Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/32"

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List

1. ; $n > 2$ ; confidence 0.915

2. ; $F ( {\cal C} )$ ; confidence 1.000

3. ; $r = r ( x )$ ; confidence 0.915

4. ; $\hat { f } ( x _ { i } ) \neq c ( x _ { i } )$ ; confidence 0.915

5. ; $x _ { + } = x _ { c } - \lambda \nabla f ( x _ { c } ).$ ; confidence 0.915

6. ; $g \geq 1$ ; confidence 0.914

7. ; $f ( t ) = \sum _ { n = - \infty } ^ { \infty } a _ { n } e ^ { i n t } , a _ { 0 } = 0,$ ; confidence 0.914

8. ; $x x ^ { \prime } \in L _ { 1 } ( \mu )$ ; confidence 0.914

9. ; $( k \in {\bf N} , N \leq x \leq N + M )$ ; confidence 1.000

10. ; $Q ( t ) = \prod _ { i } \frac { 1 + x _ { i } t } { 1 - x _ { i } t } = \sum _ { r \geq 0 } q _ { r } t ^ { r }.$ ; confidence 1.000

11. ; $( x , - \xi ) \notin \operatorname{WF} ( u )$ ; confidence 1.000

12. ; $L = ( \Delta / 2 ) - x \nabla$ ; confidence 1.000

13. ; $f_j$ ; confidence 1.000

14. ; $\frac { q ( z ) t ( w ) - q ( w ) t ( z ) } { z - w } = \sum _ { i , j = 1 } ^ { n } b _ { i , j } z ^ { i - 1 } w ^ { j - 1 }.$ ; confidence 0.914

15. ; $h$ ; confidence 0.914

16. ; $\{ {\cal L} _ { n } ^ { \prime } \}$ ; confidence 1.000

17. ; $\operatorname {spec} T ( a )$ ; confidence 1.000

18. ; $m ^ { c }$ ; confidence 0.914

19. ; $p ^ { \prime }$ ; confidence 0.914

20. ; $\{ \gamma _ { j } \} _ { j \in \mathbf Z }$ ; confidence 1.000

21. ; $Z _ { G } ( y ) = \sum _ { n = 0 } ^ { \infty } G ^ { \# } ( n ) y ^ { n }$ ; confidence 0.914

22. ; $( {\bf Z} / l ^ { n } {\bf Z} ) _ { X }$ ; confidence 1.000

23. ; $t ( M ) = t ( M / e ) + t ( M - e )$ ; confidence 0.914

24. ; $d = q ^ { - 1 } b$ ; confidence 0.914

25. ; $X = 1 ^ { p }$ ; confidence 0.914

26. ; $\mathcal {H} : {\bf X} _ { 3 } {\bf B X} _ { 4 } = 0$ ; confidence 1.000

27. ; $h \in \Omega$ ; confidence 0.914

28. ; ${\cal T} *$ ; confidence 1.000

29. ; ${\cal P} _ { 1 } ^ { 1 } = \frac { 1 } { 4 } p ^ { 2 } + \frac { 1 } { 2 } \dot { p } - q = I.$ ; confidence 1.000

30. ; $x _ { 1 } , x _ { 2 } , x , y \in \cal K$ ; confidence 1.000

31. ; $\operatorname { lim } _ { N \rightarrow \infty } \operatorname { sup } _ { \varepsilon } \| \frac { 1 } { N } \sum _ { n = 1 } ^ { N } f ( T ^ { n } x ) g ( S ^ { n } y ) e ^ { 2 \pi i n \varepsilon } \| = 0.$ ; confidence 0.914

32. ; $j a_j + a_{j - 1} = 0$ ; confidence 1.000

33. ; $a ( x , \alpha , p )$ ; confidence 0.914

34. ; $\hat {\hat {G} }$ ; confidence 1.000

35. ; $\omega e _ { i } = f _ { i }$ ; confidence 0.914

36. ; $x \neq p$ ; confidence 0.914

37. ; $L _ { 0 , n } ^ { 1 } = ( S _ { n } ) ^ { - n }$ ; confidence 0.914

38. ; $G = \operatorname{Cl} _ { 2 } ( \frac { 1 } { 2 } \pi ) = - \operatorname{Cl} _ { 2 } ( \frac { 3 } { 2 } \pi ) =$ ; confidence 1.000

39. ; $K _ { \nu } ( x )$ ; confidence 0.914

40. ; $\kappa = - 2 J$ ; confidence 0.914

41. ; $^* \tau = \xi \bigwedge d \xi$ ; confidence 1.000

42. ; $\pi _ { n } ( X , A , ^* )$ ; confidence 1.000

43. ; $\alpha ^ { \prime } . \alpha$ ; confidence 1.000

44. ; $\chi ( D ) = \sum ( - 1 ) ^ { i } \operatorname { dim } H _ { S } ^ { i } ( D )$ ; confidence 0.914

45. ; $W _ { \Theta } ( z ) = I - 2 i K ^ { * } ( {\cal A} - z I ) ^ { - 1 } K J$ ; confidence 1.000

46. ; $\leq K _ { 2 } \sum _ { i = 1 } ^ { k } | \lambda | ^ { \alpha _ { i } } | t - s | ^ { \beta _ { i } },$ ; confidence 0.914

47. ; $g : V \rightarrow W$ ; confidence 0.914

48. ; $\| S _ { N B } \|$ ; confidence 0.914

49. ; $X \subset G$ ; confidence 0.914

50. ; $f _ { \theta } ( x ) > 0$ ; confidence 0.913

51. ; $g E _ { m } = \pi ^ { - 1 } ( g m )$ ; confidence 0.913

52. ; $( W _ { k } f ) ( t ) = \int _ { 0 } ^ { \infty } k ( t - s ) f ( s ) d s , t \in {\bf R} _ { + }.$ ; confidence 1.000

53. ; $\operatorname{JC} ^ { * }$ ; confidence 1.000

54. ; $n ^ { 1 / 2 } \epsilon _ { n } \rightarrow \infty$ ; confidence 0.913

55. ; $\sum _ { \alpha } | c _ { \alpha } z ^ { \alpha } | < 1$ ; confidence 0.913

56. ; $b _ { \gamma } ( x ) = \operatorname { lim } _ { t \rightarrow \infty } ( t - d ( x , \gamma ( t ) ) ) , \quad x \in M.$ ; confidence 0.913

