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(AUTOMATIC EDIT of page 2 out of 12 with 300 lines: Updated image/latex database (currently 3466 images latexified; order by Confidence, ascending: False.)
 
(AUTOMATIC EDIT of page 2 out of 12 with 300 lines: Updated image/latex database (currently 3466 images latexified; order by Length, ascending: False.)
 
(One intermediate revision by the same user not shown)
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== List ==
 
== List ==
1. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868026.png ; $\Gamma ( G )$ ; confidence 0.998
+
1. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830326.png ; $\Sigma \subset R \{ y _ { 1 } , \ldots , y _ { n } \} \backslash R$ ; confidence 0.488
  
2. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797060.png ; $\Delta : G \rightarrow G \times G$ ; confidence 0.998
+
2. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120160.png ; $H ^ { \gamma } ( A , X ) \sim H ^ { \gamma + 1 } ( R \backslash A , X )$ ; confidence 0.364
  
3. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590142.png ; $B \times E \rightarrow B E$ ; confidence 0.998
+
3. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120292.png ; $\exists n _ { 0 } : n \geq n _ { 0 } \Rightarrow G _ { n } \subset G$ ; confidence 0.126
  
4. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020690/c02069021.png ; $80$ ; confidence 0.998
+
4. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797031.png ; $y ] = x y - ( - 1 ) ^ { p q } y x , \quad x \in A _ { p } , \quad y \in A _ { y }$ ; confidence 0.507
  
5. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r08103037.png ; $\Phi _ { k } ( G )$ ; confidence 0.998
+
5. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510213.png ; $( ad X _ { \alpha _ { i } } ) ^ { 1 - n ( i , j ) } ( X _ { \alpha _ { j } } ) = 0$ ; confidence 0.432
  
6. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012200/a01220084.png ; $0 \leq t \leq 1$ ; confidence 0.998
+
6. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868083.png ; $\mathfrak { g } 0 = \mathfrak { k } _ { 0 } + \mathfrak { p } _ { 0 }$ ; confidence 0.090
  
7. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164088.png ; $b _ { 1 } ( V ) = 2 q ( V )$ ; confidence 0.998
+
7. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690080.png ; $\delta \alpha = d \alpha - \frac { 1 } { 2 } [ \alpha , \alpha ]$ ; confidence 0.991
  
8. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010680/a01068013.png ; $F ( z )$ ; confidence 0.998
+
8. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310114.png ; $\Delta ^ { \prime } ( \alpha ) = R . \Delta ( \alpha ) . R ^ { - 1 }$ ; confidence 0.304
  
9. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140124.png ; $R = K Q$ ; confidence 0.998
+
9. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310141.png ; $T _ { 2 } = 1 \otimes T \in \text { End } ( k ^ { n } \otimes k ^ { n } )$ ; confidence 0.318
  
10. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059250/l05925088.png ; $\operatorname { dim } ( 1 - t ) V = 1$ ; confidence 0.998
+
10. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590128.png ; $\overline { U } ( 0,1 ) = \{ z \in \overline { C } : | z | \leq 1 \}$ ; confidence 0.957
  
11. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065570/m06557033.png ; $h ( X _ { 2 } ) = 1$ ; confidence 0.998
+
11. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013040.png ; $\Gamma = \operatorname { End } _ { \Lambda } ( T ) ^ { \circ p }$ ; confidence 0.240
  
12. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559035.png ; $0 \leq t < \tau _ { 1 }$ ; confidence 0.998
+
12. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014049.png ; $\operatorname { dim } : K _ { 0 } ( Q ) \rightarrow Z ^ { Q _ { 0 } }$ ; confidence 0.783
  
13. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797082.png ; $\pi ( G , K ) = \sum _ { i = 0 } ^ { \infty } \pi _ { i } ( G ) \otimes K$ ; confidence 0.998
+
13. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140117.png ; $\chi _ { R } : K _ { 0 } ( \operatorname { mod } R ) \rightarrow Z$ ; confidence 0.847
  
14. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590413.png ; $A = \pi ^ { - 1 } ( x )$ ; confidence 0.998
+
14. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u0952408.png ; $\phi ( t ) = \frac { 1 } { i t ( b - \alpha ) } ( e ^ { i t b } - e ^ { i t x } )$ ; confidence 0.594
  
15. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100191.png ; $p ( k )$ ; confidence 0.998
+
15. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070037.png ; $\pi ^ { \prime } : X ^ { \prime } \rightarrow S ^ { \prime }$ ; confidence 0.952
  
16. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070059.png ; $H ^ { 2 } ( X , \Theta ) = 0$ ; confidence 0.998
+
16. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031640/d03164012.png ; $\omega ^ { ( p ) } = ( a _ { 0 } ^ { p } , \dots , a _ { n } ^ { p } , \dots )$ ; confidence 0.284
  
17. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696091.png ; $c ( \eta ) \neq 0$ ; confidence 0.998
+
17. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h047690121.png ; $\operatorname { Sp } ( k ) \times \operatorname { Sp } ( 1 )$ ; confidence 0.853
  
18. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097710/w09771052.png ; $W ( T _ { 0 } , G )$ ; confidence 0.998
+
18. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797082.png ; $\pi ( G , K ) = \sum _ { i = 0 } ^ { \infty } \pi _ { i } ( G ) \otimes K$ ; confidence 0.998
  
19. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012540/a01254013.png ; $G = 0$ ; confidence 0.998
+
19. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852012.png ; $\mathfrak { g } _ { i } / \mathfrak { g } _ { \mathfrak { l } } + 1$ ; confidence 0.230
  
20. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032490/d03249018.png ; $d ( p ) \geq d ( q )$ ; confidence 0.998
+
20. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590118.png ; $g \rightarrow A d ( g ) = d _ { e } ( \operatorname { ln } t ( g ) )$ ; confidence 0.610
  
21. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b130290148.png ; $\operatorname { dim } A = 1$ ; confidence 0.998
+
21. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868084.png ; $\mathfrak { g } \subset \mathfrak { g } ^ { \mathfrak { C } }$ ; confidence 0.496
  
22. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a014170143.png ; $f : G \rightarrow V$ ; confidence 0.998
+
22. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690054.png ; $C ^ { k } = \operatorname { Map } ( G ^ { k } , A ) , \quad k = 0,1,2$ ; confidence 0.893
  
23. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830260.png ; $\partial _ { i } I \subset I$ ; confidence 0.998
+
23. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074640/p07464035.png ; $\alpha : H ^ { 1 } ( B , O ^ { G } ) \rightarrow H ^ { 1 } ( B , C ^ { G } )$ ; confidence 0.999
  
24. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002015.png ; $F ( z ) = P ( e ^ { z } , e ^ { \beta z } )$ ; confidence 0.998
+
24. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559054.png ; $\tau _ { 2 } - \epsilon < \tau ^ { \prime \prime } < \tau _ { 2 }$ ; confidence 0.940
  
25. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h0476906.png ; $( g h ) x = g ( h x )$ ; confidence 0.998
+
25. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590464.png ; $F ( x , y , \lambda ) = x \Phi _ { \mu - 2 } ( x , \lambda ) - x y ^ { 2 }$ ; confidence 0.854
  
26. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082077.png ; $\phi _ { F } : L \rightarrow A$ ; confidence 0.998
+
26. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095400/u09540044.png ; $n ^ { 2 } - \sum _ { i j } \operatorname { min } ( m _ { i } , m _ { j } )$ ; confidence 0.738
  
27. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559048.png ; $z ^ { \prime } = \phi _ { 1 } ( \tau ^ { \prime } )$ ; confidence 0.998
+
27. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a0115005.png ; $\frac { d x } { \sqrt { f ( x ) } } = \frac { d y } { \sqrt { f ( y ) } }$ ; confidence 0.999
  
28. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420118.png ; $H$ ; confidence 0.998
+
28. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640153.png ; $\operatorname { tim } \operatorname { Aut } ^ { 0 } ( V ) > 0$ ; confidence 0.287
  
29. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110360/a11036013.png ; $n > 1$ ; confidence 0.998
+
29. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c02057038.png ; $O ^ { p } \rightarrow O ^ { q } \rightarrow S \rightarrow 0$ ; confidence 0.899
  
30. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042090.png ; $n > 0$ ; confidence 0.998
+
30. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120203.png ; $\operatorname { Ext } _ { \Psi } ^ { n - p + 1 } ( X ; F , \Omega )$ ; confidence 0.408
  
31. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830239.png ; $G ( G / F _ { 1 } ) = G _ { 1 }$ ; confidence 0.998
+
31. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120246.png ; $A ( z ) = \sum _ { x = 0 } ^ { \infty } \frac { a _ { x } } { n ! } z ^ { N }$ ; confidence 0.156
  
32. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001078.png ; $1$ ; confidence 0.998
+
32. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820200.png ; $f ( X ) = X + \alpha _ { 2 } X ^ { 2 } + \alpha _ { 3 } X ^ { 3 } + \ldots$ ; confidence 0.751
  
33. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510198.png ; $0 \leq p \leq n / 2$ ; confidence 0.998
+
33. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820161.png ; $f _ { \pi } ( X ) = X + \pi ^ { - 1 } X ^ { q } + \pi ^ { - 2 } X ^ { q ^ { 2 } } +$ ; confidence 0.673
  
34. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690064.png ; $G \rightarrow A$ ; confidence 0.998
+
34. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002046.png ; $Q ( \alpha ^ { \beta } , \ldots , \alpha ^ { \beta ^ { d - 1 } } )$ ; confidence 0.372
  
35. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310127.png ; $R ^ { 12 } R ^ { 13 } R ^ { 23 } = R ^ { 23 } R ^ { 13 } R ^ { 12 }$ ; confidence 0.998
+
35. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058480/l05848015.png ; $[ D _ { 1 } , D _ { 2 } ] = D _ { 1 } \circ D _ { 2 } - D _ { 2 } \circ D _ { 1 }$ ; confidence 0.999
  
36. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040170.png ; $A$ ; confidence 0.998
+
36. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861016.png ; $T ^ { \prime \prime } = T ^ { 1 } \times \ldots \times T ^ { 1 }$ ; confidence 0.167
  
37. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010430/a01043023.png ; $t \rightarrow \infty$ ; confidence 0.998
+
37. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l058680100.png ; $u = \mathfrak { l } + \dot { \mathfrak { i } } \mathfrak { u }$ ; confidence 0.153
  
38. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120248.png ; $| z | > \sigma$ ; confidence 0.998
+
38. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074640/p07464012.png ; $\phi ( x , g h ) = \phi ( x , g ) h , \quad x \in U , \quad g , h \in G$ ; confidence 0.910
  
39. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120328.png ; $F ( z ) \equiv 0$ ; confidence 0.998
+
39. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085900/s08590021.png ; $F _ { i } ( X _ { 1 } , \ldots , X _ { m } ) = 0 , \quad i = 1 , \ldots , n$ ; confidence 0.562
  
40. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l058720146.png ; $p = 2,3,5$ ; confidence 0.998
+
40. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087060/s08706043.png ; $K _ { 1 } ( R ) = \operatorname { lim } GL _ { n } ( R ) / E _ { n } ( R )$ ; confidence 0.598
  
41. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h047690117.png ; $U ( k )$ ; confidence 0.998
+
41. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100169.png ; $X ^ { n } + Y ^ { n } = \sum _ { \vec { d } | n } d r _ { d } ( X , Y ) ^ { n / d }$ ; confidence 0.367
  
42. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011820/a01182079.png ; $\Delta < 0$ ; confidence 0.998
+
42. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700272.png ; $a \circ b = \Phi ^ { - 1 } ( \Phi ( \alpha ) \times \Phi ( b ) )$ ; confidence 0.109
  
43. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011370/a01137074.png ; $1 \leq i \leq m$ ; confidence 0.998
+
43. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700206.png ; $\operatorname { dim } _ { k } H ^ { 2 } ( X _ { 0 } , O _ { X _ { 0 } } )$ ; confidence 0.730
  
44. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631020.png ; $\Delta ( A )$ ; confidence 0.998
+
44. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830267.png ; $\theta = \Pi _ { i } \partial _ { i } ^ { e _ { i } ^ { e _ { i } } }$ ; confidence 0.142
  
45. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022660/c022660149.png ; $I ( f )$ ; confidence 0.998
+
45. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830165.png ; $( t _ { 1 } , \ldots , t _ { n } ) \rightarrow F ( 0 , \ldots , 0 )$ ; confidence 0.263
  
46. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004037.png ; $H _ { 1 } = H$ ; confidence 0.998
+
46. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120255.png ; $h ( \phi ) = k ( - \phi ) , \quad \sigma \leq \phi \leq 2 \pi$ ; confidence 0.997
  
47. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024780/c02478090.png ; $f ^ { - 1 } ( z )$ ; confidence 0.998
+
47. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696057.png ; $F _ { 0 } [ ( y _ { j } \theta ) _ { j \in J , \theta \in \Theta } ]$ ; confidence 0.526
  
48. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092900/t09290046.png ; $B \leq P < G$ ; confidence 0.998
+
48. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082049.png ; $F _ { 1 } ( X _ { 1 } , \ldots , X _ { x } , Y _ { 1 } , \ldots , Y _ { n } )$ ; confidence 0.336
  
49. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074640/p07464043.png ; $E \rightarrow B$ ; confidence 0.998
+
49. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082050.png ; $F _ { n } ( X _ { 1 } , \ldots , X _ { n } , Y _ { 1 } , \ldots , Y _ { n } )$ ; confidence 0.552
  
50. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011530/a01153018.png ; $\alpha ^ { \beta }$ ; confidence 0.998
+
50. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797021.png ; $\delta ^ { * } : A ^ { * } \otimes A ^ { * } \rightarrow A ^ { * }$ ; confidence 0.724
  
51. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090229.png ; $\nabla ( \lambda ) ^ { * }$ ; confidence 0.998
+
51. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058470/l05847062.png ; $\rho : \mathfrak { g } \rightarrow \mathfrak { g } [ ( V )$ ; confidence 0.317
  
52. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450248.png ; $V ( B )$ ; confidence 0.998
+
52. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872010.png ; $( x + y ) ^ { [ p ] } = x ^ { [ p ] } + y ^ { [ p ] } + \Lambda _ { p } ( x , y )$ ; confidence 0.977
  
53. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i052350101.png ; $R ^ { G } \subset R$ ; confidence 0.998
+
53. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872068.png ; $\{ \mathfrak { e } _ { 1 } , \mathfrak { e } _ { 2 } , \ldots \}$ ; confidence 0.391
  
54. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090360.png ; $G _ { K } ( V ) = G$ ; confidence 0.998
+
54. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059250/l05925025.png ; $\{ 0 \} \subset V _ { 1 } \subset \ldots \subset V _ { m } = V$ ; confidence 0.850
  
55. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082095.png ; $\alpha ( F ( X , Y ) ) = G ( \alpha ( X ) , \alpha ( Y ) )$ ; confidence 0.998
+
55. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690032.png ; $\alpha \in C ^ { 0 } , \quad b \in C ^ { 1 } , \quad c \in C ^ { 2 }$ ; confidence 0.207
  
56. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700229.png ; $K \subseteq A ( V )$ ; confidence 0.998
+
56. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690012.png ; $C ^ { * } = ( C ^ { 0 } , C ^ { 1 } , C ^ { 2 } , \rho , \sigma , \delta )$ ; confidence 0.367
  
57. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120181.png ; $( n , n )$ ; confidence 0.998
+
57. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690057.png ; $\delta ( b ) ( g , h ) = b ( g ) ^ { - 1 } b ( g h ) ( b ( h ) ^ { g } ) ^ { - 1 }$ ; confidence 0.990
  
58. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450187.png ; $D = \{ z : | z | < 1 \}$ ; confidence 0.998
+
58. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631097.png ; $\Delta ( \alpha ) = \alpha \otimes 1 + 1 \otimes \alpha$ ; confidence 0.891
  
59. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830222.png ; $F \subset F _ { 1 } \subset G$ ; confidence 0.998
+
59. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004030.png ; $X _ { g } = \operatorname { Sp } ( 2 g , Z ) \backslash H _ { g }$ ; confidence 0.844
  
60. https://www.encyclopediaofmath.org/legacyimages/i/i053/i053060/i0530609.png ; $\mathfrak { g } = \mathfrak { k } + \mathfrak { P }$ ; confidence 0.998
+
60. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590461.png ; $F ( x , y , \lambda ) = \Phi _ { \mu + 1 } ( x , \lambda ) - y ^ { 2 }$ ; confidence 0.999
  
61. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074640/p07464011.png ; $\phi : U \times G \rightarrow \pi ^ { - 1 } ( U )$ ; confidence 0.998
+
61. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013089.png ; $( T , X ) = 0 = \operatorname { Ext } _ { \gamma } ^ { 1 } ( T , X )$ ; confidence 0.465
  
62. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110070/m1100702.png ; $k = 1,2$ ; confidence 0.998
+
62. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700139.png ; $\kappa ^ { \prime } \cong \kappa \otimes O \Lambda$ ; confidence 0.541
  
63. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120503.png ; $\{ F / H , H ^ { 0 } \}$ ; confidence 0.998
+
63. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120505.png ; $\{ F _ { \alpha } , G _ { \alpha } , ( \ldots ) _ { \alpha } \}$ ; confidence 0.433
  
64. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009022.png ; $0 < \tau \leq 1$ ; confidence 0.998
+
64. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082041.png ; $D ^ { X } : B \rightarrow \operatorname { nil } ( B ) ^ { n }$ ; confidence 0.143
  
65. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w12009091.png ; $R ( t ^ { \lambda } )$ ; confidence 0.998
+
65. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820128.png ; $\gamma ( T ) + F \delta ( T ) = F ( \gamma ( T ) , \delta ( T ) )$ ; confidence 0.948
  
66. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590177.png ; $L ( B )$ ; confidence 0.998
+
66. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797023.png ; $\mu ^ { * } : A ^ { * } \rightarrow A ^ { * } \otimes A ^ { * }$ ; confidence 0.991
  
67. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590332.png ; $f ^ { - 1 } ( s _ { 0 } ) = X _ { 0 }$ ; confidence 0.998
+
67. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058500/l0585009.png ; $\mathfrak { g } = \sum _ { i = 1 } ^ { k } \mathfrak { g } _ { i }$ ; confidence 0.468
  
68. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120335.png ; $F ( z , \zeta )$ ; confidence 0.998
+
68. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851094.png ; $\mathfrak { h } _ { 1 } \rightarrow \mathfrak { h } _ { 2 }$ ; confidence 0.774
  
69. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010290/a01029012.png ; $f : X \rightarrow Y$ ; confidence 0.998
+
69. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852014.png ; $\{ \mathfrak { s } _ { 1 } ^ { \prime } \} _ { 0 } \leq i \leq m$ ; confidence 0.121
  
70. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031860/d03186076.png ; $\Gamma ( U , O _ { X } )$ ; confidence 0.998
+
70. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868024.png ; $\operatorname { exp } : \mathfrak { h } \rightarrow G$ ; confidence 0.936
  
71. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590276.png ; $\operatorname { lim } f ( z ) = \infty$ ; confidence 0.998
+
71. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868086.png ; $Z _ { g } \cong \Gamma _ { 1 } ( f _ { 0 } ) / \Gamma _ { 0 } [ e , t ]$ ; confidence 0.072
  
72. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031550/d03155053.png ; $\phi : G \rightarrow H$ ; confidence 0.998
+
72. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868033.png ; $\Gamma _ { 0 } \subset \Gamma ( G ) \subset \Gamma _ { 1 }$ ; confidence 0.991
  
73. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013490/a0134906.png ; $k > 0$ ; confidence 0.998
+
73. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058400/l0584006.png ; $\operatorname { exp } : \mathfrak { g } \rightarrow G$ ; confidence 0.996
  
74. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960139.png ; $\delta _ { i } \in \Delta$ ; confidence 0.998
+
74. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876046.png ; $[ X _ { i } , X _ { j } ] = \sum _ { k = 1 } ^ { r } c _ { i j } ^ { k } X _ { k }$ ; confidence 0.608
  
75. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450171.png ; $84 ( g - 1 )$ ; confidence 0.998
+
75. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690055.png ; $( \rho ( \alpha ) ( b ) ) ( g ) = \alpha b ( g ) ( a ^ { g } ) ^ { - 1 }$ ; confidence 0.492
  
76. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145081.png ; $( f ) + D \geq 0$ ; confidence 0.997
+
76. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267050.png ; $f ^ { \prime } ( O _ { X ^ { \prime } } ) = O _ { S ^ { \prime } }$ ; confidence 0.802
  
77. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690020.png ; $H ^ { 1 } ( C ^ { * } ) = Z ^ { 1 } / \rho$ ; confidence 0.997
+
77. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r081030104.png ; $O _ { \gamma } \subset \Delta \backslash \Delta _ { 0 }$ ; confidence 0.964
  
78. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267047.png ; $H ^ { 2 } ( F , O _ { F } ) = 0$ ; confidence 0.997
+
78. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004058.png ; $\overline { D } _ { S } \rightarrow \overline { D } _ { T }$ ; confidence 0.534
  
79. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110440/a11044012.png ; $f _ { 1 }$ ; confidence 0.997
+
79. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s0855908.png ; $U ( \zeta , R ) = \{ z \in \overline { C } : | z - \zeta | < R \}$ ; confidence 0.957
  
80. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054340/j05434023.png ; $C ^ { - 1 } A C$ ; confidence 0.997
+
80. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590133.png ; $V ( \alpha ) = \{ z \in \overline { C } : | z - \alpha | < R \}$ ; confidence 0.668
  
81. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180149.png ; $n > 2$ ; confidence 0.997
+
81. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054034.png ; $w ( \alpha ) = x ( \alpha ) y ( - \alpha ^ { - 1 } ) x ( \alpha )$ ; confidence 0.832
  
82. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a01417057.png ; $K ( \Gamma )$ ; confidence 0.997
+
82. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013037.png ; $X = \{ C : \operatorname { Hom } _ { \Lambda } ( C , Y ) = 0 \}$ ; confidence 0.907
  
83. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852020.png ; $0 \leq i < m$ ; confidence 0.997
+
83. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013088.png ; $\operatorname { Ext } _ { \mathscr { H } } ^ { 1 } ( T , T ) = 0$ ; confidence 0.420
  
84. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r08103021.png ; $W _ { k } ( S , G ) = N ( S ) / Z ( S )$ ; confidence 0.997
+
84. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013030.png ; $F = \{ C : \operatorname { Hom } _ { \Lambda } ( T , C ) = 0 \}$ ; confidence 0.896
  
85. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022660/c02266044.png ; $0 \leq t < 1$ ; confidence 0.997
+
85. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013070.png ; $( T , ) : D ^ { b } ( \Lambda ) \rightarrow D ^ { b } ( \Gamma )$ ; confidence 0.335
  
86. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524045.png ; $X = F ^ { - 1 } Y$ ; confidence 0.997
+
86. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014065.png ; $: G 1 _ { Q } ( d ) \times A _ { Q } ( d ) \rightarrow A _ { Q } ( d )$ ; confidence 0.120
  
87. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830193.png ; $p + q - n$ ; confidence 0.997
+
87. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095410/u09541032.png ; $\operatorname { exp } : \mathfrak { u } \rightarrow U$ ; confidence 0.973
  
88. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110070/e110070172.png ; $\alpha = - 1$ ; confidence 0.997
+
88. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100197.png ; $f _ { x } = \sigma ( x ) f , \quad V _ { x } = \sigma ^ { - 1 } ( x ) V$ ; confidence 0.692
  
89. https://www.encyclopediaofmath.org/legacyimages/b/b111/b111040/b11104014.png ; $p = 3$ ; confidence 0.997
+
89. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c02057048.png ; $s = h _ { 1 } ( s _ { 1 } ) _ { x } + \ldots + h _ { N } ( s _ { N } ) _ { x }$ ; confidence 0.366
  
90. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640105.png ; $p _ { 12 } = 0$ ; confidence 0.997
+
90. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700216.png ; $\mathscr { O } _ { S , s _ { 0 } } \simeq \hat { M } _ { X _ { 0 } }$ ; confidence 0.574
  
91. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110070/k11007014.png ; $U \subseteq G / B$ ; confidence 0.997
+
91. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120295.png ; $\| f \| = \operatorname { max } _ { z \in G _ { p } } | f ( z ) |$ ; confidence 0.795
  
92. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130220/a1302203.png ; $Z ( R )$ ; confidence 0.997
+
92. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120224.png ; $\operatorname { Ext } _ { c } ^ { n - p + 1 } ( Y ; F , \Omega )$ ; confidence 0.597
  
93. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013000/a013000105.png ; $A ( E )$ ; confidence 0.997
+
93. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696033.png ; $( \theta \alpha _ { i } ) _ { i \in I , \theta \in \Theta }$ ; confidence 0.719
  
94. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797035.png ; $A _ { 0 } = K$ ; confidence 0.997
+
94. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410136.png ; $\dot { x } \square ^ { 2 } + \dot { y } \square ^ { 2 } \neq 0$ ; confidence 0.459
  
95. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590479.png ; $F ( x , y , \lambda )$ ; confidence 0.997
+
95. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058480/l05848032.png ; $\phi _ { e } : A \rightarrow A / \mathfrak { m } _ { \ell }$ ; confidence 0.383
  
96. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872014.png ; $\Lambda _ { p } ( x , y )$ ; confidence 0.997
+
96. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690079.png ; $\sigma ( f ) ( \beta ) = ( \operatorname { Ad } f ) \beta$ ; confidence 0.579
  
97. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859028.png ; $f : G _ { 1 } \rightarrow G _ { 2 }$ ; confidence 0.997
+
97. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690095.png ; $\rightarrow H ^ { 1 } ( G , B ) \rightarrow H ^ { 1 } ( G , A )$ ; confidence 0.984
  
98. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590457.png ; $\Phi _ { \mu } ( x , \lambda ) =$ ; confidence 0.997
+
98. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590373.png ; $x _ { 0 } ^ { \mu + 1 } + x _ { 1 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$ ; confidence 0.952
  
99. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120255.png ; $h ( \phi ) = k ( - \phi ) , \quad \sigma \leq \phi \leq 2 \pi$ ; confidence 0.997
+
99. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590122.png ; $f _ { 0 } ( z ) = \sum _ { k = 0 } ^ { \infty } b ^ { k } z ^ { d ^ { k } }$ ; confidence 0.687
  
100. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090153.png ; $\Lambda ^ { + } ( n )$ ; confidence 0.997
+
100. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590227.png ; $\zeta = ( \zeta _ { 1 } , \ldots , \zeta _ { n } ) \in C ^ { n }$ ; confidence 0.582
  
101. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700253.png ; $H ^ { 2 } ( G , V ) = 0$ ; confidence 0.997
+
101. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095400/u09540041.png ; $\sum _ { i = 1 } ^ { j } m _ { i } \geq \sum _ { i = 1 } ^ { j } l _ { i }$ ; confidence 0.947
  
102. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590429.png ; $p ( Z ) = 1 - \operatorname { dim } H ^ { 0 } ( Z , O _ { Z } ) + \operatorname { dim } H ^ { 1 } ( Z , O _ { Z } )$ ; confidence 0.997
+
102. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100175.png ; $V _ { m } f _ { n } = f _ { n } V _ { m } \quad \text { if } ( n , m ) = 1$ ; confidence 0.135
  
103. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082021.png ; $B _ { 1 } \rightarrow B _ { 2 }$ ; confidence 0.997
+
103. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145076.png ; $\operatorname { deg } K _ { X } = ( X ) ^ { 2 } + ( X . K _ { F } )$ ; confidence 0.674
  
104. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590188.png ; $f : U _ { 1 } \rightarrow U _ { 2 }$ ; confidence 0.997
+
104. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164049.png ; $q ( V ) = \operatorname { dim } _ { k } H ^ { 1 } ( V , O _ { V } )$ ; confidence 0.987
  
105. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120291.png ; $\forall G \in O ^ { F }$ ; confidence 0.997
+
105. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031640/d03164011.png ; $\omega = ( a _ { 0 } , \ldots , a _ { n } , \ldots ) \in W ( k )$ ; confidence 0.228
  
106. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011820/a011820106.png ; $A \leq B$ ; confidence 0.997
+
106. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960185.png ; $( F \langle \alpha \rangle / F ) \rightarrow W _ { K }$ ; confidence 0.521
  
107. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872075.png ; $( L , \pi )$ ; confidence 0.997
+
107. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820162.png ; $F _ { \pi } ( X , Y ) = f \pi ^ { 1 } ( f \pi ( X ) + f _ { \pi } ( Y ) )$ ; confidence 0.543
  
108. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861013.png ; $\square ^ { t }$ ; confidence 0.997
+
108. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410142.png ; $( x , y ) = \{ ( \xi , \eta ) : F ( x , y , \xi , \eta ) \leq 1 \}$ ; confidence 0.987
  
109. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016540/b0165403.png ; $U ( G )$ ; confidence 0.997
+
109. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063010/m06301058.png ; $F ( x _ { 1 } e _ { 1 } + \square _ { \cdots } + x _ { x } e _ { x } )$ ; confidence 0.221
  
110. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472095.png ; $y = \gamma x$ ; confidence 0.997
+
110. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631043.png ; $\Delta ( x _ { j } ) = \sum _ { k } x _ { i k } \otimes x _ { k j }$ ; confidence 0.404
  
111. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145063.png ; $g = \frac { ( m - 1 ) ( m - 2 ) } { 2 }$ ; confidence 0.997
+
111. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310145.png ; $\Delta ( t _ { j } ) = \sum _ { k } t _ { i k } \otimes t _ { k j }$ ; confidence 0.449
  
112. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559027.png ; $\phi _ { 1 } ( 0 ) = \zeta$ ; confidence 0.997
+
112. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631055.png ; $\{ \alpha , b c \} = \{ \alpha , b \} c + \{ \alpha , c \} b$ ; confidence 0.756
  
113. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h04769040.png ; $g x = y$ ; confidence 0.997
+
113. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590139.png ; $V ^ { \prime } ( \infty ) = \{ z \in C : | z - \alpha | > R \}$ ; confidence 0.435
  
114. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087080/s08708088.png ; $I ( T , \lambda )$ ; confidence 0.997
+
114. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054036.png ; $\{ \alpha , b \} = h ( a b ) h ( \alpha ) ^ { - 1 } h ( b ) ^ { - 1 }$ ; confidence 0.214
  
115. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120313.png ; $E = G$ ; confidence 0.997
+
115. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013050.png ; $( T , ) : \operatorname { mod } \Lambda \rightarrow$ ; confidence 0.816
  
116. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058470/l0584708.png ; $0 \leq i < n$ ; confidence 0.997
+
116. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014042.png ; $K _ { 0 } ( Q ) = K _ { 0 } ( \operatorname { rep } _ { K } ( Q ) )$ ; confidence 0.940
  
117. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120382.png ; $\phi ^ { * } ( z ) \in E ^ { 1 }$ ; confidence 0.997
+
117. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011740/a01174032.png ; $T \mapsto \operatorname { Aut } _ { T } ( X \times T )$ ; confidence 0.864
  
118. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i052350102.png ; $\pi : X \rightarrow W$ ; confidence 0.997
+
118. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120222.png ; $\operatorname { Ext } _ { c } ^ { x - p } ( Y ; F , \Omega )$ ; confidence 0.357
  
119. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690082.png ; $H ^ { 1 } ( R _ { G } ( X ) )$ ; confidence 0.997
+
119. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820155.png ; $\alpha _ { \gamma } ( \gamma _ { 0 } ( T ) ) = \gamma ( T )$ ; confidence 0.883
  
120. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763022.png ; $X ( T ) \otimes R$ ; confidence 0.997
+
120. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h0474106.png ; $f ( t _ { 1 } , \ldots , t _ { k } , x _ { 1 } , \ldots , x _ { N } )$ ; confidence 0.252
  
121. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004016.png ; $\Gamma \backslash H ^ { * }$ ; confidence 0.997
+
121. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h04741068.png ; $\mathfrak { a } \subset k [ X _ { 1 } , \ldots , X _ { n } ]$ ; confidence 0.507
  
122. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010710/a01071032.png ; $1 \leq i \leq n$ ; confidence 0.997
+
122. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970135.png ; $f ^ { * } g = m _ { A } \circ ( f \otimes g ) \circ \mu _ { C }$ ; confidence 0.605
  
123. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120461.png ; $( F ^ { \prime } , F )$ ; confidence 0.997
+
123. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427084.png ; $\mathfrak { g } _ { 1 } = [ \mathfrak { g } _ { 0 } , p ] + k p$ ; confidence 0.395
  
124. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150014.png ; $\theta = \int _ { 0 } ^ { \lambda } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ ; confidence 0.997
+
124. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k1200302.png ; $\operatorname { Ric } ( \omega ) = \lambda \omega$ ; confidence 0.996
  
125. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700185.png ; $H ^ { 1 } ( X _ { 0 } , T _ { X _ { 0 } } )$ ; confidence 0.997
+
125. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851097.png ; $\mathfrak { g } _ { 1 } \rightarrow \mathfrak { g } 2$ ; confidence 0.364
  
126. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872023.png ; $( x , y ) \rightarrow [ x , y ] = x y - y x$ ; confidence 0.997
+
126. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852042.png ; $\rho ( \mathfrak { g } ) \subset \mathfrak { b } ( F )$ ; confidence 0.547
  
127. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047700/h04770011.png ; $\phi : G \rightarrow X$ ; confidence 0.997
+
127. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872057.png ; $\phi ( x ^ { [ p ] } ) = ( \phi ( x ) ) ^ { [ p ] } , \quad x \in L$ ; confidence 0.926
  
128. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097710/w0977105.png ; $W ( T , G ) = N _ { G } ( T ) / Z _ { G } ( T )$ ; confidence 0.997
+
128. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876017.png ; $\xi _ { i j } ( x ) = \partial f _ { j } / \partial g ( e , x )$ ; confidence 0.981
  
129. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h04769094.png ; $\Gamma \subset G$ ; confidence 0.997
+
129. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310122.png ; $R ^ { 12 } = \sum _ { i } x _ { i } \otimes y _ { i } \otimes 1$ ; confidence 0.855
  
130. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830346.png ; $( A _ { k } ) < \operatorname { rank } ( B _ { k } )$ ; confidence 0.997
+
130. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310124.png ; $R ^ { 23 } = \sum _ { i } 1 \otimes x _ { i } \otimes y _ { i }$ ; confidence 0.885
  
131. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014190/a01419020.png ; $\phi ( t )$ ; confidence 0.997
+
131. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310123.png ; $R ^ { 13 } = \sum _ { i } x _ { i } \otimes 1 \otimes y _ { i }$ ; confidence 0.882
  
132. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510181.png ; $0 \leq p \leq ( n + 1 ) / 2$ ; confidence 0.997
+
132. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310113.png ; $( \text { id } \otimes \Delta ) ( R ) = R ^ { 13 } R ^ { 12 }$ ; confidence 0.878
  
133. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k12003011.png ; $\operatorname { Ric } ( \omega ) = 0$ ; confidence 0.997
+
133. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559049.png ; $\tau _ { 1 } - \epsilon < \tau ^ { \prime } < \tau _ { 1 }$ ; confidence 0.999
  
134. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164058.png ; $\pi = \{ ( D ^ { 2 } ) + ( D K _ { V } ) \} / 2 + 1$ ; confidence 0.997
+
134. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t1301303.png ; $p \cdot \operatorname { dim } _ { \Lambda } T \leq 1$ ; confidence 0.223
  
135. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l058720136.png ; $m = n , n + 1,2 n$ ; confidence 0.997
+
135. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041060/f041060146.png ; $\lambda = ( \lambda _ { 1 } , \ldots , \lambda _ { n } )$ ; confidence 0.574
  
136. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450158.png ; $g < 11$ ; confidence 0.997
+
136. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100173.png ; $V _ { n } V _ { m } = V _ { n m } , \quad f _ { n } f _ { m } = f _ { n m }$ ; confidence 0.509
  
137. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427034.png ; $F _ { n } ^ { ( + ) }$ ; confidence 0.997
+
137. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640143.png ; $M ^ { \prime } = \operatorname { dim } S _ { \alpha }$ ; confidence 0.678
  
138. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o07001029.png ; $U \subset X / G$ ; confidence 0.997
+
138. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023470/c02347054.png ; $n _ { \alpha } = \operatorname { dim } R ^ { \alpha }$ ; confidence 0.918
  
139. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820210.png ; $F ( X , Y )$ ; confidence 0.997
+
139. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070033.png ; $X \times S S ^ { \prime } \rightarrow S ^ { \prime }$ ; confidence 0.626
  
140. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082022.png ; $H ( B _ { 1 } ) \rightarrow H ( B _ { 2 } )$ ; confidence 0.997
+
140. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h04741062.png ; $F ^ { \gamma } = A _ { 1 } F _ { 1 } + \ldots + A _ { m } F _ { m }$ ; confidence 0.375
  
141. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090248.png ; $\Phi = \Phi ^ { + } \cup \Phi ^ { - }$ ; confidence 0.997
+
141. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427022.png ; $H ( A , j ) = \{ \alpha \in A : \alpha ^ { j } = \alpha \}$ ; confidence 0.158
  
142. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023470/c02347040.png ; $\{ R ^ { \alpha } : \alpha \in I \}$ ; confidence 0.997
+
142. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872016.png ; $( \text { ad } x _ { 1 } \ldots \text { ad } x _ { p } - 1 ) x$ ; confidence 0.549
  
143. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k1200301.png ; $\operatorname { Ric } ( \omega )$ ; confidence 0.997
+
143. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690018.png ; $H ^ { 0 } ( C ^ { * } ) = \rho ^ { - 1 } ( \text { Aut } C ^ { 1 } )$ ; confidence 0.868
  
144. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150101.png ; $N \cup \{ 0 \}$ ; confidence 0.997
+
144. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900126.png ; $H _ { \alpha } ^ { 2 } ( G , A ) = \theta ^ { - 1 } ( \alpha )$ ; confidence 1.000
  
145. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012540/a0125406.png ; $D = [ Z _ { G } ( S ) , Z _ { G } ( S ) ]$ ; confidence 0.997
+
145. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310127.png ; $R ^ { 12 } R ^ { 13 } R ^ { 23 } = R ^ { 23 } R ^ { 13 } R ^ { 12 }$ ; confidence 0.998
  
146. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120304.png ; $A ( f ) = \int _ { \gamma } f ( z ) g ( z ) d z$ ; confidence 0.997
+
146. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764019.png ; $\int _ { U } \omega \wedge \overline { w } < \infty$ ; confidence 0.401
  
147. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120486.png ; $( F , \tau )$ ; confidence 0.997
+
147. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590101.png ; $\Gamma = \{ z \in \overline { C } : | z - \zeta | = R \}$ ; confidence 0.983
  
148. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074640/p0746401.png ; $( P , B , G , \pi )$ ; confidence 0.997
+
148. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012290/a01229020.png ; $O ( n , k ) = \{ g \in GL ( n , k ) : \square ^ { t } g g = 1 \}$ ; confidence 0.472
  
149. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120269.png ; $f _ { n } ( z ) \rightarrow f ( z )$ ; confidence 0.997
+
149. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830303.png ; $B \in R \{ y _ { 1 } , \ldots , y _ { x } \} \backslash R$ ; confidence 0.458
  
150. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a014170113.png ; $f : X \rightarrow V$ ; confidence 0.997
+
150. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830169.png ; $Y _ { n + 1 } G - F \in F \{ Y _ { 1 } , \ldots , Y _ { n + 1 } \}$ ; confidence 0.800
  
151. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830393.png ; $A = 0$ ; confidence 0.997
+
151. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830142.png ; $B _ { 0 } ( \zeta _ { 1 } , \ldots , \zeta _ { k } ) \neq 0$ ; confidence 0.645
  
152. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b1202103.png ; $U ( \mathfrak { g } )$ ; confidence 0.997
+
152. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830253.png ; $R = ( R , \partial _ { 1 } , \ldots , \partial _ { m } )$ ; confidence 0.340
  
153. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851051.png ; $\beta ( H _ { \alpha } ) = \frac { 2 ( \alpha , \beta ) } { ( \alpha , \alpha ) } , \quad \alpha , \beta \in \Sigma$ ; confidence 0.997
+
153. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830314.png ; $A \in R \{ y _ { 1 } , \ldots , y _ { n } \} \backslash R$ ; confidence 0.579
  
154. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640137.png ; $M = \operatorname { dim } \operatorname { Im } ( H ^ { 1 } ( V , E _ { \alpha } ) \rightarrow H ^ { 1 } ( V , T _ { V } ) )$ ; confidence 0.997
+
154. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032490/d0324909.png ; $G = F \{ \eta _ { 1 } , \ldots , \eta _ { \nwarrow } \}$ ; confidence 0.083
  
155. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764092.png ; $\operatorname { dim } X = 2$ ; confidence 0.997
+
155. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032490/d03249037.png ; $\tau = \operatorname { deg } \omega _ { \eta / F }$ ; confidence 0.965
  
156. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040270/f04027014.png ; $| G | = m n$ ; confidence 0.997
+
156. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120179.png ; $s ( \hat { \omega } ) = ( - 1 ) ^ { n } \int _ { X } \omega$ ; confidence 0.188
  
157. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065570/m06557032.png ; $h ( X _ { 1 } ) = 0$ ; confidence 0.997
+
157. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120493.png ; $X ^ { * } = ( X ^ { \prime } , \beta ( X ^ { \prime } , X ) )$ ; confidence 0.998
  
158. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d03412091.png ; $H _ { r } ( R , X )$ ; confidence 0.997
+
158. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120377.png ; $\omega ( z ) = 1 / \{ 2 \pi i ( \zeta - z _ { 0 } ) ^ { 2 } \}$ ; confidence 0.963
  
159. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002048.png ; $\geq [ ( d + 1 ) / 2 ]$ ; confidence 0.997
+
159. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120545.png ; $F ( x , y ) \rightarrow \text { inf, } \quad x \in X$ ; confidence 0.965
  
160. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590453.png ; $f _ { \lambda } ( z ) = F ( z , \lambda )$ ; confidence 0.997
+
160. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120218.png ; $\operatorname { Ext } ^ { \mu - p } ( K ; F , \Omega )$ ; confidence 0.170
  
161. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868035.png ; $\Gamma _ { 0 } \subset M \subset \Gamma _ { 1 }$ ; confidence 0.997
+
161. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120234.png ; $\alpha : H ^ { p } ( X , F ) \rightarrow H ^ { p } ( Y , F )$ ; confidence 0.994
  
162. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450251.png ; $g > 2$ ; confidence 0.997
+
162. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120210.png ; $\operatorname { Ext } ^ { \mu - p } ( X ; F , \Omega )$ ; confidence 0.230
  
163. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h0476904.png ; $G \times M$ ; confidence 0.996
+
163. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120208.png ; $\operatorname { Ext } _ { c } ^ { n } ( X ; F , \Omega )$ ; confidence 0.851
  
164. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k12003029.png ; $\operatorname { Ric } ( \omega ) = \omega$ ; confidence 0.996
+
164. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082086.png ; $\psi ^ { * } F _ { u } ( X , Y ) = F _ { u } ^ { \prime } ( X , Y )$ ; confidence 0.721
  
165. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040550/f04055046.png ; $F _ { \nu } ( V )$ ; confidence 0.996
+
165. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082051.png ; $F _ { i } ( X , 0 ) = X _ { i } , \quad F _ { i } ( 0 , Y ) = Y _ { i }$ ; confidence 0.975
  
166. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062170/m06217010.png ; $Z ( A )$ ; confidence 0.996
+
166. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i05235028.png ; $f ( x , y ) = a x ^ { 3 } + 3 b x ^ { 2 } y + 3 c x y ^ { 2 } + d y ^ { 3 }$ ; confidence 0.991
  
167. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o07001082.png ; $Y \mapsto A Y A ^ { - 1 }$ ; confidence 0.996
+
167. https://www.encyclopediaofmath.org/legacyimages/i/i053/i053060/i0530609.png ; $\mathfrak { g } = \mathfrak { k } + \mathfrak { P }$ ; confidence 0.998
  
168. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047700/h04770013.png ; $\psi \pi = \phi$ ; confidence 0.996
+
168. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510150.png ; $\mathfrak { g } = \mathfrak { g } 0 \otimes _ { k } K$ ; confidence 0.427
  
169. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l058720130.png ; $+ 1 \equiv 0$ ; confidence 0.996
+
169. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510120.png ; $\operatorname { dim } \mathfrak { g } = n ( 2 n - 1 )$ ; confidence 0.890
  
170. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150024.png ; $y ^ { 2 } = ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } )$ ; confidence 0.996
+
170. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510115.png ; $\operatorname { dim } \mathfrak { g } = n ( 2 n + 1 )$ ; confidence 0.902
  
171. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590279.png ; $z \in D \backslash P$ ; confidence 0.996
+
171. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852017.png ; $\mathfrak { g } _ { \mathfrak { i } } ^ { \prime } + 1$ ; confidence 0.346
  
172. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011520/a0115207.png ; $g ( h x ) = ( g h ) x$ ; confidence 0.996
+
172. https://www.encyclopediaofmath.org/legacyimages/g/g110/g110110/g1101103.png ; $\mathfrak { g } = \mathfrak { k } + \mathfrak { p }$ ; confidence 0.994
  
173. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640139.png ; $\operatorname { dim } _ { k } H ^ { 2 } ( V , E _ { \alpha } ) + \operatorname { dim } _ { k } H ^ { 2 } ( V , T _ { V } )$ ; confidence 0.996
+
173. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690031.png ; $( \delta b ) _ { i j k } = b _ { j } b _ { j k } b _ { i k } ^ { - 1 }$ ; confidence 0.385
  
174. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058480/l05848051.png ; $A _ { k } \subset A$ ; confidence 0.996
+
174. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900115.png ; $( m , \phi ) \sim ( m ^ { \prime } , \phi ^ { \prime } )$ ; confidence 0.996
  
175. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120257.png ; $| z | < \sigma$ ; confidence 0.996
+
175. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690014.png ; $\sigma : C ^ { 0 } \rightarrow \text { Aut } C ^ { 2 }$ ; confidence 0.563
  
176. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090449.png ; $G ( m , 1 , n )$ ; confidence 0.996
+
176. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764096.png ; $\phi : \text { Def } Y \rightarrow \text { Def } X$ ; confidence 0.355
  
177. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120301.png ; $\Lambda ( f )$ ; confidence 0.996
+
177. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590463.png ; $f ( x , y ) = x ^ { m - 1 } - x y ^ { 2 } = x ( x ^ { m - 2 } - y ^ { 2 } )$ ; confidence 0.996
  
178. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r08103072.png ; $\Phi _ { k } ( S , G )$ ; confidence 0.996
+
178. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t130130103.png ; $\operatorname { Ext } _ { \Delta } ^ { i } ( T , T ) = 0$ ; confidence 0.343
  
179. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010810/a01081039.png ; $x ( t )$ ; confidence 0.996
+
179. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t1301304.png ; $\operatorname { Ext } _ { \Delta } ^ { 1 } ( T , T ) = 0$ ; confidence 0.420
  
180. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090364.png ; $\Lambda ( V ) \neq \Lambda$ ; confidence 0.996
+
180. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014064.png ; $G l _ { Q } ( d ) = \prod _ { j \in Q _ { 0 } } Gl ( v _ { j } , K )$ ; confidence 0.225
  
181. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r0776403.png ; $\pi : Y \rightarrow X$ ; confidence 0.996
+
181. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095410/u09541051.png ; $G _ { \alpha } \times \ldots \times G _ { \alpha }$ ; confidence 0.300
  
182. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023330/c02333043.png ; $k [ Y ] \rightarrow k [ X ]$ ; confidence 0.996
+
182. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095410/u09541040.png ; $U = U _ { 1 } \supset \ldots \supset U _ { s } = \{ e \}$ ; confidence 0.931
  
183. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120272.png ; $A _ { 0 } ( G )$ ; confidence 0.996
+
183. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090164.png ; $E ^ { \otimes r } \rightarrow \Delta ( \lambda )$ ; confidence 0.978
  
184. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764046.png ; $D _ { n - 2 }$ ; confidence 0.996
+
184. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145087.png ; $l ( D ) - l ( K - D ) = \operatorname { deg } ( D ) - g + 1$ ; confidence 0.964
  
185. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095400/u09540011.png ; $( g - 1 ) ^ { n } = 0$ ; confidence 0.996
+
185. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640127.png ; $M = 10 p _ { t x } - p _ { g } - 2 p ^ { ( 1 ) } + 12 + \theta$ ; confidence 0.369
  
186. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696061.png ; $\delta \in \Delta$ ; confidence 0.996
+
186. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640140.png ; $H ^ { 2 } ( V , E _ { \alpha } ) \geq 2 p _ { g } - p _ { x } - 1$ ; confidence 0.616
  
187. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020280/c020280211.png ; $| f ( z ) | \leq 1$ ; confidence 0.996
+
187. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a014170141.png ; $\rho : K \rightarrow \operatorname { GL } ( V )$ ; confidence 0.653
  
188. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h0479705.png ; $\delta : A \rightarrow A \otimes A$ ; confidence 0.996
+
188. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a01417058.png ; $C ( f _ { 1 } , \ldots , f _ { n } ) \subset K ( \Gamma )$ ; confidence 0.356
  
189. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410105.png ; $G ( K / k )$ ; confidence 0.996
+
189. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070032.png ; $f ( \mathfrak { o } ^ { \prime } ) = \mathfrak { o }$ ; confidence 0.466
  
190. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450257.png ; $g \geq 40$ ; confidence 0.996
+
190. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120159.png ; $H _ { r } ( A , X ) \sim H _ { r + 1 } ( R \backslash A , X )$ ; confidence 0.499
  
191. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020540/c020540286.png ; $p - 1$ ; confidence 0.996
+
191. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696059.png ; $( y _ { j } \theta ) _ { j \in J , \theta \in \Theta }$ ; confidence 0.633
  
192. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590151.png ; $G / R ( G )$ ; confidence 0.996
+
192. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082095.png ; $\alpha ( F ( X , Y ) ) = G ( \alpha ( X ) , \alpha ( Y ) )$ ; confidence 0.998
  
193. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010330/a0103303.png ; $r > 0$ ; confidence 0.996
+
193. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820205.png ; $f ( p ) ( X ) = X + a _ { p } X ^ { p } + a _ { p } 2 X ^ { p ^ { 2 } } +$ ; confidence 0.909
  
194. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852072.png ; $[ s , n ] = 0$ ; confidence 0.996
+
194. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082048.png ; $X _ { 1 } , \ldots , X _ { X } , Y _ { 1 } , \ldots , Y _ { X }$ ; confidence 0.160
  
195. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559086.png ; $( b , \{ M \} )$ ; confidence 0.996
+
195. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510105.png ; $\operatorname { dim } \mathfrak { g } = n ( n + 2 )$ ; confidence 0.881
  
196. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033340/d033340242.png ; $z = z ( u , v )$ ; confidence 0.996
+
196. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510186.png ; $\mathfrak { g } 0 = \mathfrak { s o } ( p , 2 n + 1 - p )$ ; confidence 0.237
  
197. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450255.png ; $g \geq 25$ ; confidence 0.996
+
197. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868041.png ; $\pi _ { 1 } ( G ) \cong \Gamma ( G ) / \Gamma _ { 0 }$ ; confidence 0.992
  
198. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120250.png ; $k ( \phi )$ ; confidence 0.996
+
198. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023140/c023140210.png ; $\rho : G \rightarrow \operatorname { GL } ( V )$ ; confidence 0.678
  
199. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450150.png ; $+ 1$ ; confidence 0.996
+
199. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631036.png ; $[ x _ { i l } , x _ { k j } ] = ( q ^ { - 1 } - q ) x _ { j } x _ { k l }$ ; confidence 0.406
  
200. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859095.png ; $L ( G _ { 1 } ) \rightarrow L ( G _ { 2 } )$ ; confidence 0.996
+
200. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763023.png ; $\phi : G \rightarrow \operatorname { GL } ( V )$ ; confidence 0.578
  
201. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q0763106.png ; $\Delta : A \rightarrow A \otimes A$ ; confidence 0.996
+
201. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r08103092.png ; $( n _ { \alpha } + 1 ) \alpha \notin \Phi _ { k } ( G )$ ; confidence 0.771
  
202. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700260.png ; $k ( ( t ) )$ ; confidence 0.996
+
202. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r081030109.png ; $\alpha \in \Delta ( \gamma ) \cap O _ { \gamma }$ ; confidence 0.992
  
203. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120242.png ; $H ^ { p } ( X , F ) = H ^ { p + 1 } ( X , F ) = 0$ ; confidence 0.996
+
203. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590284.png ; $P = \{ z = ( z _ { 1 } , z _ { 2 } ) \in C ^ { 2 } : z _ { 2 } = 0 \}$ ; confidence 0.988
  
204. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g13006096.png ; $1 \leq i , j \leq n$ ; confidence 0.996
+
204. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590308.png ; $f \mathfrak { m } ^ { 2 } = \operatorname { dim } A$ ; confidence 0.253
  
205. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310155.png ; $U ( g )$ ; confidence 0.996
+
205. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590167.png ; $f ( z ) = \frac { 1 } { ( 1 + z ^ { 1 / 2 } ) ( 1 + z ^ { 1 / 6 } ) }$ ; confidence 0.999
  
206. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590463.png ; $f ( x , y ) = x ^ { m - 1 } - x y ^ { 2 } = x ( x ^ { m - 2 } - y ^ { 2 } )$ ; confidence 0.996
+
206. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090186.png ; $\operatorname { Ind } _ { \overline { H } } ^ { G }$ ; confidence 0.452
  
207. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011380/a011380169.png ; $i \neq j$ ; confidence 0.996
+
207. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090116.png ; $\Delta ( \lambda ) = K GL _ { n } ( K ) z _ { \lambda }$ ; confidence 0.499
  
208. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872073.png ; $\Lambda _ { p } ( x , y ) = 0$ ; confidence 0.996
+
208. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090356.png ; $\{ x _ { \alpha } ( t ) : t \in K , \alpha \in \Phi \}$ ; confidence 0.553
  
209. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k1200302.png ; $\operatorname { Ric } ( \omega ) = \lambda \omega$ ; confidence 0.996
+
209. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145045.png ; $\pi = \operatorname { dim } H ^ { 1 } ( X , O _ { X } )$ ; confidence 0.980
  
210. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a014170135.png ; $D ( G )$ ; confidence 0.996
+
210. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011530/a01153013.png ; $P ( \alpha _ { 1 } , \ldots , \alpha _ { N } ) \neq 0$ ; confidence 0.251
  
211. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023470/c02347021.png ; $( P \times C ) / Z$ ; confidence 0.996
+
211. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031550/d03155058.png ; $\hat { \phi } : \hat { H } \rightarrow \hat { G }$ ; confidence 0.723
  
212. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820177.png ; $[ n ] ( X ) = F ( X , [ n - 1 ] ( X ) )$ ; confidence 0.996
+
212. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183040.png ; $\Sigma \subset F \{ Y _ { 1 } , \ldots , Y _ { N } \}$ ; confidence 0.440
  
213. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450132.png ; $\phi _ { 3 K } ( Y )$ ; confidence 0.996
+
213. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830140.png ; $B _ { 0 } ( \eta _ { 1 } , \ldots , \eta _ { k } ) \neq 0$ ; confidence 0.724
  
214. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013820/a01382017.png ; $\theta \in \Theta$ ; confidence 0.996
+
214. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120200.png ; $\operatorname { Ext } _ { \Psi } ^ { n - p } ( X ; F )$ ; confidence 0.835
  
215. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797022.png ; $\epsilon ^ { * } : K \rightarrow A ^ { * }$ ; confidence 0.996
+
215. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120542.png ; $f ( x ) \rightarrow \text { inf, } \quad x \in X$ ; confidence 0.973
  
216. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015110/b01511048.png ; $\Gamma = \partial D$ ; confidence 0.996
+
216. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040270/f04027012.png ; $| G | = p _ { 1 } ^ { n _ { 1 } } \ldots p _ { k } ^ { n _ { k } }$ ; confidence 0.744
  
217. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058400/l0584006.png ; $\operatorname { exp } : \mathfrak { g } \rightarrow G$ ; confidence 0.996
+
217. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040370/f04037021.png ; $q + 1 \leq k \leq \operatorname { prof } F - p + 1$ ; confidence 0.687
  
218. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900115.png ; $( m , \phi ) \sim ( m ^ { \prime } , \phi ^ { \prime } )$ ; confidence 0.996
+
218. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410109.png ; $\beta = \alpha \cdot \sigma ( \alpha ) ^ { - 1 }$ ; confidence 0.924
  
219. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024330/c02433072.png ; $A \rightarrow B$ ; confidence 0.996
+
219. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054340/j05434031.png ; $+ \operatorname { rk } ( A - \lambda E ) ^ { m + 1 }$ ; confidence 0.935
  
220. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450131.png ; $\phi _ { 3 K } ( X )$ ; confidence 0.995
+
220. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510178.png ; $\mathfrak { g } 0 = \mathfrak { s u } ( p , n + 1 - p )$ ; confidence 0.444
  
221. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640131.png ; $( V , \alpha )$ ; confidence 0.995
+
221. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058480/l05848037.png ; $D \rightarrow \phi _ { \varepsilon } \circ D$ ; confidence 0.258
  
222. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830334.png ; $\Sigma \backslash \{ F \}$ ; confidence 0.995
+
222. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872040.png ; $\operatorname { dim } _ { k } U _ { p } ( L ) = p ^ { n }$ ; confidence 0.777
  
223. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a010210128.png ; $( f )$ ; confidence 0.995
+
223. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876013.png ; $g ( x ) = y = ( y _ { 1 } , \ldots , y _ { x } ) \in \Omega$ ; confidence 0.399
  
224. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054019.png ; $x y x ^ { - 1 } y ^ { - 1 }$ ; confidence 0.995
+
224. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690013.png ; $\rho : C ^ { 0 } \rightarrow \text { Aff } C ^ { 1 }$ ; confidence 0.846
  
225. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r08103045.png ; $\alpha \in \Phi _ { k } ( S , G )$ ; confidence 0.995
+
225. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o07001089.png ; $\operatorname { Fix } g = \{ x \in X : g ( x ) = x \}$ ; confidence 0.571
  
226. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150072.png ; $f : P ^ { 2 } \rightarrow X$ ; confidence 0.995
+
226. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631091.png ; $q = \operatorname { exp } h ( H _ { i } , H _ { j } ) / 2$ ; confidence 0.661
  
227. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b13029059.png ; $1 \leq i \leq d$ ; confidence 0.995
+
227. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763080.png ; $\phi _ { 1 } \otimes \ldots \otimes \phi _ { d }$ ; confidence 0.978
  
228. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820150.png ; $\gamma _ { 0 } ( T )$ ; confidence 0.995
+
228. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r077640101.png ; $\phi : \operatorname { Def } Y \rightarrow A$ ; confidence 0.641
  
229. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120388.png ; $f ^ { * } ( z )$ ; confidence 0.995
+
229. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764011.png ; $x _ { 0 } ^ { k _ { 0 } } + \ldots + x _ { x } ^ { k _ { n } } = 0$ ; confidence 0.462
  
230. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014070/a0140703.png ; $1$ ; confidence 0.995
+
230. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590409.png ; $\beta _ { v } = ( m _ { v } n ) / ( n _ { 1 } \dots n _ { v } )$ ; confidence 0.618
  
231. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872069.png ; $Z ( L )$ ; confidence 0.995
+
231. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590135.png ; $V ( \infty ) = \{ z \in \overline { C } : | z | > R \}$ ; confidence 0.989
  
232. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015560/b01556096.png ; $F , G$ ; confidence 0.995
+
232. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t130130124.png ; $\Gamma = \operatorname { End } _ { \Lambda } T$ ; confidence 0.895
  
233. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524060.png ; $\{ \alpha t + \beta \}$ ; confidence 0.995
+
233. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013057.png ; $\operatorname { Ext } _ { \Lambda } ^ { 1 } ( T , )$ ; confidence 0.425
  
234. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590282.png ; $f ( z ) = z _ { 1 } / z _ { 2 }$ ; confidence 0.995
+
234. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097710/w09771046.png ; $X ( T _ { 0 } ) _ { Q } = X ( T _ { 0 } ) \bigotimes _ { Z } Q$ ; confidence 0.369
  
235. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097710/w09771076.png ; $W = N / T$ ; confidence 0.995
+
235. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145025.png ; $D = \sum _ { X \in X } n _ { X } x , \quad n _ { X } \in Z$ ; confidence 0.583
  
236. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012460/a012460117.png ; $\lambda _ { 1 } , \lambda _ { 2 }$ ; confidence 0.995
+
236. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164060.png ; $\dot { i } = \operatorname { dim } | K _ { V } - D |$ ; confidence 0.160
  
237. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640157.png ; $p _ { 2 } > 1$ ; confidence 0.995
+
237. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031640/d0316407.png ; $F _ { M } ( \omega m ) = \omega ^ { ( p ) } F _ { M } ( m )$ ; confidence 0.963
  
238. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011520/a01152034.png ; $\tau : G \times V \rightarrow V$ ; confidence 0.995
+
238. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031640/d0316408.png ; $\omega V _ { M } ( m ) = V _ { M } ( \omega ^ { ( p ) } m )$ ; confidence 0.979
  
239. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058480/l05848075.png ; $L ( H )$ ; confidence 0.995
+
239. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830279.png ; $u \leq v \Rightarrow \theta u \leq \theta v$ ; confidence 0.592
  
240. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559028.png ; $L _ { 2 } : z = \phi _ { 2 } ( t )$ ; confidence 0.995
+
240. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820154.png ; $\alpha _ { \gamma } : \hat { W } \rightarrow F$ ; confidence 0.358
  
241. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092900/t0929001.png ; $( \Delta , A )$ ; confidence 0.995
+
241. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797028.png ; $\delta ( x ) = x \bigotimes 1 + 1 \bigotimes x$ ; confidence 0.262
  
242. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145093.png ; $l ( D ) = \operatorname { deg } ( D ) - g + 1$ ; confidence 0.995
+
242. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427039.png ; $S = \operatorname { diag } \{ Q , \ldots , Q \}$ ; confidence 0.623
  
243. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m064510130.png ; $g \geq 24$ ; confidence 0.995
+
243. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510204.png ; $\mathfrak { g } 0 = \mathfrak { s o } ( p , 2 n - p )$ ; confidence 0.141
  
244. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120460.png ; $A \subset F ^ { \prime }$ ; confidence 0.995
+
244. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851048.png ; $Y _ { \alpha } \in \mathfrak { g } _ { - \alpha }$ ; confidence 0.963
  
245. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070091.png ; $D ( S )$ ; confidence 0.995
+
245. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859083.png ; $\operatorname { exp } : L ( G ) \rightarrow G$ ; confidence 0.986
  
246. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087080/s08708085.png ; $I ( T , \aleph _ { \alpha } )$ ; confidence 0.995
+
246. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861038.png ; $\mathfrak { g } C = \mathfrak { g } \otimes R C$ ; confidence 0.493
  
247. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590493.png ; $X , Y : G \rightarrow R$ ; confidence 0.995
+
247. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868035.png ; $\Gamma _ { 0 } \subset M \subset \Gamma _ { 1 }$ ; confidence 0.997
  
248. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590632.png ; $( F _ { y } ^ { \prime } ) _ { 0 } = 0$ ; confidence 0.995
+
248. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868027.png ; $\Gamma _ { 0 } = \Gamma _ { 0 } ( \mathfrak { g } )$ ; confidence 0.946
  
249. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058480/l05848067.png ; $[ X , Y ] = X Y - Y X$ ; confidence 0.995
+
249. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l0587209.png ; $( \lambda x ) ^ { [ p ] } = \lambda ^ { p } x ^ { [ p ] }$ ; confidence 0.579
  
250. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868040.png ; $\Gamma _ { 1 } / \Gamma ( G )$ ; confidence 0.995
+
250. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872084.png ; $x ^ { [ p ^ { m } ] } = ( x ^ { [ p ^ { m - 1 } ] } ) ^ { [ p ] } = 0$ ; confidence 0.790
  
251. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700264.png ; $\phi _ { i } \in A ( V )$ ; confidence 0.995
+
251. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059250/l05925070.png ; $\Gamma \subset \operatorname { GL } ( n , F )$ ; confidence 0.801
  
252. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559031.png ; $\phi _ { 2 } ( 0 ) = \zeta$ ; confidence 0.994
+
252. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074640/p07464011.png ; $\phi : U \times G \rightarrow \pi ^ { - 1 } ( U )$ ; confidence 0.998
  
253. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559011.png ; $L : [ 0,1 ] \rightarrow \overline { C }$ ; confidence 0.994
+
253. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150023.png ; $x = \lambda ( \theta ) , y = \Delta ( \theta )$ ; confidence 0.878
  
254. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120243.png ; $H ^ { p } ( Y , F )$ ; confidence 0.994
+
254. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150024.png ; $y ^ { 2 } = ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } )$ ; confidence 0.996
  
255. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120060/b1200602.png ; $\epsilon = 1$ ; confidence 0.994
+
255. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a014170123.png ; $( x , v ) \gamma = ( x \gamma , j ( x , \gamma ) v )$ ; confidence 0.955
  
256. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025020/c02502011.png ; $f : X \rightarrow \overline { R }$ ; confidence 0.994
+
256. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031640/d0316409.png ; $F _ { M } ( V _ { M } ( m ) ) = V _ { M } ( F _ { M } ( m ) ) = p m$ ; confidence 0.976
  
257. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b130200142.png ; $i \neq 0$ ; confidence 0.994
+
257. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830302.png ; $R \{ y _ { 1 } , \ldots , y _ { N } \} \backslash R$ ; confidence 0.377
  
258. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011970/a0119703.png ; $\phi ( x )$ ; confidence 0.994
+
258. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830269.png ; $\operatorname { ord } ( \theta ) = \sum e$ ; confidence 0.833
  
259. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150018.png ; $\Delta ( \theta ) = \sqrt { ( 1 - c ^ { 2 } \lambda ^ { 2 } ) ( 1 - e ^ { 2 } \lambda ^ { 2 } ) }$ ; confidence 0.994
+
259. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830144.png ; $B ( \zeta _ { 1 } , \ldots , \zeta _ { n } ) \neq 0$ ; confidence 0.692
  
260. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017330/b01733083.png ; $f _ { 2 } ( z )$ ; confidence 0.994
+
260. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183081.png ; $\Phi \subset F \{ Y _ { 1 } , \ldots , Y _ { N } \}$ ; confidence 0.521
  
261. https://www.encyclopediaofmath.org/legacyimages/i/i053/i053060/i0530605.png ; $K , A , N$ ; confidence 0.994
+
261. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830175.png ; $\Sigma _ { 1 } , \ldots , \sum _ { p } , \ldots ,$ ; confidence 0.261
  
262. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025930/c02593073.png ; $\phi ( G )$ ; confidence 0.994
+
262. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830346.png ; $( A _ { k } ) < \operatorname { rank } ( B _ { k } )$ ; confidence 0.997
  
263. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120180/d12018083.png ; $A ( G )$ ; confidence 0.994
+
263. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120117.png ; $H _ { r } ( M ^ { n } , X ) \sim H ^ { n - r } ( M ^ { n } , X )$ ; confidence 0.868
  
264. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764012.png ; $\sum _ { i = 1 } ^ { n } k _ { i } ^ { - 1 } > 1$ ; confidence 0.994
+
264. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040370/f04037020.png ; $q + 1 \leq k \leq \operatorname { prof } F - p$ ; confidence 0.862
  
265. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696035.png ; $( \alpha _ { i } ) _ { i \in I }$ ; confidence 0.994
+
265. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040370/f04037017.png ; $p \leq k \leq \operatorname { prof } F - q - 1$ ; confidence 0.925
  
266. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110070/k11007015.png ; $L _ { \chi } ( U ) =$ ; confidence 0.994
+
266. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002049.png ; $e ^ { \beta _ { 1 } } , \ldots , e ^ { \beta _ { n } }$ ; confidence 0.462
  
267. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559062.png ; $L : z = \phi ( t )$ ; confidence 0.994
+
267. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002011.png ; $e ^ { z _ { 1 } + z _ { 2 } } = e ^ { z _ { 1 } } e ^ { z _ { 2 } }$ ; confidence 0.757
  
268. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559053.png ; $z = \phi _ { 2 } ( \tau ^ { \prime \prime } )$ ; confidence 0.994
+
268. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h04769025.png ; $g ( \alpha H ) = ( g a ) H , \quad g , \alpha \in G$ ; confidence 0.214
  
269. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310139.png ; $R T _ { 1 } T _ { 2 } = T _ { 2 } T _ { 1 } R$ ; confidence 0.994
+
269. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k1200308.png ; $\operatorname { Ric } ( \omega ) = - \omega$ ; confidence 0.994
  
270. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055570/k05557085.png ; $D ( k )$ ; confidence 0.994
+
270. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851049.png ; $[ X _ { \alpha } , Y _ { \alpha } ] = H _ { \alpha }$ ; confidence 0.998
  
271. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046550/h04655016.png ; $\{ U _ { i } \} _ { i \in I }$ ; confidence 0.994
+
271. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859094.png ; $d f _ { e } : L ( G _ { 1 } ) \rightarrow L ( G _ { 2 } )$ ; confidence 0.485
  
272. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861031.png ; $Z \times T$ ; confidence 0.994
+
272. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064510/m06451064.png ; $R ^ { 1 } f \times ( Z / n Z ) \cong ( Z / n Z ) ^ { 2 g }$ ; confidence 0.221
  
273. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472076.png ; $\gamma \in G$ ; confidence 0.994
+
273. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690021.png ; $Z ^ { 1 } = \delta ^ { - 1 } ( e ) \subseteq C ^ { 1 }$ ; confidence 0.984
  
274. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012058.png ; $( x , y )$ ; confidence 0.994
+
274. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472075.png ; $( x y ) ^ { \gamma } = x ^ { \gamma } y ^ { \gamma }$ ; confidence 0.987
  
275. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120234.png ; $\alpha : H ^ { p } ( X , F ) \rightarrow H ^ { p } ( Y , F )$ ; confidence 0.994
+
275. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r08103076.png ; $\Gamma = \operatorname { Gal } ( k _ { s } / k )$ ; confidence 0.608
  
276. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797046.png ; $U ( P _ { A } )$ ; confidence 0.994
+
276. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s1300409.png ; $H ^ { * } = H \cup P ^ { 1 } ( Q ) \subset P ^ { 1 } ( C )$ ; confidence 0.959
  
277. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k1200308.png ; $\operatorname { Ric } ( \omega ) = - \omega$ ; confidence 0.994
+
277. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559048.png ; $z ^ { \prime } = \phi _ { 1 } ( \tau ^ { \prime } )$ ; confidence 0.998
  
278. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631019.png ; $( A , \Delta , \epsilon , S )$ ; confidence 0.994
+
278. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085900/s08590024.png ; $\| \partial F _ { i } / \partial X _ { j } ( x ) \|$ ; confidence 0.994
  
279. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014030.png ; $\phi _ { \beta } : X _ { i } \rightarrow X _ { j }$ ; confidence 0.994
+
279. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087060/s08706034.png ; $\psi _ { t _ { 1 } , \ldots , t _ { x } } ^ { \prime }$ ; confidence 0.085
  
280. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410106.png ; $N _ { K / k } ( \beta )$ ; confidence 0.994
+
280. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140155.png ; $( \operatorname { prin } K I ) \simeq Z ^ { I }$ ; confidence 0.538
  
281. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410131.png ; $F = F ( x , y , \dot { x } , \dot { y } )$ ; confidence 0.994
+
281. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014030.png ; $\phi _ { \beta } : X _ { i } \rightarrow X _ { j }$ ; confidence 0.994
  
282. https://www.encyclopediaofmath.org/legacyimages/g/g110/g110110/g1101103.png ; $\mathfrak { g } = \mathfrak { k } + \mathfrak { p }$ ; confidence 0.994
+
282. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450108.png ; $G _ { n } ^ { \gamma } \geq r ( n - r + 1 ) - ( r - 1 ) g$ ; confidence 0.820
  
283. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110120/l11012076.png ; $i \geq 2$ ; confidence 0.994
+
283. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145032.png ; $\operatorname { deg } D = \sum _ { X } n _ { X }$ ; confidence 0.244
  
284. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640106.png ; $p _ { 12 } = 1$ ; confidence 0.994
+
284. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150036.png ; $\theta ( v ) = \sum _ { m } e ^ { F ( m ) + 2 ( m , v ) }$ ; confidence 0.669
  
285. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590192.png ; $f ^ { - 1 } ( u ) f ^ { - 1 } ( v ) = f ^ { - 1 } ( u v )$ ; confidence 0.994
+
285. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150049.png ; $1 , \ldots , a _ { p } , b _ { 1 } , \ldots , b _ { p }$ ; confidence 0.487
  
286. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c02057061.png ; $\overline { \partial } g = 0$ ; confidence 0.994
+
286. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150031.png ; $l ( D ) \geq \operatorname { deg } ( D ) - p + 1$ ; confidence 0.998
  
287. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085900/s08590024.png ; $\| \partial F _ { i } / \partial X _ { j } ( x ) \|$ ; confidence 0.994
+
287. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011740/a01174038.png ; $\alpha , b , c \in k , \alpha \neq 0 , c \neq 0$ ; confidence 0.727
  
288. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r08103035.png ; $W _ { k } ( S _ { i } , G )$ ; confidence 0.993
+
288. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c02057057.png ; $H ^ { p } ( X , S ) = 0 \quad \text { for } p \geq 1$ ; confidence 0.958
  
289. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032890/d03289090.png ; $\Lambda ( n )$ ; confidence 0.993
+
289. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183021.png ; $\tau = \operatorname { deg } \omega _ { V }$ ; confidence 0.992
  
290. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060124.png ; $F$ ; confidence 0.993
+
290. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120547.png ; $F : X \times U \rightarrow \overline { R }$ ; confidence 0.962
  
291. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145091.png ; $l ( K - D ) = 0$ ; confidence 0.993
+
291. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120481.png ; $\operatorname { sup } _ { A } f = f ( \alpha )$ ; confidence 0.497
  
292. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120277.png ; $O ^ { F }$ ; confidence 0.993
+
292. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120446.png ; $( F ^ { \prime } , \sigma ( F ^ { \prime } , F ) )$ ; confidence 0.999
  
293. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183090.png ; $p = p _ { F } ( B )$ ; confidence 0.993
+
293. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960138.png ; $\delta _ { i } \alpha = \alpha _ { i } \alpha$ ; confidence 0.442
  
294. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120192.png ; $H ^ { p } ( X , O _ { X } ( D ) )$ ; confidence 0.993
+
294. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j0542705.png ; $\alpha \circ b = \frac { a b + b \alpha } { 2 }$ ; confidence 0.581
  
295. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830255.png ; $\partial _ { i } : R \rightarrow R$ ; confidence 0.993
+
295. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054340/j05434037.png ; $\operatorname { rk } ( A - \lambda E ) ^ { 0 }$ ; confidence 0.967
  
296. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h047690122.png ; $n = 4 k - 1$ ; confidence 0.993
+
296. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120030/k12003029.png ; $\operatorname { Ric } ( \omega ) = \omega$ ; confidence 0.996
  
297. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058660/l05866035.png ; $G$ ; confidence 0.993
+
297. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b12040052.png ; $\mathfrak { h } \subset \mathfrak { g }$ ; confidence 0.959
  
298. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023050/c02305015.png ; $( n - p - 1 )$ ; confidence 0.993
+
298. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690084.png ; $\alpha \in R _ { \overline { \zeta } } ^ { 1 }$ ; confidence 0.161
  
299. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559026.png ; $0 < \tau _ { 1 } \leq 1$ ; confidence 0.993
+
299. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472084.png ; $( \gamma x ) ^ { g } = ( \gamma ^ { g } ) ( x ^ { g } )$ ; confidence 0.958
  
300. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090399.png ; $L ( \mu )$ ; confidence 0.993
+
300. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310112.png ; $( \Delta \otimes id ) ( R ) = R ^ { 13 } R ^ { 23 }$ ; confidence 0.501

Latest revision as of 16:00, 26 October 2019

List

1. d031830326.png ; $\Sigma \subset R \{ y _ { 1 } , \ldots , y _ { n } \} \backslash R$ ; confidence 0.488

2. d034120160.png ; $H ^ { \gamma } ( A , X ) \sim H ^ { \gamma + 1 } ( R \backslash A , X )$ ; confidence 0.364

3. d034120292.png ; $\exists n _ { 0 } : n \geq n _ { 0 } \Rightarrow G _ { n } \subset G$ ; confidence 0.126

4. h04797031.png ; $y ] = x y - ( - 1 ) ^ { p q } y x , \quad x \in A _ { p } , \quad y \in A _ { y }$ ; confidence 0.507

5. l058510213.png ; $( ad X _ { \alpha _ { i } } ) ^ { 1 - n ( i , j ) } ( X _ { \alpha _ { j } } ) = 0$ ; confidence 0.432

6. l05868083.png ; $\mathfrak { g } 0 = \mathfrak { k } _ { 0 } + \mathfrak { p } _ { 0 }$ ; confidence 0.090

7. n06690080.png ; $\delta \alpha = d \alpha - \frac { 1 } { 2 } [ \alpha , \alpha ]$ ; confidence 0.991

8. q076310114.png ; $\Delta ^ { \prime } ( \alpha ) = R . \Delta ( \alpha ) . R ^ { - 1 }$ ; confidence 0.304

9. q076310141.png ; $T _ { 2 } = 1 \otimes T \in \text { End } ( k ^ { n } \otimes k ^ { n } )$ ; confidence 0.318

10. s085590128.png ; $\overline { U } ( 0,1 ) = \{ z \in \overline { C } : | z | \leq 1 \}$ ; confidence 0.957

11. t13013040.png ; $\Gamma = \operatorname { End } _ { \Lambda } ( T ) ^ { \circ p }$ ; confidence 0.240

12. t13014049.png ; $\operatorname { dim } : K _ { 0 } ( Q ) \rightarrow Z ^ { Q _ { 0 } }$ ; confidence 0.783

13. t130140117.png ; $\chi _ { R } : K _ { 0 } ( \operatorname { mod } R ) \rightarrow Z$ ; confidence 0.847

14. u0952408.png ; $\phi ( t ) = \frac { 1 } { i t ( b - \alpha ) } ( e ^ { i t b } - e ^ { i t x } )$ ; confidence 0.594

15. d03070037.png ; $\pi ^ { \prime } : X ^ { \prime } \rightarrow S ^ { \prime }$ ; confidence 0.952

16. d03164012.png ; $\omega ^ { ( p ) } = ( a _ { 0 } ^ { p } , \dots , a _ { n } ^ { p } , \dots )$ ; confidence 0.284

17. h047690121.png ; $\operatorname { Sp } ( k ) \times \operatorname { Sp } ( 1 )$ ; confidence 0.853

18. h04797082.png ; $\pi ( G , K ) = \sum _ { i = 0 } ^ { \infty } \pi _ { i } ( G ) \otimes K$ ; confidence 0.998

19. l05852012.png ; $\mathfrak { g } _ { i } / \mathfrak { g } _ { \mathfrak { l } } + 1$ ; confidence 0.230

20. l058590118.png ; $g \rightarrow A d ( g ) = d _ { e } ( \operatorname { ln } t ( g ) )$ ; confidence 0.610

21. l05868084.png ; $\mathfrak { g } \subset \mathfrak { g } ^ { \mathfrak { C } }$ ; confidence 0.496

22. n06690054.png ; $C ^ { k } = \operatorname { Map } ( G ^ { k } , A ) , \quad k = 0,1,2$ ; confidence 0.893

23. p07464035.png ; $\alpha : H ^ { 1 } ( B , O ^ { G } ) \rightarrow H ^ { 1 } ( B , C ^ { G } )$ ; confidence 0.999

24. s08559054.png ; $\tau _ { 2 } - \epsilon < \tau ^ { \prime \prime } < \tau _ { 2 }$ ; confidence 0.940

25. s085590464.png ; $F ( x , y , \lambda ) = x \Phi _ { \mu - 2 } ( x , \lambda ) - x y ^ { 2 }$ ; confidence 0.854

26. u09540044.png ; $n ^ { 2 } - \sum _ { i j } \operatorname { min } ( m _ { i } , m _ { j } )$ ; confidence 0.738

27. a0115005.png ; $\frac { d x } { \sqrt { f ( x ) } } = \frac { d y } { \sqrt { f ( y ) } }$ ; confidence 0.999

28. a011640153.png ; $\operatorname { tim } \operatorname { Aut } ^ { 0 } ( V ) > 0$ ; confidence 0.287

29. c02057038.png ; $O ^ { p } \rightarrow O ^ { q } \rightarrow S \rightarrow 0$ ; confidence 0.899

30. d034120203.png ; $\operatorname { Ext } _ { \Psi } ^ { n - p + 1 } ( X ; F , \Omega )$ ; confidence 0.408

31. d034120246.png ; $A ( z ) = \sum _ { x = 0 } ^ { \infty } \frac { a _ { x } } { n ! } z ^ { N }$ ; confidence 0.156

32. f040820200.png ; $f ( X ) = X + \alpha _ { 2 } X ^ { 2 } + \alpha _ { 3 } X ^ { 3 } + \ldots$ ; confidence 0.751

33. f040820161.png ; $f _ { \pi } ( X ) = X + \pi ^ { - 1 } X ^ { q } + \pi ^ { - 2 } X ^ { q ^ { 2 } } +$ ; confidence 0.673

34. g13002046.png ; $Q ( \alpha ^ { \beta } , \ldots , \alpha ^ { \beta ^ { d - 1 } } )$ ; confidence 0.372

35. l05848015.png ; $[ D _ { 1 } , D _ { 2 } ] = D _ { 1 } \circ D _ { 2 } - D _ { 2 } \circ D _ { 1 }$ ; confidence 0.999

36. l05861016.png ; $T ^ { \prime \prime } = T ^ { 1 } \times \ldots \times T ^ { 1 }$ ; confidence 0.167

37. l058680100.png ; $u = \mathfrak { l } + \dot { \mathfrak { i } } \mathfrak { u }$ ; confidence 0.153

38. p07464012.png ; $\phi ( x , g h ) = \phi ( x , g ) h , \quad x \in U , \quad g , h \in G$ ; confidence 0.910

39. s08590021.png ; $F _ { i } ( X _ { 1 } , \ldots , X _ { m } ) = 0 , \quad i = 1 , \ldots , n$ ; confidence 0.562

40. s08706043.png ; $K _ { 1 } ( R ) = \operatorname { lim } GL _ { n } ( R ) / E _ { n } ( R )$ ; confidence 0.598

41. w098100169.png ; $X ^ { n } + Y ^ { n } = \sum _ { \vec { d } | n } d r _ { d } ( X , Y ) ^ { n / d }$ ; confidence 0.367

42. d030700272.png ; $a \circ b = \Phi ^ { - 1 } ( \Phi ( \alpha ) \times \Phi ( b ) )$ ; confidence 0.109

43. d030700206.png ; $\operatorname { dim } _ { k } H ^ { 2 } ( X _ { 0 } , O _ { X _ { 0 } } )$ ; confidence 0.730

44. d031830267.png ; $\theta = \Pi _ { i } \partial _ { i } ^ { e _ { i } ^ { e _ { i } } }$ ; confidence 0.142

45. d031830165.png ; $( t _ { 1 } , \ldots , t _ { n } ) \rightarrow F ( 0 , \ldots , 0 )$ ; confidence 0.263

46. d034120255.png ; $h ( \phi ) = k ( - \phi ) , \quad \sigma \leq \phi \leq 2 \pi$ ; confidence 0.997

47. e03696057.png ; $F _ { 0 } [ ( y _ { j } \theta ) _ { j \in J , \theta \in \Theta } ]$ ; confidence 0.526

48. f04082049.png ; $F _ { 1 } ( X _ { 1 } , \ldots , X _ { x } , Y _ { 1 } , \ldots , Y _ { n } )$ ; confidence 0.336

49. f04082050.png ; $F _ { n } ( X _ { 1 } , \ldots , X _ { n } , Y _ { 1 } , \ldots , Y _ { n } )$ ; confidence 0.552

50. h04797021.png ; $\delta ^ { * } : A ^ { * } \otimes A ^ { * } \rightarrow A ^ { * }$ ; confidence 0.724

51. l05847062.png ; $\rho : \mathfrak { g } \rightarrow \mathfrak { g } [ ( V )$ ; confidence 0.317

52. l05872010.png ; $( x + y ) ^ { [ p ] } = x ^ { [ p ] } + y ^ { [ p ] } + \Lambda _ { p } ( x , y )$ ; confidence 0.977

53. l05872068.png ; $\{ \mathfrak { e } _ { 1 } , \mathfrak { e } _ { 2 } , \ldots \}$ ; confidence 0.391

54. l05925025.png ; $\{ 0 \} \subset V _ { 1 } \subset \ldots \subset V _ { m } = V$ ; confidence 0.850

55. n06690032.png ; $\alpha \in C ^ { 0 } , \quad b \in C ^ { 1 } , \quad c \in C ^ { 2 }$ ; confidence 0.207

56. n06690012.png ; $C ^ { * } = ( C ^ { 0 } , C ^ { 1 } , C ^ { 2 } , \rho , \sigma , \delta )$ ; confidence 0.367

57. n06690057.png ; $\delta ( b ) ( g , h ) = b ( g ) ^ { - 1 } b ( g h ) ( b ( h ) ^ { g } ) ^ { - 1 }$ ; confidence 0.990

58. q07631097.png ; $\Delta ( \alpha ) = \alpha \otimes 1 + 1 \otimes \alpha$ ; confidence 0.891

59. s13004030.png ; $X _ { g } = \operatorname { Sp } ( 2 g , Z ) \backslash H _ { g }$ ; confidence 0.844

60. s085590461.png ; $F ( x , y , \lambda ) = \Phi _ { \mu + 1 } ( x , \lambda ) - y ^ { 2 }$ ; confidence 0.999

61. t13013089.png ; $( T , X ) = 0 = \operatorname { Ext } _ { \gamma } ^ { 1 } ( T , X )$ ; confidence 0.465

62. d030700139.png ; $\kappa ^ { \prime } \cong \kappa \otimes O \Lambda$ ; confidence 0.541

63. d034120505.png ; $\{ F _ { \alpha } , G _ { \alpha } , ( \ldots ) _ { \alpha } \}$ ; confidence 0.433

64. f04082041.png ; $D ^ { X } : B \rightarrow \operatorname { nil } ( B ) ^ { n }$ ; confidence 0.143

65. f040820128.png ; $\gamma ( T ) + F \delta ( T ) = F ( \gamma ( T ) , \delta ( T ) )$ ; confidence 0.948

66. h04797023.png ; $\mu ^ { * } : A ^ { * } \rightarrow A ^ { * } \otimes A ^ { * }$ ; confidence 0.991

67. l0585009.png ; $\mathfrak { g } = \sum _ { i = 1 } ^ { k } \mathfrak { g } _ { i }$ ; confidence 0.468

68. l05851094.png ; $\mathfrak { h } _ { 1 } \rightarrow \mathfrak { h } _ { 2 }$ ; confidence 0.774

69. l05852014.png ; $\{ \mathfrak { s } _ { 1 } ^ { \prime } \} _ { 0 } \leq i \leq m$ ; confidence 0.121

70. l05868024.png ; $\operatorname { exp } : \mathfrak { h } \rightarrow G$ ; confidence 0.936

71. l05868086.png ; $Z _ { g } \cong \Gamma _ { 1 } ( f _ { 0 } ) / \Gamma _ { 0 } [ e , t ]$ ; confidence 0.072

72. l05868033.png ; $\Gamma _ { 0 } \subset \Gamma ( G ) \subset \Gamma _ { 1 }$ ; confidence 0.991

73. l0584006.png ; $\operatorname { exp } : \mathfrak { g } \rightarrow G$ ; confidence 0.996

74. l05876046.png ; $[ X _ { i } , X _ { j } ] = \sum _ { k = 1 } ^ { r } c _ { i j } ^ { k } X _ { k }$ ; confidence 0.608

75. n06690055.png ; $( \rho ( \alpha ) ( b ) ) ( g ) = \alpha b ( g ) ( a ^ { g } ) ^ { - 1 }$ ; confidence 0.492

76. p07267050.png ; $f ^ { \prime } ( O _ { X ^ { \prime } } ) = O _ { S ^ { \prime } }$ ; confidence 0.802

77. r081030104.png ; $O _ { \gamma } \subset \Delta \backslash \Delta _ { 0 }$ ; confidence 0.964

78. s13004058.png ; $\overline { D } _ { S } \rightarrow \overline { D } _ { T }$ ; confidence 0.534

79. s0855908.png ; $U ( \zeta , R ) = \{ z \in \overline { C } : | z - \zeta | < R \}$ ; confidence 0.957

80. s085590133.png ; $V ( \alpha ) = \{ z \in \overline { C } : | z - \alpha | < R \}$ ; confidence 0.668

81. s13054034.png ; $w ( \alpha ) = x ( \alpha ) y ( - \alpha ^ { - 1 } ) x ( \alpha )$ ; confidence 0.832

82. t13013037.png ; $X = \{ C : \operatorname { Hom } _ { \Lambda } ( C , Y ) = 0 \}$ ; confidence 0.907

83. t13013088.png ; $\operatorname { Ext } _ { \mathscr { H } } ^ { 1 } ( T , T ) = 0$ ; confidence 0.420

84. t13013030.png ; $F = \{ C : \operatorname { Hom } _ { \Lambda } ( T , C ) = 0 \}$ ; confidence 0.896

85. t13013070.png ; $( T , ) : D ^ { b } ( \Lambda ) \rightarrow D ^ { b } ( \Gamma )$ ; confidence 0.335

86. t13014065.png ; $: G 1 _ { Q } ( d ) \times A _ { Q } ( d ) \rightarrow A _ { Q } ( d )$ ; confidence 0.120

87. u09541032.png ; $\operatorname { exp } : \mathfrak { u } \rightarrow U$ ; confidence 0.973

88. w098100197.png ; $f _ { x } = \sigma ( x ) f , \quad V _ { x } = \sigma ^ { - 1 } ( x ) V$ ; confidence 0.692

