f . \chi _ { A } d m$ ; confidence 0.640

48. ; $0 \leq t < \infty$ ; confidence 0.640

49. ; $\widehat { B^* } $ ; confidence 0.640

50. ; $\mathsf{E} _ { \theta } ( X _ { i } ) = \mathsf{P} _ { \theta } ( X _ { i } = 1 ) = \theta = 1 - \mathsf{P} _ { \theta } ( X _ { i } = 0 )$ ; confidence 0.640

51. ; $\mathbf{f} ^ { \text{em} } = q _ { f } \mathbf{E} + \frac { 1 } { c } \mathbf{J} \times \mathbf{B} + ( \nabla \mathbf{E} ). \mathbf{P} + ( \nabla \mathbf{B} ). \mathbf{M} +$ ; confidence 0.640

52. ; $\operatorname{II}( W , V ) = - \operatorname { Re } ( \eta ( W ) d g ( V ) ).$ ; confidence 0.640

53. ; $a , b \in \Omega$ ; confidence 0.640

54. ; $x \in \widetilde{\mathbf{Z}}$ ; confidence 0.640

55. ; $f _ { t , s }$ ; confidence 0.640

56. ; $R = \sum _ { s = 1 } ^ { n } a _ { s } \otimes b _ { s } \in A \otimes _ { k } A$ ; confidence 0.640

57. ; $\overline { m } = \{ m _ { n } \} _ { n = 0 } ^ { \infty }$ ; confidence 0.639

58. ; $S ^ { \lambda }$ ; confidence 0.639

59. ; $\operatorname{SAT}$ ; confidence 0.639

60. ; $K_n$ ; confidence 0.639

61. ; $\lambda \in \Lambda$ ; confidence 0.639

62. ; $\pi \in S _ { n }$ ; confidence 0.639

63. ; $T^+ T = I = T T^+$ ; confidence 0.639

64. ; $U _ { n + 1 } ( x ) = \sum _ { j = 0 } ^ { [ n / 2 ] } \frac { ( n - j ) ! } { j ! ( n - 2 j ) ! } x ^ { n - 2 j } , n = 0,1, \dots ,$ ; confidence 0.639

65. ; $\operatorname { Re } h ( z ) > 0$ ; confidence 0.639

66. ; $\langle A \rangle _ { T } = Z ^ { - 1 } \operatorname { Tr } \left[ \operatorname { exp } ( - \frac { \mathcal{H} } { k _ { B } T } ) A \right].$ ; confidence 0.639

67. ; $( X _ { n } ) _ { n \in \mathbf{Z} }$ ; confidence 0.639

68. ; $Z ( \mathbf{C} )$ ; confidence 0.639

69. ; $f _ { 1 } , \ldots , f _ { d }$ ; confidence 0.639

70. ; $\operatorname {dim} V _ { ( n ) } < \infty$ ; confidence 0.639

71. ; $z_1$ ; confidence 0.638

72. ; $RN_G(D)$ ; confidence 0.638

73. ; $\operatorname { gcd } ( p _ { 1 } \ldots p _ { k } , q ) = 1$ ; confidence 0.638

74. ; $U _ { t } ^ { j } = u _ { j } ( B _ { \operatorname { min }( t , \tau ) } )$ ; confidence 0.638

75. ; $\mathcal{Y} ( T _ { A } ) = \left\{ N _ { B } : \operatorname { Tor } _ { 1 } ^ { B } ( N , T ) = 0 \right\},$ ; confidence 0.638

76. ; $\{ 0 , \pm x _ { 1 } , \ldots , \pm x _ { k } \}$ ; confidence 0.638

77. ; $f _ { n } \in H ^ { \hat{\otimes} n }$ ; confidence 0.638

78. ; $K Q$ ; confidence 0.638

79. ; $H _ { z } ( t )$ ; confidence 0.638

80. ; $v ( x , \alpha , k ) = A ( \alpha ^ { \prime } , \alpha , k ) \frac { e ^ { i k r} } { r } + o \left( \frac { 1 } { r } \right),$ ; confidence 0.638

81. ; $k S _ { n }$ ; confidence 0.638

82. ; $i,j = 1 , \ldots , n$ ; confidence 0.638

83. ; $\sum _ { \nu = 1 } ^ { n } \alpha _ { \nu } \leq 2$ ; confidence 0.637

84. ; $c_j ( \lambda )$ ; confidence 0.637

85. ; $S = \{ p _ { 1 } , \dots , p _ { s } \} \cup \{ p : p \text{ is prime and divides } a\}$ ; confidence 0.637

86. ; $w = ( w _ { 1 } , \dots , w _ { n } )$ ; confidence 0.637

87. ; $\sum _ { n = 1 } ^ { \infty } y _ { n }$ ; confidence 0.637

88. ; $\overline{ \mathbf{E}}_p ( X ) \approx \overline { \mathbf{E} } \square ^ { q } ( S ^ { n } \backslash X ) , p + q = n - 1,$ ; confidence 0.637

89. ; $N ( s )$ ; confidence 0.637

90. ; $X ( p ) = \operatorname { Re } \int _ { p _ { 0 } } ^ { p } ( \omega _ { 1 } , \ldots , \omega _ { n } ).$ ; confidence 0.637

91. ; $G _ { i+1 } $ ; confidence 0.637

92. ; $q_2 ( x )$ ; confidence 0.637

93. ; $\operatorname { ker } ( \gamma \circ \alpha ^ { \prime } ) \subset \mathfrak { g }$ ; confidence 0.637

94. ; $d \circ e = f$ ; confidence 0.637

95. ; $\mathcal{A}$ ; confidence 0.637

96. ; $z _ { i } = 1 , \dots , p - 1$ ; confidence 0.637

97. ; $e _ { 1 } , \dots , e _ { s }$ ; confidence 0.637

98. ; $\operatorname { max } _ { k = m + 1 , \ldots , m + n } | g ( k ) | \geq$ ; confidence 0.637

99. ; $q + 2$ ; confidence 0.637

100. ; $h ^ { i } \left( K _ { X } + j L - \sum _ { k = 1 } ^ { r } \left[ \frac { j \alpha _ { k } } { N } \right] D _ { k } \right) = 0,$ ; confidence 0.637

101. ; $a , b \in A _ { k }$ ; confidence 0.636

102. ; $S _ { k } = \left( \begin{array} { c } { n } \\ { k } \end{array} \right) \frac { ( n - k ) ! } { n ! }$ ; confidence 0.636

103. ; $\alpha \in \mathbf{Z} \alpha _ { 1 } + \mathbf{Z} \alpha _ { 2 } + \dots$ ; confidence 0.636

104. ; $C _ { B _ { 2 } } ( L _ { n } )$ ; confidence 0.636

105. ; $\beta ( \phi , \rho ) ( t ) = \int _ { M } u _ { \Phi } \rho.$ ; confidence 0.636

106. ; $u ^ { n } = 1$ ; confidence 0.636

107. ; $\nabla _ { Z } R$ ; confidence 0.636

108. ; $V _ { \text { simp } } ( K _ { p } )$ ; confidence 0.636

109. ; $Z ( g ^ { a } h ^ { c } , g ^ { b } h ^ { d } ; z ) = \alpha Z \left( g ,h ; \frac { a z + b } { c z + d } \right)$ ; confidence 0.636

110. ; $M _ { z }$ ; confidence 0.636

111. ; $a ^ { [ N ] } ( z ) \equiv 1$ ; confidence 0.636

112. ; $v \notin [ 0,1]$ ; confidence 0.636

113. ; $a _ { 2 } = 1$ ; confidence 0.636

114. ; $\ddot { x } - \mu ( 1 - x ^ { 2 } ) \dot { x } + x = 0 , \quad \mu = \text { const } > 0 , \quad \dot { x } ( t ) \equiv \frac { d x } { d t },$ ; confidence 0.636

