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User:Maximilian Janisch/latexlist/latex/NoNroff/7

From Encyclopedia of Mathematics
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1. a12017012.png ; $\Pi ( \alpha ) = \operatorname { exp } ( - \int _ { 0 } ^ { \alpha } \mu ( \sigma ) d \sigma )$ ; confidence 0.946

2. b110220107.png ; $0 \rightarrow F ^ { i + 1 - m } H _ { DR } ^ { i } ( X / R ) \rightarrow H _ { B } ^ { i } ( X / R , R ( i - m ) )$ ; confidence 0.472

3. b12022051.png ; $\partial _ { t } u + \sum _ { j = 1 } ^ { N } \frac { \partial } { \partial x _ { j } } F _ { j } ( u ) = 0$ ; confidence 0.979

4. c120010101.png ; $L _ { \rho } ( a ; w ) = \sum _ { j , k } \rho _ { j \overline { k } } ( a ) w _ { j } \overline { w } _ { k }$ ; confidence 0.713

5. c1200204.png ; $\int _ { 0 } ^ { \infty } \frac { f ^ { * } u _ { t } ^ { * } v _ { t } } { t } d t = \sigma _ { \lambda , v } f$ ; confidence 0.117

6. c12026037.png ; $\| V ^ { n } \| ^ { 2 } \leq \| V ^ { 0 } \| ^ { 2 } + C \sum _ { m = 1 } ^ { n } k \| ( L _ { k k } V ) ^ { m } \| ^ { 2 }$ ; confidence 0.484

7. c12031039.png ; $e _ { N } ( H _ { i j } ^ { k } ) \asymp n ^ { - k } \cdot ( \operatorname { log } n ) ^ { ( \phi - 1 ) / 2 }$ ; confidence 0.058

8. e12012096.png ; $\mu ^ { ( t + 1 ) } = \frac { \sum _ { i } w _ { i } ^ { ( t + 1 ) } y _ { i } } { \sum _ { i } w _ { i } ^ { ( t + 1 ) } }$ ; confidence 0.942

9. e1300307.png ; $M _ { n } = \{ P ( X , Y ) = \sum _ { \nu = 0 } ^ { n } a _ { \nu } X ^ { \nu } Y ^ { n - \nu } : a _ { \nu } \in Q \}$ ; confidence 0.635

10. e12011060.png ; $E = - \nabla \phi - \frac { 1 } { c } \frac { \partial A } { \partial t } , B = \nabla \times A$ ; confidence 0.913

11. f13009028.png ; $U _ { n + 1 } ( x , y ) = \sum _ { j = 0 } ^ { [ n / 2 ] } \frac { ( n - j ) ! } { j ! ( n - 2 j ) ! } x ^ { n - 2 j } y ^ { j }$ ; confidence 0.865

12. f12010090.png ; $J = \left( \begin{array} { c c } { 0 } & { I _ { n } } \\ { - I _ { N } } & { 0 } \end{array} \right)$ ; confidence 0.248

13. g130060113.png ; $\cup _ { i , j = 1 \atop i \neq j } ^ { n } K _ { i } , j ( A ) \subseteq \cup _ { i = 1 } ^ { n } G _ { i } ( A )$ ; confidence 0.402

14. g0433201.png ; $\| u \| _ { \pi / 2 } ^ { 2 } \leq c _ { 1 } \operatorname { Re } B [ u , u ] = c _ { 2 } \| u \| _ { 0 } ^ { 2 }$ ; confidence 0.077

15. j13004075.png ; $( n _ { + } - n _ { - } ) - ( s ( D _ { L } ) - 1 ) \leq e \leq E \leq ( n _ { + } - n _ { - } ) + ( s ( D _ { L } ) - 1 )$ ; confidence 0.972

16. k12007018.png ; $\int _ { 0 } ^ { \pi } d s \int _ { s } ^ { \pi } f ( t - s ) \operatorname { det } C _ { s } ( t ) d t \geq$ ; confidence 0.850

17. k12012040.png ; $\int _ { 0 } ^ { \infty } \frac { - \operatorname { ln } f ( x ^ { 2 } ) } { 1 + x ^ { 2 } } d x < \infty$ ; confidence 0.999

18. k12012041.png ; $\int _ { 0 } ^ { \infty } \frac { - \operatorname { ln } f ( x ^ { 2 } ) } { 1 + x ^ { 2 } } d x = \infty$ ; confidence 0.999

19. l110020132.png ; $( M ^ { \perp } \cup N ^ { \perp } ) ^ { \perp } = M ^ { \perp \perp } \cap ^ { N ^ { \perp } \perp }$ ; confidence 0.401

20. l12006047.png ; $( \phi , e ^ { - i H t } \phi ) = \frac { 1 } { 2 \pi i } \int _ { C } e ^ { - i z t } ( \phi , G ( z ) \phi ) d z$ ; confidence 0.897

21. m12003041.png ; $\gamma ^ { * } = \operatorname { sup } _ { x } | \operatorname { IF } ( x ; T , F _ { \theta } ) |$ ; confidence 0.603

22. m12003045.png ; $\psi _ { b } ( x ) = [ x ] ^ { b } - b = \operatorname { min } ( b , \operatorname { max } ( - b , x ) )$ ; confidence 0.608

23. o13001023.png ; $A ( \alpha ^ { \prime } , \alpha , - k ) = \overline { A ( \alpha ^ { \prime } , \alpha , - k ) }$ ; confidence 0.975

24. p13009043.png ; $\operatorname { lim } _ { x \rightarrow \eta } P _ { \Omega } ( x , \xi ) = 0 , \eta \neq \xi$ ; confidence 0.994

25. p12015070.png ; $\int _ { | x - \alpha _ { j } | \leq r _ { j } } f ( x ) d x , \quad | \alpha _ { j } | + r _ { j } < 1 , j = 1,2$ ; confidence 0.075

26. q12005066.png ; $H _ { new } = H - \frac { H y y ^ { T } H } { y ^ { T } H y } + \frac { s s ^ { T } } { s ^ { T } y } + \phi . w v ^ { T }$ ; confidence 0.576

27. r1300403.png ; $0 < \lambda _ { 1 } ( \Omega ) < \lambda _ { 2 } ( \Omega ) \leq \lambda _ { 3 } ( \Omega ) \leq$ ; confidence 0.996

28. s120150133.png ; $\pi _ { G \times G _ { x } } s : G \times _ { G _ { X } } S \rightarrow ( G \times _ { G _ { X } } S ) / / G$ ; confidence 0.274

29. t12005012.png ; $\Sigma ^ { i } ( f ) = \{ x \in V : \operatorname { dim } \operatorname { Ker } d f _ { x } = i \}$ ; confidence 0.240

30. t1301406.png ; $\Phi ( x ) = \sum _ { j \in Q _ { 0 } } x _ { j } ^ { 2 } - \sum _ { i , j \in Q _ { 0 } } d _ { i j } x _ { i } x _ { j }$ ; confidence 0.648

31. w13004017.png ; $X ( p ) = \operatorname { Re } \int _ { p _ { 0 } } ^ { p } ( \omega _ { 1 } , \ldots , \omega _ { n } )$ ; confidence 0.637

32. w130080216.png ; $T _ { i } = - \frac { n + 1 } { n + 1 - i } \operatorname { Res } _ { \infty } W ^ { 1 - [ i / ( n + 1 ) ] } d p$ ; confidence 0.909

33. w13008056.png ; $\partial _ { i } \rightarrow \partial _ { i } + \epsilon ( \partial / \partial T _ { i } )$ ; confidence 0.989

34. w12018069.png ; $r _ { 2 } ( t , s ) = \prod _ { l = 1 } ^ { N } t _ { i } \wedge s _ { i } - \prod _ { l = 1 } ^ { N } t _ { l } s _ { l }$ ; confidence 0.325

35. w13017017.png ; $K _ { j } \in R ^ { n \times n } , K _ { 0 } = l , \sum _ { j = 0 } ^ { \infty } \| K _ { j } \| ^ { 2 } < \infty$ ; confidence 0.753

36. z13003070.png ; $\hat { f } ( w ) = \frac { 1 } { \sqrt { 2 \pi } } \int _ { - \infty } ^ { \infty } f ( x ) e ^ { i u x } d x$ ; confidence 0.684

