Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/64"

Latest revision as of 21:21, 10 May 2020

List

1. ; $\operatorname { Gal } ( \overline { k } _ { s } / k )$ ; confidence 0.400

2. ; $f ( x ) = ( 2 \pi ) ^ { - 2 n } \int _ { {\bf R} ^ { 2 n } } e ^ { i x \xi } \hat { f } ( \xi ) d \xi$ ; confidence 0.400

3. ; $\operatorname{PH} = \operatorname{ATIMEALT} [ n ^ { O ( 1 ) } , O ( 1 ) ]$ ; confidence 0.400

4. ; $\varphi _ { 1 } ( f ) , \dots , \varphi _ { n } ( f )$ ; confidence 0.400

5. ; $R = {\cal O} [ [ \Gamma ] ] = \text { varprojlim } {\cal O} [ \Gamma / \Gamma ^ { p ^ { n } } ]$ ; confidence 0.400

6. ; $c _ { t } ^ { \prime } \geq c _ { t }$ ; confidence 0.400

7. ; $\operatorname{DSPACE}[t(n)]$ ; confidence 0.399

8. ; $h \in {\bf R} ^ { n }$ ; confidence 0.399

9. ; $\tilde { N }$ ; confidence 0.399

10. ; $L _ { 0 , n } ^ { 1 }$ ; confidence 0.399

11. ; $O ^ { \sim }$ ; confidence 0.399

12. ; $+ \frac { 1 } { 2 } \left( 2 ^ { 12 } \frac { \eta ^ { 24 } ( q ) } { \eta ( q ^ { 1 / 2 } ) ^ { 24 } } - 2 ^ { 12 } \frac { \eta ( q ^ { 2 } ) ^ { 24 } \eta ( q ^ { 1 / 2 } ) ^ { 24 } } { \eta ( q ) ^ { 48 } } \right),$ ; confidence 0.399

13. ; $P _ { n } ( A _ { n } ) \rightarrow 0$ ; confidence 0.399

14. ; $r _ { i - 2} ( z ) = q _ { i } ( z ) r _ { i - 1} ( z ) + r _ { i } ( z ) , \quad i = 1,2 ,\dots .$ ; confidence 0.399

15. ; $h _ { j } \in H$ ; confidence 0.399

16. ; $k \in {\bf R}_+$ ; confidence 0.399

17. ; $A = \{ a _ { 1 } , \dots , a _ { q } \}$ ; confidence 0.399

18. ; $( x _ { 1 } , \dots , x _ { n } ) \in M ^ { n }$ ; confidence 0.399

19. ; $M / \mathfrak { q } M$ ; confidence 0.399

20. ; $\lambda - a_i$ ; confidence 0.399

21. ; $( - 1 ) ^ { n } f ( - z ) f ( z ) = a _ { 0 } ^ { 2 } \prod _ { i = 1 } ^ { n } ( z ^ { 2 } - r _ { i } ^ { 2 } )$ ; confidence 0.399

22. ; $w _ { 2 } = ( 1 - c ) / 2$ ; confidence 0.399

23. ; ${\bf R} _ { \xi } ^ { n }$ ; confidence 0.398

24. ; $\partial$ ; confidence 0.398

25. ; $\psi \in S$ ; confidence 0.398

26. ; $\alpha _ { n } + \beta _ { n }$ ; confidence 0.398

27. ; $F ^ { \prime }$ ; confidence 0.398

28. ; $\operatorname { max } _ { x \in K } | \partial ^ { \alpha } f ( x ) | \leq C ^ { | \alpha | + 1 } ( | \alpha ! | ) ^ { s },$ ; confidence 0.398

29. ; $w ( \{ S _ { i } \} \rightarrow \{ S _ { i } ^ { \prime } \} )$ ; confidence 0.398

30. ; $g _ { j } = \sum _ { i = 1 } ^ { M } f _ { i } h _ {i j } , j = 1 , \ldots , N,$ ; confidence 0.398

31. ; $\mathsf{E} W ^ { ( N ) } ( t ) W ^ { ( N ) } ( s ) = \prod _ { i = 1 } ^ { N } t _ { i } \bigwedge s _ { i },$ ; confidence 0.398

32. ; $x _ { 1 } \prec \ldots \prec x _ { \alpha } \prec \dots$ ; confidence 0.398

33. ; $S _ { 2 }$ ; confidence 0.398

34. ; $r_{i, j} = | L \cap e _ { j } I e _ { i } |$ ; confidence 0.398

35. ; $F - O _ { n }$ ; confidence 0.398

36. ; $b _ { j } = a _ { j } |_{x _ { 0 } = 1 / f} f ^ { \mu }$ ; confidence 0.398

37. ; $\mathsf{E} _ { \theta } [ H ( \theta , X ) ] = 0 , \quad \text { if } \theta = \theta ^ { * },$ ; confidence 0.398

38. ; $\operatorname { lim } _ { n \rightarrow \infty } m _ { i } ( E _ { n } ) = 0$ ; confidence 0.397

39. ; $\tau \in \operatorname{Wh} ( \pi )$ ; confidence 0.397

40. ; $\operatorname{NTIME} [t( n )]$ ; confidence 0.397

41. ; $\vdash ( \lambda x y . x ) : ( \sigma \rightarrow ( \tau \rightarrow \sigma ) )$ ; confidence 0.397

42. ; $\tilde {\cal A } = {\cal A} \cap K$ ; confidence 0.397

43. ; $[ K , L ] ( X _ { 1 } , \dots , X _ { k + 1 } ) =$ ; confidence 0.397

44. ; $A ( g ) = \frac { 1 } { n - 2 } \left( \operatorname { Ric } ( g ) - \frac { 1 } { 2 } \frac { S ( g ) } { n - 1 } g \right) \in \mathsf{S} ^ { 2 } \cal E$ ; confidence 0.397

45. ; $\Omega = \text{const}$ ; confidence 0.397

46. ; $x \preceq y \Rightarrow x z \preceq y z.$ ; confidence 0.397

47. ; $f ( d ) = \sum d _ { i }$ ; confidence 0.397

48. ; $= {\bf C}^ { n }$ ; confidence 0.397

49. ; $M _ { k } = \sum _ { i = 1 } ^ { k } M _ { i k }$ ; confidence 0.396

50. ; $\sigma _ { \text{p} }$ ; confidence 0.396

51. ; $x \in {\bf R} _ { + } , \psi _ { m } ( 0 , k ) = 1 , \psi _ { m } ^ { \prime } ( 0 , k ) = 0.$ ; confidence 0.396

52. ; $\Gamma \vdash ( \lambda x . M ) : ( \sigma \rightarrow \tau )$ ; confidence 0.396

53. ; $D ^ { n }$ ; confidence 0.396

54. ; $\widehat { ( I ^ { \alpha } f ) } ( \xi ) = | \xi | ^ { - \alpha } \hat { f } ( \xi )$ ; confidence 0.396

55. ; $S$ ; confidence 0.396

56. ; $\psi$ ; confidence 0.396

57. ; $M _ { t } : = \operatorname { sup } _ { s \leq t } W _ { s }$ ; confidence 0.396

58. ; $( a ^ { w } u , v ) = \int \int a ( x , \xi ) {\cal H} ( u , v ) ( x , \xi ) d x d \xi, $ ; confidence 0.396

59. ; $P _ { 2 }$ ; confidence 0.396

60. ; ${\bf C A} _ { n }$ ; confidence 0.396

61. ; $g : \otimes ^ { 2 } \cal E * \rightarrow R$ ; confidence 0.396

62. ; $X = {\cal H} _ { n }$ ; confidence 0.395

63. ; $\text{(const)} \int _ { {\bf R} ^ { 3 } } | \nabla \sqrt { \rho ( x ) } | ^ { 2 } d x$ ; confidence 0.395

64. ; $M \backslash a$ ; confidence 0.395

65. ; $x \in \Sigma ^ { i _ { 1 } } ( f )$ ; confidence 0.395

66. ; $i \in \bf N$ ; confidence 0.395

67. ; $\operatorname{SAT} \in \operatorname{NP}$ ; confidence 0.395

68. ; $\operatorname{diag} (g_1, \dots , g _ { n } )$ ; confidence 0.395

69. ; $v _ { n } 1 = 0$ ; confidence 0.395

70. ; $S A W ^ { * }$ ; confidence 0.395

71. ; $K [ X _ { 1 } , \dots , X _ { n } ]$ ; confidence 0.394

72. ; $r _ { j j } = \left( a _ { j j } - \sum _ { k = 1 } ^ { j - 1 } r _ { k j } ^ { 2 } \right) ^ { 1 / 2 }$ ; confidence 0.394

73. ; $\overline{A} \subseteq \overline { B }$ ; confidence 0.394

74. ; $M \subset {\bf R} ^ { n }$ ; confidence 0.394

75. ; $( x _ { i 1 } , \ldots , x _ { i r } )$ ; confidence 0.394

76. ; $f ( z ) = \sum _ { n = 0 } ^ { \infty } P _ { n } ( z - z _ { 0 } )$ ; confidence 0.394

77. ; ${\cal H} _ { \epsilon } ^ { \prime \prime }$ ; confidence 0.394

78. ; $x _ { n } = x / z ^ { n }$ ; confidence 0.394

79. ; $\Delta p _ { j } \Delta q_j \sim h _ { j } ^ { - 1 } \geq 1$ ; confidence 0.394

80. ; $T \subseteq X$ ; confidence 0.394

81. ; $\int _ { - \infty } ^ { \infty } \left[ \frac { - \operatorname { ln } F _ { \text{ac} } ^ { \prime } ( x ) } { 1 + x ^ { 2 } } \right] d x < \infty ,$ ; confidence 0.394

82. ; $\delta : = ( 1 / 2 ) \sum _ { \alpha \in S ^ { + } } \alpha \in {\frak h} _ {\bf R } ^ { * }$ ; confidence 0.394

83. ; $\Gamma _ { n } ^ { - 1 }$ ; confidence 0.394

84. ; $\psi _ { \mathfrak { A } } ^ { l + 1 } \overline { { a } }$ ; confidence 0.393