115. ; $Z \sim N _ { p } ( 0 , I )$ ; confidence 0.636

116. ; $x , y , z \in E _ { + }$ ; confidence 0.636

117. ; $\mathcal{L} _ { w } ( \mathcal{X} , \mathcal{Y} )$ ; confidence 0.636

118. ; $D _ { 1 }$ ; confidence 0.636

119. ; $c - 2 \operatorname { deg } I$ ; confidence 0.636

120. ; $i = 1 , \ldots , 4$ ; confidence 0.636

121. ; $S _ { f } ( a _ { 0 } )$ ; confidence 0.636

122. ; $f | _ { K }$ ; confidence 0.635

123. ; $( \alpha _ { 1 } \cup \gamma , \alpha _ { 2 } , \dots , \alpha _ { q } )$ ; confidence 0.635

124. ; $\mathsf{E} [ C ]$ ; confidence 0.635

125. ; $\mathcal{C} _ { 1 }$ ; confidence 0.635

126. ; $V ( M )$ ; confidence 0.635

127. ; $\left( \begin{array} { c c c c } { 1 } & { 2 } & { 3 } & { 4 } \\ { 5 } & { 6 } & { 7 } & { \square } \\ { 8 } & { \square } & { \square } & { \square } \\ { 9 } & { \square } & { \square } & { \square } \end{array} \right) = \left( \begin{array} { c c c c } { 4 } & { 2 } & { 1 } & { 3 } \\ { 6 } & { 5 } & { 7 } & { \square } \\ { 8 } & { \square } & { \square } & { \square } \\ { 9 } & { \square } & { \square } & { \square } \end{array} \right) \neq$ ; confidence 0.635

128. ; $E _ { 0 }$ ; confidence 0.635

129. ; $A \mathbf{x}$ ; confidence 0.635

130. ; $X = G \Lambda H$ ; confidence 0.635

131. ; $X \times X$ ; confidence 0.635

132. ; $A ( \mathbf{D} )$ ; confidence 0.635

133. ; $\mathbf{f} ^ { \text{em} } = \operatorname { div } \mathbf{t} ^ { \text{em} } - \frac { \partial \mathbf{G} ^ { \text{em} } } { \partial t },$ ; confidence 0.635

134. ; $z \in D$ ; confidence 0.635

135. ; $\dim H ^ { 2 r + 1 } ( M , \mathbf{C}) \qquad \text{is even},$ ; confidence 0.635

136. ; $\overline { \delta }_{\operatorname{BRST}}$ ; confidence 0.635

137. ; $\mathcal{P} \equiv \left( \begin{array} { c c } { \operatorname { exp } \left( \frac { J + H } { k _ { B } T } \right) } & { \operatorname { exp } \left( \frac { - J } { k _ { B } T } \right) } \\ { \operatorname { exp } \left( \frac { - J } { k _ { B } T } \right) } & { \operatorname { exp } \left( \frac { J - H } { k _ { B } T } \right) } \end{array} \right).$ ; confidence 0.635

138. ; $V _ { \alpha }$ ; confidence 0.635

139. ; $\int _ { A } \operatorname { exp } ( h ^ { \prime } \Delta _ { n } ^ { * } ( \theta ) ) d P _ { n , \theta }$ ; confidence 0.635

140. ; $T ^ { k }$ ; confidence 0.635

141. ; $\mathsf{P} _ { K } ( 1,0 ) = a _ { 2 }$ ; confidence 0.635

142. ; $\mathcal{D}$ ; confidence 0.635

143. ; $\operatorname { max } _ { k = 1 , \ldots , n } \left( \frac { 1 } { n } | s _ { k } | \right) ^ { 1 / k } > \frac { 1 } { 5 } > \frac { 1 } { 2 + \sqrt { 8 } },$ ; confidence 0.635

144. ; $\rho ( x ) = \sum _ { j = 1 } ^ { N } | u _ { j } ( x ) | ^ { 2 }.$ ; confidence 0.635

145. ; $\mathsf{P} _ { 0 } \in \mathcal{P}$ ; confidence 0.635

146. ; $\mathcal{M} _ { n } = \{ P ( X , Y ) = \sum _ { \nu = 0 } ^ { n } a _ { \nu } X ^ { \nu } Y ^ { n - \nu } : a _ { \nu } \in \mathbf{Q} \},$ ; confidence 0.635

147. ; $\sigma _ { k - 1 } ( n ) = \sum _ { 0 < d | n } d ^ { k - 1 }.$ ; confidence 0.635

148. ; $\operatorname { lim } _ { \tau \rightarrow \infty } \frac { \operatorname { det } ( I + W _ { \tau } ( k ) ) } { G ( a ) ^ { \tau } } = E ( a ),$ ; confidence 0.634

149. ; $\| \mathbf{y} - \mathbf{Xb} \| ^ { 2 }$ ; confidence 0.634

150. ; $\operatorname { Cap } ( E ) = \operatorname { exp } \left( - \operatorname { sup } _ { z \in \text{C} ^ { n } } \rho _ { L _ { E } } ( z ) \right).$ ; confidence 0.634

151. ; $\rightarrow H ^ { n + 1 } ( X , A ; G ) \rightarrow \dots $ ; confidence 0.634

152. ; $E ^ { \text{TF} } ( N )$ ; confidence 0.634

153. ; $\frac { 1 } { \beta _ { p } ( a , b ) } | V | ^ { a - ( p + 1 ) / 2 } | I _ { p } + V | ^ { - ( a + b ) },$ ; confidence 0.634

154. ; $\mod \Gamma$ ; confidence 0.634

155. ; $F ( t ) = \int _ { t } ^ { + \infty } p _ { 0 } ( a - t ) \frac { \Pi ( a ) } { \Pi ( a - t ) } d a,$ ; confidence 0.634

156. ; $B _ { r _ { 1 } } , B _ { r _ { 2 } }$ ; confidence 0.634

157. ; $Y \in \mathfrak { X } ( M )$ ; confidence 0.634

158. ; $\operatorname{diam}M \leq d,$ ; confidence 0.634

159. ; $G_1$ ; confidence 0.634

160. ; $k = 1 / 2$ ; confidence 0.633

161. ; $\operatorname { spec } ( M , \Delta ^ { ( 0 ) } ) , \ldots , \operatorname { spec } ( M , \Delta ^ { ( \dim M ) } )$ ; confidence 0.633

162. ; $\operatorname{QS} ( \mathbf{T} ) = \cup _ { M \geq 1 } M$ ; confidence 0.633

163. ; $\mathbf{E} _ { n }$ ; confidence 0.633

164. ; $z \in ( 1 , \dots , M )$ ; confidence 0.633

165. ; $\psi ( \gamma ) = \frac { 2 } { \pi ^ { 2 } \gamma } + O \left( \frac { 1 } { \gamma ^ { 3 } } \right) \text { as } \gamma \rightarrow + \infty.$ ; confidence 0.633

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

167. ; $\{ I _ { n } \} _ { n = 0 } ^ { \infty }$ ; confidence 0.633

168. ; $Q_l ^ { B }$ ; confidence 0.633

169. ; $\text{Ab} ^ { \text{ZC} }$ ; confidence 0.633

170. ; $\mathbf{Z} [ v ^ { \pm 1 } , z ^ { \pm 1 } ]$ ; confidence 0.633

171. ; $y _ { t } ^ { ( i ) }$ ; confidence 0.633

172. ; $H$ ; confidence 0.632

173. ; $\alpha \wedge \beta ^ { n } \neq 0$ ; confidence 0.632

174. ; $R _ { 1414 } = a _ { 1 } , R _ { 2323 } = a _ { 1 } , R _ { 3434 } = a _ { 2 } , R _ { 1234 } = a _ { 1 } , R _ { 1324 } = - a _ { 1 } , R _ { 1423 } = a _ { 2 },$ ; confidence 0.632

175. ; $E ( \varphi , \psi ) = \{ \epsilon _ { i } ( \varphi , \psi ) : i \in I \}$ ; confidence 0.632

176. ; $R _ { n } = I - Q _ { n }$ ; confidence 0.632

177. ; $K \subseteq \mathbf{C}$ ; confidence 0.632

178. ; $m_{ij}$ ; confidence 0.632

179. ; $g ( z ) = r ( z ) + \sum _ { i = 1 } ^ { \infty } s _ { 2 m + i } z ^ { - ( 2 m + i ) }$ ; confidence 0.632

