Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/75"

Latest revision as of 22:51, 29 June 2020

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1. ; $( 2 \pi ) ^ { - 2 n } \int _ { \mathbf{R} ^ { 2 n } } e ^ { i q \mathcal{X} } e ^ { i p \mathcal{D} } \hat { \sigma } ( p , q ) d p d q,$ ; confidence 0.122

2. ; $\Psi _ { V , W }$ ; confidence 0.122

3. ; $( \nabla ^ { 2 } + k ^ { 2_0 } + k ^ { 2_0 }v ( x ) ) u ( x , y , k _ { 0 } ) = - \delta ( x - y ) \text { in } \mathbf{R} ^ { 3 },$ ; confidence 0.122

4. ; $= ( ( F ( \cdot ) , h ( \cdot , x ) ) _ { \mathcal{H} } , ( h ( \text{..} , y ) , h ( \text{..} , x ) ) _ { \mathcal{H} } ) _ { H } =$ ; confidence 0.122

5. ; $( H , ( \cdot | \cdot ) )$ ; confidence 0.122

6. ; $\mathfrak{h} _ { R } ^ { * }$ ; confidence 0.122

7. ; $r _ { i } s _ { j } \in C _ { ( i + j ) \operatorname { mod } 2}$ ; confidence 0.122

8. ; $\langle T [ \phi ] , [ \psi ] \rangle _ { L _ { \text{C} } ^ { p } ( G ) , L _ { \text{C} } ^ { p^{\prime} } ( G ) } \neq 0.$ ; confidence 0.122

9. ; $\| G \| _ { \infty } = \operatorname { sup } _ { \| x \| _ { 2 } \leq 1 } \| y \| _ { 2 }.$ ; confidence 0.122

10. ; $d \hat { \Omega } _ { n } = P _ { + } ^ { n / N } \left( \frac { d w } { w } \right)$ ; confidence 0.122

11. ; $c_L$ ; confidence 0.121

12. ; $\left\{ \begin{array} { l } { \Delta v = 0 } & {\text{in} \ \mathbf{C}^{n} \setminus \overline{D}, }\\ { v = \phi} & { \text { on } \partial D, } \\ { | v | \leq \frac { c } { | z | ^ { 2 n - 2 } }. } \end{array} \right.$ ; confidence 0.121

13. ; $r_1 , \ldots , r_n$ ; confidence 0.121

14. ; $ c _ { 1 } / a _ { 1 } \geq \ldots \geq c _ { n } / a _ { n }$ ; confidence 0.121

15. ; $| i \rangle$ ; confidence 0.121

16. ; $\mathcal{K} =\mathcal{ I} _ { 1 } \lhd \ldots \lhd \mathcal{ I}_ { r } \lhd \mathcal{T} ( S )$ ; confidence 0.121

17. ; $\| p _ {n } ^ { \langle \alpha - 1 ,\, \beta - 1 \rangle } \| _ { \mu _ { 0 } } = o( n )$ ; confidence 0.121

18. ; $u_2$ ; confidence 0.121

19. ; $* : \mathcal{G} \text{l} _ { Q } ( d ) \times \mathcal{A} _ { Q } ( d ) \rightarrow \mathcal{A} _ { Q } ( d )$ ; confidence 0.120

20. ; $\tilde { a } ( e ^ { i \theta } ) = a ( e ^ { - i \theta } )$ ; confidence 0.120

21. ; $\mathbf{C} ^ { n } \subset \mathbf{P} ^ { n }$ ; confidence 0.120

22. ; $p _ { i } ( z ) z ^ { \lambda } = \sum _ { n = 0 } ^ { N } a ^ { n _ { i } } z ^ { n } ( \frac { \partial } { \partial z } ) ^ { n } z ^ { \lambda }.$ ; confidence 0.120

23. ; $b ( \cdot , \cdot )$ ; confidence 0.120

24. ; $l w \equiv 0$ ; confidence 0.120

25. ; $= \operatorname { lim } _ { n \rightarrow 0 } \left( \sum _ { j_n = 1 } ^ { J _ { n } } K ( x , y _ { j _n } ) c _ { j _n } , \sum _ { m_n = 1 } ^ { J _ { n } } K ( x , y _ { m_n } ) c _ { m_n } \right) _ { 1 } =$ ; confidence 0.120

26. ; $\Updownarrow a x - x c = 0 \text { and } b x - x d = 0,$ ; confidence 0.120

27. ; $e _ { 1 } , \dots , e _ { k }$ ; confidence 0.120

28. ; $\mathcal{H} _ { uc } ^ { \infty } ( B _ { E } ) \equiv$ ; confidence 0.120

29. ; $t ^ { * } : H ^ { n } ( S ^ { n } ) \rightarrow H ^ { n } ( \Gamma _ { S ^ { n } } )$ ; confidence 0.119

30. ; $\lfloor n / 2 \rfloor$ ; confidence 0.119

31. ; $\left( \begin{array} { c } { 0 } \\ { G _ { i + 1 } } \end{array} \right) = \left\{ G _ { i } + Z _ { i } G _ { i } \frac { J g _ { i } ^ { * } g _ { i } } { g _ { i } J g _ { i } ^ { * } } \right\} \Theta _ { i },$ ; confidence 0.119

32. ; $UM$ ; confidence 0.119

33. ; $\hat { \tau }_1 = \nabla \tau ,\, \hat { \tau } _ { n } = \sum _ { i + j = n } \phi ( \hat { \tau } _ { i } \bigcup \hat { \tau } _ { j } ),$ ; confidence 0.119

34. ; $\operatorname { Hom}_{K_\infty}( \Lambda ^ { \bullet } ( \mathfrak { g } / \mathfrak { k } ) , \mathcal{A} ( \Gamma \backslash G ( \mathbf{R} ) ) \bigotimes \mathcal{M} _ { \text{C} } ) \overset{\sim}{\rightarrow}$ ; confidence 0.119

35. ; $\mathbf{Me} ^ { * \text{L} _{\mathfrak { N }}}_{\mathcal{S}_P }$ ; confidence 0.119

36. ; $\Psi ( x ^ { n } \bigotimes x ^ { m } ) = q ^ { n m } x ^ { m } \bigotimes x ^ { n }$ ; confidence 0.119

37. ; $\mathcal{H} = \mathcal{H} ^ { \text{in} } = \mathcal{H} ^ { \text{out} }$ ; confidence 0.119

38. ; $\hat { G }_{\text{inn}}$ ; confidence 0.119

39. ; $x ( t + ) = x ( t ) \text { for all } \ 0 \leq t < 1 ,\, x ( t - ) = \operatorname { lim } _ { s \uparrow t } x ( s ) \text { exists for all } 0 < t \leq 1.$ ; confidence 0.118

40. ; $E ( x _ { 0 } , y _ { 0 } ) , \ldots , E ( x _ { n - 1} , y _ { n - 1} ) \vdash_ { \mathcal{D} }$ ; confidence 0.118

41. ; $( \mathcal{A} ^ { * } f ) _ { n } ( X ) = \sum _ { i = 1 } ^ { n } f _ { n - 1 } ( x _ { 1 } , \dots , x _ { i - 1} , x _ { i + 1} , \dots , x _ { n } ).$ ; confidence 0.118

42. ; $P _ { R } ^ { \# } ( n ) = \frac { 1 } { n } q ^ { n } + O \left( \frac { 1 } { n } q ^ { n / 2 } \right) \text { as } n \rightarrow \infty,$ ; confidence 0.118

43. ; $F ( \mathcal{H} ) = \mathbf{C} \oplus \oplus _ { n = 1 } ^ { \infty } \mathcal{H} ^ { \otimes n }$ ; confidence 0.118

44. ; $L = L _ { \overline{0} } \oplus L _ { \overline{1} }$ ; confidence 0.118

45. ; $\| h_n \|$ ; confidence 0.118

46. ; $q _ { \Lambda }$ ; confidence 0.118

47. ; $\sum _ { \mathbf{k} } c_{ \mathbf{k} } e ^ { i \mathbf{kx} }$ ; confidence 0.118

48. ; $O ( e ^ { - \varepsilon | \operatorname { Re } z | - H _ { L } ( \operatorname { Re } z )} )$ ; confidence 0.118

49. ; $u_{ -} \sharp$ ; confidence 0.118

50. ; $\operatorname { St } _ { G } ( n ) = \cap _ { | u | = n } \operatorname { St } _ { G } ( u )$ ; confidence 0.118

51. ; $R _ { n } \in \mathcal{B} ( E _ { n } , E _ { n - 1 } )$ ; confidence 0.118

52. ; $\left\{ \begin{array}{l}{ ( T - z I ) x = K J \varphi _ { - }, }\\{ \varphi _ { + } = \varphi _ { - } - 2 i K ^ { * } x, }\end{array} \right.$ ; confidence 0.118

53. ; $H _ { 0 } ^ { ( m ) } = 1 ,\, H _ { k } ^ { ( m ) } = \operatorname { det } ( c_{ m + i + j} ) _ { i ,\, j = 0 } ^ { k - 1 }$ ; confidence 0.117

54. ; $\sigma _ { T } ( A , \mathcal{X} ) = \left\{ ( a _ {ii} ^ { ( 1 ) } , \ldots , a _ { ii } ^ { ( n ) } ) : 1 \leq i \leq \operatorname { dim } \mathcal{X} \right\}.$ ; confidence 0.117

55. ; $\int _ { 0 } ^ { \infty } \frac { f * u _ { t } * v _ { t } } { t } d t = c _ { u , v }\, f,$ ; confidence 0.117

56. ; $\Gamma ( L ^ { 2 } ( \mathbf{R} ) ) = \bigoplus _ { n = 0 } ^ { \infty } \sqrt { n !} L ^ { 2 } ( \mathbf{R} )^{ \widehat { \bigotimes } n } \simeq \bigoplus _ { n = 0 } ^ { \infty } \sqrt { n !} \widehat{ L ^ { 2 } ( \mathbf{R} ^ { n } ) }.$ ; confidence 0.117

57. ; $\operatorname { Mod } ^ { * S} \mathcal{D}= \operatorname { Mod } ^ { * \text{L}} \mathcal{ D }$ ; confidence 0.117

58. ; $E \subseteq \operatorname { Epi } ( \mathfrak { A } )$ ; confidence 0.117

59. ; $\| x \circ y \| \leq \| x \| \| y \|$ ; confidence 0.117

60. ; $G _ { p q } ^ { mn }$ ; confidence 0.117

61. ; $k = q ^ { d - 1 }$ ; confidence 0.117

62. ; $Iq \neq 0$ ; confidence 0.117

63. ; $f ( z ) = e ^ { - ( G ( z , a ) + i \tilde{G} ( z , a ) ) }$ ; confidence 0.117

64. ; $S _ { M } ( s ) = \sum _ { m \in M } a _ { m } e ^ { - \lambda_{m} s },$ ; confidence 0.116

65. ; $u _ { n } \in \mathfrak{F}$ ; confidence 0.116

66. ; $\langle \mathbf{A} / \tilde{\Omega}_{\mathcal{D}} F , F / \tilde{\Omega}_{\mathcal{D}} F \rangle$ ; confidence 0.116

67. ; $N ^ { 1 / p }$ ; confidence 0.116

68. ; $[ X ] \mapsto \chi _ { R } ( [ X ] ) = \sum _ { m = 0 } ^ { \infty } ( - 1 ) ^ { m } \operatorname { dim } _ { K } \operatorname { Ext } _ { R } ^ { m } ( X , X )$ ; confidence 0.116

69. ; $w ^ { q } = w _ { 1 } ^ { q _ { 1 } } \ldots w _ { n } ^ { q _ { n } }$ ; confidence 0.116

70. ; $p_{ m , 1}$ ; confidence 0.116

71. ; $\nabla ( a \Phi ) = d a \bigotimes \Phi + a \nabla \Phi \in \bigotimes \square ^ { q + 1 } \mathcal{E}$ ; confidence 0.116

72. ; $\left\{ \begin{array} { l } { \operatorname{max} \ \ \sum _ { j = i } ^ { N } \beta _ { j } v _ { j } } \\ { \text { subject to } \ \ \sum _ { j = 1 } ^ { n } a _ { i j } v _ { j } \leq \mu _ { i } } \\ { v _ { j } \geq 0. } \end{array} \right.$ ; confidence 0.116

73. ; $\xi _ { 1 } ^ { i } , \ldots , \xi _ { 2 ^ { i - 1 } ( n + 1 ) } ^ { i } $ ; confidence 0.116

74. ; $d_{s}$ ; confidence 0.116

75. ; $\lambda = \left. \begin{array} { l l l } { \bullet } & { \bullet } & { \bullet } & { \bullet } \\ { \square } & { \bullet } & { \bullet } & { \square } \\ { \square } & { \square } & { \bullet } & { \square } \end{array} \right.$ ; confidence 0.116

76. ; $Q _ { 2 n + 1 } ( z ) = \frac { - 1 } { H _ { 2 n + 1 } ^ { ( - 2 n ) } } \left| \begin{array} { c c c c } { c_{ - 2 n - 1} } & { \cdots } & { c_{ - 1} } & { z ^ { - n - 1 } } \\ { \vdots } & { \square } & { \vdots } & { \vdots } \\ { c_{ - 1} } & { \cdots } & { c _ { 2 n - 1 } } & { z ^ { n - 1 } } \\ { c_0 } & { \cdots } & { c _ { 2 n } } & { z ^ { n } e n d } \end{array} \right|,$ ; confidence 0.116

77. ; $\forall x \forall v _ { 1 } \ldots \forall v _ { n } \exists y \forall v ( v \in y \leftrightarrow ( v \in x \bigwedge \varphi ) ).$ ; confidence 0.115

78. ; $a _ { n } = \sum _ { 0 } ^ { n } b _ { n - j} u _ { j } ,\; n \geq 0,$ ; confidence 0.115

79. ; $\mathfrak { g } _ { \alpha }$ ; confidence 0.115

80. ; $=\frac { m } { 1 + a ^ { 2 } } \left\{ \int _ { 0 } ^ { z } \frac { p _ { 1 } ( s ) - p _ { 0 } ( s ) } { s ^ { 1 - \frac { m } { 1 + a i } } } e ^ { \frac { m } { 1 + a ^ { 2 } } \int _ { 0 } ^ { s } \frac { p _ { 0 } ( t ) - 1 } { t } d t } d s + + \frac { 1 + a ^ { 2 } } { m } z ^ { \frac { m } { 1 + a i } } e ^ { \frac { m } { 1 + a ^ { 2 } } \int _ { 0 } ^ { z } \frac { p _ { 0 } ( t ) - 1 } { t } d t} \right\}.$ ; confidence 0.115

81. ; $u = \left\{ \begin{array} { c c } { \overline { u } } & { \text { for } \frac { i T } { k } \leq t < ( i + a ) \frac { T } { k }; } \\ { } & { 0 \leq i \leq k - 1, } \\ { 0 } & { \text { for } ( i + a ) \frac { T } { k } \leq t \leq ( i + 1 ) \frac { T } { k }, } \\ { } & { \text { and for } \ t = T ; 0 \leq i \leq k - 1. } \end{array} \right.$ ; confidence 0.115

82. ; $\operatorname{p}\cdot \operatorname{dim} _ { \Lambda } T$ ; confidence 0.114

83. ; $u _ { t } + a ( t ) u _ { x } + b ( t ) u ^ { p } u _ { x } - u _ { xxt } = 0$ ; confidence 0.114

84. ; $\Sigma _ { n = 1 } ^ { \infty } \| T _ { x _ { n } } \| _ { X } ^ { r } < \infty$ ; confidence 0.114

85. ; $\overrightarrow{ P _ { i } P _ { \text{l}_1 } } , \overrightarrow{ P _ { \text{l}_1 } P _ { \text{l}_2 } } , \dots , \overrightarrow{ P _ { \text{l}_m } P _ { \text{l}_{m+1} } },$ ; confidence 0.114

86. ; $\| \Delta _ { h _ { i } } ^ { 2 } f _ { x _ { i } } ^ { ( r _ { i } ^ { * } ) } \| _ { L _ { p } ( \Omega _ { 2 |h _ { i }| } | ) } \leq M _ { i } | h _ { i } |,$ ; confidence 0.114

87. ; $f \in \operatorname { Car } _ { \text{loc} } ( I \times G )$ ; confidence 0.114

88. ; $= \{ \langle b _ { 0 } , \dots , b _ { i - 1} , a , b _ { i + 1} , \dots , b _ { n - 1 } \rangle : a \in U \ \text{and}$ ; confidence 0.114