85. ; $A \circ B = ( a _ { i , j} b _ { i , j} )$ ; confidence 0.393

86. ; $\mathfrak { R } ( C _ { 2 } )$ ; confidence 0.393

87. ; $\varphi _ { M } ^ { i } : \operatorname { Ext } _ { A } ^ { i } ( A / \mathfrak { m } , M ) \rightarrow H _ {\frak m } ^ { i } ( M ) = \operatorname { lim } _ { n \rightarrow \infty } \operatorname { Ext } _ { A } ^ { i } ( A / \mathfrak { m } ^ { n } , M )$ ; confidence 0.393

88. ; $\theta _ { i }$ ; confidence 0.393

89. ; $\mathfrak { g } ^ { \alpha }$ ; confidence 0.393

90. ; $\frac { 1 } { \operatorname{vol} S ^ { n - 1 } } \int _ { \partial K } f ^ { * } \omega,$ ; confidence 0.393

91. ; $y ^ { q ^ { r } } \phi_f ( x / y ) - z ^ { p } = 0,$ ; confidence 0.393

92. ; $a \in {\cal S} ^ { \prime } ( {\bf R} ^ { 2 n } )$ ; confidence 0.393

93. ; ${\bf R} ^ { m } \rightarrow {\bf R} ^ { k }$ ; confidence 0.393

94. ; $k = 0,1 , \dots ,$ ; confidence 0.393

95. ; $s_0$ ; confidence 0.393

96. ; $x _ { i } = \xi _ { i } ( y _ { i } , \ldots , y _ { n } ) , \quad i = 1 , \ldots , n,$ ; confidence 0.393

97. ; $Y^{\chi}$ ; confidence 0.393

98. ; $\Lambda _ { n }$ ; confidence 0.393

99. ; $2 . \frac { \partial ^ { 2 } } { \partial x ^ { 2 } } \operatorname { log } \tau,$ ; confidence 0.393

100. ; ${\bf x} = ( x _ { 1 } , \ldots , x _ { n } )$ ; confidence 0.393

101. ; $x \rightarrow y$ ; confidence 0.392

102. ; $\tilde{u}_1$ ; confidence 0.392

103. ; $\| \frac { \partial U ( t , s ) } { \partial t } \| \leq \frac { C } { t - s } , \quad s , t \in [ 0 , T ], $ ; confidence 0.392 NOTE: why is there a single bar on the left and a double bar on the right?

104. ; $r _ { N } ( a , b ) \in S _ { \text{scl} } ^ { m _ { 1 } + m _ { 2 } - N}$ ; confidence 0.392

105. ; $\tilde{g} \in \operatorname { Gal } ( L ( k ^ { \prime } ) / k )$ ; confidence 0.392

106. ; $Y _ { m } = ( y _ { m + k - 1} , \ldots , y _ { m } ) ^ { T }$ ; confidence 0.392

107. ; $l = 0 , \dots , n _ { j } - 1$ ; confidence 0.392

108. ; $\operatorname{Fm} _ { \tau }$ ; confidence 0.392

109. ; $\int _ { - 1 } ^ { 1 } p ( x ) P _ { n } ( x ) E _ { n + 1 } ( x ) x ^ { k } d x = 0 , \quad k = 0 , \dots , n, $ ; confidence 0.392

110. ; $K ^ { 2 }$ ; confidence 0.392

111. ; $R G = B _ { 1 } \bigoplus \ldots \bigoplus B _ { n }.$ ; confidence 0.392

112. ; $\operatorname { max } _ { k = m + 1 , \ldots , m + n } | g ( k ) | \geq \frac { 1 } { 3 } | g ( 0 ) | \prod _ { j = 1 } ^ { n } \frac { | z _ { j } | - \operatorname { exp } ( - 1 / m ) } { | z _ { j } | + 1 }.$ ; confidence 0.392

113. ; $F _ { m - n + 1}$ ; confidence 0.392

114. ; $\operatorname { lim } _ { Z \rightarrow \infty } \frac { E ^ { \text{TF} } ( \lambda Z ) } { E ^ { \text{Q} } ( \lambda Z ) } = 1.$ ; confidence 0.392

115. ; $\mu_Y$ ; confidence 0.391

116. ; $q _ { 1 } ( x )$ ; confidence 0.391

117. ; $\sum _ { | \alpha | = 0 } ^ { k } \left( \frac { \partial L } { \partial y _ { \alpha } ^ { a }} \circ \sigma ^ { k } \right) ( \frac { \partial } { \partial x } ) ^ { \alpha } ( Z ^ { a } \circ \sigma ) \Delta.$ ; confidence 0.391

118. ; $K _ { 7 , 11}$ ; confidence 0.391

119. ; $E ( a ) = \operatorname { det } T ( a ) T ( a ^ { - 1 } )$ ; confidence 0.391

120. ; $\mathsf{P} ( A _ { 1 } \cup \ldots \cup A _ { n } )$ ; confidence 0.391

121. ; $q _ { \alpha } \in S ( \tilde { h } ^ { - 1 } , \tilde{g} )$ ; confidence 0.391

122. ; $v _ { 1 } , \dots , v _ { n + 1 }$ ; confidence 0.391

123. ; $a \in \operatorname { spt } \nu$ ; confidence 0.390

124. ; $k _ { n }$ ; confidence 0.390

125. ; $\| f ^ { * } g \| \leq \| f \| \| g \|$ ; confidence 0.390

126. ; $a \in G$ ; confidence 0.390

127. ; $[ ., . ] : A \times A \rightarrow A$ ; confidence 0.390

128. ; $P ( D ) ( E ^ { * } g ) = ( P ( D ) ( E ) ) ^ { * } g = \delta _ { 0 } * g = g.$ ; confidence 0.390

129. ; $\operatorname{ind} ( P ) = ( - 1 ) ^ { n } \operatorname{Ch} ( [ a ] ) {\cal T} ( M ) [ T ^ { * } M ],$ ; confidence 0.390

130. ; $\xi_ { 0 }$ ; confidence 0.390

131. ; $t _ { n + 1} - t _ { n } \sim \varepsilon$ ; confidence 0.390

132. ; $y _ { i } = z _ { 1 } ^ { \alpha _ { i 1 } } \ldots z _ { n } ^ { \alpha _ { i n } } , \quad i = 1 , \dots , n,$ ; confidence 0.390

133. ; $\bf I$ ; confidence 0.390

134. ; $\operatorname { sup } _ { \| v \| \leq 1 } | b ( u , v ) | \geq \| u \| , \forall u \in U,$ ; confidence 0.390

135. ; ${\bf V} = \{ ( u _ { 1 } , \dots , u _ { m } ) : u _ { i } \in V _ { i } , i \in \{ 1 , \dots , m \} \};$ ; confidence 0.390

136. ; $\phi_n$ ; confidence 0.390

137. ; $g \in J _ { E } ^ { \circ }$ ; confidence 0.389

138. ; $O$ ; confidence 0.389

139. ; $M ^ { \perp } = \{ x \in G : | x | \wedge | m | = e \text { for all } m \in M \}$ ; confidence 0.389

140. ; $q_j$ ; confidence 0.389

141. ; ${\bf Z} \Lambda ( n )$ ; confidence 0.389

142. ; $U ( {\frak n} )$ ; confidence 0.389

143. ; $v _ { j } \lambda _ { j } ^ { 1 / 2 } = u _ { j }$ ; confidence 0.389

144. ; $\hat { K } _ { \text{p} }$ ; confidence 0.389

145. ; $\left\| \sum _ { j = 1 } ^ { m } w _ { j } . \frac { p _ { j } - p _ { i } } { \| p _ { j } - p _ { i } \| } \right\| > w _ { i } , i \neq j,$ ; confidence 0.389

146. ; $\{ u _ { i } \}$ ; confidence 0.389

147. ; $\square \ldots \rightarrow \pi _ { n + 1 } ( X ; A , B , ^* ) \stackrel { \partial } { \rightarrow } \pi _ { n } ( A , A \bigcap B , ^* ) \rightarrow $ ; confidence 0.389

148. ; $F_{*}$ ; confidence 0.389

149. ; $S \subseteq \Sigma ^ {\color{blue} * }$ ; confidence 0.389

150. ; $z_1 , \dots ,z_n$ ; confidence 0.389

151. ; ${\bf Z} / p ^ { m }$ ; confidence 0.389

152. ; $| P |$ ; confidence 0.388

153. ; $\Delta ^ { n }$ ; confidence 0.388

154. ; $c r ^ { t } w$ ; confidence 0.388

155. ; $a \in \cal O ( U )$ ; confidence 0.388

156. ; $R ( x ; a _ { 0 } , \dots , a _ { N } ) = \sum _ { n } r _ { n } ( a _ { 0 } , \dots , a _ { N } ) \phi _ { n } ( x )$ ; confidence 0.388

157. ; $= \sum _ { j = 1 } ^ { n } ( - 1 ) ^ { j - 1 } ( \overline { \zeta _ { j } } - \overline { z _ { j } } ) d \overline { \zeta _ { 1 } } \bigwedge \ldots \bigwedge [ d \overline { \zeta _ { j } } ] \bigwedge \ldots \bigwedge d \overline { \zeta _ { n } } , \omega ( \zeta ) = d \zeta _ { 1 } \bigwedge \cdots \bigwedge d \zeta _ { n },$ ; confidence 0.388

158. ; ${\cal V} _ { g , n }$ ; confidence 0.388

159. ; $\mathsf{E} ( {\bf Z} _ { 13 } ) = 0$ ; confidence 0.388

160. ; $a \in \partial E$ ; confidence 0.388

161. ; $a ( g h ) = g ^ { - 1 } a h$ ; confidence 0.388

162. ; $C _ { i j } ( t )$ ; confidence 0.388

163. ; $D _ { r } = r . D$ ; confidence 0.388

164. ; $e_{k + 1} , \ldots , e _ { n }$ ; confidence 0.387

165. ; $a _ { k \text{l} } ( y ) \xi _ { k } \xi _ { \text{l} } \geq \alpha | \xi | ^ { 2 }$ ; confidence 0.387