57. ; $d r \neq 0$ ; confidence 0.913

58. ; $\| U ( t , s ) \| _ { Y } \leq \overline { M } e ^ { \overline { \beta } ( t - s ) } , \quad ( t , s ) \in \Delta,$ ; confidence 0.913

59. ; $b _ { j }$ ; confidence 0.913

60. ; $\operatorname {Fm}$ ; confidence 1.000

61. ; $\ddot { x } - \mu ( 1 - x ^ { 2 } ) \dot { x } + x = E _ { 0 } + E \operatorname { sin } \omega t$ ; confidence 0.913

62. ; $\Omega = \sum _ { r = 1 } ^ { R } ( \alpha _ { r } ^ { 2 } - \beta _ { r } ^ { 2 } )$ ; confidence 0.913

63. ; ${\cal M} _ { i } ( {\bf R} ^ { n } ) \subset {\cal M} _ { i + 1 } ( {\bf R} ^ { n } )$ ; confidence 1.000

64. ; $\tau _ { j } ^ { n + 1 } = \frac { u _ { j } ^ { n + 1 } - u _ { j } ^ { n } } { k } - \delta ^ { 2 } ( \frac { u _ { j } ^ { n + 1 } + u _ { j } ^ { n } } { 2 } )$ ; confidence 0.913

65. ; $\operatorname { deg } K _ { X } = 2 g - 2$ ; confidence 0.913

66. ; $t \in J$ ; confidence 0.913

67. ; $t _ { - } ( k ) = t _ { + } ( k ) : = t ( k )$ ; confidence 0.913

68. ; ${\cal E} ( \rho )$ ; confidence 1.000

69. ; $\{ z ^ { n } ( \frac { d } { d z } ) ^ { m } : n \in {\bf Z} , m \in {\bf N} _ { 0 } \}$ ; confidence 1.000

70. ; $e ^ { i \vartheta } \mapsto k _ { \vartheta } ( z ) = \frac { 1 - | z | ^ { 2 } } { | z - e ^ { i \vartheta } | ^ { 2 } }$ ; confidence 0.913

71. ; $\gamma ( F ( u ) ) = \{ \gamma ( v ) < \infty : v \in F ( u ) \};$ ; confidence 0.913

72. ; $u _ { j } ^ { n } = u ( x _ { j } , t _ { n } )$ ; confidence 0.913

73. ; $| A |$ ; confidence 0.913

74. ; $| {\phi} \rangle$ ; confidence 1.000

75. ; $A \mapsto \bar{A}$ ; confidence 1.000

76. ; $X \mapsto G _ { X }$ ; confidence 0.913

77. ; $( N , g | _ { N } )$ ; confidence 0.913

78. ; $\operatorname { im } ( \pi ^ { \prime } )$ ; confidence 0.913

79. ; $x \prec y$ ; confidence 1.000

80. ; $q = p ^ { t }$ ; confidence 0.913

81. ; $\frac { 1 } { ( 2 \pi ) ^ { n p / 2 } | \Sigma | ^ { n / 2 } | \Psi | ^ { p / 2 } } \times$ ; confidence 0.913 NOTE: it looks like something is missing at the end

82. ; ${\bf E} = - \nabla \phi - \frac { 1 } { c } \frac { \partial \bf A } { \partial t } , {\bf B} = \nabla \times {\bf A}.$ ; confidence 1.000

83. ; $H \in H ^ { 2 } ( \mu , {\bf D} )$ ; confidence 0.913

84. ; $\lambda _ { m } = \operatorname { log } m$ ; confidence 1.000

85. ; $N > 1$ ; confidence 0.912

86. ; $\varepsilon ^ { * } ( T ) = 0$ ; confidence 0.912

87. ; $\square ^ { t } M _ { \varphi }$ ; confidence 0.912

88. ; $R = 1$ ; confidence 0.912

89. ; $K \subset V$ ; confidence 0.912

90. ; $x ^ { T } A x$ ; confidence 0.912

91. ; $\angle \operatorname { lim } _ { z \rightarrow \omega } ( F ( z ) - \eta ) / ( z - \omega ) = \angle F ^ { \prime } ( \omega )$ ; confidence 0.912

92. ; $S = \{ \infty \}$ ; confidence 0.912

93. ; $X _ { t } ^ { + } = | X _ { t } | , t \geq 0,$ ; confidence 0.912

94. ; $\operatorname{Col} M$ ; confidence 1.000

95. ; $X f ( 1 ) = X f ( \theta , p ) = \int _ { - \infty } ^ { \infty } f ( x + t \theta ) d t$ ; confidence 0.912

96. ; $K \hookrightarrow \bf C$ ; confidence 1.000

97. ; $\mu ( z ) = f _ { z^- } / f _ { z }$ ; confidence 1.000

98. ; $H ( \theta , \theta _ { 0 } ) \sim c \| \theta - \theta _ { 0 } \| ^ { 2 }$ ; confidence 0.912

99. ; $0 \in D$ ; confidence 0.912

100. ; $\sum _ { \nu = 1 } ^ { n } \alpha _ { \nu } f ( x _ { \nu } ) + \sum _ { \nu = 1 } ^ { n } \beta _ { \nu } f ^ { \prime } ( x _ { \nu } )$ ; confidence 0.912

101. ; $P \times Q$ ; confidence 0.912

102. ; $n - p$ ; confidence 0.912

103. ; $f : \Omega \rightarrow T$ ; confidence 0.912

104. ; $S = \frac { 1 } { n } \sum _ { i = 1 } ^ { n } Z _ { i } ^ { \prime } Z _ { i },$ ; confidence 0.912

105. ; $L _ { p } [ 0,1 ]$ ; confidence 0.912

106. ; $d [ f , S ^ { n } , S ^ { n } ]$ ; confidence 0.912

107. ; $M _ { k } = \partial / \partial x + i x ^ { k } \partial / \partial y$ ; confidence 0.911

108. ; $J \in M _ { n \times n } ( K )$ ; confidence 0.911

109. ; $\sum _ { j = 1 } ^ { n } \Bigl( \frac { \partial X _ { j } } { \partial z } \Bigr) ^ { 2 } = 0.$ ; confidence 0.911