89. ; $\overline { A } _ { 1 } , \dots , \overline { A } _ { n }$ ; confidence 0.114

90. ; $p_3$ ; confidence 0.114

91. ; $x _ { 11 } ( \cdot ) , \ldots , x _ { p n } ( \cdot )$ ; confidence 0.113

92. ; $= \sum _ { j _ { n } ,\, m _ { n } } ^ { J _ { n } } K ( y _ { m _ { n } } , y _ { j _ { n } } ) c _ { j _ { n } } \overline { c_{m _ { n }}} =$ ; confidence 0.113

93. ; $x \rightarrow \underline { f } \square_{\alpha} ( x )$ ; confidence 0.113

94. ; $\operatorname { ch } V ( \lambda ) = \frac { \sum _ { w \in W } ( - 1 ) ^ { l ( w ) } e ^ { w ( \lambda + \rho ) - \rho } } { \prod _ { \alpha \in \Delta ^ { - }} ( 1 - e ^ { \alpha } ) ^ { \text{dim} \mathfrak{g} _ { \alpha } } }.$ ; confidence 0.113

95. ; $B _ { j } ( z ) = \sum _ { l = 0 } ^ { \rho _ { s + 1 } } R _ { l + 1 } ^ { ( s + 1 ) } ( z ) \lambda _ { l j } ^ { ( s + 1 ) },$ ; confidence 0.113

96. ; $\operatorname { SL} _ { n } ( K )$ ; confidence 0.113

97. ; $\exists v _ { i } \varphi ( v _ { 0 } , \dots , v _ { n - 1} )$ ; confidence 0.113

98. ; $h _ { z }$ ; confidence 0.113

99. ; $\{ M ( \alpha ) \text { pr} _ { \text {dom } \alpha } - \text { pr}_{ \text {codom } \alpha } \}_{ \alpha} \quad \text { for } n = 0,$ ; confidence 0.112

100. ; $q_{ R} ( x ) = \sum _ { j \in Q _ { 0 } } x _ { j } ^ { 2 } - \sum _ {( \beta : i \rightarrow j ) \in Q _ { 1 } } x _ { i } x _ { j } + \sum _ { ( \beta : i \rightarrow j ) \in Q _ { 1 } } r _ { i ,\, j } x _ { i } x _ { j },$ ; confidence 0.112

101. ; $\mathcal{X} / J$ ; confidence 0.112

102. ; $\operatorname { FMod} ^ { * \text{L}} \mathcal{D}$ ; confidence 0.112

103. ; $Y ( L ( - 1 ) v , x ) = ( d / d x ) Y ( v , x )$ ; confidence 0.112

104. ; $\sum _ { i ,\, j = 1 } ^ { m } a _ { i ,\, j } ( x ) \xi _ { i } \xi _ { j } \geq \delta | \xi | ^ { 2 }$ ; confidence 0.112

105. ; $e _ { n } ( H _ { d } ^ { k } ) \leq c _ { k , d , \delta} \cdot n ^ { - k + \delta } , \forall n,$ ; confidence 0.112

106. ; $\psi ( y + 2 \pi p ) = e ^ { 2 \pi i \eta \cdot p } \psi ( y )\, \text { for a.e. } \ y \in \mathbf{R} ^ { N }.$ ; confidence 0.112

107. ; $a _ { 1 } , \dots , a _ { n } \in G$ ; confidence 0.112

108. ; $( \text{LD} ) v ^ { * } = \left\{ \begin{array} { c l } { \operatorname { max } } & { q } \\ { s.t. } & { q \leq c ^ { T } x ^ { ( k ) } + u _ { 1 } ^ { T } ( A _ { 1 } x ^ { ( k ) } - b _ { 1 } ), } \\ { } & { \forall k \in P, } \\ { 0 \leq } & { c ^ { T } \tilde{x} ^ { ( k ) } + u _ { 1 } ^ { T } A _ { 1 } \tilde{x} ^ { ( k ) } , \forall k \in R, } \\ { u _ { 1 } \geq 0. } \end{array} \right.$ ; confidence 0.111

109. ; $x = \tilde { x }$ ; confidence 0.111

110. ; $F _ { m n } = \frac { \chi _ { m } ^ { 2 } / m } { \chi _ { n } ^ { 2 } / n },$ ; confidence 0.111

111. ; $q _ { m } ( x )$ ; confidence 0.111

112. ; $( \cap _ { n = 0 } ^ { \infty } W _ { n } ) \cap E \neq \emptyset$ ; confidence 0.111

113. ; $( d H ) ^ { c _ { n } d ^ { n^{2} } }$ ; confidence 0.111

114. ; $\operatorname { id} \bigotimes r _ { W } = \Phi _ { V , 1 , W } \circ ( l _ { V } \bigotimes \text { id } ).$ ; confidence 0.111

115. ; $\Lambda _ { n } - h ^ { \prime } T _ { n } \rightarrow - h ^ { \prime } \Gamma h / 2$ ; confidence 0.111

116. ; $\mathcal{H} ^ { n}$ ; confidence 0.111

117. ; $P ( t ) = \prod _ { m = 1 } ^ { n } ( t - t _ { m } ) ^ { r _ { m } } ; \quad q _ { i } ( t ) = \left\{ \frac { ( t - t _ { i } ) ^ { r _ { i } } } { P ( t ) } \right\} _ { ( r _ { i } - 1 ; t _ { i } ) };$ ; confidence 0.111

118. ; $d \sigma _ { r }$ ; confidence 0.110

119. ; $C^{ 2 , \lambda }$ ; confidence 0.110

120. ; $\mathsf{E} | W ^ { a } ( t ) | \sim \left\{ \begin{array} { l l } { \sqrt { \frac { 8 t } { \pi } } , } & { d = 1, } \\ { \frac { 2 \pi t } { \operatorname { log } t } , } & { d = 2, } \\ { \kappa _ { a } t , } & { d \geq 3, } \end{array} \right.$ ; confidence 0.110

121. ; $\mathbf{P} ^ { n }$ ; confidence 0.110

122. ; $\mathbf{b}$ ; confidence 0.110

123. ; $\omega _ { \text{WP} } = \Sigma _ { j } d \text{l} _ { j } \bigwedge d \tau _ { j },$ ; confidence 0.110

124. ; $\langle \cdot , \cdot \rangle : A \otimes H \rightarrow k $ ; confidence 0.110

125. ; $g _ { k , 1} ( z ) = g _ { k } ( z );$ ; confidence 0.110

126. ; $I R F$ ; confidence 0.109

127. ; $H ^ { \bullet } ( \partial ( \Gamma \backslash X ) , \tilde { \mathcal{M} } ) = H ^ { 0 } \bigoplus H ^ { 1 } \overset{\sim}{\rightarrow} \mathbf{Q} ^ { h } \bigoplus \mathbf{Q} ^ { h }.$ ; confidence 0.109

128. ; $J ( z ) = \sum _ { n } \operatorname { Tr } ( e | _{V _ { n }} ) q ^ { n }$ ; confidence 0.109

129. ; $u \in \mathfrak { F }$ ; confidence 0.109

130. ; $t ( M ; x , y ) = \sum _ { S \subseteq E } ( x - 1 ) ^ { r ( M ) - r ( S ) } ( y - 1 ) ^ { | S | - r ( S )}.$ ; confidence 0.109

131. ; $\operatorname { max} \Pi_ { \tilde{\mathbf{c}}^{ \text{T}} \mathbf{x} } ( \tilde { G } )$ ; confidence 0.109

132. ; $Y ^ { e } = X ^ { d }$ ; confidence 0.109

133. ; $\mathfrak{b}$ ; confidence 0.109

134. ; $3 ^ { C _ { m} ^ { 1 } + C _ { m } ^ { 2 } + C _ { m } ^ { 3 } }$ ; confidence 0.109

135. ; $L_{ \gamma , 1}$ ; confidence 0.109

136. ; $\mathbf{Z} ^ { + } [ x _ { 1 } , \ldots , x _ { n } ] ^ { \mathcal{S} _ { n } }$ ; confidence 0.109

137. ; $F _ { L _ { D } } ( a , x ) = a ^ { - \text { Tait } ( L _ { D } ) } \Lambda _ { D } ( a , x )$ ; confidence 0.108

138. ; $ \Xi = ( \hat { x } , \hat { \xi } )$ ; confidence 0.108

139. ; $w _ { 2 ^ { n } - 2 ^ { i } } ( \rho ) = c _ { n , i }$ ; confidence 0.108

140. ; $y _ { i t } = \alpha y _ { i , t - 1 } + \sum _ { j = 1 } ^ { N } k _ { i j t } e _ { i j } x _ { j t };$ ; confidence 0.108

141. ; $L _ { x ^ \alpha} ( x ; t ) = \partial _ { x ^ \alpha} ( g ( x ; t ) * f ( x ) ),$ ; confidence 0.108

142. ; $T _ { B \otimes A}$ ; confidence 0.107

143. ; $S ( \phi ) = \sum _ { | \alpha | = 0 } ^ { k - 1 } S _ { \alpha i } ^ { a } ( \phi ) \omega _ { \alpha } ^ { a } \bigwedge \left( \frac { \partial } { \partial x _ { i } } \lrcorner ( d x _ { 1 } \bigwedge \ldots \bigwedge d x _ { n } ) \right).$ ; confidence 0.107

144. ; $\mu _ { k + 1 } \leq \frac { 4 \pi ^ { 2 } k ^ { 2 / n } } { ( C _ { n } | \Omega | ) ^ { 2 / n } } ,\, k = 0,1\dots.$ ; confidence 0.107

145. ; $\| a \square b ^ { * } \| \leq \| a \| \cdot \| b \|$ ; confidence 0.107

146. ; $+ \frac { ( - 1 ) ^ { k \text{l} } } { ( k - 1 ) ! \text{l}! } \sum _ { \sigma } \operatorname { sign } \sigma \times \times K ( [ L ( X _ { \sigma 1 } , \ldots , X _ { \sigma \text{l} } ) , X _ { \sigma ( \text{l} + 1 ) } ] , X _ { \sigma ( \text{l} + 2 ) } , \ldots ) +$ ; confidence 0.107

147. ; $Q _ { D } ( v _ { 1 } v _ { 2 } , z ) = \sum _ { f \in \text{lbl} ( D ) }$ ; confidence 0.107

148. ; $a _ { n } = \sum _ { k = 0 } ^ { n } \left( \begin{array} { c } { n + k } \\ { k } \end{array} \right) ^ { 2 } \left( \begin{array} { c } { n } \\ { k } \end{array} \right) ^ { 2 } , \quad b _ { n } = \sum _ { k = 0 } ^ { n } \left( \begin{array} { c } { n + k } \\ { k } \end{array} \right) \left( \begin{array} { c } { n } \\ { k } \end{array} \right) ^ { 2 }$ ; confidence 0.107

149. ; $c _ { i k }$ ; confidence 0.107

150. ; $\tilde { \nabla } ^ { q } R ( \tilde { g } )$ ; confidence 0.107

151. ; $\Gamma \vdash_{\mathcal{D}} \varphi$ ; confidence 0.107

152. ; $w _ { L }$ ; confidence 0.107

153. ; $\mathfrak{H} \oplus \mathfrak{G}$ ; confidence 0.107

154. ; $ \Xi = \mathbf{R} ^ { N } \times [ 0 , \infty [$ ; confidence 0.106

155. ; $\mathsf{Q}$ ; confidence 0.106

156. ; $\mathfrak{F}$ ; confidence 0.106

157. ; $R _ { a b } \equiv R _ { a c b } ^ { c }$ ; confidence 0.106

158. ; $Q _ { s } ( R ) = \{ q \in Q_{\text{l} } ( R ) : q B \subseteq R \ \text { for some } \ 0 \neq B \lhd R \}$ ; confidence 0.106

159. ; $H ( q , d ) = \cup _ { q - d + 1 \leq | j | \leq q } ( X ^ { j _ { 1 } } \times \ldots \times X ^ { j _ { d } } ),$ ; confidence 0.106

160. ; $w _ { t }$ ; confidence 0.106

161. ; $p _ { i + 1 } = a _ { i - 1 } p _ { i } + p _ { i - 1 } ,\, i = 1,2, \dots .$ ; confidence 0.106

162. ; $z ^ { n }$ ; confidence 0.106

163. ; $\mathbf{C} ^ { k }$ ; confidence 0.105

164. ; $c ^ { a } ( x )$ ; confidence 0.105

165. ; $P _ { 1 } , \ldots , P _ { m } \in \mathbf{Z} [ x _ { 1 } , \ldots , x _ { n } ]$ ; confidence 0.105

166. ; $\sigma ( \Omega ( A ) ) \subseteq \cup _ { i , j = 1 \atop j \neq j } ^ { n } K _ { i,\, j } ( A ) \subseteq \cup _ { i = 1 } ^ { n } G _ { i } ( A ).$ ; confidence 0.105

167. ; $\mathfrak{g} = \sum _ { \alpha \in \Phi ^ { - } } ^{ \bigoplus} \mathfrak{g} _ { \alpha } \bigoplus \mathfrak{h} \bigoplus \sum_ { \gamma \in \Phi ^ { + } } ^{\bigoplus} \mathfrak{g} _ { \gamma }$ ; confidence 0.105

168. ; $| f ( V ) | \leq c _ { 1 } | V | ^ { \gamma } \quad \text { and } \quad | \sum _ { j = 1 } ^ { n } \frac { \partial f } { \partial v _ { j } } \tilde { \phi }_{j} | > c _ { 2 } | V | ^ { \gamma + m },$ ; confidence 0.105

169. ; $( x _ { 1 } , \dots , x _ { n } )$ ; confidence 0.105

170. ; $\mathcal{C} ^ { m }$ ; confidence 0.104

171. ; $G = \operatorname {SL} _ { n } ( K )$ ; confidence 0.104

172. ; $Z _ { G }$ ; confidence 0.104

173. ; $\mathbf{Z} _ { l } ( m ) _ { X } = ( \mu _ { l ^ { n } ,\, X } ^ { \otimes^m } ) _ { n \in \mathbf{N} }$ ; confidence 0.104

174. ; $\|\, f \| = ( f , f ) ^ { 1 / 2 } _ { H }$ ; confidence 0.104

175. ; $T = \{ ( t _ { 1 } , \dots , t _ { m } ) : t _ { \operatorname { min } } < t _ { 1 } < \ldots < t _ { m } < t _ { \operatorname { max } } ,\; t_{j} \text{ non} \square \text{critical} \}$ ; confidence 0.104

176. ; $- \{ d y ^ { 1 } \bigotimes d y ^ { 1 } + \ldots + d y ^ { q } \bigotimes d y ^ { q } \}$ ; confidence 0.104

177. ; $( x _ { + } , u _ { - } \sharp w ) \equiv \tilde{x} _ { + }$ ; confidence 0.104

178. ; $r _ { \mathcal{D} } : H _ { \mathcal{M} } ^ { i } ( X , \mathbf{Q} (\, j ) ) _ { \mathbf{Z} } \rightarrow H _ { \mathcal{D} } ^ { i } ( X _ { / \mathbf{R} } , \mathbf{R} (\, j ) )$ ; confidence 0.103

179. ; $L _ { \gamma , n _ { 1 }}$ ; confidence 0.103

180. ; $\theta _ { \tau _ { n } } = \theta + h \tau _ { n } ^ { - 1 / 2 }$ ; confidence 0.103

181. ; $| \widehat { \varphi u } ( \xi ) | \leq c ^ { - 1 } e ^ { - c | \xi | ^ { 1 / s } }$ ; confidence 0.103

182. ; $a \leftrightarrow a b ^ { \pm 1 }_ { n }$ ; confidence 0.103

183. ; $\hat{c}_{k} ^ { 2 } \geq 0$ ; confidence 0.103

184. ; $\operatorname { ind } _ { g } ( P ) = ( - 1 ) ^ { n } \operatorname { Ch } ( [ a | _ { T ^ { * } M ^ { g } } ] ) \mathcal{T} ( M ^ { g } ) L ( N , g ) [ T ^ { * } M ^ { g } ].$ ; confidence 0.103

185. ; $C _ { d } ^ { k }$ ; confidence 0.103

186. ; $\times G _ { p + 2 ,\, q } ^ { q - m ,\, p - n + 2 } \left( x\left| \begin{array} { c } { \mu + i \tau , \mu - i \tau , - ( \alpha _ { p } ^ { n + 1 } ) , - ( \alpha _ { n } ) } \\ { - ( \beta _ { q } ^ { m + 1 } ) , - ( \beta _ { m } ) } \end{array} \right. \right);$ ; confidence 0.103