166. ; $\sum _ { | X | \geq n } \mu ( X ) \frac { T ^ { - 1 } ( \operatorname { time } _ {\cal A } ( X ) ) } { | X | } \leq \sum _ { | X | \geq n } \mu ( X ),$ ; confidence 0.387

167. ; $\dot { v } _ { i } = \tilde { \psi } _ { i } ( V ) , \quad i = 1 , \dots , n,$ ; confidence 0.387

168. ; ${ j}_g = 1 / q + a _ { 1 } ( g ) q +\dots$ ; confidence 0.387

169. ; $i = 1 , \dots , \nu$ ; confidence 0.387

170. ; $\bar{x} \square ^ { i } ( t ) = x ^ { i } ( t ) + \xi ^ { i } ( t ) \eta,$ ; confidence 0.387

171. ; $h = ( b - a ) / N$ ; confidence 0.387

172. ; $\left. \begin{cases} { \frac { \partial u } { \partial t } + \sum _ { j = 1 } ^ { m } a _ { j } ( x ) \frac { \partial u } { \partial x _ { j } } + c ( x ) u = f ( x , t ) }, \\ { ( x , t ) \in \Omega \times [ 0 , T ] }, \\ { u ( x , 0 ) = u _ { 0 } ( x ) , \quad x \in \Omega, } \end{cases} \right.$ ; confidence 0.387

173. ; $\phi_S$ ; confidence 0.387

174. ; ${\cal C} ( Z \times _ { S } Y , X ) \cong {\cal C} ( Z , {\cal C} ( Y , X ) )$ ; confidence 0.387

175. ; $R _ { j } = {\bf R} _ { \geq 0 } v_j$ ; confidence 0.386

176. ; $( F f ) ( z ) = \sum _ { j = 1 } ^ { n } \left( z _ { j } \frac { \partial f ( z ) } { \partial z _ { j } } + \bar{z} _ { j } \frac { \partial f ( z ) } { \partial \bar{z} _ { j } } \right).$ ; confidence 0.386

177. ; $X _ { g } ^ { * } = {\color{blue} \cup} _ { r \leq g } X _ { r }$ ; confidence 0.386

178. ; $( u , v ) = \int _ { a } ^ { b } u ( x ) v ( x ) \rho ( x ) d x$ ; confidence 0.386

179. ; $\{ B _ { n } \}$ ; confidence 0.386

180. ; $K = k _ { 1 } + \ldots + k _ { n }$ ; confidence 0.386

181. ; $T ^ { t }$ ; confidence 0.386

182. ; $\operatorname { Im } z$ ; confidence 0.386

183. ; $A ( X _ { 1 } , \dots , X _ { s _ { i } } )$ ; confidence 0.386

184. ; $a _ { s t }$ ; confidence 0.386

185. ; $\mathsf{E} [ W _ { p } ] _ { \text{NP} } =$ ; confidence 0.386

186. ; $c_1 \operatorname{deg} I + c _ { 2 } \operatorname{log} \operatorname{ht} I$ ; confidence 0.386

187. ; $| E |$ ; confidence 0.386

188. ; $\| A \| \| A ^ { - 1 } \|$ ; confidence 0.386

189. ; $[ S _ { i } ( S _ { i - 1 } + S _ { i + 1 } ) ]$ ; confidence 0.386

190. ; $\{ a , b \} = d a / a \wedge d b / b$ ; confidence 0.386

191. ; $X : M \rightarrow {\bf R} ^ { n }$ ; confidence 0.386

192. ; $A \equiv ( A _ { 1 } , \dots , A _ { n } )$ ; confidence 0.385

193. ; $L _ { i , j } u _ { j } = f _ { i }$ ; confidence 0.385

194. ; $\operatorname{ASPACE}[\operatorname{log} n] = P$ ; confidence 0.385

195. ; $\lambda = e _ { \lambda _ { 1 } } \cdots e _ { \lambda _ { l } }$ ; confidence 0.385

196. ; $H ^ { \otimes 2 }$ ; confidence 0.385

197. ; $\frac { \pi ^ { n p / 2 } } { \Gamma _ { p } ( n / 2 ) } | S | ^ { ( n - p - 1 ) / 2 } f ( S ) , \quad S > 0.$ ; confidence 0.385

198. ; $r _ { P } : K _ { P } ^ { * } / K _ { P } ^ { * 2 } \rightarrow C ^ { * }$ ; confidence 0.385

199. ; $\operatorname{sg} ( \pi )$ ; confidence 0.385

200. ; $( n + 1 ) a _ { n + 1 } + a _ { n } = \tau$ ; confidence 0.385

201. ; $\frac { 1 } { p _ { 2 } ( \xi , \tau ) + a i } = \frac { p _ { 3 } ( \xi , \tau ) } { 1 + a ^ { 2 } } - \frac { a i } { 1 + a ^ { 2 } }$ ; confidence 0.385

202. ; $W _ { k }$ ; confidence 0.385

203. ; $f _ { I \cap P }$ ; confidence 0.385

204. ; $\operatorname { Tr } [ A \operatorname { exp } ( - i h ^ { - 1 } H ( t ) ) ] = \sum _ { k = 1 } ^ { n } a _ { 0 } ( x _ { k } ) d _ { k } e ^ { b _ { k } } + O ( h ).$ ; confidence 0.385

205. ; $d r = L ^ { * } r + \langle f ^ { - 1 } ( t , Y ( t ) ) g ( t , X ( t ) , Y ( t ) ) , d Y ( t ) \rangle { r },$ ; confidence 0.385

206. ; $\gamma _ { 1 } ^ { 2 } = 1 , \gamma _ { 2 } ^ { 2 } = \gamma _ { 3 } ^ { 2 } = \gamma _ { 4 } ^ { 2 } = - 1,$ ; confidence 0.385

207. ; $f \in I _ { E }$ ; confidence 0.385

208. ; $( F ^ {\bf Z } , {\cal B} ^ {\bf Z } , \mathsf{P} )$ ; confidence 0.385

209. ; $\frak B$ ; confidence 0.385

210. ; $w _ { i } ^ { l } = a _ { l }$ ; confidence 0.385

211. ; $X ^ { * }$ ; confidence 0.384

212. ; ${\bf C} [ [ \hbar ] ]$ ; confidence 0.384

213. ; $l_i$ ; confidence 0.384

214. ; $X A X ^ { \prime } \sim L _ { 1 } ^ { ( 1 ) } \left( f _ { 1 } , \frac { { k } } { 2 } \right),$ ; confidence 0.384

215. ; $c_{i j k}$ ; confidence 0.384

216. ; $y _ { i j k } = \mu + \alpha _ { i } + \beta _ { j } + \gamma _ { i j } + e _ { i j k },$ ; confidence 0.384

217. ; $E ( {\bf Q} )$ ; confidence 0.384

218. ; $\operatorname { lim } _ { \varepsilon \downarrow 0 } \frac { \mu _ { \varepsilon } ^ { x } ( \phi ) } { \mu _ { \varepsilon } ^ { x } ( \psi ) }$ ; confidence 0.384

219. ; $\sum _ { j } g _ { j } = \sum _ { i } f _ { i } = \sum _ { j } h _ { i j } = 1$ ; confidence 0.384

220. ; $c _ { \beta }$ ; confidence 0.384

221. ; $P _ { K } ( v , z ) = v ^ { 2 c } \sum c _ { i, j } ( v ^ { 2 } - 1 ) ^ { i } z ^ { j }$ ; confidence 0.384

222. ; $\int _ { E } \operatorname { log } ( d \mathsf{P} / d \mu ) d \mathsf{P}$ ; confidence 0.384

223. ; $\tau ( \varphi ) ^ { \alpha } ( x ) = g ^ { i j } ( x ) \left( \frac { \partial ^ { 2 } \varphi ^ { \alpha } } { \partial x ^ { i } \partial x ^ { j } } - \square ^ { M } \Gamma _ { i j } ^ { k } ( x ) \frac { \partial \varphi ^ { \alpha } } { \partial x ^ { k } } + + \square ^ { N } \Gamma _ { \beta \gamma } ^ { \alpha } ( \varphi ( x ) ) \frac { \partial \varphi \beta } { \partial x ^ { i } } \frac { \partial \varphi ^ { \gamma } } { \partial x ^ { j } } \right),$ ; confidence 0.384

224. ; $V_{( n )} = 0$ ; confidence 0.384

225. ; $1, Z , \bar{Z} , Z ^ { 2 } , \bar{Z} Z , Z ^ { 2 } , \ldots , Z ^ { n } , \ldots , \bar{Z} ^ { n }$ ; confidence 0.384

226. ; $X \in \mathfrak { h }$ ; confidence 0.384

227. ; $\widehat{{\frak sl}(2)}$ ; confidence 0.384

228. ; $n _ { s }$ ; confidence 0.383

229. ; $( P _ { n } ) = ( P _ { n } ( z _ { 0 } ) )$ ; confidence 0.383

230. ; $\sum _ { \alpha } \operatorname { sup } _ { D _ { r } } | c _ { \alpha } z ^ { \alpha } | < 1,$ ; confidence 0.383

231. ; $\bar { A } _ { i j }$ ; confidence 0.383

232. ; $X_{*}$ ; confidence 0.383

233. ; $x \in G_1$ ; confidence 0.383

234. ; $\Delta _ { n } = \{ ( t _ { 2 } , \dots , t _ { n } ) : t _ { 2 } , \dots , t _ { n } \geq 0 , t _ { 2 } + \dots + t _ { n } \leq 1 \}$ ; confidence 0.383

235. ; $= \int _ { \xi \in {\bf R} ^ { 2 } } \left( \begin{array} { c c } { L _ { x } ^ { 2 } } & { L _ { x } L _ { y } } \\ { L _ { x } L _ { y } } & { L _ { y } ^ { 2 } } \end{array} \right) g ( x - \xi ; s ) d x,$ ; confidence 0.382

236. ; $\operatorname { inf } _ { z _ { j } } \operatorname { max } _ { k \in S } \frac { | g _ { 2 } ( k ) | } { M _ { d } ( k ) }$ ; confidence 0.382

