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(AUTOMATIC EDIT of page 1 out of 12 with 300 lines: Updated image/latex database (currently 3466 images latexified; order by Length, ascending: False.)
 
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== List ==
 
== List ==
1. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420110.png ; $f$ ; confidence 1.000
+
1. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054340/j0543406.png ; $J _ { m } ( \lambda ) = \| \begin{array} { c c c c c c } { \lambda } & { 1 } & { \square } & { \square } & { \square } & { \square } \\ { \square } & { \lambda } & { 1 } & { \square } & { 0 } & { \square } \\ { \square } & { \square } & { \cdots } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { \cdots } & { \square } & { \square } \\ { \square } & { 0 } & { \square } & { \square } & { \lambda } & { 1 } \\ { \square } & { \square } & { \square } & { \square } & { \square } & { \lambda } \end{array} ]$ ; confidence 0.098
  
2. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420166.png ; $2 n$ ; confidence 1.000
+
2. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510132.png ; $\left. \begin{array} { r l l l l l l l } { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right.$ ; confidence 0.354
  
3. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001074.png ; $2$ ; confidence 1.000
+
3. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510129.png ; $\| \left. \begin{array} { r r r r r r r } { 2 } & { - 1 } & { 0 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 } \\ { - 1 } & { 2 } & { - 1 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { 2 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { - 1 } & { 2 } & { - 1 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 0 } & { - 1 } & { 2 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 0 } & { - 1 } & { 0 } & { 2 } \end{array} \right. |$ ; confidence 0.055
  
4. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026010/c026010588.png ; $J ( \alpha )$ ; confidence 1.000
+
4. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510131.png ; $\left\| \begin{array} { r r r r r r r } { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right\|$ ; confidence 0.278
  
5. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859076.png ; $x ( 1 )$ ; confidence 1.000
+
5. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510127.png ; $\left\| \begin{array} { r r r r r r } { 2 } & { - 1 } & { 0 } & { \dots } & { 0 } & { 0 } \\ { - 1 } & { 2 } & { - 1 } & { \dots } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { 2 } & { \dots } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 2 } & { - 2 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { - 1 } & { 2 } \end{array} \right\|$ ; confidence 0.232
  
6. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310117.png ; $R ^ { 12 }$ ; confidence 1.000
+
6. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054340/j0543403.png ; $J = \left| \begin{array} { c c c c } { J _ { n _ { 1 } } ( \lambda _ { 1 } ) } & { \square } & { \square } & { \square } \\ { \square } & { \ldots } & { \square } & { 0 } \\ { 0 } & { \square } & { \ldots } & { \square } \\ { \square } & { \square } & { \square } & { J _ { n _ { S } } ( \lambda _ { s } ) } \end{array} \right|$ ; confidence 0.072
  
7. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012250/a01225011.png ; $R > 0$ ; confidence 1.000
+
7. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023330/c02333033.png ; $H = \frac { 1 } { 36 } \left| \begin{array} { c c } { \frac { \partial ^ { 2 } f } { \partial x ^ { 2 } } } & { \frac { \partial ^ { 2 } f } { \partial x \partial y } } \\ { \frac { \partial ^ { 2 } f } { \partial x \partial y } } & { \frac { \partial ^ { 2 } f } { \partial y ^ { 2 } } } \end{array} \right| =$ ; confidence 0.956
  
8. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010139.png ; $3$ ; confidence 1.000
+
8. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510130.png ; $\left\| \begin{array} { r r r r r r } { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } \\ { - 1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right\|$ ; confidence 0.628
  
9. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090131.png ; $\Delta ( \lambda ) ^ { \mu }$ ; confidence 1.000
+
9. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524027.png ; $u _ { 3 } ( x ) = \left\{ \begin{array} { l l } { \frac { x ^ { 2 } } { 2 } , } & { 0 \leq x < 1 } \\ { \frac { [ x ^ { 2 } - 3 ( x - 1 ) ^ { 2 } ] } { 2 } , } & { 1 \leq x < 2 } \\ { \frac { [ x ^ { 2 } - 3 ( x - 1 ) ^ { 2 } + 3 ( x - 2 ) ^ { 2 } ] } { 2 } , } & { 2 \leq x < 3 } \\ { 0 , } & { x \notin [ 0,3 ] } \end{array} \right.$ ; confidence 0.733
  
10. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a11001057.png ; $10$ ; confidence 1.000
+
10. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510133.png ; $\left\| \begin{array} { r r r r } { 2 } & { - 1 } & { 0 } & { 0 } \\ { - 1 } & { 2 } & { - 2 } & { 0 } \\ { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right\| , \quad G _ { 2 } : \quad \left\| \begin{array} { r r } { 2 } & { - 1 } \\ { - 3 } & { 2 } \end{array} \right\|$ ; confidence 0.374
  
11. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a01160016.png ; $- 1$ ; confidence 1.000
+
11. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023330/c02333035.png ; $( \alpha _ { 0 } , \alpha _ { 1 } , \alpha _ { 2 } , \alpha _ { 3 } ) \mapsto ( \alpha _ { 0 } \alpha _ { 2 } - \alpha _ { 1 } ^ { 2 } , \frac { 1 } { 2 } ( \alpha _ { 0 } \alpha _ { 3 } - \alpha _ { 1 } \alpha _ { 2 } ) , \alpha _ { 1 } \alpha _ { 3 } - \alpha _ { 2 } ^ { 2 } )$ ; confidence 0.521
  
12. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410100.png ; $90$ ; confidence 1.000
+
12. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590458.png ; $= \left\{ \begin{array} { l l } { ( x + \lambda ) ^ { 2 } \ldots ( x + k \lambda ) ^ { 2 } } & { \text { if } \mu = 2 k } \\ { ( x + \lambda ) ^ { 2 } \ldots ( x + k \lambda ) ^ { 2 } ( x + ( k + 1 ) \lambda ) } & { \text { if } \mu = 2 k + 1 } \end{array} \right.$ ; confidence 0.870
  
13. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011380/a011380171.png ; $1 + 1$ ; confidence 1.000
+
13. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851074.png ; $[ X _ { \alpha } , X _ { \beta } ] = \left\{ \begin{array} { l l } { N _ { \alpha , \beta } X _ { \alpha + \beta } } & { \text { if } \alpha + \beta \in \Sigma } \\ { 0 } & { \text { if } \alpha + \beta \notin \Sigma } \end{array} \right.$ ; confidence 0.988
  
14. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150026.png ; $3 p - 3$ ; confidence 1.000
+
14. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876052.png ; $\left. \begin{array} { c } { c _ { i j } ^ { k } = - c _ { j i } ^ { k } } \\ { \sum _ { l = 1 } ^ { r } ( c _ { i l } ^ { m } c _ { j k } ^ { l } + c _ { k l } ^ { m } c _ { i j } ^ { l } + c _ { j l } ^ { m } c _ { k i } ^ { l } ) = 0 , \quad 1 \leq i , j , k , l , m \leq r } \end{array} \right.$ ; confidence 0.085
  
15. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450258.png ; $75$ ; confidence 1.000
+
15. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120376.png ; $\operatorname { sup } _ { f \in B ^ { 1 } } | \int _ { \partial G } f ( \zeta ) \omega ( \zeta ) d \zeta | = \operatorname { inf } _ { \phi \in E ^ { 1 } } \int _ { \partial G } | \omega ( \zeta ) - \phi ( \zeta ) \| d \zeta |$ ; confidence 0.508
  
16. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090217.png ; $\nabla ( \lambda )$ ; confidence 1.000
+
16. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590645.png ; $\left| \begin{array} { l l l } { F _ { X } ^ { \prime } } & { F _ { y } ^ { \prime } } & { F _ { z } ^ { \prime } } \\ { G _ { \chi } ^ { \prime } } & { G _ { y } ^ { \prime } } & { G _ { Z } ^ { \prime } } \end{array} \right|$ ; confidence 0.230
  
17. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150017.png ; $\lambda ( \theta )$ ; confidence 1.000
+
17. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150078.png ; $\left( \begin{array} { l l } { \alpha } & { b } \\ { c } & { d } \end{array} \right) \equiv \left( \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) ( \operatorname { mod } 7 )$ ; confidence 0.440
  
18. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018062.png ; $\lambda \neq 0$ ; confidence 1.000
+
18. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140104.png ; $q R ( x ) = \sum _ { j \in Q _ { 0 } } x _ { j } ^ { 2 } - \sum _ { \langle \beta : i \rightarrow j ) \in Q _ { 1 } } x _ { i } x _ { j } + \sum _ { \langle \beta : i \rightarrow j ) \in Q _ { 1 } } x _ { , j } x _ { i } x _ { j }$ ; confidence 0.112
  
19. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h04769089.png ; $\Gamma ( \pi )$ ; confidence 1.000
+
19. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876037.png ; $\sum _ { k = 1 } ^ { N } ( \xi _ { i k } \frac { \partial \xi _ { j l } } { \partial x _ { k } } - \xi _ { j k } \frac { \partial \xi _ { i l } } { \partial x _ { k } } ) = \sum _ { k = 1 } ^ { r } c _ { i j } ^ { k } \xi _ { k l }$ ; confidence 0.157
  
20. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011480/a01148050.png ; $p ^ { 2 }$ ; confidence 1.000
+
20. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631092.png ; $\sum _ { k = 0 } ^ { n } ( - 1 ) ^ { k } \left( \begin{array} { l } { n } \\ { k } \end{array} \right) q ^ { - k ( n - k ) / 2 } ( X _ { i } ^ { \pm } ) ^ { k } X _ { j } ^ { \pm } \cdot ( X _ { i } ^ { \pm } ) ^ { n - k } = 0$ ; confidence 0.055
  
21. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970110.png ; $x ^ { 2 } = 0$ ; confidence 1.000
+
21. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631099.png ; $\Delta ( X _ { i } ^ { \pm } ) = X _ { i } ^ { \pm } \bigotimes \operatorname { exp } ( \frac { h H _ { i } } { 4 } ) + \operatorname { exp } ( \frac { - h H _ { i } } { 4 } ) \otimes x _ { i } ^ { \pm }$ ; confidence 0.212
  
22. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025830/c0258308.png ; $\{ 0 \}$ ; confidence 1.000
+
22. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045210/g04521075.png ; $\left. \begin{array} { l l l } { A } & { \rightarrow Y } & { \square } \\ { \downarrow } & { \square } & { } & { \square } \\ { X } & { \square } & { } & { A } \end{array} \right.$ ; confidence 0.226
  
23. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590466.png ; $f ( x , y ) = x ^ { 3 } + y ^ { 4 }$ ; confidence 1.000
+
23. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145065.png ; $g \leq \left\{ \begin{array} { l l } { \frac { ( n - 2 ) ^ { 2 } } { 4 } } & { \text { for even } n } \\ { \frac { ( n - 1 ) ( n - 3 ) } { 4 } } & { \text { for odd } n } \end{array} \right.$ ; confidence 0.698
  
24. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590469.png ; $f ( x , y ) = x ^ { 3 } + x y ^ { 3 }$ ; confidence 1.000
+
24. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054017.png ; $( x _ { i j } ( a ) , x _ { k l } ( b ) ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } i \neq 1 , j \neq k } \\ { x _ { 1 } ( a b ) } & { \text { if } i \neq 1 , j = k } \end{array} \right.$ ; confidence 0.381
  
25. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010120/a01012051.png ; $f ( \infty ) = 0$ ; confidence 1.000
+
25. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014048.png ; $[ X ] \mapsto \chi _ { Q } ( [ X ] ) = \operatorname { dim } _ { K } \operatorname { End } _ { Q } ( X ) - \operatorname { dim } _ { K } \operatorname { Ext } _ { Q } ^ { 1 } ( X , X )$ ; confidence 0.661
  
26. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120100/f12010077.png ; $27$ ; confidence 1.000
+
26. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700175.png ; $\operatorname { Aut } _ { R ^ { \prime } } ( X ^ { \prime } | X _ { 0 } ) \rightarrow \operatorname { Aut } _ { R } ( X _ { R ^ { \prime } } ^ { \prime } \otimes R | X _ { 0 } )$ ; confidence 0.683
  
27. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s130540120.png ; $\{ - 1 , - 1 \}$ ; confidence 1.000
+
27. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700190.png ; $\operatorname { dim } _ { k } H ^ { 1 } ( X _ { 0 } , T _ { X _ { 0 } } ) - \operatorname { dim } M _ { X _ { 0 } } \leq \operatorname { dim } _ { k } H ^ { 2 } ( X _ { 0 } , T _ { X _ { 0 } } )$ ; confidence 0.944
  
28. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145010.png ; $f ( x , y )$ ; confidence 1.000
+
28. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w12009095.png ; $\mathfrak { S } _ { \{ 1 , \ldots , \lambda _ { 1 } \} } \times \mathfrak { S } _ { \{ \lambda _ { 1 } + 1 , \ldots , \lambda _ { 1 } + \lambda _ { 2 } \} } \times$ ; confidence 0.312
  
29. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031890/d03189020.png ; $( \xi , \eta )$ ; confidence 1.000
+
29. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120236.png ; $\beta : \operatorname { Ext } _ { c } ^ { n - p - 1 } ( X ; F , \Omega ) \rightarrow \operatorname { Ext } _ { c } ^ { n - p - 1 } ( X \backslash Y ; F , \Omega )$ ; confidence 0.634
  
30. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025140/c025140126.png ; $p ^ { - 1 } ( b )$ ; confidence 1.000
+
30. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631095.png ; $\left( \begin{array} { l } { n } \\ { k } \end{array} \right) _ { q } = \frac { ( q ^ { n } - 1 ) \ldots ( q ^ { n - k + 1 } - 1 ) } { ( q ^ { k } - 1 ) \ldots ( q - 1 ) }$ ; confidence 0.443
  
31. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310118.png ; $R ^ { 13 }$ ; confidence 1.000
+
31. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590225.png ; $\sum _ { k _ { 1 } , \ldots , k _ { n } = 0 } ^ { \infty } c _ { k _ { 1 } \cdots k _ { n } } ( z _ { 1 } - \zeta _ { 1 } ) ^ { k _ { 1 } } \ldots ( z _ { n } - \zeta _ { n } ) ^ { k _ { n } }$ ; confidence 0.324
  
32. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120210/s12021024.png ; $\lambda \leq \mu$ ; confidence 1.000
+
32. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u0952403.png ; $p ( x ) = \left\{ \begin{array} { l l } { \frac { 1 } { b - \alpha } , } & { x \in [ \alpha , b ] } \\ { 0 , } & { x \notin [ \alpha , b ] } \end{array} \right.$ ; confidence 0.681
  
33. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090206.png ; $\mu - \lambda$ ; confidence 1.000
+
33. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020550/c0205509.png ; $\mathfrak { g } 0 = \{ X \in \mathfrak { g } : \forall H \in \mathfrak { t } \exists \mathfrak { n } X , H \in Z ( ( \text { ad } H ) ^ { n } X , H ( X ) = 0 ) \}$ ; confidence 0.110
  
34. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h04741012.png ; $f ( t , x ) = t - x ^ { 2 }$ ; confidence 1.000
+
34. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524030.png ; $u _ { n } ( x ) = \frac { 1 } { ( n - 1 ) ! } \sum _ { k = 0 } ^ { n } ( - 1 ) ^ { k } \left( \begin{array} { l } { n } \\ { k } \end{array} \right) ( x - k ) _ { + } ^ { n - 1 }$ ; confidence 0.569
  
35. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a01021052.png ; $f ( z )$ ; confidence 1.000
+
35. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l058680102.png ; $L ( \mathfrak { g } ) \cong \Gamma _ { 0 } ( \mathfrak { u } ) \cap \mathfrak { h } ^ { \prime } / \Gamma _ { 0 } ( [ \mathfrak { k } , \mathfrak { k } ] )$ ; confidence 0.659
  
36. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013900/a0139002.png ; $\partial G$ ; confidence 1.000
+
36. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872026.png ; $( \operatorname { ad } x ) ^ { n } y = \sum _ { j = 1 } ^ { n } ( - 1 ) ^ { j } \left( \begin{array} { c } { n } \\ { j } \end{array} \right) x ^ { n - j } y x ^ { j }$ ; confidence 0.356
  
37. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015540/b01554032.png ; $( 0,0 )$ ; confidence 1.000
+
37. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140140.png ; $q ( x ) = \sum _ { i \in I } x _ { i } ^ { 2 } + \sum _ { i \prec j } x _ { i } x _ { j } - \sum _ { p \in \operatorname { max } l } ( \sum _ { i \prec p } x _ { i } ) x _ { p }$ ; confidence 0.197
  
38. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s130540101.png ; $G = E ( R )$ ; confidence 1.000
+
38. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014056.png ; $A _ { Q } ( v ) = \prod _ { i , j \in Q _ { 0 } } \prod _ { \langle \beta : j \rightarrow i \rangle \in Q _ { 1 } } M _ { v _ { i } \times v _ { j } } ( K ) _ { \beta }$ ; confidence 0.481
  
39. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120433.png ; $\sigma ( G , F )$ ; confidence 1.000
+
39. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267025.png ; $\operatorname { Pic } _ { X / k } ( S ^ { \prime } ) = \operatorname { Fic } ( X \times k S ^ { \prime } ) / \operatorname { Fic } ( S ^ { \prime } )$ ; confidence 0.345
  
40. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017330/b01733082.png ; $f _ { 1 } ( z )$ ; confidence 1.000
+
40. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140118.png ; $[ X ] \mapsto \chi _ { R } ( [ X ] ) = \sum _ { m = 0 } ^ { \infty } ( - 1 ) ^ { m } \operatorname { dim } _ { K } \operatorname { Ext } _ { R } ^ { m } ( X , X )$ ; confidence 0.116
  
41. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120020/c12002069.png ; $1 \leq k \leq n - 1$ ; confidence 1.000
+
41. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093350/t0933502.png ; $r = \alpha \operatorname { sin } u k + l ( 1 + \epsilon \operatorname { cos } u ) ( i \operatorname { cos } v + j \operatorname { sin } v )$ ; confidence 0.585
  
42. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023720/c02372059.png ; $U ( 0,1 )$ ; confidence 1.000
+
42. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427031.png ; $\Gamma = \operatorname { diag } \{ \gamma _ { 1 } , \gamma _ { 2 } , \gamma _ { 3 } \} , \quad \gamma _ { i } \neq 0 , \quad \gamma _ { i } \in F$ ; confidence 0.987
  
43. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h04741044.png ; $3 g + 6$ ; confidence 1.000
+
43. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u0952407.png ; $F ( x ) = \left\{ \begin{array} { l l } { 0 , } & { x \leq a } \\ { \frac { x - a } { b - a } , } & { a < x \leq b } \\ { 1 , } & { x > b } \end{array} \right.$ ; confidence 0.468
  
44. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145094.png ; $2 g - 2$ ; confidence 1.000
+
44. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690016.png ; $\delta ( e ) = e \quad \text { and } \quad \delta ( \rho ( a ) b ) = \sigma ( a ) \delta ( b ) , \quad \alpha \in C ^ { 0 } , \quad b \in C ^ { 1 }$ ; confidence 0.400
  
45. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018075.png ; $\lambda = 1$ ; confidence 1.000
+
45. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763055.png ; $\chi = \delta _ { \phi } - \sum _ { \alpha \in \Delta } m _ { \alpha } \alpha , \quad m _ { \alpha } \in Z , \quad m _ { \alpha } \geq 0$ ; confidence 0.862
  
46. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450155.png ; $3 g - 3$ ; confidence 1.000
+
46. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590404.png ; $\frac { m _ { 1 } } { n _ { 1 } } < \frac { m _ { 2 } } { n _ { 1 } n _ { 2 } } < \ldots < \frac { m _ { g } } { n _ { 1 } \ldots n _ { g } } = \frac { m _ { g } } { n }$ ; confidence 0.459
  
47. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120158.png ; $( r + 1 )$ ; confidence 1.000
+
47. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524072.png ; $p ( x _ { 1 } , \ldots , x _ { n } ) = \left\{ \begin{array} { l l } { C \neq 0 , } & { x \in D } \\ { 0 , } & { x \notin D } \end{array} \right.$ ; confidence 0.705
  
48. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g1300209.png ; $\beta = - i$ ; confidence 1.000
+
48. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032490/d03249029.png ; $\omega _ { \eta / F } ( x ) = \sum _ { 0 \leq i \leq m } \alpha _ { i } \left( \begin{array} { c } { x + i } \\ { i } \end{array} \right)$ ; confidence 0.968
  
49. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080900/r08090012.png ; $\phi ( T , G )$ ; confidence 1.000
+
49. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c0205704.png ; $f _ { j } ] = \delta _ { i j } h _ { i } , \quad [ h _ { i } , e _ { j } ] = \alpha _ { i j } e _ { j } , \quad [ h _ { i } , f _ { j } ] = - \alpha _ { j } f _ { j }$ ; confidence 0.149
  
50. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063010/m06301075.png ; $p = ( n + 1 ) / 2$ ; confidence 1.000
+
50. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859086.png ; $( X , Y ) \rightarrow \operatorname { exp } ^ { - 1 } ( \operatorname { exp } X \operatorname { exp } Y ) , \quad X , Y \in L ( G )$ ; confidence 0.856
  
51. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f130090107.png ; $( r - 1 )$ ; confidence 1.000
+
51. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090122.png ; $\operatorname { diag } ( t _ { 1 } , \ldots , t _ { n } ) \mapsto t _ { 1 } ^ { \lambda _ { 1 } } \ldots t _ { n } ^ { \lambda _ { n } } \in K$ ; confidence 0.507
  
52. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120407.png ; $f ( x , y ) = ( x , y )$ ; confidence 1.000
+
52. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120509.png ; $f = \{ f _ { \alpha } \} \in \prod _ { \alpha } F _ { \alpha } , \quad g = \{ g _ { \alpha } \} \in \oplus _ { \alpha } G _ { \alpha }$ ; confidence 0.491
  
53. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310119.png ; $R ^ { 23 }$ ; confidence 1.000
+
53. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590634.png ; $\Delta = ( F _ { x x } ^ { \prime \prime } ) _ { 0 } ( F _ { y y } ^ { \prime \prime } ) _ { 0 } - ( F _ { x y } ^ { \prime \prime } ) _ { 0 } ^ { 2 }$ ; confidence 0.920
  
54. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859090.png ; $G _ { 1 } \cong G _ { 2 }$ ; confidence 1.000
+
54. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090135.png ; $\chi _ { \lambda } = \sum _ { \mu \in \Lambda ( n ) } \operatorname { dim } _ { K } ( \Delta ( \lambda ) ^ { \mu } ) _ { e _ { \mu } }$ ; confidence 0.461
  
55. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a0115008.png ; $s ^ { 2 } = f ( t )$ ; confidence 1.000
+
55. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c02057064.png ; $\rightarrow H ^ { p } ( X , S ) \rightarrow H ^ { p } ( X , F ) \stackrel { \phi p } { \rightarrow } H ^ { p } ( X , G ) \rightarrow$ ; confidence 0.853
  
56. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110160/c11016038.png ; $[ 0,1 ]$ ; confidence 1.000
+
56. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631072.png ; $\delta ( \alpha ) = \operatorname { lim } _ { h \rightarrow 0 } h ^ { - 1 } ( \Delta ( a ) - \Delta ^ { \prime } ( \alpha ) )$ ; confidence 0.304
  
57. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472051.png ; $\square ( \Gamma )$ ; confidence 1.000
+
57. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183016.png ; $\omega _ { V } = \sum _ { 0 \leq i \leq m } \alpha _ { i } \left( \begin{array} { c } { x + i } \\ { i } \end{array} \right)$ ; confidence 0.780
  
58. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070095.png ; $\delta \in D ( S )$ ; confidence 1.000
+
58. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120253.png ; $h ( \phi ) = \operatorname { lim } _ { r \rightarrow \infty } \frac { \operatorname { ln } | A ( r e ^ { i \phi } ) | } { r }$ ; confidence 0.861
  
59. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013610/a0136105.png ; $- \infty$ ; confidence 1.000
+
59. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120175.png ; $H ^ { p } ( X , F ) \times H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( F , \Omega ) ) \rightarrow H _ { c } ^ { n } ( X , \Omega )$ ; confidence 0.921
  
60. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013180/a013180166.png ; $( k - 1 )$ ; confidence 1.000
+
60. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690028.png ; $C ^ { * } ( \mathfrak { U } , F ) = ( C ^ { 0 } ( \mathfrak { U } , F ) , C ^ { 1 } ( \mathfrak { U } , F ) , C ^ { 2 } ( \mathfrak { U } , F ) )$ ; confidence 0.205
  
61. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024670/c02467029.png ; $x$ ; confidence 1.000
+
61. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851044.png ; $\mathfrak { g } _ { \alpha } = \operatorname { dim } [ \mathfrak { g } _ { \alpha } , \mathfrak { g } _ { - \alpha } ] = 1$ ; confidence 0.520
  
62. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120475.png ; $\sigma ( F , F ^ { \prime } )$ ; confidence 1.000
+
62. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590115.png ; $( G ) \cong \operatorname { Aut } ( L ( G ) ) \quad \text { and } \quad L ( \operatorname { Aut } ( G ) ) \cong D ( L ( G ) )$ ; confidence 0.693
  
63. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011300/a011300114.png ; $A ( k )$ ; confidence 1.000
+
63. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696024.png ; $F _ { 1 } F _ { 2 } = F _ { 1 } \langle F _ { 2 } \rangle = F _ { 1 } ( F _ { 2 } ) = F _ { 2 } ( F _ { 1 } ) = F _ { 2 } \langle F _ { 1 } \rangle$ ; confidence 0.628
  
64. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097590/w0975906.png ; $H ^ { 1 } ( k , A )$ ; confidence 1.000
+
64. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054340/j05434030.png ; $C _ { m } ( \lambda ) = \operatorname { rk } ( A - \lambda E ) ^ { m - 1 } - 2 \operatorname { rk } ( A - \lambda E ) ^ { m } +$ ; confidence 0.955
  
65. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590115.png ; $U ( \zeta , R )$ ; confidence 1.000
+
65. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851050.png ; $[ H _ { \alpha } , X _ { \alpha } ] = 2 X _ { \alpha } \quad \text { and } \quad [ H _ { \alpha } , Y _ { \alpha } ] = - 2 Y _ { 0 }$ ; confidence 0.539
  
66. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183093.png ; $\{ F \}$ ; confidence 1.000
+
66. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876030.png ; $\frac { \partial f _ { j } } { \partial g _ { i } } ( g , x ) = \sum _ { k = 1 } ^ { r } \xi _ { k j } ( f ( g _ { s } x ) ) \psi _ { k i } ( g )$ ; confidence 0.336
  
67. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010460/a01046080.png ; $f ( x )$ ; confidence 1.000
+
67. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150022.png ; $\overline { w } = 2 \int _ { 0 } ^ { 1 / \varepsilon } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ ; confidence 0.107
  
68. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900136.png ; $H _ { \alpha } ^ { 2 } ( G , A )$ ; confidence 1.000
+
68. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164047.png ; $p _ { x } ( V ) = - \operatorname { dim } _ { k } H _ { 1 } ( V , O _ { V } ) + \operatorname { dim } _ { k } H ^ { 2 } ( V , O _ { V } ) =$ ; confidence 0.756
  
69. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012810/a01281012.png ; $F ( x , y )$ ; confidence 1.000
+
69. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120360.png ; $\operatorname { sup } _ { l \in E ^ { \perp } } | l ( \omega ) | = \operatorname { inf } _ { x \in E } \| \omega - x \|$ ; confidence 0.293
  
70. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030240/d03024010.png ; $\gamma ( 0 ) = 0$ ; confidence 1.000
+
70. 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
  
71. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590116.png ; $D ( L ( G ) )$ ; confidence 1.000
+
71. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087060/s08706033.png ; $\psi _ { t _ { 1 } , \ldots , t _ { R } } ^ { \prime } : S K _ { 1 } ( R ) \rightarrow S K _ { 1 } ( R ( t _ { 1 } , \ldots , t _ { n } ) )$ ; confidence 0.379
  
72. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082027.png ; $G : B \rightarrow G ( B )$ ; confidence 1.000
+
72. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164029.png ; $p _ { \alpha } ( V ) = \left( \begin{array} { c } { n - 1 } \\ { 3 } \end{array} \right) - d ( n - 1 ) + 2 t + \tau + p - 1$ ; confidence 0.396
  
73. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590173.png ; $0 , \infty$ ; confidence 1.000
+
73. 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
  
74. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082088.png ; $\alpha : F ( X , Y ) \rightarrow G ( X , Y )$ ; confidence 1.000
+
74. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d03412079.png ; $( c _ { \gamma } , c ^ { r } ) = \sum _ { t ^ { r } \in K } c _ { r } ( t ^ { \prime } ) c ^ { r } ( t ^ { r } ) \operatorname { mod } 1$ ; confidence 0.117
  
75. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012270/a01227047.png ; $F ( x , y ) = 0$ ; confidence 1.000
+
75. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590482.png ; $( \frac { \partial F ( x , y , \lambda ) } { \partial x } , \frac { \partial F ( x , y , \lambda ) } { \partial y } )$ ; confidence 0.986
  
76. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640145.png ; $\omega = M - M ^ { \prime }$ ; confidence 1.000
+
76. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023330/c02333034.png ; $= ( a _ { 0 } a _ { 2 } - a _ { 1 } ^ { 2 } ) x ^ { 2 } + ( a _ { 0 } a _ { 3 } - a _ { 1 } a _ { 2 } ) x y + ( a _ { 1 } a _ { 3 } - a _ { 2 } ^ { 2 } ) y ^ { 2 }$ ; confidence 0.549
  
77. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900100.png ; $H ^ { 2 } ( G , B )$ ; confidence 1.000
+
77. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120247.png ; $\underset { n \rightarrow \infty } { \operatorname { lim } } | \alpha _ { n } | ^ { 1 / n } = \sigma < + \infty$ ; confidence 0.521
  
78. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524047.png ; $F ^ { - 1 } ( y )$ ; confidence 1.000
+
78. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700263.png ; $\alpha \circ b = \alpha b + \sum _ { i = 1 } ^ { \infty } \phi _ { i } ( \alpha , b ) t ^ { i } , \quad \alpha , b \in V$ ; confidence 0.097
  
79. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764054.png ; $x ^ { 3 } + y ^ { 5 } + z ^ { 2 }$ ; confidence 1.000
+
79. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851073.png ; $n ( i , j ) = \alpha _ { j } ( H _ { i } ) = \frac { 2 ( \alpha _ { i } , \alpha _ { j } ) } { ( \alpha _ { j } , \alpha _ { j } ) }$ ; confidence 0.992
  
80. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120172.png ; $0 \leq p \leq n$ ; confidence 1.000
+
80. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851078.png ; $N _ { \alpha , \beta } = - N _ { - \alpha , - \beta } \quad \text { and } \quad N _ { \alpha , \beta } = \pm ( p + 1 )$ ; confidence 0.961
  
81. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120337.png ; $| \zeta | < P$ ; confidence 1.000
+
81. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868032.png ; $\Gamma _ { 1 } = \Gamma _ { 1 } ( g ) = \{ X \in h : \alpha ( X ) \in 2 \pi i Z \text { for all } \alpha \in \Sigma \}$ ; confidence 0.183
  
82. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s130540102.png ; $( \infty \times \infty )$ ; confidence 1.000
+
82. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090342.png ; $\left( \begin{array} { c } { h } \\ { i } \end{array} \right) = \frac { h ( h - 1 ) \ldots ( h - i + 1 ) } { i ! }$ ; confidence 0.487
  
83. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010520/a01052024.png ; $f ( n )$ ; confidence 1.000
+
83. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058660/l0586604.png ; $N ( F ) = \{ g \in GL ( V ) : g v \equiv v \operatorname { mod } V _ { i } \text { for all } v \in V _ { i } , i \geq 1 \}$ ; confidence 0.466
  
84. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590431.png ; $- ( Z ^ { 2 } )$ ; confidence 1.000
+
84. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t130130105.png ; $0 \rightarrow \Lambda \rightarrow T _ { 1 } \rightarrow \ldots \rightarrow T _ { n } \rightarrow 0$ ; confidence 0.946
  
85. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012270/a01227054.png ; $F ( x , y , z ) = 0$ ; confidence 1.000
+
85. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851085.png ; $X _ { \alpha } - X _ { - \alpha } , \quad i ( X _ { \alpha } + X _ { - \alpha } ) \quad ( \alpha \in \Sigma _ { + } )$ ; confidence 0.691
  
86. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011490/a011490110.png ; $p > 0$ ; confidence 1.000
+
86. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876016.png ; $X _ { i } = \sum _ { j = 1 } ^ { n } \xi _ { i j } ( x ) \frac { \partial } { \partial x _ { j } } , \quad i = 1 , \ldots , r$ ; confidence 0.656
  
87. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016800/b0168003.png ; $b - a$ ; confidence 1.000
+
87. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100172.png ; $\langle \alpha > < b \rangle = \langle \alpha b \rangle , \quad \langle 1 \rangle = f _ { 1 } = V _ { 1 } =$ ; confidence 0.351
  
88. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450199.png ; $f ( x , y ) = 0$ ; confidence 1.000
+
88. 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
  
89. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696092.png ; $c ( \eta ^ { \prime } ) = 0$ ; confidence 1.000
+
89. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h04769069.png ; $\mathfrak { g } = \mathfrak { f } + \mathfrak { m } , \quad \mathfrak { f } \cap \mathfrak { m } = \{ 0 \}$ ; confidence 0.793
  
90. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590460.png ; $f ( x , y ) = x ^ { \mu + 1 } - y ^ { 2 }$ ; confidence 1.000
+
90. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900118.png ; $( g _ { 1 } , g _ { 2 } ) = h ( g _ { 1 } ) ( \phi ( g _ { 1 } ) ( h ( g _ { 2 } ) ) ) m ( g _ { 1 } , g _ { 2 } ) h ( g _ { 1 } , g _ { 2 } ) ^ { - 1 }$ ; confidence 0.764
  
91. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090163.png ; $\Delta ( \lambda ) ^ { \perp }$ ; confidence 1.000
+
91. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r077630100.png ; $0 \leq \frac { 2 ( \chi , \alpha ) } { ( \alpha , \alpha ) } < p \quad \text { for all } \alpha \in \Delta$ ; confidence 0.879
  
92. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s0855909.png ; $\zeta \neq \infty$ ; confidence 1.000
+
92. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590653.png ; $( F _ { X } ^ { \prime } ) _ { 0 } = 0 , \quad ( F _ { y } ^ { \prime } ) _ { 0 } = 0 , \quad ( F _ { z } ^ { \prime } ) _ { 0 } = 0$ ; confidence 0.300
  
93. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097710/w09771030.png ; $\Phi ( T , G )$ ; confidence 1.000
+
93. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164053.png ; $1 + p _ { x } ( V ) = \frac { \operatorname { deg } ( c _ { 1 } ^ { 2 } ) + \operatorname { deg } ( c _ { 2 } ) } { 12 }$ ; confidence 0.752
  
94. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090149.png ; $\Delta ( \lambda )$ ; confidence 1.000
+
94. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120555.png ; $f _ { 0 } ( x ) \rightarrow \text { inf, } \quad f _ { i } ( x ) \leq 0 , \quad i = 1 , \ldots , m , \quad x \in B$ ; confidence 0.810
  
95. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900135.png ; $H ^ { 2 } ( G , Z ( A ) )$ ; confidence 1.000
+
95. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063010/m06301072.png ; $F ( x _ { 1 } f _ { 1 } + \ldots + x _ { x } f _ { n } ) = x _ { 1 } x _ { n } + x _ { 2 } x _ { n } - 1 + \ldots + x _ { p } x _ { n } - p + 1$ ; confidence 0.198
  
96. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082094.png ; $\alpha _ { i } ( 0 ) = 0$ ; confidence 1.000
+
96. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700270.png ; $\Phi ( \alpha ) = \alpha + \sum _ { i = 1 } ^ { \infty } t ^ { i } \phi _ { i } ( \alpha ) , \quad \alpha \in V$ ; confidence 0.873
  
97. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090110.png ; $\lambda \in \Lambda ^ { + } ( n , r )$ ; confidence 1.000
+
97. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797042.png ; $\epsilon ( x ) = 0 , \quad \delta ( x ) = x \bigotimes 1 + 1 \bigotimes x , \quad x \in \mathfrak { g }$ ; confidence 0.213
  
98. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023620/c0236204.png ; $A ( z )$ ; confidence 1.000
+
98. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851030.png ; $\mathfrak { g } _ { \alpha } = \{ X \in \mathfrak { g } : [ H , X ] = \alpha ( H ) X , H \in \mathfrak { h } \}$ ; confidence 0.976
  
99. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868038.png ; $\Gamma ( G ) = M$ ; confidence 1.000
+
99. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872078.png ; $\pi ( x + y ) = \pi ( x ) + \pi ( y ) , \quad \pi ( \lambda x ) = \lambda ^ { p } \pi ( x ) , \quad \lambda \in k$ ; confidence 0.964
  
100. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120495.png ; $\beta ( X ^ { \prime } , X )$ ; confidence 1.000
+
100. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074640/p07464025.png ; $g j : U _ { i } \cap U _ { j } \rightarrow G , \quad i , j \in I , \quad U _ { i } \cap U _ { j } \neq \emptyset$ ; confidence 0.184
  
101. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764048.png ; $x ^ { 3 } + y ^ { 4 } + z ^ { 2 }$ ; confidence 1.000
+
101. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631062.png ; $\phi ^ { * } : \mathfrak { g } ^ { * } \otimes \mathfrak { g } ^ { * } \rightarrow \mathfrak { g } ^ { * }$ ; confidence 0.837
  
102. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097710/w09771048.png ; $\Phi ( T _ { 0 } , G )$ ; confidence 1.000
+
102. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100190.png ; $\sigma ( \alpha _ { 1 } , \alpha _ { 2 } , \ldots ) = ( \alpha _ { 1 } ^ { p } , \alpha _ { 2 } ^ { p } , \ldots )$ ; confidence 0.771
  
103. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l058720143.png ; $p > 7$ ; confidence 1.000
+
103. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970129.png ; $m \circ ( \iota \otimes 1 ) \circ \mu = m \circ ( 1 \otimes \iota ) \circ \mu = e \circ \epsilon$ ; confidence 0.618
  
104. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r081030110.png ; $\Delta ( \gamma )$ ; confidence 1.000
+
104. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w12009096.png ; $\ldots \times \mathfrak { S } _ { \{ \lambda _ { 1 } + \ldots + \lambda _ { n - 1 } + 1 , \ldots , r \} }$ ; confidence 0.259
  
105. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l0587607.png ; $G \times \Omega$ ; confidence 1.000
+
105. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150044.png ; $\theta ( v + \pi i r ) = \theta ( r ) , \quad \theta ( v + \alpha _ { j } ) = e ^ { L _ { j } ( v ) } \theta ( v )$ ; confidence 0.775
  
106. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900126.png ; $H _ { \alpha } ^ { 2 } ( G , A ) = \theta ^ { - 1 } ( \alpha )$ ; confidence 1.000
+
106. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830107.png ; $S ^ { t } F = \sum _ { j = 1 } ^ { r } c _ { j } A ^ { p _ { j } } A _ { 1 } ^ { i _ { 1 j } } \dots A _ { m - l } ^ { i _ { m - l } , j }$ ; confidence 0.149
  
107. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590141.png ; $G = B E$ ; confidence 1.000
+
107. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970139.png ; $F _ { 1 } ( X ; Y ) , \ldots , F _ { n } ( X ; Y ) \in K [ X _ { 1 } , \ldots , X _ { n } ; Y _ { 1 } , \ldots , Y _ { n } ] \}$ ; confidence 0.353
  
108. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900134.png ; $H ^ { 3 } ( G , Z ( A ) )$ ; confidence 1.000
+
108. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631071.png ; $\delta : U _ { \mathfrak { g } } \rightarrow U _ { \mathfrak { g } } \otimes U _ { \mathfrak { g } }$ ; confidence 0.648
  
109. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027020.png ; $R ( t )$ ; confidence 1.000
+
109. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524034.png ; $z _ { + } = \left\{ \begin{array} { l l } { z , } & { z > 0 } \\ { 0 , } & { z \leq 0 } \end{array} \right.$ ; confidence 0.676
  
110. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110210/b11021056.png ; $p \neq 2$ ; confidence 1.000
+
110. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090259.png ; $\mathfrak { B } = \{ e _ { \pm } \alpha , h _ { \beta } : \alpha \in \Phi ^ { + } , \beta \in \Sigma \}$ ; confidence 0.381
  
111. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082085.png ; $\psi : L \rightarrow L ^ { \prime }$ ; confidence 1.000
+
111. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183043.png ; $e _ { i j } = \operatorname { ord } _ { Y } _ { j } F _ { i } , \quad 1 \leq i \leq n , \quad i \leq j \leq n$ ; confidence 0.187
  
112. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472098.png ; $H ^ { 1 } ( G , \Gamma )$ ; confidence 1.000
+
112. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851057.png ; $[ \mathfrak { g } _ { \alpha } , \mathfrak { g } _ { \beta } ] = \mathfrak { g } _ { \alpha + \beta }$ ; confidence 0.917
  
113. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041320/f04132021.png ; $G ( k )$ ; confidence 1.000
+
113. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851069.png ; $[ [ X _ { \alpha _ { i } } , X _ { - } \alpha _ { i } ] , X _ { - \alpha _ { j } } ] = - n ( i , j ) X _ { \alpha _ { j } }$ ; confidence 0.628
  
114. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024960/c02496012.png ; $p \neq 0$ ; confidence 1.000
+
114. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900110.png ; $\phi ( g _ { 1 } ) \phi ( g ) \phi ( g _ { 1 } g _ { 2 } ) ^ { - 1 } = \operatorname { Int } m ( g _ { 1 } , g _ { 2 } )$ ; confidence 0.443
  
115. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559016.png ; $\zeta = \phi ( 0 )$ ; confidence 1.000
+
115. 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
  
116. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410140.png ; $\xi ^ { 2 } + \eta ^ { 2 } = 1$ ; confidence 1.000
+
116. 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
  
117. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851054.png ; $\alpha + \beta \neq 0$ ; confidence 1.000
+
117. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164027.png ; $N _ { m } = \left( \begin{array} { c } { m + 3 } \\ { 3 } \end{array} \right) - d m + 2 t + \tau + p - 1$ ; confidence 0.369
  
118. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004025.png ; $( \Gamma \cap P ) \backslash H ^ { 1 }$ ; confidence 1.000
+
118. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120173.png ; $H ^ { p } ( X , F ) \times H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( F , \Omega ) ) \rightarrow C$ ; confidence 0.824
  
119. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120391.png ; $\{ F , G , f \}$ ; confidence 1.000
+
119. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852011.png ; $[ \mathfrak { g } _ { i } , \mathfrak { g } _ { i } ] \subset \mathfrak { g } _ { \mathfrak { i } } + 1$ ; confidence 0.276
  
120. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017340/b017340120.png ; $n < 0$ ; confidence 1.000
+
120. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820118.png ; $\operatorname { og } F _ { MU } ( X ) = \sum _ { i = 1 } ^ { \infty } i ^ { - 1 } [ C ^ { - } P ^ { - 1 } ] X ^ { i }$ ; confidence 0.098
  
121. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120431.png ; $\mu ( F , G )$ ; confidence 1.000
+
121. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861012.png ; $J = \left\| \begin{array} { c c } { 0 } & { E _ { x } } \\ { - E _ { x } } & { 0 } \end{array} \right\|$ ; confidence 0.364
  
122. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590430.png ; $p ( Z ) = 0$ ; confidence 1.000
+
122. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093350/t0933507.png ; $d s ^ { 2 } = \alpha ^ { 2 } d u ^ { 2 } + l ^ { 2 } ( 1 + \epsilon \operatorname { cos } u ) ^ { 2 } d v ^ { 2 }$ ; confidence 0.696
  
123. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590540.png ; $( x = 0 )$ ; confidence 1.000
+
123. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100177.png ; $\langle \alpha + b \rangle = \sum _ { n = 1 } ^ { \infty } V _ { n } \langle r _ { n } ( \alpha , b ) f$ ; confidence 0.143
  
124. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120483.png ; $\sigma ( F , G )$ ; confidence 1.000
+
124. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120184.png ; $( H ^ { p } ( X , F ) ) ^ { \prime } \cong H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( F , \Omega ) )$ ; confidence 0.829
  
125. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872053.png ; $\phi : L \rightarrow K$ ; confidence 1.000
+
125. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427077.png ; $\mathfrak { g } = \mathfrak { g } - 1 + \mathfrak { g } \mathfrak { d } + \mathfrak { g } _ { 1 }$ ; confidence 0.598
  
126. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590467.png ; $F ( x , y , \lambda ) = ( x - \mu ) ( x ^ { 2 } - \lambda y ^ { 2 } ) + y ^ { 4 }$ ; confidence 1.000
+
126. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851037.png ; $\mathfrak { g } = \mathfrak { h } + \sum _ { \alpha \in \Sigma } \mathfrak { g } _ { \alpha }$ ; confidence 0.945
  
127. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120438.png ; $( G , \sigma ( G , F ) )$ ; confidence 1.000
+
127. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851064.png ; $H _ { \alpha _ { 1 } } , \ldots , H _ { \alpha _ { k } } , X _ { \alpha } \quad ( \alpha \in \Sigma )$ ; confidence 0.432
  
128. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016970/b0169705.png ; $\sigma = 0$ ; confidence 1.000
+
128. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631089.png ; $[ X _ { i } ^ { + } , X _ { j } ^ { - } ] = 2 \delta _ { i j } h ^ { - 1 } \operatorname { sinh } ( h H _ { i } / 2 )$ ; confidence 0.893
  
129. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057620/l05762041.png ; $\alpha \neq \beta$ ; confidence 0.999
+
129. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631088.png ; $[ \alpha , X _ { i } ^ { \pm } ] = \pm \alpha _ { i } ( \alpha ) X _ { i } ^ { \pm } \quad \text { for } a$ ; confidence 0.544
  
130. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031540/d0315402.png ; $G \times G$ ; confidence 0.999
+
130. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130530/s13053016.png ; $e = \frac { | U | } { | G | } ( \sum _ { b \in B } b ) ( \sum _ { w \in W } \operatorname { sign } ( w ) w )$ ; confidence 0.138
  
131. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011300/a011300153.png ; $\mu = 1$ ; confidence 0.999
+
131. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014044.png ; $X \mapsto \operatorname { dim } X = ( \operatorname { dim } _ { K } X _ { j } ) _ { j \in Q _ { 0 } }$ ; confidence 0.819
  
132. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i0523504.png ; $\alpha \delta - \beta \gamma = 1$ ; confidence 0.999
+
132. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140119.png ; $\operatorname { dim } _ { 1 } : K _ { 0 } ( \operatorname { mod } R ) \rightarrow Z ^ { Q _ { 0 } }$ ; confidence 0.287
  
133. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524020.png ; $[ 0,2 ]$ ; confidence 0.999
+
133. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150021.png ; $\omega = 2 \int _ { 0 } ^ { 1 / c } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ ; confidence 0.973
  
134. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025470/c02547040.png ; $2 n + 1$ ; confidence 0.999
+
134. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876010.png ; $y _ { i } = f _ { i } ( g _ { 1 } , \ldots , g _ { i } ; x _ { 1 } , \ldots , x _ { n } ) , \quad i = 1 , \ldots , n$ ; confidence 0.276
  
135. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067280/n06728054.png ; $M ( \lambda )$ ; confidence 0.999
+
135. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r077630104.png ; $\phi _ { 0 } \bigotimes \phi _ { 1 } ^ { Fr } \otimes \ldots \otimes \phi _ { d } ^ { FF ^ { d } }$ ; confidence 0.136
  
136. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450231.png ; $\sigma = 1 / 2$ ; confidence 0.999
+
136. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590440.png ; $X _ { \epsilon } = \{ ( x _ { 0 } , \ldots , x _ { x } ) : f ( x _ { 0 } , \ldots , x _ { x } ) = \epsilon \}$ ; confidence 0.433
  
137. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120485.png ; $( F , \tau ) ^ { \prime } = G$ ; confidence 0.999
+
137. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590515.png ; $\frac { d x _ { i } } { d x _ { i _ { 0 } } } = f _ { i } ( x ) , \quad f _ { i } \in C ( U ) , \quad i \neq i _ { 0 }$ ; confidence 0.594
  
138. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w12009060.png ; $[ \lambda ]$ ; confidence 0.999
+
138. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086100/s08610054.png ; $\{ e \} \rightarrow \Delta \rightarrow \pi \rightarrow Z ^ { s } \rightarrow \{ e \}$ ; confidence 0.972
  
139. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022065.png ; $m - 1$ ; confidence 0.999
+
139. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t1301406.png ; $\Phi ( x ) = \sum _ { j \in Q _ { 0 } } x _ { j } ^ { 2 } - \sum _ { i , j \in Q _ { 0 } } d _ { i j } x _ { i } x _ { j }$ ; confidence 0.648
  
140. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035700/e03570021.png ; $F = \{ V _ { i } \}$ ; confidence 0.999
+
140. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120535.png ; $f ^ { * } ( x ^ { * } ) = \operatorname { sup } _ { x \in X } ( \langle x ^ { * } , x \rangle - f ( x ) )$ ; confidence 0.900
  
141. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763052.png ; $( \delta _ { \phi } , \alpha ) \geq 0$ ; confidence 0.999
+
141. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852046.png ; $\operatorname { dim } \mathfrak { g } _ { i } = \operatorname { dim } \mathfrak { g } - i$ ; confidence 0.901
  
142. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c02057072.png ; $H ^ { 1 } ( X , S ) = 0$ ; confidence 0.999
+
142. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590527.png ; $A = \| \left. \begin{array} { l l } { \alpha } & { b } \\ { c } & { e } \end{array} \right. |$ ; confidence 0.506
  
143. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002056.png ; $\Gamma ( 1 / 4 )$ ; confidence 0.999
+
143. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095410/u0954106.png ; $\{ g \in \operatorname { GL } ( V ) : ( 1 - g ) ^ { n } = 0 \} , \quad n = \operatorname { dim } V$ ; confidence 0.287
  
144. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590106.png ; $z = \phi ( t )$ ; confidence 0.999
+
144. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640132.png ; $0 \rightarrow O _ { V } \rightarrow E _ { \alpha } \rightarrow T _ { V } \rightarrow 0$ ; confidence 0.981
  
145. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690035.png ; $H ^ { i } ( X , F )$ ; confidence 0.999
+
145. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830150.png ; $( \eta _ { 1 } , \ldots , \eta _ { n } ) \rightarrow F ( \zeta _ { 1 } , \ldots , \zeta _ { n } )$ ; confidence 0.376
  
146. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764051.png ; $x ^ { 3 } + x y ^ { 3 } + z ^ { 2 }$ ; confidence 0.999
+
146. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830141.png ; $( \eta _ { 1 } , \ldots , \eta _ { k } ) \rightarrow F ( \zeta _ { 1 } , \ldots , \zeta _ { k } )$ ; confidence 0.562
  
147. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004035.png ; $( 2 g ) \times ( 2 g )$ ; confidence 0.999
+
147. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082059.png ; $( x _ { 1 } , \ldots , x _ { x } ) \circ ( y _ { 1 } , \ldots , y _ { n } ) = ( z _ { 1 } , \ldots , z _ { x } )$ ; confidence 0.553
  
148. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058690/l05869015.png ; $( G ) _ { 0 }$ ; confidence 0.999
+
148. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g1300205.png ; $\alpha ^ { \beta } = \operatorname { exp } \{ \beta \operatorname { log } \alpha \}$ ; confidence 0.979
  
149. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150084.png ; $\int \int R ( x , y , z ) d x d y$ ; confidence 0.999
+
149. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i05235015.png ; $\alpha _ { 1 } , \ldots , i _ { R } \rightarrow \alpha _ { 2 } ^ { \prime } , \ldots , i _ { R }$ ; confidence 0.142
  
150. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690085.png ; $H ^ { 1 } ( \pi _ { 1 } ( M ) , G )$ ; confidence 0.999
+
150. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427030.png ; $H ( C _ { 3 } , \Gamma ) = \{ X \in C _ { 3 } : X = \Gamma ^ { - 1 } X \square ^ { \prime } \Gamma \}$ ; confidence 0.651
  
151. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130530/s13053085.png ; $1 \leq s \leq n$ ; confidence 0.999
+
151. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590158.png ; $A _ { n } , n \geq 1 , \quad B _ { n } , n \geq 2 , \quad C _ { n } , n \geq 3 , \quad D _ { n } , n \geq 4$ ; confidence 0.956
  
152. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002036.png ; $0 < | \alpha | < 1$ ; confidence 0.999
+
152. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058690/l0586905.png ; $B ( F ) = \{ g \in \operatorname { GL } ( V ) : g V _ { i } \subset V _ { i } \text { for all } i \}$ ; confidence 0.454
  
153. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450116.png ; $\operatorname { deg } ( D ) \geq 2 g + 1$ ; confidence 0.999
+
153. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100199.png ; $x _ { 0 } + \sum _ { i = 1 } ^ { \infty } x _ { i } V ^ { i } + \sum _ { j = 1 } ^ { < \infty } y _ { j } f ^ { j }$ ; confidence 0.575
  
154. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058690/l05869027.png ; $\rho ( G ) \subset B ( F )$ ; confidence 0.999
+
154. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851068.png ; $[ [ X _ { \alpha _ { i } } , X _ { - } , _ { i } ] , X _ { \alpha _ { j } } ] = n ( i , j ) X _ { \alpha _ { j } }$ ; confidence 0.186
  
155. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590432.png ; $p ( Z ) = 1$ ; confidence 0.999
+
155. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631087.png ; $[ \alpha _ { 1 } , \alpha _ { 2 } ] = 0 \quad \text { for } \alpha _ { 1 } , \alpha _ { 2 } \in h$ ; confidence 0.597
  
156. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590450.png ; $F ( z , 0 ) = f ( z )$ ; confidence 0.999
+
156. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590226.png ; $U ^ { n } ( \zeta , r ) = \{ z \in C ^ { n } : | z _ { v } - \zeta _ { v } | < R _ { v } , v = 1 , \ldots , n \}$ ; confidence 0.427
  
157. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900132.png ; $H ^ { k } ( G , Z ( A ) )$ ; confidence 0.999
+
157. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100192.png ; $x _ { 0 } + \sum _ { i = 1 } ^ { \infty } x _ { i } V ^ { i } + \sum _ { j = 1 } ^ { \infty } y _ { j } f ^ { i }$ ; confidence 0.498
  
158. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820183.png ; $[ p ] ( X )$ ; confidence 0.999
+
158. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a014170108.png ; $j ( x , \gamma \gamma ^ { \prime } ) = j ( x , \gamma ) j ( x \gamma , \gamma ^ { \prime } )$ ; confidence 0.838
  
159. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090178.png ; $B = T U$ ; confidence 0.999
+
159. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120540.png ; $x , c \in R ^ { n } , \quad ( c , x ) = \sum _ { i = 1 } ^ { n } c _ { i } x _ { i } , \quad y , b \in R ^ { m }$ ; confidence 0.334
  
160. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i0523501.png ; $a x ^ { 2 } + 2 b x y + c y ^ { 2 }$ ; confidence 0.999
+
160. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852019.png ; $\mathfrak { g } _ { i } ^ { \prime } / \mathfrak { g } _ { \mathfrak { i } } ^ { \prime } + 1$ ; confidence 0.518
  
161. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110350/c11035022.png ; $\gamma \in \Gamma$ ; confidence 0.999
+
161. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087060/s08706029.png ; $R ( t _ { 1 } , \ldots , t _ { n } ) = R \bigotimes _ { Z } ( R ) Z ( R ) ( t _ { 1 } , \ldots , t _ { n } )$ ; confidence 0.249
  
162. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097590/w09759042.png ; $\square ( A )$ ; confidence 0.999
+
162. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120240/d12024033.png ; $\operatorname { im } \mathfrak { g } - \operatorname { dim } \mathfrak { g } ( f )$ ; confidence 0.575
  
163. 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
+
163. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120532.png ; $A ^ { 0 } = \{ x ^ { * } \in X ^ { * } : \langle x ^ { * } , x \rangle \leq 1 , \square x \in A \}$ ; confidence 0.424
  
164. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145057.png ; $\pi = \frac { ( m - 1 ) ( m - 2 ) } { 2 }$ ; confidence 0.999
+
164. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120552.png ; $- F ^ { * } ( 0 , y ^ { * } ) \rightarrow \operatorname { sup } , \quad y ^ { * } \in Y ^ { * }$ ; confidence 0.892
  
165. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450113.png ; $P ^ { l } ( D ) - 1$ ; confidence 0.999
+
165. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i05235012.png ; $x _ { i } \rightarrow \sum _ { j = 1 } ^ { n } \alpha _ { i j } x _ { j } , \quad 1 \leq i \leq n$ ; confidence 0.546
  
166. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872038.png ; $U _ { p } ( L )$ ; confidence 0.999
+
166. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690094.png ; $e \rightarrow H ^ { 0 } ( G , B ) \rightarrow H ^ { 0 } ( G , A ) \rightarrow ( A / B ) ^ { G }$ ; confidence 0.580
  
167. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120334.png ; $0 < R , P \leq \infty$ ; confidence 0.999
+
167. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t1301305.png ; $0 \rightarrow \Lambda \rightarrow T _ { 0 } \rightarrow T _ { 1 } \rightarrow 0$ ; confidence 0.974
  
168. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023330/c0233305.png ; $g ( \phi ( x ) ) = \phi ( g ( x ) )$ ; confidence 0.999
+
168. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140109.png ; $j = \operatorname { dim } _ { K } \operatorname { Ext } _ { R } ^ { 2 } ( S _ { j } , s _ { i } )$ ; confidence 0.262
  
169. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690086.png ; $\pi _ { 1 } ( M ) \rightarrow G$ ; confidence 0.999
+
169. 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
  
170. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830343.png ; $k \leq \operatorname { min } ( r , s )$ ; confidence 0.999
+
170. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011740/a01174017.png ; $1 \rightarrow A ( k ) \rightarrow \text { Aut } A \rightarrow G \rightarrow 1$ ; confidence 0.794
  
171. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590461.png ; $F ( x , y , \lambda ) = \Phi _ { \mu + 1 } ( x , \lambda ) - y ^ { 2 }$ ; confidence 0.999
+
171. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120205.png ; $( H ^ { p } ( X , F ) ) ^ { \prime } \cong \operatorname { Ext } ^ { n - p } ( X ; F , \Omega )$ ; confidence 0.667
  
172. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036280/e03628014.png ; $H ^ { 1 } ( X , F )$ ; confidence 0.999
+
172. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852024.png ; $b ( F ) = \{ x \in \mathfrak { g } | ( V ) : x V _ { i } \subset V _ { i } \text { for all } i \}$ ; confidence 0.136
  
173. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410138.png ; $( x , y ) \in G$ ; confidence 0.999
+
173. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310136.png ; $R = ( \rho \otimes \rho ) ( R ) \in \operatorname { End } ( k ^ { n } \otimes k ^ { n } )$ ; confidence 0.930
  
174. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183091.png ; $\{ B \}$ ; confidence 0.999
+
174. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590489.png ; $\operatorname { det } \| \frac { \partial x ^ { i } } { \partial a ^ { j } } \| \neq 0$ ; confidence 0.409
  
175. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074640/p07464031.png ; $H ^ { 1 } ( B , O ^ { G } )$ ; confidence 0.999
+
175. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090295.png ; $\mathfrak { n } ^ { + } = \sum _ { \alpha \in \Phi ^ { + } } \mathfrak { g } _ { \alpha }$ ; confidence 0.882
  
176. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012380/a01238019.png ; $2 n - 1$ ; confidence 0.999
+
176. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090354.png ; $x _ { \alpha } ( t ) = \sum _ { i = 0 } ^ { \infty } t ^ { i } \otimes e _ { \alpha } ^ { i } / i !$ ; confidence 0.841
  
177. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472024.png ; $H ^ { 1 } ( k , \Gamma )$ ; confidence 0.999
+
177. https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100171.png ; $\sum _ { i , j \in \{ 1,2 , \ldots \} } V _ { i } \langle \alpha _ { i j } \rangle f _ { j }$ ; confidence 0.145
  
178. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120548.png ; $F ( x , 0 ) = f ( x )$ ; confidence 0.999
+
178. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031640/d03164018.png ; $F \omega = \omega ^ { ( p ) } F , \quad \omega V = V \omega ^ { ( p ) } , \quad F V = V F = p$ ; confidence 0.970
  
179. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120207.png ; $H ^ { 0 } ( X , F )$ ; confidence 0.999
+
179. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960177.png ; $( \delta _ { i } \alpha ) ^ { 2 } - \alpha _ { i } ^ { 2 } ( 4 \alpha ^ { 3 } - 8 \alpha - 88 )$ ; confidence 0.712
  
180. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065040/m06504010.png ; $V ( k )$ ; confidence 0.999
+
180. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427013.png ; $( \alpha e 0 + u ) ( \beta e 0 + v ) = [ \alpha \beta + f ( u , v ) ] e 0 + \alpha v + \beta u$ ; confidence 0.094
  
181. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310146.png ; $\gamma \subset R ^ { 3 }$ ; confidence 0.999
+
181. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590356.png ; $J ( f ) = ( \partial f / \partial x _ { 0 } , \ldots , \partial f / \partial x _ { n } )$ ; confidence 0.591
  
182. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120410.png ; $G = ( ( F , \tau ) ) ^ { \prime }$ ; confidence 0.999
+
182. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110070/k11007016.png ; $= \{ f : \pi ^ { - 1 } ( U ) \rightarrow k : f ( g b ) = f ( g ) \chi ( b ) , g \in G , b \in B \}$ ; confidence 0.929
  
183. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861026.png ; $( G \times T ) / D$ ; confidence 0.999
+
183. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763061.png ; $k [ G ] _ { \chi } = \{ f \in k [ G ] : f ( g b ) = \chi ( b ) f ( g ) \forall b \in B , g \in G \}$ ; confidence 0.930
  
184. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120446.png ; $( F ^ { \prime } , \sigma ( F ^ { \prime } , F ) )$ ; confidence 0.999
+
184. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s0855907.png ; $f _ { \zeta } = f _ { \zeta } ( z ) = \sum _ { k = 0 } ^ { \infty } c _ { k } ( z - \zeta ) ^ { k }$ ; confidence 0.992
  
185. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700105.png ; $k ( s _ { 0 } ) = k$ ; confidence 0.999
+
185. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150040.png ; $F ( m ) = \sum \alpha _ { j k } m _ { j } m _ { k } , \quad \alpha _ { j k } = \alpha _ { k j }$ ; confidence 0.940
  
186. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970121.png ; $( A , \mu , \epsilon )$ ; confidence 0.999
+
186. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120263.png ; $p _ { Y } ( f ) = \operatorname { max } _ { z \in K _ { R } } | f ( z ) | , \quad f \in A ( G )$ ; confidence 0.227
  
187. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022970/c02297052.png ; $A ^ { G }$ ; confidence 0.999
+
187. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120541.png ; $( b , y ) = \sum _ { i = 1 } ^ { m } b _ { i } y _ { b } , \quad A : R ^ { n } \rightarrow R ^ { m }$ ; confidence 0.277
  
188. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064250/m0642507.png ; $\Delta = 0$ ; confidence 0.999
+
188. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427040.png ; $Q = \left( \begin{array} { l l } { 0 } & { 1 } \\ { 1 } & { 0 } \end{array} \right)$ ; confidence 0.925
  
189. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110070/k11007038.png ; $p ^ { \nu } - 1$ ; confidence 0.999
+
189. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058500/l0585006.png ; $\mathfrak { g } = \mathfrak { z } ( \mathfrak { g } ) \dot { + } \mathfrak { g } 0$ ; confidence 0.735
  
190. 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
+
190. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859071.png ; $z ( s ) = x ( \sqrt { s } ) y ( \sqrt { s } ) x ( \sqrt { s } ) ^ { - 1 } y ( \sqrt { s } ) ^ { - 1 }$ ; confidence 0.991
  
191. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164041.png ; $q ( V ) = 0$ ; confidence 0.999
+
191. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l058720135.png ; $k [ X _ { 1 } , \ldots , X _ { m } ; \square X _ { 1 } ^ { p } = 0 , \ldots , X _ { m } ^ { p } = 0 ]$ ; confidence 0.412
  
192. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090304.png ; $W ( \lambda )$ ; confidence 0.999
+
192. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631061.png ; $\phi : \mathfrak { g } \rightarrow \mathfrak { g } \otimes \mathfrak { g }$ ; confidence 0.982
  
193. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058480/l0584807.png ; $A = K [ G ]$ ; confidence 0.999
+
193. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590470.png ; $F ( x , y , \lambda ) = ( x - \mu ) ( x ^ { 2 } + y ^ { 3 } + \lambda y ^ { 2 } - 6 \lambda x y )$ ; confidence 0.998
  
194. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590654.png ; $F ( x , y , z )$ ; confidence 0.999
+
194. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014066.png ; $( h _ { j } ) ^ { * } ( M _ { i j } ^ { \beta } ) = ( h _ { i } ^ { - 1 } M _ { i j } ^ { \beta } h _ { j } )$ ; confidence 0.942
  
195. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031640/d03164019.png ; $\omega \in W ( k )$ ; confidence 0.999
+
195. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090160.png ; $\langle g x , y \rangle = \langle x , g ^ { T } y \rangle , \quad \forall g \in G$ ; confidence 0.652
  
196. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120436.png ; $\beta ( F , G )$ ; confidence 0.999
+
196. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183044.png ; $h = \operatorname { max } _ { \pi } ( e _ { 1 } \pi ( 1 ) + \ldots + e _ { n } \pi ( n ) )$ ; confidence 0.715
  
197. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559069.png ; $0 \leq t < \tau$ ; confidence 0.999
+
197. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120121.png ; $H _ { r } ( M ^ { n } , X ) | H _ { n - r } ( M ^ { n } , X ^ { * } ) , \quad \text { for } X | X ^ { * }$ ; confidence 0.734
  
198. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164062.png ; $H ^ { 1 } ( V , O _ { V } ( D ) )$ ; confidence 0.999
+
198. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690056.png ; $( \sigma ( \alpha ) ( c ) ) ( g , h ) = \alpha ^ { g } c ( g , h ) ( \alpha ^ { g } ) ^ { - 1 }$ ; confidence 0.301
  
199. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011520/a01152018.png ; $( G , G , \tau )$ ; confidence 0.999
+
199. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081370/r08137022.png ; $\sum _ { \alpha \in I } ( \operatorname { dim } \rho ^ { \alpha } ) ^ { 2 } = | G |$ ; confidence 0.960
  
200. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080900/r08090015.png ; $\alpha \in \phi ( T , G )$ ; confidence 0.999
+
200. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014072.png ; $q ( v ) = \operatorname { dim } G _ { Q } ( v ) - \operatorname { dim } A _ { Q } ( v )$ ; confidence 0.221
  
201. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027270/c0272705.png ; $\neq 2$ ; confidence 0.999
+
201. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164076.png ; $H ^ { p } ( V , \Omega ^ { q } ) = \operatorname { dim } H ^ { q } ( V , \Omega ^ { p } )$ ; confidence 0.943
  
202. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032490/d03249033.png ; $F ( \eta ) = F ( \zeta )$ ; confidence 0.999
+
202. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120235.png ; $\gamma : H _ { X \backslash Y } ^ { p + 1 } ( X , F ) \rightarrow H ^ { p + 1 } ( X , F )$ ; confidence 0.715
  
203. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120237.png ; $\beta$ ; confidence 0.999
+
203. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o07001058.png ; $t ( z _ { 1 } , z _ { 2 } ) = ( e ^ { i t } z _ { 1 } , e ^ { i \alpha t } z _ { 2 } ) , \quad t \in R$ ; confidence 0.800
  
204. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097710/w09771039.png ; $W ( T , G )$ ; confidence 0.999
+
204. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o07001044.png ; $( g f ) ( u , v ) = f ( g ^ { - 1 } ( u ) , g ^ { - 1 } ( v ) ) \quad \text { for any } u , v \in V$ ; confidence 0.987
  
205. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410137.png ; $F ( x , y , \xi , \eta ) > 0$ ; confidence 0.999
+
205. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590376.png ; $x _ { 0 } ^ { \mu - 1 } + x _ { 0 } x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$ ; confidence 0.937
  
206. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120408.png ; $F = ( F , \tau )$ ; confidence 0.999
+
206. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140147.png ; $0 \rightarrow P _ { 1 } \rightarrow P _ { 0 } \rightarrow X \rightarrow 0$ ; confidence 0.747
  
207. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011800/a01180073.png ; $n ^ { 2 }$ ; confidence 0.999
+
207. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093350/t0933508.png ; $K = ( \operatorname { cos } u ) / a l ( 1 + \epsilon \operatorname { cos } u )$ ; confidence 0.499
  
208. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590109.png ; $z = \phi ( t ) \in U ( \zeta , R )$ ; confidence 0.999
+
208. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c02057019.png ; $\rho ( e _ { i } ) v = 0 , \quad \rho ( h _ { i } ) v = k _ { i } v , \quad i = 1 , \dots , r$ ; confidence 0.484
  
209. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764025.png ; $E = \pi ^ { - 1 } ( P )$ ; confidence 0.999
+
209. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070052.png ; $\gamma : H ^ { 1 } ( X _ { 0 } , \Theta ) \rightarrow H ^ { 2 } ( X _ { 0 } , \Theta )$ ; confidence 0.700
  
210. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590377.png ; $\mu \geq 4$ ; confidence 0.999
+
210. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120244.png ; $H _ { c } ^ { n - p - 1 } ( X \backslash Y , \operatorname { Hom } ( F , \Omega ) )$ ; confidence 0.923
  
211. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559052.png ; $( U ( \zeta , r ) , f _ { \zeta } )$ ; confidence 0.999
+
211. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120424.png ; $A ^ { o } = \{ y \in G : \operatorname { Re } ( x , y ) \leq 1 , \forall x \in A \}$ ; confidence 0.603
  
212. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010930/a01093032.png ; $n + 1$ ; confidence 0.999
+
212. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960187.png ; $X _ { 0 } X _ { 2 } ^ { 2 } - ( 4 X _ { 1 } ^ { 3 } - 8 X _ { 0 } ^ { 2 } X _ { 1 } - 8 X _ { 0 } ^ { 3 } ) = 0$ ; confidence 0.432
  
213. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150079.png ; $x _ { 0 } ^ { 3 } x _ { 1 } + x _ { 1 } ^ { 3 } x _ { 2 } + x _ { 2 } ^ { 3 } x _ { 0 } = 0$ ; confidence 0.999
+
213. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851045.png ; $H _ { \alpha } \in [ \mathfrak { g } _ { \alpha } , \mathfrak { g } - \alpha ]$ ; confidence 0.566
  
214. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830152.png ; $G \neq 0$ ; confidence 0.999
+
214. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859082.png ; $\operatorname { exp } X = \sum _ { m = 0 } ^ { \infty } \frac { 1 } { m ! } X ^ { m }$ ; confidence 0.976
  
215. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830116.png ; $\{ A \}$ ; confidence 0.999
+
215. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690078.png ; $\rho ( f ) ( \alpha ) = d f \cdot f ^ { - 1 } + ( \operatorname { Ad } f ) \alpha$ ; confidence 0.231
  
216. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o0700104.png ; $G ( x ) = \{ g ( x ) : g \in G \}$ ; confidence 0.999
+
216. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093350/t09335012.png ; $x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } = a ^ { 2 } , \quad x _ { 3 } ^ { 2 } + x _ { 4 } ^ { 2 } = b ^ { 2 }$ ; confidence 0.863
  
217. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014052.png ; $( Q )$ ; confidence 0.999
+
217. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700167.png ; $\tilde { \rho } : \tilde { \kappa } \rightarrow \tilde { M } _ { X _ { 0 } }$ ; confidence 0.601
  
218. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011460/a01146063.png ; $p > 1$ ; confidence 0.999
+
218. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830344.png ; $\operatorname { rank } ( A _ { i } ) = \operatorname { rank } ( B _ { i } )$ ; confidence 0.983
  
219. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062620/m06262059.png ; $\mu \geq 1$ ; confidence 0.999
+
219. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082053.png ; $= F _ { i } ( F _ { 1 } ( X , Y ) , \ldots , F _ { n } ( X , Y ) , Z _ { 1 } , \ldots , Z _ { n } )$ ; confidence 0.658
  
220. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410112.png ; $\beta = \alpha - \sigma ( \alpha )$ ; confidence 0.999
+
220. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082052.png ; $F _ { i } ( X _ { 1 } , \ldots , X _ { n } , F _ { 1 } ( Y , Z ) , \ldots , F _ { n } ( Y , Z ) ) =$ ; confidence 0.659
  
221. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590190.png ; $f ( x ) f ( y ) = f ( x y )$ ; confidence 0.999
+
221. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900125.png ; $G \rightarrow \text { Out } A = \text { Aut } A / \operatorname { Int } A$ ; confidence 0.290
  
222. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011530/a01153020.png ; $\alpha \neq 0,1$ ; confidence 0.999
+
222. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690058.png ; $\alpha \in C ^ { 0 } , \quad b \in C ^ { 1 } , \quad c \in C ^ { 2 } , \quad g \in G$ ; confidence 0.173
  
223. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690098.png ; $H ^ { 1 } ( G , A / B )$ ; confidence 0.999
+
223. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q076310140.png ; $T _ { 1 } = T \otimes 1 \in \operatorname { End } ( k ^ { n } \otimes k ^ { n } )$ ; confidence 0.284
  
224. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861085.png ; $\Gamma = g ( \Gamma _ { 1 } )$ ; confidence 0.999
+
224. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631052.png ; $\{ a , b \} = \operatorname { lim } _ { h \rightarrow 0 } h ^ { - 1 } ( a b - b a )$ ; confidence 0.345
  
225. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763048.png ; $\delta _ { \phi } \in P _ { \phi }$ ; confidence 0.999
+
225. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014060.png ; $M _ { v _ { i } \times v _ { j } } ( K ) _ { \beta } = M _ { v _ { i } \times v _ { j } } ( K )$ ; confidence 0.814
  
226. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090385.png ; $W ( \lambda ) ^ { \lambda }$ ; confidence 0.999
+
226. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097590/w09759034.png ; $\phi = \sum \phi _ { v } : WC ( A , k ) \rightarrow \sum _ { v } WC ( A , k _ { v } )$ ; confidence 0.221
  
227. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047700/h04770018.png ; $\psi : G / H \rightarrow M$ ; confidence 0.999
+
227. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090100.png ; $\lambda = ( \lambda _ { 1 } , \ldots , \lambda _ { n } ) \in \Lambda ( n , r )$ ; confidence 0.455
  
228. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450104.png ; $\operatorname { deg } D = n$ ; confidence 0.999
+
228. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h047690105.png ; $P ( G / H , t ) = \prod _ { i = 1 } ^ { r } \frac { 1 - t ^ { 2 k } i } { 1 - t ^ { 2 l _ { i } } }$ ; confidence 0.529
  
229. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164042.png ; $q ( V ) > 0$ ; confidence 0.999
+
229. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h04769085.png ; $( g , f ) \sim ( g h ^ { - 1 } , h f ) , \quad g \in G , \quad k \in H , \quad f \in F$ ; confidence 0.494
  
230. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820112.png ; $F ( X , Y ) = f ^ { - 1 } ( f ( X ) + f ( Y ) )$ ; confidence 0.999
+
230. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851071.png ; $( \text { ad } X _ { - } \alpha _ { i } ) ^ { 1 - n ( i , j ) } X _ { - } \alpha _ { j } = 0$ ; confidence 0.289
  
231. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120381.png ; $f ^ { * } ( z ) \in B ^ { 1 }$ ; confidence 0.999
+
231. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590498.png ; $\frac { d x _ { 1 } } { X _ { 1 } ( x ) } = \ldots = \frac { d x _ { x } } { X _ { x } ( x ) }$ ; confidence 0.695
  
232. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763047.png ; $V ( \delta _ { \phi } )$ ; confidence 0.999
+
232. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590138.png ; $V ^ { \prime } ( \alpha ) = \{ z \in \overline { C } : 0 < | z - \alpha | < R \}$ ; confidence 0.853
  
233. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023250/c02325068.png ; $1 \leq k \leq n$ ; confidence 0.999
+
233. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054078.png ; $\{ \alpha , b \} _ { p } = ( - 1 ) ^ { \alpha \beta } r ^ { \beta } s ^ { \alpha }$ ; confidence 0.934
  
234. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040600/f04060023.png ; $f ^ { - 1 } ( f ( x ) )$ ; confidence 0.999
+
234. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097710/w09771045.png ; $X ( T _ { 0 } / Z ( G ) ^ { 0 } ) _ { Q } = X ( T _ { 0 } / Z ( G ) ^ { 0 } ) \bigotimes _ { Z } Q$ ; confidence 0.558
  
235. 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
+
235. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090106.png ; $y _ { \lambda } = \sum _ { \pi \in C ( t ) } \operatorname { sg } ( \pi ) \pi$ ; confidence 0.648
  
236. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h047690123.png ; $G = \operatorname { Spin } ( 7 )$ ; confidence 0.999
+
236. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090109.png ; $z _ { \lambda } = e _ { \lambda } y _ { \lambda } \in E \otimes ^ { \gamma }$ ; confidence 0.166
  
237. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450244.png ; $f : V \rightarrow B$ ; confidence 0.999
+
237. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164011.png ; $p ^ { ( 1 ) } = ( K _ { V } ^ { 2 } ) + 1 = \operatorname { deg } ( c _ { 1 } ^ { 2 } ) + 1$ ; confidence 0.919
  
238. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640135.png ; $O _ { V }$ ; confidence 0.999
+
238. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d03070043.png ; $T _ { \emptyset } ( S ) \rightarrow H ^ { 1 } ( X _ { \diamond } , \Theta )$ ; confidence 0.185
  
239. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023150/c023150179.png ; $\{ \Phi \}$ ; confidence 0.999
+
239. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830164.png ; $( t _ { 1 } , \ldots , t _ { n } , u ) \rightarrow F ( 0 , \ldots , 0 , \alpha )$ ; confidence 0.606
  
240. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023720/c02372033.png ; $( U ( \zeta , R ) , f _ { \zeta } )$ ; confidence 0.999
+
240. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830160.png ; $u = \frac { F ( t _ { 1 } , \ldots , t _ { x } ) } { G ( t _ { 1 } , \ldots , t _ { x } ) }$ ; confidence 0.902
  
241. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081490/r08149043.png ; $V ( \lambda )$ ; confidence 0.999
+
241. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120468.png ; $f \in ( F ^ { \prime } , \sigma ( F ^ { \prime } , F ) ) \square ^ { \prime }$ ; confidence 0.990
  
242. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450100.png ; $J ( X )$ ; confidence 0.999
+
242. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267014.png ; $T \rightarrow H ^ { 1 } ( T _ { f } p q c , G _ { m } ) = H ^ { 1 } ( T _ { et } , G _ { m } )$ ; confidence 0.492
  
243. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110250/c1102505.png ; $( p , q )$ ; confidence 0.999
+
243. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590381.png ; $x _ { 0 } ^ { 3 } x _ { 1 } + x _ { 1 } ^ { 3 } + x _ { 2 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$ ; confidence 0.934
  
244. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032150/d032150200.png ; $\Delta > 0$ ; confidence 0.999
+
244. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s130540122.png ; $= y ( - b ( 1 + a b ) ^ { - 1 } ) x ( a ) y ( b ) x ( - ( 1 + a b ) ^ { - 1 } a ) h ( 1 + a b ) ^ { - 1 }$ ; confidence 0.572
  
245. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120351.png ; $\phi ( \zeta ) \equiv 0$ ; confidence 0.999
+
245. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524049.png ; $F ^ { - 1 } ( y ) = \operatorname { inf } \{ x : F ( x ) \leq y \leq F ( x + 0 ) \}$ ; confidence 0.904
  
246. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700173.png ; $X ^ { \prime } \rightarrow R ^ { \prime }$ ; confidence 0.999
+
246. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097590/w09759027.png ; $\phi _ { v } : \operatorname { WC } ( A , k ) \rightarrow WC ( A , k _ { v } )$ ; confidence 0.456
  
247. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640146.png ; $\omega \leq \operatorname { dim } H ^ { 2 } ( V , E _ { \alpha } )$ ; confidence 0.999
+
247. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150012.png ; $( x , \sqrt { f ( x ) } ) \oplus ( c , \sqrt { f ( c ) } ) = ( y , \sqrt { f ( y ) } )$ ; confidence 0.980
  
248. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590490.png ; $X ( x , y ) d y = Y ( x , y ) d x$ ; confidence 0.999
+
248. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700137.png ; $\kappa ^ { \prime } \rightarrow \operatorname { Spec } \Lambda$ ; confidence 0.898
  
249. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820160.png ; $( A , \pi )$ ; confidence 0.999
+
249. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851070.png ; $( \text { ad } X _ { \alpha _ { i } } ) ^ { 1 - n ( i , j ) } X _ { \alpha _ { j } } = 0$ ; confidence 0.438
  
250. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059250/l05925058.png ; $[ \Gamma : H ]$ ; confidence 0.999
+
250. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o07001086.png ; $| X / G | = \frac { 1 } { | G | } \sum _ { g \in G } | \operatorname { Fix } g |$ ; confidence 0.300
  
251. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559049.png ; $\tau _ { 1 } - \epsilon < \tau ^ { \prime } < \tau _ { 1 }$ ; confidence 0.999
+
251. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267053.png ; $f ^ { \prime } : X ^ { \prime } = X \times S S ^ { \prime } \rightarrow S$ ; confidence 0.259
  
252. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014120/a01412076.png ; $n ( n - 1 ) / 2$ ; confidence 0.999
+
252. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763029.png ; $V ( \chi ) = \{ v \in V : \phi ( t ) v = \chi ( t ) v \forall t \in T \} \neq 0$ ; confidence 0.311
  
253. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081030/r08103019.png ; $Z ( S )$ ; confidence 0.999
+
253. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031640/d03164021.png ; $D _ { k } / D _ { k } V ^ { n } \simeq \operatorname { End } _ { k } ( W _ { n k }$ ; confidence 0.576
  
254. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797081.png ; $U ( \pi ( G , K ) )$ ; confidence 0.999
+
254. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830322.png ; $\operatorname { deg } _ { A } ( F ) < \operatorname { deg } _ { A } ( A )$ ; confidence 0.907
  
255. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035550/e03555059.png ; $k = 0$ ; confidence 0.999
+
255. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830310.png ; $\operatorname { deg } _ { A } ( A ) = \operatorname { deg } _ { A } ( B )$ ; confidence 0.865
  
256. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a0115009.png ; $s ^ { - 1 } d t$ ; confidence 0.999
+
256. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830306.png ; $\operatorname { deg } _ { A } ( A ) < \operatorname { deg } _ { A } ( B )$ ; confidence 0.560
  
257. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830224.png ; $F _ { 1 }$ ; confidence 0.999
+
257. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120508.png ; $( f , g ) = \sum _ { \alpha } ( f _ { \alpha } , g _ { \alpha } ) _ { \alpha }$ ; confidence 0.947
  
258. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040370/f04037016.png ; $H ^ { k } ( X , F )$ ; confidence 0.999
+
258. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120522.png ; $\| f | H \| = \operatorname { dist } ( f , H ^ { 0 } ) , \quad f \in F ^ { * }$ ; confidence 0.990
  
259. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820179.png ; $[ 1 ] ( X ) = X$ ; confidence 0.999
+
259. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i05235025.png ; $\Delta = 3 b ^ { 2 } c ^ { 2 } + 6 a b c d - 4 b ^ { 3 } d - 4 a c ^ { 3 } - a ^ { 2 } d ^ { 2 }$ ; confidence 0.992
  
260. 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
+
260. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427038.png ; $J _ { \Im } : X \rightarrow S _ { \square } ^ { \prime } X ^ { \prime } S$ ; confidence 0.174
  
261. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120348.png ; $\phi \in \Omega$ ; confidence 0.999
+
261. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087060/s08706024.png ; $S K _ { 1 } ( R ) \simeq \operatorname { SL } ( 1 , R ) / [ R ^ { * } , R ^ { * } ]$ ; confidence 0.445
  
262. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032780/d03278014.png ; $G \subset R ^ { 2 }$ ; confidence 0.999
+
262. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090294.png ; $\mathfrak { b } ^ { + } = \mathfrak { h } \oplus \mathfrak { n } ^ { + }$ ; confidence 0.723
  
263. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054024.png ; $\pi : H \rightarrow G$ ; confidence 0.999
+
263. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023470/c02347043.png ; $j = 1 , \ldots , n _ { \alpha } = \operatorname { dim } R ^ { \alpha }$ ; confidence 0.704
  
264. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012540/a01254012.png ; $D = G$ ; confidence 0.999
+
264. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700219.png ; $\tilde { p } : \tilde { \kappa } \rightarrow \hat { M } _ { X _ { 0 } }$ ; confidence 0.375
  
265. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700172.png ; $R ^ { \prime } \rightarrow R$ ; confidence 0.999
+
265. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120245.png ; $\alpha ( z ) = \sum _ { x = 0 } ^ { \infty } \frac { a _ { x } } { z ^ { x + 1 } }$ ; confidence 0.561
  
266. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830361.png ; $A \subset I$ ; confidence 0.999
+
266. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960202.png ; $B _ { \nu } = y ^ { \prime \prime } + x ^ { - 1 } + ( 1 - \nu ^ { 2 } x ^ { - 2 } ) y$ ; confidence 0.963
  
267. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011520/a01152024.png ; $( G , V , \tau )$ ; confidence 0.999
+
267. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082060.png ; $z _ { i } = F _ { i } ( x _ { 1 } , \ldots , x _ { n } , y _ { 1 } , \ldots , y _ { n } )$ ; confidence 0.408
  
268. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590644.png ; $G ( x , y , z ) = 0$ ; confidence 0.999
+
268. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i05235032.png ; $f _ { i } ( x _ { 1 } , \ldots , x _ { n } ) = \sum _ { j = 1 } ^ { n } a _ { j } x _ { j }$ ; confidence 0.612
  
269. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081370/r08137025.png ; $\{ \rho ^ { \alpha } : \alpha \in I \}$ ; confidence 0.999
+
269. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058500/l05850020.png ; $: \mathfrak { h } \rightarrow \mathfrak { g } ( \mathfrak { g } )$ ; confidence 0.180
  
270. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410130.png ; $I = \int F d t$ ; confidence 0.999
+
270. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267011.png ; $f ^ { \prime } : X \times s S ^ { \prime } \rightarrow S ^ { \prime }$ ; confidence 0.505
  
271. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861035.png ; $( [ x , y ] , z ) + ( y , [ x , z ] ) = 0$ ; confidence 0.999
+
271. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086830/s0868309.png ; $B = B _ { 0 } \supset B _ { 1 } \supset \ldots \supset B _ { t } = \{ 1 \}$ ; confidence 0.917
  
272. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763098.png ; $k = p > 0$ ; confidence 0.999
+
272. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054040.png ; $\operatorname { diag } ( \alpha , \alpha ^ { - 1 } , 1,1 , \ldots )$ ; confidence 0.671
  
273. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110160/f110160109.png ; $i < j$ ; confidence 0.999
+
273. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t13013048.png ; $\operatorname { Ext } _ { \Lambda } ^ { 1 } ( T , ) : F \rightarrow X$ ; confidence 0.653
  
274. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145033.png ; $P ( X )$ ; confidence 0.999
+
274. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140157.png ; $\chi _ { K I } : K _ { 0 } ( \operatorname { prin } K l ) \rightarrow Z$ ; confidence 0.497
  
275. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524026.png ; $[ 0,3 ]$ ; confidence 0.999
+
275. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095410/u09541046.png ; $G _ { \alpha } \times \ldots \times G _ { \alpha } \rightarrow U$ ; confidence 0.129
  
276. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074640/p07464013.png ; $p : V \rightarrow B$ ; confidence 0.999
+
276. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014170/a0141703.png ; $f ( \gamma ( x ) ) = f ( x ) , \quad x \in M , \quad \gamma \in \Gamma$ ; confidence 0.691
  
277. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120140.png ; $( n - r - 1 )$ ; confidence 0.998
+
277. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c02057062.png ; $0 \rightarrow S \rightarrow F \rightarrow G \rightarrow 0$ ; confidence 0.972
  
278. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559064.png ; $\phi ( 0 ) = \zeta$ ; confidence 0.998
+
278. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023330/c02333031.png ; $f = a _ { 0 } x ^ { 3 } + 3 a _ { 1 } x ^ { 2 } y + 3 a _ { 2 } x y ^ { 2 } + a _ { 3 } y ^ { 3 }$ ; confidence 0.852
  
279. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851049.png ; $[ X _ { \alpha } , Y _ { \alpha } ] = H _ { \alpha }$ ; confidence 0.998
+
279. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120378.png ; $\operatorname { sup } _ { f \in B ^ { 1 } } | f ^ { \prime } ( z _ { 0 } ) |$ ; confidence 0.660
  
280. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110070/k11007041.png ; $G / B \times G / B$ ; confidence 0.998
+
280. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970136.png ; $\iota * \text { id } = \text { id } * _ { \iota } = e \circ \epsilon$ ; confidence 0.102
  
281. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150080.png ; $f : X \rightarrow P ^ { 1 }$ ; confidence 0.998
+
281. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851066.png ; $X _ { \alpha _ { i } } , X _ { - \alpha _ { i } } \quad ( i = 1 , \ldots , n )$ ; confidence 0.447
  
282. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120413.png ; $( x , x ^ { \prime } ) = x ^ { \prime } ( x )$ ; confidence 0.998
+
282. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872082.png ; $L _ { 0 } = < e _ { 1 } , \ldots , e _ { \gamma } : e _ { z } ^ { [ p ] } = e _ { i } >$ ; confidence 0.131
  
283. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022530/c02253040.png ; $\pi _ { 1 } ( M )$ ; confidence 0.998
+
283. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058770/l05877094.png ; $T ^ { 2 } = \{ ( z _ { 1 } , z _ { 2 } ) : z _ { i } \in C , | z _ { i } | = 1 , i = 1,2 \}$ ; confidence 0.972
  
284. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120445.png ; $( F , \sigma ( F , G ) ) ^ { \prime }$ ; confidence 0.998
+
284. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004014.png ; $H ^ { L } = \{ z \in H : \operatorname { Im } z > L \} \text { for } L > 0$ ; confidence 0.977
  
285. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120493.png ; $X ^ { * } = ( X ^ { \prime } , \beta ( X ^ { \prime } , X ) )$ ; confidence 0.998
+
285. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150079.png ; $x _ { 0 } ^ { 3 } x _ { 1 } + x _ { 1 } ^ { 3 } x _ { 2 } + x _ { 2 } ^ { 3 } x _ { 0 } = 0$ ; confidence 0.999
  
286. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s08559034.png ; $z = \phi _ { 1 } ( t )$ ; confidence 0.998
+
286. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150039.png ; $v = ( v _ { 1 } , \ldots , v _ { p } ) , \quad ( m , v ) = \sum m _ { i } v _ { i }$ ; confidence 0.458
  
287. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l0585902.png ; $\mu : ( x , y ) \rightarrow x y ^ { - 1 }$ ; confidence 0.998
+
287. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120507.png ; $\{ \alpha : g _ { \alpha } \neq 0 \square \text { is finite } \}$ ; confidence 0.495
  
288. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590470.png ; $F ( x , y , \lambda ) = ( x - \mu ) ( x ^ { 2 } + y ^ { 3 } + \lambda y ^ { 2 } - 6 \lambda x y )$ ; confidence 0.998
+
288. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d03412098.png ; $H _ { r } ( R , X ) | H ^ { r } ( R , X ^ { * } ) , \quad \text { for } X | X ^ { * }$ ; confidence 0.972
  
289. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150031.png ; $l ( D ) \geq \operatorname { deg } ( D ) - p + 1$ ; confidence 0.998
+
289. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e036960194.png ; $y ^ { ( n ) } + \alpha _ { 1 } y ^ { ( n - 1 ) } + \ldots + \alpha _ { n } y = 0$ ; confidence 0.817
  
290. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590104.png ; $L ( G / H ) \cong L ( G ) / L ( H )$ ; confidence 0.998
+
290. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820105.png ; $G _ { \alpha } ( X , Y ) = ( X _ { 1 } + Y _ { 1 } , \ldots , X _ { n } + Y _ { n } )$ ; confidence 0.419
  
291. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524031.png ; $0 \leq x \leq n$ ; confidence 0.998
+
291. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h04741010.png ; $f ( t _ { 1 } ^ { 0 } , \ldots , t _ { x } ^ { 0 } , x _ { 1 } , \ldots , x _ { x } )$ ; confidence 0.418
  
292. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082097.png ; $\alpha ( \beta ( X ) ) = X$ ; confidence 0.998
+
292. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h04769076.png ; $[ \mathfrak { m } , \mathfrak { m } ] \subseteq \mathfrak { f }$ ; confidence 0.914
  
293. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120186.png ; $( F , \Omega )$ ; confidence 0.998
+
293. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690030.png ; $( \sigma ( a ) ( c ) ) _ { i j k } = \alpha _ { i } c _ { i j k } a _ { i } ^ { - 1 }$ ; confidence 0.186
  
294. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872099.png ; $L = L _ { k } / Z ( L _ { k } )$ ; confidence 0.998
+
294. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900117.png ; $\phi ^ { \prime } ( g ) = ( \operatorname { Int } h ( g ) ) \phi ( g )$ ; confidence 0.698
  
295. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a0114506.png ; $k ( x , y )$ ; confidence 0.998
+
295. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590383.png ; $x _ { 0 } ^ { 5 } + x _ { 1 } ^ { 3 } + x _ { 2 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$ ; confidence 0.985
  
296. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427018.png ; $C ( V , f )$ ; confidence 0.998
+
296. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590379.png ; $x _ { 0 } ^ { 4 } + x _ { 1 } ^ { 3 } + x _ { 2 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$ ; confidence 0.987
  
297. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074720/p07472082.png ; $\Gamma \times E \rightarrow E$ ; confidence 0.998
+
297. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590467.png ; $F ( x , y , \lambda ) = ( x - \mu ) ( x ^ { 2 } - \lambda y ^ { 2 } ) + y ^ { 4 }$ ; confidence 1.000
  
298. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064060/m06406040.png ; $G ( y )$ ; confidence 0.998
+
298. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014069.png ; $M _ { i j } ^ { \beta } \in M _ { v _ { j } \times v _ { i } } ( K ) _ { \beta }$ ; confidence 0.705
  
299. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047410/h047410161.png ; $R ^ { G }$ ; confidence 0.998
+
299. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014026.png ; $X = ( X _ { i } , \phi _ { \beta } ) _ { j \in Q _ { 0 } , } \beta \in Q _ { 1 }$ ; confidence 0.354
  
300. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077640/r07764057.png ; $A ^ { 3 }$ ; confidence 0.998
+
300. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640146.png ; $\omega \leq \operatorname { dim } H ^ { 2 } ( V , E _ { \alpha } )$ ; confidence 0.999

Latest revision as of 16:00, 26 October 2019

List

1. j0543406.png ; $J _ { m } ( \lambda ) = \| \begin{array} { c c c c c c } { \lambda } & { 1 } & { \square } & { \square } & { \square } & { \square } \\ { \square } & { \lambda } & { 1 } & { \square } & { 0 } & { \square } \\ { \square } & { \square } & { \cdots } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { \cdots } & { \square } & { \square } \\ { \square } & { 0 } & { \square } & { \square } & { \lambda } & { 1 } \\ { \square } & { \square } & { \square } & { \square } & { \square } & { \lambda } \end{array} ]$ ; confidence 0.098

2. l058510132.png ; $\left. \begin{array} { r l l l l l l l } { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right.$ ; confidence 0.354

3. l058510129.png ; $\| \left. \begin{array} { r r r r r r r } { 2 } & { - 1 } & { 0 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 } \\ { - 1 } & { 2 } & { - 1 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { 2 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { - 1 } & { 2 } & { - 1 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 0 } & { - 1 } & { 2 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 0 } & { - 1 } & { 0 } & { 2 } \end{array} \right. |$ ; confidence 0.055

4. l058510131.png ; $\left\| \begin{array} { r r r r r r r } { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right\|$ ; confidence 0.278

5. l058510127.png ; $\left\| \begin{array} { r r r r r r } { 2 } & { - 1 } & { 0 } & { \dots } & { 0 } & { 0 } \\ { - 1 } & { 2 } & { - 1 } & { \dots } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { 2 } & { \dots } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 2 } & { - 2 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { - 1 } & { 2 } \end{array} \right\|$ ; confidence 0.232

6. j0543403.png ; $J = \left| \begin{array} { c c c c } { J _ { n _ { 1 } } ( \lambda _ { 1 } ) } & { \square } & { \square } & { \square } \\ { \square } & { \ldots } & { \square } & { 0 } \\ { 0 } & { \square } & { \ldots } & { \square } \\ { \square } & { \square } & { \square } & { J _ { n _ { S } } ( \lambda _ { s } ) } \end{array} \right|$ ; confidence 0.072

7. c02333033.png ; $H = \frac { 1 } { 36 } \left| \begin{array} { c c } { \frac { \partial ^ { 2 } f } { \partial x ^ { 2 } } } & { \frac { \partial ^ { 2 } f } { \partial x \partial y } } \\ { \frac { \partial ^ { 2 } f } { \partial x \partial y } } & { \frac { \partial ^ { 2 } f } { \partial y ^ { 2 } } } \end{array} \right| =$ ; confidence 0.956

8. l058510130.png ; $\left\| \begin{array} { r r r r r r } { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } \\ { - 1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right\|$ ; confidence 0.628

9. u09524027.png ; $u _ { 3 } ( x ) = \left\{ \begin{array} { l l } { \frac { x ^ { 2 } } { 2 } , } & { 0 \leq x < 1 } \\ { \frac { [ x ^ { 2 } - 3 ( x - 1 ) ^ { 2 } ] } { 2 } , } & { 1 \leq x < 2 } \\ { \frac { [ x ^ { 2 } - 3 ( x - 1 ) ^ { 2 } + 3 ( x - 2 ) ^ { 2 } ] } { 2 } , } & { 2 \leq x < 3 } \\ { 0 , } & { x \notin [ 0,3 ] } \end{array} \right.$ ; confidence 0.733

10. l058510133.png ; $\left\| \begin{array} { r r r r } { 2 } & { - 1 } & { 0 } & { 0 } \\ { - 1 } & { 2 } & { - 2 } & { 0 } \\ { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right\| , \quad G _ { 2 } : \quad \left\| \begin{array} { r r } { 2 } & { - 1 } \\ { - 3 } & { 2 } \end{array} \right\|$ ; confidence 0.374

11. c02333035.png ; $( \alpha _ { 0 } , \alpha _ { 1 } , \alpha _ { 2 } , \alpha _ { 3 } ) \mapsto ( \alpha _ { 0 } \alpha _ { 2 } - \alpha _ { 1 } ^ { 2 } , \frac { 1 } { 2 } ( \alpha _ { 0 } \alpha _ { 3 } - \alpha _ { 1 } \alpha _ { 2 } ) , \alpha _ { 1 } \alpha _ { 3 } - \alpha _ { 2 } ^ { 2 } )$ ; confidence 0.521

12. s085590458.png ; $= \left\{ \begin{array} { l l } { ( x + \lambda ) ^ { 2 } \ldots ( x + k \lambda ) ^ { 2 } } & { \text { if } \mu = 2 k } \\ { ( x + \lambda ) ^ { 2 } \ldots ( x + k \lambda ) ^ { 2 } ( x + ( k + 1 ) \lambda ) } & { \text { if } \mu = 2 k + 1 } \end{array} \right.$ ; confidence 0.870

13. l05851074.png ; $[ X _ { \alpha } , X _ { \beta } ] = \left\{ \begin{array} { l l } { N _ { \alpha , \beta } X _ { \alpha + \beta } } & { \text { if } \alpha + \beta \in \Sigma } \\ { 0 } & { \text { if } \alpha + \beta \notin \Sigma } \end{array} \right.$ ; confidence 0.988

14. l05876052.png ; $\left. \begin{array} { c } { c _ { i j } ^ { k } = - c _ { j i } ^ { k } } \\ { \sum _ { l = 1 } ^ { r } ( c _ { i l } ^ { m } c _ { j k } ^ { l } + c _ { k l } ^ { m } c _ { i j } ^ { l } + c _ { j l } ^ { m } c _ { k i } ^ { l } ) = 0 , \quad 1 \leq i , j , k , l , m \leq r } \end{array} \right.$ ; confidence 0.085

15. d034120376.png ; $\operatorname { sup } _ { f \in B ^ { 1 } } | \int _ { \partial G } f ( \zeta ) \omega ( \zeta ) d \zeta | = \operatorname { inf } _ { \phi \in E ^ { 1 } } \int _ { \partial G } | \omega ( \zeta ) - \phi ( \zeta ) \| d \zeta |$ ; confidence 0.508