187. ; $\operatorname{HF} _ { * } ^ { \text { symp } } ( M , \text { id } ) \cong H ^ { * } ( M )$ ; confidence 0.103

188. ; $\varphi : X \rightarrow \Lambda ^ { r } \bigoplus\bigoplus _ { i = 1 } ^ { s } \Lambda / (\, f _ { i } ( T ) ^ { l _i} ) \bigoplus \bigoplus _ { j = 1 } ^ { t } \Lambda / ( \pi ^ { m _ { j } } )$ ; confidence 0.103

189. ; $g _ { k , p } ( z )$ ; confidence 0.102

190. ; $\ldots - ( i _ { r - 1} - i _ { r } ) \cdot \mu _ { i _ { r } },$ ; confidence 0.102

191. ; $\overline{x} \in \tilde { \mathbf{Q} } _ { p } ^ { n }$ ; confidence 0.102

192. ; $O ( | V | | E | )$ ; confidence 0.101

193. ; $( k _ { 1 } , \dots , k _ { m } ) \in ( \mathbf{N} \cup \{ 0 \} ) ^ { m }$ ; confidence 0.101

194. ; $\mathcal{E} ^ { a } ( L ) = \sum _ { | \alpha | = 0 } ^ { k } ( - 1 ) ^ { | \alpha | } \gamma ^ { - 1 } D ^ { \alpha } \left( \gamma \frac { \partial L } { \partial y _ { \alpha } ^ { a } } \right).$ ; confidence 0.101

195. ; $ \operatorname { Bel } _ { X } = \operatorname { Bel } ^ { \downarrow X - R _ { T | X - T - R} } \bigoplus \operatorname { Bel } ^ { \downarrow X - T _ { R | X - T - R} } \bigoplus \operatorname { Bel } ^ { \downarrow X - T - R _ { X } }.$ ; confidence 0.101

196. ; $\mathcal{E} ( L ) = \mathcal{E} ^ { a } ( L ) \omega ^ { a } \bigotimes \Delta,$ ; confidence 0.101

197. ; $\operatorname { dim } \tilde { H } ^ { 1 } = \operatorname { dim } C ^ { 0 } ( \Gamma , k + 2 , \overline{\mathbf{v}} ) + \operatorname { dim } C ^ { 0 } ( \Gamma , k + 2 ,\mathbf{v} )$ ; confidence 0.101

198. ; $v_0$ ; confidence 0.101

199. ; $d = \{ d_{ k } \} ^ { \infty } _ { k = - \infty}$ ; confidence 0.101

200. ; $T x _ { j } = t _ { j } x _ { j }\, \text { for } x _ { j } \in X _ { j } \quad (\, j = 1 , \dots , n ).$ ; confidence 0.101

201. ; $r _ { \mathcal{D} } \bigoplus z _ { \mathcal{D} } : R \bigoplus ( N S ( X ) \bigotimes \mathbf{Q} ) \rightarrow H _ { \mathcal{D} } ^ { 3 } ( X , \mathbf{R} ( 2 ) )$ ; confidence 0.101

202. ; $L _ { a } ^ { 1 * } \cong B$ ; confidence 0.100

203. ; $ \mathbf{SP\mathsf{Alg}} _{\models}( \mathcal{L} ) = \mathbf{SP\mathsf{Alg}} _ { \vdash } ( \mathcal{L} )$ ; confidence 0.100

204. ; $\operatorname { cos } \alpha = \operatorname { sup } \left\{ \begin{array} { r l } {} &{ u \in U \bigcap V ^ { \perp }, } \\ { \langle u , v \rangle : } & { v \in V \cap U ^ { \perp }, } \\{} & { \| u \| , \| v \| \leq 1 } \end{array} \right\}.$ ; confidence 0.100

205. ; $\omega ^ { a } = d y ^ { a } - y _ { e _ { i } } ^ { a } d x _ { i }$ ; confidence 0.100

206. ; $\mathbf{\mathsf{RCA}}_{ \omega}$ ; confidence 0.099

207. ; $\left\{ \begin{array} { l } { p_{ t } ( a , t ) + p _ { a } ( a , t ) + \mu ( a ) p ( a , t ) = 0, } \\ { p ( 0 , t ) = \int _ { 0 } ^ { + \infty } \beta ( a ) p ( a , t ) d a, } \\ { p ( a , 0 ) = p _ { 0 } ( a ) \geq 0, } \end{array} \right.$ ; confidence 0.099

208. ; $= g ^ { - 1 } \{ 1,4 \} \nabla C ( g ) - g ^ { - 1 } \{ 1,3 ; 2,5 \} ( A ( g ) \bigotimes W ( g ) ) \subset \subset \bigotimes \square ^ { 2 } \mathcal{E},$ ; confidence 0.099

209. ; $d ^ { \prime }$ ; confidence 0.099

210. ; $\mathcal{A} _ { n } = \sigma ( X _ { 0 } , \dots , X _ { n } )$ ; confidence 0.099

211. ; $\hat { c } _ { l } ^ { 1 } = c ^ { T } x ^ { ( l ) } + ( A _ { 1 } x ^ { ( l ) } - b _ { 1 } ) ^ { T } \overline { u } _ { 1 } - \overline { q } < 0$ ; confidence 0.098

212. ; $d _ { 1 } ( e _ { 1 } ^ { i } ) = g _ { i } e _ { 0 } - e _ { 0 }$ ; confidence 0.098

213. ; $\tilde{v} ( \tilde { u } _ { 1 } )$ ; confidence 0.098

214. ; $\overline { u }_1$ ; confidence 0.098

215. ; $\Gamma \vdash_{\mathcal{ L}} \phi$ ; confidence 0.098

216. ; $H = \tilde{I} \tilde { H } \square ^{*}$ ; confidence 0.098

217. ; $\operatorname{varprojlim}_{k}( X _ { 1 } \vee \ldots \vee X _ { k } ) = \operatorname{Cl} _ { i = 1 } ^ { \infty } ( X _ { i } , x _ { i 0 } ).$ ; confidence 0.098

218. ; $( a \bigotimes c ) ( b \bigotimes d ) = a \cdot \Psi _ { C , B } ( c \bigotimes b ) \cdot d$ ; confidence 0.098

219. ; $c _ { n } = q ^ { - n - n ^ { 2 } / 2 } , n = 0 , \pm 1 , \pm 2 , \ldots ,$ ; confidence 0.098

220. ; $\partial _ { q , y } ( x ^ { n } y ^ { m } ) = q ^ { n } [ m ] _ { q ^ { 2 } } x ^ { n } y ^ { m - 1 }.$ ; confidence 0.097

221. ; $\frac { F _ { 1 } z } { 1 + G _ { 1 } z } \square _ { + } \frac { F _ { 2 } z } { 1 + G _ { 2 } z } \square _ { + } \frac { F _ { 3 } } { 1 + G _ { 3 } z } \square _ { + } \dots$ ; confidence 0.097

222. ; $\Psi ( E _ { i } \bigotimes E _ { j } ) = q ^ { a _ { i j} } E _ { j } \bigotimes E _ { i },$ ; confidence 0.097

223. ; $f ( x ) = \sum _ { n \in \mathbf{Z} } \sum _ { m \in \mathbf{Z} } c _ { n , m } (\, f ) g _ { n , m } ( x ),$ ; confidence 0.097

224. ; $V = \bigoplus _ { \lambda \in \mathfrak { h } ^ { e * } } V ^ { \lambda },$ ; confidence 0.097

225. ; $\pi : \mathcal{FT} \text{op} \rightarrow \mathcal{C} \text{rs}$ ; confidence 0.097

226. ; $\tilde { \mathfrak{E} } ( \mu )$ ; confidence 0.096

227. ; $\hat { f } ( m ) = ( 2 \pi ) ^ { - 1 } \int _ { - \pi } ^ { \pi } f ( u ) e ^ { - i m u } d u$ ; confidence 0.096

228. ; $R _ { S } ^ { * } = \{ x \in \mathbf{Q} : | x | _ { v } = 1 , \forall | \cdot | _ { v } \notin S \}$ ; confidence 0.096

229. ; $u_{xx}$ ; confidence 0.096

230. ; $\pi /n$ ; confidence 0.096

231. ; $T_{\text{min}} \times T_{\text{prod}}$ ; confidence 0.096

232. ; $d _ { 0 } \in \cap _ { \mathsf{P} \in \mathcal{P} } L _ { 2 } ( \Omega , \mathcal{A} , \mathsf{P} )$ ; confidence 0.096

233. ; $\hat { p }$ ; confidence 0.096

234. ; $a _ { m - 1 } = b _ { m - 1 } - \frac { 1 } { 2 \iota } \sum _ { 1 \leq j \leq n } \frac { \partial ^ { 2 } b _ { m } } { \partial x _ { j } \partial \xi _ { j } } = b _ { m - 1 } ^ { s }.$ ; confidence 0.096

235. ; $z _ { 1 } ^ { ( 1 ) } , \dots , z _ { 1 } ^ { ( M ) }$ ; confidence 0.096

236. ; $\langle a , b \rangle = a _ { 1 } b _ { 1 } + \ldots + a _ { n } b _ { n }$ ; confidence 0.095

237. ; $\mu _ { n } ( x ) / \mu _ { n }$ ; confidence 0.095

238. ; $f _ { L } ^ {\rightarrow} \dashv f _ { L } ^ { \leftarrow }$ ; confidence 0.095

239. ; $[ H _ { \mathfrak{M} } ^ { i } ( R ) ] _ { n }$ ; confidence 0.095

240. ; $H ( a ) = ( a _ { 1 + j + k} )_{ j,k = 0}^{\infty}$ ; confidence 0.095

241. ; $\lambda \varphi_{0} , \ldots , \varphi _ { n - 1}$ ; confidence 0.095

242. ; $I_{0}$ ; confidence 0.095

243. ; $\mathcal{H} ^ { m } ( E ) = \operatorname { sup } _ { \delta > 0 } \operatorname { inf } \left\{ c _ { m } \sum _ { i } | E _ { i } | ^ { m } : \quad \begin{array} { c } { E \subset \cup _ { i } E _ { i } } \\ { | E _ { i } | < \delta \text { for all } } \ i \end{array} \right\},$ ; confidence 0.095

244. ; $g_{l}$ ; confidence 0.095

245. ; $L _ { t }$ ; confidence 0.095

246. ; $( A _ { i , r + j} , A _ { i + 1 , r + j} , \dots , A _ { r, r + j} ; \Delta \mathbf{e} _ { j } ) ,\; j = 1 , \dots , l - r,$ ; confidence 0.095

247. ; $E / F$ ; confidence 0.095

248. ; $A _ { 2 } = \prod _ { rm ^ { 2 } \geq 2 } ^ { 2 } \zeta ( rm ^ { 2 } ) = 2.49 \dots$ ; confidence 0.094

249. ; $h _ { 2 }$ ; confidence 0.094

250. ; $\mathcal{L} = \langle \operatorname{Fm} _ { \mathcal{L} } , \operatorname { Mod } _ { \mathcal{L} } , \vDash _ { \mathcal{L} } , \operatorname { mng } _ { \mathcal{L} } , \vdash _ { \mathcal{L} } \rangle ,$ ; confidence 0.094

251. ; $\tilde { \mathbf{D} } _ { n }$ ; confidence 0.094

252. ; $\left\{ \begin{array} { l } { x _ { 1 } ^ { 3 } + \sum _ { i + j + k \leq 2 } a _ { i j k } x _ { 1 } ^ { i } x _ { 2 } ^ { j } x _ { 3 } ^ { k } = 0, } \\ { x _ { 2 } ^ { 3 } + \sum _ { i + j + k \leq 2 } b _ { i j k } x _ { 1 } ^ { i } x _ { 2 } ^ { j } x _ { 3 } ^ { k } = 0, } \\ { x _ { 3 } ^ { 3 } + \sum _ { i + j + k \leq 2 } c _ { i j k } x _ { 1 } ^ { i } x _ { 2 } ^ { j } x _ { 3 } ^ { k } = 0, } \end{array} \right.$ ; confidence 0.094

253. ; $\epsilon _ { n }$ ; confidence 0.093

254. ; $\vdash_{\mathcal{D}} E ( x , x ) \text { and } x ,\, E ( x , y )\vdash_{\mathcal{D}} y$ ; confidence 0.093

255. ; $L _ { \frac { 3 } { 2 } ,\, n } = L _ { \frac { 3 } { 2 } ,\, n } ^ { c }$ ; confidence 0.093

256. ; $a _ { n } = N \left( \frac { a _ { n - 1} ^ { 2 } } { a _ { n - 2} } \right),$ ; confidence 0.093

257. ; $a_{ ( n _ { + } - n _ { - } - s ( D _ { L } ) + 1 ) , ( n - s ( D _ { L } ) + 1 ) } \neq 0$ ; confidence 0.093

258. ; $g _ { u } \in A / B$ ; confidence 0.093

259. ; $K _ { x }$ ; confidence 0.093

260. ; $\Delta H \vdash_{\mathcal{L}} \phi $ ; confidence 0.093

261. ; $\mathbf{r} = ( r _ { 1 } , \dots , r _ { n } ) \in \mathbf{R} ^ { n }$ ; confidence 0.093

262. ; $L^{\infty}$ ; confidence 0.093

263. ; $\tilde { x } _ { + }$ ; confidence 0.093

264. ; $U = \left( \begin{array} { l l } { U _ { 11 } } & { U _ { 12 } } \\ { U _ { 21 } } & { U _ { 22 } } \end{array} \right) : \mathcal{K} \oplus \mathcal{K} _ { 1 } \rightarrow \mathcal{K} \oplus \mathcal{K} _ { 2 },$ ; confidence 0.092

265. ; $F ( x ) = \frac { x ^ { - a } ( 1 + x ) ^ { 2 a - c } } { \Gamma ( c ) } \times$ ; confidence 0.092

266. ; $\operatorname { lim } _ { r \rightarrow 0 } \frac { \mathcal{H} ^ { m } \left( \left\{ y \in E \cap B ( x , r ) : \begin{array} { l } { \text { dist } ( y - x , V ) >} \\ {> s | y - x | }\end{array} \right\} \right) } { r^m } ) = 0.$ ; confidence 0.092

267. ; $\left\| \theta _ { n } ( h _ { 1 } \bigotimes \ldots \bigotimes h _ { n } ) \right\| _ { L ^ { 2 } ( \mu ) } = \sqrt { n ! } \left| h _ { 1 } \widehat{\bigotimes} \ldots \widehat{\bigotimes} h _ { n } \right| _ { H ^{ \bigotimes n }}.$ ; confidence 0.092

268. ; $\varphi _ { 0 } ^ { 0 } , \ldots , \varphi _ { n _ { 0 } - 1} ^ { 0 } \rhd \psi ^ { 0 } ; \ldots ; \varphi _ { 0 } ^ { m - 1 } , \ldots , \varphi _ { n _ { m - 1 } -1 } ^ { m - 1 } \rhd \psi ^ { m - 1 } \vdash _ { \mathcal{G} }$ ; confidence 0.092

269. ; $d _ { j } ^ { * } \in \cap _ { \mathsf{P} \in \mathcal{P} } L _ { 2 } ( \Omega , \mathcal{A} , \mathsf{P} )$ ; confidence 0.092

270. ; $[ - \nabla ^ { 2 } + q ( x ) - k ^ { 2 } ] u = 0\, \operatorname { in } \mathbf{R} ^ { 3 } ,\, k = \text{const} > 0,$ ; confidence 0.092

271. ; $W ( \tilde { g } ) = R ( \tilde { g } ) \in \mathsf{A} ^ { 2 } \tilde{\mathcal{E}} \otimes \mathsf{A} ^ { 2 } \tilde{\mathcal{E}}$ ; confidence 0.092

272. ; $c \mathsf{E} \left[ \left| U _ { \tau } ^ { * } \right| ^ { p } \right] \leq \operatorname { sup } _ { 0 < r < 1 } \int _ { \partial D } | f ( r e ^ { i \vartheta } ) | ^ { p } \frac { d \vartheta } { 2 \pi } \leq C \mathsf{E} \left[ \left| U _ { \tau } ^ { * } \right| ^ { p } \right],$ ; confidence 0.092

273. ; $a_1$ ; confidence 0.091

274. ; $F ( D _ { a } ) \subset D _ { a }$ ; confidence 0.091

275. ; $A = [ A_{l} , A _ { 2 } ] \in C ^ { mn \times ( m n + p )}$ ; confidence 0.091