180. ; $V _ { \pm }$ ; confidence 0.632

181. ; $f = ( f _ { 1 } , \ldots , f _ { M } )$ ; confidence 0.632

182. ; $C_l$ ; confidence 0.632

183. ; $\bigwedge _ { j = 1 } ^ { m } \frac { d z _ { j } - d z _ { j } ^ { \prime } } { z _ { j } - z _ { j } ^ { \prime } }$ ; confidence 0.632

184. ; $x _ { 0 } > 0$ ; confidence 0.632

185. ; $\mathsf{P} _ { n }$ ; confidence 0.632

186. ; $\mathbf{C} \in \mathsf{K}_0$ ; confidence 0.632

187. ; $T _ { 0 }$ ; confidence 0.632

188. ; $\Sigma _ { P } = \{ ( x , \xi ) \in \Omega \times ( \mathbf{R} ^ { n } \backslash \{ 0 \} ) : p _ { m } ( x , \xi ) = 0 \},$ ; confidence 0.632

189. ; $D _ { x } ^ { \alpha } = D _ { x _ { 1 } } ^ { \alpha _ { 1 } } \ldots D _ { x _ { n } } ^ { \alpha _ { n } }$ ; confidence 0.632

190. ; $f _ { j k l } = \frac { - i } { 4 } \operatorname { Tr } [ ( \lambda _ { j } \lambda _ { k } - \lambda _ { k } \lambda _ { j } ) \lambda _ { l } ].$ ; confidence 0.632

191. ; $W ^ { n }$ ; confidence 0.632

192. ; $\frac { \partial u ( t , x ) } { \partial t } + \frac { 1 } { 2 } \| d _ { x } u ( t , x ) \| ^ { 2 } = 0 , \quad ( t , x ) \in ( 0 , T ) \times H,$ ; confidence 0.632

193. ; $\mathcal{A} ( X )$ ; confidence 0.632

194. ; $( \alpha _ { 1 } , \dots , \alpha _ { n } )$ ; confidence 0.632

195. ; $( A , [. ,. ] )$ ; confidence 0.632

196. ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { T _ { n } - S } { S _ { n } - S } = 0.$ ; confidence 0.632

197. ; $\partial _ { s }$ ; confidence 0.631

198. ; $T \in \operatorname{GL} ( n , \mathbf{R} )$ ; confidence 0.631

199. ; $\mathsf{E} \varepsilon _ { t } \varepsilon _ { s } ^ { \prime } = \delta _ { s t } \Sigma$ ; confidence 0.631

200. ; $B ( x _ { 0 } , r ) = \{ x \in \mathbf{R} ^ { n } : | x - x _ { 0 } | < r \}$ ; confidence 0.631

201. ; $F _ { K } \circ \Phi$ ; confidence 0.631

202. ; $| x | | y | \bigwedge | y | ^ { 2 } | x | ^ { 2 } = | x | | y |$ ; confidence 0.631

203. ; $\mathcal{E} _ { \text{avg} } ( \mu , m ) = \int | \epsilon ( p , m ) | d \mu ( p )$ ; confidence 0.631

204. ; $\pi ( a ) M ^ { U } ( [ t , \infty ) ) \subseteq M ^ { U } ( [ t + s , \infty ) )$ ; confidence 0.631

205. ; $( \text{l} _ { m } - k ^ { 2 } ) f _ { m } = 0,$ ; confidence 0.631

206. ; $g _ { j } \in L ^ { 2 } ( [ 0,1 ] )$ ; confidence 0.631

207. ; $\mathsf{E} ( \mathbf{Z} _ { 3 } ) = 0$ ; confidence 0.631

208. ; $+ O \left( \frac { ( \operatorname { log } n ) ^ { 1 / 2 } ( \operatorname { log } \operatorname { log } n ) ^ { 1 / 4 } } { n ^ { 3 / 4 } } \right) \text{ a.s..}$ ; confidence 0.631

209. ; $\gamma_j = 0$ ; confidence 0.631

210. ; $\{ F _ { n } \} _ { n = 0 } ^ { \infty }$ ; confidence 0.631

211. ; $B U _ { q } ( \mathfrak{g} )$ ; confidence 0.631

212. ; $t _ { \operatorname { min } } < t _ { 1 } < \ldots < t _ { m } < t _ { \operatorname { max } }$ ; confidence 0.631

213. ; $\sigma _ { \pi } ( A , \mathcal{X} ) = \sigma _ { \delta } ( A , \mathcal{X} ) = \sigma _ { \text{T} } ( A , \mathcal{X} )$ ; confidence 0.631

214. ; $\operatorname{ad}( \mathfrak{g} ) = \operatorname { Der } (\mathfrak{g} )$ ; confidence 0.631

215. ; $p_y$ ; confidence 0.630

216. ; $\mathbf{N} ( X )$ ; confidence 0.630

217. ; $1 , \dots , n$ ; confidence 0.630

218. ; $P _ { \Omega } ( . , \xi )$ ; confidence 0.630

219. ; $D _ { 1 } \subset \mathbf{R} ^ { 2 }$ ; confidence 0.630

220. ; $\zeta _ { \lambda } ^ { \pi }$ ; confidence 0.630

221. ; $\overline{A} \in \mathcal{S}$ ; confidence 0.630

222. ; $L _ { i } \in \Omega ^ { l } ( N ; T N )$ ; confidence 0.630

223. ; $C _ { 1 } N ^ { ( n - 1 ) / 2 } \leq \| S _ { N } \| \leq C _ { 2 } N ^ { ( n - 1 ) / 2 }.$ ; confidence 0.630

224. ; $ax \leq ay$ ; confidence 0.630

225. ; $\{ r _ { i } ( A ) \} _ { i = 1 } ^ { n }$ ; confidence 0.630

226. ; $m _ { s } = \operatorname { lim } _ { H \rightarrow 0 } m ( T , H ) > 0.$ ; confidence 0.630

227. ; $K I = K ( I , \preceq )$ ; confidence 0.630

228. ; $\sum | c_k| < \infty$ ; confidence 0.630

229. ; $( \mathcal{L} _ { K } \omega ) ( X _ { 1 } , \dots , X _ { k + 1 } ) =$ ; confidence 0.630

230. ; $A _ { \alpha }$ ; confidence 0.630

231. ; $\mathbf{N}$ ; confidence 0.630

232. ; $a + b \in F$ ; confidence 0.629

233. ; $r ( 1 + 2.78 / \lambda )$ ; confidence 0.629

234. ; $( u = v ) \in S$ ; confidence 0.629

235. ; $R$ ; confidence 0.629

236. ; $\overline { R } = \sum _ { i = 1 } ^ { n } R _ { i } / n = ( n + 1 ) / 2 = \sum _ { i = 1 } ^ { n } S _ { i } / n = \overline { S }$ ; confidence 0.629

237. ; $\overline { H } \square ^ { * }$ ; confidence 0.629

238. ; $G \subset \operatorname { GL } ( V )$ ; confidence 0.629

239. ; $H ^ { n } ( S ^ { n } )$ ; confidence 0.629

240. ; $\widetilde { D } = \{ \alpha \in G : \alpha D \alpha ^ { - 1 } \text { is commensurable with} \ D\}$ ; confidence 0.629

241. ; $p _ { m } ( z ) = m ! \sum _ { 0 \leq n \leq m - 1 } b _ { m } ( n + 1 ) z ^ { n } , \quad z \in \mathbf{C},$ ; confidence 0.629

242. ; $c _ { 1 } ( M ) _ { \mathbf{R} } > 0$ ; confidence 0.629

243. ; $x , y , z _ { 1 } , \dots , z _ { s } \in \mathbf{Z}$ ; confidence 0.629

244. ; $X ^ { 2 n + 1 }$ ; confidence 0.629

245. ; $k = i k_j$ ; confidence 0.629

246. ; $H _ { p }$ ; confidence 0.629

247. ; $\Gamma = \operatorname { Gal } ( K / k )$ ; confidence 0.628

248. ; $\mathbf{x} = ( x , \ldots , x )$ ; confidence 0.628

249. ; $q_l : \mathbf{Z} ^ { l } \rightarrow \mathbf{Z}$ ; confidence 0.628

250. ; $\operatorname { su } ( 2 )$ ; confidence 0.628

251. ; $y _ { n } \geq 0$ ; confidence 0.628

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

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

254. ; $\operatorname{TD} [ r , s ]$ ; confidence 0.628

255. ; $\| W _ { k } \| = \| \mathcal{F} k \| _ { L^\infty } $ ; confidence 0.628