37. a130050169.png ; $\zeta _ { K } ( z ) = \sum _ { I \in G _ { K } } | I | ^ { - z } = \sum _ { n = 1 } ^ { \infty } K ( n ) n ^ { - z }$ ; confidence 0.465

38. a12006027.png ; $A u = \sum _ { j = 1 } ^ { m } \alpha _ { j } ( x ) \frac { \partial u } { \partial x _ { j } } + c ( x ) u$ ; confidence 0.749

39. a12007096.png ; $B _ { j } ( t , x , D _ { x } ) u = 0 , \text { on } [ 0 , T ] \times \partial \Omega , j = 1 , \ldots , m$ ; confidence 0.592

40. a12007076.png ; $| \frac { d } { d t } A ( t ) ^ { - 1 } - \frac { d } { d s } A ( s ) ^ { - 1 } \| \leq K _ { 2 } | t - s | ^ { \eta }$ ; confidence 0.840

41. a13006086.png ; $\overline { H _ { 1 } } \cdot \overline { H _ { 2 } } = \overline { H _ { 1 } \cup _ { d } H _ { 2 } }$ ; confidence 0.417

42. a130060133.png ; $F ^ { \# } ( n ) \sim K _ { 0 } C _ { 0 } q _ { 0 } ^ { n } n ^ { - 5 / 2 } \text { asn } \rightarrow \infty$ ; confidence 0.297

43. a13031080.png ; $\sum _ { X } \mu ( X ) \frac { ( \operatorname { tim } e _ { A } ( X ) ) ^ { 1 / k } } { | X | } < \infty$ ; confidence 0.274

44. b12009017.png ; $\frac { \partial f ( z , t ) } { \partial t } = - z f ^ { \prime } ( z , t ) \frac { 1 + k z } { 1 - k z }$ ; confidence 0.996

45. b110220181.png ; $r _ { D } \oplus z _ { D } : R \oplus ( N S ( X ) \otimes Q ) \rightarrow H _ { D } ^ { 3 } ( X , R ( 2 ) )$ ; confidence 0.101

46. b11022054.png ; $\operatorname { ch } _ { M } : K _ { i } ( X ) \rightarrow \oplus H ^ { 2 j - i _ { M } ( X , Q ( j ) ) }$ ; confidence 0.241

47. b11022096.png ; $\operatorname { ch } _ { D } : K _ { i } ( X ) \rightarrow \oplus H ^ { 2 j - i _ { D } } ( X , A ( j ) )$ ; confidence 0.151

48. b12030029.png ; $f ( y ) = \frac { 1 } { ( 2 \pi ) ^ { N / 2 } } \int _ { R ^ { N } } \hat { f } ( \eta ) e ^ { i \eta y } d \eta$ ; confidence 0.715

49. b12001023.png ; $\frac { \partial ^ { 2 } u } { \partial \xi \partial \eta } = \operatorname { sin } ( u )$ ; confidence 1.000

50. c13004029.png ; $\sum _ { k = 1 } ^ { \infty } ( \frac { ( 2 k + 1 ) ! } { k ! ( k + 1 ) ! } ) ^ { 2 } \frac { 2 ^ { - 4 k } } { k } =$ ; confidence 0.919

51. c12029018.png ; $\operatorname { St } ( \Lambda , I ) \rightarrow \operatorname { GL } ( \Lambda , I )$ ; confidence 0.299

52. d12019026.png ; $\lambda ( L ) = \operatorname { sup } \{ E ( f ) : f \in L , \| f \| _ { L _ { 2 } ( \Omega ) } = 1 \}$ ; confidence 0.899

53. f12002046.png ; $A ( ( X ) ) = \{ \sum _ { n \geq n _ { 0 } } ^ { \infty } a _ { n } X ^ { n } : n _ { 0 } \in Z , a _ { n } \in A \}$ ; confidence 0.737

54. f13009011.png ; $U _ { n + 1 } ( x ) = \sum _ { j = 0 } ^ { [ n / 2 ] } \frac { ( n - j ) ! } { j ! ( n - 2 j ) ! } x ^ { n - 2 j } , n = 0,1$ ; confidence 0.639

55. f120110193.png ; $\{ z = x + i y : x _ { 1 } > \frac { | x ^ { \prime } | + 1 } { \varepsilon } , | y | < \varepsilon \}$ ; confidence 0.899

56. g13001046.png ; $a _ { n - 1 } = - \operatorname { Tr } ( \alpha ) \text { and } a _ { 0 } = ( - 1 ) ^ { n } N ( \alpha )$ ; confidence 0.966

57. h13003073.png ; $\frac { q ( z ) t ( w ) - q ( w ) t ( z ) } { z - w } = \sum _ { i , j = 1 } ^ { n } b _ { i , j } z ^ { i - 1 } w ^ { j - 1 }$ ; confidence 0.914

58. h12013027.png ; $\operatorname { Top } ( X , Y ) _ { n } = \operatorname { To } p ( X \times \Delta ^ { n } , Y )$ ; confidence 0.557

59. j13003055.png ; $\{ x y z \} = x \circ ( y ^ { * } \circ z ) + z \circ ( y ^ { * } \circ x ) - ( x \circ z ) \circ y ^ { * }$ ; confidence 0.755

60. k05508020.png ; $\omega = \frac { i } { 2 } \sum _ { \mu , \nu } h _ { \mu \nu } ( z ) d z _ { \mu } \wedge d z _ { \nu }$ ; confidence 0.856

61. l11001011.png ; $( c > 0 ) \& ( \alpha \preceq b ) \Rightarrow ( \alpha c \preceq b c ) \& ( c a \preceq c b )$ ; confidence 0.463

62. l11001014.png ; $( \alpha > 0 ) \& ( \alpha \preceq b ) \Rightarrow ( \alpha \alpha \preceq \alpha c )$ ; confidence 0.924

63. l12010082.png ; $\int _ { R ^ { n N } } | \nabla \Phi | ^ { 2 } \geq K _ { n } \int _ { R ^ { n } } \rho ( x ) ^ { 1 + 2 / n } d x$ ; confidence 0.955

64. l06004014.png ; $g _ { k + 1 } ( z ) = z g _ { k } ( z ) - \phi _ { k } f ( z ) , \quad k = 0,1 , \ldots ; \quad g _ { 0 } ( z ) = 1$ ; confidence 0.153

65. m1300203.png ; $\int ( F _ { A } , F _ { A } ) + ( D _ { A } \phi , D _ { A } \phi ) - \lambda ( 1 - \| \phi \| ^ { 2 } ) ^ { 2 }$ ; confidence 0.995

66. m12015067.png ; $\frac { 1 } { \beta _ { p } ( a , b ) } | V | ^ { \alpha - ( p + 1 ) / 2 } | I _ { p } + V | ^ { - ( \alpha + b ) }$ ; confidence 0.634

67. m12023069.png ; $\operatorname { lim } _ { t \downarrow 0 } u ( t , x ) = f ( x ) \quad \text { for all } x \in H$ ; confidence 0.931

68. m130230147.png ; $( ( X _ { n } + 1 , B _ { n } + 1 ) , f _ { n + 1 } ) = ( ( Y , \phi , \Phi _ { n } ) , f _ { n } \circ \phi ^ { - 1 } )$ ; confidence 0.068

69. n0669608.png ; $\phi ( t ) = ( 1 - 2 i t ) ^ { - N / 2 } \operatorname { exp } \{ \frac { \lambda i t } { 1 - 2 i t } \}$ ; confidence 0.674

70. n067520395.png ; $y _ { i } = z _ { 1 } ^ { \alpha _ { i 1 } } \ldots z _ { n } ^ { \alpha _ { i n } } , \quad i = 1 , \dots , n$ ; confidence 0.390

71. o1200507.png ; $I ( \lambda f ) : = \int _ { 0 } ^ { \infty } \varphi ( \lambda f ^ { * } ( s ) ) w ( s ) d s < \infty$ ; confidence 0.956

72. p13009044.png ; $\operatorname { lim } _ { x \rightarrow \eta } \mu _ { x } ^ { \Omega } = \delta _ { \eta }$ ; confidence 0.993

73. q12001038.png ; $\sum _ { k } \sum _ { l } \overline { c } _ { k } c _ { l } S ( f _ { k } - \overline { f } _ { l } ) \geq 0$ ; confidence 0.228

