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(AUTOMATIC EDIT of page 10 out of 11 with 300 lines: Updated image/latex database (currently 3083 images latexified; order by Confidence, ascending: False.)
(AUTOMATIC EDIT of page 10 out of 11 with 300 lines: Updated image/latex database (currently 3083 images latexified; order by Confidence, ascending: False.)
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== List ==
 
== List ==
1. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085620/s085620184.png ; $f _ { t } = h _ { t } \circ f _ { 0 } \circ k _ { t }$ ; confidence 0.837
+
1. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110140/l11014014.png ; $\tilde { y } ( x ) = \operatorname { exp } ( - \epsilon ) f ( x \operatorname { exp } ( - \epsilon ) )$ ; confidence 0.405
  
2. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130360/s13036039.png ; $\int _ { 0 } ^ { t } I _ { \partial D } ( Y _ { s } ) d l _ { s } = 1 _ { t }$ ; confidence 0.676
+
2. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s120340135.png ; $\alpha _ { H } ( \tilde { x } _ { + } ) - \alpha _ { H } ( \tilde { x } _ { - } ) = 1$ ; confidence 0.404
  
3. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120150/s120150139.png ; $\varphi H G$ ; confidence 0.652
+
3. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240452.png ; $P$ ; confidence 0.403
  
4. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085790/s08579085.png ; $\sum _ { l = 1 } ^ { \infty } \frac { \operatorname { ln } q + 1 } { q l }$ ; confidence 0.755
+
4. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020740/c020740324.png ; $( \alpha _ { e } ) _ { é \in E }$ ; confidence 0.403
  
5. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085810/s0858103.png ; $\phi : U \rightarrow \sum _ { i \in I } U _ { l }$ ; confidence 0.895
+
5. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025180/c02518096.png ; $T _ { s ( x ) } ( E ) = \Delta _ { s ( x ) } \oplus T _ { s ( x ) } ( F _ { x } )$ ; confidence 0.402
  
6. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085820/s085820238.png ; $b ( x ) < 0$ ; confidence 1.000
+
6. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052260/i05226072.png ; $Z \in G$ ; confidence 0.401
  
7. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085830/s08583016.png ; $| w | = \rho < 1$ ; confidence 0.874
+
7. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013036.png ; $\partial / \partial x = \partial / \partial t _ { 1 }$ ; confidence 0.401
  
8. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086020/s08602026.png ; $\overline { D ^ { + } } = D ^ { + } \cup \Gamma$ ; confidence 0.709
+
8. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072830/p07283021.png ; $\epsilon _ { i j } ^ { k }$ ; confidence 0.400
  
9. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120180/s12018056.png ; $M = M ^ { \perp \perp }$ ; confidence 0.970
+
9. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060090/l060090100.png ; $\operatorname { dim } Z \cap \overline { S _ { k + q + 1 } } ( F | _ { X \backslash Z } ) \leq k$ ; confidence 0.399
  
10. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086160/s0861605.png ; $J _ { m + n + 1 } ( x ) =$ ; confidence 0.892
+
10. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052150/i0521507.png ; $\forall x ( P ( x ) \vee \neg P ( x ) ) \wedge \neg \neg \neg x P ( x ) \supset \exists x P ( x )$ ; confidence 0.397
  
11. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086190/s086190182.png ; $s \in E ^ { n }$ ; confidence 0.570
+
11. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022033.png ; $5$ ; confidence 0.396
  
12. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086330/s086330106.png ; $\| x \| ^ { 2 } = \int _ { \sigma ( A ) } | f _ { \lambda } ( x ) | ^ { 2 } d \rho ( \lambda )$ ; confidence 0.635
+
12. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042079.png ; $25$ ; confidence 0.396
  
13. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086330/s08633021.png ; $\sigma _ { d x } ( A )$ ; confidence 0.138
+
13. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120500/b12050014.png ; $M _ { t } : = \operatorname { sup } _ { s \leq t } W _ { s }$ ; confidence 0.396
  
14. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086330/s08633098.png ; $A \Phi \subset \Phi$ ; confidence 0.973
+
14. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081560/r081560116.png ; $R _ { V } = \frac { 1 } { ( 2 \pi i ) ^ { n } } \int _ { \sigma _ { V } } f ( z ) d z$ ; confidence 0.396
  
15. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086360/s086360102.png ; $B ( r ) = \int _ { 0 } ^ { \infty } J _ { 0 } ( \lambda r ) d F ( \lambda )$ ; confidence 0.998
+
15. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027180/c02718064.png ; $H ( K )$ ; confidence 0.395
  
16. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086380/s0863808.png ; $s _ { 1 } - t _ { 1 } = s _ { 2 } - t _ { 2 }$ ; confidence 0.998
+
16. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030020/d030020144.png ; $\operatorname { gr } D _ { X }$ ; confidence 0.395
  
17. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086450/s08645013.png ; $A _ { \delta }$ ; confidence 0.997
+
17. https://www.encyclopediaofmath.org/legacyimages/e/e110/e110080/e11008028.png ; $P _ { n } ( f ) = \int _ { S } f d P _ { n } = \frac { 1 } { n } \sum _ { i = 1 } ^ { n } f ( X _ { i } )$ ; confidence 0.394
  
18. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086480/s0864803.png ; $E | X ( t ) | ^ { n } \leq C < \infty$ ; confidence 0.578
+
18. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093570/t0935701.png ; $x = \pm \alpha \operatorname { ln } \frac { \alpha + \sqrt { \alpha ^ { 2 } - y ^ { 2 } } } { y } - \sqrt { \alpha ^ { 2 } - y ^ { 2 } }$ ; confidence 0.391
  
19. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086490/s086490118.png ; $d ^ { \prime }$ ; confidence 0.445
+
19. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780377.png ; $1 B S G$ ; confidence 0.389
  
20. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086520/s08652091.png ; $| T | _ { p }$ ; confidence 0.714
+
20. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240508.png ; $E ( Z _ { 13 } ) = 0$ ; confidence 0.388
  
21. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086520/s086520138.png ; $\theta _ { T } = \theta$ ; confidence 0.989
+
21. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032330/d03233041.png ; $r : h \rightarrow f ( x _ { 0 } + h ) - f ( x _ { 0 } ) - h _ { 0 } ( h )$ ; confidence 0.388
  
22. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086550/s0865507.png ; $B _ { N } A ( B _ { N } ( \lambda - \lambda _ { 0 } ) )$ ; confidence 0.980
+
22. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130040/t13004015.png ; $( n + 1 ) a _ { n + 1 } + \alpha _ { n } = \tau$ ; confidence 0.385
  
23. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086590/s08659060.png ; $\mathfrak { p } \not p \not \sum _ { n = 1 } ^ { \infty } A _ { n }$ ; confidence 0.075
+
23. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110990/b11099015.png ; $P _ { \alpha }$ ; confidence 0.384
  
24. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086620/s08662027.png ; $\Sigma ( \Sigma ^ { n } X ) \rightarrow \Sigma ^ { n + 1 } X$ ; confidence 0.992
+
24. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041320/f04132023.png ; $v _ { 0 } ^ { k }$ ; confidence 0.384
  
25. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086620/s08662031.png ; $( \pi )$ ; confidence 1.000
+
25. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c1202805.png ; $X *$ ; confidence 0.383
  
26. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086650/s086650167.png ; $Z _ { 24 }$ ; confidence 0.663
+
26. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a0100204.png ; $\{ E _ { n _ { 1 } } \ldots n _ { k } \}$ ; confidence 0.382
  
27. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086650/s08665020.png ; $i > 2 n - 1$ ; confidence 0.989
+
27. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013023.png ; $= \operatorname { exp } ( x P _ { 0 } z + \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } ) g ( z ) . . \operatorname { exp } ( - x P _ { 0 } z - \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { \gamma } )$ ; confidence 0.382
  
28. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086700/s08670044.png ; $e ^ { - k - s | / \mu } / \mu$ ; confidence 0.763
+
28. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050970/i05097047.png ; $F ( M ^ { k } ) \subset \nabla \square ^ { n }$ ; confidence 0.382
  
29. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086720/s086720108.png ; $V ^ { 3 } = E ^ { 3 }$ ; confidence 0.992
+
29. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025920/c02592019.png ; $631$ ; confidence 0.381
  
30. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086720/s086720109.png ; $K ( d s ) = K$ ; confidence 0.996
+
30. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301307.png ; $Q$ ; confidence 0.380
  
31. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086720/s08672038.png ; $\pi = n \sqrt { 1 + \sum p ^ { 2 } }$ ; confidence 0.678
+
31. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087780/s08778021.png ; $w ^ { \prime }$ ; confidence 0.380
  
32. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s1202309.png ; $O ( r )$ ; confidence 0.866
+
32. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096350/v09635060.png ; $\left. \begin{array} { l l l } { \alpha _ { 1 } } & { \alpha _ { 2 } } & { \alpha _ { 3 } } \\ { b _ { 1 } } & { b _ { 2 } } & { b _ { 3 } } \\ { c _ { 1 } } & { c _ { 2 } } & { c _ { 3 } } \end{array} \right| = 0$ ; confidence 0.378
  
33. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110240/s11024022.png ; $\lambda _ { m } ( t )$ ; confidence 0.691
+
33. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010108.png ; $Sp ( 0 )$ ; confidence 0.378
  
34. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086770/s08677096.png ; $5 + 7 n$ ; confidence 0.141
+
34. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240236.png ; $n - r$ ; confidence 0.377
  
35. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086810/s086810102.png ; $f \in W _ { 2 } ^ { 3 } ( \Omega )$ ; confidence 0.999
+
35. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120150/a12015019.png ; $( g )$ ; confidence 0.376
  
36. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086810/s08681080.png ; $( 2 m - 2 )$ ; confidence 1.000
+
36. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110120/p110120321.png ; $4 x$ ; confidence 0.375
  
37. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086810/s086810108.png ; $W _ { p } ^ { m } ( I ^ { d } )$ ; confidence 0.958
+
37. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047160/h0471603.png ; $H ( z ) = \sum _ { i = 1 } ^ { n } \sum _ { j = 1 } ^ { n } a _ { i j } z _ { i } z _ { j }$ ; confidence 0.374
  
38. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510139.png ; $L \subset Z ^ { 0 }$ ; confidence 0.864
+
38. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055850/k055850103.png ; $D _ { \alpha }$ ; confidence 0.374
  
39. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051063.png ; $\Gamma = \Gamma _ { 1 } + \ldots + \Gamma _ { m }$ ; confidence 0.966
+
39. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301305.png ; $P = P _ { 0 } z + P _ { 1 } : = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) z + \left( \begin{array} { l l } { 0 } & { q } \\ { r } & { 0 } \end{array} \right)$ ; confidence 0.374
  
40. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510126.png ; $\gamma ( u ) < \infty$ ; confidence 0.997
+
40. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017030/b01703046.png ; $\mathfrak { M } _ { n }$ ; confidence 0.373
  
41. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086940/s086940114.png ; $\operatorname { det } S \neq 0$ ; confidence 0.896
+
41. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008028.png ; $A _ { j } A _ { k l } = A _ { k l } A _ { j }$ ; confidence 0.372
  
42. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086940/s086940100.png ; $- \infty \leq w \leq + \infty$ ; confidence 0.301
+
42. https://www.encyclopediaofmath.org/legacyimages/i/i053/i053020/i05302096.png ; $\beta _ { k } q _ { k + 1 } = A q _ { k } - \beta _ { k - 1 } q _ { k - 1 } - \alpha _ { k } q _ { k k }$ ; confidence 0.371
  
43. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086940/s086940134.png ; $0 \leq \omega \leq \infty$ ; confidence 0.754
+
43. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087030/s0870309.png ; $f _ { h } \in U _ { k }$ ; confidence 0.371
  
44. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086940/s08694070.png ; $\| \eta ( \cdot ) \| ^ { 2 } = \int _ { 0 } ^ { \infty } | \eta ( t ) | ^ { 2 } d t$ ; confidence 0.669
+
44. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041060/f041060205.png ; $d _ { C } ^ { - 1 } = \operatorname { det } \left\| \begin{array} { c c } { \phi _ { \theta } \theta } & { \phi _ { \theta x } } \\ { \phi _ { y } \theta } & { \phi _ { y x } } \end{array} \right\|$ ; confidence 0.370
  
45. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086960/s08696030.png ; $\| x _ { 0 } \| \leq \delta$ ; confidence 0.966
+
45. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013099.png ; $z \in C$ ; confidence 0.369
  
46. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086960/s08696076.png ; $V < 0$ ; confidence 0.854
+
46. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640127.png ; $M = 10 p _ { t x } - p _ { g } - 2 p ^ { ( 1 ) } + 12 + \theta$ ; confidence 0.369
  
47. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086960/s08696095.png ; $k \leq p \leq n$ ; confidence 0.985
+
47. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110410/a11041070.png ; $K _ { X } ^ { v } \otimes L ^ { i }$ ; confidence 0.368
  
48. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087030/s0870309.png ; $f _ { h } \in U _ { k }$ ; confidence 0.371
+
48. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f120150202.png ; $n \| < C$ ; confidence 0.368
  
49. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087030/s08703096.png ; $\operatorname { max } _ { n \atop n } \| u ^ { n } \| _ { H } \leq e ^ { C _ { 1 } T } \{ \| \phi \| _ { H } + C _ { 0 } \sum _ { n } \tau \| f ^ { n + 1 } \| _ { H } \}$ ; confidence 0.172
+
49. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075660/p07566043.png ; $\partial _ { x } = \partial / \partial x$ ; confidence 0.368
  
50. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087110/s08711028.png ; $\delta < \alpha$ ; confidence 0.956
+
50. https://www.encyclopediaofmath.org/legacyimages/p/p075/p075190/p07519074.png ; $E _ { i j }$ ; confidence 0.366
  
51. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087130/s08713053.png ; $m < \infty$ ; confidence 0.973
+
51. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032330/d03233040.png ; $b _ { 0 }$ ; confidence 0.363
  
52. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087260/s08726044.png ; $\eta _ { 0 } ( i )$ ; confidence 0.979
+
52. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l13006070.png ; $\frac { 1 } { 4 n } \operatorname { max } \{ \alpha _ { i } : 0 \leq i \leq t \} \leq \Delta _ { 2 } \leq \frac { 1 } { 4 n } ( \sum _ { i = 0 } ^ { t } \alpha _ { i } + 2 )$ ; confidence 0.363
  
53. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087270/s08727063.png ; $V _ { x } 0 ( \lambda ) \sim \operatorname { exp } [ i \lambda S ( x ^ { 0 } ) ] \sum _ { k = 0 } ^ { \infty } ( \sum _ { l = 0 } ^ { N } \alpha _ { k l } \lambda ^ { - r _ { k } } ( \operatorname { ln } \lambda ) ^ { l } \}$ ; confidence 0.167
+
53. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032320/d03232015.png ; $u _ { R } ^ { k } ( x ) = \sum _ { i = 1 } ^ { n } u _ { i } a _ { i } ^ { k } ( x )$ ; confidence 0.362
  
54. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087280/s087280193.png ; $m = E X ( s )$ ; confidence 0.808
+
54. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090670/s09067035.png ; $j _ { X } ^ { k } ( u )$ ; confidence 0.362
  
55. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087300/s08730040.png ; $Q _ { 1 }$ ; confidence 0.060
+
55. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539040.png ; $E [ L ( \theta , d ) | x ]$ ; confidence 0.361
  
56. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087320/s08732031.png ; $\Pi ^ { * } \in C$ ; confidence 0.864
+
56. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094440/t09444040.png ; $u _ { m } = u ( M _ { m } )$ ; confidence 0.360
  
57. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087320/s08732041.png ; $\mathfrak { R } _ { \mu } ( \Pi _ { 0 } ) = \operatorname { inf } _ { \Pi } \Re _ { \mu } ( \Pi )$ ; confidence 0.658
+
57. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032150/d032150132.png ; $\hat { V }$ ; confidence 0.359
  
58. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087330/s08733032.png ; $H _ { i } ( \omega )$ ; confidence 0.983
+
58. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020950/c02095032.png ; $L u = \sum _ { | \alpha | \leq m } \alpha _ { \alpha } ( x ) \frac { \partial ^ { \alpha } u } { \partial x ^ { \alpha } } = f ( x )$ ; confidence 0.358
  
59. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087350/s08735095.png ; $I _ { n } ( \theta ) = n I ( \theta )$ ; confidence 0.870
+
59. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005087.png ; $v _ { n } \in G$ ; confidence 0.357
  
60. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087360/s087360228.png ; $P \{ s ^ { 2 } < \frac { \sigma ^ { 2 } x } { n - 1 } \} = G _ { n - 1 } ( x ) = D _ { n - 1 } \int _ { 0 } ^ { x } v ^ { ( n - 3 ) } / 2 e ^ { - v / 2 } d v$ ; confidence 0.622
+
60. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110269.png ; $g _ { 1 } = | d x | ^ { 2 } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } } \leq g = \frac { | d x | ^ { 2 } } { | x | ^ { 2 } } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } }$ ; confidence 0.357
  
61. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087360/s087360105.png ; $\operatorname { lim } _ { n \rightarrow \infty } P \{ \frac { \alpha - \alpha } { \sigma _ { n } ( \alpha ) } < x \} = \frac { 1 } { \sqrt { 2 \pi } } \int _ { - \infty } ^ { x } e ^ { - t ^ { 2 } / 2 } d t \equiv \Phi ( x )$ ; confidence 0.827
+
61. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b120210148.png ; $\mathfrak { p } \supset b$ ; confidence 0.356
  
62. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087400/s087400105.png ; $\in \Theta _ { 0 } \beta _ { n } ( \theta ) \leq \alpha$ ; confidence 0.815
+
62. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063760/m063760111.png ; $0 \rightarrow A \rightarrow B \stackrel { sp } { \rightarrow } \pi * C \rightarrow 0$ ; confidence 0.355
  
63. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110260/s11026022.png ; $\eta \in R ^ { k }$ ; confidence 0.999
+
63. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001085.png ; $0$ ; confidence 0.355
  
64. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087420/s08742011.png ; $H = H _ { V } ( \omega )$ ; confidence 0.988
+
64. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013088.png ; $t$ ; confidence 0.354
  
65. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087420/s087420178.png ; $\mathfrak { A } _ { \infty } = \overline { U _ { V \subset R ^ { 3 } } } A ( \mathcal { H } _ { V } )$ ; confidence 0.216
+
65. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110630/a11063032.png ; $\rho _ { 0 n + } = \operatorname { sin } A$ ; confidence 0.354
  
66. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087420/s08742067.png ; $\{ f \rangle _ { P } \sim | V |$ ; confidence 0.071
+
66. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097790/w09779041.png ; $\pi _ { 4 n - 1 } ( S ^ { 2 n } ) \rightarrow \pi _ { 4 n } ( S ^ { 2 n + 1 } )$ ; confidence 0.354
  
67. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450224.png ; $\frac { 1 } { 2 \pi } \sum _ { t = - T + 1 } ^ { T - 1 } e ^ { - i t \lambda } r ^ { * } ( t ) c T ( t )$ ; confidence 0.607
+
67. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301303.png ; $P _ { 1 } = \left( \begin{array} { c c c } { 0 } & { \square } & { q } \\ { r } & { \square } & { 0 } \end{array} \right) , Q _ { 2 } = \left( \begin{array} { c c } { - \frac { i } { 2 } q r } & { \frac { i } { 2 } q x } \\ { - \frac { i } { 2 } r _ { x } } & { \frac { i } { 2 } q r } \end{array} \right)$ ; confidence 0.352
  
68. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450112.png ; $\xi = \sum b _ { j } x ( t _ { j } )$ ; confidence 0.942
+
68. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097510/w09751010.png ; $m _ { k } = \dot { k }$ ; confidence 0.352
  
69. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450113.png ; $\sum b _ { j } \phi _ { l } ( t _ { j } ) = 0$ ; confidence 0.990
+
69. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065460/m06546014.png ; $( \alpha \vee ( b . e ) ) : e = ( \alpha : e ) \vee b$ ; confidence 0.351
  
70. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450208.png ; $I _ { T } ( \lambda ) = \frac { 1 } { 2 \pi T } | \int _ { 0 } ^ { T } e ^ { - i t \lambda } x ( t ) d t |$ ; confidence 0.646
+
70. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872090.png ; $l _ { k } ( A )$ ; confidence 0.348
  
71. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450221.png ; $a T \rightarrow \infty$ ; confidence 0.506
+
71. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240276.png ; $\leq F _ { \alpha ; q , x - \gamma }$ ; confidence 0.345
  
72. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087450/s087450204.png ; $\theta _ { T } ^ { * }$ ; confidence 0.481
+
72. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087690/s0876903.png ; $f _ { h } ( t ) = \frac { 1 } { h } \int _ { t - k / 2 } ^ { t + k / 2 } f ( u ) d u = \frac { 1 } { h } \int _ { - k / 2 } ^ { k / 2 } f ( t + v ) d v$ ; confidence 0.345
  
73. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087460/s08746026.png ; $\{ \epsilon _ { t } \}$ ; confidence 0.993
+
73. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025720/c02572034.png ; $y _ { 0 } = A _ { x }$ ; confidence 0.344
  
74. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120240/s12024033.png ; $h ^ { S * } ( . ) \approx \overline { E } \times ( . )$ ; confidence 0.489
+
74. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060310/l06031040.png ; $R = \{ \alpha \in K : \operatorname { mod } _ { K } ( \alpha ) \leq 1 \}$ ; confidence 0.342
  
75. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087550/s08755019.png ; $\alpha < p b$ ; confidence 0.578
+
75. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150743.png ; $\left. \begin{array} { c c c } { B _ { i } } & { \stackrel { h _ { i } } { \rightarrow } } & { A _ { i } } \\ { g _ { i } \downarrow } & { \square } & { \downarrow f _ { i } } \\ { B } & { \vec { f } } & { A } \end{array} \right.$ ; confidence 0.342
  
76. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087550/s08755022.png ; $\alpha \leq p b$ ; confidence 0.784
+
76. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015019.png ; $\frac { D \xi ^ { i } } { d t } = \frac { d \xi ^ { i } } { d t } + \frac { 1 } { 2 } g ^ { i } r \xi ^ { r }$ ; confidence 0.338
  
77. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087640/s08764034.png ; $g \neq 0$ ; confidence 1.000
+
77. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067110/n06711048.png ; $\phi _ { i } / \partial x _ { Y }$ ; confidence 0.338
  
78. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087640/s08764060.png ; $I = \{ f \in O ( X ) : f ( x ) = 0 \}$ ; confidence 0.993
+
78. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062360/m06236012.png ; $T _ { i j }$ ; confidence 0.337
  
79. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087640/s08764057.png ; $I \subset O ( X )$ ; confidence 0.970
+
79. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043780/g043780168.png ; $T _ { \nu }$ ; confidence 0.336
  
80. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087640/s08764086.png ; $n ( O _ { x } ) = 0$ ; confidence 0.322
+
80. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050230/i050230379.png ; $\| f \| _ { \Lambda _ { p } ^ { r } ( R ^ { n } ) } \leq K$ ; confidence 0.335
  
81. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087690/s0876903.png ; $f _ { h } ( t ) = \frac { 1 } { h } \int _ { t - k / 2 } ^ { t + k / 2 } f ( u ) d u = \frac { 1 } { h } \int _ { - k / 2 } ^ { k / 2 } f ( t + v ) d v$ ; confidence 0.345
+
81. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057050/l057050123.png ; $c \rightarrow N$ ; confidence 0.335
  
82. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087710/s08771037.png ; $\omega ( R )$ ; confidence 0.999
+
82. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057150/l05715031.png ; $\mu$ ; confidence 0.335
  
83. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110280/s11028060.png ; $\sum _ { i = 1 } ^ { r } \alpha _ { i } \theta ( b _ { i } ) \in Z [ G ]$ ; confidence 0.947
+
83. https://www.encyclopediaofmath.org/legacyimages/s/s085/s085400/s085400325.png ; $\tilde { f } : \Delta ^ { n + 1 } \rightarrow E$ ; confidence 0.333
  
84. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087790/s08779013.png ; $RP ^ { \infty }$ ; confidence 0.165
+
84. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110470/c11047054.png ; $h : H \rightarrow ( C \bigotimes T M ) / ( H \oplus \overline { H } )$ ; confidence 0.332
  
85. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087770/s08777049.png ; $V _ { k } ( H ^ { n } ) = \frac { Sp ( n ) } { Sp ( n - k ) }$ ; confidence 0.259
+
85. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c1202808.png ; $F T op$ ; confidence 0.332
  
86. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087780/s08778069.png ; $x [ M ^ { n } ] = \alpha ( x )$ ; confidence 0.933
+
86. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082500/r08250032.png ; $\| u - P _ { n } u \| _ { A } \rightarrow 0$ ; confidence 0.332
  
87. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087780/s08778021.png ; $w ^ { \prime }$ ; confidence 0.380
+
87. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057510/l05751032.png ; $\Delta ( \alpha _ { 1 } \ldots i _ { p } d x ^ { i _ { 1 } } \wedge \ldots \wedge d x ^ { i p } ) =$ ; confidence 0.331
  
88. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087800/s08780026.png ; $x + C$ ; confidence 0.988
+
88. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020740/c020740394.png ; $( \alpha \circ \beta ) ( c ) _ { d x } = \sum _ { b } \alpha ( b ) _ { a } \beta ( c ) _ { b }$ ; confidence 0.330
  
89. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087800/s08780044.png ; $| u ( x _ { 1 } ) - u ( x _ { 2 } ) | \leq C | x _ { 1 } - x _ { 2 }$ ; confidence 0.995
+
89. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180420.png ; $C ^ { \infty } ( \tilde { N } )$ ; confidence 0.330
  
90. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120250/s1202506.png ; $h _ { n } = \int _ { a } ^ { b } x ^ { n } h ( x ) d x$ ; confidence 0.183
+
90. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062220/m06222011.png ; $\Delta \lambda _ { i } ^ { \alpha }$ ; confidence 0.329
  
91. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087820/s08782077.png ; $| \frac { 1 } { 1 - H \lambda _ { i } } | < 1$ ; confidence 0.997
+
91. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082210/r08221030.png ; $o = e K$ ; confidence 0.327
  
92. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087820/s087820210.png ; $y _ { n + 1 } = y _ { n } + \int _ { 0 } ^ { H / 2 } e ^ { A \tau } d \tau \times$ ; confidence 0.976
+
92. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001099.png ; $_ { \nabla } ( G / K )$ ; confidence 0.326
  
93. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087820/s08782061.png ; $\alpha _ { 1 } = - 3$ ; confidence 0.753
+
93. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110440/b1104407.png ; $\overline { \Xi } \epsilon = 0$ ; confidence 0.326
  
94. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087820/s087820182.png ; $\| y \| = \operatorname { max } _ { i } | y _ { i } |$ ; confidence 0.800
+
94. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240141.png ; $c$ ; confidence 0.324
  
95. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090130/s09013024.png ; $H \mapsto \alpha ( H )$ ; confidence 0.996
+
95. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520141.png ; $N _ { 2 } = \left| \begin{array} { c c c c c } { . } & { \square } & { \square } & { \square } & { 0 } \\ { \square } & { . } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { L ( e _ { j } ^ { n _ { i j } } ) } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { . } & { \square } \\ { \square } & { \square } & { \square } & { \square } & { \square } \\ { 0 } & { \square } & { \square } & { \square } & { . } \end{array} \right|$ ; confidence 0.323
  
96. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090130/s09013055.png ; $K . ( H X ) = ( K H ) X$ ; confidence 0.766
+
96. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041620/f04162020.png ; $X _ { i } \cap X _ { j } =$ ; confidence 0.322
  
97. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026061.png ; $\partial _ { s }$ ; confidence 0.939
+
97. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087640/s08764086.png ; $n ( O _ { x } ) = 0$ ; confidence 0.322
  
98. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110290/s11029032.png ; $t / \lambda ^ { 2 } \rightarrow + \infty$ ; confidence 0.986
+
98. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001033.png ; $[ \xi ^ { \alpha } , \xi ^ { b } ] = 2 \epsilon _ { \alpha b c } \xi ^ { c }$ ; confidence 0.322
  
99. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090170/s09017045.png ; $E$ ; confidence 0.923
+
99. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240339.png ; $\Sigma _ { 1 } = X _ { 4 } ^ { \prime } \Sigma X _ { 4 }$ ; confidence 0.322
  
100. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090170/s09017090.png ; $B \in \mathfrak { B } _ { 0 }$ ; confidence 0.992
+
100. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110880/b11088033.png ; $P _ { I } ^ { f } : C ^ { \infty } \rightarrow L$ ; confidence 0.321
  
101. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090170/s0901702.png ; $\ldots < t _ { - 1 } < t _ { 0 } \leq 0 < t _ { 1 } < t _ { 2 } <$ ; confidence 0.500
+
101. https://www.encyclopediaofmath.org/legacyimages/k/k110/k110030/k11003029.png ; $\frac { x ^ { \rho + 1 } f ( x ) } { \int _ { x } ^ { x } t ^ { \sigma } f ( t ) d t } \rightarrow \sigma + \rho + 1 \quad ( x \rightarrow \infty )$ ; confidence 0.320
  
102. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090180/s0901802.png ; $\square \ldots < t _ { - 1 } < t _ { 0 } \leq 0 < t _ { 1 } < t _ { 2 } < \ldots$ ; confidence 0.740
+
102. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047020/h04702011.png ; $F _ { n } ( x ) = ( x _ { 1 } ^ { 2 } + \ldots + x _ { y } ^ { 2 } ) ^ { 1 / 2 }$ ; confidence 0.316
  
103. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090190/s090190160.png ; $X ( t _ { 1 } ) = x$ ; confidence 0.980
+
103. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120010/o12001037.png ; $\left. \begin{array} { l } { \nabla p _ { 1 } = \nabla p _ { 2 } = 0 } \\ { \frac { \partial v _ { 0 } } { \partial t } + [ \nabla v _ { 0 } ] v _ { 0 } = \frac { 1 } { Re } \Delta v _ { 0 } + \operatorname { Re } \nabla p _ { 3 } + \theta _ { 0 } b } \end{array} \right.$ ; confidence 0.316
  
104. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090190/s09019043.png ; $t = Z$ ; confidence 0.971
+
104. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013078.png ; $q ^ { ( l ) } = 2 i \frac { \tau _ { l } + 1 } { \tau _ { l } } , r ^ { ( l ) } = - 2 i \frac { \tau _ { l } - 1 } { \tau _ { l } }$ ; confidence 0.315
  
105. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090220/s09022010.png ; $x ( \phi )$ ; confidence 0.999
+
105. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015024.png ; $x = \frac { 1 } { n } \sum _ { j = 1 } ^ { n } x$ ; confidence 0.315
  
106. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090230/s09023035.png ; $\overline { w }$ ; confidence 0.553
+
106. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024100/c024100277.png ; $\partial _ { r }$ ; confidence 0.315
  
107. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090260/s09026037.png ; $d x = A ( t ) x d t + B ( t ) d w ( t )$ ; confidence 0.986
+
107. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120100/w12010028.png ; $\nabla _ { i g j k } = \gamma _ { i } g _ { j k }$ ; confidence 0.315
  
108. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090260/s09026014.png ; $d X ( t ) = a ( t ) Z ( t ) d t + d Y ( t )$ ; confidence 0.505
+
108. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014310/a0143102.png ; $e$ ; confidence 0.314
  
109. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090270/s0902702.png ; $\alpha < t < b$ ; confidence 0.786
+
109. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023045.png ; $\therefore M \rightarrow F$ ; confidence 0.313
  
110. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090450/s09045062.png ; $\zeta ^ { \phi } \in C ^ { d }$ ; confidence 0.837
+
110. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054050/j05405048.png ; $\theta _ { 3 } ( v \pm \frac { 1 } { 2 } \tau ) = e ^ { - i \pi \tau / 4 } \cdot e ^ { - i \pi v } \cdot \theta _ { 2 } ( v )$ ; confidence 0.312
  
111. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090450/s09045037.png ; $W ^ { ( n ) } ( s )$ ; confidence 0.986
+
111. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073400/p07340055.png ; $M ^ { 0 }$ ; confidence 0.312
  
112. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090590/s0905905.png ; $J ( y ) \leq J ( y )$ ; confidence 0.683
+
112. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001057.png ; $0$ ; confidence 0.311
  
113. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120280/s1202804.png ; $\overline { f } : X \rightarrow Y$ ; confidence 0.998
+
113. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055520/k05552082.png ; $\Gamma 20$ ; confidence 0.310
  
114. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120280/s12028015.png ; $\overline { E } * ( X )$ ; confidence 0.554
+
114. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076830/q07683071.png ; $p _ { m } = ( \sum _ { j = 0 } ^ { m } A _ { j } ) ^ { - 1 }$ ; confidence 0.310
  
115. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090670/s09067035.png ; $j _ { X } ^ { k } ( u )$ ; confidence 0.362
+
115. https://www.encyclopediaofmath.org/legacyimages/f/f042/f042150/f04215011.png ; $\left. \begin{array} { l l } { F _ { 1 } ( A ) } & { \frac { F _ { 1 } ( \alpha ) } { \rightarrow } } & { F _ { 1 } ( B ) } \\ { \phi _ { A } \downarrow } & { \square } & { \downarrow \phi _ { B } } \\ { F _ { 2 } ( A ) } & { \vec { F _ { 2 } ( \alpha ) } } & { F _ { 2 } ( B ) } \end{array} \right.$ ; confidence 0.308
  
116. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090710/s09071014.png ; $f = 1$ ; confidence 1.000
+
116. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093900/t093900115.png ; $l \mu \frac { \partial W ^ { k } } { \partial x } + ( 1 - c ) W ^ { k } = c ( \Phi _ { 0 } ^ { k } - \phi _ { 0 } ^ { k } )$ ; confidence 0.308
  
117. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090720/s09072010.png ; $a \neq a _ { 0 }$ ; confidence 0.773
+
117. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110110/d11011051.png ; $M _ { 1 } = H \cap _ { k \tau _ { S } } H ^ { \prime }$ ; confidence 0.307
  
118. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090760/s09076059.png ; $p ( \alpha )$ ; confidence 0.904
+
118. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050230/i050230319.png ; $f \in S _ { y } ^ { \prime }$ ; confidence 0.307
  
119. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090760/s09076071.png ; $l [ f ] = 0$ ; confidence 0.979
+
119. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420128.png ; $h$ ; confidence 0.307
  
120. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090760/s09076026.png ; $L _ { 0 } ^ { * } = L _ { 1 }$ ; confidence 0.957
+
120. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110820/b11082017.png ; $\pi _ { i } / ( \pi _ { i } + \pi _ { j } )$ ; confidence 0.304
  
121. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090770/s090770137.png ; $\lambda _ { 1 } < \lambda _ { 2 } < \ldots$ ; confidence 0.830
+
121. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082790/r08279064.png ; $\operatorname { Pic } ( F ) \cong p ^ { * } \operatorname { Pic } ( C ) \oplus Z ^ { 5 }$ ; confidence 0.304
  
122. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090780/s09078074.png ; $\Phi ^ { \prime \prime } ( + 0 ) = - h$ ; confidence 0.997
+
122. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073540/p07354050.png ; $P \{ X _ { v + 1 } = k + 1 | X _ { k } = k \} = \frac { b + k c } { b + r + n c } = \frac { p + k \gamma } { 1 + n \gamma }$ ; confidence 0.303
  
123. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s13062062.png ; $m _ { 0 } ( \lambda ) = A + \int _ { - \infty } ^ { \infty } ( \frac { 1 } { t - \lambda } - \frac { t } { t ^ { 2 } + 1 } ) d \rho _ { 0 } ( t )$ ; confidence 0.926
+
123. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036910/e03691017.png ; $a ^ { X } = e ^ { X \operatorname { ln } \alpha }$ ; confidence 0.301
  
124. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090820/s0908209.png ; $X ^ { * }$ ; confidence 0.447
+
124. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086940/s086940100.png ; $- \infty \leq w \leq + \infty$ ; confidence 0.301
  
125. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090830/s0908308.png ; $m : B \rightarrow A$ ; confidence 0.962
+
125. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021100/c02110012.png ; $x \in \operatorname { Dom } A$ ; confidence 0.300
  
126. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090900/s09090088.png ; $\xi = \infty \in \partial D$ ; confidence 0.998
+
126. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080850/r08085028.png ; $e \omega ^ { r } f$ ; confidence 0.300
  
127. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090900/s09090090.png ; $V = V ( \infty ) = \{ x \in R ^ { n } : | x | > R \}$ ; confidence 0.624
+
127. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900234.png ; $\Pi I _ { \lambda }$ ; confidence 0.300
  
128. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091010/s09101020.png ; $c = \operatorname { const } \neq 0$ ; confidence 0.470
+
128. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d120280147.png ; $\overline { U }$ ; confidence 0.299
  
129. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091070/s09107089.png ; $P _ { \theta } ( A | B )$ ; confidence 0.963
+
129. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057740/l05774010.png ; $\operatorname { lim } _ { n \rightarrow \infty } \operatorname { sup } \frac { S _ { n } } { c _ { n } } = 1 \quad ( \alpha . s . )$ ; confidence 0.299
  
130. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091080/s09108054.png ; $\sum _ { n < x } f ( n ) = R ( x ) + O ( x ^ { \{ ( \alpha + 1 ) ( 2 \eta - 1 ) / ( 2 \eta + 1 ) \} + \epsilon } )$ ; confidence 0.795
+
130. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092650/t09265033.png ; $\{ \partial f \rangle$ ; confidence 0.295
  
131. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091100/s0911009.png ; $\lambda _ { n } = 1 / ( n + 1 ) ^ { s }$ ; confidence 0.931
+
131. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014230/a0142305.png ; $\{ A \rangle$ ; confidence 0.294
  
132. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091140/s09114035.png ; $s _ { n } \rightarrow s$ ; confidence 0.696
+
132. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072430/p072430105.png ; $\phi _ { im }$ ; confidence 0.294
  
133. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091140/s09114030.png ; $\sum _ { k = 0 } ^ { \infty } \lambda _ { k } u _ { k }$ ; confidence 0.542
+
133. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070150/o07015054.png ; $\alpha ^ { n } < b ^ { n + 1 }$ ; confidence 0.291
  
134. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091200/s09120056.png ; $\operatorname { psq } ( n ) = \operatorname { sq } ( n ) / \{ c E : c \in C \}$ ; confidence 0.425
+
134. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082160/r082160299.png ; $\{ \operatorname { exp } _ { m } ( \text { Cutval } ( \xi ) \xi ) \} = \text { Cutloc } ( m )$ ; confidence 0.291
  
135. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s12032058.png ; $S ( L )$ ; confidence 0.980
+
135. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031380/d031380384.png ; $\sum _ { \mathfrak { D } _ { 1 } ^ { 1 } } ( E \times N ^ { N } )$ ; confidence 0.290
  
136. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091390/s09139063.png ; $x _ { 1 } ^ { 2 } = 0$ ; confidence 0.997
+
136. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044680/g04468049.png ; $t \circ \in E$ ; confidence 0.290
  
137. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091390/s0913909.png ; $\frac { x ^ { 2 } } { p } - \frac { y ^ { 2 } } { q } = 2 z$ ; confidence 0.932
+
137. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052130/i05213037.png ; $\forall y \exists z ( \gamma ( y ) + 1 = \alpha ( g * \overline { \beta } ( z ) ) )$ ; confidence 0.288
  
138. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091570/s09157097.png ; $T ^ { * } Y \backslash 0$ ; confidence 0.994
+
138. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130230/a13023034.png ; $\| f _ { 1 } - P _ { U \cap V ^ { J } } f \| \leq c ^ { 2 l - 1 } \| f \|$ ; confidence 0.287
  
139. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091580/s09158080.png ; $\Phi ( f ( w ) ) = \sigma ( \Phi ( w ) )$ ; confidence 0.999
+
139. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014190/a0141905.png ; $x _ { y } + 1 = t$ ; confidence 0.287
  
140. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091670/s09167062.png ; $S ( B _ { n } ^ { m } )$ ; confidence 0.719
+
140. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041940/f041940310.png ; $A \in \mathfrak { S }$ ; confidence 0.285
  
141. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091730/s09173026.png ; $H ^ { n - k } \cap S ^ { k }$ ; confidence 0.502
+
141. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027270/c02727013.png ; $j = \frac { 1728 g _ { 2 } ^ { 3 } } { g _ { 2 } ^ { 3 } - 27 g _ { 3 } ^ { 2 } }$ ; confidence 0.284
  
142. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s120340135.png ; $\alpha _ { H } ( \tilde { x } _ { + } ) - \alpha _ { H } ( \tilde { x } _ { - } ) = 1$ ; confidence 0.404
+
142. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013031.png ; $( \partial / \partial t _ { x } ) - Q _ { 0 } z ^ { x }$ ; confidence 0.284
  
143. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091910/s09191051.png ; $\sim \frac { 2 ^ { n } } { \operatorname { log } _ { 2 } n }$ ; confidence 0.975
+
143. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240196.png ; $\sqrt { 3 }$ ; confidence 0.281
  
144. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091910/s091910121.png ; $T _ { i } = C A ^ { i } B ^ { i } B$ ; confidence 0.233
+
144. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040685.png ; $X \in X$ ; confidence 0.278
  
145. https://www.encyclopediaofmath.org/legacyimages/s/s110/s110330/s11033016.png ; $- 5 \rightarrow - 14 \rightarrow - 7 \rightarrow - 20 \rightarrow - 10 \rightarrow - 5$ ; confidence 0.902
+
145. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082060/r082060102.png ; $f ^ { \mu } | _ { K }$ ; confidence 0.278
  
146. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091960/s0919603.png ; $R = \{ \pi ( i ) : \square i \in I \}$ ; confidence 0.950
+
146. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240191.png ; $X ^ { \prime } X \hat { \beta } = X ^ { \prime } y$ ; confidence 0.277
  
147. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091960/s09196011.png ; $\{ \pi ( i ) : \square i \in I _ { 0 } \}$ ; confidence 0.752
+
147. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240430.png ; $a ^ { \prime } \Theta$ ; confidence 0.275
  
148. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064057.png ; $L ^ { 1 } ( R ) \cap L ^ { \infty } ( R )$ ; confidence 0.831
+
148. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027051.png ; $\{ x _ { n j } ^ { \prime } \}$ ; confidence 0.273
  
149. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120020/t12002014.png ; $T ^ { + } = \cap _ { N > 0 } \sigma ( X _ { n } : n \geq N )$ ; confidence 0.699
+
149. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045090/g045090279.png ; $G _ { A B } ^ { ( c ) } ( t - t ^ { \prime } ) = \ll A ( t ) | B ( t ^ { \prime } ) \gg ( c ) \equiv \langle T _ { \eta } A ( t ) B ( t ^ { \prime } ) \rangle$ ; confidence 0.272
  
150. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092240/t0922406.png ; $k = R / m$ ; confidence 0.483
+
150. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012410/a01241063.png ; $s = s ^ { * } \cup ( s \backslash s ^ { * } ) ^ { * } U \ldots$ ; confidence 0.271
  
151. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092250/t09225012.png ; $g ^ { ( i ) }$ ; confidence 0.484
+
151. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016960/b016960150.png ; $99$ ; confidence 0.271
  
152. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130040/t13004015.png ; $( n + 1 ) a _ { n + 1 } + \alpha _ { n } = \tau$ ; confidence 0.385
+
152. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a1202207.png ; $| e | | < 1$ ; confidence 0.271
  
153. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130040/t13004014.png ; $\tau x ^ { n }$ ; confidence 0.790
+
153. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058920/l05892067.png ; $Z y \rightarrow \infty$ ; confidence 0.270
  
154. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005033.png ; $D _ { A } ^ { 2 } = 0$ ; confidence 0.998
+
154. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040230/f040230147.png ; $\sum _ { \nu = 1 } ^ { k - 1 } \frac { B _ { \nu } } { \nu ! } \{ f ^ { \langle \nu - 1 \rangle } ( n ) - f ^ { \langle \nu - 1 \rangle } ( 0 ) \} + \frac { B _ { k } } { k ! } \sum _ { x = 0 } ^ { n - 1 } f ^ { ( k ) } ( x + \theta )$ ; confidence 0.269
  
155. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005053.png ; $\sigma ^ { \prime } ( A )$ ; confidence 0.999
+
155. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120190/f12019010.png ; $N = \{ G \backslash ( \cup _ { x \in G } x ^ { - 1 } H x ) \} \cup \{ 1 \}$ ; confidence 0.269
  
156. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120030/t12003042.png ; $\psi = \Psi ^ { \prime }$ ; confidence 0.559
+
156. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021570/c02157044.png ; $\chi \pi _ { \alpha }$ ; confidence 0.268
  
157. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092470/t09247071.png ; $E _ { 1 } E _ { 2 } E _ { 3 }$ ; confidence 0.997
+
157. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200105.png ; $( C ( S ) , \overline { g } ) = ( R _ { + } \times S , d \nu ^ { 2 } + r ^ { 2 } g )$ ; confidence 0.265
  
158. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092470/t092470182.png ; $e _ { v } \leq \mathfrak { e } _ { v } + 1$ ; confidence 0.197
+
158. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i130030178.png ; $h ( [ a ] )$ ; confidence 0.265
  
159. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092470/t092470133.png ; $R _ { T ^ { \prime \prime } }$ ; confidence 0.675
+
159. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080940/r08094048.png ; $\{ \alpha _ { n } \} _ { \aleph = 0 } ^ { \infty }$ ; confidence 0.264
  