89. c02057048.png ; $s = h _ { 1 } ( s _ { 1 } ) _ { x } + \ldots + h _ { N } ( s _ { N } ) _ { x }$ ; confidence 0.366

90. d030700216.png ; $\mathscr { O } _ { S , s _ { 0 } } \simeq \hat { M } _ { X _ { 0 } }$ ; confidence 0.574

91. d034120295.png ; $\| f \| = \operatorname { max } _ { z \in G _ { p } } | f ( z ) |$ ; confidence 0.795

92. d034120224.png ; $\operatorname { Ext } _ { c } ^ { n - p + 1 } ( Y ; F , \Omega )$ ; confidence 0.597

93. e03696033.png ; $( \theta \alpha _ { i } ) _ { i \in I , \theta \in \Theta }$ ; confidence 0.719

94. h047410136.png ; $\dot { x } \square ^ { 2 } + \dot { y } \square ^ { 2 } \neq 0$ ; confidence 0.459

95. l05848032.png ; $\phi _ { e } : A \rightarrow A / \mathfrak { m } _ { \ell }$ ; confidence 0.383

96. n06690079.png ; $\sigma ( f ) ( \beta ) = ( \operatorname { Ad } f ) \beta$ ; confidence 0.579

97. n06690095.png ; $\rightarrow H ^ { 1 } ( G , B ) \rightarrow H ^ { 1 } ( G , A )$ ; confidence 0.984

98. s085590373.png ; $x _ { 0 } ^ { \mu + 1 } + x _ { 1 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$ ; confidence 0.952

99. s085590122.png ; $f _ { 0 } ( z ) = \sum _ { k = 0 } ^ { \infty } b ^ { k } z ^ { d ^ { k } }$ ; confidence 0.687

100. s085590227.png ; $\zeta = ( \zeta _ { 1 } , \ldots , \zeta _ { n } ) \in C ^ { n }$ ; confidence 0.582

101. u09540041.png ; $\sum _ { i = 1 } ^ { j } m _ { i } \geq \sum _ { i = 1 } ^ { j } l _ { i }$ ; confidence 0.947

102. w098100175.png ; $V _ { m } f _ { n } = f _ { n } V _ { m } \quad \text { if } ( n , m ) = 1$ ; confidence 0.135

103. a01145076.png ; $\operatorname { deg } K _ { X } = ( X ) ^ { 2 } + ( X . K _ { F } )$ ; confidence 0.674

104. a01164049.png ; $q ( V ) = \operatorname { dim } _ { k } H ^ { 1 } ( V , O _ { V } )$ ; confidence 0.987

105. d03164011.png ; $\omega = ( a _ { 0 } , \ldots , a _ { n } , \ldots ) \in W ( k )$ ; confidence 0.228

106. e036960185.png ; $( F \langle \alpha \rangle / F ) \rightarrow W _ { K }$ ; confidence 0.521

107. f040820162.png ; $F _ { \pi } ( X , Y ) = f \pi ^ { 1 } ( f \pi ( X ) + f _ { \pi } ( Y ) )$ ; confidence 0.543

108. h047410142.png ; $( x , y ) = \{ ( \xi , \eta ) : F ( x , y , \xi , \eta ) \leq 1 \}$ ; confidence 0.987

109. m06301058.png ; $F ( x _ { 1 } e _ { 1 } + \square _ { \cdots } + x _ { x } e _ { x } )$ ; confidence 0.221

110. q07631043.png ; $\Delta ( x _ { j } ) = \sum _ { k } x _ { i k } \otimes x _ { k j }$ ; confidence 0.404

111. q076310145.png ; $\Delta ( t _ { j } ) = \sum _ { k } t _ { i k } \otimes t _ { k j }$ ; confidence 0.449

112. q07631055.png ; $\{ \alpha , b c \} = \{ \alpha , b \} c + \{ \alpha , c \} b$ ; confidence 0.756

113. s085590139.png ; $V ^ { \prime } ( \infty ) = \{ z \in C : | z - \alpha | > R \}$ ; confidence 0.435

114. s13054036.png ; $\{ \alpha , b \} = h ( a b ) h ( \alpha ) ^ { - 1 } h ( b ) ^ { - 1 }$ ; confidence 0.214

115. t13013050.png ; $( T , ) : \operatorname { mod } \Lambda \rightarrow$ ; confidence 0.816

116. t13014042.png ; $K _ { 0 } ( Q ) = K _ { 0 } ( \operatorname { rep } _ { K } ( Q ) )$ ; confidence 0.940

117. a01174032.png ; $T \mapsto \operatorname { Aut } _ { T } ( X \times T )$ ; confidence 0.864

118. d034120222.png ; $\operatorname { Ext } _ { c } ^ { x - p } ( Y ; F , \Omega )$ ; confidence 0.357

119. f040820155.png ; $\alpha _ { \gamma } ( \gamma _ { 0 } ( T ) ) = \gamma ( T )$ ; confidence 0.883

120. h0474106.png ; $f ( t _ { 1 } , \ldots , t _ { k } , x _ { 1 } , \ldots , x _ { N } )$ ; confidence 0.252

121. h04741068.png ; $\mathfrak { a } \subset k [ X _ { 1 } , \ldots , X _ { n } ]$ ; confidence 0.507

122. h047970135.png ; $f ^ { * } g = m _ { A } \circ ( f \otimes g ) \circ \mu _ { C }$ ; confidence 0.605

123. j05427084.png ; $\mathfrak { g } _ { 1 } = [ \mathfrak { g } _ { 0 } , p ] + k p$ ; confidence 0.395

124. k1200302.png ; $\operatorname { Ric } ( \omega ) = \lambda \omega$ ; confidence 0.996

125. l05851097.png ; $\mathfrak { g } _ { 1 } \rightarrow \mathfrak { g } 2$ ; confidence 0.364

126. l05852042.png ; $\rho ( \mathfrak { g } ) \subset \mathfrak { b } ( F )$ ; confidence 0.547

127. l05872057.png ; $\phi ( x ^ { [ p ] } ) = ( \phi ( x ) ) ^ { [ p ] } , \quad x \in L$ ; confidence 0.926

128. l05876017.png ; $\xi _ { i j } ( x ) = \partial f _ { j } / \partial g ( e , x )$ ; confidence 0.981

129. q076310122.png ; $R ^ { 12 } = \sum _ { i } x _ { i } \otimes y _ { i } \otimes 1$ ; confidence 0.855

130. q076310124.png ; $R ^ { 23 } = \sum _ { i } 1 \otimes x _ { i } \otimes y _ { i }$ ; confidence 0.885

131. q076310123.png ; $R ^ { 13 } = \sum _ { i } x _ { i } \otimes 1 \otimes y _ { i }$ ; confidence 0.882

132. q076310113.png ; $( \text { id } \otimes \Delta ) ( R ) = R ^ { 13 } R ^ { 12 }$ ; confidence 0.878

133. s08559049.png ; $\tau _ { 1 } - \epsilon < \tau ^ { \prime } < \tau _ { 1 }$ ; confidence 0.999

134. t1301303.png ; $p \cdot \operatorname { dim } _ { \Lambda } T \leq 1$ ; confidence 0.223

135. f041060146.png ; $\lambda = ( \lambda _ { 1 } , \ldots , \lambda _ { n } )$ ; confidence 0.574

136. w098100173.png ; $V _ { n } V _ { m } = V _ { n m } , \quad f _ { n } f _ { m } = f _ { n m }$ ; confidence 0.509

137. a011640143.png ; $M ^ { \prime } = \operatorname { dim } S _ { \alpha }$ ; confidence 0.678

138. c02347054.png ; $n _ { \alpha } = \operatorname { dim } R ^ { \alpha }$ ; confidence 0.918

139. d03070033.png ; $X \times S S ^ { \prime } \rightarrow S ^ { \prime }$ ; confidence 0.626

140. h04741062.png ; $F ^ { \gamma } = A _ { 1 } F _ { 1 } + \ldots + A _ { m } F _ { m }$ ; confidence 0.375

141. j05427022.png ; $H ( A , j ) = \{ \alpha \in A : \alpha ^ { j } = \alpha \}$ ; confidence 0.158

142. l05872016.png ; $( \text { ad } x _ { 1 } \ldots \text { ad } x _ { p } - 1 ) x$ ; confidence 0.549

143. n06690018.png ; $H ^ { 0 } ( C ^ { * } ) = \rho ^ { - 1 } ( \text { Aut } C ^ { 1 } )$ ; confidence 0.868

144. n066900126.png ; $H _ { \alpha } ^ { 2 } ( G , A ) = \theta ^ { - 1 } ( \alpha )$ ; confidence 1.000

145. q076310127.png ; $R ^ { 12 } R ^ { 13 } R ^ { 23 } = R ^ { 23 } R ^ { 13 } R ^ { 12 }$ ; confidence 0.998

146. r07764019.png ; $\int _ { U } \omega \wedge \overline { w } < \infty$ ; confidence 0.401

147. s085590101.png ; $\Gamma = \{ z \in \overline { C } : | z - \zeta | = R \}$ ; confidence 0.983

148. a01229020.png ; $O ( n , k ) = \{ g \in GL ( n , k ) : \square ^ { t } g g = 1 \}$ ; confidence 0.472

149. d031830303.png ; $B \in R \{ y _ { 1 } , \ldots , y _ { x } \} \backslash R$ ; confidence 0.458

150. d031830169.png ; $Y _ { n + 1 } G - F \in F \{ Y _ { 1 } , \ldots , Y _ { n + 1 } \}$ ; confidence 0.800

151. d031830142.png ; $B _ { 0 } ( \zeta _ { 1 } , \ldots , \zeta _ { k } ) \neq 0$ ; confidence 0.645

152. d031830253.png ; $R = ( R , \partial _ { 1 } , \ldots , \partial _ { m } )$ ; confidence 0.340

153. d031830314.png ; $A \in R \{ y _ { 1 } , \ldots , y _ { n } \} \backslash R$ ; confidence 0.579

154. d0324909.png ; $G = F \{ \eta _ { 1 } , \ldots , \eta _ { \nwarrow } \}$ ; confidence 0.083

155. d03249037.png ; $\tau = \operatorname { deg } \omega _ { \eta / F }$ ; confidence 0.965

156. d034120179.png ; $s ( \hat { \omega } ) = ( - 1 ) ^ { n } \int _ { X } \omega$ ; confidence 0.188

157. d034120493.png ; $X ^ { * } = ( X ^ { \prime } , \beta ( X ^ { \prime } , X ) )$ ; confidence 0.998

158. d034120377.png ; $\omega ( z ) = 1 / \{ 2 \pi i ( \zeta - z _ { 0 } ) ^ { 2 } \}$ ; confidence 0.963

159. d034120545.png ; $F ( x , y ) \rightarrow \text { inf, } \quad x \in X$ ; confidence 0.965

160. d034120218.png ; $\operatorname { Ext } ^ { \mu - p } ( K ; F , \Omega )$ ; confidence 0.170

161. d034120234.png ; $\alpha : H ^ { p } ( X , F ) \rightarrow H ^ { p } ( Y , F )$ ; confidence 0.994

162. d034120210.png ; $\operatorname { Ext } ^ { \mu - p } ( X ; F , \Omega )$ ; confidence 0.230

163. d034120208.png ; $\operatorname { Ext } _ { c } ^ { n } ( X ; F , \Omega )$ ; confidence 0.851

164. f04082086.png ; $\psi ^ { * } F _ { u } ( X , Y ) = F _ { u } ^ { \prime } ( X , Y )$ ; confidence 0.721

165. f04082051.png ; $F _ { i } ( X , 0 ) = X _ { i } , \quad F _ { i } ( 0 , Y ) = Y _ { i }$ ; confidence 0.975

166. i05235028.png ; $f ( x , y ) = a x ^ { 3 } + 3 b x ^ { 2 } y + 3 c x y ^ { 2 } + d y ^ { 3 }$ ; confidence 0.991

167. i0530609.png ; $\mathfrak { g } = \mathfrak { k } + \mathfrak { P }$ ; confidence 0.998

168. l058510150.png ; $\mathfrak { g } = \mathfrak { g } 0 \otimes _ { k } K$ ; confidence 0.427

169. l058510120.png ; $\operatorname { dim } \mathfrak { g } = n ( 2 n - 1 )$ ; confidence 0.890

170. l058510115.png ; $\operatorname { dim } \mathfrak { g } = n ( 2 n + 1 )$ ; confidence 0.902

171. l05852017.png ; $\mathfrak { g } _ { \mathfrak { i } } ^ { \prime } + 1$ ; confidence 0.346

172. g1101103.png ; $\mathfrak { g } = \mathfrak { k } + \mathfrak { p }$ ; confidence 0.994

173. n06690031.png ; $( \delta b ) _ { i j k } = b _ { j } b _ { j k } b _ { i k } ^ { - 1 }$ ; confidence 0.385

174. n066900115.png ; $( m , \phi ) \sim ( m ^ { \prime } , \phi ^ { \prime } )$ ; confidence 0.996

175. n06690014.png ; $\sigma : C ^ { 0 } \rightarrow \text { Aut } C ^ { 2 }$ ; confidence 0.563

176. r07764096.png ; $\phi : \text { Def } Y \rightarrow \text { Def } X$ ; confidence 0.355

177. s085590463.png ; $f ( x , y ) = x ^ { m - 1 } - x y ^ { 2 } = x ( x ^ { m - 2 } - y ^ { 2 } )$ ; confidence 0.996

178. t130130103.png ; $\operatorname { Ext } _ { \Delta } ^ { i } ( T , T ) = 0$ ; confidence 0.343

179. t1301304.png ; $\operatorname { Ext } _ { \Delta } ^ { 1 } ( T , T ) = 0$ ; confidence 0.420

180. t13014064.png ; $G l _ { Q } ( d ) = \prod _ { j \in Q _ { 0 } } Gl ( v _ { j } , K )$ ; confidence 0.225

181. u09541051.png ; $G _ { \alpha } \times \ldots \times G _ { \alpha }$ ; confidence 0.300

182. u09541040.png ; $U = U _ { 1 } \supset \ldots \supset U _ { s } = \{ e \}$ ; confidence 0.931

183. w120090164.png ; $E ^ { \otimes r } \rightarrow \Delta ( \lambda )$ ; confidence 0.978

184. a01145087.png ; $l ( D ) - l ( K - D ) = \operatorname { deg } ( D ) - g + 1$ ; confidence 0.964

185. a011640127.png ; $M = 10 p _ { t x } - p _ { g } - 2 p ^ { ( 1 ) } + 12 + \theta$ ; confidence 0.369

186. a011640140.png ; $H ^ { 2 } ( V , E _ { \alpha } ) \geq 2 p _ { g } - p _ { x } - 1$ ; confidence 0.616

187. a014170141.png ; $\rho : K \rightarrow \operatorname { GL } ( V )$ ; confidence 0.653

188. a01417058.png ; $C ( f _ { 1 } , \ldots , f _ { n } ) \subset K ( \Gamma )$ ; confidence 0.356

189. d03070032.png ; $f ( \mathfrak { o } ^ { \prime } ) = \mathfrak { o }$ ; confidence 0.466