74. s12023051.png ; $| I _ { p } + \Sigma ^ { - 1 } X X ^ { \prime } | ^ { - ( \delta + n + p - 1 ) / 2 } , X \in R ^ { p \times n }$ ; confidence 0.357

75. s12026017.png ; $[ D _ { t } , D _ { s } ^ { * } ] = \delta ( t - s ) , [ D _ { t } , D _ { s } ] = [ D _ { t } ^ { * } , D _ { s } ^ { * } ] = 0$ ; confidence 0.980

76. t130050180.png ; $\sigma _ { T } ( ( L _ { A } , R _ { B } ) , L ( H ) ) = \sigma _ { T } ( A , H ) \times \sigma _ { T } ( B , H )$ ; confidence 0.334

77. v13011081.png ; $\approx \rho \frac { V ^ { 2 } } { l } [ 1.587 \frac { U } { V } - 0.628 ( \frac { U } { V } ) ^ { 2 } ]$ ; confidence 0.990

78. w13007019.png ; $S _ { \lambda } = e ^ { \lambda + \rho } \sum _ { \gamma } ( - 1 ) ^ { | \gamma | } e ^ { - \gamma }$ ; confidence 0.564

79. w13008028.png ; $\oint _ { A _ { j } } d \omega _ { 1 } = \oint _ { A _ { j } } d \omega _ { 3 } = 0 , j = 1 , \dots , g _ { s }$ ; confidence 0.474

80. w13010037.png ; $\operatorname { exp } [ - \frac { 1 } { 2 } \lambda _ { d } \frac { t } { f ( t ) ^ { 2 / d ^ { 2 } } } ]$ ; confidence 0.317

81. z13010030.png ; $\forall x \forall y ( \forall z ( z \in x \leftrightarrow z \in y ) \rightarrow x = y )$ ; confidence 0.521

82. z13010051.png ; $\forall x \exists z \forall v ( v \in z \leftrightarrow \exists y ( y \in x / v \in y ) )$ ; confidence 0.462

83. z13008053.png ; $\int _ { 0 } ^ { 1 } R _ { k + } ^ { k - l } ( r , \alpha ) J _ { k - l } ( r s ) ( 1 - r ^ { 2 } ) ^ { \alpha } r d r =$ ; confidence 0.550

84. a13013029.png ; $\phi _ { + } = \operatorname { exp } ( \sum _ { j = 1 } ^ { \infty } \phi _ { j } ( x , t ) z ^ { j } )$ ; confidence 0.999

85. a130180124.png ; $= \{ \langle b _ { 0 } , \dots , b _ { 2 } - 1 , a , b _ { 2 } + 1 , \dots , b _ { n - 1 } \rangle : a \in U$ ; confidence 0.114

86. a1303205.png ; $E _ { \theta } ( X _ { i } ) = P _ { \theta } ( X _ { i } = 1 ) = \theta = 1 - P _ { \theta } ( X _ { i } = 0 )$ ; confidence 0.640

87. b12004047.png ; $\mu _ { f } ( \lambda ) = \mu \{ t \in \Omega : | f ( t ) | > \lambda \} = \mu _ { g } ( \lambda )$ ; confidence 0.693

88. b12009066.png ; $f ( z ) = ( \beta \int _ { 0 } ^ { z } h ( \xi ) \xi ^ { - 1 } g ( \xi ) ^ { \beta } d \xi ) ^ { 1 / \beta }$ ; confidence 0.991

89. b110220220.png ; $H _ { B } : \operatorname { Ext } _ { M M _ { O } } ^ { 1 } ( Q ( 0 ) , h ^ { i } ( X ) ( j ) ) \rightarrow$ ; confidence 0.307

90. b110220221.png ; $\rightarrow \operatorname { Ext } _ { M H _ { R } ^ { + } } ( R ( 0 ) , H _ { B } ^ { i } ( X ) , R ( j ) )$ ; confidence 0.159

91. b13012017.png ; $\sum _ { n = - \infty } ^ { \infty } | b _ { n } | \leq 10 \sum _ { n = 1 } ^ { \infty } a _ { n } ^ { * }$ ; confidence 0.938

92. b12022011.png ; $\partial _ { t } \int \phi ( v ) f d v + \operatorname { div } _ { x } \int v \phi ( v ) f d v = 0$ ; confidence 0.530

93. b13023034.png ; $\operatorname { St } _ { G } ( n ) = \cap _ { | \alpha | = n } \operatorname { St } _ { G } ( u )$ ; confidence 0.118

94. b130290137.png ; $G ( \mathfrak { q } ) = \oplus _ { n } \geq 0 \mathfrak { q } ^ { n } / \mathfrak { q } ^ { n + 1 }$ ; confidence 0.652

95. b130300102.png ; $B ( m , n , i ) = \{ \alpha _ { 1 } , \dots , a _ { m } | A _ { 1 } ^ { n } , \dots , A _ { i } ^ { n } \rangle$ ; confidence 0.074

96. c12001098.png ; $\rho _ { j \overline { k } } = \partial ^ { 2 } \rho / \partial z _ { j } \partial z _ { k }$ ; confidence 0.185

97. c120010186.png ; $P ( \partial ) = P ( \partial / \partial z _ { 1 } , \dots , \partial / \partial z _ { n } )$ ; confidence 0.600

98. c12004069.png ; $f ( z ) = \operatorname { lim } _ { m \rightarrow \infty } \int _ { \Gamma } f ( \zeta ) x$ ; confidence 0.863

99. c02211043.png ; $\partial ^ { 2 } p _ { i } ( \theta ) \nmid \partial \theta _ { j } \partial \theta _ { r }$ ; confidence 0.679

100. c13011014.png ; $\partial f ( x ) : = \{ \zeta : f ^ { \circ } ( x ; v ) \geq \{ \zeta , v \} , \forall v \in X \}$ ; confidence 0.739

101. c13014058.png ; $\forall 1 \leq i \leq r : R _ { i } \subseteq M ^ { 2 } \vee R _ { i } \cap M ^ { 2 } = \emptyset$ ; confidence 0.653

102. c120180194.png ; $\operatorname { Ric } ( g ) = g ^ { - 1 } \{ 2,3 \} R ( g ) = g ^ { - 1 } \{ 1,4 \} R ( g ) \in S ^ { 2 } E$ ; confidence 0.604

103. c12021089.png ; $L ( \Lambda _ { n } | P _ { n } ^ { \prime } ) \Rightarrow N ( \sigma ^ { 2 } / 2 , \sigma ^ { 2 } )$ ; confidence 0.978

104. c120210132.png ; $L [ \sqrt { n } ( T _ { n } - \theta _ { n } ) | P _ { n , \theta _ { n } } ] \Rightarrow L ( \theta )$ ; confidence 0.929

105. c12031010.png ; $e ( Q _ { n } , F _ { d } ) = \operatorname { sup } \{ | I _ { d } ( f ) - Q _ { n } ( f ) | : f \in F _ { d } \}$ ; confidence 0.347

106. c12031018.png ; $n ( \epsilon , F _ { d } ) = \operatorname { min } \{ n : e _ { X } ( F _ { d } ) \leq \epsilon \}$ ; confidence 0.524

107. d12012014.png ; $d _ { 0 } : O G \rightarrow O G ^ { \prime } , \quad d _ { A } : A G \rightarrow A G ^ { \prime }$ ; confidence 0.899

108. d13018083.png ; $\alpha \mapsto \operatorname { sup } \{ \| f g _ { \alpha } \| / \| f \| : f \in I _ { E } \}$ ; confidence 0.952

109. e12009012.png ; $R _ { \mu \nu } - \frac { 1 } { 2 } R g _ { \mu \nu } - \Lambda g _ { \mu \nu } = \chi T _ { \mu \nu }$ ; confidence 0.485

110. e12015019.png ; $\frac { D \xi ^ { i } } { d t } = \frac { d \xi ^ { i } } { d t } + \frac { 1 } { 2 } g ^ { i } r \xi ^ { r }$ ; confidence 0.338

111. e13007074.png ; $\ll A ^ { 2 / K } N \lambda _ { k } ^ { 1 / ( 2 K - 2 ) } + M ^ { 1 - 2 / K } \lambda _ { k } ^ { - 1 / ( 2 K - 2 ) }$ ; confidence 0.849