256. ; $u_-$ ; confidence 0.628

257. ; $f \in X \text{ implies } \bar{f} \in X \text{ and } \mathcal{P}_-f \in X,$ ; confidence 0.628

258. ; $n ^ { \text { th } }$ ; confidence 0.628

259. ; $A X B + C \sim E _ { q , n } ( A M B + C , ( A \Sigma A ^ { \prime } ) \otimes ( B ^ { \prime } \Phi B ) , \psi )$ ; confidence 0.628

260. ; $x . D _ { x }$ ; confidence 0.628

261. ; $x \notin - \Delta ^ { \circ }$ ; confidence 0.628

262. ; $\partial _ { t } \eta ( u ) + \operatorname { div } _ { x } G ( u ) \leq 0,$ ; confidence 0.627

263. ; $\operatorname { St } _ { G } ( u )$ ; confidence 0.627

264. ; $\frac { 1 } { ( 2 \pi ) ^ { n p / 2 } } | \Sigma | ^ { - n / 2 } \operatorname { etr } \left\{ - \frac { 1 } { 2 } \Sigma ^ { - 1 } X X ^ { \prime } \right\} , X \in \mathbf{R} ^ { p \times n },$ ; confidence 0.627

265. ; $3 / 2$ ; confidence 0.627

266. ; $P \subset X$ ; confidence 0.627

267. ; $x _ { 0 } \in F ( x _ { 0 } )$ ; confidence 0.627

268. ; $K \subset \mathbf{C} ^ { n + 1 }$ ; confidence 0.627

269. ; $W = p ^ { n + 1 } - q _ { 1 } p ^ { n - 1 } - \ldots - q _ { n }$ ; confidence 0.627

270. ; $0 = ( \delta ( x ) x ) \operatorname { vp } \frac { 1 } { x } \neq \delta ( x ) \left( x \operatorname{vp} \frac { 1 } { x } \right) = \delta ( x )$ ; confidence 0.627

271. ; $\sigma _ { \delta }$ ; confidence 0.627

272. ; $D _ { j }$ ; confidence 0.627

273. ; $\lambda = ( \lambda _ { 1 } , \dots , \lambda _ { s } , \dots , \lambda _ { t } )$ ; confidence 0.627

274. ; $\Gamma \subset \Omega \times ( \mathbf{R} ^ { n } \backslash \{ 0 \} )$ ; confidence 0.627

275. ; $c _ { t } ^ { \prime } > c _ { t }$ ; confidence 0.627

276. ; $a _ { n^i } = ( a _ { n } )^i$ ; confidence 0.627

277. ; $G /G_x$ ; confidence 0.627

278. ; $l ^ { 2 } ( \Gamma )$ ; confidence 0.627

279. ; $u_{m + 1}$ ; confidence 0.627

280. ; $\rho \otimes x$ ; confidence 0.627

281. ; $S _ { i } > 0 , i = 1 , \dots , r.$ ; confidence 0.627

282. ; $y _ { j } < y _ { k }$ ; confidence 0.627

283. ; $= \pi ^ { 2 } \sqrt { \frac { \pi } { 2 } } \int _ { 0 } ^ { \infty } \tau \frac { \operatorname { sinh } ( \pi \tau ) } { \operatorname { cosh } ^ { 3 } ( \pi \tau ) } P _ { i \tau - 1 / 2 } ( x ) F ( \tau ) G ( \tau ) d \tau,$ ; confidence 0.627

284. ; $n/ ( k - 1 )$ ; confidence 0.627

285. ; $p _ { i } ( \theta ) = \mathsf{P} \{ X _ { i } \in ( x _ { i - 1} , x _ { i } ] \} > 0,$ ; confidence 0.626

286. ; $\operatorname{rank} ( \mathbf{X} ) = r$ ; confidence 0.626

287. ; $\rho : G / \mathbf{Q} \rightarrow \operatorname{GL} (\mathcal{M} )$ ; confidence 0.626

288. ; $\rho _ { \text{atom} } ^ { \text{TF} } ( x , N = Z , Z ) \sim \gamma ^ { 3 } \left( \frac { 3 } { \pi } \right) ^ { 3 } | x | ^ { - 6 },$ ; confidence 0.626

289. ; $\forall x \forall y \exists z \forall v ( v \in z \leftrightarrow ( v = x \vee v = y ) ).$ ; confidence 0.626

290. ; $\operatorname{Ch} ( [ a ] ) \mathcal{T} ( M )$ ; confidence 0.626

291. ; $i = 1 , \ldots , k$ ; confidence 0.626

292. ; $\operatorname{CL} ( X )$ ; confidence 0.626

293. ; $( q _ { 1 } , \dots , q _ { m } )$ ; confidence 0.626

294. ; $B / A$ ; confidence 0.626

295. ; $\mathbf{A} \Theta \mathbf{B}$ ; confidence 0.626

296. ; $s = ( s _ { 1 } , \dots , s _ { n } ) : \partial D \times D \rightarrow \mathbf{C} ^ { n }$ ; confidence 0.626

297. ; $G _ { X } ( X - Y) \leq \rho ^ { 2 } \Rightarrow G _ { Y } \leq C G _ { X };$ ; confidence 0.626

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

299. ; $\mathcal{M}$ ; confidence 0.626

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

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/50. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/50&oldid=45702

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Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/50"