237. ; $H ^ { s } ( {\bf R} ^ { n } )$ ; confidence 0.382

238. ; $r _ { 1 } ( t , s ) = \prod _ { i = 1 } ^ { N } ( t _ { i } \bigwedge s _ { i } - t _ { i } s _ { i } ),$ ; confidence 0.382

239. ; $\{ E _ { n _ { 1 } \ldots n _ { k } }\}$ ; confidence 0.382

240. ; $= \operatorname { exp } \left( x P _ { 0 } z + \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } \right) g ( z ) . . \operatorname { exp } \left( - x P _ { 0 } z - \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } \right),$ ; confidence 0.382

241. ; $E_i$ ; confidence 0.382

242. ; $\overline { d } _ { \chi } ^ { G } ( A ) \geq \operatorname { det } ( A ) = \overline { d } _ { ( 1 ^ { n } )} ( A ).$ ; confidence 0.382

243. ; $l = \{ . , e , ^{- 1} , \vee , \wedge \}$ ; confidence 0.382

244. ; $f _ { 1 } , \dots , f _ { m } \in {\bf Q} ( X _ { 1 } , \dots , X _ { n } )$ ; confidence 0.382

245. ; $c _ { q } = ( - 1 ) ^ { q } q ! / ( 2 q ) !$ ; confidence 0.382

246. ; ${\frak G} _ { D }$ ; confidence 0.382

247. ; $q_1$ ; confidence 0.381

248. ; $\{ a _ { 1 } + 1 , \dots , a _ { k } + 1 \}$ ; confidence 0.381

249. ; $\operatorname{ATIME} [ n ^ { O ( 1 ) } ] = \operatorname { PSPACE }$ ; confidence 0.381

250. ; ${\cal E} \overset{\approx}{\to} {\cal E} _ {* * }$ ; confidence 0.381

251. ; $( x _ { i j } ( a ) , x _ { k \text{l} } ( b ) ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } i \neq \text{l} , j \neq k }, \\ { x _ { i \text{l} } ( a b ) } & { \text { if } i \neq \text{l} , j = k }. \end{array} \right.$ ; confidence 0.381

252. ; ${\bf P} _ { \text{U} } \mathsf{K}$ ; confidence 0.381

253. ; $v _ { n } = v / z ^ { n }$ ; confidence 0.381

254. ; $K = D ^ { n }$ ; confidence 0.381

255. ; $\mathfrak { B } = \{ e _ { \pm \alpha} , h _ { \beta } : \alpha \in \Phi ^ { + } , \beta \in \Sigma \}.$ ; confidence 0.381

256. ; $Q _ { n } [ f ] = \sum _ { v = 1 } ^ { n } a _ { v , n } f ( x _ { v , n } ),$ ; confidence 0.381

257. ; $C _ { 0 } ( t )$ ; confidence 0.381

258. ; $T ( n , k , r ) \geq \frac { n - k + 1 } { n - r + 1 } \left( \begin{array} { c } { n } \\ { r } \end{array} \right) / \left( \begin{array} { c } { k - 1 } \\ { r - 1 } \end{array} \right)$ ; confidence 0.381

259. ; $\partial T$ ; confidence 0.381

260. ; $\kappa = 2 J$ ; confidence 0.381

261. ; $i j$ ; confidence 0.381

262. ; $\operatorname{mod} R$ ; confidence 0.381

263. ; $r _ { j }$ ; confidence 0.381

264. ; $( \phi \bigotimes \text { id } ) \Psi _ { V , W } = \Psi _ { V , Z } ( \text { id } \bigotimes \phi ) , \forall \phi : W \rightarrow Z,$ ; confidence 0.381

265. ; $\langle p , q \rangle = \int _ {\bf R } p q d \mu _ { 0 } + \lambda \int _ {\bf R } p ^ { \prime } q ^ { \prime } d \mu _ { 1 },$ ; confidence 0.381

266. ; $J _ { t }$ ; confidence 0.380

267. ; $H ^ { n } ( {\cal C} , M ) = \operatorname { Ext } _ { Z {\bf C} } ^ { n } ( {\cal Z} , M ),$ ; confidence 0.380

268. ; $\underline{\operatorname{lim}} \leftarrow$ ; confidence 0.380

269. ; $\frac { d N ^ { i } } { d t } = \lambda _ { ( i ) } N ^ { i } \left( 1 - \frac { N ^ { i } } { K _ { ( i ) } } \right) , \quad i = 1 , \ldots , n,$ ; confidence 0.380

270. ; $G ^ { 3 }$ ; confidence 0.380

271. ; $M _ { m } ( P _ { n } )$ ; confidence 0.380

272. ; $H H ^ { T } = H ^ { T } H = n I _ { n }$ ; confidence 0.380

273. ; ${\bf l}^ { 1 } ( G )$ ; confidence 0.380

274. ; $Q_i$ ; confidence 0.380

275. ; $\operatorname{Alg} \operatorname{Mod}^ { *S } \operatorname{S} 5$ ; confidence 0.380

276. ; $0 \leq r \in \bf Z$ ; confidence 0.380

277. ; $z _ { k } ^ { T } ( t ) = ( z _ { k , 1 } ( t ) , \dots , z _ { k , p } ( t ) )$ ; confidence 0.380

278. ; $j_1 , \dots , j _ { k }$ ; confidence 0.380

279. ; ${\bf Alg} : \text{ ''logics"}\to \text{''pairs of classes of algebras"}$ ; confidence 0.380

280. ; $v _ { j }$ ; confidence 0.380

281. ; $y _ { t }$ ; confidence 0.380

282. ; $s \in S , u , v \in H , \phi : S \times H \rightarrow S,$ ; confidence 0.380

283. ; $P _ { 2 _ { 1 } } = \frac { v - v ^ { 3 } } { z } + v z.$ ; confidence 0.380

284. ; $| I _ { 1 } ( f ) - U ^ { i } ( f ) |$ ; confidence 0.379

285. ; $\operatorname { lcm } ( 1 , \ldots , n ) ^ { 3 }$ ; confidence 0.379

286. ; $w _ { 1 } , \dots , w _ { m }$ ; confidence 0.379

287. ; $G ^ { * } \mu$ ; confidence 0.379

288. ; $( \mathfrak { S } ( T R _ { 1 } \ldots R _ { n} ) : n \in \bf N )$ ; confidence 0.379

289. ; $r = r_2$ ; confidence 0.379

290. ; $P _ { n - 1 }$ ; confidence 0.379

291. ; $u \in S ^ { n - 1 } : = \{ v \in {\bf E} : \langle v , v \rangle = 1 \}$ ; confidence 0.379

292. ; $P _ { \theta }$ ; confidence 0.379

293. ; $d | n$ ; confidence 0.379

294. ; $H _ { 2n }$ ; confidence 0.379

295. ; $K \cap {\bf R} ^ { n }$ ; confidence 0.379

296. ; $G ( \zeta ) = O ( e ^ { \varepsilon | \zeta | + H _ { K } ( \operatorname { lm } \zeta ) } )$ ; confidence 0.379

297. ; $\hat { K } _ { \text{p} } = \bf R$ ; confidence 0.379

298. ; $R _ { \nu }$ ; confidence 0.379

299. ; $h _ { d } = \operatorname { rank } _ { A } M - \sum _ { i = 1 } ^ { d - 1 } \left( \begin{array} { c } { d - 1 } \\ { i - 1 } \end{array} \right) h _ { i }$ ; confidence 0.379

300. ; $X = \bf R$ ; confidence 0.378

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/64. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/64&oldid=45671

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Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/64"