112. f13007031.png ; $F ( r , m ) = \langle x _ { 1 } , \dots , x _ { m } | x _ { i } \dots x _ { i + r } - 1 = x _ { i + r } \rangle$ ; confidence 0.159

113. f13009070.png ; $R _ { c } ( p ; k , n ) = p q ^ { n - 1 } \sum _ { j = 1 } ^ { k } j F _ { n - j + 1 } ^ { ( k ) } + 1 ( \frac { p } { q } )$ ; confidence 0.318

114. f12011086.png ; $Q ( \Omega ) = \tilde { O } ( U \# \Omega ) / \sum _ { j = 1 } ^ { n } \tilde { O } ( U \# ; \Omega )$ ; confidence 0.210

115. f13024046.png ; $L ( \varepsilon ) = L _ { - 2 } \oplus L _ { - 1 } \oplus L _ { 0 } \oplus L _ { 1 } \oplus L _ { 2 }$ ; confidence 0.293

116. g1300205.png ; $\alpha ^ { \beta } = \operatorname { exp } \{ \beta \operatorname { log } \alpha \}$ ; confidence 0.979

117. h13002075.png ; $\gamma ^ { d } \cap \alpha _ { 1 } = \ldots = \gamma ^ { d } \cap \alpha _ { q } = \emptyset$ ; confidence 0.878

118. h120020113.png ; $\rho _ { n } ( \phi ) = \operatorname { inf } \{ \| \phi - r \| _ { BMO } : \rho \in R _ { n } \}$ ; confidence 0.359

119. i12005084.png ; $\operatorname { log } \alpha _ { n } = o ( n ^ { 1 / 3 } ) \text { as } n \rightarrow \infty$ ; confidence 0.683

120. i130090227.png ; $Y ^ { \chi } = \{ y \in Y : \delta . y = \chi ( \delta ) \text { yfor } \delta \in \Delta \}$ ; confidence 0.672

121. k13001041.png ; $A | D _ { + } \rangle - A ^ { - 1 } \langle D _ { - } \} = ( A ^ { 2 } - A ^ { - 2 } ) \langle D _ { 0 } \}$ ; confidence 0.230

122. m12009048.png ; $E ( x ) = \frac { 1 } { ( 2 \pi ) ^ { N } } \int _ { R ^ { n } } \frac { 1 } { P ( \xi ) } e ^ { i \xi x } d \xi$ ; confidence 0.605

123. m12019022.png ; $( f ^ { * } g ) ( x ) = \int _ { 1 } ^ { \infty } \int _ { 1 } ^ { \infty } S ( x , y , t ) f ( t ) g ( y ) d t d y$ ; confidence 0.942

124. m12027038.png ; $\Gamma ( z _ { 1 } ) = z _ { 1 } ^ { M } + b _ { 1 } z _ { 1 } ^ { M - 1 } + \ldots + b _ { M - 1 } z _ { 1 } + b _ { M }$ ; confidence 0.665

125. n06663095.png ; $_ { 1 } , \ldots , v _ { n } ( f ) \leq c \sum _ { l = 1 } ^ { n } \frac { M _ { i } } { v _ { i } ^ { r _ { i } } }$ ; confidence 0.064

126. n066630107.png ; $f - q \in H _ { p } ^ { r _ { 1 } , \ldots , r _ { n } } ( M _ { 1 } ^ { * } , \ldots , M _ { n } ^ { * } ; R ^ { n } )$ ; confidence 0.418

127. o13001089.png ; $A ( \alpha ^ { \prime } , \alpha , k ) \approx - \frac { h | S | } { 4 \pi ( 1 + h | S | C ^ { - 1 } ) }$ ; confidence 0.853

128. o13006059.png ; $\operatorname { det } ( \xi _ { 1 } \sigma _ { 1 } + \xi _ { 2 } \sigma _ { 2 } ) \not \equiv 0$ ; confidence 0.662

129. o1300805.png ; $q _ { m } ( x ) \in L _ { 1,1 } ( R _ { + } ) : = \{ q : \int _ { 0 } ^ { \infty } x | q ( x ) | d x < \infty \}$ ; confidence 0.509

130. q12005059.png ; $H _ { k + 1 } = H _ { k } + \beta _ { k } u ^ { k } ( u ^ { k } ) ^ { T } + \gamma _ { k } v ^ { k } ( v ^ { k } ) ^ { T }$ ; confidence 0.757

131. r13007046.png ; $\| B ( x , y ) \| _ { + } \leq c \sum _ { j = 1 } ^ { \infty } \| \lambda ; \varphi ; ( x ) \| _ { + } =$ ; confidence 0.442

132. r12002012.png ; $M ( q ) \ddot { q } + C ( q , \dot { q } ) \dot { q } + g ( q ) + f ( \dot { q } ) + J ( q ) ^ { T } \phi = \tau$ ; confidence 0.983

133. s13051051.png ; $P _ { n } = \{ u \in V : n = \operatorname { min } m , F ( u ) \subseteq \cup _ { i < m } N _ { i } \}$ ; confidence 0.773

134. s13059025.png ; $H _ { 0 } ^ { ( m ) } = 1 , H _ { k } ^ { ( m ) } = \operatorname { det } ( ( m + i + j ) _ { l , j = 0 } ^ { k - 1 }$ ; confidence 0.117

135. s12034027.png ; $SH ^ { * } ( M , \omega ) \otimes SH ^ { * } ( M , \omega ) \rightarrow SH ^ { * } ( M , \omega )$ ; confidence 0.732

136. t120060108.png ; $\rho _ { atom } ^ { TF } ( x , N = Z , Z ) \sim \gamma ^ { 3 } ( \frac { 3 } { \pi } ) ^ { 3 } | x | ^ { - 6 }$ ; confidence 0.626

137. t13021037.png ; $R ( x ; a _ { 0 } , \dots , a _ { N } ) = \sum _ { n } r _ { n } ( a _ { 0 } , \dots , a _ { N } ) \phi _ { n } ( x )$ ; confidence 0.388

138. t12020065.png ; $R _ { n } > \frac { \operatorname { log } 2 } { 1 + \frac { 1 } { 2 } + \ldots + \frac { 1 } { n } }$ ; confidence 0.506

139. t12021067.png ; $A ( C , q , z ) = ( 1 - z ) ^ { r } z ^ { n - r } t ( M _ { C } ; \frac { 1 + ( q - 1 ) z } { 1 - z } , \frac { 1 } { z } )$ ; confidence 0.261

140. v13005064.png ; $- x _ { 0 } ^ { - 1 } \delta ( \frac { x _ { 2 } - x _ { 1 } } { - x _ { 0 } } ) Y ( v , x _ { 2 } ) Y ( u , x _ { 1 } ) =$ ; confidence 0.981

141. v13007057.png ; $k = \frac { \gamma \dot { b } ^ { 2 } \pi ^ { 2 } } { 12 \mu U \alpha ^ { 2 } ( 1 - \lambda ) ^ { 2 } }$ ; confidence 0.566

142. w13004022.png ; $\operatorname { Re } \int _ { C } ( \omega _ { 1 } , \dots , \omega _ { n } ) = ( 0 , \dots , 0 )$ ; confidence 0.450

143. w12007012.png ; $\{ p _ { j } , p _ { k } \} = \{ q _ { j } , q _ { k } \} = 0 , \quad \{ p _ { j } , q _ { k } \} = \delta _ { j k }$ ; confidence 0.922

144. w1201106.png ; $= \int \int e ^ { 2 i \pi ( x - y ) \cdot \xi } \alpha ( \frac { x + y } { 2 } , \xi ) u ( y ) d y d \xi$ ; confidence 0.682

145. z13010037.png ; $\forall x \forall y \exists z \forall v ( v \in z \leftrightarrow ( v = x \vee v = y ) )$ ; confidence 0.626

146. z13008035.png ; $V _ { k + l } ^ { k - l } ( x , y ; \alpha ) = e ^ { i ( k - l ) \theta } R _ { k + l } ^ { k - l } ( r , \alpha ) =$ ; confidence 0.555

147. z13011059.png ; $R _ { n } ( x ) = \frac { G _ { p , n } ( x ) } { \int _ { 0 } ^ { \infty } ( 1 - e ^ { - z } ) G _ { p , n } ( d z ) }$ ; confidence 0.934