16. s085590645.png ; $\left| \begin{array} { l l l } { F _ { X } ^ { \prime } } & { F _ { y } ^ { \prime } } & { F _ { z } ^ { \prime } } \\ { G _ { \chi } ^ { \prime } } & { G _ { y } ^ { \prime } } & { G _ { Z } ^ { \prime } } \end{array} \right|$ ; confidence 0.230

17. a01150078.png ; $\left( \begin{array} { l l } { \alpha } & { b } \\ { c } & { d } \end{array} \right) \equiv \left( \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) ( \operatorname { mod } 7 )$ ; confidence 0.440

18. t130140104.png ; $q R ( x ) = \sum _ { j \in Q _ { 0 } } x _ { j } ^ { 2 } - \sum _ { \langle \beta : i \rightarrow j ) \in Q _ { 1 } } x _ { i } x _ { j } + \sum _ { \langle \beta : i \rightarrow j ) \in Q _ { 1 } } x _ { , j } x _ { i } x _ { j }$ ; confidence 0.112

19. l05876037.png ; $\sum _ { k = 1 } ^ { N } ( \xi _ { i k } \frac { \partial \xi _ { j l } } { \partial x _ { k } } - \xi _ { j k } \frac { \partial \xi _ { i l } } { \partial x _ { k } } ) = \sum _ { k = 1 } ^ { r } c _ { i j } ^ { k } \xi _ { k l }$ ; confidence 0.157

20. q07631092.png ; $\sum _ { k = 0 } ^ { n } ( - 1 ) ^ { k } \left( \begin{array} { l } { n } \\ { k } \end{array} \right) q ^ { - k ( n - k ) / 2 } ( X _ { i } ^ { \pm } ) ^ { k } X _ { j } ^ { \pm } \cdot ( X _ { i } ^ { \pm } ) ^ { n - k } = 0$ ; confidence 0.055

21. q07631099.png ; $\Delta ( X _ { i } ^ { \pm } ) = X _ { i } ^ { \pm } \bigotimes \operatorname { exp } ( \frac { h H _ { i } } { 4 } ) + \operatorname { exp } ( \frac { - h H _ { i } } { 4 } ) \otimes x _ { i } ^ { \pm }$ ; confidence 0.212

22. g04521075.png ; $\left. \begin{array} { l l l } { A } & { \rightarrow Y } & { \square } \\ { \downarrow } & { \square } & { } & { \square } \\ { X } & { \square } & { } & { A } \end{array} \right.$ ; confidence 0.226

23. a01145065.png ; $g \leq \left\{ \begin{array} { l l } { \frac { ( n - 2 ) ^ { 2 } } { 4 } } & { \text { for even } n } \\ { \frac { ( n - 1 ) ( n - 3 ) } { 4 } } & { \text { for odd } n } \end{array} \right.$ ; confidence 0.698

24. s13054017.png ; $( x _ { i j } ( a ) , x _ { k l } ( b ) ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } i \neq 1 , j \neq k } \\ { x _ { 1 } ( a b ) } & { \text { if } i \neq 1 , j = k } \end{array} \right.$ ; confidence 0.381

25. t13014048.png ; $[ X ] \mapsto \chi _ { Q } ( [ X ] ) = \operatorname { dim } _ { K } \operatorname { End } _ { Q } ( X ) - \operatorname { dim } _ { K } \operatorname { Ext } _ { Q } ^ { 1 } ( X , X )$ ; confidence 0.661

26. d030700175.png ; $\operatorname { Aut } _ { R ^ { \prime } } ( X ^ { \prime } | X _ { 0 } ) \rightarrow \operatorname { Aut } _ { R } ( X _ { R ^ { \prime } } ^ { \prime } \otimes R | X _ { 0 } )$ ; confidence 0.683

27. d030700190.png ; $\operatorname { dim } _ { k } H ^ { 1 } ( X _ { 0 } , T _ { X _ { 0 } } ) - \operatorname { dim } M _ { X _ { 0 } } \leq \operatorname { dim } _ { k } H ^ { 2 } ( X _ { 0 } , T _ { X _ { 0 } } )$ ; confidence 0.944

28. w12009095.png ; $\mathfrak { S } _ { \{ 1 , \ldots , \lambda _ { 1 } \} } \times \mathfrak { S } _ { \{ \lambda _ { 1 } + 1 , \ldots , \lambda _ { 1 } + \lambda _ { 2 } \} } \times$ ; confidence 0.312

29. d034120236.png ; $\beta : \operatorname { Ext } _ { c } ^ { n - p - 1 } ( X ; F , \Omega ) \rightarrow \operatorname { Ext } _ { c } ^ { n - p - 1 } ( X \backslash Y ; F , \Omega )$ ; confidence 0.634

30. q07631095.png ; $\left( \begin{array} { l } { n } \\ { k } \end{array} \right) _ { q } = \frac { ( q ^ { n } - 1 ) \ldots ( q ^ { n - k + 1 } - 1 ) } { ( q ^ { k } - 1 ) \ldots ( q - 1 ) }$ ; confidence 0.443

31. s085590225.png ; $\sum _ { k _ { 1 } , \ldots , k _ { n } = 0 } ^ { \infty } c _ { k _ { 1 } \cdots k _ { n } } ( z _ { 1 } - \zeta _ { 1 } ) ^ { k _ { 1 } } \ldots ( z _ { n } - \zeta _ { n } ) ^ { k _ { n } }$ ; confidence 0.324

32. u0952403.png ; $p ( x ) = \left\{ \begin{array} { l l } { \frac { 1 } { b - \alpha } , } & { x \in [ \alpha , b ] } \\ { 0 , } & { x \notin [ \alpha , b ] } \end{array} \right.$ ; confidence 0.681

33. c0205509.png ; $\mathfrak { g } 0 = \{ X \in \mathfrak { g } : \forall H \in \mathfrak { t } \exists \mathfrak { n } X , H \in Z ( ( \text { ad } H ) ^ { n } X , H ( X ) = 0 ) \}$ ; confidence 0.110

34. u09524030.png ; $u _ { n } ( x ) = \frac { 1 } { ( n - 1 ) ! } \sum _ { k = 0 } ^ { n } ( - 1 ) ^ { k } \left( \begin{array} { l } { n } \\ { k } \end{array} \right) ( x - k ) _ { + } ^ { n - 1 }$ ; confidence 0.569

35. l058680102.png ; $L ( \mathfrak { g } ) \cong \Gamma _ { 0 } ( \mathfrak { u } ) \cap \mathfrak { h } ^ { \prime } / \Gamma _ { 0 } ( [ \mathfrak { k } , \mathfrak { k } ] )$ ; confidence 0.659

36. l05872026.png ; $( \operatorname { ad } x ) ^ { n } y = \sum _ { j = 1 } ^ { n } ( - 1 ) ^ { j } \left( \begin{array} { c } { n } \\ { j } \end{array} \right) x ^ { n - j } y x ^ { j }$ ; confidence 0.356

37. t130140140.png ; $q ( x ) = \sum _ { i \in I } x _ { i } ^ { 2 } + \sum _ { i \prec j } x _ { i } x _ { j } - \sum _ { p \in \operatorname { max } l } ( \sum _ { i \prec p } x _ { i } ) x _ { p }$ ; confidence 0.197

38. t13014056.png ; $A _ { Q } ( v ) = \prod _ { i , j \in Q _ { 0 } } \prod _ { \langle \beta : j \rightarrow i \rangle \in Q _ { 1 } } M _ { v _ { i } \times v _ { j } } ( K ) _ { \beta }$ ; confidence 0.481

39. p07267025.png ; $\operatorname { Pic } _ { X / k } ( S ^ { \prime } ) = \operatorname { Fic } ( X \times k S ^ { \prime } ) / \operatorname { Fic } ( S ^ { \prime } )$ ; confidence 0.345

40. t130140118.png ; $[ X ] \mapsto \chi _ { R } ( [ X ] ) = \sum _ { m = 0 } ^ { \infty } ( - 1 ) ^ { m } \operatorname { dim } _ { K } \operatorname { Ext } _ { R } ^ { m } ( X , X )$ ; confidence 0.116

41. t0933502.png ; $r = \alpha \operatorname { sin } u k + l ( 1 + \epsilon \operatorname { cos } u ) ( i \operatorname { cos } v + j \operatorname { sin } v )$ ; confidence 0.585

42. j05427031.png ; $\Gamma = \operatorname { diag } \{ \gamma _ { 1 } , \gamma _ { 2 } , \gamma _ { 3 } \} , \quad \gamma _ { i } \neq 0 , \quad \gamma _ { i } \in F$ ; confidence 0.987

43. u0952407.png ; $F ( x ) = \left\{ \begin{array} { l l } { 0 , } & { x \leq a } \\ { \frac { x - a } { b - a } , } & { a < x \leq b } \\ { 1 , } & { x > b } \end{array} \right.$ ; confidence 0.468

44. n06690016.png ; $\delta ( e ) = e \quad \text { and } \quad \delta ( \rho ( a ) b ) = \sigma ( a ) \delta ( b ) , \quad \alpha \in C ^ { 0 } , \quad b \in C ^ { 1 }$ ; confidence 0.400

45. r07763055.png ; $\chi = \delta _ { \phi } - \sum _ { \alpha \in \Delta } m _ { \alpha } \alpha , \quad m _ { \alpha } \in Z , \quad m _ { \alpha } \geq 0$ ; confidence 0.862

46. s085590404.png ; $\frac { m _ { 1 } } { n _ { 1 } } < \frac { m _ { 2 } } { n _ { 1 } n _ { 2 } } < \ldots < \frac { m _ { g } } { n _ { 1 } \ldots n _ { g } } = \frac { m _ { g } } { n }$ ; confidence 0.459

47. u09524072.png ; $p ( x _ { 1 } , \ldots , x _ { n } ) = \left\{ \begin{array} { l l } { C \neq 0 , } & { x \in D } \\ { 0 , } & { x \notin D } \end{array} \right.$ ; confidence 0.705

48. d03249029.png ; $\omega _ { \eta / F } ( x ) = \sum _ { 0 \leq i \leq m } \alpha _ { i } \left( \begin{array} { c } { x + i } \\ { i } \end{array} \right)$ ; confidence 0.968

49. c0205704.png ; $f _ { j } ] = \delta _ { i j } h _ { i } , \quad [ h _ { i } , e _ { j } ] = \alpha _ { i j } e _ { j } , \quad [ h _ { i } , f _ { j } ] = - \alpha _ { j } f _ { j }$ ; confidence 0.149

50. l05859086.png ; $( X , Y ) \rightarrow \operatorname { exp } ^ { - 1 } ( \operatorname { exp } X \operatorname { exp } Y ) , \quad X , Y \in L ( G )$ ; confidence 0.856

51. w120090122.png ; $\operatorname { diag } ( t _ { 1 } , \ldots , t _ { n } ) \mapsto t _ { 1 } ^ { \lambda _ { 1 } } \ldots t _ { n } ^ { \lambda _ { n } } \in K$ ; confidence 0.507

52. d034120509.png ; $f = \{ f _ { \alpha } \} \in \prod _ { \alpha } F _ { \alpha } , \quad g = \{ g _ { \alpha } \} \in \oplus _ { \alpha } G _ { \alpha }$ ; confidence 0.491

53. s085590634.png ; $\Delta = ( F _ { x x } ^ { \prime \prime } ) _ { 0 } ( F _ { y y } ^ { \prime \prime } ) _ { 0 } - ( F _ { x y } ^ { \prime \prime } ) _ { 0 } ^ { 2 }$ ; confidence 0.920

54. w120090135.png ; $\chi _ { \lambda } = \sum _ { \mu \in \Lambda ( n ) } \operatorname { dim } _ { K } ( \Delta ( \lambda ) ^ { \mu } ) _ { e _ { \mu } }$ ; confidence 0.461

55. c02057064.png ; $\rightarrow H ^ { p } ( X , S ) \rightarrow H ^ { p } ( X , F ) \stackrel { \phi p } { \rightarrow } H ^ { p } ( X , G ) \rightarrow$ ; confidence 0.853

56. q07631072.png ; $\delta ( \alpha ) = \operatorname { lim } _ { h \rightarrow 0 } h ^ { - 1 } ( \Delta ( a ) - \Delta ^ { \prime } ( \alpha ) )$ ; confidence 0.304

57. d03183016.png ; $\omega _ { V } = \sum _ { 0 \leq i \leq m } \alpha _ { i } \left( \begin{array} { c } { x + i } \\ { i } \end{array} \right)$ ; confidence 0.780

58. d034120253.png ; $h ( \phi ) = \operatorname { lim } _ { r \rightarrow \infty } \frac { \operatorname { ln } | A ( r e ^ { i \phi } ) | } { r }$ ; confidence 0.861

59. d034120175.png ; $H ^ { p } ( X , F ) \times H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( F , \Omega ) ) \rightarrow H _ { c } ^ { n } ( X , \Omega )$ ; confidence 0.921

60. n06690028.png ; $C ^ { * } ( \mathfrak { U } , F ) = ( C ^ { 0 } ( \mathfrak { U } , F ) , C ^ { 1 } ( \mathfrak { U } , F ) , C ^ { 2 } ( \mathfrak { U } , F ) )$ ; confidence 0.205

61. l05851044.png ; $\mathfrak { g } _ { \alpha } = \operatorname { dim } [ \mathfrak { g } _ { \alpha } , \mathfrak { g } _ { - \alpha } ] = 1$ ; confidence 0.520

62. l058590115.png ; $( G ) \cong \operatorname { Aut } ( L ( G ) ) \quad \text { and } \quad L ( \operatorname { Aut } ( G ) ) \cong D ( L ( G ) )$ ; confidence 0.693

63. e03696024.png ; $F _ { 1 } F _ { 2 } = F _ { 1 } \langle F _ { 2 } \rangle = F _ { 1 } ( F _ { 2 } ) = F _ { 2 } ( F _ { 1 } ) = F _ { 2 } \langle F _ { 1 } \rangle$ ; confidence 0.628

64. j05434030.png ; $C _ { m } ( \lambda ) = \operatorname { rk } ( A - \lambda E ) ^ { m - 1 } - 2 \operatorname { rk } ( A - \lambda E ) ^ { m } +$ ; confidence 0.955

65. l05851050.png ; $[ H _ { \alpha } , X _ { \alpha } ] = 2 X _ { \alpha } \quad \text { and } \quad [ H _ { \alpha } , Y _ { \alpha } ] = - 2 Y _ { 0 }$ ; confidence 0.539

66. l05876030.png ; $\frac { \partial f _ { j } } { \partial g _ { i } } ( g , x ) = \sum _ { k = 1 } ^ { r } \xi _ { k j } ( f ( g _ { s } x ) ) \psi _ { k i } ( g )$ ; confidence 0.336

67. a01150022.png ; $\overline { w } = 2 \int _ { 0 } ^ { 1 / \varepsilon } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ ; confidence 0.107

68. a01164047.png ; $p _ { x } ( V ) = - \operatorname { dim } _ { k } H _ { 1 } ( V , O _ { V } ) + \operatorname { dim } _ { k } H ^ { 2 } ( V , O _ { V } ) =$ ; confidence 0.756

69. d034120360.png ; $\operatorname { sup } _ { l \in E ^ { \perp } } | l ( \omega ) | = \operatorname { inf } _ { x \in E } \| \omega - x \|$ ; confidence 0.293

70. l05851051.png ; $\beta ( H _ { \alpha } ) = \frac { 2 ( \alpha , \beta ) } { ( \alpha , \alpha ) } , \quad \alpha , \beta \in \Sigma$ ; confidence 0.997

71. s08706033.png ; $\psi _ { t _ { 1 } , \ldots , t _ { R } } ^ { \prime } : S K _ { 1 } ( R ) \rightarrow S K _ { 1 } ( R ( t _ { 1 } , \ldots , t _ { n } ) )$ ; confidence 0.379

72. a01164029.png ; $p _ { \alpha } ( V ) = \left( \begin{array} { c } { n - 1 } \\ { 3 } \end{array} \right) - d ( n - 1 ) + 2 t + \tau + p - 1$ ; confidence 0.396

73. a011640137.png ; $M = \operatorname { dim } \operatorname { Im } ( H ^ { 1 } ( V , E _ { \alpha } ) \rightarrow H ^ { 1 } ( V , T _ { V } ) )$ ; confidence 0.997

74. d03412079.png ; $( c _ { \gamma } , c ^ { r } ) = \sum _ { t ^ { r } \in K } c _ { r } ( t ^ { \prime } ) c ^ { r } ( t ^ { r } ) \operatorname { mod } 1$ ; confidence 0.117

75. s085590482.png ; $( \frac { \partial F ( x , y , \lambda ) } { \partial x } , \frac { \partial F ( x , y , \lambda ) } { \partial y } )$ ; confidence 0.986

76. c02333034.png ; $= ( a _ { 0 } a _ { 2 } - a _ { 1 } ^ { 2 } ) x ^ { 2 } + ( a _ { 0 } a _ { 3 } - a _ { 1 } a _ { 2 } ) x y + ( a _ { 1 } a _ { 3 } - a _ { 2 } ^ { 2 } ) y ^ { 2 }$ ; confidence 0.549

77. d034120247.png ; $\underset { n \rightarrow \infty } { \operatorname { lim } } | \alpha _ { n } | ^ { 1 / n } = \sigma < + \infty$ ; confidence 0.521

78. d030700263.png ; $\alpha \circ b = \alpha b + \sum _ { i = 1 } ^ { \infty } \phi _ { i } ( \alpha , b ) t ^ { i } , \quad \alpha , b \in V$ ; confidence 0.097

79. l05851073.png ; $n ( i , j ) = \alpha _ { j } ( H _ { i } ) = \frac { 2 ( \alpha _ { i } , \alpha _ { j } ) } { ( \alpha _ { j } , \alpha _ { j } ) }$ ; confidence 0.992

80. l05851078.png ; $N _ { \alpha , \beta } = - N _ { - \alpha , - \beta } \quad \text { and } \quad N _ { \alpha , \beta } = \pm ( p + 1 )$ ; confidence 0.961

81. l05868032.png ; $\Gamma _ { 1 } = \Gamma _ { 1 } ( g ) = \{ X \in h : \alpha ( X ) \in 2 \pi i Z \text { for all } \alpha \in \Sigma \}$ ; confidence 0.183

82. w120090342.png ; $\left( \begin{array} { c } { h } \\ { i } \end{array} \right) = \frac { h ( h - 1 ) \ldots ( h - i + 1 ) } { i ! }$ ; confidence 0.487

83. l0586604.png ; $N ( F ) = \{ g \in GL ( V ) : g v \equiv v \operatorname { mod } V _ { i } \text { for all } v \in V _ { i } , i \geq 1 \}$ ; confidence 0.466

84. t130130105.png ; $0 \rightarrow \Lambda \rightarrow T _ { 1 } \rightarrow \ldots \rightarrow T _ { n } \rightarrow 0$ ; confidence 0.946

85. l05851085.png ; $X _ { \alpha } - X _ { - \alpha } , \quad i ( X _ { \alpha } + X _ { - \alpha } ) \quad ( \alpha \in \Sigma _ { + } )$ ; confidence 0.691

86. l05876016.png ; $X _ { i } = \sum _ { j = 1 } ^ { n } \xi _ { i j } ( x ) \frac { \partial } { \partial x _ { j } } , \quad i = 1 , \ldots , r$ ; confidence 0.656

87. w098100172.png ; $\langle \alpha > < b \rangle = \langle \alpha b \rangle , \quad \langle 1 \rangle = f _ { 1 } = V _ { 1 } =$ ; confidence 0.351

88. a011640139.png ; $\operatorname { dim } _ { k } H ^ { 2 } ( V , E _ { \alpha } ) + \operatorname { dim } _ { k } H ^ { 2 } ( V , T _ { V } )$ ; confidence 0.996

89. h04769069.png ; $\mathfrak { g } = \mathfrak { f } + \mathfrak { m } , \quad \mathfrak { f } \cap \mathfrak { m } = \{ 0 \}$ ; confidence 0.793

90. n066900118.png ; $( g _ { 1 } , g _ { 2 } ) = h ( g _ { 1 } ) ( \phi ( g _ { 1 } ) ( h ( g _ { 2 } ) ) ) m ( g _ { 1 } , g _ { 2 } ) h ( g _ { 1 } , g _ { 2 } ) ^ { - 1 }$ ; confidence 0.764