110. ; ${\cal T} ({\bf T} ) : = C ^ { * } ( T _ { f } : f \in {\cal C} ({\bf T} ) )$ ; confidence 1.000

111. ; $\gamma = | \partial z / \partial \Gamma | ^ { - 1 }$ ; confidence 0.911

112. ; $g_2 ( k )$ ; confidence 1.000

113. ; $+ \Delta t \partial _ { t } ^ { ( 1 ) } u ( x _ { i } , t ^ { n } ) + \frac { \Delta t ^ { 2 } } { 2 } \partial _ { t } ^ { ( 2 ) } u ( x _ { i } , t ^ { n } ) + O ( \Delta t ^ { 2 } ).$ ; confidence 0.911

114. ; $.17.19 .23 .29 .31 .41 .47 .59 .71.$ ; confidence 1.000

115. ; $v = v ( t _ { 1 } , t _ { 2 } )$ ; confidence 0.911

116. ; $1000$ ; confidence 1.000

117. ; $\tilde{\eta} ( x ) = \eta ( x ^ { - 1 } )$ ; confidence 1.000

118. ; $P > 0$ ; confidence 0.911

119. ; $- t / 2 < t _ { 1 } \leq \ldots \leq t _ { n } < t / 2$ ; confidence 0.911

120. ; $\phi * {\cal O} _ { X } = {\cal O} _ { Y }$ ; confidence 1.000

121. ; $\eta_n ^ { 2 }$ ; confidence 1.000

122. ; $A _ { \alpha } ( x ) = o ( \frac { x } { \operatorname { log } x } )$ ; confidence 0.911

123. ; $\lambda = \lambda _ { j }$ ; confidence 0.911

124. ; $\beta_l$ ; confidence 1.000

125. ; $\varphi_+ = W _ { \Theta } ( z ) \varphi _ { - }$ ; confidence 1.000

126. ; $| ( A ( t ) - A ( s ) ) A ( 0 ) ^ { - 1 } \| \leq C _ { 2 } | t - s | ^ { \alpha } , \quad t , s \in [ 0 , T ].$ ; confidence 1.000

127. ; $X = \{ x : A _ { 2 } x \leq b _ { 2 } , x \geq 0 \}$ ; confidence 0.911

128. ; $\| f ( x + y ) - f ( x ) - f ( y ) \| \leq \theta ( \| x \| ^ { p } + \| y \| ^ { p } )$ ; confidence 0.911

129. ; $p \in P _ { k - 1 }$ ; confidence 0.911

130. ; $q ^ { \prime } = q$ ; confidence 0.911

131. ; $( A - \mu I ) ^ { - 1 }$ ; confidence 0.911

132. ; $\| . \| _ { 1 }$ ; confidence 0.911

133. ; ${\cal S} : = \{ S ( k ) , i k _ { j } , s _ { j } : 1 \leq j \leq J \}$ ; confidence 1,000

134. ; $p \geq n$ ; confidence 0.911

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

136. ; $R \subset \operatorname {DB} _ { 1 }$ ; confidence 0.911

137. ; $T = \operatorname { Sym } ^ { 2 } T _ { p } ( E )$ ; confidence 0.911

138. ; $\operatorname{limsup} n ^ { \prime 0 } / n ^ { 0 } \geq 2 ^ { 1 / 4 } \sim 1,19$ ; confidence 1.000

139. ; $\operatorname { rist } _ { G } ( n )$ ; confidence 0.911

140. ; $\operatorname { var } ( X ) \sim \overline { \Delta }$ ; confidence 0.910

141. ; $E \subset {\bf C} ^ { n } \subset {\bf P} ^ { n }$ ; confidence 1.000

142. ; $L ( E / {\bf Q }; s )$ ; confidence 1.000

143. ; $= \sum _ { j = 1 } ^ { J } K ( y , y _ { j } ) c _ { j } = f ( y ) , \forall y \in E.$ ; confidence 0.910

144. ; $\forall \alpha ^ { \prime } \in S ^ { 2 }$ ; confidence 0.910

145. ; $\sigma_y$ ; confidence 1.000

146. ; $u ( z , \lambda _ { i } ) = z ^ { \lambda _ { i } } + \ldots$ ; confidence 0.910

147. ; $\lambda _ { 2 }$ ; confidence 0.910

148. ; $\dot { x } = v , \quad \dot { v } = - x + \mu ( 1 - x ^ { 2 } ) v$ ; confidence 0.910

149. ; $( \nabla _ { X } J ) Y = g ( X , Y ) Z - \alpha ( Y ) X$ ; confidence 0.910

150. ; $x _ { 1 } ^ { \prime } = x _ { 1 } ( s + v ),$ ; confidence 0.910

151. ; $d M _ { 1 } = \rho \frac { \Gamma { b } } { l } ( - U )$ ; confidence 1.000

152. ; $\operatorname{SL} _ { 2 } ( {\bf C })$ ; confidence 1.000

153. ; $X \leftarrow ( U - 1 / 2 ) / ( \sqrt { ( U - U ^ { 2 } ) } / 2 )$ ; confidence 0.910

154. ; $e ^ { i t {\cal A}}$ ; confidence 1.000

155. ; $6_\beta$ ; confidence 1.000

156. ; $a ^ { - 1 } b ^ { m } a b ^ { - n }$ ; confidence 0.910

157. ; $\dot { x } _ { i } = x _ { i } y _ { i },$ ; confidence 0.910

158. ; ${\bf R} _ { + } ^ { N }$ ; confidence 1.000

159. ; $\rho ( x , \theta ) = - \operatorname { ln } f _ { \theta } ( x )$ ; confidence 0.910

160. ; $( f _ { \alpha } , f _ { \beta } ) \mapsto ( \beta - \alpha + h ( \alpha ) \beta - h ( \beta ) \alpha ) f _ { \alpha + \beta }$ ; confidence 0.910

161. ; $| u - u _ { N } | = O ( h ^ { \alpha } )$ ; confidence 0.910

162. ; $\mu ( \alpha , x ) = \mu _ { 0 } ( \alpha ) + \mu _ { 1 } ( \alpha ) K \Psi ( x ),$ ; confidence 0.910

163. ; $p _ { i } = 1 - p _ { j }$ ; confidence 0.910

164. ; $L ( x , y ) , D , E \in \operatorname { Inn } \operatorname { Der } A$ ; confidence 0.910