Revision as of 14:55, 10 May 2020

List

@@ Line 6: / Line 6: @@
 . https://www.encyclopediaofmath.org/legacyimages/k/k120/k120050/k12005017.png ; $r ( K _ { X } + B )$ ; confidence 0.643
-. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015160/b0151607.png ; $1$ ; confidence 0.643
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015160/b0151607.png ; $\mathbf{1}$ ; confidence 0.643
 . https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080180.png ; $\widetilde { F B }$ ; confidence 0.643
@@ Line 26: / Line 26: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120250/s12025030.png ; $\sqrt { 1 - x ^ { 2 } } w ( x ) > 0$ ; confidence 0.642
-. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048070/h04807042.png ; $S = \frac { 1 } { n - 1 } \sum _ { i = 1 } ^ { n } ( X _ { i } - X ) ( X _ { i } - X ) ^ { \prime },$ ; confidence 0.642
+. https://www.encyclopediaofmath.org/legacyimages/h/h048/h048070/h04807042.png ; $S = \frac { 1 } { n - 1 } \sum _ { i = 1 } ^ { n } ( X _ { i } - \overline{X} ) ( X _ { i } - \overline{X} ) ^ { \prime },$ ; confidence 0.642
 . https://www.encyclopediaofmath.org/legacyimages/b/b017/b017380/b01738052.png ; $\phi_j$ ; confidence 0.642
@@ Line 36: / Line 36: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110580/a11058065.png ; $l_2$ ; confidence 0.642
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011090.png ; $F _ { \sigma } \in \widetilde { O } ( ( \Omega + \Gamma _ { \sigma } ) \cap U ).$ ; confidence 0.642
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011090.png ; $F _ { \sigma } \in \widetilde { \mathcal{O} } ( ( \Omega + \Gamma _ { \sigma } ) \cap U ).$ ; confidence 0.642
 . https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e03500038.png ; $N _ { \epsilon } ( C )$ ; confidence 0.642
@@ Line 48: / Line 48: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120220/s12022037.png ; $t \searrow 0$ ; confidence 0.641
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006026.png ; $E ^ { TF } ( N ) = \operatorname { inf } \{ \mathcal{E} ( \rho ) : \rho \in L ^ { 5 / 3 } , \int \rho = N , \rho \geq 0 \},$ ; confidence 0.641
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006026.png ; $E ^ { \text{TF} } ( N ) = \operatorname { inf } \{ \mathcal{E} ( \rho ) : \rho \in L ^ { 5 / 3 } , \int \rho = N , \rho \geq 0 \},$ ; confidence 0.641
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f13010058.png ; $L _ { C } ^ { p } ( G )$ ; confidence 0.641
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f13010058.png ; $L _ { \text{C} } ^ { p } ( G )$ ; confidence 0.641
 . https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t09408036.png ; $\pi _ { n } ( X ; A , B , * ) = \pi _ { n - 1 } ( \Omega ( X ; A , B ) , * ).$ ; confidence 0.641
@@ Line 68: / Line 68: @@
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023089.png ; $E ^ { k } = M \times F \times F ^ { ( 1 ) } \times \ldots F ^ { ( k ) }$ ; confidence 0.641
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032042.png ; $E _ { \theta } ( N ) = \frac { P _ { \theta } ( S _ { N } = K ) K - P _ { \theta } ( S _ { N } = - J ) J } { 2 \theta - 1 }.$ ; confidence 0.641
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032042.png ; $\mathsf{E} _ { \theta } ( N ) = \frac { \mathsf{P} _ { \theta } ( S _ { N } = K ) K - \mathsf{P} _ { \theta } ( S _ { N } = - J ) J } { 2 \theta - 1 }.$ ; confidence 0.641
 . https://www.encyclopediaofmath.org/legacyimages/s/s090/s090670/s0906703.png ; $U : \mathcal{C} \rightarrow \operatorname{Set}$ ; confidence 0.641
@@ Line 78: / Line 78: @@
 . https://www.encyclopediaofmath.org/legacyimages/c/c130/c130190/c13019048.png ; $A = \operatorname { diag } ( \lambda _ { 1 } , \dots , \lambda _ { n } )$ ; confidence 0.641
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170281.png ; $d _ { 2 } ( \theta _ { 2 } ^ { j } )$ ; confidence 0.640
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170281.png ; $d _ { 2 } ( e _ { 2 } ^ { j } )$ ; confidence 0.640
 . https://www.encyclopediaofmath.org/legacyimages/m/m130/m130050/m1300501.png ; $a \leftrightarrow b a b ^ { - 1 }$ ; confidence 0.640
@@ Line 90: / Line 90: @@
 . https://www.encyclopediaofmath.org/legacyimages/h/h130/h130020/h13002064.png ; $R \subseteq A ^ { n }$ ; confidence 0.640
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015037.png ; $\text{E} _ { P } ( d _ { 0 } ) = 0$ ; confidence 0.640
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015037.png ; $\text{E} _ { \mathsf{P} } ( d _ { 0 } ) = 0$ ; confidence 0.640
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130100/c13010027.png ; $( C ) \int _ { A } f d m = ( C ) \int f \cdot \chi _ { A } d m$ ; confidence 0.640
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130100/c13010027.png ; $( C ) \int _ { A } f d m = ( C ) \int f . \chi _ { A } d m$ ; confidence 0.640
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009020.png ; $0 \leq t < \infty$ ; confidence 0.640
@@ Line 98: / Line 98: @@
 . https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p12017037.png ; $\widehat { B^* }  $ ; confidence 0.640
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a1303205.png ; $E _ { \theta } ( X _ { i } ) = P _ { \theta } ( X _ { i } = 1 ) = \theta = 1 - P _ { \theta } ( X _ { i } = 0 )$ ; confidence 0.640
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a1303205.png ; $\mathsf{E} _ { \theta } ( X _ { i } ) = \mathsf{P} _ { \theta } ( X _ { i } = 1 ) = \theta = 1 - \mathsf{P} _ { \theta } ( X _ { i } = 0 )$ ; confidence 0.640
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120100/e12010015.png ; $\mathbf{f} ^ { em } = q _ { f } \mathbf{E} + \frac { 1 } { c } \mathbf{J} \times \mathbf{B} + ( \nabla \mathbf{E} ) \mathbf{P} + ( \nabla \mathbf{B} ) M +$ ; confidence 0.640
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120100/e12010015.png ; $\mathbf{f} ^ { \text{em} } = q _ { f } \mathbf{E} + \frac { 1 } { c } \mathbf{J} \times \mathbf{B} + ( \nabla \mathbf{E} ). \mathbf{P} + ( \nabla \mathbf{B} ). \mathbf{M} +$ ; confidence 0.640
 . https://www.encyclopediaofmath.org/legacyimages/w/w130/w130040/w13004048.png ; $\operatorname{II}( W , V ) = - \operatorname { Re } ( \eta ( W ) d g ( V ) ).$ ; confidence 0.640
-. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130050/r1300508.png ; $\alpha , b \in \Omega$ ; confidence 0.640
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130050/r1300508.png ; $a , b \in \Omega$ ; confidence 0.640
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120130/l12013020.png ; $x \in \widetilde{\mathbf{Z}}$ ; confidence 0.640
@@ Line 120: / Line 120: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120340/b12034016.png ; $K_n$ ; confidence 0.639
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040338.png ; $\lambda \in \Delta$ ; confidence 0.639
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040338.png ; $\lambda \in \Lambda$ ; confidence 0.639
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020064.png ; $\pi \in S _ { n }$ ; confidence 0.639
@@ Line 130: / Line 130: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009062.png ; $\operatorname { Re } h ( z ) > 0$ ; confidence 0.639
-. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008037.png ; $\langle A \rangle _ { T } = Z ^ { - 1 } \operatorname { Tr } [ \operatorname { exp } ( - \frac { \mathcal{H} } { k _ { B } T } ) A ].$ ; confidence 0.639
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008037.png ; $\langle A \rangle _ { T } = Z ^ { - 1 } \operatorname { Tr } \left[ \operatorname { exp } ( - \frac { \mathcal{H} } { k _ { B } T } ) A \right].$ ; confidence 0.639
-. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062000/m0620002.png ; $( X _ { n } ) _ { n \in Z }$ ; confidence 0.639
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062000/m0620002.png ; $( X _ { n } ) _ { n \in \mathbf{Z} }$ ; confidence 0.639
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120240/a12024027.png ; $Z ( C )$ ; confidence 0.639
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120240/a12024027.png ; $Z ( \mathbf{C} )$ ; confidence 0.639
 . https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002023.png ; $f _ { 1 } , \ldots , f _ { d }$ ; confidence 0.639
-. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005078.png ; $V _ { ( n ) } < \infty$ ; confidence 0.639
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005078.png ; $\operatorname {dim} V _ { ( n ) } < \infty$ ; confidence 0.639
