View source for User:Maximilian Janisch/latexlist/latex/Algebraic Groups/3

== List ==
1. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763026.png ; $V = \oplus _ { \chi \in P _ { \phi } } V ( \chi )$ ; confidence 0.914

2. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023720/c02372058.png ; $\Gamma = \{ z \in \overline { C } : | z | = 1 \}$ ; confidence 0.985

3. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t1301306.png ; $T _ { 0 } , T _ { 1 } \in \operatorname { add } T$ ; confidence 0.822

4. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014054.png ; $v = ( v _ { j } ) _ { j \in Q _ { 0 } } \in N ^ { Q _ { 0 } }$ ; confidence 0.787

5. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t1301407.png ; $x = ( x _ { i } ) _ { i \in Q _ { 0 } } \in Z ^ { Q _ { 0 } }$ ; confidence 0.557

6. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090223.png ; $V ^ { * } = \operatorname { Hom } _ { K } ( V , K )$ ; confidence 0.975

7. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011740/a01174031.png ; $\operatorname { Aut } _ { T } ( X \times T )$ ; confidence 0.916

8. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031550/d03155045.png ; $G = G _ { \mathscr { L } } G _ { \mathscr { G } }$ ; confidence 0.052

9. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830290.png ; $A = \sum _ { i = 0 } ^ { d } A _ { i } u _ { A } ^ { i }$ ; confidence 0.523

10. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830138.png ; $B ( \eta _ { 1 } , \ldots , \eta _ { n } ) \neq 0$ ; confidence 0.425

11. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032490/d03249036.png ; $\omega _ { \eta } / F = \omega _ { \zeta / F }$ ; confidence 0.463

12. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032490/d03249023.png ; $F = G _ { 0 } \subset G _ { 1 } \subset \ldots$ ; confidence 0.888

13. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120252.png ; $\operatorname { Re } ( z e ^ { - i \phi } ) > c$ ; confidence 0.886

14. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d03412068.png ; $\{ H ^ { \gamma } ( X , A ) , f ^ { * } , \delta \}$ ; confidence 0.761

15. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120471.png ; $\operatorname { lim } _ { n } f ( x _ { n } ) = 0$ ; confidence 0.651

16. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960196.png ; $( F \{ \eta _ { 1 } , \ldots , \eta _ { n } ) / F )$ ; confidence 0.134

17. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960192.png ; $\alpha _ { 1 } , \ldots , \alpha _ { n } \in F$ ; confidence 0.053

18. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040370/f04037018.png ; $p \leq k \leq \operatorname { prof } F - q$ ; confidence 0.505

19. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040550/f04055028.png ; $V _ { 1 } \subset \ldots \subset V _ { n - 1 }$ ; confidence 0.899

20. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h04769037.png ; $M \supset y \Leftrightarrow g H \in G / H$ ; confidence 0.473

21. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797043.png ; $P _ { U ( \mathfrak { g } ) } = \mathfrak { g }$ ; confidence 0.817

22. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i05235057.png ; $\phi = F ( \phi _ { 1 } , \ldots , \phi _ { m } )$ ; confidence 0.556

23. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510194.png ; $\mathfrak { g } 0 = \mathfrak { s p } ( n , R )$ ; confidence 0.335

24. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063010/m06301089.png ; $F ( x _ { 1 } h _ { 1 } + \ldots + x _ { n } h _ { n } ) =$ ; confidence 0.983

25. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451074.png ; $\operatorname { pec } Z [ 1 / n , \xi _ { n } ]$ ; confidence 0.133

26. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080900/r08090014.png ; $S \subset \operatorname { Ker } \alpha$ ; confidence 0.262

27. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590390.png ; $\delta _ { x } = \operatorname { dim } A / A$ ; confidence 0.580

28. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087060/s08706017.png ; $Nrd _ { R } : R ^ { * } \rightarrow Z ( R ) ^ { * }$ ; confidence 0.683

29. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524012.png ; $X = \sum _ { n = 1 } ^ { \infty } X _ { n } 2 ^ { - n }$ ; confidence 0.978

30. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700173.png ; $X ^ { \prime } \rightarrow R ^ { \prime }$ ; confidence 0.999

31. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830139.png ; $B _ { 0 } \in F \{ Y _ { 1 } , \ldots , Y _ { k } \}$ ; confidence 0.707

32. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032490/d03249011.png ; $p \subset F \{ Y _ { 1 } , \ldots , Y _ { N } \}$ ; confidence 0.193

33. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120226.png ; $\Gamma ( Y , O _ { X } / \Gamma ( X , O _ { X } ) )$ ; confidence 0.989

34. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002021.png ; $( \alpha , b ) \in ( Q \backslash Z ) ^ { 2 }$ ; confidence 0.548

35. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970144.png ; $\mu : A \rightarrow A \otimes \cdots A$ ; confidence 0.562

36. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510191.png ; $\mathfrak { g } = \mathfrak { s p } ( n , C )$ ; confidence 0.532

37. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851058.png ; $\{ \alpha _ { 1 } , \dots , \alpha _ { n } \}$ ; confidence 0.463

38. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876012.png ; $x = ( x _ { 1 } , \ldots , x _ { x } ) \in \Omega$ ; confidence 0.694

39. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072140/p07214067.png ; $\Phi _ { 1 } ( s _ { 0 } ) = \Phi _ { 2 } ( s _ { 0 } )$ ; confidence 0.814

40. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004056.png ; $\overline { D } = \overline { D } _ { S }$ ; confidence 0.978

41. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590492.png ; $X ( x _ { 0 } , y _ { 0 } ) = Y ( x _ { 0 } , y _ { 0 } ) = 0$ ; confidence 0.915

42. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590408.png ; $\{ n , \beta _ { 1 } , \dots , \beta _ { g } \}$ ; confidence 0.568

43. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590437.png ; $f : C ^ { x + 1 } \rightarrow D ( \epsilon )$ ; confidence 0.168

44. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590616.png ; $\| \partial y ^ { i } / \partial x ^ { j } \|$ ; confidence 0.969

45. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559053.png ; $z = \phi _ { 2 } ( \tau ^ { \prime \prime } )$ ; confidence 0.994

46. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t130130113.png ; $K ^ { b } ( F _ { \Lambda } ) ^ { ( T , T [ i ] ) } = 0$ ; confidence 0.257

47. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145093.png ; $l ( D ) = \operatorname { deg } ( D ) - g + 1$ ; confidence 0.995

48. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150074.png ; $z \rightarrow ( \alpha z + b ) f ( c z + d )$ ; confidence 0.402

49. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a01417023.png ; $\{ z \in C : \operatorname { Im } z > 0 \}$ ; confidence 0.951

50. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023330/c02333013.png ; $\prod _ { i \in I } X _ { i } \rightarrow Y$ ; confidence 0.946

51. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025930/c02593057.png ; $( d \phi ( X ) ( x ) , y ) = - ( x , d \psi ( X ) y )$ ; confidence 0.843

52. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025930/c02593022.png ; $( \phi ( g ) x , y ) = ( x , \psi ( g ^ { - 1 } ) y )$ ; confidence 0.983

53. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120557.png ; $f _ { i } : X \rightarrow \overline { R }$ ; confidence 0.983

54. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040550/f0405508.png ; $V _ { 1 } \subset \ldots \subset V _ { k }$ ; confidence 0.965

55. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082045.png ; $H ( B ) = \operatorname { nil } ( B ) ^ { n }$ ; confidence 0.784

56. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082088.png ; $\alpha : F ( X , Y ) \rightarrow G ( X , Y )$ ; confidence 1.000

57. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410110.png ; $\operatorname { Tr } _ { K / k } ( \beta )$ ; confidence 0.968

58. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h0474108.png ; $t _ { 1 } ^ { 0 } , \ldots , t _ { x } ^ { 0 } \in Q$ ; confidence 0.199

59. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h047690120.png ; $\operatorname { Sp } ( k ) \times U ( 1 )$ ; confidence 0.901

60. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h04769082.png ; $\pi : G \times _ { H } F \rightarrow G / H$ ; confidence 0.775

61. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797063.png ; $\Delta ( \alpha ) = ( \alpha , \alpha )$ ; confidence 0.595

62. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797022.png ; $\epsilon ^ { * } : K \rightarrow A ^ { * }$ ; confidence 0.996

63. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j0542701.png ; $x y = y x , \quad ( x ^ { 2 } y ) x = x ^ { 2 } ( y x )$ ; confidence 0.973

64. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590178.png ; $H ^ { 1 } ( R , \operatorname { Aut } ( G ) )$ ; confidence 0.711

65. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876031.png ; $i = 1 , \ldots , r , \quad j = 1 , \ldots , n$ ; confidence 0.616

66. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876038.png ; $1 \leq i , j \leq r , \quad 1 \leq l \leq n$ ; confidence 0.955

67. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451033.png ; $\phi : M ( pt ) \rightarrow h _ { M } ( pt )$ ; confidence 0.886

68. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r0776408.png ; $\pi * : \omega Y \rightarrow \omega X$ ; confidence 0.746

69. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r08103091.png ; $n _ { \alpha } \alpha \in \Phi _ { k } ( G )$ ; confidence 0.368

70. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590370.png ; $x _ { 0 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$ ; confidence 0.863

71. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590593.png ; $h ( x ) = \frac { \rho X ( x ) } { \| X ( x ) \| }$ ; confidence 0.990

72. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559011.png ; $L : [ 0,1 ] \rightarrow \overline { C }$ ; confidence 0.994

73. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590364.png ; $f ( x _ { 0 } , \ldots , x _ { x } ) = \epsilon$ ; confidence 0.572

74. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094200/t09420027.png ; $\operatorname { ad } _ { x } ( y ) = [ x , y ]$ ; confidence 0.196

75. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110050/f11005024.png ; $\alpha 1 , \ldots , \alpha _ { \gamma }$ ; confidence 0.371

76. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450116.png ; $\operatorname { deg } ( D ) \geq 2 g + 1$ ; confidence 0.999

77. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164054.png ; $I = \operatorname { deg } ( c _ { 2 } ) - 4$ ; confidence 0.490

78. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023470/c02347029.png ; $g \notin \operatorname { Ker } \rho$ ; confidence 0.676

79. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830151.png ; $F , G \in F \{ Y _ { 1 } , \ldots , Y _ { n } \}$ ; confidence 0.749

80. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183094.png ; $F , A \in F \{ Y _ { 1 } , \ldots , Y _ { n } \}$ ; confidence 0.665

81. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082078.png ; $\phi _ { F } ^ { * } F _ { u } ( X , Y ) = F ( X , Y )$ ; confidence 0.958

82. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g1300208.png ; $\operatorname { log } \alpha = i \pi$ ; confidence 0.977

83. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970142.png ; $1 \otimes X _ { i } \in A \otimes \sim A$ ; confidence 0.699

84. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851047.png ; $X _ { \alpha } \in \mathfrak { g } _ { Q }$ ; confidence 0.651

85. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590172.png ; $\operatorname { spin } ( f _ { 2 n + 1 } )$ ; confidence 0.457

86. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590192.png ; $f ^ { - 1 } ( u ) f ^ { - 1 } ( v ) = f ^ { - 1 } ( u v )$ ; confidence 0.994

87. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590159.png ; $G _ { 2 } , F _ { 4 } , E _ { 6 } , E _ { 7 } , E _ { 8 }$ ; confidence 0.956

88. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451022.png ; $h _ { M } = \operatorname { Hom } ( S , M )$ ; confidence 0.426

89. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451090.png ; $( S , \operatorname { Pic } ^ { 0 } X / S )$ ; confidence 0.966

90. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900111.png ; $g ) = \phi ( g _ { 1 } ) ( m ( g _ { 2 } , g _ { 3 } )$ ; confidence 0.237

91. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004069.png ; $X ^ { * } = \Gamma \backslash D ^ { * }$ ; confidence 0.822

92. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590276.png ; $\operatorname { lim } f ( z ) = \infty$ ; confidence 0.998

93. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590599.png ; $w , w ^ { \prime } , \ldots , w ^ { ( x - 1 ) }$ ; confidence 0.604

94. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054016.png ; $x _ { i j } ( a ) x _ { j } ( b ) = x _ { i j } ( a + b )$ ; confidence 0.234

95. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092900/t09290048.png ; $\{ P n : B \leq P < G , \square n \in N \} g$ ; confidence 0.485

96. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014047.png ; $\chi _ { Q } : K _ { 0 } ( Q ) \rightarrow Z$ ; confidence 0.972

97. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140164.png ; $q _ { \Lambda } : Z ^ { n } \rightarrow Z$ ; confidence 0.561

98. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140172.png ; $q _ { C } : Z ^ { ( l _ { C } ) } \rightarrow Z$ ; confidence 0.490

99. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145072.png ; $\operatorname { deg } K _ { X } = 2 g - 2$ ; confidence 0.913

100. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450136.png ; $\phi _ { K } : X \rightarrow P ^ { g - 1 }$ ; confidence 0.974

101. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a0116402.png ; $f ( x _ { 0 } , x _ { 1 } , x _ { 2 } , x _ { 3 } ) = 0$ ; confidence 0.993

102. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164058.png ; $\pi = \{ ( D ^ { 2 } ) + ( D K _ { V } ) \} / 2 + 1$ ; confidence 0.997

103. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025930/c0259308.png ; $\phi ^ { * } ( g ) = \phi ( g ^ { - 1 } ) ^ { * }$ ; confidence 0.989

104. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070053.png ; $\gamma ( \xi ) = [ \xi , \xi ] + \ldots$ ; confidence 0.841

105. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830122.png ; $( \zeta _ { 1 } , \ldots , \zeta _ { n } )$ ; confidence 0.478

106. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830147.png ; $\zeta _ { k + 1 } , \ldots , \zeta _ { x }$ ; confidence 0.483

107. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830337.png ; $A = \{ A _ { 1 } , \ldots , A _ { \cdot } \}$ ; confidence 0.354

108. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830343.png ; $k \leq \operatorname { min } ( r , s )$ ; confidence 0.999

109. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120304.png ; $A ( f ) = \int _ { \gamma } f ( z ) g ( z ) d z$ ; confidence 0.997

110. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120413.png ; $( x , x ^ { \prime } ) = x ^ { \prime } ( x )$ ; confidence 0.998

111. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960148.png ; $\operatorname { GL } ( 1 , K ) = K ^ { * }$ ; confidence 0.533

112. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696099.png ; $\eta _ { 1 } , \ldots , \eta _ { n } \in G$ ; confidence 0.669

113. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820135.png ; $V _ { n } \gamma ( T ) = \gamma ( T ^ { x } )$ ; confidence 0.168

114. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h0479705.png ; $\delta : A \rightarrow A \otimes A$ ; confidence 0.996

115. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427036.png ; $J _ { 1 } : X \rightarrow X ^ { \prime }$ ; confidence 0.990

116. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k12003011.png ; $\operatorname { Ric } ( \omega ) = 0$ ; confidence 0.997

117. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851020.png ; $( \text { Aut } \mathfrak { g } ) ^ { 0 }$ ; confidence 0.717

118. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510199.png ; $\operatorname { su } ( 2 p , 2 ( n - p ) )$ ; confidence 0.801

119. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510175.png ; $90 = \operatorname { su } ^ { x } ( 2 n )$ ; confidence 0.349

120. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852015.png ; $\mathscr { C } _ { 0 } = \mathfrak { g }$ ; confidence 0.191

121. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868023.png ; $\Gamma ( G ) \subset \mathfrak { h }$ ; confidence 0.891

122. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900109.png ; $\phi : G \rightarrow \text { Aut } A$ ; confidence 0.720

123. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690059.png ; $H ^ { 0 } ( G , A ) = H ^ { 0 } ( C ^ { * } ( G , A ) )$ ; confidence 0.986

124. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690033.png ; $H ^ { i } ( C ^ { * } ( \mathfrak { U } , F ) )$ ; confidence 0.769

125. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690063.png ; $H ^ { 1 } ( G , A ) = H ^ { 1 } ( C ^ { * } ( G , A ) )$ ; confidence 0.973

126. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690015.png ; $\delta : C ^ { 1 } \rightarrow C ^ { 2 }$ ; confidence 0.985

127. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267042.png ; $\operatorname { Pic } _ { X / k } ^ { 0 }$ ; confidence 0.272

128. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267044.png ; $\operatorname { Pic } _ { K / k } ^ { Q }$ ; confidence 0.366

129. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631070.png ; $\delta \operatorname { lg } = \phi$ ; confidence 0.586

130. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q0763106.png ; $\Delta : A \rightarrow A \otimes A$ ; confidence 0.996

131. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081370/r08137025.png ; $\{ \rho ^ { \alpha } : \alpha \in I \}$ ; confidence 0.999

132. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004021.png ; $\operatorname { Im } ( \gamma z ) > 1$ ; confidence 0.951

133. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004025.png ; $( \Gamma \cap P ) \backslash H ^ { 1 }$ ; confidence 1.000

134. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004038.png ; $X _ { g } ^ { * } = \cup _ { r \leq g } X _ { r }$ ; confidence 0.386

135. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590511.png ; $\dot { i } _ { 0 } \in \{ 1 , \ldots , n \}$ ; confidence 0.377

136. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590228.png ; $R = \{ R _ { 1 } > 0 , \ldots , R _ { n } > 0 \}$ ; confidence 0.785

137. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590359.png ; $C \{ x _ { 0 } , \ldots , x _ { x } \} / J ( f )$ ; confidence 0.320

138. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590271.png ; $\phi _ { a } ( z ) = \psi _ { a x } ( z ) f ( z )$ ; confidence 0.163

139. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590613.png ; $f : M ^ { \aleph } \rightarrow N ^ { x }$ ; confidence 0.136

140. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087060/s08706014.png ; $K _ { 1 } ( R [ t _ { 1 } , \ldots , t _ { x } ] )$ ; confidence 0.460

141. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054035.png ; $h ( \alpha ) = w ( \alpha ) w ( 1 ) ^ { - 1 }$ ; confidence 0.731

142. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140108.png ; $\sum _ { i , j \in Q _ { 0 } } e _ { j } I _ { e }$ ; confidence 0.361

143. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090195.png ; $\operatorname { PSL } _ { \eta } ( K )$ ; confidence 0.528

144. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145043.png ; $Cl ( P ^ { 1 } ) = Z , Cl ^ { 0 } ( P ^ { 1 } ) = 0$ ; confidence 0.119

145. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011520/a01152034.png ; $\tau : G \times V \rightarrow V$ ; confidence 0.995

146. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164016.png ; $\operatorname { lim } | K _ { i } | + 1$ ; confidence 0.865

147. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164065.png ; $H ^ { \prime } ( V , O _ { V } ( D + n H ) ) = 0$ ; confidence 0.983

148. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a014170107.png ; $j : X \times \Gamma \rightarrow H$ ; confidence 0.927

149. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020560/c02056028.png ; $\phi : G \rightarrow G ^ { \prime }$ ; confidence 0.985

150. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070065.png ; $H ^ { 0 } ( X _ { s } , \Theta _ { X _ { S } } )$ ; confidence 0.295

151. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700128.png ; $\hat { \mathscr { O } } _ { S , s _ { 0 } }$ ; confidence 0.480

152. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830281.png ; $A \in R \{ y _ { 1 } , \ldots , y _ { n } \}$ ; confidence 0.345

153. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830315.png ; $F \in R \{ y _ { 1 } , \ldots , y _ { n } \}$ ; confidence 0.267

154. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830137.png ; $B \in F \{ Y _ { 1 } , \ldots , Y _ { N } \}$ ; confidence 0.377

155. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183092.png ; $A \in F \{ Y _ { 1 } , \ldots , Y _ { N } \}$ ; confidence 0.404

156. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120346.png ; $\Lambda _ { \zeta , n } F ( z , \zeta )$ ; confidence 0.511

157. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120561.png ; $y \in \overline { R } \square ^ { m }$ ; confidence 0.544

158. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960158.png ; $\delta _ { i } \alpha = \alpha _ { i }$ ; confidence 0.862

159. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082085.png ; $\psi : L \rightarrow L ^ { \prime }$ ; confidence 1.000

160. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082022.png ; $H ( B _ { 1 } ) \rightarrow H ( B _ { 2 } )$ ; confidence 0.997

161. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410112.png ; $\beta = \alpha - \sigma ( \alpha )$ ; confidence 0.999

162. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797060.png ; $\Delta : G \rightarrow G \times G$ ; confidence 0.998

163. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797024.png ; $\iota ^ { * } : A ^ { * } \rightarrow K$ ; confidence 0.977

164. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797018.png ; $A ^ { * } = \sum _ { n \in Z } A _ { n } ^ { * }$ ; confidence 0.525

165. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i0523503.png ; $y \rightarrow \gamma x + \delta y$ ; confidence 0.885

166. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510183.png ; $g = \operatorname { so } ( 2 n + 1 , C )$ ; confidence 0.198

167. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859095.png ; $L ( G _ { 1 } ) \rightarrow L ( G _ { 2 } )$ ; confidence 0.996

168. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l0585902.png ; $\mu : ( x , y ) \rightarrow x y ^ { - 1 }$ ; confidence 0.998

169. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868042.png ; $Z _ { g } = \Gamma _ { 1 } / \Gamma _ { 0 }$ ; confidence 0.875

170. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872023.png ; $( x , y ) \rightarrow [ x , y ] = x y - y x$ ; confidence 0.997

171. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451040.png ; $\overline { \mathfrak { M } } _ { g }$ ; confidence 0.963

172. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o070010110.png ; $X = \cup _ { \alpha } X _ { \alpha }$ ; confidence 0.245

173. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267030.png ; $\operatorname { Pic } _ { X / k } ( k )$ ; confidence 0.713

174. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310135.png ; $A \rightarrow \text { Mat } ( n , k )$ ; confidence 0.772

175. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310120.png ; $R = \sum _ { i } x _ { i } \otimes y _ { i }$ ; confidence 0.487

176. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r077630107.png ; $\alpha \mapsto \alpha ^ { p ^ { i } }$ ; confidence 0.478

177. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763052.png ; $( \delta _ { \phi } , \alpha ) \geq 0$ ; confidence 0.999

178. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077670/r0776707.png ; $L = K ( \sqrt { \alpha } , \sqrt { b } )$ ; confidence 0.629

179. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590325.png ; $H ^ { i } ( X , O _ { \overline { X } } ) = 0$ ; confidence 0.534

180. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590453.png ; $f _ { \lambda } ( z ) = F ( z , \lambda )$ ; confidence 0.997

181. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590327.png ; $H ^ { n - 1 } ( X , O _ { \overline { X } } )$ ; confidence 0.718

182. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590403.png ; $y = \sum _ { i } \alpha _ { i } x ^ { i / n }$ ; confidence 0.722

183. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087060/s08706047.png ; $n \geq \operatorname { sr } ( R ) + 1$ ; confidence 0.511

184. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087060/s08706046.png ; $K _ { 1 } ( R ) = GL _ { n } ( R ) / E _ { n } ( R )$ ; confidence 0.156

185. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t130130106.png ; $T _ { i } \in \operatorname { add } T$ ; confidence 0.665

186. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095400/u09540036.png ; $\lambda = ( m _ { 1 } , \dots , m _ { s } )$ ; confidence 0.450

187. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097590/w09759011.png ; $I = \operatorname { ind } _ { k } ( D )$ ; confidence 0.955

188. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164094.png ; $b _ { 2 } ( V ) \geq \rho + 2 p _ { g } ( V )$ ; confidence 0.767

189. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a014170114.png ; $f ( x ) = j ( x , \gamma ) f ( x \gamma )$ ; confidence 0.623

190. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a01417072.png ; $| \phi ( x ) | \geq | \phi ( x _ { 0 } ) |$ ; confidence 0.992

191. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025930/c02593092.png ; $\Lambda \in \mathfrak { g } ^ { * }$ ; confidence 0.899

192. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070025.png ; $\phi : \tilde { X } \rightarrow X$ ; confidence 0.732

193. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070055.png ; $H ^ { * } ( X _ { \diamond } , \Theta )$ ; confidence 0.861

194. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700202.png ; $M X _ { 0 } , \alpha \subset M X _ { 0 }$ ; confidence 0.868

195. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021460/c0214607.png ; $( \eta _ { 1 } , \ldots , \eta _ { n } )$ ; confidence 0.232

196. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830255.png ; $\partial _ { i } : R \rightarrow R$ ; confidence 0.993

197. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830390.png ; $A \in k \{ y _ { 1 } , \dots , y _ { n } \}$ ; confidence 0.407

198. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183027.png ; $a _ { \tau \langle V \rangle } ( V )$ ; confidence 0.402

199. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120227.png ; $\Gamma ( X \backslash Y , O _ { X } )$ ; confidence 0.983

200. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025020/c02502011.png ; $f : X \rightarrow \overline { R }$ ; confidence 0.994

201. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d03412066.png ; $\{ H _ { r } ( X , A ) , f * , \partial \}$ ; confidence 0.923

202. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120506.png ; $F = \prod _ { \alpha } F _ { \alpha }$ ; confidence 0.991

203. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027270/c0272709.png ; $g _ { 2 } ^ { 3 } - 27 g _ { 3 } ^ { 2 } \neq 0$ ; confidence 0.254

204. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960198.png ; $y ^ { \prime } + \alpha _ { 1 } y = 0$ ; confidence 0.639

205. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082093.png ; $\alpha ( Z _ { 1 } , \ldots , Z _ { n } )$ ; confidence 0.480

206. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820169.png ; $\alpha + b = F _ { \pi } ( \alpha , b )$ ; confidence 0.393

207. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024890/c02489024.png ; $\beta _ { 1 } , \ldots , \beta _ { n }$ ; confidence 0.525

208. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i0523504.png ; $\alpha \delta - \beta \gamma = 1$ ; confidence 0.999

209. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i0523502.png ; $X \rightarrow \alpha X + \beta y$ ; confidence 0.474

210. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427089.png ; $Kan ^ { - 1 } ( g ) = \mathfrak { g } - 1$ ; confidence 0.529

211. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k1200301.png ; $\operatorname { Ric } ( \omega )$ ; confidence 0.997

212. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058430/l05843089.png ; $\mathfrak { g } _ { \alpha } \neq 0$ ; confidence 0.985

213. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058480/l05848090.png ; $L ( G ) \subset \mathfrak { d } ( V )$ ; confidence 0.673

214. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l0587208.png ; $( x ^ { [ p ] } ) = ( \text { ad } x ) ^ { p }$ ; confidence 0.500

215. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059250/l05925088.png ; $\operatorname { dim } ( 1 - t ) V = 1$ ; confidence 0.998

216. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451037.png ; $\chi : h _ { M } \rightarrow h _ { N }$ ; confidence 0.488

217. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267028.png ; $k ( k ) = \operatorname { Pic } ( X )$ ; confidence 0.992

218. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631033.png ; $x _ { i l } | x _ { k j } = x _ { k } ; x _ { i l }$ ; confidence 0.069

219. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764012.png ; $\sum _ { i = 1 } ^ { n } k _ { i } ^ { - 1 } > 1$ ; confidence 0.994

220. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r081030102.png ; $\Delta \backslash \Delta _ { 0 }$ ; confidence 0.556

221. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590274.png ; $\phi _ { \alpha } ( \alpha ) \neq 0$ ; confidence 0.873

222. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590223.png ; $( U ^ { n } ( \zeta , R ) , f _ { \zeta } )$ ; confidence 0.977

223. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524066.png ; $0 \leq a \leq \{ n a \} \leq b \leq 1$ ; confidence 0.463

224. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090110.png ; $\lambda \in \Lambda ^ { + } ( n , r )$ ; confidence 1.000

225. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145036.png ; $\operatorname { iv } ( X ) / P ( X )$ ; confidence 0.590

226. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011530/a01153014.png ; $\alpha 1 , \ldots , \alpha _ { x }$ ; confidence 0.154

227. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011530/a0115307.png ; $f ( b _ { 1 } , \dots , b _ { n } ) \neq 0$ ; confidence 0.554

228. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164059.png ; $| D | \geq n - \pi + p _ { x } ( V ) + 1 - i$ ; confidence 0.785

229. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011740/a01174012.png ; $\operatorname { PLG } ( n + 1 , k )$ ; confidence 0.708

230. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a01417028.png ; $\{ z \rightarrow z + n : n \in Z \}$ ; confidence 0.948

231. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023470/c02347040.png ; $\{ R ^ { \alpha } : \alpha \in I \}$ ; confidence 0.997

232. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120298.png ; $F = \overline { C } \backslash G$ ; confidence 0.990

233. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120344.png ; $\Lambda _ { \zeta } F ( z , \zeta )$ ; confidence 0.938

234. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120518.png ; $\alpha \text { pr } F _ { \alpha }$ ; confidence 0.862

235. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120242.png ; $H ^ { p } ( X , F ) = H ^ { p + 1 } ( X , F ) = 0$ ; confidence 0.996

236. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960169.png ; $( F \langle \alpha \rangle / F )$ ; confidence 0.388

237. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040550/f04055041.png ; $G _ { n , n _ { 1 } } = Gr _ { n _ { 1 } } ( V )$ ; confidence 0.649

238. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h0479703.png ; $\mu : A \otimes A \rightarrow A$ ; confidence 0.952

239. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970118.png ; $\mu : A \rightarrow A \otimes A$ ; confidence 0.952

240. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i05235024.png ; $f ( x , y ) = a x ^ { 2 } + 2 b x y + c y ^ { 2 }$ ; confidence 0.986

241. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427061.png ; $\{ a b c \} = ( a b ) c + ( b c ) a - ( c a ) b$ ; confidence 0.872

242. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427080.png ; $[ \alpha , \mathfrak { g } - 1 ] = 0$ ; confidence 0.882

243. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k12003036.png ; $F _ { M } : G \rightarrow C ^ { * }$ ; confidence 0.933

244. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k12003017.png ; $c _ { 1 } ( S ) ^ { 2 } \leq 3 _ { C 2 } ( S )$ ; confidence 0.319

245. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510234.png ; $\alpha _ { j i } = \alpha _ { i j } = 0$ ; confidence 0.722

246. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510118.png ; $g = \operatorname { so } ( 2 n , k )$ ; confidence 0.273

247. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510201.png ; $g = \operatorname { so } ( 2 n , C )$ ; confidence 0.268

248. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852018.png ; $\mathfrak { g } _ { i } ^ { \prime }$ ; confidence 0.212

249. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045030/g04503014.png ; $\operatorname { lim } V _ { k } = k$ ; confidence 0.978

250. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872087.png ; $\operatorname { Der } _ { k } ( A )$ ; confidence 0.991

251. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451089.png ; $( S , \operatorname { Pic } X / S )$ ; confidence 0.976

252. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451011.png ; $\{ X _ { S } : s \in S , X _ { S } \in A \}$ ; confidence 0.842

253. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451017.png ; $f ^ { * } : M ( S ) \rightarrow M ( T )$ ; confidence 0.973

254. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451092.png ; $\operatorname { Pic } ^ { 0 } X / S$ ; confidence 0.620

255. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451031.png ; $S = \operatorname { Spec } K = pt$ ; confidence 0.383

256. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o07001018.png ; $\pi _ { X , G } : X \rightarrow X / G$ ; confidence 0.693

257. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472082.png ; $\Gamma \times E \rightarrow E$ ; confidence 0.998

258. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631031.png ; $x _ { j } ; x _ { k } j = q x _ { k } ; x _ { j }$ ; confidence 0.084

259. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631017.png ; $m ( \alpha \otimes b ) = \alpha b$ ; confidence 0.443

260. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080900/r0809006.png ; $\lambda : G _ { m } \rightarrow S$ ; confidence 0.380

261. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004033.png ; $G = \operatorname { Sp } ( 2 g , R )$ ; confidence 0.940

262. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012200/a01220076.png ; $\alpha \in C ^ { \prime \prime }$ ; confidence 0.154

263. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559025.png ; $\alpha = \phi _ { 1 } ( \tau _ { 1 } )$ ; confidence 0.853

264. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559029.png ; $\alpha = \phi _ { 2 } ( \tau _ { 2 } )$ ; confidence 0.777

265. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590323.png ; $H ^ { i } ( X , O _ { \overline { X } } )$ ; confidence 0.623

266. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054070.png ; $K _ { 2 } Q = \coprod _ { p } \mu _ { p }$ ; confidence 0.907

267. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090248.png ; $\Phi = \Phi ^ { + } \cup \Phi ^ { - }$ ; confidence 0.997

268. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145057.png ; $\pi = \frac { ( m - 1 ) ( m - 2 ) } { 2 }$ ; confidence 0.999

269. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145058.png ; $g = \frac { ( m - 1 ) ( m - 2 ) } { 2 } - d$ ; confidence 0.992

270. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c02057067.png ; $H ^ { p } ( X , S ) = 0 , \quad p \geq 1$ ; confidence 0.983

271. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700177.png ; $H ^ { 0 } ( X _ { 0 } , T _ { X _ { 0 } } ) = 0$ ; confidence 0.979

272. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700232.png ; $K = \operatorname { Comm } ( V )$ ; confidence 0.897

273. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700197.png ; $H ^ { 2 } ( X _ { 0 } , T _ { X _ { 0 } } ) = 0$ ; confidence 0.977

274. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070039.png ; $f : S ^ { \prime } \rightarrow S$ ; confidence 0.500

275. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700154.png ; $H ^ { 1 } ( X _ { 0 } , T _ { X _ { 0 } } ) = 0$ ; confidence 0.958

276. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070027.png ; $\pi \circ \phi = \tilde { \pi }$ ; confidence 0.616

277. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830371.png ; $\partial A / \partial u \neq 0$ ; confidence 0.824

278. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830375.png ; $\partial A / \partial v \neq 0$ ; confidence 0.669

279. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830198.png ; $\partial F / \partial Y _ { i j }$ ; confidence 0.903

280. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830338.png ; $B = \{ B _ { 1 } , \ldots , B _ { s } \}$ ; confidence 0.684

281. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830297.png ; $= \partial A / \partial u _ { A }$ ; confidence 0.942

282. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120445.png ; $( F , \sigma ( F , G ) ) ^ { \prime }$ ; confidence 0.998

283. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120514.png ; $\prod _ { \alpha } F _ { \alpha }$ ; confidence 0.986

284. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120469.png ; $\operatorname { ln } x _ { x } = 0$ ; confidence 0.810

285. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696090.png ; $c \in F \{ ( y _ { j } ) _ { j \in J } \}$ ; confidence 0.942

286. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696068.png ; $F _ { 0 } \{ ( y _ { j } ) _ { j \in J } \}$ ; confidence 0.745

287. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820112.png ; $F ( X , Y ) = f ^ { - 1 } ( f ( X ) + f ( Y ) )$ ; confidence 0.999

288. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g1300202.png ; $\operatorname { log } \alpha$ ; confidence 0.981

289. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002015.png ; $F ( z ) = P ( e ^ { z } , e ^ { \beta z } )$ ; confidence 0.998

290. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410131.png ; $F = F ( x , y , \dot { x } , \dot { y } )$ ; confidence 0.994

291. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h047690123.png ; $G = \operatorname { Spin } ( 7 )$ ; confidence 0.999

292. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970140.png ; $A = K [ [ X _ { 1 } , \dots , X _ { x } ] ]$ ; confidence 0.230

293. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050100/i0501008.png ; $\phi ( x _ { 1 } , \ldots , x _ { x } )$ ; confidence 0.259

294. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031850/d031850348.png ; $\phi _ { 1 } , \ldots , \phi _ { m }$ ; confidence 0.611

295. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876024.png ; $\psi _ { k i } ( e ) = \delta _ { k i }$ ; confidence 0.977

296. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267035.png ; $S = \operatorname { Spec } ( k )$ ; confidence 0.869

297. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472041.png ; $\Gamma = \Gamma _ { \alpha , S }$ ; confidence 0.986

298. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763082.png ; $\phi _ { 1 } , \ldots , \phi _ { d }$ ; confidence 0.566

299. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763048.png ; $\delta _ { \phi } \in P _ { \phi }$ ; confidence 0.999

300. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763081.png ; $\chi _ { 1 } + \ldots + \chi _ { d }$ ; confidence 0.362