165. ; $j \neq l$ ; confidence 0.910

166. ; $g : h \mapsto h g ^ { - 1 }$ ; confidence 0.910

167. ; $A _ { 2 l } ^ { ( * ) }$ ; confidence 0.910

168. ; $n = \operatorname { max } ( \operatorname { dim } ( K _ { 0 } - L ) , \operatorname { dim } ( K _ { 1 } - L ) )$ ; confidence 0.910

169. ; $F ^ { * }$ ; confidence 0.910

170. ; $\| \mu \|$ ; confidence 0.910

171. ; $D _ { f , i }$ ; confidence 0.910

172. ; $S ( m , G )$ ; confidence 0.909

173. ; $W ( \Pi ^ { re } )$ ; confidence 0.909

174. ; $G _ { \cal C } ^ { \# } ( n )$ ; confidence 1.000

175. ; $V _ { Z }$ ; confidence 0.909

176. ; ${\bf K} _ { 0 } \subseteq {\bf K} $ ; confidence 1.000

177. ; $< 1 / 3$ ; confidence 0.909

178. ; $\sigma _ { 1 } = \sum _ { i = 0 } ^ { 2 g } \lambda _ { i }$ ; confidence 0.909

179. ; $0 , - b _ { 1 } , - b _ { 2 } , \dots$ ; confidence 0.909

180. ; $\| T _ { i t } \|$ ; confidence 0.909

181. ; $\operatorname{Hom}_{\cal U_*}( G ( n ) , M ) \cong M _ { x }$ ; confidence 1.000

182. ; $\frac { 1 } { \lambda } \leq \operatorname { max } _ { \varphi } | \operatorname { cos } \alpha ( \varphi ) |$ ; confidence 0.909

183. ; $R _ { 11 } = - T$ ; confidence 0.909

184. ; $\| \varphi \| _ { L ^ { 2 } ( \mu ) } = \sqrt { n ! } | f | _ { H ^ { \otimes n } }$ ; confidence 0.909

185. ; $x _ { n + 1 } = u _ { 0 } - \frac { \Delta u _ { 0 } } { \Delta ^ { 2 } u _ { 0 } }.$ ; confidence 0.909

186. ; $\{ u x \{ v y w \} \} - \{ v y \{ u x w \} \} = \{ \{ u x v \} y w \} - \{ v \{ x u y \} w \}$ ; confidence 0.909

187. ; $f : \Delta \rightarrow {\bf C} ^ { n }$ ; confidence 1.000

188. ; $T _ { i } = - \frac { n + 1 } { n + 1 - i } \operatorname { Res } _ { \infty } W ^ { 1 - [ i / ( n + 1 ) ] } d p$ ; confidence 0.909

189. ; $\varphi \in H ^ { 2 m } ( \Gamma , {\bf C} )$ ; confidence 1.000

190. ; $( p : A \rightarrow D , q : B \rightarrow D )$ ; confidence 0.909

191. ; $y _ { n } ^ { * } ( x ) = \tau \sum _ { k = 0 } ^ { n } c _ { k } ^ { n } Q _ { k } ( x )$ ; confidence 0.909

192. ; $z \in \overline { B } _ { E ^{* *}}$ ; confidence 1.000

193. ; $GF ( 2 ^ { 155 } )$ ; confidence 0.909

194. ; $C _ { F }$ ; confidence 0.909

195. ; ${\cal L} : \Omega ( M , T M ) \rightarrow \operatorname { Der } \Omega ( M )$ ; confidence 1.000

196. ; $\operatorname { inf } ( x , y ) = 0 \Rightarrow \operatorname { inf } ( z x , y ) = \operatorname { inf } ( x z , y ) = 0 , \forall z \in A ^ { + }.$ ; confidence 0.909

197. ; $\lambda _ { 1 } \geq \ldots \geq \lambda _ { k } > 0 > \lambda _ { k + 1 } \geq \ldots \geq \lambda _ { n }$ ; confidence 0.909

198. ; $\top$ ; confidence 1.000

199. ; $V ( O _ { K , p } ) \neq \emptyset$ ; confidence 0.909

200. ; $C ( g ) + \tau _ { 3 } C ( g ) + \tau ^ { 2 } 3 C ( g ) = 0$ ; confidence 0.908

201. ; $k \geq n + 1$ ; confidence 0.908

202. ; $e \wedge | x | = 0$ ; confidence 0.908

203. ; $w \in H _ { 0 }$ ; confidence 0.908

204. ; $h \mapsto [ h \circ f ] \in C ^ { \infty } ( {\bf R }^ { n } , {\bf R} ) /{\cal A}$ ; confidence 1.000

205. ; $q = \nu + 1$ ; confidence 0.908

206. ; $\tilde{g} _ { i j } ( x , 0 ) = g _ { j } ( x )$ ; confidence 1.000

207. ; $\frac { D \phi } { D t } = \frac { \partial \phi } { \partial t } + v _ { i } \phi _ { , i } = \frac { \partial \phi } { \partial t } + ( {\bf v} . \nabla ) \phi$ ; confidence 1.000

208. ; $K _ { 0 } > 0$ ; confidence 0.908

209. ; $C ^ { 1 + \delta } ( [ 0 , T ] ; X )$ ; confidence 0.908

210. ; $G _ { 2 } ( r ) = \sum _ { j = 1 } ^ { n } b _ { j } \phi ( z _ { j } ) z _ { j } ^ { k }$ ; confidence 0.908

211. ; $C ( T )$ ; confidence 0.908

212. ; $x \in J$ ; confidence 0.908

213. ; $S = o ( \# A )$ ; confidence 0.908

214. ; $T \beta$ ; confidence 0.908

215. ; $X = G ( {\bf R} ) / K _ { \infty }$ ; confidence 1.000

216. ; $f = \sum _ { j = 1 } ^ { n } f _ { j } d \overline { z _ { j } }$ ; confidence 0.908

217. ; $\mu ( d x ) = \sum _ { k = 0 } ^ { n } \left( \begin{array} { l } { n } \\ { k } \end{array} \right) \delta _ { k } ( d x )$ ; confidence 0.908

218. ; $\langle w , f \rangle = w _ { 1 } f _ { 1 } + \ldots + w _ { n } f _ { n }$ ; confidence 0.908

219. ; $\left( \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right)$ ; confidence 0.908