148. a13026023.png ; $\alpha _ { \langle p - 1 \rangle / 2 } \equiv \gamma _ { p } ( \operatorname { mod } p )$ ; confidence 0.294

149. b12010010.png ; $H _ { n } = \sum _ { i = 1 } ^ { n } p _ { i } ^ { 2 } / 2 + \sum _ { 1 = i < j } ^ { n } \Phi ( q _ { i } - q _ { j } )$ ; confidence 0.334

150. b12021070.png ; $\mathfrak { F } _ { \lambda } ( M ) = ( M \otimes L ( \lambda ) ) _ { \theta _ { \lambda } }$ ; confidence 0.779

151. b12002011.png ; $\operatorname { lim } _ { x \rightarrow \infty } \| \alpha _ { x } + \beta _ { x } \| = 0$ ; confidence 0.331

152. b12022038.png ; $\partial _ { t } f + \alpha ( \xi ) . \nabla _ { x } f = \frac { M _ { f } - f } { \varepsilon }$ ; confidence 0.336

153. b12027050.png ; $U ( t ) = \sum _ { 1 } ^ { \infty } P ( S _ { k } \leq t ) = \sum _ { 1 } ^ { \infty } F ^ { ( k ) } ( t )$ ; confidence 0.917

154. b13022060.png ; $| F ( u ) | \leq C _ { 1 } \sum _ { \alpha \in K } \rho ^ { m - N / p } \| D ^ { \alpha } u \| _ { p , T }$ ; confidence 0.372

155. b13025059.png ; $\overline { O K } = \frac { \overline { O \Omega } } { \operatorname { cos } \omega }$ ; confidence 0.970

156. c120180332.png ; $C ( g ) = \nabla A ( g ) - \tau ^ { - 1 } _ { 3 } \nabla A ( g ) \in \varnothing \square ^ { 3 } E$ ; confidence 0.179

157. c12026052.png ; $\| \Delta ( U ^ { n } - u ^ { n } ) \| \leq \| \Delta ( U ^ { 0 } - u ^ { 0 } ) \| + O ( h ^ { 2 } + k ^ { 2 } )$ ; confidence 0.873

158. d11008071.png ; $[ L : K ] = \sum _ { i = 1 } ^ { m } \delta ( w _ { i } | v ) \cdot e ( w _ { i } | v ) \cdot f ( w _ { i } | w )$ ; confidence 0.295

159. d1301108.png ; $H = c \frac { \hbar } { i } \vec { \alpha } . \vec { \nabla } + \vec { \beta } m _ { 0 } c ^ { 2 }$ ; confidence 0.348

160. e1201106.png ; $\nabla \times H - \frac { 1 } { c } \frac { \partial D } { \partial t } = \frac { 1 } { c } J$ ; confidence 0.977

161. f1201105.png ; $| \varphi ( z ) | e ^ { \delta | \overline { | } | } < \infty \text { for some } \delta > 0$ ; confidence 0.071

162. f13019031.png ; $L u = \operatorname { sin } ( x ) \frac { d ^ { 2 } u } { d x ^ { 2 } } - ( \frac { d u } { d x } ) ^ { 2 }$ ; confidence 0.951

163. f12014035.png ; $z ( \zeta ) = \zeta + \frac { a _ { 1 } } { \zeta } + \frac { a _ { 2 } } { \zeta ^ { 2 } } + \ldots$ ; confidence 0.907

164. f12015057.png ; $r ^ { \prime } ( A ) = \operatorname { lim } _ { n \rightarrow \infty } \beta ( A ^ { n } )$ ; confidence 0.897

165. f12021081.png ; $m _ { j } = \sum \{ n _ { i } : 1 \leq i < \text { jand } \lambda _ { i } - \lambda _ { j } \in N \}$ ; confidence 0.732

166. f12024070.png ; $\overline { t } _ { 0 } : = \operatorname { inf } _ { t \geq t _ { 0 } } [ t - h ( t ) ] > - \infty$ ; confidence 0.789

167. g12004073.png ; $D _ { x } ^ { \alpha } = D _ { x _ { 1 } } ^ { \alpha _ { 1 } } \ldots D _ { x _ { n } } ^ { \alpha _ { n } }$ ; confidence 0.632

168. g0433706.png ; $= \operatorname { lim } _ { t \rightarrow 0 } \frac { f ( x _ { 0 } + t h ) - f ( x _ { 0 } ) } { t }$ ; confidence 0.996

169. g0433906.png ; $= \operatorname { lim } _ { t \rightarrow 0 } \frac { f ( x _ { 0 } + t h ) - f ( x _ { 0 } ) } { t }$ ; confidence 0.986

170. i12001028.png ; $\operatorname { lim } _ { t \rightarrow \infty } \Phi _ { 1 } ( t ) / \Phi _ { 2 } ( s t ) = 0$ ; confidence 0.996

171. j12002072.png ; $A ^ { * } = \operatorname { sup } _ { t \geq 0 } | A _ { t } | \leq \frac { 1 } { P [ T < \infty ] }$ ; confidence 0.925

172. j12002012.png ; $f ( z ) = \int k _ { \vartheta } ( z ) f ( e ^ { i \vartheta } ) \frac { d \vartheta } { 2 \pi }$ ; confidence 0.960

173. j120020196.png ; $E [ | Y _ { \infty } - Y _ { T } | ^ { 2 } | F _ { T } ] = w ( B _ { \operatorname { min } } ( T , \tau ) )$ ; confidence 0.484

174. j13004022.png ; $P _ { L } ( v , z ) = P _ { L } ( - v , - z ) = ( - 1 ) ^ { \operatorname { com } ( L ) - 1 } P _ { L } ( - v , z )$ ; confidence 0.974

175. j130040136.png ; $P _ { L } ( i , i ) = ( i \sqrt { 2 } ) ^ { \operatorname { dim } ( H _ { 1 } ( M ^ { ( 3 ) } , Z _ { 2 } ) ) }$ ; confidence 0.365

176. k12007019.png ; $\int _ { 0 } ^ { \pi } d s \int _ { s } ^ { \pi } f ( t - s ) \operatorname { sin } ^ { N } ( t - s ) d t$ ; confidence 0.967

177. k13006059.png ; $| \Delta ( F ) | \geq \left( \begin{array} { c } { x } \\ { k - 1 } \end{array} \right)$ ; confidence 0.984

178. m13008041.png ; $A ^ { in / 0 ut } ( f ) = \operatorname { lim } _ { t \rightarrow \pm \infty } A _ { f } ^ { t }$ ; confidence 0.209

179. m13020026.png ; $\operatorname { ker } ( \gamma \circ \alpha ^ { \prime } ) \subset \mathfrak { g }$ ; confidence 0.637

180. n12010017.png ; $\operatorname { Re } \langle f ( x , y ) - f ( x , z ) , y - z \rangle \leq 0 , y , z \in C ^ { n }$ ; confidence 0.273

181. n067520408.png ; $\sum _ { k = 1 } ^ { \infty } 2 ^ { - k } \operatorname { log } \omega _ { k } ^ { - 1 } < \infty$ ; confidence 0.997

182. o12001018.png ; $Re = \frac { \rho L U } { \mu } , \quad \varepsilon = U ( \frac { \rho } { g \mu } ) ^ { 1 / 3 }$ ; confidence 0.565

183. q12003056.png ; $\pi : \operatorname { Fun } _ { q } ( G ) \rightarrow \operatorname { Fun } _ { q } ( H )$ ; confidence 0.774

184. q12005045.png ; $\frac { d } { d \alpha } f ( x ^ { k } + \alpha d ^ { k } ) | _ { \alpha = 0 } = D f ( x ^ { k } ) d ^ { k } =$ ; confidence 0.926

185. r13008057.png ; $f ( z , z 0 ) = \frac { 1 } { K _ { D } ( z 0 , z _ { 0 } ) } \int _ { z _ { 0 } } ^ { z } K _ { D } ( t , z _ { 0 } ) d t$ ; confidence 0.349

186. r13013012.png ; $P _ { \sigma } = \frac { 1 } { 2 \pi i } \int _ { \Gamma } ( \lambda - A ) ^ { - 1 } d \lambda$ ; confidence 0.932

187. s120050114.png ; $B ( z ) = C \prod _ { j = 1 } ^ { \kappa } \frac { z - \alpha j } { 1 - \overline { \alpha } j z }$ ; confidence 0.579