 . https://www.encyclopediaofmath.org/legacyimages/a/a010/a010240/a01024018.png ; $z_1$ ; confidence 0.638
@@ Line 148: / Line 148: @@
 . https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020178.png ; $U _ { t } ^ { j } = u _ { j } ( B _ { \operatorname { min }( t , \tau ) }  )$ ; confidence 0.638
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130110/t13011019.png ; $\mathcal{Y} ( T _ { A } ) = \{ N _ { B } : \operatorname { Tor } _ { 1 } ^ { B } ( N , T ) = 0 \},$ ; confidence 0.638
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130110/t13011019.png ; $\mathcal{Y} ( T _ { A } ) = \left\{ N _ { B } : \operatorname { Tor } _ { 1 } ^ { B } ( N , T ) = 0 \right\},$ ; confidence 0.638
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021070.png ; $\{ 0 , \pm x _ { 1 } , \ldots , \pm x _ { k } \}$ ; confidence 0.638
@@ Line 156: / Line 156: @@
 . https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014092.png ; $K Q$ ; confidence 0.638
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017041.png ; $H _ { Z } ( t )$ ; confidence 0.638
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017041.png ; $H _ { z } ( t )$ ; confidence 0.638
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007014.png ; $v ( x , \alpha , k ) = A ( \alpha ^ { \prime } , \alpha , k ) \frac { e ^ { i k r} } { r } + o ( \frac { 1 } { r } ),$ ; confidence 0.638
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007014.png ; $v ( x , \alpha , k ) = A ( \alpha ^ { \prime } , \alpha , k ) \frac { e ^ { i k r} } { r } + o \left( \frac { 1 } { r } \right),$ ; confidence 0.638
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020046.png ; $k S _ { n }$ ; confidence 0.638
@@ Line 198: / Line 198: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120250/a12025063.png ; $q + 2$ ; confidence 0.637
-. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120060/k12006050.png ; $h ^ { i } ( K _ { X } + j L - \sum _ { k = 1 } ^ { r } [ \frac { j \alpha _ { k } } { N } ] D _ { k } ) = 0,$ ; confidence 0.637
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120060/k12006050.png ; $h ^ { i } \left( K _ { X } + j L - \sum _ { k = 1 } ^ { r } \left[ \frac { j \alpha _ { k } } { N } \right] D _ { k } \right) = 0,$ ; confidence 0.637
-. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120070/h12007028.png ; $\alpha , b \in A _ { k }$ ; confidence 0.636
+. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120070/h12007028.png ; $a , b \in A _ { k }$ ; confidence 0.636
 . https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002022.png ; $S _ { k } = \left( \begin{array} { c } { n } \\ { k } \end{array} \right) \frac { ( n - k ) ! } { n ! }$ ; confidence 0.636
@@ Line 216: / Line 216: @@
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l120120108.png ; $V _ { \text { simp } } ( K _ { p } )$ ; confidence 0.636
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130220/m13022048.png ; $Z ( g ^ { \alpha } h ^ { c } , g ^ { b } h ^ { d } ; z ) = \alpha Z ( g ,h ; \frac { a z + b } { c z + d } )$ ; confidence 0.636
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130220/m13022048.png ; $Z ( g ^ { a } h ^ { c } , g ^ { b } h ^ { d } ; z ) = \alpha Z \left( g ,h ; \frac { a z + b } { c z + d } \right)$ ; confidence 0.636
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c120170110.png ; $M _ { Z }$ ; confidence 0.636
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c120170110.png ; $M _ { z }$ ; confidence 0.636
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f1202109.png ; $a ^ { [ N ] } ( z ) \equiv 1$ ; confidence 0.636
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130090/b13009016.png ; $v \notin [ 0,1$ ; confidence 0.636
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130090/b13009016.png ; $v \notin [ 0,1]$ ; confidence 0.636
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032077.png ; $\alpha _ { 2 } = 1$ ; confidence 0.636
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032077.png ; $a _ { 2 } = 1$ ; confidence 0.636
 . https://www.encyclopediaofmath.org/legacyimages/v/v096/v096030/v0960301.png ; $\ddot { x } - \mu ( 1 - x ^ { 2 } ) \dot { x } + x = 0 , \quad \mu = \text { const } > 0 , \quad \dot { x } ( t ) \equiv \frac { d x } { d t },$ ; confidence 0.636
@@ Line 236: / Line 236: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110020/a11002019.png ; $D _ { 1 }$ ; confidence 0.636
-. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l13008036.png ; $c - 2 \operatorname { deg } l$ ; confidence 0.636
+. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l13008036.png ; $c - 2 \operatorname { deg } I$ ; confidence 0.636
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040176.png ; $i = 1 , \ldots , 4$ ; confidence 0.636
@@ Line 246: / Line 246: @@
 . https://www.encyclopediaofmath.org/legacyimages/h/h130/h130020/h13002047.png ; $( \alpha _ { 1 } \cup \gamma , \alpha _ { 2 } , \dots , \alpha _ { q } )$ ; confidence 0.635
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008070.png ; $E [ C ]$ ; confidence 0.635
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008070.png ; $\mathsf{E} [ C ]$ ; confidence 0.635
 . https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p12017083.png ; $\mathcal{C} _ { 1 }$ ; confidence 0.635
@@ Line 258: / Line 258: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f130/f130280/f13028021.png ; $A \mathbf{x}$ ; confidence 0.635
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023099.png ; $X = G \wedge H$ ; confidence 0.635
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023099.png ; $X = G \Lambda H$ ; confidence 0.635
 . https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150086.png ; $X \times X$ ; confidence 0.635
@@ Line 264: / Line 264: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120180/d12018029.png ; $A ( \mathbf{D} )$ ; confidence 0.635
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120100/e12010041.png ; $\mathbf{f} ^ { em } = \operatorname { div } \mathbf{t} ^ { em } - \frac { \partial \mathbf{G} ^ { em } } { \partial t }$ ; confidence 0.635
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120100/e12010041.png ; $\mathbf{f} ^ { \text{em} } = \operatorname { div } \mathbf{t} ^ { \text{em} } - \frac { \partial \mathbf{G} ^ { \text{em} } } { \partial t },$ ; confidence 0.635
 . https://www.encyclopediaofmath.org/legacyimages/a/a012/a012200/a01220053.png ; $z \in D$ ; confidence 0.635
@@ Line 272: / Line 272: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f130/f130020/f13002019.png ; $\overline { \delta }_{\operatorname{BRST}}$ ; confidence 0.635
-. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008076.png ; $\mathcal{P} \equiv \left( \begin{array} { c c } { \operatorname { exp } ( \frac { J + H } { k _ { B } T } ) } & { \operatorname { exp } ( \frac { - J } { k _ { B } T } ) } \\ { \operatorname { exp } ( \frac { - J } { k _ { B } T } ) } & { \operatorname { exp } ( \frac { J - H } { k _ { B } T } ) } \end{array} \right).$ ; confidence 0.635
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008076.png ; $\mathcal{P} \equiv \left( \begin{array} { c c } { \operatorname { exp } \left( \frac { J + H } { k _ { B } T } \right) } & { \operatorname { exp } \left( \frac { - J } { k _ { B } T } \right) } \\ { \operatorname { exp } \left( \frac { - J } { k _ { B } T } \right) } & { \operatorname { exp } \left( \frac { J - H } { k _ { B } T } \right) } \end{array} \right).$ ; confidence 0.635
 . https://www.encyclopediaofmath.org/legacyimages/c/c024/c024780/c024780257.png ; $V _ { \alpha }$ ; confidence 0.635
@@ Line 280: / Line 280: @@
 . https://www.encyclopediaofmath.org/legacyimages/k/k110/k110010/k11001048.png ; $T ^ { k }$ ; confidence 0.635
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j130040101.png ; $\mathbf{P} _ { K } ( 1,0 ) = \alpha _ { 2 }$ ; confidence 0.635
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j130040101.png ; $\mathsf{P} _ { K } ( 1,0 ) = a _ { 2 }$ ; confidence 0.635
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040321.png ; $\mathcal{D}$ ; confidence 0.635
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200211.png ; $\operatorname { max } _ { k = 1 , \ldots , n } ( \frac { 1 } { n } | s _ { k } | ) ^ { 1 / k } > \frac { 1 } { 5 } > \frac { 1 } { 2 + \sqrt { 8 } },$ ; confidence 0.635