220. ; $\Omega ^ { i _X}$ ; confidence 1.000

221. ; $k = m$ ; confidence 0.908

222. ; $R _ { j } = \{ k : X _ { k } \geq T _ { j } \}$ ; confidence 0.908

223. ; $\operatorname { im } ( \pi )$ ; confidence 0.908

224. ; $Q C$ ; confidence 0.908

225. ; $\operatorname { lim } _ { s \rightarrow \pm \infty } w ( s , t ) = x _ { \pm } ( t )$ ; confidence 0.908

226. ; $m = \frac { \operatorname { exp } \Bigl( \frac { H _ { \text{eff} } } { k _ { B } T }\Bigr ) - \operatorname { exp } \Bigl( - \frac { H _ {\text{eff} } } { k _ { B } T }\Bigr ) } { \operatorname { exp }\Bigl ( \frac { H _ { \text{eff} } } { k _ { B } T }\Bigr ) + \operatorname { exp } \Bigl( - \frac { H _ { \text{eff} } } { k _ { B } T } \Bigr) } =$ ; confidence 1.000

227. ; $A A ^ { T } = A ^ { T } A = ( \sum _ { i = 1 } ^ { k } s _ { i } x _ { i } ^ { 2 } ) I _ { n }$ ; confidence 0.907

228. ; $\pi ( \alpha _ { t } ( \alpha ) ) = U _ { t } \pi ( \alpha ) U _ { t } ^ { * }$ ; confidence 0.907

229. ; $G \rightarrow G / A$ ; confidence 0.907

230. ; $X = - \int _ { - \infty } ^ { t } X _ { A } ( t , z ) C ( z ) X _ { A } ( t , z ) \,d z$ ; confidence 1.000

231. ; $L _ { 2 } ( {\bf R} _ { + } ; x ^ { - 1 } )$ ; confidence 1.000

232. ; $\varepsilon : B \rightarrow \underline{1}$ ; confidence 1.000

233. ; $u , v , w \in V ^ { \pm }$ ; confidence 0.907

234. ; $\sum _ { k = 0 } ^ { n } \frac { f _ { k } } { \left( \begin{array} { l } { n } \\ { k } \end{array} \right) } \leq 1$ ; confidence 0.907

235. ; $m _ { - k } = L ( z ^ { - k } ) = \overline { L ( z ^ { k } ) } = \overline { m } _ { k }$ ; confidence 0.907

236. ; $y \in A ^ { S }$ ; confidence 0.907

237. ; $F \mapsto h ^ { - 1 } ( F )$ ; confidence 0.907

238. ; $S ( t )$ ; confidence 0.907

239. ; $f _ { 2 }$ ; confidence 0.907

240. ; $r s = \frac { n ( n ^ { 2 } - 1 ) - 6 \sum _ { i = 1 } ^ { n } ( R _ { i } - S _ { i } ) ^ { 2 } - 6 ( T + U ) } { \sqrt { n ( n ^ { 2 } - 1 ) - 12 T } \sqrt { n ( n ^ { 2 } - 1 ) - 12 U } }$ ; confidence 0.907

241. ; $\operatorname{ad}({\frak g} )$ ; confidence 1.000

242. ; ${\cal X} = \{ C : \operatorname { Hom } _ { \Lambda } ( C , {\cal Y} ) = 0 \}$ ; confidence 1.000

243. ; $B _ { R } [ H \times H ]$ ; confidence 0.907

244. ; $C \in M _ { n \times n } ( K )$ ; confidence 0.907

245. ; $\bf C \subseteq D$ ; confidence 1.000

246. ; $\theta$ ; confidence 1.000

247. ; $K ( {\cal U} )$ ; confidence 1.000

248. ; $E = E_r$ ; confidence 1.000

249. ; $s = s ( ( A ^ { * } ) ^ { ( B ^ { * } ) } , ( B ^ { * } ) ^ { ( C ^ { * } ) } )$ ; confidence 0.907

250. ; $h , g , f \in H$ ; confidence 0.907

251. ; $G : S N \times R \rightarrow U M$ ; confidence 0.907

252. ; $c = 5$ ; confidence 0.907

253. ; $K _ { 2 } {\bf Q} = \coprod _ { p } \mu _ { p }$ ; confidence 1.000

254. ; $( a - \delta , a )$ ; confidence 0.907

255. ; $| \mu | = \operatorname { sup } ( \mu , - \mu ) \in \operatorname {ca} ( \Omega , {\cal F} )$ ; confidence 1.000

256. ; $\kappa > 0$ ; confidence 1.000

257. ; $\pi _ { 2 } ( X , A , x ) \rightarrow \pi _ { 1 } ( A , x )$ ; confidence 0.907

258. ; $+ \int _ { C _ { N } } \phi _ { ; m } \rho \,d y$ ; confidence 1.000

259. ; $u \in D ( \Delta )$ ; confidence 0.907

260. ; $f _ { n }$ ; confidence 0.907

261. ; ${\cal D} _ { j , k } ^ { p } ( a ) =$ ; confidence 1.000

262. ; $\mu ^ { * } : {\cal H} ( \Omega + K ) \rightarrow {\cal H} ( \Omega )$ ; confidence 1.000

263. ; ${\bf E} [ W _ { p } ]$ ; confidence 1.000

264. ; $z ( \zeta ) = \zeta + \frac { a _ { 1 } } { \zeta } + \frac { a _ { 2 } } { \zeta ^ { 2 } } + \ldots$ ; confidence 0.907

265. ; $k \langle E _ { 1 } , E _ { 2 } \rangle$ ; confidence 0.907

266. ; $X B X + X A + A ^ { * } X - C = 0$ ; confidence 0.907

267. ; $q ^ { ( l + 1 ) } = - ( q ^ { ( l ) } ) ^ { 2 } r ^ { ( l ) } + q ^ { ( l ) } \operatorname { log } ( q ^ { ( l ) } ) , r ^ { ( l + 1 ) } = \frac { 1 } { q ^ { ( l ) } }$ ; confidence 0.906

268. ; $\cal K = K _ { + } + K _ { - },$ ; confidence 1.000

269. ; $p - n$ ; confidence 0.906

270. ; $u \in X$ ; confidence 0.906

271. ; $D = \sum _ { k = 1 } ^ { s } D _ { k }$ ; confidence 0.906

272. ; $\{ x : \sigma \} \vdash x : \sigma$ ; confidence 0.906

273. ; $\{ D _ { m } \}$ ; confidence 0.906

274. ; $[ x , y ] = ( G x , y ) , \quad x , y \in \cal K )$ ; confidence 0.906 NOTE: why is there a parentesis closed that was never opened?