Latest revision as of 21:21, 10 May 2020

List

@@ Line 1: / Line 1: @@
 == List ==
-. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057020/l05702053.png ; $\operatorname { Gal } ( \overline { k } _ { S } / k )$ ; confidence 0.400
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057020/l05702053.png ; $\operatorname { Gal } ( \overline { k } _ { s } / k )$ ; confidence 0.400
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007046.png ; $f ( x ) = ( 2 \pi ) ^ { - 2 n } \int _ { {\bf R} ^ { 2 n } } e ^ { i x \xi } \hat { f } ( \xi ) d \xi$ ; confidence 0.400
@@ Line 8: / Line 8: @@
 . https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q1200104.png ; $\varphi _ { 1 } ( f ) , \dots , \varphi _ { n } ( f )$ ; confidence 0.400
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009060.png ; $R = {\cal O} [ [ \Gamma ] ] = \text { varprojlim } O [ \Gamma / \Gamma ^ { p ^ { n } } ]$ ; confidence 0.400
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009060.png ; $R = {\cal O} [ [ \Gamma ] ] = \text { varprojlim } {\cal O} [ \Gamma / \Gamma ^ { p ^ { n } } ]$ ; confidence 0.400
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012084.png ; $c _ { t } ^ { \prime } \geq c _ { t }$ ; confidence 0.400
@@ Line 22: / Line 22: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f130/f130010/f13001053.png ; $O ^ { \sim }$ ; confidence 0.399
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t120070118.png ; $+ \frac { 1 } { 2 } ( 2 ^ { 12 } \frac { \eta ^ { 24 } ( q ) } { \eta ( q ^ { 1 / 2 } ) ^ { 24 } } - 2 ^ { 12 } \frac { \eta ( q ^ { 2 } ) ^ { 24 } \eta ( q ^ { 1 / 2 } ) ^ { 24 } } { \eta ( q ) ^ { 48 } } ),$ ; confidence 0.399
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t120070118.png ; $+ \frac { 1 } { 2 } \left( 2 ^ { 12 } \frac { \eta ^ { 24 } ( q ) } { \eta ( q ^ { 1 / 2 } ) ^ { 24 } } - 2 ^ { 12 } \frac { \eta ( q ^ { 2 } ) ^ { 24 } \eta ( q ^ { 1 / 2 } ) ^ { 24 } } { \eta ( q ) ^ { 48 } } \right),$ ; confidence 0.399
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c1202104.png ; $P _ { n } ( A _ { n } ) \rightarrow 0$ ; confidence 0.399
@@ Line 54: / Line 54: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110490/a11049023.png ; $F ^ { \prime }$ ; confidence 0.398
-. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g1200409.png ; $\operatorname { max } _ { x \in X } | \partial ^ { \alpha } f ( x ) | \leq C ^ { | \alpha | + 1 } ( | \alpha ! | ) ^ { s }$ ; confidence 0.398
+. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g1200409.png ; $\operatorname { max } _ { x \in K } | \partial ^ { \alpha } f ( x ) | \leq C ^ { | \alpha | + 1 } ( | \alpha ! | ) ^ { s },$ ; confidence 0.398
 . https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i120080136.png ; $w ( \{ S _ { i } \} \rightarrow \{ S _ { i } ^ { \prime } \} )$ ; confidence 0.398
@@ Line 60: / Line 60: @@
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012034.png ; $g _ { j } = \sum _ { i = 1 } ^ { M } f _ { i } h _ {i j } , j = 1 , \ldots , N,$ ; confidence 0.398
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w1201804.png ; $\operatorname{E} W ^ { ( N ) } ( t ) W ^ { ( N ) } ( s ) = \prod _ { i = 1 } ^ { N } t _ { i } \bigwedge s _ { i },$ ; confidence 0.398
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w1201804.png ; $\mathsf{E} W ^ { ( N ) } ( t ) W ^ { ( N ) } ( s ) = \prod _ { i = 1 } ^ { N } t _ { i } \bigwedge s _ { i },$ ; confidence 0.398
-. https://www.encyclopediaofmath.org/legacyimages/r/r110/r110110/r11011028.png ; $x _ { 1 } \prec \ldots \prec x _ { \alpha } \prec . .$ ; confidence 0.398
+. https://www.encyclopediaofmath.org/legacyimages/r/r110/r110110/r11011028.png ; $x _ { 1 } \prec \ldots \prec x _ { \alpha } \prec \dots$ ; confidence 0.398
 . https://www.encyclopediaofmath.org/legacyimages/a/a012/a012270/a01227058.png ; $S _ { 2 }$ ; confidence 0.398
@@ Line 72: / Line 72: @@
 . https://www.encyclopediaofmath.org/legacyimages/r/r130/r130010/r13001010.png ; $b _ { j } = a _ { j } |_{x _ { 0 } = 1 / f} f ^ { \mu }$ ; confidence 0.398
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a1201304.png ; $\operatorname{E} _ { \theta } [ H ( \theta , X ) ] = 0 , \quad \text { if } \theta = \theta ^ { * },$ ; confidence 0.398
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a1201304.png ; $\mathsf{E} _ { \theta } [ H ( \theta , X ) ] = 0 , \quad \text { if } \theta = \theta ^ { * },$ ; confidence 0.398
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120490/b12049010.png ; $\operatorname { lim } _ { n \rightarrow \infty } m _ { i } ( E _ { n } ) = 0$ ; confidence 0.397
@@ Line 86: / Line 86: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230130.png ; $[ K , L ] ( X _ { 1 } , \dots , X _ { k + 1 } ) =$ ; confidence 0.397
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180198.png ; $A ( g ) = \frac { 1 } { n - 2 } ( \operatorname { Ric } ( g ) - \frac { 1 } { 2 } \frac { S ( g ) } { n - 1 } g ) \in \operatorname{S} ^ { 2 } \cal E$ ; confidence 0.397
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180198.png ; $A ( g ) = \frac { 1 } { n - 2 } \left( \operatorname { Ric } ( g ) - \frac { 1 } { 2 } \frac { S ( g ) } { n - 1 } g \right) \in \mathsf{S} ^ { 2 } \cal E$ ; confidence 0.397
 . https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520490.png ; $\Omega = \text{const}$ ; confidence 0.397
@@ Line 98: / Line 98: @@
 . https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z130110131.png ; $M _ { k } = \sum _ { i = 1 } ^ { k } M _ { i k }$ ; confidence 0.396
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005080.png ; $\sigma _ { p }$ ; confidence 0.396
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005080.png ; $\sigma _ { \text{p} }$ ; confidence 0.396
 . https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o13008011.png ; $x \in {\bf R} _ { + } , \psi _ { m } ( 0 , k ) = 1 , \psi _ { m } ^ { \prime } ( 0 , k ) = 0.$ ; confidence 0.396
@@ Line 134: / Line 134: @@
 . https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c13016032.png ; $\operatorname{SAT} \in \operatorname{NP}$ ; confidence 0.395
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007059.png ; $\operatorname{diag} g_1, \dots , g _ { x } )$ ; confidence 0.395
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007059.png ; $\operatorname{diag} (g_1, \dots , g _ { n } )$ ; confidence 0.395
 . https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t120070100.png ; $v _ { n } 1 = 0$ ; confidence 0.395
@@ Line 142: / Line 142: @@
 . https://www.encyclopediaofmath.org/legacyimages/h/h130/h130070/h13007063.png ; $K [ X _ { 1 } , \dots , X _ { n } ]$ ; confidence 0.394
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120160/c12016019.png ; $r _ { j j } = ( a _ { j j } - \sum _ { k = 1 } ^ { j - 1 } r _ { k j } ^ { 2 } ) ^ { 1 / 2 }$ ; confidence 0.394
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120160/c12016019.png ; $r _ { j j } = \left( a _ { j j } - \sum _ { k = 1 } ^ { j - 1 } r _ { k j } ^ { 2 } \right) ^ { 1 / 2 }$ ; confidence 0.394
-. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023270/c0232707.png ; $\overline{A} \subset \overline { B }$ ; confidence 0.394
+. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023270/c0232707.png ; $\overline{A} \subseteq \overline { B }$ ; confidence 0.394
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180380.png ; $M \subset {\bf R} ^ { n }$ ; confidence 0.394
@@ Line 160: / Line 160: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d130060126.png ; $T \subseteq X$ ; confidence 0.394
-. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k12012065.png ; $\int _ { - \infty } ^ { \infty } [ \frac { - \operatorname { ln } F _ { \text{ac} } ^ { \prime } ( x ) } { 1 + x ^ { 2 } } ] d x < \infty ,$ ; confidence 0.394
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k12012065.png ; $\int _ { - \infty } ^ { \infty } \left[ \frac { - \operatorname { ln } F _ { \text{ac} } ^ { \prime } ( x ) } { 1 + x ^ { 2 } } \right] d x < \infty ,$ ; confidence 0.394
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b120400125.png ; $\delta : = ( 1 / 2 ) \sum _ { \alpha \in S ^ { + } } \alpha \in {\frak h} _ {\bf R } ^ { * }$ ; confidence 0.394
@@ Line 178: / Line 178: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020083.png ; $\mathfrak { g } ^ { \alpha }$ ; confidence 0.393
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026010.png ; $\frac { 1 } { \text{vol} S ^ { n - 1 } } \int _ { \partial K } f ^ { * } \omega,$ ; confidence 0.393
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026010.png ; $\frac { 1 } { \operatorname{vol} S ^ { n - 1 } } \int _ { \partial K } f ^ { * } \omega,$ ; confidence 0.393
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120050/f12005028.png ; $y ^ { q ^ { r } } \phi_f ( x / y ) - z ^ { p } = 0,$ ; confidence 0.393
@@ Line 186: / Line 186: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120050/w12005062.png ; ${\bf R} ^ { m } \rightarrow {\bf R} ^ { k }$ ; confidence 0.393
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012057.png ; $k = 0,1 , \ldots ,$ ; confidence 0.393
+. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012057.png ; $k = 0,1 , \dots ,$ ; confidence 0.393
 . https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700109.png ; $s_0$ ; confidence 0.393
@@ Line 192: / Line 192: @@
 . https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520364.png ; $x _ { i } = \xi _ { i } ( y _ { i } , \ldots , y _ { n } ) , \quad i = 1 , \ldots , n,$ ; confidence 0.393
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090229.png ; $Y {\chi}$ ; confidence 0.393
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090229.png ; $Y^{\chi}$ ; confidence 0.393
 . https://www.encyclopediaofmath.org/legacyimages/b/b015/b015350/b015350206.png ; $\Lambda _ { n }$ ; confidence 0.393
-. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120110/k1201103.png ; $2 . \frac { \partial ^ { 2 } } { \partial x ^ { 2 } } \operatorname { log } \tau$ ; confidence 0.393
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120110/k1201103.png ; $2 . \frac { \partial ^ { 2 } } { \partial x ^ { 2 } } \operatorname { log } \tau,$ ; confidence 0.393
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110500/a11050066.png ; ${\bf x} = ( x _ { 1 } , \ldots , x _ { n } )$ ; confidence 0.393