276. ; $Z ^ { i } Z ^ { j }$ ; confidence 0.091

277. ; $\| T \| =\underset{ \zeta \in Z }{ \operatorname { ess } \operatorname { sup }} \| T ( \zeta ) \| . $ ; confidence 0.091

278. ; $R _ { ab } = 0$ ; confidence 0.091

279. ; $\forall x _ { n + 1} \vee \{ \psi _ { \mathfrak { A } } ^ { l } \overline { a } a : a \in A \}.$ ; confidence 0.091

280. ; $\mathcal{E} ^ { a } ( L )$ ; confidence 0.091

281. ; $\widehat { CH \square } ^ { 1 } ( \operatorname { Spec } ( \mathbf{Z} ) ) = \mathbf{R}$ ; confidence 0.091

282. ; $\prod _ { j = 1 } ^ { \infty } \frac { | a | } { a } \frac { z - a } { 1 - \overline { a } z } , \quad \sum ( 1 - | a _ { j } | ) < \infty .$ ; confidence 0.091

283. ; $\{ e _ { i_1 } , \ldots , e _ { i_k } , i , 1 \leq i _ { 1 } < \ldots < i _ { k } \leq n \}$ ; confidence 0.091

284. ; $P _ { \operatorname { min } } \leq \mathsf{P} ( A _ { 1 } \bigcup \dots \bigcup A _ { n } ) \leq P _ { \text{max} }$ ; confidence 0.090

285. ; $d ^ { * } \in \cap _ { \mathsf{P} \in \mathcal{P} } L _ { 1 } ( \Omega , \mathcal{A} , \mathsf{P} ) \cap L _ { 2 } ( \Omega ,\mathcal{A} , \mathsf{P}_ { 0 } )$ ; confidence 0.090

286. ; $ f _ { i + 1 / 2 } ^ { \text{waf} } = \frac { 1 } { \Delta x } \int _ { - \frac { 1 } { 2 } \Delta x } ^ { \frac { 1 } { 2 } \Delta x } f \left[ u _ { i + 1 / 2 } \left( x , \frac { 1 } { 2 } \Delta t \right) \right] d x, $ ; confidence 0.090

287. ; $B _ { k }$ ; confidence 0.090

288. ; $\left\{ \begin{array} { c c c c }{ \hat{ \theta }_{N} =\hat{\theta }_{N-1}+ \gamma (N) Q_1(X(N),y(N),u(N)), }\\{X_{N}= X _ { N - 1 } + \mu _ { N } Q _ { 2 } ( X _ { N-1} ,y(N), u(N)), }\end{array} \right. $ ; confidence 0.090

289. ; $\sum _ { k } \sum _ { l } \overline { c } _ { k } c_{ l} S ( \theta (\, f _ { k } ) - f _ { l } ) \geq 0$ ; confidence 0.090

290. ; $\tau ^ { * }$ ; confidence 0.090

291. ; $a _ { r }$ ; confidence 0.090

292. ; $N _ { k , r }$ ; confidence 0.090

293. ; $( a ^ { w } ) ^ { * } = \operatorname { Op } \left( J ( \overline { ( J ^ { 1 / 2 } a ) } \right) = \operatorname { Op } ( J ^ { 1 / 2 } \overline { a } ) = ( \overline { a } ) ^ { w },$ ; confidence 0.090

294. ; $w C ^ { + }$ ; confidence 0.089

295. ; $\operatorname { map }_{ *}( X \bigwedge Z , Y ) \approx \operatorname { map }_{ *} ( X , \operatorname { map } _ { * } ( Z , Y ) ),$ ; confidence 0.089

296. ; $\mathfrak{U} ( \mathfrak{g} )$ ; confidence 0.089

297. ; $\alpha_{y} = \left( \begin{array} { c c c c } { 0 } & { 0 } & { 0 } & { - i } \\ { 0 } & { 0 } & { i } & { 0 } \\ { 0 } & { - i } & { 0 } & { 0 } \\ { i } & { 0 } & { 0 } & { 0 } \end{array} \right) = \left( \begin{array} { c c } { \mathbf{0} } & { \sigma_ y } \\ { \sigma_ y } & { \mathbf{0} } \end{array} \right) , \alpha _ { z } = \left( \begin{array} { c c c c } { 0 } & { 0 } & { 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } \\ { 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { 0 } & { 0 } \end{array} \right) = \left( \begin{array} { c c } { \mathbf{0} } & { \sigma _ { z } } \\ { \sigma _ { z } } & { \mathbf{0} } \end{array} \right),$ ; confidence 0.089

298. ; $\mathfrak { S } _ { u } = x _ {1 } ^ {m }$ ; confidence 0.089

299. ; $\left\{ \begin{array}{l}{ \frac { d N ^ { 1 } } { d t } = \lambda _ { ( 1 ) } N ^ { 1 } \left( 1 - \frac { N ^ { 1 } } { K _ { ( 1 ) } } - \delta _ { ( 1 ) } \frac { N ^ { 2 } } { K _ { ( 1 ) } } \right), }\\{ \frac { d N ^ { 2 } } { d t } = \lambda _ { ( 2 ) } N ^ { 2 } \left( 1 - \frac { N ^ { 2 } } { K _ { ( 2 ) } } - \delta _ { ( 2 ) } \frac { N ^ { 1 } } { K _ { ( 2 ) } } \right). }\end{array} \right.$ ; confidence 0.089

300. ; $\mathsf{E} [ W ] _ { \text{gated} } = \frac { \delta ^ { 2 } } { 2 r } + \frac { P \lambda b ^ { ( 2 ) } + r ( P + \rho ) } { 2 ( 1 - \rho ) } , \mathsf{E} [ W ] _ { \text{lim} } = \frac { \delta ^ { 2 } } { 2 r } + \frac { P \lambda b ^ { ( 2 ) } + r ( P + \rho ) + P \lambda \delta ^ { 2 } } { 2 ( 1 - \rho - P \lambda r ) },$ ; confidence 0.089

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/75. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/75&oldid=44485

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Difference between revisions of "User:Maximilian Janisch/latexlist/latex/NoNroff/75"