275. ; $\operatorname { dim } D _ { s } = n + 1$ ; confidence 0.906

276. ; $x , y \in A$ ; confidence 0.906

277. ; $\operatorname { adj } ( L ) = \tau ( G ) J$ ; confidence 0.906

278. ; $\operatorname { lim } _ { n \rightarrow \infty } t ( n ) ( \operatorname { log } t ( n ) ) / s ( n ) = 0$ ; confidence 0.906

279. ; $\phi _ { i j } : \phi _ { j } ( U _ { i } \cap U _ { j } ) \rightarrow \phi _ { i } ( U _ { i } \cap U _ { j } )$ ; confidence 0.906

280. ; $L \subseteq \operatorname{NL} \subseteq \operatorname{NC} \subseteq P \subseteq \operatorname{NP} \subseteq \operatorname{PH} \subseteq \operatorname{PSPACE}$ ; confidence 1.000

281. ; $C ^ { 1 }$ ; confidence 0.906

282. ; $SO ( 4 n + 3 )$ ; confidence 0.906

283. ; $R = \sum _ { i = 0 } ^ { n - 1 } Z ^ { i } G J G ^ { * } Z ^ { * i } =$ ; confidence 0.906

284. ; $\psi_0$ ; confidence 1.000

285. ; $W ( f \times g ) = W ( f ) . W ( g )$ ; confidence 0.906

286. ; $| x - \frac { p } { q } | < f ( q ) , \quad \operatorname { gcd } ( p , q ) = 1 , q > 0$ ; confidence 0.906

287. ; $\| x + y \| = \| u + v \|$ ; confidence 0.906

288. ; $R _ { 1212 } = \alpha _ { 2 } , R _ { 1313 } = \alpha _ { 2 } , R _ { 2424 } = \alpha _ { 2 }$ ; confidence 0.906

289. ; $\partial _ { q , x } ( x ^ { n } y ^ { m } ) = [ n ] _ { q ^ { 2 } } x ^ { n - 1 } y ^ { m },$ ; confidence 0.906

290. ; $H _ { S } = 0$ ; confidence 0.906

291. ; $\operatorname{SO} ( n )$ ; confidence 1.000

292. ; $H ^ { 1 }$ ; confidence 0.906

293. ; $i - 1$ ; confidence 0.906

294. ; $\square ^ { \color{blue} * }$ ; confidence 1.000

295. ; $\sum _ { i = 1 } ^ { n } \psi \Bigl( \frac { x _ { i } - T _ { n } } { S _ { n } }\Bigr ) = 0,$ ; confidence 1.000

296. ; $\Lambda _ { n } = \operatorname { log } ( d P _ { n } ^ { \prime } / d P _ { n } )$ ; confidence 0.906

297. ; $B ( \zeta , \alpha ) = \{ x \in X : \rho ( x , \zeta ) \leq \alpha \}$ ; confidence 0.906

298. ; $\sum _ { i = 1 } ^ { r } n _ { i } = n$ ; confidence 0.906

299. ; $\Theta_i$ ; confidence 1.000

300. ; $\lambda ^ { k } T ( \lambda g ) = T ( g )$ ; confidence 0.905

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/32. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/32&oldid=45563