@@ Line 204: / Line 204: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020171.png ; $\tilde{u}_1$ ; confidence 0.392
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007019.png ; $| \frac { \partial U ( t , s ) } { \partial t } \| \leq \frac { C } { t - s } , \quad s , t \in [ 0 , T ], $ ; confidence 0.392 NOTE: why is there a single bar on the left and a double bar on the right?
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007019.png ; $\| \frac { \partial U ( t , s ) } { \partial t } \| \leq \frac { C } { t - s } , \quad s , t \in [ 0 , T ], $ ; confidence 0.392 NOTE: why is there a single bar on the left and a double bar on the right?
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110139.png ; $r _ { N } ( a , b ) \in S _ { \text{scl} } ^ { m _ { 1 }  + m _ { 2 } - N}$ ; confidence 0.392
@@ Line 214: / Line 214: @@
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021084.png ; $l = 0 , \dots , n _ { j } - 1$ ; confidence 0.392
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018027.png ; $\operatorname{Fm} _ { T }$ ; confidence 0.392
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018027.png ; $\operatorname{Fm} _ { \tau }$ ; confidence 0.392
 . https://www.encyclopediaofmath.org/legacyimages/g/g120/g120030/g12003016.png ; $\int _ { - 1 } ^ { 1 } p ( x ) P _ { n } ( x ) E _ { n + 1 } ( x ) x ^ { k } d x = 0 , \quad k = 0 , \dots , n, $ ; confidence 0.392
@@ Line 220: / Line 220: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a012/a012090/a012090101.png ; $K ^ { 2 }$ ; confidence 0.392
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120440/b12044028.png ; $R G = B _ { 1 } \bigoplus \ldots \bigoplus B _ { n }$ ; confidence 0.392
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120440/b12044028.png ; $R G = B _ { 1 } \bigoplus \ldots \bigoplus B _ { n }.$ ; confidence 0.392
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200101.png ; $\operatorname { max } _ { k = m + 1 , \ldots , m + n } | g ( k ) | \geq \frac { 1 } { 3 } | g ( 0 ) | \prod _ { j = 1 } ^ { n } \frac { | z _ { j } | - \operatorname { exp } ( - 1 / m ) } { | z _ { j } | + 1 }$ ; confidence 0.392
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200101.png ; $\operatorname { max } _ { k = m + 1 , \ldots , m + n } | g ( k ) | \geq \frac { 1 } { 3 } | g ( 0 ) | \prod _ { j = 1 } ^ { n } \frac { | z _ { j } | - \operatorname { exp } ( - 1 / m ) } { | z _ { j } | + 1 }.$ ; confidence 0.392
 . https://www.encyclopediaofmath.org/legacyimages/z/z120/z120020/z12002037.png ; $F _ { m - n  + 1}$ ; confidence 0.392
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006094.png ; $\operatorname { lim } _ { Z \rightarrow \infty } \frac { E ^ { \text{TF} } ( \lambda Z ) } { E ^ { \text{Q} } ( \lambda Z ) } = 1$ ; confidence 0.392
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006094.png ; $\operatorname { lim } _ { Z \rightarrow \infty } \frac { E ^ { \text{TF} } ( \lambda Z ) } { E ^ { \text{Q} } ( \lambda Z ) } = 1.$ ; confidence 0.392
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d12030037.png ; $\mu_Y$ ; confidence 0.391
@@ Line 232: / Line 232: @@
 . https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o13008055.png ; $q _ { 1 } ( x )$ ; confidence 0.391
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230171.png ; $\sum _ { | \alpha | = 0 } ^ { k } ( \frac { \partial L } { \partial y _ { \alpha } ^ { \alpha }}  \circ \sigma ^ { k }  ) ( \frac { \partial } { \partial x } ) ^ { \alpha } ( Z ^ { \alpha } \circ \sigma ) \Delta.$ ; confidence 0.391
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230171.png ; $\sum _ { | \alpha | = 0 } ^ { k } \left( \frac { \partial L } { \partial y _ { \alpha } ^ { a }}  \circ \sigma ^ { k }  \right) ( \frac { \partial } { \partial x } ) ^ { \alpha } ( Z ^ { a } \circ \sigma ) \Delta.$ ; confidence 0.391
 . https://www.encyclopediaofmath.org/legacyimages/z/z130/z130040/z13004024.png ; $K _ { 7  , 11}$ ; confidence 0.391
@@ Line 238: / Line 238: @@
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064037.png ; $E ( a ) = \operatorname { det } T ( a ) T ( a ^ { - 1 } )$ ; confidence 0.391
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002036.png ; $\operatorname{P} ( A _ { 1 } \cup \ldots \cup A _ { n } )$ ; confidence 0.391
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002036.png ; $\mathsf{P} ( A _ { 1 } \cup \ldots \cup A _ { n } )$ ; confidence 0.391
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110254.png ; $q _ { \alpha } \in S ( \tilde { h } ^ { - 1 } , \tilde{g} )$ ; confidence 0.391
@@ Line 262: / Line 262: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b120220103.png ; $t _ { n  + 1} - t _ { n } \sim \varepsilon$ ; confidence 0.390
-. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520395.png ; $y _ { i } = z _ { 1 } ^ { \alpha _ { i 1 } } \ldots z _ { n } ^ { \alpha _ { i n } } , \quad i = 1 , \dots , n$ ; confidence 0.390
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520395.png ; $y _ { i } = z _ { 1 } ^ { \alpha _ { i 1 } } \ldots z _ { n } ^ { \alpha _ { i n } } , \quad i = 1 , \dots , n,$ ; confidence 0.390
 . https://www.encyclopediaofmath.org/legacyimages/d/d031/d031380/d031380221.png ; $\bf I$ ; confidence 0.390
@@ Line 280: / Line 280: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023066.png ; $q_j$ ; confidence 0.389
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090137.png ; $Z \Lambda ( n )$ ; confidence 0.389
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090137.png ; ${\bf Z} \Lambda ( n )$ ; confidence 0.389
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021057.png ; $U ( {\frak n} )$ ; confidence 0.389
@@ Line 288: / Line 288: @@
 . https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l12012033.png ; $\hat { K } _ { \text{p} }$ ; confidence 0.389
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130050/f13005026.png ; $\| \sum _ { j = 1 } ^ { m } w _ { j } . \frac { p _ { j } - p _ { i } } { \| p _ { j } - p _ { i } \| } \| > w _ { i } , i \neq j$ ; confidence 0.389
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130050/f13005026.png ; $\left\| \sum _ { j = 1 } ^ { m } w _ { j } . \frac { p _ { j } - p _ { i } } { \| p _ { j } - p _ { i } \| } \right\| > w _ { i } , i \neq j,$ ; confidence 0.389
 . https://www.encyclopediaofmath.org/legacyimages/c/c022/c022440/c022440108.png ; $\{ u _ { i } \}$ ; confidence 0.389
-. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t09408033.png ; $\square \ldots \rightarrow \pi _ { n + 1 } ( X ; A , B , ^* ) \stackrel { \partial } { \rightarrow } \pi _ { n } ( A , A \bigcap B , ^* )$ ; confidence 0.389
+. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t09408033.png ; $\square \ldots \rightarrow \pi _ { n + 1 } ( X ; A , B , ^* ) \stackrel { \partial } { \rightarrow } \pi _ { n } ( A , A \bigcap B , ^* ) \rightarrow $ ; confidence 0.389
-. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110470/c11047044.png ; $F *$ ; confidence 0.389
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110470/c11047044.png ; $F_{*}$ ; confidence 0.389
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c1301604.png ; $S \subset \Sigma ^ {\color{blue} * }$ ; confidence 0.389
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c1301604.png ; $S \subseteq \Sigma ^ {\color{blue} * }$ ; confidence 0.389
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240224.png ; $z_1 , \dots ,z_n$ ; confidence 0.389
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120240/e12024012.png ; $Z / p ^ { m }$ ; confidence 0.389 FIN QUI
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120240/e12024012.png ; ${\bf Z} / p ^ { m }$ ; confidence 0.389
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002065.png ; $| P |$ ; confidence 0.388
@@ Line 316: / Line 316: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w130/w130060/w13006030.png ; ${\cal V} _ { g , n }$ ; confidence 0.388
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240508.png ; $\operatorname{E} ( {\bf Z} _ { 13 } ) = 0$ ; confidence 0.388
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240508.png ; $\mathsf{E} ( {\bf Z} _ { 13 } ) = 0$ ; confidence 0.388
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c120010109.png ; $a \in \partial E$ ; confidence 0.388
@@ Line 328: / Line 328: @@
 . https://www.encyclopediaofmath.org/legacyimages/c/c130/c130190/c13019056.png ; $e_{k + 1} , \ldots , e _ { n }$ ; confidence 0.387
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030037.png ; $a _ { k l } ( y ) \xi _ { k } \xi _ { l } \geq \alpha | \xi | ^ { 2 }$ ; confidence 0.387
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030037.png ; $a _ { k \text{l} } ( y ) \xi _ { k } \xi _ { \text{l} } \geq \alpha | \xi | ^ { 2 }$ ; confidence 0.387
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130310/a130310110.png ; $\sum _ { | X | \geq n } \mu ( X ) \frac { T ^ { - 1 } ( \operatorname { time } _ {\cal  A } ( X ) ) } { | X | } \leq \sum _ { | X | \geq n } \mu ( X ),$ ; confidence 0.387
@@ Line 334: / Line 334: @@
 . https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520435.png ; $\dot { v } _ { i } = \tilde { \psi } _ { i } ( V ) , \quad i = 1 , \dots , n,$ ; confidence 0.387
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t120070150.png ; ${ j}_g = 1 / q + a _ { 1 } ( g ) q +ldots$ ; confidence 0.387
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t120070150.png ; ${ j}_g = 1 / q + a _ { 1 } ( g ) q +\dots$ ; confidence 0.387
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021059.png ; $i = 1 , \dots , \nu$ ; confidence 0.387
@@ Line 348: / Line 348: @@
 . https://www.encyclopediaofmath.org/legacyimages/e/e130/e130060/e13006038.png ; ${\cal C} ( Z \times _ { S } Y , X ) \cong {\cal C} ( Z , {\cal C} ( Y , X ) )$ ; confidence 0.387
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130230/m13023043.png ; $R _ { j } = {\bf R} _ { \geq 0 } v$ ; confidence 0.386
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130230/m13023043.png ; $R _ { j } = {\bf R} _ { \geq 0 } v_j$ ; confidence 0.386
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140163.png ; $( F f ) ( z ) = \sum _ { j = 1 } ^ { n } ( z _ { j } \frac { \partial f ( z ) } { \partial z _ { j } } + \bar{z} _ { j } \frac { \partial f ( z ) } { \partial \bar{z} _ { j } } )$ ; confidence 0.386