190. d034120159.png ; $H _ { r } ( A , X ) \sim H _ { r + 1 } ( R \backslash A , X )$ ; confidence 0.499

191. e03696059.png ; $( y _ { j } \theta ) _ { j \in J , \theta \in \Theta }$ ; confidence 0.633

192. f04082095.png ; $\alpha ( F ( X , Y ) ) = G ( \alpha ( X ) , \alpha ( Y ) )$ ; confidence 0.998

193. f040820205.png ; $f ( p ) ( X ) = X + a _ { p } X ^ { p } + a _ { p } 2 X ^ { p ^ { 2 } } +$ ; confidence 0.909

194. f04082048.png ; $X _ { 1 } , \ldots , X _ { X } , Y _ { 1 } , \ldots , Y _ { X }$ ; confidence 0.160

195. l058510105.png ; $\operatorname { dim } \mathfrak { g } = n ( n + 2 )$ ; confidence 0.881

196. l058510186.png ; $\mathfrak { g } 0 = \mathfrak { s o } ( p , 2 n + 1 - p )$ ; confidence 0.237

197. l05868041.png ; $\pi _ { 1 } ( G ) \cong \Gamma ( G ) / \Gamma _ { 0 }$ ; confidence 0.992

198. c023140210.png ; $\rho : G \rightarrow \operatorname { GL } ( V )$ ; confidence 0.678

199. q07631036.png ; $[ x _ { i l } , x _ { k j } ] = ( q ^ { - 1 } - q ) x _ { j } x _ { k l }$ ; confidence 0.406

200. r07763023.png ; $\phi : G \rightarrow \operatorname { GL } ( V )$ ; confidence 0.578

201. r08103092.png ; $( n _ { \alpha } + 1 ) \alpha \notin \Phi _ { k } ( G )$ ; confidence 0.771

202. r081030109.png ; $\alpha \in \Delta ( \gamma ) \cap O _ { \gamma }$ ; confidence 0.992

203. s085590284.png ; $P = \{ z = ( z _ { 1 } , z _ { 2 } ) \in C ^ { 2 } : z _ { 2 } = 0 \}$ ; confidence 0.988

204. s085590308.png ; $f \mathfrak { m } ^ { 2 } = \operatorname { dim } A$ ; confidence 0.253

205. s085590167.png ; $f ( z ) = \frac { 1 } { ( 1 + z ^ { 1 / 2 } ) ( 1 + z ^ { 1 / 6 } ) }$ ; confidence 0.999

206. w120090186.png ; $\operatorname { Ind } _ { \overline { H } } ^ { G }$ ; confidence 0.452

207. w120090116.png ; $\Delta ( \lambda ) = K GL _ { n } ( K ) z _ { \lambda }$ ; confidence 0.499

208. w120090356.png ; $\{ x _ { \alpha } ( t ) : t \in K , \alpha \in \Phi \}$ ; confidence 0.553

209. a01145045.png ; $\pi = \operatorname { dim } H ^ { 1 } ( X , O _ { X } )$ ; confidence 0.980

210. a01153013.png ; $P ( \alpha _ { 1 } , \ldots , \alpha _ { N } ) \neq 0$ ; confidence 0.251

211. d03155058.png ; $\hat { \phi } : \hat { H } \rightarrow \hat { G }$ ; confidence 0.723

212. d03183040.png ; $\Sigma \subset F \{ Y _ { 1 } , \ldots , Y _ { N } \}$ ; confidence 0.440

213. d031830140.png ; $B _ { 0 } ( \eta _ { 1 } , \ldots , \eta _ { k } ) \neq 0$ ; confidence 0.724

214. d034120200.png ; $\operatorname { Ext } _ { \Psi } ^ { n - p } ( X ; F )$ ; confidence 0.835

215. d034120542.png ; $f ( x ) \rightarrow \text { inf, } \quad x \in X$ ; confidence 0.973

216. f04027012.png ; $| G | = p _ { 1 } ^ { n _ { 1 } } \ldots p _ { k } ^ { n _ { k } }$ ; confidence 0.744

217. f04037021.png ; $q + 1 \leq k \leq \operatorname { prof } F - p + 1$ ; confidence 0.687

218. h047410109.png ; $\beta = \alpha \cdot \sigma ( \alpha ) ^ { - 1 }$ ; confidence 0.924

219. j05434031.png ; $+ \operatorname { rk } ( A - \lambda E ) ^ { m + 1 }$ ; confidence 0.935

220. l058510178.png ; $\mathfrak { g } 0 = \mathfrak { s u } ( p , n + 1 - p )$ ; confidence 0.444

221. l05848037.png ; $D \rightarrow \phi _ { \varepsilon } \circ D$ ; confidence 0.258

222. l05872040.png ; $\operatorname { dim } _ { k } U _ { p } ( L ) = p ^ { n }$ ; confidence 0.777

223. l05876013.png ; $g ( x ) = y = ( y _ { 1 } , \ldots , y _ { x } ) \in \Omega$ ; confidence 0.399

224. n06690013.png ; $\rho : C ^ { 0 } \rightarrow \text { Aff } C ^ { 1 }$ ; confidence 0.846

225. o07001089.png ; $\operatorname { Fix } g = \{ x \in X : g ( x ) = x \}$ ; confidence 0.571

226. q07631091.png ; $q = \operatorname { exp } h ( H _ { i } , H _ { j } ) / 2$ ; confidence 0.661

227. r07763080.png ; $\phi _ { 1 } \otimes \ldots \otimes \phi _ { d }$ ; confidence 0.978

228. r077640101.png ; $\phi : \operatorname { Def } Y \rightarrow A$ ; confidence 0.641

229. r07764011.png ; $x _ { 0 } ^ { k _ { 0 } } + \ldots + x _ { x } ^ { k _ { n } } = 0$ ; confidence 0.462

230. s085590409.png ; $\beta _ { v } = ( m _ { v } n ) / ( n _ { 1 } \dots n _ { v } )$ ; confidence 0.618

231. s085590135.png ; $V ( \infty ) = \{ z \in \overline { C } : | z | > R \}$ ; confidence 0.989

232. t130130124.png ; $\Gamma = \operatorname { End } _ { \Lambda } T$ ; confidence 0.895

233. t13013057.png ; $\operatorname { Ext } _ { \Lambda } ^ { 1 } ( T , )$ ; confidence 0.425

234. w09771046.png ; $X ( T _ { 0 } ) _ { Q } = X ( T _ { 0 } ) \bigotimes _ { Z } Q$ ; confidence 0.369

235. a01145025.png ; $D = \sum _ { X \in X } n _ { X } x , \quad n _ { X } \in Z$ ; confidence 0.583

236. a01164060.png ; $\dot { i } = \operatorname { dim } | K _ { V } - D |$ ; confidence 0.160

237. d0316407.png ; $F _ { M } ( \omega m ) = \omega ^ { ( p ) } F _ { M } ( m )$ ; confidence 0.963

238. d0316408.png ; $\omega V _ { M } ( m ) = V _ { M } ( \omega ^ { ( p ) } m )$ ; confidence 0.979

239. d031830279.png ; $u \leq v \Rightarrow \theta u \leq \theta v$ ; confidence 0.592

240. f040820154.png ; $\alpha _ { \gamma } : \hat { W } \rightarrow F$ ; confidence 0.358

241. h04797028.png ; $\delta ( x ) = x \bigotimes 1 + 1 \bigotimes x$ ; confidence 0.262

242. j05427039.png ; $S = \operatorname { diag } \{ Q , \ldots , Q \}$ ; confidence 0.623

243. l058510204.png ; $\mathfrak { g } 0 = \mathfrak { s o } ( p , 2 n - p )$ ; confidence 0.141

244. l05851048.png ; $Y _ { \alpha } \in \mathfrak { g } _ { - \alpha }$ ; confidence 0.963

245. l05859083.png ; $\operatorname { exp } : L ( G ) \rightarrow G$ ; confidence 0.986

246. l05861038.png ; $\mathfrak { g } C = \mathfrak { g } \otimes R C$ ; confidence 0.493

247. l05868035.png ; $\Gamma _ { 0 } \subset M \subset \Gamma _ { 1 }$ ; confidence 0.997

248. l05868027.png ; $\Gamma _ { 0 } = \Gamma _ { 0 } ( \mathfrak { g } )$ ; confidence 0.946

249. l0587209.png ; $( \lambda x ) ^ { [ p ] } = \lambda ^ { p } x ^ { [ p ] }$ ; confidence 0.579

250. l05872084.png ; $x ^ { [ p ^ { m } ] } = ( x ^ { [ p ^ { m - 1 } ] } ) ^ { [ p ] } = 0$ ; confidence 0.790

251. l05925070.png ; $\Gamma \subset \operatorname { GL } ( n , F )$ ; confidence 0.801

252. p07464011.png ; $\phi : U \times G \rightarrow \pi ^ { - 1 } ( U )$ ; confidence 0.998

253. a01150023.png ; $x = \lambda ( \theta ) , y = \Delta ( \theta )$ ; confidence 0.878

254. a01150024.png ; $y ^ { 2 } = ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } )$ ; confidence 0.996

255. a014170123.png ; $( x , v ) \gamma = ( x \gamma , j ( x , \gamma ) v )$ ; confidence 0.955

256. d0316409.png ; $F _ { M } ( V _ { M } ( m ) ) = V _ { M } ( F _ { M } ( m ) ) = p m$ ; confidence 0.976

257. d031830302.png ; $R \{ y _ { 1 } , \ldots , y _ { N } \} \backslash R$ ; confidence 0.377

258. d031830269.png ; $\operatorname { ord } ( \theta ) = \sum e$ ; confidence 0.833

259. d031830144.png ; $B ( \zeta _ { 1 } , \ldots , \zeta _ { n } ) \neq 0$ ; confidence 0.692

260. d03183081.png ; $\Phi \subset F \{ Y _ { 1 } , \ldots , Y _ { N } \}$ ; confidence 0.521

261. d031830175.png ; $\Sigma _ { 1 } , \ldots , \sum _ { p } , \ldots ,$ ; confidence 0.261

262. d031830346.png ; $( A _ { k } ) < \operatorname { rank } ( B _ { k } )$ ; confidence 0.997

263. d034120117.png ; $H _ { r } ( M ^ { n } , X ) \sim H ^ { n - r } ( M ^ { n } , X )$ ; confidence 0.868

264. f04037020.png ; $q + 1 \leq k \leq \operatorname { prof } F - p$ ; confidence 0.862

265. f04037017.png ; $p \leq k \leq \operatorname { prof } F - q - 1$ ; confidence 0.925

266. g13002049.png ; $e ^ { \beta _ { 1 } } , \ldots , e ^ { \beta _ { n } }$ ; confidence 0.462

267. g13002011.png ; $e ^ { z _ { 1 } + z _ { 2 } } = e ^ { z _ { 1 } } e ^ { z _ { 2 } }$ ; confidence 0.757

268. h04769025.png ; $g ( \alpha H ) = ( g a ) H , \quad g , \alpha \in G$ ; confidence 0.214

269. k1200308.png ; $\operatorname { Ric } ( \omega ) = - \omega$ ; confidence 0.994

270. l05851049.png ; $[ X _ { \alpha } , Y _ { \alpha } ] = H _ { \alpha }$ ; confidence 0.998

271. l05859094.png ; $d f _ { e } : L ( G _ { 1 } ) \rightarrow L ( G _ { 2 } )$ ; confidence 0.485

272. m06451064.png ; $R ^ { 1 } f \times ( Z / n Z ) \cong ( Z / n Z ) ^ { 2 g }$ ; confidence 0.221

273. n06690021.png ; $Z ^ { 1 } = \delta ^ { - 1 } ( e ) \subseteq C ^ { 1 }$ ; confidence 0.984

274. p07472075.png ; $( x y ) ^ { \gamma } = x ^ { \gamma } y ^ { \gamma }$ ; confidence 0.987

275. r08103076.png ; $\Gamma = \operatorname { Gal } ( k _ { s } / k )$ ; confidence 0.608

276. s1300409.png ; $H ^ { * } = H \cup P ^ { 1 } ( Q ) \subset P ^ { 1 } ( C )$ ; confidence 0.959

277. s08559048.png ; $z ^ { \prime } = \phi _ { 1 } ( \tau ^ { \prime } )$ ; confidence 0.998

278. s08590024.png ; $\| \partial F _ { i } / \partial X _ { j } ( x ) \|$ ; confidence 0.994

279. s08706034.png ; $\psi _ { t _ { 1 } , \ldots , t _ { x } } ^ { \prime }$ ; confidence 0.085

280. t130140155.png ; $( \operatorname { prin } K I ) \simeq Z ^ { I }$ ; confidence 0.538

281. t13014030.png ; $\phi _ { \beta } : X _ { i } \rightarrow X _ { j }$ ; confidence 0.994

282. a011450108.png ; $G _ { n } ^ { \gamma } \geq r ( n - r + 1 ) - ( r - 1 ) g$ ; confidence 0.820

283. a01145032.png ; $\operatorname { deg } D = \sum _ { X } n _ { X }$ ; confidence 0.244

284. a01150036.png ; $\theta ( v ) = \sum _ { m } e ^ { F ( m ) + 2 ( m , v ) }$ ; confidence 0.669

285. a01150049.png ; $1 , \ldots , a _ { p } , b _ { 1 } , \ldots , b _ { p }$ ; confidence 0.487

286. a01150031.png ; $l ( D ) \geq \operatorname { deg } ( D ) - p + 1$ ; confidence 0.998

287. a01174038.png ; $\alpha , b , c \in k , \alpha \neq 0 , c \neq 0$ ; confidence 0.727

288. c02057057.png ; $H ^ { p } ( X , S ) = 0 \quad \text { for } p \geq 1$ ; confidence 0.958

289. d03183021.png ; $\tau = \operatorname { deg } \omega _ { V }$ ; confidence 0.992

290. d034120547.png ; $F : X \times U \rightarrow \overline { R }$ ; confidence 0.962

291. d034120481.png ; $\operatorname { sup } _ { A } f = f ( \alpha )$ ; confidence 0.497

292. d034120446.png ; $( F ^ { \prime } , \sigma ( F ^ { \prime } , F ) )$ ; confidence 0.999

293. e036960138.png ; $\delta _ { i } \alpha = \alpha _ { i } \alpha$ ; confidence 0.442

294. j0542705.png ; $\alpha \circ b = \frac { a b + b \alpha } { 2 }$ ; confidence 0.581

295. j05434037.png ; $\operatorname { rk } ( A - \lambda E ) ^ { 0 }$ ; confidence 0.967

296. k12003029.png ; $\operatorname { Ric } ( \omega ) = \omega$ ; confidence 0.996

297. b12040052.png ; $\mathfrak { h } \subset \mathfrak { g }$ ; confidence 0.959

298. n06690084.png ; $\alpha \in R _ { \overline { \zeta } } ^ { 1 }$ ; confidence 0.161

299. p07472084.png ; $( \gamma x ) ^ { g } = ( \gamma ^ { g } ) ( x ^ { g } )$ ; confidence 0.958

300. q076310112.png ; $( \Delta \otimes id ) ( R ) = R ^ { 13 } R ^ { 23 }$ ; confidence 0.501

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/Algebraic Groups/2. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/Algebraic_Groups/2&oldid=44077