Latest revision as of 22:51, 29 June 2020

List

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 == List ==
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120200/c12020065.png ; $> 2$ ; confidence 0.983
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007078.png ; $( 2 \pi ) ^ { - 2 n } \int _ { \mathbf{R} ^ { 2 n } } e ^ { i q \mathcal{X} } e ^ { i p \mathcal{D} } \hat { \sigma } ( p , q ) d p d q,$ ; confidence 0.122
-. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025830/c02583068.png ; $i A$ ; confidence 0.534
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042046.png ; $\Psi _ { V , W }$ ; confidence 0.122
-. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130210/c13021017.png ; $78$ ; confidence 0.129
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007054.png ; $( \nabla ^ { 2 } +  k  ^ { 2_0 }  + k  ^ { 2_0 }v ( x ) ) u ( x , y , k _ { 0 } ) = - \delta ( x - y ) \text { in } \mathbf{R}  ^ { 3 },$ ; confidence 0.122
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110580/a11058065.png ; $12$ ; confidence 0.642
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070136.png ; $= ( ( F ( \cdot ) , h ( \cdot , x ) ) _ { \mathcal{H} } , ( h ( \text{..} , y ) , h ( \text{..} , x ) ) _ { \mathcal{H} } ) _ { H } =$ ; confidence 0.122
-. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c120300127.png ; $K K$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130020/b13002080.png ; $( H , ( \cdot | \cdot ) )$ ; confidence 0.122
-. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013180/a013180167.png ; $d T$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b12040073.png ; $\mathfrak{h} _ { R } ^ { * }$ ; confidence 0.122
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020171.png ; $21$ ; confidence 0.392
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011041.png ; $r _ { i } s _ { j } \in C _ {  ( i + j ) \operatorname { mod } 2}$ ; confidence 0.122
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002088.png ; $14$ ; confidence 0.135
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f130100109.png ; $\langle T [ \phi ] , [ \psi ] \rangle _ { L _ { \text{C} } ^ { p } ( G ) , L _ { \text{C} } ^ { p^{\prime} } ( G ) } \neq 0.$ ; confidence 0.122
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002066.png ; $| R$ ; confidence 0.431
+. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046020/h04602020.png ; $\| G \| _ { \infty } = \operatorname { sup } _ { \| x \| _ { 2 } \leq 1 } \| y \| _ { 2 }.$ ; confidence 0.122
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002065.png ; $| F$ ; confidence 0.388
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008091.png ; $d \hat { \Omega } _ { n } = P _ { + } ^ { n / N } \left( \frac { d w } { w } \right)$ ; confidence 0.122
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120030/d12003080.png ; $* 1$ ; confidence 0.973
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120240/e12024027.png ; $c_L$ ; confidence 0.121
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120050/d12005065.png ; $- 1$ ; confidence 0.491
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d12028097.png ; $\left\{ \begin{array} { l } { \Delta v = 0 } & {\text{in} \ \mathbf{C}^{n} \setminus \overline{D}, }\\ { v = \phi} & { \text { on } \partial D, } \\ { | v | \leq \frac { c } { | z | ^ { 2 n - 2 } }. } \end{array} \right.$ ; confidence 0.121
-. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110080/d11008029.png ; $K v$ ; confidence 0.677
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020064.png ; $r_1 , \ldots , r_n$ ; confidence 0.121
-. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110430/c11043084.png ; $24$ ; confidence 0.527
+. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130040/k13004011.png ; $ c  _ { 1 } / a  _ { 1 } \geq \ldots \geq c  _ { n } / a  _ { n }$ ; confidence 0.121
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120120/d12012011.png ; $A G$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130020/q1300204.png ; $|  i  \rangle$ ; confidence 0.121
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120120/d12012021.png ; $U C$ ; confidence 0.760
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130150/t13015044.png ; $\mathcal{K} =\mathcal{ I} _ { 1 } \lhd \ldots \lhd  \mathcal{ I}_ { r } \lhd  \mathcal{T} ( S )$ ; confidence 0.121
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120120/d12012017.png ; $O G$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130410/s13041055.png ; $\| p _ {n } ^ { \langle \alpha - 1 ,\, \beta - 1 \rangle } \| _ { \mu _ { 0 } } = o( n )$ ; confidence 0.121
-. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110180/d11018018.png ; $> y$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018099.png ; $u_2$ ; confidence 0.121
-. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024120/c02412050.png ; $> 4$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014065.png ; $* : \mathcal{G} \text{l} _ { Q } ( d ) \times  \mathcal{A} _ { Q } ( d ) \rightarrow  \mathcal{A} _ { Q } ( d )$ ; confidence 0.120
-. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011048.png ; $73$ ; confidence 0.513
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064040.png ; $\tilde { a } ( e ^ { i \theta } ) = a ( e ^ { - i \theta } )$ ; confidence 0.120
-. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026390/c02639034.png ; $72$ ; confidence 0.746
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c12001057.png ; $\mathbf{C} ^ { n } \subset \mathbf{P} ^ { n }$ ; confidence 0.120
-. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011049.png ; $74$ ; confidence 0.870
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f120210111.png ; $p _ { i } ( z ) z ^ { \lambda } = \sum _ { n = 0 } ^ { N } a ^ { n _ { i } } z ^ { n } ( \frac { \partial } { \partial z } ) ^ { n } z ^ { \lambda }.$ ; confidence 0.120
-. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130130/d13013078.png ; $A +$ ; confidence 0.774
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110020/b11002043.png ; $b ( \cdot , \cdot )$ ; confidence 0.120
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230138.png ; $n r$ ; confidence 0.240
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013074.png ; $l w \equiv 0$ ; confidence 0.120
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110660/a11066029.png ; $f g$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070105.png ; $= \operatorname { lim } _ { n \rightarrow 0 } \left( \sum _ { j_n = 1 } ^ { J _ { n } } K ( x , y _ { j _n } ) c _ { j _n } , \sum _ { m_n = 1 } ^ { J _ { n } } K ( x , y _ { m_n } ) c _ { m_n } \right) _ { 1 } =$ ; confidence 0.120
-. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d13018018.png ; $15$ ; confidence 0.272
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p12017094.png ; $\Updownarrow a x - x c = 0 \text { and } b x - x d = 0,$ ; confidence 0.120
-. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012900/a01290018.png ; $9 x$ ; confidence 0.452
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130190/c13019055.png ; $e _ { 1 } , \dots , e _ { k }$ ; confidence 0.120
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029092.png ; $9 m$ ; confidence 0.256
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120050/b12005035.png ; $\mathcal{H} _ { uc } ^ { \infty } ( B _ { E } ) \equiv$ ; confidence 0.120
-. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120320/d12032021.png ; $11$ ; confidence 0.333
+. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020188.png ; $t ^ { * } : H ^ { n } ( S ^ { n } ) \rightarrow H ^ { n } ( \Gamma _ { S ^ { n } } )$ ; confidence 0.119
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e12006031.png ; $V Y$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120140/d1201404.png ; $\lfloor n / 2 \rfloor$ ; confidence 0.119
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e12006032.png ; $T Y$ ; confidence 0.889
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230161.png ; $\left( \begin{array} { c } { 0 } \\ { G _ { i + 1 } } \end{array} \right) = \left\{ G _ { i } + Z _ { i } G _ { i } \frac { J g _ { i } ^ { * } g _ { i } } { g _ { i } J g _ { i } ^ { * } } \right\} \Theta _ { i },$ ; confidence 0.119
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e12007094.png ; $98$ ; confidence 0.414
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130020/s1300206.png ; $UM$ ; confidence 0.119
-. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003084.png ; $G L$ ; confidence 0.867
+. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120120/h120120131.png ; $\hat { \tau }_1 = \nabla \tau ,\, \hat { \tau } _ { n } = \sum _ { i + j = n } \phi ( \hat { \tau } _ { i } \bigcup \hat { \tau } _ { j } ),$ ; confidence 0.119
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120100/e12010030.png ; $75$ ; confidence 0.268
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003080.png ; $\operatorname { Hom}_{K_\infty}( \Lambda ^ { \bullet } ( \mathfrak { g } / \mathfrak { k } ) , \mathcal{A} ( \Gamma \backslash G ( \mathbf{R} ) ) \bigotimes \mathcal{M} _ { \text{C} } ) \overset{\sim}{\rightarrow}$ ; confidence 0.119
-. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017030/b01703032.png ; $90$ ; confidence 0.129
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040654.png ; $\mathbf{Me} ^ { * \text{L} _{\mathfrak { N }}}_{\mathcal{S}_P }$ ; confidence 0.119
-. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031010/d03101075.png ; $4 k$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043042.png ; $\Psi ( x ^ { n } \bigotimes x ^ { m } ) = q ^ { n m } x ^ { m } \bigotimes x ^ { n }$ ; confidence 0.119
-. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022920/c02292065.png ; $13$ ; confidence 0.242
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001020.png ; $\mathcal{H} = \mathcal{H} ^ { \text{in} } = \mathcal{H} ^ { \text{out} }$ ; confidence 0.119
-. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015210/b01521045.png ; $a b$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/x/x120/x120010/x12001046.png ; $\hat { G }_{\text{inn}}$ ; confidence 0.119
-. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016120/b01612010.png ; $x y$ ; confidence 0.947
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130370/s1303705.png ; $x ( t + ) = x ( t ) \text { for all } \ 0 \leq t < 1 ,\, x ( t - ) = \operatorname { lim } _ { s \uparrow t } x ( s ) \text { exists for all } 0 < t \leq 1.$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120240/e12024027.png ; $[ 1$ ; confidence 0.121
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040336.png ; $E ( x _ { 0 } , y _ { 0 } ) , \ldots , E ( x _ { n  - 1} , y _ { n  - 1} ) \vdash_ { \mathcal{D} }$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120240/e12024021.png ; $Fr$ ; confidence 0.719
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120100/b12010031.png ; $( \mathcal{A} ^ { * } f ) _ { n } ( X ) = \sum _ { i = 1 } ^ { n } f _ { n - 1 } ( x _ { 1 } , \dots , x _ { i  - 1} , x _ { i  + 1} , \dots , x _ { n } ).$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027560/c02756035.png ; $2 i$ ; confidence 0.454
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a13006060.png ; $P _ { R } ^ { \# } ( n ) = \frac { 1 } { n } q ^ { n } + O \left( \frac { 1 } { n } q ^ { n / 2 } \right) \text { as } n \rightarrow \infty,$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a011600210.png ; $A f$ ; confidence 0.471
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030056.png ; $F ( \mathcal{H} ) = \mathbf{C} \oplus \oplus _ { n = 1 } ^ { \infty }  \mathcal{H} ^ { \otimes n }$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110010/f1100107.png ; $< a$ ; confidence 0.630
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s12032013.png ; $L = L _ { \overline{0} } \oplus L _ { \overline{1} }$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130020/f13002018.png ; $.0$ ; confidence 0.141
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120160/d12016072.png ; $\| h_n  \|$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120020/f12002087.png ; $Q +$ ; confidence 0.694
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140169.png ; $q _ { \Lambda  }$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120100/f12010062.png ; $26$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130130/h1301305.png ; $\sum _ { \mathbf{k} } c_{ \mathbf{k} } e ^ { i \mathbf{kx} }$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120100/f12010077.png ; $27$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f120110218.png ; $O ( e ^ { - \varepsilon | \operatorname { Re } z | - H _ { L } ( \operatorname { Re } z )} )$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120100/f12010040.png ; $18$ ; confidence 0.426
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s120340121.png ; $u_{ -} \sharp$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f120110225.png ; $- K$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130230/b13023034.png ; $\operatorname { St } _ { G } ( n ) = \cap _ { | u | = n } \operatorname { St } _ { G } ( u )$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011380/a011380139.png ; $85$ ; confidence 0.385
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130300/a13030054.png ; $R _ { n } \in \mathcal{B} ( E _ { n } , E _ { n - 1 } )$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012340/a01234030.png ; $> 1$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005023.png ; $\left\{ \begin{array}{l}{ ( T - z I ) x = K J \varphi _ { - }, }\\{ \varphi _ { + } = \varphi _ { - } - 2 i K ^ { * } x, }\end{array} \right.$ ; confidence 0.118
-. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120170/f12017024.png ; $* A$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059025.png ; $H _ { 0 } ^ { ( m ) } = 1 ,\, H _ { k } ^ { ( m ) } = \operatorname { det } ( c_{ m + i + j} ) _ { i ,\, j = 0 } ^ { k - 1 }$ ; confidence 0.117
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130280/f13028021.png ; $A x$ ; confidence 0.635
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t130050108.png ; $\sigma _ { T } ( A , \mathcal{X} ) = \left\{ ( a _ {ii} ^ { ( 1 ) } , \ldots , a _ { ii } ^ { ( n ) } ) : 1 \leq i \leq \operatorname { dim } \mathcal{X} \right\}.$ ; confidence 0.117
-. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130280/f13028022.png ; $A x$ ; confidence 0.165
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120020/c1200204.png ; $\int _ { 0 } ^ { \infty } \frac { f  *  u _ { t }  *  v _ { t } } { t } d t = c _ { u , v }\, f,$ ; confidence 0.117
-. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002018.png ; $D Q$ ; confidence 0.060
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026011.png ; $\Gamma ( L ^ { 2 } ( \mathbf{R} ) ) = \bigoplus _ { n = 0 } ^ { \infty } \sqrt { n !} L ^ { 2 } ( \mathbf{R} )^{ \widehat { \bigotimes } n } \simeq \bigoplus _ { n = 0 } ^ { \infty } \sqrt { n !} \widehat{ L ^ { 2 } ( \mathbf{R} ^ { n } ) }.$ ; confidence 0.117
-. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130030/g13003084.png ; $j 0$ ; confidence 0.375
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040397.png ; $\operatorname { Mod } ^ { *  S} \mathcal{D}= \operatorname { Mod } ^ { *  \text{L}} \mathcal{ D }$ ; confidence 0.117
-. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700109.png ; $S D$ ; confidence 0.393
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120010/e12001012.png ; $E \subseteq \operatorname { Epi } ( \mathfrak { A } )$ ; confidence 0.117
-. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120070/g12007021.png ; $2 z$ ; confidence 0.533
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130020/b1300202.png ; $\| x \circ y  \| \leq \| x \| \| y \|$ ; confidence 0.117
-. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046010/h046010144.png ; $> 5$ ; confidence 0.867
+. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110110/m11011039.png ; $G _ { p q } ^ { mn }$ ; confidence 0.117
-. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130020/h13002070.png ; $> N$ ; confidence 0.517
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130120/a13012054.png ; $k = q ^ { d - 1 }$ ; confidence 0.117
-. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130030/h13003046.png ; $70$ ; confidence 0.251
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120120/m12012030.png ; $Iq  \neq 0$ ; confidence 0.117
-. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120020/h120020166.png ; $5 p$ ; confidence 0.346
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120280/b12028010.png ; $f ( z ) = e ^ { - ( G ( z , a ) + i \tilde{G} ( z , a ) ) }$ ; confidence 0.117
-. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120050/h12005040.png ; $86$ ; confidence 0.548
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120200/d1202002.png ; $S _ { M } ( s ) = \sum _ { m \in M } a _ { m } e ^ { - \lambda_{m} s },$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120050/h12005039.png ; $85$ ; confidence 0.939
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005086.png ; $u _ { n } \in \mathfrak{F}$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130070/h13007047.png ; $r D$ ; confidence 0.778
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040186.png ; $\langle \mathbf{A} / \tilde{\Omega}_{\mathcal{D}} F , F / \tilde{\Omega}_{\mathcal{D}} F \rangle$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120070/h120070122.png ; $4 D$ ; confidence 0.771
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l120100149.png ; $N ^ { 1 / p }$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120120/h12012013.png ; $d x$ ; confidence 0.857
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140118.png ; $[ X ] \mapsto \chi _ { R } ( [ X ] ) = \sum _ { m = 0 } ^ { \infty } ( - 1 ) ^ { m } \operatorname { dim } _ { K } \operatorname { Ext } _ { R } ^ { m } ( X , X )$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120120/h12012076.png ; $t d$ ; confidence 0.972
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023061.png ; $w ^ { q } = w _ { 1 } ^ { q _ { 1 } } \ldots w _ { n } ^ { q _ { n } }$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120120/h12012059.png ; $d y$ ; confidence 0.919
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130040/r13004055.png ; $p_{ m , 1}$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130010/i13001026.png ; $i 0$ ; confidence 0.349
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180280.png ; $\nabla ( a \Phi ) = d a \bigotimes \Phi + a \nabla \Phi \in \bigotimes \square ^ { q + 1 } \mathcal{E}$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020740/c020740250.png ; $> 0$ ; confidence 0.926
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012032.png ; $\left\{ \begin{array} { l } { \operatorname{max} \ \ \sum _ { j = i } ^ { N } \beta _ { j } v _ { j } } \\ { \text { subject to } \ \ \sum _ { j = 1 } ^ { n } a _ { i j } v _ { j } \leq \mu _ { i } } \\ { v _ { j } \geq 0. } \end{array} \right.$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i130030162.png ; $11$ ; confidence 0.614
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120130/k1201309.png ; $\xi _ { 1 } ^ { i } , \ldots , \xi _ { 2 ^ { i - 1 } ( n + 1 ) } ^ { i } $ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i13004018.png ; $0 t$ ; confidence 0.228
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015077.png ; $d_{s}$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i13004020.png ; $a y$ ; confidence 0.329
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130140/s13014037.png ; $\lambda = \left. \begin{array} { l l l } { \bullet } & { \bullet } & { \bullet } & { \bullet }  \\ { \square } & { \bullet } & { \bullet } & { \square } \\ { \square } & { \square } & { \bullet } & { \square }  \end{array} \right.$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i13004034.png ; $B V$ ; confidence 0.810
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059034.png ; $Q _ { 2 n + 1 } ( z ) = \frac { - 1 } { H _ { 2 n + 1 } ^ { ( - 2 n ) } } \left| \begin{array} { c c c c } { c_{ - 2 n - 1} } & { \cdots } & { c_{ - 1} } & { z ^ { - n - 1 } } \\ { \vdots } & { \square } & { \vdots } & { \vdots } \\ { c_{ - 1} } & { \cdots } & { c _ { 2 n - 1 } } & { z ^ { n - 1 } } \\ { c_0 } & { \cdots } & { c _ { 2 n } } & { z ^ { n } e n d } \end{array} \right|,$ ; confidence 0.116
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i1300509.png ; $i k$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z13010086.png ; $\forall x \forall v _ { 1 } \ldots \forall v _ { n } \exists y \forall v ( v \in y \leftrightarrow ( v \in x \bigwedge \varphi ) ).$ ; confidence 0.115
-. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007075.png ; $83$ ; confidence 0.483
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027070.png ; $a _ { n } = \sum _ { 0 } ^ { n } b _ { n  - j} u _ { j } ,\; n \geq 0,$ ; confidence 0.115
-. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j12002033.png ; $42$ ; confidence 0.844
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b12040057.png ; $\mathfrak { g } _ { \alpha }$ ; confidence 0.115
-. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032600/d032600120.png ; $| I$ ; confidence 0.350
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009052.png ; $=\frac { m } { 1 + a ^ { 2 } } \left\{ \int _ { 0 } ^ { z } \frac { p _ { 1 } ( s ) - p _ { 0 } ( s ) } { s ^ { 1 - \frac { m } { 1 + a i } } } e ^ { \frac { m } { 1 + a ^ { 2 } } \int _ { 0 } ^ { s } \frac { p _ { 0 } ( t ) - 1 } { t } d t } d s + + \frac { 1 + a ^ { 2 } } { m } z ^ { \frac { m } { 1 + a i } } e ^ { \frac { m } { 1 + a ^ { 2 } } \int _ { 0 } ^ { z } \frac { p _ { 0 } ( t ) - 1 } { t } d t} \right\}.$ ; confidence 0.115
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004028.png ; $31$ ; confidence 0.927
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016034.png ; $u = \left\{ \begin{array} { c c } { \overline { u } } & { \text { for } \frac { i T } { k } \leq t < ( i + a ) \frac { T } { k }; } \\ { } & { 0 \leq i \leq k - 1, } \\ { 0 } & { \text { for } ( i + a ) \frac { T } { k } \leq t \leq ( i + 1 ) \frac { T } { k }, } \\ { } & { \text { and for } \ t = T ; 0 \leq i \leq k - 1. } \end{array} \right.$ ; confidence 0.115
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110610/a110610114.png ; $12$ ; confidence 0.465
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t1301307.png ; $\operatorname{p}\cdot \operatorname{dim} _ { \Lambda } T$ ; confidence 0.114
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004030.png ; $41$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130090/b13009039.png ; $u _ { t } + a ( t ) u _ { x } + b ( t ) u ^ { p } u _ { x } - u _ { xxt } = 0$ ; confidence 0.114
-. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004023.png ; $21$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040184.png ; $\Sigma _ { n = 1 } ^ { \infty } \| T _ { x _ { n } } \| _ { X } ^ { r } < \infty$ ; confidence 0.114
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040145.png ; $18$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g13006083.png ; $\overrightarrow{ P _ { i } P _ { \text{l}_1 } } , \overrightarrow{ P _ { \text{l}_1 } P _ { \text{l}_2 } }  , \dots , \overrightarrow{ P _ { \text{l}_m } P _ { \text{l}_{m+1} } },$ ; confidence 0.114
-. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120060/k12006041.png ; $N L$ ; confidence 0.871
+. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066630/n06663030.png ; $\| \Delta _ { h _ { i } } ^ { 2 } f _ { x _ { i } } ^ { ( r _ { i } ^ { * } ) } \| _ { L _ { p } ( \Omega _ { 2 |h _ { i }| } | ) } \leq M _ { i } | h _ { i } |,$ ; confidence 0.114
-. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145024.png ; $p 3$ ; confidence 0.875
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120030/c12003023.png ; $f \in \operatorname { Car }  _ { \text{loc} } ( I \times G )$ ; confidence 0.114
-. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023380/c023380105.png ; $< m$ ; confidence 0.772
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180124.png ; $= \{ \langle b _ { 0 } , \dots , b _ { i  - 1} , a , b _ { i + 1} , \dots , b _ { n - 1 } \rangle : a \in U \ \text{and}$ ; confidence 0.114
-. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k05584075.png ; $10$ ; confidence 0.688
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002013.png ; $\overline { A } _ { 1 } , \dots , \overline { A } _ { n }$ ; confidence 0.114
-. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k05584087.png ; $< k$ ; confidence 0.729
+. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130120/p13012025.png ; $p_3$ ; confidence 0.114
-. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840243.png ; $99$ ; confidence 0.814
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m1201506.png ; $x _ { 11 } ( \cdot ) , \ldots , x _ { p n } ( \cdot )$ ; confidence 0.113
-. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110590/b11059029.png ; $40$ ; confidence 0.096
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070106.png ; $= \sum _ { j _ { n } ,\, m _ { n } } ^ { J _ { n } } K ( y _ { m _ { n } } , y _ { j _ { n } } ) c _ { j _ { n } } \overline { c_{m _ { n }}} =$ ; confidence 0.113
-. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130070/k1300709.png ; $48$ ; confidence 0.152
+. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120110/n12011078.png ; $x \rightarrow \underline { f } \square_{\alpha} ( x )$ ; confidence 0.113
-. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110010/l1100107.png ; $- x$ ; confidence 0.756
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130070/w13007046.png ; $\operatorname { ch } V ( \lambda ) = \frac { \sum _ { w \in W } ( - 1 ) ^ { l ( w ) } e ^ { w ( \lambda + \rho ) - \rho } } { \prod _ { \alpha \in \Delta ^ { - }} ( 1 - e ^ { \alpha } ) ^ { \text{dim} \mathfrak{g} _ { \alpha }  } }.$ ; confidence 0.113
-. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110020/l11002088.png ; $r 0$ ; confidence 0.142
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110320/a11032023.png ; $B _ { j } ( z ) = \sum _ { l = 0 } ^ { \rho _ { s + 1 } } R _ { l + 1 } ^ { ( s + 1 ) } ( z ) \lambda _ { l j } ^ { ( s + 1 ) },$ ; confidence 0.113
-. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700093.png ; $Q x$ ; confidence 0.433
+. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059120/l0591204.png ; $\operatorname { SL} _ { n } ( K )$ ; confidence 0.113
-. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040210/f04021083.png ; $M L$ ; confidence 0.956
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180111.png ; $\exists v _ { i } \varphi ( v _ { 0 } , \dots , v _ { n - 1} )$ ; confidence 0.113
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120050/l1200505.png ; $R e$ ; confidence 0.234
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012049.png ; $h _ { z }$ ; confidence 0.113
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120050/l1200507.png ; $Im$ ; confidence 0.433
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007013.png ; $\{ M ( \alpha ) \text { pr} _ { \text {dom } \alpha } - \text { pr}_{ \text {codom } \alpha } \}_{ \alpha} \quad \text { for } n = 0,$ ; confidence 0.112
-. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130010/l13001017.png ; $N B$ ; confidence 0.185
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140104.png ; $q_{ R} ( x ) = \sum _ { j \in Q _ { 0 } } x _ { j } ^ { 2 } - \sum _ {( \beta : i \rightarrow j ) \in Q _ { 1 } } x _ { i } x _ { j } + \sum _ { ( \beta : i \rightarrow j ) \in Q _ { 1 } } r _ { i ,\, j } x _ { i } x _ { j },$ ; confidence 0.112
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006088.png ; $71$ ; confidence 0.832
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020086.png ; $\mathcal{X} / J$ ; confidence 0.112
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010098.png ; $- E$ ; confidence 0.202
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040520.png ; $\operatorname { FMod} ^ { *  \text{L}} \mathcal{D}$ ; confidence 0.112
-. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110590/b11059060.png ; $O A$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005093.png ; $Y ( L ( - 1 ) v , x ) = ( d / d x ) Y ( v , x )$ ; confidence 0.112
-. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060030/l06003068.png ; $P T$ ; confidence 0.897
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008010.png ; $\sum _ { i ,\, j = 1 } ^ { m } a _ { i ,\, j } ( x ) \xi _ { i } \xi _ { j } \geq \delta | \xi | ^ { 2 }$ ; confidence 0.112
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120130/l12013098.png ; $17$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120310/c12031040.png ; $e _ { n } ( H _ { d } ^ { k } ) \leq c _ { k , d  , \delta} \cdot n ^ { - k + \delta } , \forall n,$ ; confidence 0.112
-. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130100/l13010054.png ; $B f$ ; confidence 0.997
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b1203006.png ; $\psi ( y + 2 \pi p ) = e ^ { 2 \pi i \eta \cdot p } \psi ( y )\, \text { for a.e. } \ y  \in \mathbf{R} ^ { N }.$ ; confidence 0.112
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120150/l12015048.png ; $d a$ ; confidence 0.446
+. https://www.encyclopediaofmath.org/legacyimages/o/o110/o110010/o11001036.png ; $a _ { 1 } , \dots , a _ { n } \in G$ ; confidence 0.112
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l1201706.png ; $C W$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002053.png ; $( \text{LD} ) v ^ { * } = \left\{ \begin{array} { c l } { \operatorname { max } } & { q } \\ { s.t. } & { q \leq c ^ { T } x ^ { ( k ) } + u _ { 1 } ^ { T } ( A _ { 1 } x ^ { ( k ) } - b _ { 1 } ), } \\ { } & { \forall k \in P, } \\ { 0 \leq } & { c ^ { T } \tilde{x} ^ { ( k ) } + u _ { 1 } ^ { T } A _ { 1 } \tilde{x} ^ { ( k ) } , \forall k \in R, } \\ { u _ { 1 } \geq 0. } \end{array} \right.$ ; confidence 0.111
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l12017021.png ; $13$ ; confidence 0.823
+. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130020/k13002068.png ; $x = \tilde { x }$ ; confidence 0.111
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l12017011.png ; $> 6$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040490/f04049030.png ; $F _ { m n } = \frac { \chi _ { m } ^ { 2 } / m } { \chi _ { n } ^ { 2 } / n },$ ; confidence 0.111
-. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120190/l1201905.png ; $- B$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o1300804.png ; $q _ { m } ( x )$ ; confidence 0.111
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120020/m12002017.png ; $- T$ ; confidence 0.558
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130040/b13004040.png ; $( \cap _ { n = 0 } ^ { \infty } W _ { n } ) \cap E \neq \emptyset$ ; confidence 0.111
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120070/m12007041.png ; $50$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130010/e13001019.png ; $( d H ) ^ { c _ { n } d ^ { n^{2} } }$ ; confidence 0.111
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120120/m12012059.png ; $R C$ ; confidence 0.816
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042027.png ; $\operatorname { id} \bigotimes r _ { W } = \Phi _ { V , 1 , W } \circ ( l _ { V } \bigotimes \text { id } ).$ ; confidence 0.111
-. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120120/m12012056.png ; $R C$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c12021092.png ; $\Lambda _ { n } - h ^ { \prime } T _ { n } \rightarrow - h ^ { \prime } \Gamma h / 2$ ; confidence 0.111
-. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110260/c11026032.png ; $R N$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840343.png ; $\mathcal{H} ^ { n}$ ; confidence 0.111
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130130/m13013025.png ; $i j$ ; confidence 0.234
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020042.png ; $P ( t ) = \prod _ { m = 1 } ^ { n } ( t - t _ { m } ) ^ { r _ { m } } ; \quad q _ { i } ( t ) = \left\{ \frac { ( t - t _ { i } ) ^ { r _ { i } } } { P ( t ) } \right\} _ { ( r _ { i } - 1 ; t _ { i } ) };$ ; confidence 0.111
-. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040760/f0407606.png ; $n p$ ; confidence 0.961
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m1301405.png ; $d \sigma _ { r }$ ; confidence 0.110
-. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110110/m11011041.png ; $L =$ ; confidence 0.943
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o130010133.png ; $C^{ 2 , \lambda }$ ; confidence 0.110
-. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a011600262.png ; $> 0$ ; confidence 0.998
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130100/w13010015.png ; $\mathsf{E} | W ^ { a } ( t ) | \sim \left\{ \begin{array} { l l } { \sqrt { \frac { 8 t } { \pi } } , } & { d = 1, } \\ { \frac { 2 \pi t } { \operatorname { log } t } , } & { d = 2, } \\ { \kappa _ { a } t , } & { d \geq 3, } \end{array} \right.$ ; confidence 0.110
-. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130230/m13023019.png ; $20$ ; confidence 0.760
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c12001040.png ; $\mathbf{P} ^ { n }$ ; confidence 0.110
-. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057780/l05778081.png ; $30$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030210/d03021016.png ; $\mathbf{b}$ ; confidence 0.110
-. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120120/n12012075.png ; $H C$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130060/w13006036.png ; $\omega _ { \text{WP} } = \Sigma _ { j } d \text{l} _ { j } \bigwedge d \tau _ { j },$ ; confidence 0.110
-. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130020/n13002030.png ; $11$ ; confidence 0.924
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q120070140.png ; $\langle \cdot , \cdot \rangle : A \otimes H \rightarrow  k $ ; confidence 0.110
-. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130030/n13003037.png ; $B w$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060040/l06004018.png ; $g _ { k  , 1} ( z ) = g _ { k } ( z );$ ; confidence 0.110
-. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130030/n13003035.png ; $A w$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120360/b12036028.png ; $I R F$ ; confidence 0.109
-. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120030/n12003028.png ; $L A$ ; confidence 0.281
+. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003048.png ; $H ^ { \bullet } ( \partial ( \Gamma \backslash X ) , \tilde { \mathcal{M} } ) = H ^ { 0 } \bigoplus H ^ { 1 } \overset{\sim}{\rightarrow} \mathbf{Q} ^ { h } \bigoplus \mathbf{Q} ^ { h }.$ ; confidence 0.109
-. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120040/n1200409.png ; $G M$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t12007046.png ; $J ( z ) = \sum _ { n } \operatorname { Tr } ( e | _{V _ { n }} ) q ^ { n }$ ; confidence 0.109
-. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120040/n1200407.png ; $F M$ ; confidence 0.982
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005094.png ; $u \in \mathfrak { F }$ ; confidence 0.109
-. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120060/n12006032.png ; $T T$ ; confidence 0.512
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120210/t1202106.png ; $t ( M ; x , y ) = \sum _ { S \subseteq E } ( x - 1 ) ^ { r ( M ) - r ( S ) } ( y - 1 ) ^ { | S |  - r ( S )}.$ ; confidence 0.109
-. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041250/f04125056.png ; $52$ ; confidence 0.574
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130280/f13028035.png ; $\operatorname { max}  \Pi_ { \tilde{\mathbf{c}}^{ \text{T}}  \mathbf{x} } ( \tilde { G } )$ ; confidence 0.109
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010240/a01024018.png ; $Z ]$ ; confidence 0.638
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007066.png ; $Y ^ { e } = X ^ { d }$ ; confidence 0.109
-. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030810/d03081019.png ; $d j$ ; confidence 0.528
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021082.png ; $\mathfrak{b}$ ; confidence 0.109
-. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023130/c02313032.png ; $d x$ ; confidence 0.279
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030034.png ; $3 ^ { C _ {  m} ^ { 1 } + C _ { m } ^ { 2 } + C _ { m } ^ { 3 } }$ ; confidence 0.109
-. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110820/b11082010.png ; $n j$ ; confidence 0.724
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l120100152.png ; $L_{ \gamma , 1}$ ; confidence 0.109
-. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520326.png ; $A =$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130110/s1301105.png ; $\mathbf{Z} ^ { + } [ x _ { 1 } , \ldots , x _ { n } ] ^ { \mathcal{S} _ { n } }$ ; confidence 0.109
-. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057780/l05778080.png ; $20$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120040/k12004014.png ; $F _ { L _ { D } } ( a , x ) = a ^ { - \text { Tait } ( L _ { D } ) } \Lambda _ { D } ( a , x )$ ; confidence 0.108
-. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012790/a0127908.png ; $98$ ; confidence 0.337
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011047.png ; $ \Xi  = ( \hat { x } , \hat { \xi } )$ ; confidence 0.108
-. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130020/o13002022.png ; $41$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120130/d12013038.png ; $w _ { 2 ^ { n } - 2 ^ { i } } ( \rho ) = c _ { n , i }$ ; confidence 0.108
-. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130020/o13002020.png ; $22$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a120160161.png ; $y _ { i t } = \alpha y _ { i , t - 1 } + \sum _ { j = 1 } ^ { N } k _ { i j t } e _ { i j } x _ { j t };$ ; confidence 0.108
-. https://www.encyclopediaofmath.org/legacyimages/o/o110/o110050/o11005097.png ; $60$ ; confidence 0.984
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120020/s12002010.png ; $L _ { x ^ \alpha} ( x ; t ) = \partial _ { x ^ \alpha}  ( g ( x ; t ) * f ( x ) ),$ ; confidence 0.108
-. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033890/d03389020.png ; $X Y$ ; confidence 0.858
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120060/w12006067.png ; $T _ { B  \otimes A}$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120110/p1201104.png ; $19$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230189.png ; $S ( \phi ) = \sum _ { | \alpha | = 0 } ^ { k - 1 } S _ { \alpha i } ^ { a } ( \phi ) \omega _ { \alpha } ^ { a } \bigwedge \left( \frac { \partial } { \partial x _ { i } } \lrcorner ( d x _ { 1 } \bigwedge \ldots \bigwedge d x _ { n } ) \right).$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120110/p1201105.png ; $10$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130060/n13006047.png ; $\mu _ { k + 1 } \leq \frac { 4 \pi ^ { 2 } k ^ { 2 / n } } { ( C _ { n } | \Omega | ) ^ { 2 / n } } ,\, k = 0,1\dots.$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120110/p1201103.png ; $15$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130030/j13003039.png ; $\| a \square b ^ { * } \| \leq \| a \| \cdot \|  b \|$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p13007065.png ; $15$ ; confidence 0.416
+. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230133.png ; $+ \frac { ( - 1 ) ^ { k \text{l} } } { ( k - 1 ) ! \text{l}! } \sum _ { \sigma } \operatorname { sign } \sigma \times \times K ( [ L ( X _ { \sigma 1 } , \ldots , X _ { \sigma \text{l} } ) , X _ { \sigma ( \text{l} + 1 ) } ] , X _ { \sigma ( \text{l} + 2 ) } , \ldots ) +$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015028.png ; $12$ ; confidence 0.447
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130010/j13001015.png ; $Q _ { D } ( v _ { 1 } v _ { 2 } , z ) = \sum _ { f \in \text{lbl} ( D ) }$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p1201509.png ; $g x$ ; confidence 0.794
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130260/a1302603.png ; $a _ { n } = \sum _ { k = 0 } ^ { n } \left( \begin{array} { c } { n + k } \\ { k } \end{array} \right) ^ { 2 } \left( \begin{array} { c } { n } \\ { k } \end{array} \right) ^ { 2 } , \quad b _ { n } = \sum _ { k = 0 } ^ { n } \left( \begin{array} { c } { n + k } \\ { k } \end{array} \right) \left( \begin{array} { c } { n } \\ { k } \end{array} \right) ^ { 2 }$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130120/p13012038.png ; $K >$ ; confidence 0.943
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120160/b12016045.png ; $c _ { i k }$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130120/p13012033.png ; $L >$ ; confidence 0.891
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180399.png ; $\tilde { \nabla } ^ { q } R ( \tilde { g } )$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110580/a11058010.png ; $p 2$ ; confidence 0.191
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a13004045.png ; $\Gamma \vdash_{\mathcal{D}} \varphi$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130120/p13012041.png ; $62$ ; confidence 0.826
+. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130210/c13021020.png ; $w _ { L }$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110580/a110580133.png ; $20$ ; confidence 0.237
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005068.png ; $\mathfrak{H} \oplus \mathfrak{G}$ ; confidence 0.107
-. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q1200505.png ; $D F$ ; confidence 0.996
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022088.png ; $ \Xi  = \mathbf{R} ^ { N } \times [ 0 , \infty [$ ; confidence 0.106
-. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130040/r13004036.png ; $11$ ; confidence 0.051
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040548.png ; $\mathsf{Q}$ ; confidence 0.106
-. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027270/c02727071.png ; $> 4$ ; confidence 0.990
+. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011650/a011650305.png ; $\mathfrak{F}$ ; confidence 0.106
-. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010091.png ; $Z D$ ; confidence 0.462
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012017.png ; $R _ { a b } \equiv R _ { a c b } ^ { c }$ ; confidence 0.106
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110580/a11058037.png ; $91$ ; confidence 0.381
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120120/m12012067.png ; $Q _ { s } ( R ) = \{ q \in Q_{\text{l} } ( R ) : q B \subseteq R \ \text { for some } \ 0 \neq B \lhd R \}$ ; confidence 0.106
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110580/a11058038.png ; $92$ ; confidence 0.691
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120160/s12016027.png ; $H ( q , d ) = \cup _ { q - d + 1 \leq | j | \leq q } ( X ^ { j _ { 1 } } \times \ldots \times X ^ { j _ { d } } ),$ ; confidence 0.106
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130010/s13001013.png ; $R s$ ; confidence 0.433
+. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110220/a11022079.png ; $w _ { t }$ ; confidence 0.106
-. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031850/d031850197.png ; $d u$ ; confidence 0.892
+. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l13006067.png ; $p _ { i + 1 } = a _ { i - 1 } p _ { i } + p _ { i - 1 } ,\,  i = 1,2, \dots .$ ; confidence 0.106
-. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110760/b11076044.png ; $d x$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067110/n06711024.png ; $z ^ { n }$ ; confidence 0.106
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004083.png ; $GL$ ; confidence 0.507
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c12017016.png ; $\mathbf{C} ^ { k }$ ; confidence 0.105
-. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021620/c021620383.png ; $ch$ ; confidence 0.251
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130020/f1300201.png ; $c ^ { a } ( x )$ ; confidence 0.105
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110530/a11053020.png ; $F G$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l1300801.png ; $P _ { 1 } , \ldots , P _ { m } \in \mathbf{Z} [ x _ { 1 } , \ldots , x _ { n } ]$ ; confidence 0.105
-. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033020/d03302028.png ; $52$ ; confidence 0.810
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g130060127.png ; $\sigma ( \Omega ( A ) ) \subseteq \cup _ { i , j = 1 \atop j \neq j } ^ { n } K _ { i,\, j } ( A ) \subseteq \cup _ { i = 1 } ^ { n } G _ { i } ( A ).$ ; confidence 0.105
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130400/s13040038.png ; $E G$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090249.png ; $\mathfrak{g} = \sum _ { \alpha \in \Phi ^ { - } } ^{ \bigoplus} \mathfrak{g} _ { \alpha } \bigoplus \mathfrak{h} \bigoplus \sum_ { \gamma \in \Phi ^ { + } } ^{\bigoplus}  \mathfrak{g} _ { \gamma  }$ ; confidence 0.105
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130440/s13044011.png ; $D X$ ; confidence 0.988
+. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520446.png ; $| f ( V ) | \leq c  _ { 1 } | V | ^ { \gamma } \quad \text { and } \quad | \sum _ { j = 1 } ^ { n } \frac { \partial f } { \partial v _ { j } } \tilde { \phi }_{j}  | > c _ { 2 } | V | ^ { \gamma + m },$ ; confidence 0.105
-. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110410/c11041034.png ; $F y$ ; confidence 0.529
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d13006038.png ; $( x _ { 1 } , \dots , x _ { n } )$ ; confidence 0.105
-. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h047690110.png ; $< 6$ ; confidence 0.938
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130160/r13016039.png ; $\mathcal{C} ^ { m }$ ; confidence 0.104
-. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035800/e03580021.png ; $12$ ; confidence 0.770
+. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095400/u09540031.png ; $G = \operatorname {SL} _ { n } ( K )$ ; confidence 0.104
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023057.png ; $X K$ ; confidence 0.953
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120150/a12015014.png ; $Z _ { G }$ ; confidence 0.104
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023015.png ; $- X$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057020/l05702022.png ; $\mathbf{Z} _ { l } ( m ) _ { X } = ( \mu _ { l ^ { n } ,\, X } ^ { \otimes^m } ) _ { n \in \mathbf{N} }$ ; confidence 0.104
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023076.png ; $Q X$ ; confidence 0.974
+. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070160.png ; $\|\, f \| = ( f , f ) ^ { 1 / 2 } _ { H }$ ; confidence 0.104
-. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110450/b11045014.png ; $43$ ; confidence 0.229
+. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120100/k12010016.png ; $T = \{ ( t _ { 1 } , \dots , t _ { m } ) : t _ { \operatorname { min } } < t _ { 1 } < \ldots < t _ { m } < t _ { \operatorname { max } } ,\; t_{j} \text{ non} \square \text{critical} \}$ ; confidence 0.104
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051049.png ; $| V$ ; confidence 0.199
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c12018026.png ; $- \{ d y ^ { 1 } \bigotimes d y ^ { 1 } + \ldots + d y ^ { q } \bigotimes d y ^ { q } \}$ ; confidence 0.104
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130530/s130530117.png ; $St$ ; confidence 0.422
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s120340110.png ; $( x _ { + } , u _ { - } \sharp  w ) \equiv \tilde{x} _ { + }$ ; confidence 0.104
-. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130530/s130530120.png ; $B N$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b110220118.png ; $r _ { \mathcal{D} } : H _ {  \mathcal{M} } ^ { i } ( X , \mathbf{Q} (\, j ) ) _ {  \mathbf{Z} } \rightarrow H _ { \mathcal{D} } ^ { i } ( X _ { /  \mathbf{R} } ,  \mathbf{R} (\, j ) )$ ; confidence 0.103
-. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040340/f04034086.png ; $< k$ ; confidence 0.931
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010093.png ; $L _ { \gamma  , n _ { 1 }}$ ; confidence 0.103
-. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090670/s0906706.png ; $U f$ ; confidence 0.994
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c120210142.png ; $\theta _ { \tau _ { n } } = \theta + h \tau _ { n } ^ { - 1 / 2 }$ ; confidence 0.103
-. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025860/c02586026.png ; $O D$ ; confidence 0.407
+. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g12004053.png ; $| \widehat { \varphi u } ( \xi ) | \leq c ^ { - 1 } e ^ { - c | \xi | ^ { 1 / s } }$ ; confidence 0.103
-. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s12032017.png ; $40$ ; confidence 0.323
+. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130050/m1300502.png ; $a \leftrightarrow a b ^ { \pm 1 }_ { n }$ ; confidence 0.103
-. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021900/c02190072.png ; $2 N$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020109.png ; $\hat{c}_{k} ^ { 2 } \geq 0$ ; confidence 0.103
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130100/t13010062.png ; $H e$ ; confidence 0.660
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i13003056.png ; $\operatorname { ind } _ { g } ( P ) = ( - 1 ) ^ { n } \operatorname { Ch } ( [ a | _ { T ^ { * } M ^ { g } } ] ) \mathcal{T} ( M ^ { g } ) L ( N , g ) [ T ^ { * } M ^ { g } ].$ ; confidence 0.103
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140174.png ; $96$ ; confidence 0.255
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120310/c12031029.png ; $C _ { d } ^ { k }$ ; confidence 0.103
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014081.png ; $98$ ; confidence 0.966
+. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120020/i1200207.png ; $\times G _ { p + 2 ,\, q } ^ { q - m ,\, p - n + 2 } \left( x\left| \begin{array} { c } {  \mu + i \tau , \mu - i \tau , - ( \alpha _ { p } ^ { n + 1 } ) , - ( \alpha _ { n } ) } \\ { - ( \beta _ { q } ^ { m + 1 } ) , - ( \beta _ { m } ) } \end{array} \right. \right);$ ; confidence 0.103
-. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014092.png ; $K Q$ ; confidence 0.638
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130290/a13029057.png ; $\operatorname{HF} _ { * } ^ { \text { symp } } ( M , \text { id } ) \cong H ^ { * } ( M )$ ; confidence 0.103
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t120140152.png ; $= -$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009090.png ; $\varphi : X \rightarrow \Lambda ^ { r } \bigoplus\bigoplus _ { i = 1 } ^ { s } \Lambda / (\, f _ { i } ( T ) ^ { l _i} ) \bigoplus \bigoplus _ { j = 1 } ^ { t } \Lambda / ( \pi ^ { m _ { j } } )$ ; confidence 0.103
-. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t120140108.png ; $1 f$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060040/l06004017.png ; $g _ { k , p } ( z )$ ; confidence 0.102
-. https://www.encyclopediaofmath.org/legacyimages/v/v110/v110050/v11005033.png ; $Q C$ ; confidence 0.908
+. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120050/t12005089.png ; $\ldots - ( i _ { r  - 1} - i _ { r } ) \cdot \mu _ { i _ { r } },$ ; confidence 0.102
-. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005053.png ; $D v$ ; confidence 0.813
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120130/l12013028.png ; $\overline{x} \in \tilde { \mathbf{Q} } _ { p } ^ { n }$ ; confidence 0.102
-. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110470/c11047044.png ; $F x$ ; confidence 0.389
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510155.png ; $O ( | V | | E | )$ ; confidence 0.101
-. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022860/c02286045.png ; $82$ ; confidence 0.809
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150137.png ; $( k _ { 1 } , \dots , k _ { m } ) \in ( \mathbf{N} \cup \{ 0 \} ) ^ { m }$ ; confidence 0.101
-. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023150/c023150262.png ; $83$ ; confidence 0.817
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230123.png ; $\mathcal{E} ^ { a } ( L ) = \sum _ { | \alpha | = 0 } ^ { k } ( - 1 ) ^ { | \alpha | } \gamma ^ { - 1 } D ^ { \alpha } \left( \gamma \frac { \partial L } { \partial y _ { \alpha } ^ { a } } \right).$ ; confidence 0.101
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110680/a11068027.png ; $p *$ ; confidence 0.532
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d130060129.png ; $ \operatorname { Bel } _ { X } = \operatorname { Bel } ^ { \downarrow X - R _ { T  | X - T - R} } \bigoplus \operatorname { Bel } ^ { \downarrow X - T _ { R  | X - T - R} } \bigoplus \operatorname { Bel } ^ {  \downarrow X - T - R _ { X } }.$ ; confidence 0.101
-. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014060/a01406027.png ; $90$ ; confidence 0.566
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230115.png ; $\mathcal{E} ( L ) = \mathcal{E} ^ { a } ( L ) \omega ^ { a } \bigotimes \Delta,$ ; confidence 0.101
-. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011085.png ; $Cd$ ; confidence 0.137
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e120070127.png ; $\operatorname { dim } \tilde { H } ^ { 1 } = \operatorname { dim } C ^ { 0 } ( \Gamma , k + 2 , \overline{\mathbf{v}} ) + \operatorname { dim } C ^ { 0 } ( \Gamma , k + 2 ,\mathbf{v} )$ ; confidence 0.101
-. https://www.encyclopediaofmath.org/legacyimages/f/f038/f038070/f0380707.png ; $I I$ ; confidence 0.418
+. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044910/g04491082.png ; $v_0$ ; confidence 0.101
-. https://www.encyclopediaofmath.org/legacyimages/f/f038/f038070/f0380708.png ; $I I$ ; confidence 0.731
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012057.png ; $d = \{ d_{ k } \} ^ { \infty } _ { k  =  - \infty}$ ; confidence 0.101
-. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v09690038.png ; $P H$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020071.png ; $T x _ { j } = t _ { j } x _ { j }\, \text { for } x  _ { j } \in X _ { j } \quad (\, j = 1 , \dots , n ).$ ; confidence 0.101
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120020/w12002031.png ; $12$ ; confidence 0.992
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b110220181.png ; $r _ { \mathcal{D} } \bigoplus z _ { \mathcal{D} } : R \bigoplus ( N S ( X ) \bigotimes \mathbf{Q} ) \rightarrow H _ { \mathcal{D} } ^ { 3 } ( X , \mathbf{R} ( 2 ) )$ ; confidence 0.101
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120060/w120060107.png ; $F R$ ; confidence 0.771
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120130/b12013065.png ; $L _ { a } ^ { 1 * } \cong B$ ; confidence 0.100
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120060/w12006023.png ; $M f$ ; confidence 0.732
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018053.png ; $ \mathbf{SP\mathsf{Alg}} _{\models}(  \mathcal{L} ) = \mathbf{SP\mathsf{Alg}} _ { \vdash } ( \mathcal{L} )$ ; confidence 0.100
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120100/w12010011.png ; $25$ ; confidence 0.273
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130230/a13023041.png ; $\operatorname { cos } \alpha = \operatorname { sup } \left\{ \begin{array} { r l } {} &{ u \in U \bigcap V ^ { \perp }, } \\ { \langle u , v \rangle : } & { v \in V \cap U ^ { \perp }, } \\{} & { \| u \| , \| v \| \leq 1 } \end{array} \right\}.$ ; confidence 0.100
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007010.png ; $p j$ ; confidence 0.622
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230118.png ; $\omega ^ { a } = d y ^ { a } - y _ { e _ { i } } ^ { a } d x _ { i }$ ; confidence 0.100
-. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110850/b11085034.png ; $K G$ ; confidence 0.920
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018068.png ; $\mathbf{\mathsf{RCA}}_{ \omega}$ ; confidence 0.099
-. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090348.png ; $U z$ ; confidence 0.170
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a1201707.png ; $\left\{ \begin{array} { l } { p_{ t } ( a , t ) + p _ { a } ( a , t ) + \mu ( a ) p ( a , t ) = 0, } \\ { p ( 0 , t ) = \int _ { 0 } ^ { + \infty } \beta ( a ) p ( a , t ) d a, } \\ { p ( a , 0 ) = p _ { 0 } ( a ) \geq 0, } \end{array} \right.$ ; confidence 0.099
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008064.png ; $t m$ ; confidence 0.583
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180352.png ; $= g ^ { - 1 } \{ 1,4 \} \nabla C ( g ) - g ^ { - 1 } \{ 1,3 ; 2,5 \} ( A ( g ) \bigotimes W ( g ) ) \subset \subset \bigotimes \square ^ { 2 } \mathcal{E},$ ; confidence 0.099
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080115.png ; $d E$ ; confidence 0.985
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120120/d12012030.png ; $d ^ { \prime }$ ; confidence 0.099
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080121.png ; $d Q$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c120210108.png ; $\mathcal{A} _ { n } = \sigma ( X _ { 0 } , \dots , X _ { n } )$ ; confidence 0.099
-. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080176.png ; $F B$ ; confidence 0.989
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020123.png ; $\hat { c } _ { l } ^ { 1 } = c ^ { T } x ^ { ( l ) } + ( A _ { 1 } x ^ { ( l ) } - b _ { 1 } ) ^ { T } \overline { u } _ { 1 } - \overline { q } < 0$ ; confidence 0.098
-. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022020/c02202042.png ; $k ]$ ; confidence 0.192
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170262.png ; $d _ { 1 } ( e _ { 1 } ^ { i } ) = g _ { i } e _ { 0 } - e _ { 0 }$ ; confidence 0.098
-. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032000/d03200040.png ; $k 2$ ; confidence 0.205
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020198.png ; $\tilde{v} ( \tilde { u } _ { 1 } )$ ; confidence 0.098
-. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032130/d03213020.png ; $X f$ ; confidence 0.888
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020250.png ; $\overline { u }_1$ ; confidence 0.098
-. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120010/y120010111.png ; $A I$ ; confidence 0.134
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018020.png ; $\Gamma \vdash_{\mathcal{ L}} \phi$ ; confidence 0.098
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130030/z13003014.png ; $z f$ ; confidence 0.478
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023079.png ; $H = \tilde{I} \tilde { H } \square ^{*}$ ; confidence 0.098
-. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120010/z12001065.png ; $> 3$ ; confidence 0.991
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120240/s12024022.png ; $\operatorname{varprojlim}_{k}( X _ { 1 } \vee \ldots \vee X _ { k } ) = \operatorname{Cl} _ { i = 1 } ^ { \infty } ( X _ { i } , x _ { i 0 } ).$ ; confidence 0.098
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007031.png ; $Z H$ ; confidence 0.873
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043013.png ; $( a \bigotimes c ) ( b \bigotimes d ) = a \cdot \Psi _ { C , B } ( c \bigotimes b ) \cdot d$ ; confidence 0.098
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007044.png ; $Z A$ ; confidence 0.957
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059055.png ; $c _ { n } = q ^ { - n - n ^ { 2 } / 2 } , n = 0 , \pm 1 , \pm 2 , \ldots ,$ ; confidence 0.098
-. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020280/c02028061.png ; $d s$ ; confidence 0.743
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430175.png ; $\partial _ { q , y } ( x ^ { n } y ^ { m } ) = q ^ { n } [ m ] _ { q ^ { 2 } } x ^ { n } y ^ { m - 1 }.$ ; confidence 0.097
-. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011014.png ; $, 4$ ; confidence 0.560
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059040.png ; $\frac { F _ { 1 } z } { 1 + G _ { 1 } z } \square _ { + } \frac { F _ { 2 } z } { 1 + G _ { 2 } z } \square _ { + } \frac { F _ { 3 } } { 1 + G _ { 3 } z } \square _ { + } \dots$ ; confidence 0.097
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240329.png ; $x$ ; confidence 0.527
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043089.png ; $\Psi ( E _ { i } \bigotimes E _ { j } ) = q ^ { a _ { i  j} } E _ { j } \bigotimes E _ { i },$ ; confidence 0.097
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240438.png ; $1$ ; confidence 0.630
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120030/b1200306.png ; $f ( x ) = \sum _ { n \in \mathbf{Z} } \sum _ { m \in \mathbf{Z} } c _ { n , m } (\, f ) g _ { n , m } ( x ),$ ; confidence 0.097
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240305.png ; $4$ ; confidence 0.475
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b130200166.png ; $V = \bigoplus _ { \lambda \in \mathfrak { h } ^ { e * } } V ^ { \lambda },$ ; confidence 0.097
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024094.png ; $m$ ; confidence 0.709
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c12028037.png ; $\pi : \mathcal{FT} \text{op} \rightarrow \mathcal{C} \text{rs}$ ; confidence 0.097
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240186.png ; $b$ ; confidence 0.975
+. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060134.png ; $\tilde { \mathfrak{E} } ( \mu )$ ; confidence 0.096
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240337.png ; $1$ ; confidence 0.560
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b1301202.png ; $\hat { f } ( m ) = ( 2 \pi ) ^ { - 1 } \int _ { - \pi } ^ { \pi } f ( u ) e ^ { - i m u } d u$ ; confidence 0.096