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140163.png ; $( F f ) ( z ) = \sum _ { j = 1 } ^ { n } \left( z _ { j } \frac { \partial f ( z ) } { \partial z _ { j } } + \bar{z} _ { j } \frac { \partial f ( z ) } { \partial \bar{z} _ { j } } \right).$ ; confidence 0.386
 . https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004038.png ; $X _ { g } ^ { * } = {\color{blue} \cup} _ { r \leq g } X _ { r }$ ; confidence 0.386
@@ Line 368: / Line 368: @@
 . https://www.encyclopediaofmath.org/legacyimages/g/g043/g043320/g0433206.png ; $a _ { s t }$ ; confidence 0.386
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008038.png ; $\operatorname{E} [ W _ { p } ] _ { \text{NP} } =$ ; confidence 0.386
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008038.png ; $\mathsf{E} [ W _ { p } ] _ { \text{NP} } =$ ; confidence 0.386
-. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l13008034.png ; $c_1 \operatorname{deg} I + c _ { 2 } \operatorname{log] \operatorname{ht} I$ ; confidence 0.386
+. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l13008034.png ; $c_1 \operatorname{deg} I + c _ { 2 } \operatorname{log} \operatorname{ht} I$ ; confidence 0.386
 . https://www.encyclopediaofmath.org/legacyimages/b/b130/b130060/b13006043.png ; $| E |$ ; confidence 0.386
@@ Line 398: / Line 398: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090107.png ; $\operatorname{sg} ( \pi )$ ; confidence 0.385
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130040/t13004015.png ; $( n + 1 ) a _ { n + 1 } + \alpha _ { n } = \tau$ ; confidence 0.385
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130040/t13004015.png ; $( n + 1 ) a _ { n + 1 } + a _ { n } = \tau$ ; confidence 0.385
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009035.png ; $\frac { 1 } { p _ { 2 } ( \xi , \tau ) + a i } = \frac { p _ { 3 } ( \xi , \tau ) } { 1 + a ^ { 2 } } - \frac { a i } { 1 + a ^ { 2 } }$ ; confidence 0.385
@@ Line 410: / Line 410: @@
 . https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d12030055.png ; $d r = L ^ { * } r + \langle f ^ { - 1 } ( t , Y ( t ) ) g ( t , X ( t ) , Y ( t ) ) , d Y ( t ) \rangle  { r },$ ; confidence 0.385
-. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011031.png ; $\gamma _ { 1 } ^ { 2 } = 1 , \eta _ { 2 } ^ { 2 } = \gamma _ { 3 } ^ { 2 } = \gamma _ { 4 } ^ { 2 } = - 1$ ; confidence 0.385
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011031.png ; $\gamma _ { 1 } ^ { 2 } = 1 , \gamma _ { 2 } ^ { 2 } = \gamma _ { 3 } ^ { 2 } = \gamma _ { 4 } ^ { 2 } = - 1,$ ; confidence 0.385
 . https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d13018089.png ; $f \in I _ { E }$ ; confidence 0.385
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120020/t1200204.png ; $( F ^ {\bf Z } , {\cal B} ^ {\bf Z } , \operatorname{P} )$ ; confidence 0.385
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120020/t1200204.png ; $( F ^ {\bf Z } , {\cal B} ^ {\bf Z } , \mathsf{P} )$ ; confidence 0.385
 . https://www.encyclopediaofmath.org/legacyimages/a/a011/a011380/a011380139.png ; $\frak B$ ; confidence 0.385
@@ Line 426: / Line 426: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b01747062.png ; $l_i$ ; confidence 0.384
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230147.png ; $X A X ^ { \prime } \sim L _ { 1 } ^ { ( 1 ) } ( f _ { 1 } , \frac { { k } } { 2 } ).$ ; confidence 0.384
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230147.png ; $X A X ^ { \prime } \sim L _ { 1 } ^ { ( 1 ) } \left( f _ { 1 } , \frac { { k } } { 2 } \right),$ ; confidence 0.384
 . https://www.encyclopediaofmath.org/legacyimages/m/m120/m120270/m12027045.png ; $c_{i j k}$ ; confidence 0.384
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024066.png ; $y _ { i j k } = \mu + \alpha _ { i } + \beta _ { j } + \gamma _ { i j } + e _ { i j k }$ ; confidence 0.384
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024066.png ; $y _ { i j k } = \mu + \alpha _ { i } + \beta _ { j } + \gamma _ { i j } + e _ { i j k },$ ; confidence 0.384
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120240/e12024044.png ; $E ( {\bf Q} )$ ; confidence 0.384
-. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130040/o13004014.png ; $\operatorname { lim } _ { \varepsilon \downarrow 0 } \frac { \mu _ { \varepsilon } ^ { X } ( \phi ) } { \mu _ { \varepsilon } ^ { X } ( \psi ) }$ ; confidence 0.384
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130040/o13004014.png ; $\operatorname { lim } _ { \varepsilon \downarrow 0 } \frac { \mu _ { \varepsilon } ^ { x } ( \phi ) } { \mu _ { \varepsilon } ^ { x } ( \psi ) }$ ; confidence 0.384
 . https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012039.png ; $\sum _ { j } g _ { j }  = \sum _ { i } f _ { i } = \sum _ { j } h _ { i j } = 1$ ; confidence 0.384
@@ Line 440: / Line 440: @@
 . https://www.encyclopediaofmath.org/legacyimages/c/c130/c130010/c13001037.png ; $c _ { \beta }$ ; confidence 0.384
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j130040116.png ; $P _ { K } ( v , z ) = v ^ { 2 c } \sum   c _ { i  j } ( v ^ { 2 } - 1 ) ^ { i } z ^ { j }$ ; confidence 0.384
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j130040116.png ; $P _ { K } ( v , z ) = v ^ { 2 c } \sum   c _ { i, j } ( v ^ { 2 } - 1 ) ^ { i } z ^ { j }$ ; confidence 0.384
-. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n12002072.png ; $\int _ { E } \operatorname { log } ( d \operatorname{P} / d \mu ) d \operatorname{P}$ ; confidence 0.384
+. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n12002072.png ; $\int _ { E } \operatorname { log } ( d \mathsf{P} / d \mu ) d \mathsf{P}$ ; confidence 0.384
-. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120030/h12003018.png ; $\tau ( \varphi ) ^ { \alpha } ( x ) = g ^ { i j } ( x ) ( \frac { \partial ^ { 2 } \varphi ^ { \alpha } } { \partial x ^ { i } \partial x ^ { j } } - \square ^ { M } \Gamma _ { i j } ^ { k } ( x ) \frac { \partial \varphi ^ { \alpha } } { \partial x ^ { k } } + + \square ^ { N } \Gamma _ { \beta \gamma } ^ { \alpha } ( \varphi ( x ) ) \frac { \partial \varphi \beta } { \partial x ^ { i } } \frac { \partial \varphi ^ { \gamma } } { \partial x ^ { j } } )$ ; confidence 0.384
+. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120030/h12003018.png ; $\tau ( \varphi ) ^ { \alpha } ( x ) = g ^ { i j } ( x ) \left( \frac { \partial ^ { 2 } \varphi ^ { \alpha } } { \partial x ^ { i } \partial x ^ { j } } - \square ^ { M } \Gamma _ { i j } ^ { k } ( x ) \frac { \partial \varphi ^ { \alpha } } { \partial x ^ { k } } + + \square ^ { N } \Gamma _ { \beta \gamma } ^ { \alpha } ( \varphi ( x ) ) \frac { \partial \varphi \beta } { \partial x ^ { i } } \frac { \partial \varphi ^ { \gamma } } { \partial x ^ { j } } \right),$ ; confidence 0.384
 . https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005080.png ; $V_{( n )} = 0$ ; confidence 0.384
@@ Line 458: / Line 458: @@
 . https://www.encyclopediaofmath.org/legacyimages/b/b120/b120050/b12005020.png ; $( P _ { n } ) = ( P _ { n } ( z _ { 0 } ) )$ ; confidence 0.383
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120340/b12034031.png ; $\sum _ { \alpha } \operatorname { sup } _ { D _ { r } } | c _ { \alpha } z ^ { \alpha } | < 1$ ; confidence 0.383
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120340/b12034031.png ; $\sum _ { \alpha } \operatorname { sup } _ { D _ { r } } | c _ { \alpha } z ^ { \alpha } | < 1,$ ; confidence 0.383
 . https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520243.png ; $\bar { A } _ { i j }$ ; confidence 0.383
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c1202805.png ; $X *$ ; confidence 0.383
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c1202805.png ; $X_{*}$ ; confidence 0.383
 . https://www.encyclopediaofmath.org/legacyimages/h/h130/h130120/h13012011.png ; $x \in G_1$ ; confidence 0.383
@@ Line 474: / Line 474: @@
 . https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m130250102.png ; $H ^ { s } ( {\bf R} ^ { n } )$ ; confidence 0.382
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018068.png ; $r _ { 1 } ( t , s ) = \prod _ { i = 1 } ^ { N } ( t _ { i } \bigwedge s _ { i } - t _ { i } s _ { i } )$ ; confidence 0.382
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018068.png ; $r _ { 1 } ( t , s ) = \prod _ { i = 1 } ^ { N } ( t _ { i } \bigwedge s _ { i } - t _ { i } s _ { i } ),$ ; confidence 0.382
 . https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a0100204.png ; $\{ E _ { n _ { 1 }  \ldots n _ { k } }\}$ ; confidence 0.382
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013023.png ; $= \operatorname { exp } ( x P _ { 0 } z + \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } ) g ( z ) . . \operatorname { exp } ( - x P _ { 0 } z - \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } ),$ ; confidence 0.382
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013023.png ; $= \operatorname { exp } \left( x P _ { 0 } z + \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } \right) g ( z ) . . \operatorname { exp } \left( - x P _ { 0 } z - \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } \right),$ ; confidence 0.382
 . https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010222.png ; $E_i$ ; confidence 0.382
@@ Line 486: / Line 486: @@
 . https://www.encyclopediaofmath.org/legacyimages/l/l110/l110040/l11004017.png ; $l = \{ . , e , ^{- 1} , \vee , \wedge \}$ ; confidence 0.382
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120130/l12013026.png ; $f _ { 1 } , \dots , f _ { m } \in Q ( X _ { 1 } , \dots , X _ { n } )$ ; confidence 0.382
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120130/l12013026.png ; $f _ { 1 } , \dots , f _ { m } \in {\bf Q} ( X _ { 1 } , \dots , X _ { n } )$ ; confidence 0.382
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120190/c12019051.png ; $c _ { q } = ( - 1 ) ^ { q } q ! / ( 2 q ) !$ ; confidence 0.382
@@ Line 496: / Line 496: @@
 . https://www.encyclopediaofmath.org/legacyimages/k/k130/k130060/k1300609.png ; $\{ a _ { 1 } + 1 , \dots , a _ { k } + 1 \}$ ; confidence 0.381
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c130160141.png ; $\operatorname{ATIME} [ n ^ { Q ( 1 ) } ] = \operatorname { PSPAce }$ ; confidence 0.381
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c130160141.png ; $\operatorname{ATIME} [ n ^ { O ( 1 ) } ] = \operatorname { PSPACE }$ ; confidence 0.381