188. s13045060.png ; $\rho _ { S } = 12 \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { 1 } u v d C _ { X , Y } ( u , v ) - 3 =$ ; confidence 0.259

189. s12021013.png ; $0 \neq \phi \in E ( \lambda , D _ { Y } ) \text { with } \pi ^ { * } \phi \in E ( \mu , D _ { Z } )$ ; confidence 0.819

190. s120230115.png ; $\lambda ( T T ^ { \prime } ) = \operatorname { diag } ( \tau _ { 1 } , \dots , \tau _ { 1 } )$ ; confidence 0.625

191. s13066018.png ; $\lambda _ { n k } = \frac { 1 } { \sum _ { j = 0 } ^ { n - 1 } | \phi _ { j } ( \xi _ { n k } ) | ^ { 2 } } > 0$ ; confidence 0.992

192. t130050172.png ; $\sigma _ { T } ( N , K ) \subseteq \sigma _ { T } ( S , H ) \subseteq \hat { \sigma } ( N , K )$ ; confidence 0.477

193. t12013012.png ; $( L _ { 1 } , L _ { 2 } ) = ( S _ { 1 } \Lambda S _ { 1 } ^ { - 1 } , S _ { 2 } \Lambda ^ { t } S _ { 2 } ^ { - 1 } )$ ; confidence 0.756

194. t09408031.png ; $\pi _ { n } ( X ; A , B , ^ { * } ) = \pi _ { n - 1 } ( \Omega ( X ; B , * ) , \Omega ( A ; A \cap B , * ) , * )$ ; confidence 0.193

195. t1202106.png ; $t ( M ; x , y ) = \sum _ { S \subseteq E } ( x - 1 ) ^ { r ( M ) - \gamma ( S ) } ( y - 1 ) ^ { | S | } - r ( S )$ ; confidence 0.109

196. v120020220.png ; $\delta ^ { * } \circ ( t - r ) ^ { * } \beta _ { 1 } = k ( t ^ { * } \square ^ { - 1 } \beta _ { 3 } )$ ; confidence 0.259

197. v13011080.png ; $D = \rho \frac { \Gamma b } { l } ( V - 2 U ) + \rho \frac { \Gamma ^ { 2 } } { 2 \pi l } \approx$ ; confidence 0.884

198. v096900176.png ; $\| T \| = \operatorname { ess } _ { S \in Z } \operatorname { sup } _ { \| T ( \zeta ) \| }$ ; confidence 0.091

199. w12003034.png ; $\operatorname { dens } ( P _ { \alpha } ( X ) ) \leq \operatorname { card } ( \alpha )$ ; confidence 0.954

200. w1300505.png ; $W ( \mathfrak { g } ) = \bigwedge \mathfrak { g } ^ { * } \otimes S \mathfrak { g } ^ { * }$ ; confidence 0.334

201. w13007020.png ; $\gamma = \sum _ { i = 1 } ^ { \gamma } \alpha _ { i } + \sum _ { j = 1 } ^ { s } p _ { j } \beta _ { j }$ ; confidence 0.597

202. w1200809.png ; $\Omega ( q , p ) \psi ( x ) = 2 ^ { n } \operatorname { exp } \{ 2 i p . ( x - q ) \} \psi ( 2 q - x )$ ; confidence 0.600

203. w120110233.png ; $H ( X ) = \operatorname { sup } _ { T \neq 0 } \sqrt { \frac { G X ( T ) } { G _ { X } ^ { g } ( T ) } }$ ; confidence 0.528

204. w120110258.png ; $\{ u \in S ^ { \prime } ( R ^ { n } ) : \forall a \in S ( m , G ) , a ^ { w } u \in L ^ { 2 } ( R ^ { n } ) \}$ ; confidence 0.264

205. w130080172.png ; $\omega ^ { 0 } = \int \Sigma _ { g } \langle \delta A , \delta \overline { A } \rangle$ ; confidence 0.582

206. w13014026.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { n } { 2 } r ( n x ) = \delta ( x )$ ; confidence 0.904

207. z130110133.png ; $\alpha ( x ) = \frac { \beta \Gamma ( x - \beta ) } { \Gamma ( 1 - \beta ) \Gamma ( x + 1 ) }$ ; confidence 0.987

208. a13002017.png ; $\nu = \operatorname { lim } \sum _ { k = 0 } ^ { n - 1 } \frac { 1 } { n } \delta _ { T ^ { n } x }$ ; confidence 0.751

209. a1200803.png ; $\sum _ { i , j = 1 } ^ { m } \alpha _ { i , j } ( x ) n _ { i } ( x ) \partial u / \partial x _ { j } = 0$ ; confidence 0.254

210. a12008010.png ; $\sum _ { i , j = 1 } ^ { m } \alpha _ { i , j } ( x ) \xi _ { i } \xi _ { j } \geq \delta | \xi | ^ { 2 }$ ; confidence 0.112

211. a12018010.png ; $\Delta ^ { 2 } S _ { n } = \Delta S _ { n + 1 } - \Delta S _ { n } = S _ { n + 2 } - 2 S _ { n + 1 } + S _ { n }$ ; confidence 0.895

212. a12018050.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { T _ { x } - S } { S _ { x } - S } = 0$ ; confidence 0.632

213. a12027068.png ; $h _ { p } = ( 2 , d ) _ { P } \cdot W _ { P } ( \rho ) / W _ { P } ( \operatorname { det } _ { \rho } )$ ; confidence 0.615

214. b12021050.png ; $\overline { \delta } k : \overline { D } _ { k } \rightarrow \overline { D } _ { k - 1 }$ ; confidence 0.420

215. b120040184.png ; $\Sigma _ { \gamma = 1 } ^ { \infty } \| T _ { X _ { \gamma } } \| _ { X } ^ { \gamma } < \infty$ ; confidence 0.114

216. b12005061.png ; $M ( H _ { b } ( \mathfrak { c } _ { 0 } ) ) = \{ \tilde { \delta _ { z } } : z \in l _ { \infty } \}$ ; confidence 0.053

217. b1200605.png ; $\Delta u + \epsilon \frac { 4 n ( n + 1 ) } { ( 1 + \epsilon ( x ^ { 2 } + y ^ { 2 } ) ) ^ { 2 } } u = 0$ ; confidence 0.991

218. b12016066.png ; $x _ { 2 } ^ { \prime } = x _ { 3 } ^ { \prime } = \frac { 1 } { 2 } [ ( x _ { 1 } + x _ { 2 } ) s - x _ { 1 } v ]$ ; confidence 0.971

219. b12020018.png ; $\theta ( e ^ { i t } ) = \operatorname { lim } _ { r \rightarrow 1 } \theta ( r e ^ { i t } )$ ; confidence 0.968

220. b13012036.png ; $( f ^ { * } d \mu ) _ { N } ( x ) = \sum _ { k } \lambda ( \frac { k } { N } ) \hat { f } ( k ) e ^ { i k x }$ ; confidence 0.140

221. b13030047.png ; $| B ( m , 6 ) | = 2 ^ { \alpha } 3 ^ { C _ { \beta } ^ { 1 } + C _ { \beta } ^ { 2 } + C _ { \beta } ^ { 3 } }$ ; confidence 0.861

222. c12008069.png ; $= \sum _ { i = 0 } ^ { m } D _ { i , m - i } \Lambda ^ { i } M ^ { m - i } , D _ { i j } \in C ^ { n \times n }$ ; confidence 0.619

223. c13010021.png ; $f = \sum _ { i = 1 } ^ { n } a _ { i } \chi _ { B _ { i } } , \quad B _ { i } = \cup _ { j = i } ^ { n } A _ { i }$ ; confidence 0.197

224. c120210121.png ; $L [ \Delta _ { n } ( \theta ) | P _ { n , \theta } ] \Rightarrow N ( 0 , \Gamma ( \theta ) )$ ; confidence 0.975

225. d1200604.png ; $\psi [ 1 ] = \psi _ { x } + \sigma \psi ; \quad \sigma = - \varphi _ { x } \varphi ^ { - 1 }$ ; confidence 0.835

226. d13006029.png ; $m _ { E _ { 1 } , E _ { 2 } } ( A ) = c . \sum _ { B , C , A = B \cap C } m _ { E _ { 1 } } ( B ) m _ { E _ { 2 } } ( C )$ ; confidence 0.208