@@ Line 20: / Line 20: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130140/s1301406.png ; $Q ( t ) = \prod _ { i } \frac { 1 + x _ { i } t } { 1 - x _ { i } t } = \sum _ { r \geq 0 } q _ { r } t ^ { r }.$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m13025053.png ; $( x , - \xi ) \notin \operatorname{W F} ( u )$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m13025053.png ; $( x , - \xi ) \notin \operatorname{WF} ( u )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031095.png ; $L = ( \Delta / 2 ) - x  \nabla$ ; confidence 1.000
@@ Line 82: / Line 82: @@
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120160/e1201605.png ; $^* \tau = \xi \bigwedge d \xi$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t09408027.png ; $\pi _ { N } ( X , A , ^* )$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t09408027.png ; $\pi _ { n } ( X , A , ^* )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001039.png ; $\alpha ^ { \prime } . \alpha$ ; confidence 1.000
@@ Line 102: / Line 102: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b1204007.png ; $g E _ { m } = \pi ^ { - 1 } ( g m )$ ; confidence 0.913
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t12014025.png ; $( W _ { k } f ) ( t ) = \int _ { 0 } ^ { \infty } k ( t - s ) f ( s ) d s , t \in R _ { + }.$ ; confidence 0.913
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t12014025.png ; $( W _ { k } f ) ( t ) = \int _ { 0 } ^ { \infty } k ( t - s ) f ( s ) d s , t \in {\bf R} _ { + }.$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130030/j13003059.png ; $JC ^ { * }$ ; confidence 0.913
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130030/j13003059.png ; $\operatorname{JC} ^ { * }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/i/i120/i120050/i120050111.png ; $n ^ { 1 / 2 } \epsilon _ { n } \rightarrow \infty$ ; confidence 0.913
@@ Line 162: / Line 162: @@
 . https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015057.png ; $\frac { 1 } { ( 2 \pi ) ^ { n p / 2 } | \Sigma | ^ { n / 2 } | \Psi | ^ { p / 2 } } \times$ ; confidence 0.913  NOTE: it looks like something is missing at the end
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120110/e12011060.png ; ${\bf E} = - \nabla \phi - \frac { 1 } { c } \frac { \partial \bf A } { \partial t } , {\bf B} = \nabla \times {\bf A}$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120110/e12011060.png ; ${\bf E} = - \nabla \phi - \frac { 1 } { c } \frac { \partial \bf A } { \partial t } , {\bf B} = \nabla \times {\bf A}.$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065014.png ; $H \in H ^ { 2 } ( \mu , {\bf D} )$ ; confidence 0.913
@@ Line 238: / Line 238: @@
 . https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001030.png ; $- t / 2 < t _ { 1 } \leq \ldots \leq t _ { n } < t / 2$ ; confidence 0.911
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130230/m13023062.png ; $\phi * {\cal O} _ { X } = {\cal O} _ { Y }$ ; confidence 1,000
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130230/m13023062.png ; $\phi * {\cal O} _ { X } = {\cal O} _ { Y }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040490/f04049032.png ; $\eta_n ^ { 2 }$ ; confidence 1,000
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040490/f04049032.png ; $\eta_n ^ { 2 }$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007057.png ; $A _ { \alpha } ( x ) = o ( \frac { x } { \operatorname { log } x } )$ ; confidence 0.911
@@ Line 246: / Line 246: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021085.png ; $\lambda = \lambda _ { j }$ ; confidence 0.911
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130070/w13007023.png ; $\beta_l$ ; confidence 1,000
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130070/w13007023.png ; $\beta_l$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005028.png ; $\varphi_+ = W _ { \Theta } ( z ) \varphi _ { - }$ ; confidence 1,000
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005028.png ; $\varphi_+ = W _ { \Theta } ( z ) \varphi _ { - }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007068.png ; $| ( A ( t ) - A ( s ) ) A ( 0 ) ^ { - 1 } \| \leq C _ { 2 } | t - s | ^ { \alpha } , \quad t , s \in [ 0 , T ].$ ; confidence 1,000
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007068.png ; $| ( A ( t ) - A ( s ) ) A ( 0 ) ^ { - 1 } \| \leq C _ { 2 } | t - s | ^ { \alpha } , \quad t , s \in [ 0 , T ].$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002025.png ; $X = \{ x : A _ { 2 } x \leq b _ { 2 } , x \geq 0 \}$ ; confidence 0.911
@@ Line 284: / Line 284: @@
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120240/e12024046.png ; $L ( E / {\bf Q }; s )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007074.png ; $= \sum _ { j = 1 } ^ { J } K ( y , y _ { j } ) c _ { j } = f ( y ) , \forall y \in E$ ; confidence 0.910
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007074.png ; $= \sum _ { j = 1 } ^ { J } K ( y , y _ { j } ) c _ { j } = f ( y ) , \forall y \in E.$ ; confidence 0.910
 . https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007046.png ; $\forall \alpha ^ { \prime } \in S ^ { 2 }$ ; confidence 0.910
@@ Line 298: / Line 298: @@
 . https://www.encyclopediaofmath.org/legacyimages/k/k110/k110010/k11001038.png ; $( \nabla _ { X } J ) Y = g ( X , Y ) Z - \alpha ( Y ) X$ ; confidence 0.910
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120160/b12016065.png ; $x _ { 1 } ^ { \prime } = x _ { 1 } ( s + v )$ ; confidence 0.910
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120160/b12016065.png ; $x _ { 1 } ^ { \prime } = x _ { 1 } ( s + v ),$ ; confidence 0.910
 . https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011074.png ; $d M _ { 1 } = \rho \frac { \Gamma  { b } } { l } ( - U )$ ; confidence 1.000
@@ Line 312: / Line 312: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130070/b1300706.png ; $a ^ { - 1 } b ^ { m } a b ^ { - n }$ ; confidence 0.910
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013078.png ; $\dot { x } _ { i } = x _ { i } y _ { i }$ ; confidence 0.910
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013078.png ; $\dot { x } _ { i } = x _ { i } y _ { i },$ ; confidence 0.910
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018015.png ; ${\bf R} _ { + } ^ { N }$ ; confidence 1.000
@@ Line 322: / Line 322: @@
 . https://www.encyclopediaofmath.org/legacyimages/t/t130/t130210/t13021041.png ; $| u - u _ { N } | = O ( h ^ { \alpha } )$ ; confidence 0.910
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a12017048.png ; $\mu ( \alpha , x ) = \mu _ { 0 } ( \alpha ) + \mu _ { 1 } ( \alpha ) K \Psi ( x )$ ; confidence 0.910
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a12017048.png ; $\mu ( \alpha , x ) = \mu _ { 0 } ( \alpha ) + \mu _ { 1 } ( \alpha ) K \Psi ( x ),$ ; confidence 0.910
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150157.png ; $p _ { i } = 1 - p _ { j }$ ; confidence 0.910
@@ Line 350: / Line 350: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120210/s1202107.png ; $V _ { Z }$ ; confidence 0.909
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040791.png ; $K _ { 0 } \subseteq K$ ; confidence 0.909
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040791.png ; ${\bf K} _ { 0 } \subseteq {\bf K} $ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/q/q130/q130020/q13002025.png ; $< 1 / 3$ ; confidence 0.909
@@ Line 368: / Line 368: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009053.png ; $\| \varphi \| _ { L ^ { 2 } ( \mu ) } = \sqrt { n ! } | f | _ { H ^ { \otimes n } }$ ; confidence 0.909