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180122.png ; ${\cal E} \overset{\approx}{\to} {\cal E}  {* * }$ ; confidence 0.381
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180122.png ; ${\cal E} \overset{\approx}{\to} {\cal E} _ {* * }$ ; confidence 0.381
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054017.png ; $( x _ { i j } ( a ) , x _ { k l } ( b ) ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } i \neq 1 , j \neq k }, \\ { x _ { il } ( a b ) } & { \text { if } i \neq 1 , j = k }. \end{array} \right.$ ; confidence 0.381
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054017.png ; $( x _ { i j } ( a ) , x _ { k \text{l} } ( b ) ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } i \neq \text{l} , j \neq k }, \\ { x _ { i \text{l} } ( a b ) } & { \text { if } i \neq \text{l} , j = k }. \end{array} \right.$ ; confidence 0.381
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040405.png ; ${\bf P} _ { U }\bf K$ ; confidence 0.381
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040405.png ; ${\bf P} _ { \text{U} } \mathsf{K}$ ; confidence 0.381
 . https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005092.png ; $v _ { n } = v / z ^ { n }$ ; confidence 0.381
@@ Line 510: / Line 510: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090259.png ; $\mathfrak { B } = \{ e _ { \pm \alpha} , h _ { \beta } : \alpha \in \Phi ^ { + } , \beta \in \Sigma \}.$ ; confidence 0.381
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120270/s1202705.png ; $Q _ { n } [ f ] = \sum _ { v = 1 } ^ { n } a _ { v , n } f ( x _ { v , n } )$ ; confidence 0.381
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120270/s1202705.png ; $Q _ { n } [ f ] = \sum _ { v = 1 } ^ { n } a _ { v , n } f ( x _ { v , n } ),$ ; confidence 0.381
 . https://www.encyclopediaofmath.org/legacyimages/k/k120/k120070/k12007011.png ; $C _ { 0 } ( t )$ ; confidence 0.381
@@ Line 526: / Line 526: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a011/a011650/a01165043.png ; $r _ { j }$ ; confidence 0.381
-. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042010.png ; $( \phi \bigotimes \text { id } ) \Psi _ { V , W } = \Psi _ { V , Z } ( \text { id } \bigotimes \phi ) , \forall \phi : W \rightarrow Z$ ; confidence 0.381
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042010.png ; $( \phi \bigotimes \text { id } ) \Psi _ { V , W } = \Psi _ { V , Z } ( \text { id } \bigotimes \phi ) , \forall \phi : W \rightarrow Z,$ ; confidence 0.381
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130410/s13041026.png ; $\langle p , q \rangle = \int _ {\bf R } p q d \mu _ { 0 } + \lambda \int _ {\bf R } p ^ { \prime } q ^ { \prime } d \mu _ { 1 }$ ; confidence 0.381
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130410/s13041026.png ; $\langle p , q \rangle = \int _ {\bf R } p q d \mu _ { 0 } + \lambda \int _ {\bf R } p ^ { \prime } q ^ { \prime } d \mu _ { 1 },$ ; confidence 0.381
 . https://www.encyclopediaofmath.org/legacyimages/f/f120/f120240/f12024053.png ; $J _ { t }$ ; confidence 0.380
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007062.png ; $H ^ { n } ( {\cal C} , M ) = \operatorname { Ext } _ { Z {\bf C} } ^ { n } ( {\cal Z} , M )$ ; confidence 0.380
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007062.png ; $H ^ { n } ( {\cal C} , M ) = \operatorname { Ext } _ { Z {\bf C} } ^ { n } ( {\cal Z} , M ),$ ; confidence 0.380
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007043.png ; $\underline{\operatorname{lim}} \leftarrow$ ; confidence 0.380
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013043.png ; $\frac { d N ^ { i } } { d t } = \lambda _ { ( i ) } N ^ { i } ( 1 - \frac { N ^ { i } } { K _ { ( i ) } } ) , \quad i = 1 , \ldots , n$ ; confidence 0.380
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013043.png ; $\frac { d N ^ { i } } { d t } = \lambda _ { ( i ) } N ^ { i } \left( 1 - \frac { N ^ { i } } { K _ { ( i ) } } \right) , \quad i = 1 , \ldots , n,$ ; confidence 0.380
 . https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g120040136.png ; $G ^ { 3 }$ ; confidence 0.380
@@ Line 544: / Line 544: @@
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w1202106.png ; $H H ^ { T } = H ^ { T } H = n I _ { n }$ ; confidence 0.380
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130300/a13030094.png ; $I ^ { 1 } ( G )$ ; confidence 0.380
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130300/a13030094.png ; ${\bf l}^ { 1 } ( G )$ ; confidence 0.380
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301307.png ; $Q_i$ ; confidence 0.380
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040213.png ; $\operatorname{Alg} \operatorname{Mod}^ { *S } S5$ ; confidence 0.380
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040213.png ; $\operatorname{Alg} \operatorname{Mod}^ { *S } \operatorname{S} 5$ ; confidence 0.380
 . https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w12009024.png ; $0 \leq r \in \bf Z$ ; confidence 0.380
@@ Line 554: / Line 554: @@
 . https://www.encyclopediaofmath.org/legacyimages/c/c130/c130250/c13025012.png ; $z _ { k } ^ { T } ( t ) = ( z _ { k , 1 } ( t ) , \dots , z _ { k , p } ( t ) )$ ; confidence 0.380
-. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d13006041.png ; $j_1 , \dots , j _ { k }$ ; confidence 0.380 FIN QUI
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d13006041.png ; $j_1 , \dots , j _ { k }$ ; confidence 0.380
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018084.png ; $s ^ { \prime \prime } \rightarrow$ ; confidence 0.380
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018084.png ; ${\bf Alg} : \text{ ''logics"}\to \text{''pairs of classes of algebras"}$ ; confidence 0.380
 . https://www.encyclopediaofmath.org/legacyimages/g/g044/g044980/g04498039.png ; $v _ { j }$ ; confidence 0.380
-. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080650/r0806501.png ; $y _ { i }$ ; confidence 0.380
+. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080650/r0806501.png ; $y _ { t }$ ; confidence 0.380
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130070/s1300709.png ; $s \in S , u , v \in H , \phi : S \times H \rightarrow S$ ; confidence 0.380
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130070/s1300709.png ; $s \in S , u , v \in H , \phi : S \times H \rightarrow S,$ ; confidence 0.380
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004024.png ; $P _ { 2 _ { 1 } } = \frac { v - v ^ { 3 } } { z } + v z$ ; confidence 0.380
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004024.png ; $P _ { 2 _ { 1 } } = \frac { v - v ^ { 3 } } { z } + v z.$ ; confidence 0.380
 . https://www.encyclopediaofmath.org/legacyimages/s/s120/s120160/s12016019.png ; $| I _ { 1 } ( f ) - U ^ { i } ( f ) |$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130260/a1302609.png ; $\operatorname { tcm } ( 1 , \ldots , n ) ^ { 3 }$ ; confidence 0.379
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130260/a1302609.png ; $\operatorname { lcm } ( 1 , \ldots , n ) ^ { 3 }$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110080/d11008053.png ; $w _ { 1 } , \dots , w _ { w }$ ; confidence 0.379
+. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110080/d11008053.png ; $w _ { 1 } , \dots , w _ { m }$ ; confidence 0.379
 . https://www.encyclopediaofmath.org/legacyimages/h/h130/h130090/h13009033.png ; $G ^ { * } \mu$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130300/a13030056.png ; $( \mathfrak { S } ( T R _ { 1 } \ldots R _ { N } ) : n \in N )$ ; confidence 0.379
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130300/a13030056.png ; $( \mathfrak { S } ( T R _ { 1 } \ldots R _ { n} ) : n \in \bf N )$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m13014023.png ; $r = r 2$ ; confidence 0.379
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m13014023.png ; $r = r_2$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062220/m06222062.png ; $P _ { y } - 1$ ; confidence 0.379
+. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062220/m06222062.png ; $P _ { n - 1 }$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120210/m12021013.png ; $u \in S ^ { n - 1 } : = \{ v \in E : \langle v , v \} = 1 \}$ ; confidence 0.379
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120210/m12021013.png ; $u \in S ^ { n - 1 } : = \{ v \in {\bf E} : \langle v , v \rangle = 1 \}$ ; confidence 0.379
 . https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c120210102.png ; $P _ { \theta }$ ; confidence 0.379
@@ Line 586: / Line 586: @@
 . https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a130070106.png ; $d | n$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140100.png ; $H _ { 2 }$ ; confidence 0.379
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140100.png ; $H _ { 2n }$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f120110149.png ; $K \cap R ^ { x }$ ; confidence 0.379
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f120110149.png ; $K \cap {\bf R} ^ { n }$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f120110157.png ; $G ( \zeta ) = O ( e ^ { \varepsilon | \zeta | + H _ { K } \langle \operatorname { lm } \zeta \rangle } )$ ; confidence 0.379
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f120110157.png ; $G ( \zeta ) = O ( e ^ { \varepsilon | \zeta | + H _ { K } ( \operatorname { lm } \zeta ) } )$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l12012041.png ; $\hat { K } _ { p } = R$ ; confidence 0.379
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l12012041.png ; $\hat { K } _ { \text{p} } = \bf R$ ; confidence 0.379
 . https://www.encyclopediaofmath.org/legacyimages/d/d030/d030090/d0300902.png ; $R _ { \nu }$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b130290169.png ; $h _ { \phi } = \operatorname { rank } _ { A } M - \sum _ { i = 1 } ^ { d - 1 } \left( \begin{array} { c } { d - 1 } \\ { i - 1 } \end{array} \right) h _ { i }$ ; confidence 0.379
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b130290169.png ; $h _ { d } = \operatorname { rank } _ { A } M - \sum _ { i = 1 } ^ { d - 1 } \left( \begin{array} { c } { d - 1 } \\ { i - 1 } \end{array} \right) h _ { i }$ ; confidence 0.379
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010035.png ; $X = R$ ; confidence 0.378
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010035.png ; $X = \bf R$ ; confidence 0.378