227. d12013022.png ; $f ( X ) = X ^ { q ^ { n } } + \sum _ { i = 0 } ^ { n - 1 } ( - 1 ) ^ { n - i } c _ { n , i } X ^ { q ^ { i } } \in K [ X ]$ ; confidence 0.576

228. d13011045.png ; $\gamma _ { 1 } ^ { 2 } = - 1 , \gamma _ { 2 } ^ { 2 } = \gamma _ { 3 } ^ { 2 } = \gamma _ { 4 } ^ { 2 } = 1$ ; confidence 0.610

229. d12029050.png ; $\sum _ { q = 2 , q \text { prime } } ^ { \infty } f ( q ) q ( \operatorname { log } q ) ^ { - 1 }$ ; confidence 0.608

230. e12010041.png ; $f ^ { em } = \operatorname { div } t ^ { em } - \frac { \partial G ^ { em } } { \partial t }$ ; confidence 0.635

231. e13004046.png ; $= ( \Omega _ { + } - 1 ) g _ { 0 } P _ { + } \psi ( t ) + ( \Omega _ { + } - 1 ) g _ { 0 } P _ { - } \psi ( t )$ ; confidence 0.653

232. e12023091.png ; $y ^ { ( r ) } = \{ y _ { \alpha } ^ { \alpha } \} _ { | \alpha | = r } ^ { \alpha = 1 , \ldots , m }$ ; confidence 0.062

233. f1300908.png ; $U _ { n } ( x ) = \frac { \alpha ^ { n } ( x ) - \beta ^ { n } ( x ) } { \alpha ( x ) - \beta ( x ) }$ ; confidence 0.947

234. f12009030.png ; $H _ { K } ( \zeta ) = \operatorname { sup } _ { z \in K } \operatorname { Re } ( \zeta z )$ ; confidence 0.936

235. f110160130.png ; $\forall x _ { n } + 1 \vee \{ \psi _ { \mathfrak { A } } ^ { l } \overline { a } a : a \in A \}$ ; confidence 0.091

236. g12004077.png ; $P ( x , D ) u = ( 2 \pi ) ^ { - n } \int _ { R ^ { n } } e ^ { i x \xi } p ( x , \xi ) \hat { u } ( \xi ) d \xi$ ; confidence 0.187

237. h04601091.png ; $\tau ( W \cup W ^ { \prime } , M _ { 0 } ) = \tau ( W , M _ { 0 } ) + \tau ( W ^ { \prime } , M _ { 1 } )$ ; confidence 0.702

238. h13003032.png ; $\frac { r ( z ^ { - 1 } ) } { z } - \frac { p ( z ) } { q ( z ) } = w _ { 0 } z ^ { 2 n } + w _ { 1 } z ^ { 2 n + 1 } +$ ; confidence 0.830

239. h13005011.png ; $\frac { d ^ { 2 } \psi } { d x ^ { 2 } } + [ \lambda - u ( x , t ) ] \psi = 0 , - \infty < x < \infty$ ; confidence 0.997

240. h13005038.png ; $\frac { d ^ { 2 } \psi } { d x ^ { 2 } } + \lambda \rho ( x , t ) \psi = 0 , - \infty < x < \infty$ ; confidence 0.997

241. h13012022.png ; $\alpha ( x ) = \operatorname { lim } _ { n \rightarrow \infty } 2 ^ { - n } f ( 2 ^ { n } x )$ ; confidence 0.568

242. i13002023.png ; $P ( A _ { 1 } \cap \ldots \cap A _ { n } ) = \sum _ { k = 1 } ^ { n } ( - 1 ) ^ { k - 1 } \frac { 1 } { k ! }$ ; confidence 0.569

243. i12004050.png ; $K ( s ) = \frac { ( n - 1 ) ! } { ( 2 \pi i ) ^ { N } } \frac { 1 } { \{ s , \zeta - z \} ^ { n } } \times$ ; confidence 0.278

244. i12005085.png ; $e ( T , V ) = \operatorname { lim } _ { n \rightarrow \infty } \frac { m ( n ; T , V ) } { n }$ ; confidence 0.988

245. i13005078.png ; $R _ { + } ( x ) : = \frac { 1 } { 2 \pi } \int _ { - \infty } ^ { \infty } r _ { + } ( k ) e ^ { i k x } d k$ ; confidence 0.481

246. k12010015.png ; $t _ { \operatorname { min } } < t _ { 1 } < \ldots < t _ { m } < t _ { \operatorname { max } }$ ; confidence 0.631

247. l110010121.png ; $( a \wedge b = 0 ) \& ( c \succeq 0 ) \Rightarrow ( c a \wedge b = 0 ) \& ( a c \wedge b = 0 )$ ; confidence 0.318

248. l1200501.png ; $F ( \tau ) = \int _ { 0 } ^ { \infty } \operatorname { Re } K _ { 1 / 2 } + i \tau ( x ) f ( x ) d x$ ; confidence 0.594

249. l1200508.png ; $F ( \tau ) = \int _ { 0 } ^ { \infty } \operatorname { Im } K _ { 1 / 2 } + i \tau ( x ) f ( x ) d x$ ; confidence 0.896

250. m13003020.png ; $\underline { \beta } ^ { ( l ) } = ( \beta _ { 0 } ^ { ( l ) } , \beta _ { 1 } ^ { ( l ) } , \ldots )$ ; confidence 0.688

251. m130110138.png ; $( v . \nabla ) v = \frac { 1 } { 2 } \nabla v ^ { 2 } + ( \operatorname { curl } v ) \times v$ ; confidence 0.508

252. m12016064.png ; $\psi ( u ) = \int _ { 0 } ^ { \infty } \Omega _ { p _ { 1 } n _ { 1 } } ( r ^ { 2 } u ) d F ( r ) , u \geq 0$ ; confidence 0.607

253. n13006047.png ; $\mu _ { k + 1 } \leq \frac { 4 \pi ^ { 2 } k ^ { 2 / N } } { ( C _ { N } | \Omega | ) ^ { 2 / N } } , k = 0,1$ ; confidence 0.107

254. n06663089.png ; $\mathfrak { W } _ { 1 } , \ldots , v _ { n } ( x _ { 1 } , \ldots , x _ { n } ) \in L _ { p } ( R ^ { n } )$ ; confidence 0.070

255. n067520278.png ; $\int _ { - \infty } ^ { + \infty } | F ( \xi ) | ^ { 2 } d ( E _ { \xi } h _ { 0 } , h _ { 0 } ) < \infty$ ; confidence 0.998

256. o12005068.png ; $\operatorname { inf } \{ \lambda > 0 : \int \psi ( f ^ { * } / \lambda w ) w < \infty \}$ ; confidence 0.693

257. q12001026.png ; $\int _ { \Omega } f _ { 1 } \circ X _ { t _ { 1 } } \ldots f _ { n } \circ X _ { t _ { n } } d P \geq 0$ ; confidence 0.785

258. q12007039.png ; $g E g ^ { - 1 } = q ^ { 2 } E , g F g ^ { - 1 } = q ^ { - 2 } F , [ E , F ] = \frac { g - g ^ { - 1 } } { q - q ^ { - 1 } }$ ; confidence 0.851

259. r12002019.png ; $F _ { 1 } ( q , \dot { q } ) = C _ { 1 } ( q , \dot { q } ) \dot { q } + g _ { 1 } ( q ) + f _ { 1 } ( \dot { q } )$ ; confidence 0.929

260. r12002020.png ; $F _ { 2 } ( q , \dot { q } ) = C _ { 2 } ( q , \dot { q } ) \dot { q } + g _ { 2 } ( q ) + f _ { 2 } ( \dot { q } )$ ; confidence 0.598

261. s13011038.png ; $\mathfrak { S } _ { w } = x _ { r } \mathfrak { S } _ { v } + \sum \mathfrak { S } _ { v ( q , r ) }$ ; confidence 0.423

262. s13066019.png ; $\operatorname { span } \{ z ^ { - n - 1 } , \ldots , z ^ { - 1 } , 1 , z , \ldots , z ^ { n - 1 } \}$ ; confidence 0.219

263. t130050161.png ; $\sigma _ { 1 } ( A ) = \sigma _ { le } ( A ) = \sigma _ { re } ( A ) = \sigma _ { Te } ( A ) = S ^ { 3 }$ ; confidence 0.531