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a120180102.png ; $x _ { n + 1 } = u _ { 0 } - \frac { \Delta u _ { 0 } } { \Delta ^ { 2 } u _ { 0 } }$ ; confidence 0.909
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a120180102.png ; $x _ { n + 1 } = u _ { 0 } - \frac { \Delta u _ { 0 } } { \Delta ^ { 2 } u _ { 0 } }.$ ; confidence 0.909
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b1300305.png ; $\{ u x \{ v y w \} \} - \{ v y \{ u x w \} \} = \{ \{ u x v \} y w \} - \{ v \{ x u y \} w \}$ ; confidence 0.909
@@ Line 390: / Line 390: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f12023082.png ; ${\cal L} : \Omega ( M , T M ) \rightarrow \operatorname { Der } \Omega ( M )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110010/f11001021.png ; $\operatorname { inf } ( x , y ) = 0 \Rightarrow \operatorname { inf } ( z x , y ) = \operatorname { inf } ( x z , y ) = 0 , \forall z \in A ^ { + }$ ; confidence 0.909
+. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110010/f11001021.png ; $\operatorname { inf } ( x , y ) = 0 \Rightarrow \operatorname { inf } ( z x , y ) = \operatorname { inf } ( x z , y ) = 0 , \forall z \in A ^ { + }.$ ; confidence 0.909
 . https://www.encyclopediaofmath.org/legacyimages/c/c130/c130190/c13019049.png ; $\lambda _ { 1 } \geq \ldots \geq \lambda _ { k } > 0 > \lambda _ { k + 1 } \geq \ldots \geq \lambda _ { n }$ ; confidence 0.909
@@ Line 450: / Line 450: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s120340109.png ; $\operatorname { lim } _ { s \rightarrow \pm \infty } w ( s , t ) = x _ { \pm } ( t )$ ; confidence 0.908
-. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i120080104.png ; $m = \frac { \operatorname { exp } \Bigl( \frac { H _ { eff } } { k _ { B } T }\Bigr ) - \operatorname { exp } \Bigl( - \frac { H _ { eff } } { k _ { B } T }\Bigr ) } { \operatorname { exp }\Bigl ( \frac { H _ { eff } } { k _ { B } T }\Bigr ) + \operatorname { exp } \Bigl( - \frac { H _ { eff } } { k _ { B } T } \Bigr) } =$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i120080104.png ; $m = \frac { \operatorname { exp } \Bigl( \frac { H _ { \text{eff} } } { k _ { B } T }\Bigr ) - \operatorname { exp } \Bigl( - \frac { H _ {\text{eff} } } { k _ { B } T }\Bigr ) } { \operatorname { exp }\Bigl ( \frac { H _ { \text{eff} } } { k _ { B } T }\Bigr ) + \operatorname { exp } \Bigl( - \frac { H _ { \text{eff} } } { k _ { B } T } \Bigr) } =$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021071.png ; $A A ^ { T } = A ^ { T } A = ( \sum _ { i = 1 } ^ { k } s _ { i } x _ { i } ^ { 2 } ) I _ { n }$ ; confidence 0.907
@@ Line 480: / Line 480: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130450/s13045011.png ; $r s = \frac { n ( n ^ { 2 } - 1 ) - 6 \sum _ { i = 1 } ^ { n } ( R _ { i } - S _ { i } ) ^ { 2 } - 6 ( T + U ) } { \sqrt { n ( n ^ { 2 } - 1 ) - 12 T } \sqrt { n ( n ^ { 2 } - 1 ) - 12 U } }$ ; confidence 0.907
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120150/a12015028.png ; $\operatorname{ad}({\frack g} )$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120150/a12015028.png ; $\operatorname{ad}({\frak g} )$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013037.png ; ${\cal X} = \{ C : \operatorname { Hom } _ { \Lambda } ( C , {\cal Y} ) = 0 \}$ ; confidence 1.000
@@ Line 508: / Line 508: @@
 . https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i130060156.png ; $( a - \delta , a )$ ; confidence 0.907
-. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110030/l11003018.png ; $| \mu | = \operatorname { sup } ( \mu , - \mu ) \in ca ( \Omega , {\cal F} )$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110030/l11003018.png ; $| \mu | = \operatorname { sup } ( \mu , - \mu ) \in \operatorname {ca} ( \Omega , {\cal F} )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050268.png ; $\ka > 0$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050268.png ; $\kappa > 0$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120290/c12029014.png ; $\pi _ { 2 } ( X , A , x ) \rightarrow \pi _ { 1 } ( A , x )$ ; confidence 0.907
@@ Line 524: / Line 524: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120090/f12009067.png ; $\mu ^ { * } : {\cal H} ( \Omega + K ) \rightarrow {\cal H} ( \Omega )$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008020.png ; $\operatorname{E} [ W _ { p } ]$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008020.png ; ${\bf E} [ W _ { p } ]$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120140/f12014035.png ; $z ( \zeta ) = \zeta + \frac { a _ { 1 } } { \zeta } + \frac { a _ { 2 } } { \zeta ^ { 2 } } + \ldots$ ; confidence 0.907
@@ Line 534: / Line 534: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013052.png ; $q ^ { ( l + 1 ) } = - ( q ^ { ( l ) } ) ^ { 2 } r ^ { ( l ) } + q ^ { ( l ) } \operatorname { log } ( q ^ { ( l ) } ) , r ^ { ( l + 1 ) } = \frac { 1 } { q ^ { ( l ) } }$ ; confidence 0.906
-. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k05584012.png ; $\cal K = K _ { + } + K _ { - }$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k05584012.png ; $\cal K = K _ { + } + K _ { - },$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120050/t12005035.png ; $p - n$ ; confidence 0.906
@@ Line 558: / Line 558: @@
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120020/l1200208.png ; $\phi _ { i j } : \phi _ { j } ( U _ { i } \cap U _ { j } ) \rightarrow \phi _ { i } ( U _ { i } \cap U _ { j } )$ ; confidence 0.906
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c130160189.png ; $L \subseteq NL \subseteq NC \subseteq P \subseteq NP \subseteq PH \subseteq PSPACE$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c130160189.png ; $L \subseteq \operatorname{NL} \subseteq \operatorname{NC} \subseteq P \subseteq \operatorname{NP} \subseteq \operatorname{PH} \subseteq \operatorname{PSPACE}$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/a/a013/a013180/a01318019.png ; $C ^ { 1 }$ ; confidence 0.906
@@ Line 576: / Line 576: @@
 . https://www.encyclopediaofmath.org/legacyimages/i/i120/i120100/i12010051.png ; $R _ { 1212 } = \alpha _ { 2 } , R _ { 1313 } = \alpha _ { 2 } , R _ { 2424 } = \alpha _ { 2 }$ ; confidence 0.906
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430174.png ; $\partial _ { q , x } ( x ^ { n } y ^ { m } ) = [ n ] _ { q ^ { 2 } } x ^ { n - 1 } y ^ { m }$ ; confidence 0.906
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430174.png ; $\partial _ { q , x } ( x ^ { n } y ^ { m } ) = [ n ] _ { q ^ { 2 } } x ^ { n - 1 } y ^ { m },$ ; confidence 0.906
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130210/b13021028.png ; $H _ { S } = 0$ ; confidence 0.906
@@ Line 588: / Line 588: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d032/d032240/d032240238.png ; $\square ^ { \color{blue} * }$ ; confidence 1.000
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003054.png ; $\sum _ { i = 1 } ^ { n } \psi \Bigl( \frac { x _ { i } - T _ { n } } { S _ { n } }\Bigr ) = 0$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003054.png ; $\sum _ { i = 1 } ^ { n } \psi \Bigl( \frac { x _ { i } - T _ { n } } { S _ { n } }\Bigr ) = 0,$ ; confidence 1.000
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c12021054.png ; $\Lambda _ { n } = \operatorname { log } ( d P _ { n } ^ { \prime } / d P _ { n } )$ ; confidence 0.906

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