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200211.png ; $\operatorname { max } _ { k = 1 , \ldots , n } \left( \frac { 1 } { n } | s _ { k } | \right) ^ { 1 / k } > \frac { 1 } { 5 } > \frac { 1 } { 2 + \sqrt { 8 } },$ ; confidence 0.635
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l120100128.png ; $\rho ( x ) = \sum _ { j = 1 } ^ { N } | u _ { j } ( x ) | ^ { 2 }.$ ; confidence 0.635
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015091.png ; $\mathbf{P} _ { 0 } \in P$ ; confidence 0.635
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015091.png ; $\mathsf{P} _ { 0 } \in \mathcal{P}$ ; confidence 0.635
 . https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e1300307.png ; $\mathcal{M} _ { n } = \{ P ( X , Y ) = \sum _ { \nu = 0 } ^ { n } a _ { \nu } X ^ { \nu } Y ^ { n - \nu } : a _ { \nu } \in \mathbf{Q} \},$ ; confidence 0.635
@@ Line 298: / Line 298: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240187.png ; $\| \mathbf{y} - \mathbf{Xb} \| ^ { 2 }$ ; confidence 0.634
-. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p13007072.png ; $\operatorname { Cap } ( E ) = \operatorname { exp } ( - \operatorname { sup } _ { z \in C ^ { n } } \rho _ { L _ { E } } ( z ) ).$ ; confidence 0.634
+. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p13007072.png ; $\operatorname { Cap } ( E ) = \operatorname { exp } \left( - \operatorname { sup } _ { z \in \text{C} ^ { n } } \rho _ { L _ { E } } ( z ) \right).$ ; confidence 0.634
 . https://www.encyclopediaofmath.org/legacyimages/c/c021/c021110/c02111013.png ; $\rightarrow H ^ { n + 1 } ( X , A ; G ) \rightarrow \dots $ ; confidence 0.634
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006080.png ; $E ^ { TF } ( N )$ ; confidence 0.634
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006080.png ; $E ^ { \text{TF} } ( N )$ ; confidence 0.634
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015067.png ; $\frac { 1 } { \beta _ { p } ( a , b ) } | V | ^ { \alpha - ( p + 1 ) / 2 } | I _ { p } + V | ^ { - ( \alpha + b ) },$ ; confidence 0.634
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015067.png ; $\frac { 1 } { \beta _ { p } ( a , b ) } | V | ^ { a - ( p + 1 ) / 2 } | I _ { p } + V | ^ { - ( a + b ) },$ ; confidence 0.634
 . https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t130130123.png ; $\mod \Gamma$ ; confidence 0.634
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a12017017.png ; $F ( t ) = \int _ { t } ^ { + \infty } p _ { 0 } ( \alpha - t ) \frac { \Pi ( \alpha ) } { \Pi ( \alpha - t ) } d \alpha,$ ; confidence 0.634
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a12017017.png ; $F ( t ) = \int _ { t } ^ { + \infty } p _ { 0 } ( a - t ) \frac { \Pi ( a ) } { \Pi ( a - t ) } d a,$ ; confidence 0.634
 . https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015067.png ; $B _ { r _ { 1 } } , B _ { r _ { 2 } }$ ; confidence 0.634
@@ Line 322: / Line 322: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120220/s12022075.png ; $\operatorname { spec } ( M , \Delta ^ { ( 0 ) } ) , \ldots , \operatorname { spec } ( M , \Delta ^ { ( \dim M ) } )$ ; confidence 0.633
-. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130050/q13005064.png ; $\operatorname{QS} ( T ) = \cup _ { M \geq 1 } M$ ; confidence 0.633
+. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130050/q13005064.png ; $\operatorname{QS} ( \mathbf{T} ) = \cup _ { M \geq 1 } M$ ; confidence 0.633
 . https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010037.png ; $\mathbf{E} _ { n }$ ; confidence 0.633
@@ Line 328: / Line 328: @@
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012046.png ; $z \in ( 1 , \dots , M )$ ; confidence 0.633
-. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p13014058.png ; $\psi ( \gamma ) = \frac { 2 } { \pi ^ { 2 } \gamma } + O ( \frac { 1 } { \gamma ^ { 3 } } ) \text { as } \gamma \rightarrow + \infty.$ ; confidence 0.633
+. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p13014058.png ; $\psi ( \gamma ) = \frac { 2 } { \pi ^ { 2 } \gamma } + O \left( \frac { 1 } { \gamma ^ { 3 } } \right) \text { as } \gamma \rightarrow + \infty.$ ; confidence 0.633
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001060.png ; $S ^ { 3 } / \Gamma$ ; confidence 0.633
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130040/b13004016.png ; $\{ l _ { n } \} _ { n = 0 } ^ { \infty }$ ; confidence 0.633
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130040/b13004016.png ; $\{ I _ { n } \} _ { n = 0 } ^ { \infty }$ ; confidence 0.633
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120270/s12027026.png ; $Q_l ^ { B }$ ; confidence 0.633
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007071.png ; $A b ^ { Z C }$ ; confidence 0.633
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007071.png ; $\text{Ab} ^ { \text{ZC} }$ ; confidence 0.633
 . https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004018.png ; $\mathbf{Z} [ v ^ { \pm 1 } , z ^ { \pm 1 } ]$ ; confidence 0.633
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017031.png ; $y _ { t } ^ { ( l ) }$ ; confidence 0.633
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017031.png ; $y _ { t } ^ { ( i ) }$ ; confidence 0.633
 . https://www.encyclopediaofmath.org/legacyimages/p/p120/p120140/p12014031.png ; $H$ ; confidence 0.632
@@ Line 346: / Line 346: @@
 . https://www.encyclopediaofmath.org/legacyimages/h/h120/h120010/h12001052.png ; $\alpha \wedge \beta ^ { n } \neq 0$ ; confidence 0.632
-. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120100/i12010052.png ; $R _ { 1414 } = \alpha _ { 1 } , R _ { 2323 } = \alpha _ { 1 } , R _ { 3434 } = \alpha _ { 2 } , R _ { 1234 } = \alpha _ { 1 } , R _ { 1324 } = - \alpha _ { 1 } , R _ { 1423 } = \alpha _ { 2 },$ ; confidence 0.632
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120100/i12010052.png ; $R _ { 1414 } = a _ { 1 } , R _ { 2323 } = a _ { 1 } , R _ { 3434 } = a _ { 2 } , R _ { 1234 } = a _ { 1 } , R _ { 1324 } = - a _ { 1 } , R _ { 1423 } = a _ { 2 },$ ; confidence 0.632
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040232.png ; $E ( \varphi , \psi ) = \{ \epsilon _ { i } ( \varphi , \psi ) : i \in I \}$ ; confidence 0.632
@@ Line 352: / Line 352: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120270/s12027013.png ; $R _ { n } = I - Q _ { n }$ ; confidence 0.632
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c12017015.png ; $K \subset \mathbf{C}$ ; confidence 0.632
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c12017015.png ; $K \subseteq \mathbf{C}$ ; confidence 0.632
-. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b017470280.png ; $m$ ; confidence 0.632
+. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b017470280.png ; $m_{ij}$ ; confidence 0.632
 . https://www.encyclopediaofmath.org/legacyimages/h/h130/h130030/h13003060.png ; $g ( z ) = r ( z ) + \sum _ { i = 1 } ^ { \infty } s _ { 2 m + i } z ^ { - ( 2 m + i ) }$ ; confidence 0.632
@@ Line 368: / Line 368: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b015/b015160/b01516022.png ; $x _ { 0 } > 0$ ; confidence 0.632
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150107.png ; $\mathbf{P} _ { n }$ ; confidence 0.632
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150107.png ; $\mathsf{P} _ { n }$ ; confidence 0.632
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040797.png ; $C \in K_0$ ; confidence 0.632
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040797.png ; $\mathbf{C} \in \mathsf{K}_0$ ; confidence 0.632
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110250/a11025019.png ; $T _ { 0 }$ ; confidence 0.632
@@ Line 390: / Line 390: @@
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120150/l12015014.png ; $( A , [. ,. ] )$ ; confidence 0.632
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018050.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { T _ { x } - S } { S _ { n } - S } = 0.$ ; confidence 0.632
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018050.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { T _ { n } - S } { S _ { n } - S } = 0.$ ; confidence 0.632
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026053.png ; $\partial _ { S }$ ; confidence 0.631
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026053.png ; $\partial _ { s }$ ; confidence 0.631
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011094.png ; $T \in \operatorname{GL} ( n , \mathbf{R} )$ ; confidence 0.631
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017020.png ; $\mathbf{E} \varepsilon _ { t } \varepsilon _ { s } ^ { \prime } = \delta _ { s t } \Sigma$ ; confidence 0.631