264. v13005063.png ; $x _ { 0 } ^ { - 1 } \delta ( \frac { x _ { 1 } - x _ { 2 } } { x _ { 0 } } ) Y ( u , x _ { 1 } ) Y ( v , x _ { 2 } ) +$ ; confidence 0.917

265. v13005065.png ; $= x _ { 2 } ^ { - 1 } \delta ( \frac { x _ { 1 } - x _ { 0 } } { x _ { 2 } } ) Y ( Y ( u , x _ { 0 } ) v , x _ { 2 } )$ ; confidence 0.904

266. w12011045.png ; $= \int _ { R ^ { 2 n } } \hat { \alpha } ( \Xi ) \operatorname { exp } ( 2 i \pi \Xi M ) d \Xi$ ; confidence 0.522

267. w12011058.png ; $\alpha ( x , \xi ) = \int k ( x + \frac { t } { 2 } , x - \frac { t } { 2 } ) e ^ { - 2 i \pi t \xi } d t$ ; confidence 0.841

268. w130080189.png ; $\omega = \omega ^ { 0 } - ( 1 / \kappa ) \sum \delta H _ { \alpha } \delta t _ { \alpha }$ ; confidence 0.984

269. w13009075.png ; $\{ \varphi _ { n _ { 1 } , n _ { 2 } , \ldots } : n _ { j } \geq 0 , n _ { 1 } + n _ { 2 } + \ldots = n \}$ ; confidence 0.325

270. w13017051.png ; $f ( \lambda ) = ( 2 \pi ) ^ { - 1 } k ( e ^ { - i \lambda } ) \Sigma k ^ { * } ( e ^ { - i \lambda } )$ ; confidence 0.817

271. z13001011.png ; $Z ( \delta _ { k } ( n ) ) = \sum _ { j = 0 } ^ { \infty } \delta _ { k } ( j ) z ^ { - j } = z ^ { - k } fo$ ; confidence 0.550

272. z13003026.png ; $f ( t ) = ( 2 \gamma ) ^ { 1 / 4 } \operatorname { exp } ( - \pi \gamma t ^ { 2 } ) , \gamma > 0$ ; confidence 0.998

273. a12007068.png ; $| ( A ( t ) - A ( s ) ) A ( 0 ) ^ { - 1 } \| \leq C _ { 2 } | t - s | ^ { \alpha } , \quad t , s \in [ 0 , T ]$ ; confidence 0.911

274. a13008072.png ; $t _ { N } ( x ) = \frac { c _ { N } } { s } ( 1 + \frac { ( x - m ) ^ { 2 } } { s ^ { 2 } n } ) ^ { - ( n + 1 ) / 2 }$ ; confidence 0.342

275. a12028064.png ; $\langle U _ { \mu } ( x ) , \rho \rangle = \int \{ U _ { t } ( x ) , \rho \rangle d \mu ( t )$ ; confidence 0.507

276. b12010033.png ; $F ( 0 ) = ( F _ { 1 } ( 0 , x _ { 1 } ) , \ldots , F _ { N } ( 0 , x _ { 1 } , \ldots , x _ { N } ) , \ldots )$ ; confidence 0.084

277. b1201001.png ; $F ( t ) = ( F _ { 1 } ( t , x _ { 1 } ) , \ldots , F _ { n } ( t , x _ { 1 } , \ldots , x _ { n } ) , \ldots )$ ; confidence 0.326

278. b120210112.png ; $( - , N ) : N ^ { \prime } \rightarrow \operatorname { Hom } _ { a } ( N ^ { \prime } , N )$ ; confidence 0.774

279. b110220133.png ; $_ { S = m } L ( h ^ { i } ( X ) , s ) = \operatorname { dim } H _ { D } ^ { i + 1 } ( X / R , R ( i + 1 - m ) )$ ; confidence 0.273

280. b110220192.png ; $F ^ { m } H _ { DR } ^ { 2 m - 1 } ( X / R ) \rightleftarrows H _ { B } ^ { 2 m - 1 } ( X / R , R ( m - 1 ) )$ ; confidence 0.242

281. b13009018.png ; $d ( u , \phi ) ( t ) = \operatorname { inf } \{ \| u - \phi ( x - v t - c ) \| _ { 1 } : c \in R \}$ ; confidence 0.953

282. b12014052.png ; $S ( z ) \equiv \frac { \omega ( z ) } { \sigma ( z ) } ( \operatorname { mod } z ^ { 2 t } )$ ; confidence 0.978

283. b13016052.png ; $C ( X , \tau ) : = \{ f \in C ( X ) : f ( \tau ( x ) ) = \overline { f ( x ) } , \forall x \in X \}$ ; confidence 0.953

284. b12034031.png ; $\sum _ { \alpha } \operatorname { sup } _ { D _ { r } } | c _ { \alpha } z ^ { \alpha } | < 1$ ; confidence 0.383

285. b12043068.png ; $\Psi ( y \bigotimes y ) = q ^ { 2 } y \otimes y \Psi ( x \varnothing y ) = q y \otimes x$ ; confidence 0.176

286. b13026044.png ; $y \notin f ( \overline { \Omega } \backslash ( \Omega _ { 1 } \cup \Omega _ { 2 } ) )$ ; confidence 0.656

287. b12052061.png ; $( B + u v ^ { T } ) ^ { - 1 } = ( I - \frac { ( B ^ { - 1 } u ) v ^ { T } } { 1 + v ^ { T } B ^ { - 1 } u } ) B ^ { - 1 }$ ; confidence 0.954

288. c12007014.png ; $\{ M ( \alpha _ { n } + 1 ) \text { pr } \{ \alpha _ { 1 } , \dots , \alpha _ { n } \rangle +$ ; confidence 0.465

289. d12002033.png ; $v ^ { * } = \sum _ { k \in P } \lambda _ { k } x ^ { ( k ) } + \sum _ { k \in R } \mu _ { k } x ^ { ( k ) }$ ; confidence 0.323

290. d1301107.png ; $= ( \alpha _ { x } p _ { x } + \alpha _ { y } p y + \alpha _ { z } p _ { z } + \beta m _ { 0 } c ) ^ { 2 }$ ; confidence 0.359

291. d13017034.png ; $\lambda _ { k } \approx \frac { 4 \pi ^ { 2 } k ^ { 2 / n } } { ( C _ { n } | \Omega | ) ^ { 2 / n } }$ ; confidence 0.935

292. d12020017.png ; $\int _ { 0 } ^ { 1 } | p _ { R } ( i t ) | ^ { 2 } d t = \sum _ { m = 1 } ^ { n } | a _ { m } | ^ { 2 } ( T + O ( m ) )$ ; confidence 0.464

293. d12020012.png ; $\zeta ( s ) = \sum _ { m \leq x } m ^ { - s } + \frac { x ^ { 1 - s } } { s - 1 } + O ( x ^ { - \sigma } )$ ; confidence 0.949

294. d12024033.png ; $\operatorname { im } \mathfrak { g } - \operatorname { dim } \mathfrak { g } ( f )$ ; confidence 0.575

295. e035000109.png ; $I _ { \epsilon } = \operatorname { inf } _ { \rho \in R _ { \epsilon } ( X ) } I ( \rho )$ ; confidence 0.469

296. e1201508.png ; $\frac { d ^ { 2 } x ^ { i } } { d t ^ { 2 } } + g ^ { i } ( x , \dot { x } , t ) = 0 , \quad i = 1 , \dots , n$ ; confidence 0.531

297. e120240130.png ; $c _ { l } \in H ^ { 1 } ( G ( \overline { Q } / Q ) ; \operatorname { Sym } ^ { 2 } T _ { p } ( E ) )$ ; confidence 0.588

298. f120150182.png ; $\nu ( A ) = \operatorname { sup } _ { M } \text { inf } \{ \| A x \| : x \in M , \| x \| = 1 \}$ ; confidence 0.250

299. f1202303.png ; $\Omega ( M , T M ) = \oplus _ { k = 0 } ^ { \operatorname { dim } M } \Omega ^ { k } ( M , T M )$ ; confidence 0.926

300. g12004053.png ; $| \tilde { \varphi } \mathfrak { u } ( \xi ) | \leq c ^ { - 1 } e ^ { - c | \xi | ^ { 1 / s } }$ ; confidence 0.103

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/7. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/7&oldid=44495