91. r077630100.png ; $0 \leq \frac { 2 ( \chi , \alpha ) } { ( \alpha , \alpha ) } < p \quad \text { for all } \alpha \in \Delta$ ; confidence 0.879

92. s085590653.png ; $( F _ { X } ^ { \prime } ) _ { 0 } = 0 , \quad ( F _ { y } ^ { \prime } ) _ { 0 } = 0 , \quad ( F _ { z } ^ { \prime } ) _ { 0 } = 0$ ; confidence 0.300

93. a01164053.png ; $1 + p _ { x } ( V ) = \frac { \operatorname { deg } ( c _ { 1 } ^ { 2 } ) + \operatorname { deg } ( c _ { 2 } ) } { 12 }$ ; confidence 0.752

94. d034120555.png ; $f _ { 0 } ( x ) \rightarrow \text { inf, } \quad f _ { i } ( x ) \leq 0 , \quad i = 1 , \ldots , m , \quad x \in B$ ; confidence 0.810

95. m06301072.png ; $F ( x _ { 1 } f _ { 1 } + \ldots + x _ { x } f _ { n } ) = x _ { 1 } x _ { n } + x _ { 2 } x _ { n } - 1 + \ldots + x _ { p } x _ { n } - p + 1$ ; confidence 0.198

96. d030700270.png ; $\Phi ( \alpha ) = \alpha + \sum _ { i = 1 } ^ { \infty } t ^ { i } \phi _ { i } ( \alpha ) , \quad \alpha \in V$ ; confidence 0.873

97. h04797042.png ; $\epsilon ( x ) = 0 , \quad \delta ( x ) = x \bigotimes 1 + 1 \bigotimes x , \quad x \in \mathfrak { g }$ ; confidence 0.213

98. l05851030.png ; $\mathfrak { g } _ { \alpha } = \{ X \in \mathfrak { g } : [ H , X ] = \alpha ( H ) X , H \in \mathfrak { h } \}$ ; confidence 0.976

99. l05872078.png ; $\pi ( x + y ) = \pi ( x ) + \pi ( y ) , \quad \pi ( \lambda x ) = \lambda ^ { p } \pi ( x ) , \quad \lambda \in k$ ; confidence 0.964

100. p07464025.png ; $g j : U _ { i } \cap U _ { j } \rightarrow G , \quad i , j \in I , \quad U _ { i } \cap U _ { j } \neq \emptyset$ ; confidence 0.184

101. q07631062.png ; $\phi ^ { * } : \mathfrak { g } ^ { * } \otimes \mathfrak { g } ^ { * } \rightarrow \mathfrak { g } ^ { * }$ ; confidence 0.837

102. w098100190.png ; $\sigma ( \alpha _ { 1 } , \alpha _ { 2 } , \ldots ) = ( \alpha _ { 1 } ^ { p } , \alpha _ { 2 } ^ { p } , \ldots )$ ; confidence 0.771

103. h047970129.png ; $m \circ ( \iota \otimes 1 ) \circ \mu = m \circ ( 1 \otimes \iota ) \circ \mu = e \circ \epsilon$ ; confidence 0.618

104. w12009096.png ; $\ldots \times \mathfrak { S } _ { \{ \lambda _ { 1 } + \ldots + \lambda _ { n - 1 } + 1 , \ldots , r \} }$ ; confidence 0.259

105. a01150044.png ; $\theta ( v + \pi i r ) = \theta ( r ) , \quad \theta ( v + \alpha _ { j } ) = e ^ { L _ { j } ( v ) } \theta ( v )$ ; confidence 0.775

106. d031830107.png ; $S ^ { t } F = \sum _ { j = 1 } ^ { r } c _ { j } A ^ { p _ { j } } A _ { 1 } ^ { i _ { 1 j } } \dots A _ { m - l } ^ { i _ { m - l } , j }$ ; confidence 0.149

107. h047970139.png ; $F _ { 1 } ( X ; Y ) , \ldots , F _ { n } ( X ; Y ) \in K [ X _ { 1 } , \ldots , X _ { n } ; Y _ { 1 } , \ldots , Y _ { n } ] \}$ ; confidence 0.353

108. q07631071.png ; $\delta : U _ { \mathfrak { g } } \rightarrow U _ { \mathfrak { g } } \otimes U _ { \mathfrak { g } }$ ; confidence 0.648

109. u09524034.png ; $z _ { + } = \left\{ \begin{array} { l l } { z , } & { z > 0 } \\ { 0 , } & { z \leq 0 } \end{array} \right.$ ; confidence 0.676

110. w120090259.png ; $\mathfrak { B } = \{ e _ { \pm } \alpha , h _ { \beta } : \alpha \in \Phi ^ { + } , \beta \in \Sigma \}$ ; confidence 0.381

111. d03183043.png ; $e _ { i j } = \operatorname { ord } _ { Y } _ { j } F _ { i } , \quad 1 \leq i \leq n , \quad i \leq j \leq n$ ; confidence 0.187

112. l05851057.png ; $[ \mathfrak { g } _ { \alpha } , \mathfrak { g } _ { \beta } ] = \mathfrak { g } _ { \alpha + \beta }$ ; confidence 0.917

113. l05851069.png ; $[ [ X _ { \alpha _ { i } } , X _ { - } \alpha _ { i } ] , X _ { - \alpha _ { j } } ] = - n ( i , j ) X _ { \alpha _ { j } }$ ; confidence 0.628

114. n066900110.png ; $\phi ( g _ { 1 } ) \phi ( g ) \phi ( g _ { 1 } g _ { 2 } ) ^ { - 1 } = \operatorname { Int } m ( g _ { 1 } , g _ { 2 } )$ ; confidence 0.443

115. s085590429.png ; $p ( Z ) = 1 - \operatorname { dim } H ^ { 0 } ( Z , O _ { Z } ) + \operatorname { dim } H ^ { 1 } ( Z , O _ { Z } )$ ; confidence 0.997

116. a01150014.png ; $\theta = \int _ { 0 } ^ { \lambda } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ ; confidence 0.997

117. a01164027.png ; $N _ { m } = \left( \begin{array} { c } { m + 3 } \\ { 3 } \end{array} \right) - d m + 2 t + \tau + p - 1$ ; confidence 0.369

118. d034120173.png ; $H ^ { p } ( X , F ) \times H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( F , \Omega ) ) \rightarrow C$ ; confidence 0.824

119. l05852011.png ; $[ \mathfrak { g } _ { i } , \mathfrak { g } _ { i } ] \subset \mathfrak { g } _ { \mathfrak { i } } + 1$ ; confidence 0.276

120. f040820118.png ; $\operatorname { og } F _ { MU } ( X ) = \sum _ { i = 1 } ^ { \infty } i ^ { - 1 } [ C ^ { - } P ^ { - 1 } ] X ^ { i }$ ; confidence 0.098

121. l05861012.png ; $J = \left\| \begin{array} { c c } { 0 } & { E _ { x } } \\ { - E _ { x } } & { 0 } \end{array} \right\|$ ; confidence 0.364

122. t0933507.png ; $d s ^ { 2 } = \alpha ^ { 2 } d u ^ { 2 } + l ^ { 2 } ( 1 + \epsilon \operatorname { cos } u ) ^ { 2 } d v ^ { 2 }$ ; confidence 0.696

123. w098100177.png ; $\langle \alpha + b \rangle = \sum _ { n = 1 } ^ { \infty } V _ { n } \langle r _ { n } ( \alpha , b ) f$ ; confidence 0.143

124. d034120184.png ; $( H ^ { p } ( X , F ) ) ^ { \prime } \cong H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( F , \Omega ) )$ ; confidence 0.829

125. j05427077.png ; $\mathfrak { g } = \mathfrak { g } - 1 + \mathfrak { g } \mathfrak { d } + \mathfrak { g } _ { 1 }$ ; confidence 0.598

126. l05851037.png ; $\mathfrak { g } = \mathfrak { h } + \sum _ { \alpha \in \Sigma } \mathfrak { g } _ { \alpha }$ ; confidence 0.945

127. l05851064.png ; $H _ { \alpha _ { 1 } } , \ldots , H _ { \alpha _ { k } } , X _ { \alpha } \quad ( \alpha \in \Sigma )$ ; confidence 0.432

128. q07631089.png ; $[ X _ { i } ^ { + } , X _ { j } ^ { - } ] = 2 \delta _ { i j } h ^ { - 1 } \operatorname { sinh } ( h H _ { i } / 2 )$ ; confidence 0.893

129. q07631088.png ; $[ \alpha , X _ { i } ^ { \pm } ] = \pm \alpha _ { i } ( \alpha ) X _ { i } ^ { \pm } \quad \text { for } a$ ; confidence 0.544

130. s13053016.png ; $e = \frac { | U | } { | G | } ( \sum _ { b \in B } b ) ( \sum _ { w \in W } \operatorname { sign } ( w ) w )$ ; confidence 0.138

131. t13014044.png ; $X \mapsto \operatorname { dim } X = ( \operatorname { dim } _ { K } X _ { j } ) _ { j \in Q _ { 0 } }$ ; confidence 0.819

132. t130140119.png ; $\operatorname { dim } _ { 1 } : K _ { 0 } ( \operatorname { mod } R ) \rightarrow Z ^ { Q _ { 0 } }$ ; confidence 0.287

133. a01150021.png ; $\omega = 2 \int _ { 0 } ^ { 1 / c } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ ; confidence 0.973

134. l05876010.png ; $y _ { i } = f _ { i } ( g _ { 1 } , \ldots , g _ { i } ; x _ { 1 } , \ldots , x _ { n } ) , \quad i = 1 , \ldots , n$ ; confidence 0.276

135. r077630104.png ; $\phi _ { 0 } \bigotimes \phi _ { 1 } ^ { Fr } \otimes \ldots \otimes \phi _ { d } ^ { FF ^ { d } }$ ; confidence 0.136

136. s085590440.png ; $X _ { \epsilon } = \{ ( x _ { 0 } , \ldots , x _ { x } ) : f ( x _ { 0 } , \ldots , x _ { x } ) = \epsilon \}$ ; confidence 0.433

137. s085590515.png ; $\frac { d x _ { i } } { d x _ { i _ { 0 } } } = f _ { i } ( x ) , \quad f _ { i } \in C ( U ) , \quad i \neq i _ { 0 }$ ; confidence 0.594

138. s08610054.png ; $\{ e \} \rightarrow \Delta \rightarrow \pi \rightarrow Z ^ { s } \rightarrow \{ e \}$ ; confidence 0.972

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

140. d034120535.png ; $f ^ { * } ( x ^ { * } ) = \operatorname { sup } _ { x \in X } ( \langle x ^ { * } , x \rangle - f ( x ) )$ ; confidence 0.900

141. l05852046.png ; $\operatorname { dim } \mathfrak { g } _ { i } = \operatorname { dim } \mathfrak { g } - i$ ; confidence 0.901

142. s085590527.png ; $A = \| \left. \begin{array} { l l } { \alpha } & { b } \\ { c } & { e } \end{array} \right. |$ ; confidence 0.506

143. u0954106.png ; $\{ g \in \operatorname { GL } ( V ) : ( 1 - g ) ^ { n } = 0 \} , \quad n = \operatorname { dim } V$ ; confidence 0.287

144. a011640132.png ; $0 \rightarrow O _ { V } \rightarrow E _ { \alpha } \rightarrow T _ { V } \rightarrow 0$ ; confidence 0.981

145. d031830150.png ; $( \eta _ { 1 } , \ldots , \eta _ { n } ) \rightarrow F ( \zeta _ { 1 } , \ldots , \zeta _ { n } )$ ; confidence 0.376

146. d031830141.png ; $( \eta _ { 1 } , \ldots , \eta _ { k } ) \rightarrow F ( \zeta _ { 1 } , \ldots , \zeta _ { k } )$ ; confidence 0.562

147. f04082059.png ; $( x _ { 1 } , \ldots , x _ { x } ) \circ ( y _ { 1 } , \ldots , y _ { n } ) = ( z _ { 1 } , \ldots , z _ { x } )$ ; confidence 0.553

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

149. i05235015.png ; $\alpha _ { 1 } , \ldots , i _ { R } \rightarrow \alpha _ { 2 } ^ { \prime } , \ldots , i _ { R }$ ; confidence 0.142

150. j05427030.png ; $H ( C _ { 3 } , \Gamma ) = \{ X \in C _ { 3 } : X = \Gamma ^ { - 1 } X \square ^ { \prime } \Gamma \}$ ; confidence 0.651

151. l058590158.png ; $A _ { n } , n \geq 1 , \quad B _ { n } , n \geq 2 , \quad C _ { n } , n \geq 3 , \quad D _ { n } , n \geq 4$ ; confidence 0.956

152. l0586905.png ; $B ( F ) = \{ g \in \operatorname { GL } ( V ) : g V _ { i } \subset V _ { i } \text { for all } i \}$ ; confidence 0.454

153. w098100199.png ; $x _ { 0 } + \sum _ { i = 1 } ^ { \infty } x _ { i } V ^ { i } + \sum _ { j = 1 } ^ { < \infty } y _ { j } f ^ { j }$ ; confidence 0.575

154. l05851068.png ; $[ [ X _ { \alpha _ { i } } , X _ { - } , _ { i } ] , X _ { \alpha _ { j } } ] = n ( i , j ) X _ { \alpha _ { j } }$ ; confidence 0.186

155. q07631087.png ; $[ \alpha _ { 1 } , \alpha _ { 2 } ] = 0 \quad \text { for } \alpha _ { 1 } , \alpha _ { 2 } \in h$ ; confidence 0.597

156. s085590226.png ; $U ^ { n } ( \zeta , r ) = \{ z \in C ^ { n } : | z _ { v } - \zeta _ { v } | < R _ { v } , v = 1 , \ldots , n \}$ ; confidence 0.427

157. w098100192.png ; $x _ { 0 } + \sum _ { i = 1 } ^ { \infty } x _ { i } V ^ { i } + \sum _ { j = 1 } ^ { \infty } y _ { j } f ^ { i }$ ; confidence 0.498

158. a014170108.png ; $j ( x , \gamma \gamma ^ { \prime } ) = j ( x , \gamma ) j ( x \gamma , \gamma ^ { \prime } )$ ; confidence 0.838

159. d034120540.png ; $x , c \in R ^ { n } , \quad ( c , x ) = \sum _ { i = 1 } ^ { n } c _ { i } x _ { i } , \quad y , b \in R ^ { m }$ ; confidence 0.334

160. l05852019.png ; $\mathfrak { g } _ { i } ^ { \prime } / \mathfrak { g } _ { \mathfrak { i } } ^ { \prime } + 1$ ; confidence 0.518

161. s08706029.png ; $R ( t _ { 1 } , \ldots , t _ { n } ) = R \bigotimes _ { Z } ( R ) Z ( R ) ( t _ { 1 } , \ldots , t _ { n } )$ ; confidence 0.249

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

163. d034120532.png ; $A ^ { 0 } = \{ x ^ { * } \in X ^ { * } : \langle x ^ { * } , x \rangle \leq 1 , \square x \in A \}$ ; confidence 0.424

164. d034120552.png ; $- F ^ { * } ( 0 , y ^ { * } ) \rightarrow \operatorname { sup } , \quad y ^ { * } \in Y ^ { * }$ ; confidence 0.892

165. i05235012.png ; $x _ { i } \rightarrow \sum _ { j = 1 } ^ { n } \alpha _ { i j } x _ { j } , \quad 1 \leq i \leq n$ ; confidence 0.546

166. n06690094.png ; $e \rightarrow H ^ { 0 } ( G , B ) \rightarrow H ^ { 0 } ( G , A ) \rightarrow ( A / B ) ^ { G }$ ; confidence 0.580

167. t1301305.png ; $0 \rightarrow \Lambda \rightarrow T _ { 0 } \rightarrow T _ { 1 } \rightarrow 0$ ; confidence 0.974

168. t130140109.png ; $j = \operatorname { dim } _ { K } \operatorname { Ext } _ { R } ^ { 2 } ( S _ { j } , s _ { i } )$ ; confidence 0.262

169. a01150018.png ; $\Delta ( \theta ) = \sqrt { ( 1 - c ^ { 2 } \lambda ^ { 2 } ) ( 1 - e ^ { 2 } \lambda ^ { 2 } ) }$ ; confidence 0.994

170. a01174017.png ; $1 \rightarrow A ( k ) \rightarrow \text { Aut } A \rightarrow G \rightarrow 1$ ; confidence 0.794

171. d034120205.png ; $( H ^ { p } ( X , F ) ) ^ { \prime } \cong \operatorname { Ext } ^ { n - p } ( X ; F , \Omega )$ ; confidence 0.667

172. l05852024.png ; $b ( F ) = \{ x \in \mathfrak { g } | ( V ) : x V _ { i } \subset V _ { i } \text { for all } i \}$ ; confidence 0.136

173. q076310136.png ; $R = ( \rho \otimes \rho ) ( R ) \in \operatorname { End } ( k ^ { n } \otimes k ^ { n } )$ ; confidence 0.930

174. s085590489.png ; $\operatorname { det } \| \frac { \partial x ^ { i } } { \partial a ^ { j } } \| \neq 0$ ; confidence 0.409

175. w120090295.png ; $\mathfrak { n } ^ { + } = \sum _ { \alpha \in \Phi ^ { + } } \mathfrak { g } _ { \alpha }$ ; confidence 0.882

176. w120090354.png ; $x _ { \alpha } ( t ) = \sum _ { i = 0 } ^ { \infty } t ^ { i } \otimes e _ { \alpha } ^ { i } / i !$ ; confidence 0.841

177. w098100171.png ; $\sum _ { i , j \in \{ 1,2 , \ldots \} } V _ { i } \langle \alpha _ { i j } \rangle f _ { j }$ ; confidence 0.145

178. d03164018.png ; $F \omega = \omega ^ { ( p ) } F , \quad \omega V = V \omega ^ { ( p ) } , \quad F V = V F = p$ ; confidence 0.970

179. e036960177.png ; $( \delta _ { i } \alpha ) ^ { 2 } - \alpha _ { i } ^ { 2 } ( 4 \alpha ^ { 3 } - 8 \alpha - 88 )$ ; confidence 0.712

180. j05427013.png ; $( \alpha e 0 + u ) ( \beta e 0 + v ) = [ \alpha \beta + f ( u , v ) ] e 0 + \alpha v + \beta u$ ; confidence 0.094

181. s085590356.png ; $J ( f ) = ( \partial f / \partial x _ { 0 } , \ldots , \partial f / \partial x _ { n } )$ ; confidence 0.591

182. k11007016.png ; $= \{ f : \pi ^ { - 1 } ( U ) \rightarrow k : f ( g b ) = f ( g ) \chi ( b ) , g \in G , b \in B \}$ ; confidence 0.929

183. r07763061.png ; $k [ G ] _ { \chi } = \{ f \in k [ G ] : f ( g b ) = \chi ( b ) f ( g ) \forall b \in B , g \in G \}$ ; confidence 0.930

184. s0855907.png ; $f _ { \zeta } = f _ { \zeta } ( z ) = \sum _ { k = 0 } ^ { \infty } c _ { k } ( z - \zeta ) ^ { k }$ ; confidence 0.992

185. a01150040.png ; $F ( m ) = \sum \alpha _ { j k } m _ { j } m _ { k } , \quad \alpha _ { j k } = \alpha _ { k j }$ ; confidence 0.940

186. d034120263.png ; $p _ { Y } ( f ) = \operatorname { max } _ { z \in K _ { R } } | f ( z ) | , \quad f \in A ( G )$ ; confidence 0.227

187. d034120541.png ; $( b , y ) = \sum _ { i = 1 } ^ { m } b _ { i } y _ { b } , \quad A : R ^ { n } \rightarrow R ^ { m }$ ; confidence 0.277

188. j05427040.png ; $Q = \left( \begin{array} { l l } { 0 } & { 1 } \\ { 1 } & { 0 } \end{array} \right)$ ; confidence 0.925

189. l0585006.png ; $\mathfrak { g } = \mathfrak { z } ( \mathfrak { g } ) \dot { + } \mathfrak { g } 0$ ; confidence 0.735

190. l05859071.png ; $z ( s ) = x ( \sqrt { s } ) y ( \sqrt { s } ) x ( \sqrt { s } ) ^ { - 1 } y ( \sqrt { s } ) ^ { - 1 }$ ; confidence 0.991