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240370.png ; $2$ ; confidence 0.235
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130010/s13001041.png ; $R _ { S } ^ { * } = \{ x \in \mathbf{Q} : | x | _ { v } = 1 , \forall | \cdot | _ { v } \notin S \}$ ; confidence 0.096
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240546.png ; $7$ ; confidence 0.941
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110590/b11059029.png ; $u_{xx}$ ; confidence 0.096
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240105.png ; $y$ ; confidence 0.961
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130190/a13019017.png ; $\pi /n$ ; confidence 0.096
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240222.png ; $r$ ; confidence 0.879
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130290/f13029018.png ; $T_{\text{min}} \times T_{\text{prod}}$ ; confidence 0.096
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240470.png ; $n$ ; confidence 0.474
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015036.png ; $d _ { 0 } \in \cap _ { \mathsf{P} \in \mathcal{P} } L _ { 2 } ( \Omega , \mathcal{A} , \mathsf{P} )$ ; confidence 0.096
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240422.png ; $1$ ; confidence 0.077
+. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015400/b01540030.png ; $\hat { p }$ ; confidence 0.096
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240501.png ; $9$ ; confidence 0.481
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110175.png ; $a _ { m - 1 } = b _ { m - 1 } - \frac { 1 } { 2 \iota } \sum _ { 1 \leq j \leq n } \frac { \partial ^ { 2 } b _ { m } } { \partial x _ { j } \partial \xi _ { j } } = b _ { m - 1 } ^ { s }.$ ; confidence 0.096
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240529.png ; $R$ ; confidence 0.962
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120270/m12027039.png ; $z _ { 1 } ^ { ( 1 ) } , \dots , z _ { 1 } ^ { ( M ) }$ ; confidence 0.096
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120310/a12031010.png ; $N$ ; confidence 0.325
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023048.png ; $\langle a , b \rangle = a _ { 1 } b _ { 1 } + \ldots + a _ { n } b _ { n }$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120310/a120310136.png ; $A$ ; confidence 0.309
+. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011072.png ; $\mu _ { n } ( x ) / \mu _ { n }$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120310/a120310115.png ; $G$ ; confidence 0.975
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130290/f13029067.png ; $f _ { L } ^ {\rightarrow} \dashv  f _ { L } ^ { \leftarrow }$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120310/a12031042.png ; $k$ ; confidence 0.496
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b130290197.png ; $[ H _ { \mathfrak{M} } ^ { i } ( R ) ] _ { n }$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120310/a120310114.png ; $G$ ; confidence 0.634
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064039.png ; $H ( a ) = ( a _ { 1  + j + k} )_{ j,k = 0}^{\infty}$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040126.png ; $4$ ; confidence 0.882
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a13004010.png ; $\lambda \varphi_{0} , \ldots , \varphi _ { n  - 1}$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120020/a12002036.png ; $8$ ; confidence 0.713
+. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130040/b13004010.png ; $I_{0}$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110020/a11002017.png ; $N$ ; confidence 0.161
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g13004016.png ; $\mathcal{H} ^ { m } ( E ) = \operatorname { sup } _ { \delta > 0 } \operatorname { inf } \left\{ c _ { m } \sum _ { i } | E _ { i } | ^ { m } : \quad \begin{array} { c } { E \subset \cup _ { i } E _ { i } } \\ { | E _ { i } | < \delta \text { for all } } \ i \end{array} \right\},$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130020/a1300203.png ; $1$ ; confidence 0.724
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013073.png ; $g_{l}$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040321.png ; $D$ ; confidence 0.635
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120120/c1201202.png ; $L _ { t }$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020082.png ; $3$ ; confidence 0.218
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130070/h13007040.png ; $( A _ { i  , r + j} , A _ { i  + 1 , r + j} , \dots , A _ { r, r + j} ; \Delta \mathbf{e} _ { j } ) ,\; j = 1 , \dots , l - r,$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040116.png ; $2$ ; confidence 0.401
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130010/g1300101.png ; $E / F$ ; confidence 0.095
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010180/a01018013.png ; $R$ ; confidence 0.629
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050216.png ; $A _ { 2 } = \prod _ { rm ^ { 2 } \geq 2 } ^ { 2 }  \zeta ( rm ^ { 2 } ) = 2.49 \dots$ ; confidence 0.094
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012013.png ; $h$ ; confidence 0.914
+. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110370/c11037053.png ; $h _ { 2 }$ ; confidence 0.094
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040349.png ; $8$ ; confidence 0.330
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a1301804.png ; $\mathcal{L} = \langle \operatorname{Fm} _ { \mathcal{L} } , \operatorname { Mod } _ { \mathcal{L} } , \vDash _ { \mathcal{L} } , \operatorname { mng } _ { \mathcal{L} } , \vdash _ { \mathcal{L} } \rangle ,$ ; confidence 0.094
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040548.png ; $v$ ; confidence 0.106
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014038.png ; $\tilde { \mathbf{D} } _ { n }$ ; confidence 0.094
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110020/a1100202.png ; $v$ ; confidence 0.560
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120270/m12027042.png ; $\left\{ \begin{array} { l } { x _ { 1 } ^ { 3 } + \sum _ { i + j + k \leq 2 } a _ { i j k } x _ { 1 } ^ { i } x _ { 2 } ^ { j } x _ { 3 } ^ { k } = 0, } \\ { x _ { 2 } ^ { 3 } + \sum _ { i + j + k \leq 2 } b _ { i j k } x _ { 1 } ^ { i } x _ { 2 } ^ { j } x _ { 3 } ^ { k } = 0, } \\ { x _ { 3 } ^ { 3 } + \sum _ { i + j + k \leq 2 } c _ { i j k } x _ { 1 } ^ { i } x _ { 2 } ^ { j } x _ { 3 } ^ { k } = 0, } \end{array} \right.$ ; confidence 0.094
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a13004074.png ; $5$ ; confidence 0.478
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013970/a01397010.png ; $\epsilon _ { n }$ ; confidence 0.093
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040583.png ; $1$ ; confidence 0.266
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040331.png ; $\vdash_{\mathcal{D}} E ( x , x ) \text { and } x ,\, E ( x , y )\vdash_{\mathcal{D}} y$ ; confidence 0.093
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a11001069.png ; $b$ ; confidence 0.809
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010040.png ; $L _ { \frac { 3 } { 2 } ,\, n } = L _ { \frac { 3 } { 2 } ,\, n } ^ { c }$ ; confidence 0.093
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040570.png ; $D$ ; confidence 0.545
+. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120140/p1201406.png ; $a _ { n } = N \left( \frac { a _ { n - 1} ^ { 2 }  } { a _ { n  - 2} } \right),$ ; confidence 0.093
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040553.png ; $G$ ; confidence 0.453
+. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004087.png ; $a_{ ( n _ { + } - n _ { - } - s ( D _ { L } ) + 1 ) , ( n - s ( D _ { L } ) + 1 )  } \neq 0$ ; confidence 0.093
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040205.png ; $T$ ; confidence 0.909
+. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d120280155.png ; $g _ { u } \in A / B$ ; confidence 0.093
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040105.png ; $D$ ; confidence 0.999
+. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032130/d032130316.png ; $K _ { x }$ ; confidence 0.093
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040594.png ; $P$ ; confidence 0.673
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018022.png ; $\Delta H \vdash_{\mathcal{L}} \phi $ ; confidence 0.093
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010266.png ; $2$ ; confidence 0.484
+. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130130/h1301309.png ; $\mathbf{r} = ( r _ { 1 } , \dots , r _ { n } ) \in \mathbf{R} ^ { n }$ ; confidence 0.093
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040519.png ; $D$ ; confidence 0.538
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120100/b12010051.png ; $L^{\infty}$ ; confidence 0.093
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050179.png ; $G$ ; confidence 0.737
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s120340116.png ; $\tilde { x } _ { + }$ ; confidence 0.093
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010277.png ; $C$ ; confidence 0.563
+. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840308.png ; $U = \left( \begin{array} { l l } { U _ { 11 } } & { U _ { 12 } } \\ { U _ { 21 } } & { U _ { 22 } } \end{array} \right) : \mathcal{K} \oplus  \mathcal{K} _ { 1 } \rightarrow  \mathcal{K} \oplus  \mathcal{K} _ { 2 },$ ; confidence 0.092
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050203.png ; $P$ ; confidence 0.779
+. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120020/o1200209.png ; $F ( x ) = \frac { x ^ { - a } ( 1 + x ) ^ { 2 a - c } } { \Gamma ( c ) } \times$ ; confidence 0.092
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050228.png ; $G$ ; confidence 0.533
+. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g13004048.png ; $\operatorname { lim } _ { r \rightarrow 0 } \frac { \mathcal{H} ^ { m } \left( \left\{ y \in E \cap B ( x , r ) : \begin{array} { l } { \text { dist } ( y - x , V ) >} \\ {> s | y - x | }\end{array} \right\} \right) } { r^m } ) = 0.$ ; confidence 0.092
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005089.png ; $t$ ; confidence 0.691
+. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009042.png ; $\left\| \theta _ { n } ( h _ { 1 } \bigotimes \ldots \bigotimes h _ { n } ) \right\| _ { L ^ { 2 } ( \mu ) } = \sqrt { n ! } \left| h _ { 1 } \widehat{\bigotimes} \ldots \widehat{\bigotimes} h _ { n } \right| _ { H ^{ \bigotimes  n }}.$ ; confidence 0.092
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060124.png ; $F$ ; confidence 0.993
+. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040538.png ; $\varphi _ { 0 } ^ { 0 } , \ldots , \varphi _ { n _ { 0 } - 1} ^ { 0 }  \rhd \psi ^ { 0 } ; \ldots ; \varphi _ { 0 } ^ { m - 1 } , \ldots , \varphi _ { n _ { m - 1 } -1 } ^ { m - 1 }  \rhd \psi ^ { m - 1 } \vdash _ { \mathcal{G} }$ ; confidence 0.092
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040142.png ; $6$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015046.png ; $d _ { j } ^ { * } \in \cap _ { \mathsf{P} \in \mathcal{P} } L _ { 2 } ( \Omega , \mathcal{A} , \mathsf{P} )$ ; confidence 0.092
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007017.png ; $1$ ; confidence 0.911
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i1300701.png ; $[ - \nabla ^ { 2 } + q ( x ) - k ^ { 2 } ] u = 0\, \operatorname { in } \mathbf{R} ^ { 3 } ,\, k = \text{const} > 0,$ ; confidence 0.092
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110020/a11002062.png ; $3$ ; confidence 0.876
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180482.png ; $W ( \tilde { g } ) = R ( \tilde { g } ) \in \mathsf{A} ^ { 2 } \tilde{\mathcal{E}} \otimes \mathsf{A} ^ { 2 } \tilde{\mathcal{E}}$ ; confidence 0.092
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020084.png ; $r$ ; confidence 0.144
+. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020170.png ; $c \mathsf{E} \left[ \left| U _ { \tau } ^ { * } \right| ^ { p } \right] \leq \operatorname { sup } _ { 0 < r < 1 } \int _ { \partial D } | f ( r e ^ { i \vartheta } ) | ^ { p } \frac { d \vartheta } { 2 \pi } \leq C \mathsf{E} \left[ \left| U _ { \tau } ^ { * } \right| ^ { p } \right],$ ; confidence 0.092
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008084.png ; $8$ ; confidence 0.482
+. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014060/a014060108.png ; $a_1$ ; confidence 0.091
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008069.png ; $-$ ; confidence 0.560
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d13008032.png ; $F ( D _ { a } ) \subset D _ { a }$ ; confidence 0.091
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010460/a01046011.png ; $1$ ; confidence 0.986
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008038.png ; $A = [ A_{l} , A _ { 2 } ] \in C ^ { mn \times ( m n + p )}$ ; confidence 0.091
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010075.png ; $R$ ; confidence 0.859
+. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c12017071.png ; $Z ^ { i } Z ^ { j }$ ; confidence 0.091
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010032.png ; $i$ ; confidence 0.270
+. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900176.png ; $\| T \| =\underset{ \zeta \in Z }{ \operatorname { ess } \operatorname { sup }}  \| T ( \zeta ) \| . $ ; confidence 0.091
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110300/a11030020.png ; $r$ ; confidence 0.461
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120160/e12016027.png ; $R _ { ab } = 0$ ; confidence 0.091
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110320/a11032015.png ; $C$ ; confidence 0.533
+. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110160/f110160130.png ; $\forall x _ { n  + 1} \vee \{ \psi _ { \mathfrak { A } } ^ { l } \overline { a } a : a \in A \}.$ ; confidence 0.091
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a12013020.png ; $X$ ; confidence 0.869
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e1202304.png ; $\mathcal{E} ^ { a } ( L )$ ; confidence 0.091
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010220/a01022046.png ; $v$ ; confidence 0.193
+. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120240/a12024049.png ; $\widehat { CH   \square } ^ { 1 } ( \operatorname { Spec } ( \mathbf{Z} ) ) = \mathbf{R}$ ; confidence 0.091
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a010210120.png ; $1$ ; confidence 0.751
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120280/b1202805.png ; $\prod _ { j = 1 } ^ { \infty } \frac { | a | } { a } \frac { z - a } { 1 - \overline { a } z } , \quad \sum ( 1 - | a _ { j } | ) < \infty .$ ; confidence 0.091
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016084.png ; $5$ ; confidence 1.000
+. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005013.png ; $\{ e _ { i_1 } , \ldots , e _ { i_k } , i , 1 \leq i _ { 1 } < \ldots < i _ { k } \leq n \}$ ; confidence 0.091
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016052.png ; $N$ ; confidence 0.651
+. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002046.png ; $P _ { \operatorname { min } } \leq \mathsf{P} ( A _ { 1 } \bigcup \dots  \bigcup A _ { n } ) \leq P _ { \text{max} }$ ; confidence 0.090
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016019.png ; $U$ ; confidence 0.512
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015092.png ; $d ^ { * } \in \cap _ { \mathsf{P} \in \mathcal{P} } L _ { 1 } ( \Omega , \mathcal{A} , \mathsf{P} ) \cap L _ { 2 } ( \Omega ,\mathcal{A} , \mathsf{P}_ { 0 } )$ ; confidence 0.090
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a120160164.png ; $e$ ; confidence 0.192
+. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004056.png ; $ f _ { i + 1 / 2 } ^ { \text{waf} } = \frac { 1 } { \Delta x } \int _ { - \frac { 1 } { 2 } \Delta x } ^ { \frac { 1 } { 2 } \Delta x } f \left[ u _ { i + 1 / 2 } \left( x , \frac { 1 } { 2 } \Delta t \right) \right] d x, $ ; confidence 0.090
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016020.png ; $I$ ; confidence 0.366
+. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013220/a01322030.png ; $B _ {  k }$ ; confidence 0.090
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010299.png ; $m$ ; confidence 0.874
+. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120350/s12035037.png ; $\left\{ \begin{array} { c c c c }{   \hat{ \theta }_{N} =\hat{\theta }_{N-1}+ \gamma (N) Q_1(X(N),y(N),u(N)),    }\\{X_{N}= X _ { N - 1 } + \mu _ { N } Q _ { 2 } ( X _ { N-1} ,y(N), u(N)), }\end{array} \right. $ ; confidence 0.090
-. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018096.png ; $E$ ; confidence 0.841
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q12001050.png ; $\sum _ { k } \sum _ { l } \overline { c } _ { k } c_{ l} S ( \theta (\, f _ { k } ) - f _ { l } ) \geq 0$ ; confidence 0.090
-. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010200/a01020036.png ; $M$ ; confidence 0.347
+. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110200/b11020015.png ; $\tau ^ { * }$ ; confidence 0.090
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a11004045.png ; $a$ ; confidence 0.199
+. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110110/m1101107.png ; $a _ { r }$ ; confidence 0.090
-. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110060/a11006020.png ; $8$ ; confidence 0.970
+. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f13009076.png ; $N _ { k , r }$ ; confidence 0.090
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180105.png ; $I$ ; confidence 0.411
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011026.png ; $( a ^ { w } ) ^ { * } = \operatorname { Op } \left( J ( \overline { ( J ^ { 1 / 2 } a ) } \right) = \operatorname { Op } ( J ^ { 1 / 2 } \overline { a } ) = ( \overline { a } ) ^ { w },$ ; confidence 0.090
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018065.png ; $i$ ; confidence 0.063
+. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b12040083.png ; $w C ^ { + }$ ; confidence 0.089
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180148.png ; $D$ ; confidence 0.754
+. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120020/e12002046.png ; $\operatorname { map }_{ *}( X \bigwedge Z , Y ) \approx \operatorname { map }_{ *} ( X , \operatorname { map } _ { * } ( Z , Y ) ),$ ; confidence 0.089
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180147.png ; $5$ ; confidence 0.154
+. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090335.png ; $\mathfrak{U} ( \mathfrak{g} )$ ; confidence 0.089
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a1301807.png ; $1$ ; confidence 0.473
+. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011019.png ; $\alpha_{y} = \left( \begin{array} { c c c c } { 0 } & { 0 } & { 0 } & { - i } \\ { 0 } & { 0 } & { i } & { 0 } \\ { 0 } & { - i } & { 0 } & { 0 } \\ { i } & { 0 } & { 0 } & { 0 } \end{array} \right) = \left( \begin{array} { c c } { \mathbf{0} } & { \sigma_ y } \\ { \sigma_ y } & { \mathbf{0}  } \end{array} \right) , \alpha _ { z } = \left( \begin{array} { c c c c } { 0 } & { 0 } & { 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } \\ { 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { 0 } & { 0 } \end{array} \right) = \left( \begin{array} { c c } { \mathbf{0}  } & { \sigma _ { z } } \\ { \sigma _ { z } } & { \mathbf{0}  } \end{array} \right),$ ; confidence 0.089
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018014.png ; $C$ ; confidence 0.281
+. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130110/s13011045.png ; $\mathfrak { S } _ { u } = x  _ {1 } ^ {m }$ ; confidence 0.089
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018012.png ; $1$ ; confidence 0.977
+. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013051.png ; $\left\{ \begin{array}{l}{ \frac { d N ^ { 1 } } { d t } = \lambda _ { ( 1 ) } N ^ { 1 } \left( 1 - \frac { N ^ { 1 } } { K _ { ( 1 ) } } - \delta _ { ( 1 ) } \frac { N ^ { 2 } } { K _ { ( 1 ) } } \right), }\\{ \frac { d N ^ { 2 } } { d t } = \lambda _ { ( 2 ) } N ^ { 2 } \left( 1 - \frac { N ^ { 2 } } { K _ { ( 2 ) } } - \delta _ { ( 2 ) } \frac { N ^ { 1 } } { K _ { ( 2 ) } } \right). }\end{array} \right.$ ; confidence 0.089
-. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018024.png ; $L$ ; confidence 0.758
+. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008058.png ; $\mathsf{E} [ W ] _ { \text{gated} } = \frac { \delta ^ { 2 } } { 2 r } + \frac { P \lambda b ^ { ( 2 ) } + r ( P + \rho ) } { 2 ( 1 - \rho ) } , \mathsf{E} [ W ] _ { \text{lim} } = \frac { \delta ^ { 2 } } { 2 r } + \frac { P \lambda b ^ { ( 2 ) } + r ( P + \rho ) + P \lambda \delta ^ { 2 } } { 2 ( 1 - \rho - P \lambda r ) },$ ; confidence 0.089