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017020.png ; $\mathsf{E} \varepsilon _ { t } \varepsilon _ { s } ^ { \prime } = \delta _ { s t } \Sigma$ ; confidence 0.631
 . https://www.encyclopediaofmath.org/legacyimages/p/p130/p130090/p1300906.png ; $B ( x _ { 0 } , r ) = \{ x \in \mathbf{R} ^ { n } : | x - x _ { 0 } | < r \}$ ; confidence 0.631
@@ Line 408: / Line 408: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120280/a120280172.png ; $\pi ( a ) M ^ { U } ( [ t , \infty ) ) \subseteq M ^ { U } ( [ t + s , \infty ) )$ ; confidence 0.631
-. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o1300806.png ; $( l _ { m } - k ^ { 2 } ) f _ { m } = 0,$ ; confidence 0.631
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o1300806.png ; $( \text{l} _ { m } - k ^ { 2 } ) f _ { m } = 0,$ ; confidence 0.631
 . https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009092.png ; $g _ { j } \in L ^ { 2 } ( [ 0,1 ] )$ ; confidence 0.631
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240353.png ; $\mathbf{E} ( \mathbf{Z} _ { 3 } ) = 0$ ; confidence 0.631
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240353.png ; $\mathsf{E} ( \mathbf{Z} _ { 3 } ) = 0$ ; confidence 0.631
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120020/b12002054.png ; $+ O ( \frac { ( \operatorname { log } n ) ^ { 1 / 2 } ( \operatorname { log } \operatorname { log } n ) ^ { 1 / 4 } } { n ^ { 3 / 4 } } ) \text{ a.s..}$ ; confidence 0.631
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120020/b12002054.png ; $+ O \left( \frac { ( \operatorname { log } n ) ^ { 1 / 2 } ( \operatorname { log } \operatorname { log } n ) ^ { 1 / 4 } } { n ^ { 3 / 4 } } \right) \text{ a.s..}$ ; confidence 0.631
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022040.png ; $\gamma_jj = 0$ ; confidence 0.631
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022040.png ; $\gamma_j = 0$ ; confidence 0.631
 . https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009019.png ; $\{ F _ { n } \} _ { n = 0 } ^ { \infty }$ ; confidence 0.631
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043095.png ; $B U _ { q } ( g )$ ; confidence 0.631
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043095.png ; $B U _ { q } ( \mathfrak{g} )$ ; confidence 0.631
 . https://www.encyclopediaofmath.org/legacyimages/k/k120/k120100/k12010015.png ; $t _ { \operatorname { min } } < t _ { 1 } < \ldots < t _ { m } < t _ { \operatorname { max } }$ ; confidence 0.631
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t130050114.png ; $\sigma _ { \pi } ( A , \mathcal{X} ) = \sigma _ { \delta } ( A , \mathcal{X} ) = \sigma _ { T } ( A , \mathcal{X} )$ ; confidence 0.631
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t130050114.png ; $\sigma _ { \pi } ( A , \mathcal{X} ) = \sigma _ { \delta } ( A , \mathcal{X} ) = \sigma _ { \text{T} } ( A , \mathcal{X} )$ ; confidence 0.631
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120150/a12015033.png ; $\operatorname{ad}( \mathfrak{g} ) = \operatorname { Der } (\mathfrak{g} )$ ; confidence 0.631
@@ Line 478: / Line 478: @@
 . https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020197.png ; $H ^ { n } ( S ^ { n } )$ ; confidence 0.629
-. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130060/h13006030.png ; $\widetilde { D } = \{ \alpha \in G : \alpha D \alpha ^ { - 1 } \text { is commensurable with} D\}$ ; confidence 0.629
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130060/h13006030.png ; $\widetilde { D } = \{ \alpha \in G : \alpha D \alpha ^ { - 1 } \text { is commensurable with} \ D\}$ ; confidence 0.629
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120210/e12021041.png ; $p _ { m } ( z ) = m ! \sum _ { 0 \leq n \leq m - 1 } b _ { m } ( n + 1 ) z ^ { n } , \quad z \in \mathbf{C},$ ; confidence 0.629
@@ Line 522: / Line 522: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011044.png ; $x \notin - \Delta ^ { \circ }$ ; confidence 0.628
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022072.png ; $\partial _ { t } \eta ( u ) + \operatorname { div } _ { X } G ( u ) \leq 0,$ ; confidence 0.627
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022072.png ; $\partial _ { t } \eta ( u ) + \operatorname { div } _ { x } G ( u ) \leq 0,$ ; confidence 0.627
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130230/b13023047.png ; $\operatorname { St } _ { G } ( u )$ ; confidence 0.627
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023044.png ; $\frac { 1 } { ( 2 \pi ) ^ { n p / 2 } } | \Sigma | ^ { - n / 2 } \operatorname { etr } \{ - \frac { 1 } { 2 } \Sigma ^ { - 1 } X X ^ { \prime } \} , X \in \mathbf{R} ^ { p \times n },$ ; confidence 0.627
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023044.png ; $\frac { 1 } { ( 2 \pi ) ^ { n p / 2 } } | \Sigma | ^ { - n / 2 } \operatorname { etr } \left\{ - \frac { 1 } { 2 } \Sigma ^ { - 1 } X X ^ { \prime } \right\} , X \in \mathbf{R} ^ { p \times n },$ ; confidence 0.627
 . https://www.encyclopediaofmath.org/legacyimages/a/a010/a010520/a01052030.png ; $3 / 2$ ; confidence 0.627
@@ Line 538: / Line 538: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080215.png ; $W = p ^ { n + 1 } - q _ { 1 } p ^ { n - 1 } - \ldots - q _ { n }$ ; confidence 0.627
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m1302507.png ; $0 = ( \delta ( x ) x ) \operatorname { vp } \frac { 1 } { x } \neq \delta ( x ) ( x \operatorname{vp} \frac { 1 } { x } ) = \delta ( x )$ ; confidence 0.627
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m1302507.png ; $0 = ( \delta ( x ) x ) \operatorname { vp } \frac { 1 } { x } \neq \delta ( x ) \left( x \operatorname{vp} \frac { 1 } { x } \right) = \delta ( x )$ ; confidence 0.627
 . https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005082.png ; $\sigma _ { \delta }$ ; confidence 0.627
@@ Line 552: / Line 552: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032088.png ; $a _ { n^i }  = ( a _ { n } )^i$ ; confidence 0.627
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120150/s120150127.png ; $G /G_X$ ; confidence 0.627
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120150/s120150127.png ; $G /G_x$ ; confidence 0.627
 . https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i130030161.png ; $l ^ { 2 } ( \Gamma )$ ; confidence 0.627
@@ Line 568: / Line 568: @@
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120190/t12019021.png ; $n/ ( k - 1 )$ ; confidence 0.627
-. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022110/c02211030.png ; $p _ { i } ( \theta ) = \mathbf{P} \{ X _ { i } \in ( x _ { i } - 1 , x _ { i } ] \} > 0,$ ; confidence 0.626
+. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022110/c02211030.png ; $p _ { i } ( \theta ) = \mathsf{P} \{ X _ { i } \in ( x _ { i  - 1} , x _ { i } ] \} > 0,$ ; confidence 0.626
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240206.png ; $\operatorname{rank} ( X ) = r$ ; confidence 0.626
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240206.png ; $\operatorname{rank} ( \mathbf{X} ) = r$ ; confidence 0.626
 . https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e1300303.png ; $\rho : G / \mathbf{Q} \rightarrow \operatorname{GL} (\mathcal{M} )$ ; confidence 0.626
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t120060108.png ; $\rho _ { \text{atom} } ^ { \text{TF} } ( x , N = Z , Z ) \sim \gamma ^ { 3 } ( \frac { 3 } { \pi } ) ^ { 3 } | x | ^ { - 6 },$ ; confidence 0.626
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t120060108.png ; $\rho _ { \text{atom} } ^ { \text{TF} } ( x , N = Z , Z ) \sim \gamma ^ { 3 } \left( \frac { 3 } { \pi } \right) ^ { 3 } | x | ^ { - 6 },$ ; confidence 0.626
 . https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z13010037.png ; $\forall x \forall y \exists z \forall v ( v \in z \leftrightarrow ( v = x \vee v = y ) ).$ ; confidence 0.626
@@ Line 588: / Line 588: @@
 . https://www.encyclopediaofmath.org/legacyimages/c/c023/c023130/c02313056.png ; $B / A$ ; confidence 0.626
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240433.png ; $A \Theta B$ ; confidence 0.626
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240433.png ; $\mathbf{A} \Theta \mathbf{B}$ ; confidence 0.626
 . https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i12004044.png ; $s = ( s _ { 1 } , \dots , s _ { n } ) : \partial D \times D \rightarrow \mathbf{C} ^ { n }$ ; confidence 0.626