191. l058720135.png ; $k [ X _ { 1 } , \ldots , X _ { m } ; \square X _ { 1 } ^ { p } = 0 , \ldots , X _ { m } ^ { p } = 0 ]$ ; confidence 0.412

192. q07631061.png ; $\phi : \mathfrak { g } \rightarrow \mathfrak { g } \otimes \mathfrak { g }$ ; confidence 0.982

193. s085590470.png ; $F ( x , y , \lambda ) = ( x - \mu ) ( x ^ { 2 } + y ^ { 3 } + \lambda y ^ { 2 } - 6 \lambda x y )$ ; confidence 0.998

194. t13014066.png ; $( h _ { j } ) ^ { * } ( M _ { i j } ^ { \beta } ) = ( h _ { i } ^ { - 1 } M _ { i j } ^ { \beta } h _ { j } )$ ; confidence 0.942

195. w120090160.png ; $\langle g x , y \rangle = \langle x , g ^ { T } y \rangle , \quad \forall g \in G$ ; confidence 0.652

196. d03183044.png ; $h = \operatorname { max } _ { \pi } ( e _ { 1 } \pi ( 1 ) + \ldots + e _ { n } \pi ( n ) )$ ; confidence 0.715

197. d034120121.png ; $H _ { r } ( M ^ { n } , X ) | H _ { n - r } ( M ^ { n } , X ^ { * } ) , \quad \text { for } X | X ^ { * }$ ; confidence 0.734

198. n06690056.png ; $( \sigma ( \alpha ) ( c ) ) ( g , h ) = \alpha ^ { g } c ( g , h ) ( \alpha ^ { g } ) ^ { - 1 }$ ; confidence 0.301

199. r08137022.png ; $\sum _ { \alpha \in I } ( \operatorname { dim } \rho ^ { \alpha } ) ^ { 2 } = | G |$ ; confidence 0.960

200. t13014072.png ; $q ( v ) = \operatorname { dim } G _ { Q } ( v ) - \operatorname { dim } A _ { Q } ( v )$ ; confidence 0.221

201. a01164076.png ; $H ^ { p } ( V , \Omega ^ { q } ) = \operatorname { dim } H ^ { q } ( V , \Omega ^ { p } )$ ; confidence 0.943

202. d034120235.png ; $\gamma : H _ { X \backslash Y } ^ { p + 1 } ( X , F ) \rightarrow H ^ { p + 1 } ( X , F )$ ; confidence 0.715

203. o07001058.png ; $t ( z _ { 1 } , z _ { 2 } ) = ( e ^ { i t } z _ { 1 } , e ^ { i \alpha t } z _ { 2 } ) , \quad t \in R$ ; confidence 0.800

204. o07001044.png ; $( g f ) ( u , v ) = f ( g ^ { - 1 } ( u ) , g ^ { - 1 } ( v ) ) \quad \text { for any } u , v \in V$ ; confidence 0.987

205. s085590376.png ; $x _ { 0 } ^ { \mu - 1 } + x _ { 0 } x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$ ; confidence 0.937

206. t130140147.png ; $0 \rightarrow P _ { 1 } \rightarrow P _ { 0 } \rightarrow X \rightarrow 0$ ; confidence 0.747

207. t0933508.png ; $K = ( \operatorname { cos } u ) / a l ( 1 + \epsilon \operatorname { cos } u )$ ; confidence 0.499

208. c02057019.png ; $\rho ( e _ { i } ) v = 0 , \quad \rho ( h _ { i } ) v = k _ { i } v , \quad i = 1 , \dots , r$ ; confidence 0.484

209. d03070052.png ; $\gamma : H ^ { 1 } ( X _ { 0 } , \Theta ) \rightarrow H ^ { 2 } ( X _ { 0 } , \Theta )$ ; confidence 0.700

210. d034120244.png ; $H _ { c } ^ { n - p - 1 } ( X \backslash Y , \operatorname { Hom } ( F , \Omega ) )$ ; confidence 0.923

211. d034120424.png ; $A ^ { o } = \{ y \in G : \operatorname { Re } ( x , y ) \leq 1 , \forall x \in A \}$ ; confidence 0.603

212. e036960187.png ; $X _ { 0 } X _ { 2 } ^ { 2 } - ( 4 X _ { 1 } ^ { 3 } - 8 X _ { 0 } ^ { 2 } X _ { 1 } - 8 X _ { 0 } ^ { 3 } ) = 0$ ; confidence 0.432

213. l05851045.png ; $H _ { \alpha } \in [ \mathfrak { g } _ { \alpha } , \mathfrak { g } - \alpha ]$ ; confidence 0.566

214. l05859082.png ; $\operatorname { exp } X = \sum _ { m = 0 } ^ { \infty } \frac { 1 } { m ! } X ^ { m }$ ; confidence 0.976

215. n06690078.png ; $\rho ( f ) ( \alpha ) = d f \cdot f ^ { - 1 } + ( \operatorname { Ad } f ) \alpha$ ; confidence 0.231

216. t09335012.png ; $x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } = a ^ { 2 } , \quad x _ { 3 } ^ { 2 } + x _ { 4 } ^ { 2 } = b ^ { 2 }$ ; confidence 0.863

217. d030700167.png ; $\tilde { \rho } : \tilde { \kappa } \rightarrow \tilde { M } _ { X _ { 0 } }$ ; confidence 0.601

218. d031830344.png ; $\operatorname { rank } ( A _ { i } ) = \operatorname { rank } ( B _ { i } )$ ; confidence 0.983

219. f04082053.png ; $= F _ { i } ( F _ { 1 } ( X , Y ) , \ldots , F _ { n } ( X , Y ) , Z _ { 1 } , \ldots , Z _ { n } )$ ; confidence 0.658

220. f04082052.png ; $F _ { i } ( X _ { 1 } , \ldots , X _ { n } , F _ { 1 } ( Y , Z ) , \ldots , F _ { n } ( Y , Z ) ) =$ ; confidence 0.659

221. n066900125.png ; $G \rightarrow \text { Out } A = \text { Aut } A / \operatorname { Int } A$ ; confidence 0.290

222. n06690058.png ; $\alpha \in C ^ { 0 } , \quad b \in C ^ { 1 } , \quad c \in C ^ { 2 } , \quad g \in G$ ; confidence 0.173

223. q076310140.png ; $T _ { 1 } = T \otimes 1 \in \operatorname { End } ( k ^ { n } \otimes k ^ { n } )$ ; confidence 0.284

224. q07631052.png ; $\{ a , b \} = \operatorname { lim } _ { h \rightarrow 0 } h ^ { - 1 } ( a b - b a )$ ; confidence 0.345

225. t13014060.png ; $M _ { v _ { i } \times v _ { j } } ( K ) _ { \beta } = M _ { v _ { i } \times v _ { j } } ( K )$ ; confidence 0.814

226. w09759034.png ; $\phi = \sum \phi _ { v } : WC ( A , k ) \rightarrow \sum _ { v } WC ( A , k _ { v } )$ ; confidence 0.221

227. w120090100.png ; $\lambda = ( \lambda _ { 1 } , \ldots , \lambda _ { n } ) \in \Lambda ( n , r )$ ; confidence 0.455

228. h047690105.png ; $P ( G / H , t ) = \prod _ { i = 1 } ^ { r } \frac { 1 - t ^ { 2 k } i } { 1 - t ^ { 2 l _ { i } } }$ ; confidence 0.529

229. h04769085.png ; $( g , f ) \sim ( g h ^ { - 1 } , h f ) , \quad g \in G , \quad k \in H , \quad f \in F$ ; confidence 0.494

230. l05851071.png ; $( \text { ad } X _ { - } \alpha _ { i } ) ^ { 1 - n ( i , j ) } X _ { - } \alpha _ { j } = 0$ ; confidence 0.289

231. s085590498.png ; $\frac { d x _ { 1 } } { X _ { 1 } ( x ) } = \ldots = \frac { d x _ { x } } { X _ { x } ( x ) }$ ; confidence 0.695

232. s085590138.png ; $V ^ { \prime } ( \alpha ) = \{ z \in \overline { C } : 0 < | z - \alpha | < R \}$ ; confidence 0.853

233. s13054078.png ; $\{ \alpha , b \} _ { p } = ( - 1 ) ^ { \alpha \beta } r ^ { \beta } s ^ { \alpha }$ ; confidence 0.934

234. w09771045.png ; $X ( T _ { 0 } / Z ( G ) ^ { 0 } ) _ { Q } = X ( T _ { 0 } / Z ( G ) ^ { 0 } ) \bigotimes _ { Z } Q$ ; confidence 0.558

235. w120090106.png ; $y _ { \lambda } = \sum _ { \pi \in C ( t ) } \operatorname { sg } ( \pi ) \pi$ ; confidence 0.648

236. w120090109.png ; $z _ { \lambda } = e _ { \lambda } y _ { \lambda } \in E \otimes ^ { \gamma }$ ; confidence 0.166

237. a01164011.png ; $p ^ { ( 1 ) } = ( K _ { V } ^ { 2 } ) + 1 = \operatorname { deg } ( c _ { 1 } ^ { 2 } ) + 1$ ; confidence 0.919

238. d03070043.png ; $T _ { \emptyset } ( S ) \rightarrow H ^ { 1 } ( X _ { \diamond } , \Theta )$ ; confidence 0.185

239. d031830164.png ; $( t _ { 1 } , \ldots , t _ { n } , u ) \rightarrow F ( 0 , \ldots , 0 , \alpha )$ ; confidence 0.606

240. d031830160.png ; $u = \frac { F ( t _ { 1 } , \ldots , t _ { x } ) } { G ( t _ { 1 } , \ldots , t _ { x } ) }$ ; confidence 0.902

241. d034120468.png ; $f \in ( F ^ { \prime } , \sigma ( F ^ { \prime } , F ) ) \square ^ { \prime }$ ; confidence 0.990

242. p07267014.png ; $T \rightarrow H ^ { 1 } ( T _ { f } p q c , G _ { m } ) = H ^ { 1 } ( T _ { et } , G _ { m } )$ ; confidence 0.492

243. s085590381.png ; $x _ { 0 } ^ { 3 } x _ { 1 } + x _ { 1 } ^ { 3 } + x _ { 2 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$ ; confidence 0.934

244. s130540122.png ; $= y ( - b ( 1 + a b ) ^ { - 1 } ) x ( a ) y ( b ) x ( - ( 1 + a b ) ^ { - 1 } a ) h ( 1 + a b ) ^ { - 1 }$ ; confidence 0.572

245. u09524049.png ; $F ^ { - 1 } ( y ) = \operatorname { inf } \{ x : F ( x ) \leq y \leq F ( x + 0 ) \}$ ; confidence 0.904

246. w09759027.png ; $\phi _ { v } : \operatorname { WC } ( A , k ) \rightarrow WC ( A , k _ { v } )$ ; confidence 0.456

247. a01150012.png ; $( x , \sqrt { f ( x ) } ) \oplus ( c , \sqrt { f ( c ) } ) = ( y , \sqrt { f ( y ) } )$ ; confidence 0.980

248. d030700137.png ; $\kappa ^ { \prime } \rightarrow \operatorname { Spec } \Lambda$ ; confidence 0.898

249. l05851070.png ; $( \text { ad } X _ { \alpha _ { i } } ) ^ { 1 - n ( i , j ) } X _ { \alpha _ { j } } = 0$ ; confidence 0.438

250. o07001086.png ; $| X / G | = \frac { 1 } { | G | } \sum _ { g \in G } | \operatorname { Fix } g |$ ; confidence 0.300

251. p07267053.png ; $f ^ { \prime } : X ^ { \prime } = X \times S S ^ { \prime } \rightarrow S$ ; confidence 0.259

252. r07763029.png ; $V ( \chi ) = \{ v \in V : \phi ( t ) v = \chi ( t ) v \forall t \in T \} \neq 0$ ; confidence 0.311

253. d03164021.png ; $D _ { k } / D _ { k } V ^ { n } \simeq \operatorname { End } _ { k } ( W _ { n k }$ ; confidence 0.576

254. d031830322.png ; $\operatorname { deg } _ { A } ( F ) < \operatorname { deg } _ { A } ( A )$ ; confidence 0.907

255. d031830310.png ; $\operatorname { deg } _ { A } ( A ) = \operatorname { deg } _ { A } ( B )$ ; confidence 0.865

256. d031830306.png ; $\operatorname { deg } _ { A } ( A ) < \operatorname { deg } _ { A } ( B )$ ; confidence 0.560

257. d034120508.png ; $( f , g ) = \sum _ { \alpha } ( f _ { \alpha } , g _ { \alpha } ) _ { \alpha }$ ; confidence 0.947

258. d034120522.png ; $\| f | H \| = \operatorname { dist } ( f , H ^ { 0 } ) , \quad f \in F ^ { * }$ ; confidence 0.990

259. i05235025.png ; $\Delta = 3 b ^ { 2 } c ^ { 2 } + 6 a b c d - 4 b ^ { 3 } d - 4 a c ^ { 3 } - a ^ { 2 } d ^ { 2 }$ ; confidence 0.992

260. j05427038.png ; $J _ { \Im } : X \rightarrow S _ { \square } ^ { \prime } X ^ { \prime } S$ ; confidence 0.174

261. s08706024.png ; $S K _ { 1 } ( R ) \simeq \operatorname { SL } ( 1 , R ) / [ R ^ { * } , R ^ { * } ]$ ; confidence 0.445

262. w120090294.png ; $\mathfrak { b } ^ { + } = \mathfrak { h } \oplus \mathfrak { n } ^ { + }$ ; confidence 0.723

263. c02347043.png ; $j = 1 , \ldots , n _ { \alpha } = \operatorname { dim } R ^ { \alpha }$ ; confidence 0.704

264. d030700219.png ; $\tilde { p } : \tilde { \kappa } \rightarrow \hat { M } _ { X _ { 0 } }$ ; confidence 0.375

265. d034120245.png ; $\alpha ( z ) = \sum _ { x = 0 } ^ { \infty } \frac { a _ { x } } { z ^ { x + 1 } }$ ; confidence 0.561

266. e036960202.png ; $B _ { \nu } = y ^ { \prime \prime } + x ^ { - 1 } + ( 1 - \nu ^ { 2 } x ^ { - 2 } ) y$ ; confidence 0.963

267. f04082060.png ; $z _ { i } = F _ { i } ( x _ { 1 } , \ldots , x _ { n } , y _ { 1 } , \ldots , y _ { n } )$ ; confidence 0.408

268. i05235032.png ; $f _ { i } ( x _ { 1 } , \ldots , x _ { n } ) = \sum _ { j = 1 } ^ { n } a _ { j } x _ { j }$ ; confidence 0.612

269. l05850020.png ; $: \mathfrak { h } \rightarrow \mathfrak { g } ( \mathfrak { g } )$ ; confidence 0.180

270. p07267011.png ; $f ^ { \prime } : X \times s S ^ { \prime } \rightarrow S ^ { \prime }$ ; confidence 0.505

271. s0868309.png ; $B = B _ { 0 } \supset B _ { 1 } \supset \ldots \supset B _ { t } = \{ 1 \}$ ; confidence 0.917

272. s13054040.png ; $\operatorname { diag } ( \alpha , \alpha ^ { - 1 } , 1,1 , \ldots )$ ; confidence 0.671

273. t13013048.png ; $\operatorname { Ext } _ { \Lambda } ^ { 1 } ( T , ) : F \rightarrow X$ ; confidence 0.653

274. t130140157.png ; $\chi _ { K I } : K _ { 0 } ( \operatorname { prin } K l ) \rightarrow Z$ ; confidence 0.497

275. u09541046.png ; $G _ { \alpha } \times \ldots \times G _ { \alpha } \rightarrow U$ ; confidence 0.129

276. a0141703.png ; $f ( \gamma ( x ) ) = f ( x ) , \quad x \in M , \quad \gamma \in \Gamma$ ; confidence 0.691

277. c02057062.png ; $0 \rightarrow S \rightarrow F \rightarrow G \rightarrow 0$ ; confidence 0.972

278. c02333031.png ; $f = a _ { 0 } x ^ { 3 } + 3 a _ { 1 } x ^ { 2 } y + 3 a _ { 2 } x y ^ { 2 } + a _ { 3 } y ^ { 3 }$ ; confidence 0.852

279. d034120378.png ; $\operatorname { sup } _ { f \in B ^ { 1 } } | f ^ { \prime } ( z _ { 0 } ) |$ ; confidence 0.660

280. h047970136.png ; $\iota * \text { id } = \text { id } * _ { \iota } = e \circ \epsilon$ ; confidence 0.102

281. l05851066.png ; $X _ { \alpha _ { i } } , X _ { - \alpha _ { i } } \quad ( i = 1 , \ldots , n )$ ; confidence 0.447

282. l05872082.png ; $L _ { 0 } = < e _ { 1 } , \ldots , e _ { \gamma } : e _ { z } ^ { [ p ] } = e _ { i } >$ ; confidence 0.131

283. l05877094.png ; $T ^ { 2 } = \{ ( z _ { 1 } , z _ { 2 } ) : z _ { i } \in C , | z _ { i } | = 1 , i = 1,2 \}$ ; confidence 0.972

284. s13004014.png ; $H ^ { L } = \{ z \in H : \operatorname { Im } z > L \} \text { for } L > 0$ ; confidence 0.977

285. a01150079.png ; $x _ { 0 } ^ { 3 } x _ { 1 } + x _ { 1 } ^ { 3 } x _ { 2 } + x _ { 2 } ^ { 3 } x _ { 0 } = 0$ ; confidence 0.999

286. a01150039.png ; $v = ( v _ { 1 } , \ldots , v _ { p } ) , \quad ( m , v ) = \sum m _ { i } v _ { i }$ ; confidence 0.458

287. d034120507.png ; $\{ \alpha : g _ { \alpha } \neq 0 \square \text { is finite } \}$ ; confidence 0.495

288. d03412098.png ; $H _ { r } ( R , X ) | H ^ { r } ( R , X ^ { * } ) , \quad \text { for } X | X ^ { * }$ ; confidence 0.972

289. e036960194.png ; $y ^ { ( n ) } + \alpha _ { 1 } y ^ { ( n - 1 ) } + \ldots + \alpha _ { n } y = 0$ ; confidence 0.817

290. f040820105.png ; $G _ { \alpha } ( X , Y ) = ( X _ { 1 } + Y _ { 1 } , \ldots , X _ { n } + Y _ { n } )$ ; confidence 0.419

291. h04741010.png ; $f ( t _ { 1 } ^ { 0 } , \ldots , t _ { x } ^ { 0 } , x _ { 1 } , \ldots , x _ { x } )$ ; confidence 0.418

292. h04769076.png ; $[ \mathfrak { m } , \mathfrak { m } ] \subseteq \mathfrak { f }$ ; confidence 0.914

293. n06690030.png ; $( \sigma ( a ) ( c ) ) _ { i j k } = \alpha _ { i } c _ { i j k } a _ { i } ^ { - 1 }$ ; confidence 0.186

294. n066900117.png ; $\phi ^ { \prime } ( g ) = ( \operatorname { Int } h ( g ) ) \phi ( g )$ ; confidence 0.698

295. s085590383.png ; $x _ { 0 } ^ { 5 } + x _ { 1 } ^ { 3 } + x _ { 2 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$ ; confidence 0.985

296. s085590379.png ; $x _ { 0 } ^ { 4 } + x _ { 1 } ^ { 3 } + x _ { 2 } ^ { 2 } + \ldots + x _ { n } ^ { 2 } = 0$ ; confidence 0.987

297. s085590467.png ; $F ( x , y , \lambda ) = ( x - \mu ) ( x ^ { 2 } - \lambda y ^ { 2 } ) + y ^ { 4 }$ ; confidence 1.000

298. t13014069.png ; $M _ { i j } ^ { \beta } \in M _ { v _ { j } \times v _ { i } } ( K ) _ { \beta }$ ; confidence 0.705

299. t13014026.png ; $X = ( X _ { i } , \phi _ { \beta } ) _ { j \in Q _ { 0 } , } \beta \in Q _ { 1 }$ ; confidence 0.354

300. a011640146.png ; $\omega \leq \operatorname { dim } H ^ { 2 } ( V , E _ { \alpha } )$ ; confidence 0.999

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/Algebraic Groups/1. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/Algebraic_Groups/1&oldid=44141