160. https://www.encyclopediaofmath.org/legacyimages/t/t110/t110020/t11002078.png ; $M _ { \mathscr { C } } M _ { b } M _ { \alpha ^ { \prime } } M _ { \phi }$ ; confidence 0.076
+
160. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059110/l05911071.png ; $+ \sum _ { i = 1 } ^ { s } \| k _ { i k } [ u ] _ { k } - \{ l _ { i } u \} _ { i k } \| _ { \Phi _ { i k } } + \| p _ { i k } \phi _ { i } - \{ \phi _ { i } \} _ { i k } \| _ { \Phi _ { i k } }$ ; confidence 0.263
  
161. https://www.encyclopediaofmath.org/legacyimages/t/t110/t110020/t11002049.png ; $e ^ { \prime }$ ; confidence 0.559
+
161. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023150/c023150187.png ; $\alpha : H ^ { n } ( : Z ) \rightarrow H ^ { n + 3 } ( : Z _ { 2 } )$ ; confidence 0.262
  
162. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092530/t09253011.png ; $( \pi | \tau _ { 1 } | \tau _ { 2 } )$ ; confidence 0.977
+
162. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l057000153.png ; $+ ( \lambda x y \cdot y ) : ( \sigma \rightarrow ( \tau \rightarrow \tau ) )$ ; confidence 0.262
  
163. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092600/t09260017.png ; $\theta ( z + \tau ) = \operatorname { exp } ( - 2 \pi i k z ) . \theta ( z )$ ; confidence 0.660
+
163. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076610/q07661044.png ; $\beta X = S \square x = \omega _ { \kappa } X$ ; confidence 0.261
  
164. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092600/t09260081.png ; $\delta = 2$ ; confidence 0.999
+
164. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301301.png ; $\left. \begin{array} { l } { i \frac { \partial } { \partial t } q ( x , t ) = i q t = - \frac { 1 } { 2 } q x x + q ^ { 2 } r } \\ { i \frac { \partial } { \partial t } r ( x , t ) = i r t = \frac { 1 } { 2 } r x - q r ^ { 2 } } \end{array} \right.$ ; confidence 0.260
  
165. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092600/t09260032.png ; $\operatorname { lm } A = \| \operatorname { lm } \alpha _ { \mu \nu } |$ ; confidence 0.510
+
165. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022037.png ; $r _ { ess } ( T )$ ; confidence 0.259
  
166. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092600/t092600123.png ; $B = I _ { p }$ ; confidence 0.852
+
166. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a1201308.png ; $m$ ; confidence 0.259
  
167. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120050/t12005046.png ; $d f _ { x } : R ^ { n } \rightarrow R ^ { p }$ ; confidence 0.932
+
167. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087770/s08777049.png ; $V _ { k } ( H ^ { n } ) = \frac { Sp ( n ) } { Sp ( n - k ) }$ ; confidence 0.259
  
168. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130090/t13009023.png ; $f ^ { - 1 } ( S )$ ; confidence 0.998
+
168. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020220.png ; $\delta ^ { * } \circ ( t - r ) ^ { * } \beta _ { 1 } = k ( t ^ { * } \square ^ { - 1 } \beta _ { 3 } )$ ; confidence 0.259
  
169. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092650/t09265044.png ; $c < 2$ ; confidence 0.987
+
169. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v09638089.png ; $\pi : B \rightarrow G ^ { k } ( V )$ ; confidence 0.258
  
170. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092650/t09265019.png ; $u x + v x ^ { 2 } + w x ^ { 3 } + t x ^ { 4 }$ ; confidence 0.989
+
170. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052500/i05250054.png ; $L ^ { \prime }$ ; confidence 0.256
  
171. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092650/t09265033.png ; $\{ \partial f \rangle$ ; confidence 0.295
+
171. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068370/o06837057.png ; $x _ { C }$ ; confidence 0.256
  
172. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092650/t09265012.png ; $x ^ { 3 } + x y ^ { 2 }$ ; confidence 1.000
+
172. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073700/p07370045.png ; $[ f _ { G } ]$ ; confidence 0.256
  
173. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t120060116.png ; $E ^ { Q } ( N )$ ; confidence 0.962
+
173. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044350/g044350101.png ; $D \Re \subset M$ ; confidence 0.255
  
174. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006058.png ; $N \geq Z$ ; confidence 0.919
+
174. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010710/a01071024.png ; $A = A _ { 1 } \cap \ldots \cap A _ { n }$ ; confidence 0.254
  
175. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092720/t09272013.png ; $\Delta _ { i j } = \Delta _ { j i } = \sqrt { ( x _ { i } - x _ { j } ) ^ { 2 } + ( y _ { i } - y _ { j } ) ^ { 2 } + ( z _ { i } - z _ { j } ) ^ { 2 } }$ ; confidence 0.489
+
175. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027180/c027180124.png ; $7$ ; confidence 0.254
  
176. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092730/t09273032.png ; $M = M _ { 1 } \# M _ { 2 }$ ; confidence 0.954
+
176. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030053.png ; $\sum _ { i = 1 } ^ { n } S _ { i } S _ { i } ^ { * } < I$ ; confidence 0.253
  
177. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120080/t12008015.png ; $O _ { S } ^ { * }$ ; confidence 0.936
+
177. https://www.encyclopediaofmath.org/legacyimages/i/i052/i052980/i05298049.png ; $L ^ { \prime } ( T _ { x } M )$ ; confidence 0.252
  
178. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120080/t12008049.png ; $( 5 \times 10 ^ { 6 } r ) ^ { 3 }$ ; confidence 0.525
+
178. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076800/q07680094.png ; $\tau _ { 0 } ^ { e ^ { 3 } }$ ; confidence 0.252
  
179. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092800/t09280017.png ; $X _ { ( \tau _ { 1 } + \ldots + \tau _ { j - 1 } + 1 ) } = \ldots = X _ { ( \tau _ { 1 } + \ldots + \tau _ { j } ) }$ ; confidence 0.575
+
179. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010820/a01082073.png ; $X \in Ob \odot$ ; confidence 0.251
  
180. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092810/t092810186.png ; $B s$ ; confidence 0.576
+
180. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120370/b12037092.png ; $\sum \frac { 1 } { 1 }$ ; confidence 0.251
  
181. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092810/t092810205.png ; $\beta ( M )$ ; confidence 0.995
+
181. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240242.png ; $SS _ { H } = \sum _ { i = 1 } ^ { \Psi } z _ { i } ^ { 2 }$ ; confidence 0.251
  
182. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130100/t1301005.png ; $\square _ { H } T$ ; confidence 0.979
+
182. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110910/b11091027.png ; $\frac { \partial N _ { i } } { \partial t } + u _ { i } \nabla N _ { i } = G _ { i } - L _ { i }$ ; confidence 0.250
  
183. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014052.png ; $( Q )$ ; confidence 0.999
+
183. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073830/p07383050.png ; $E \subset X = R ^ { \prime }$ ; confidence 0.250
  
184. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140116.png ; $q R$ ; confidence 0.245
+
184. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076850/q07685043.png ; $E [ \tau _ { j } ^ { S } - \tau _ { j } ^ { \dot { e } } ] ^ { 2 + \gamma }$ ; confidence 0.250
  
185. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140169.png ; $q _ { A }$ ; confidence 0.118
+
185. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033190/d03319041.png ; $t _ { 8 } + 1 / 2 = t _ { n } + \tau / 2$ ; confidence 0.248
  
186. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013055.png ; $M = M \Lambda ^ { t }$ ; confidence 0.505
+
186. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006043.png ; $\int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle ^ { 2 } } { \lambda } _ { d } \lambda < E _ { 0 }$ ; confidence 0.248
  
187. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130150/t13015070.png ; $C ^ { * } E ( S ) \otimes _ { \delta } C _ { 0 } ( S )$ ; confidence 0.440
+
187. https://www.encyclopediaofmath.org/legacyimages/q/q076/q076500/q07650033.png ; $3 r ( L _ { 1 } \cap L _ { 2 } ) = 3 _ { r } ( L _ { 1 } ) + 3 r ( L _ { 2 } )$ ; confidence 0.248
  
188. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130150/t13015064.png ; $K ( L ^ { 2 } ( S ) )$ ; confidence 0.779
+
188. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a1301308.png ; $s l _ { 2 }$ ; confidence 0.247
  
189. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120150/t12015061.png ; $( \Delta ^ { \alpha } \xi ) ^ { \# } = \Delta ^ { - \overline { \alpha } } \xi ^ { \# }$ ; confidence 0.710
+
189. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055630/k0556303.png ; $| m K _ { V ^ { \prime } } | ^ { J }$ ; confidence 0.246
  
190. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120150/t1201505.png ; $\eta \in A \mapsto \xi \eta \in A$ ; confidence 0.962
+
190. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010217.png ; $1 / | y ^ { i } _ { x ^ { i } } ^ { * }$ ; confidence 0.245
  
191. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092980/t09298063.png ; $f \in S ( R ^ { n } )$ ; confidence 0.981
+
191. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035170/e03517056.png ; $\| \hat { A } - A \| \leq \delta$ ; confidence 0.245
  
192. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150622.png ; $( f _ { i } : B _ { i } \rightarrow B ) _ { i \in l }$ ; confidence 0.575
+
192. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055080/k05508019.png ; $\nu _ { 0 } \in C ^ { n }$ ; confidence 0.245
  
193. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150169.png ; $F \in \gamma$ ; confidence 0.994
+
193. https://www.encyclopediaofmath.org/legacyimages/o/o070/o070010/o070010110.png ; $X = \cup _ { \alpha } X _ { \alpha }$ ; confidence 0.245
  
194. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150743.png ; $\left. \begin{array} { c c c } { B _ { i } } & { \stackrel { h _ { i } } { \rightarrow } } & { A _ { i } } \\ { g _ { i } \downarrow } & { \square } & { \downarrow f _ { i } } \\ { B } & { \vec { f } } & { A } \end{array} \right.$ ; confidence 0.342
+
194. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140116.png ; $q R$ ; confidence 0.245
  
195. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150395.png ; $A \wedge B$ ; confidence 0.923
+
195. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110990/b11099011.png ; $V _ { Q }$ ; confidence 0.244
  
196. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150306.png ; $= C$ ; confidence 0.931
+
196. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110130/b110130209.png ; $v ( \lambda ) = ( y _ { 0 } + \lambda ^ { - 1 } y _ { - 1 } + \ldots + \lambda ^ { - p } y - p ) y _ { 0 } ^ { - 1 / 2 }$ ; confidence 0.241
  
197. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150450.png ; $\operatorname { sin } 0$ ; confidence 0.092
+
197. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013045.png ; $= \frac { 1 } { 2 } \operatorname { Tr } ( \sum _ { r = 0 } ^ { j } ( j - r ) Q _ { r } Q _ { k + j - r } + \frac { 1 } { 2 } \sum _ { r = 0 } ^ { j } ( r - k ) Q _ { r } Q _ { k + j - r } )$ ; confidence 0.240
  
198. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150393.png ; $\{ p _ { i } ^ { - 1 } U _ { i } : U _ { i } \in \mu _ { i \square } \text { and } i \in I \}$ ; confidence 0.601
+
198. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240527.png ; $( n$ ; confidence 0.239
  
199. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093150/t093150728.png ; $A ^ { * } = A \cup \{ \infty _ { A } \}$ ; confidence 0.980
+
199. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097870/w09787060.png ; $\prod _ { \nu } : \prod _ { i \in I _ { \nu } } f _ { i } : = \sum _ { G } \prod _ { e \in G } < f _ { e _ { 1 } } f _ { e _ { 2 } } > : \prod _ { i \notin [ G ] } f _ { i : }$ ; confidence 0.238
  
200. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093160/t09316047.png ; $p _ { 1 } \otimes \sim p _ { 2 }$ ; confidence 0.782
+
200. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013020.png ; $0.00$ ; confidence 0.237
  
201. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093160/t09316053.png ; $\sum _ { k = 1 } ^ { \infty } p _ { 1 } ( x _ { k } ) p _ { 2 } ( y _ { k } ) \leq p _ { 1 } \overline { Q } p _ { 2 } ( u ) + \epsilon$ ; confidence 0.229
+
201. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026450/c02645091.png ; $X _ { 1 }$ ; confidence 0.237
  
202. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093180/t093180434.png ; $D ( R ^ { n + k } )$ ; confidence 0.995
+
202. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015400/b01540091.png ; $\Psi _ { 1 } ( Y ) / \hat { q } ( Y ) \leq \psi ( Y ) \leq \Psi _ { 2 } ( Y ) / \hat { q } ( Y )$ ; confidence 0.236
  
203. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093230/t09323048.png ; $H \rightarrow TOP$ ; confidence 0.688
+
203. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047070/h0470704.png ; $\alpha _ { i k } = \overline { a _ { k i } }$ ; confidence 0.235
  
204. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093230/t093230103.png ; $\left. \begin{array} { c c c } { \square } & { \square } & { B P L } \\ { \square } & { \square } & { \downarrow } \\ { X } & { \vec { \tau } _ { X } } & { B G } \end{array} \right.$ ; confidence 0.066
+
204. https://www.encyclopediaofmath.org/legacyimages/j/j054/j054050/j05405038.png ; $\theta _ { 2 } ( v \pm \tau ) = e ^ { - i \pi \tau } \cdot e ^ { - 2 i \pi v } \cdot \theta _ { 2 } ( v )$ ; confidence 0.234
  
205. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093230/t09323071.png ; $X \rightarrow P L / O$ ; confidence 0.928
+
205. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083170/s08317062.png ; $\tilde { D } = E \{ M | m = 0 \} = \frac { ( \sum _ { r = 1 } ^ { N - n } r \frac { C _ { N - r } ^ { n } } { C _ { N } ^ { n } } p _ { r } ) } { P \{ m = 0 \} }$ ; confidence 0.234
  
206. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093260/t09326056.png ; $d \Phi$ ; confidence 0.791
+
206. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110370/b11037052.png ; $= 0 \text { as. } \cdot P _ { \theta _ { 0 } } ]$ ; confidence 0.233
  
207. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093260/t09326078.png ; $d = 6$ ; confidence 0.998
+
207. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091910/s091910121.png ; $T _ { i } = C A ^ { i } B ^ { i } B$ ; confidence 0.233
  
208. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093260/t09326038.png ; $( X ) \in M$ ; confidence 0.998
+
208. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020190/c02019023.png ; $C A$ ; confidence 0.232
  
209. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093330/t09333059.png ; $r _ { 2 } \in R$ ; confidence 0.862
+
209. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031380/d031380303.png ; $\Pi \stackrel { D } { 3 } = F _ { \sigma \delta }$ ; confidence 0.232
  
210. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093340/t0933407.png ; $S _ { j } ^ { k } = \Gamma _ { i j } ^ { k } - \Gamma _ { j i } ^ { k }$ ; confidence 0.505
+
210. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015560/b01556018.png ; $D \times D \in \Gamma ^ { 2 }$ ; confidence 0.230
  
211. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093570/t0935701.png ; $x = \pm \alpha \operatorname { ln } \frac { \alpha + \sqrt { \alpha ^ { 2 } - y ^ { 2 } } } { y } - \sqrt { \alpha ^ { 2 } - y ^ { 2 } }$ ; confidence 0.391
+
211. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022780/c022780328.png ; $im ( \Omega _ { S C } \rightarrow \Omega _ { O } )$ ; confidence 0.230
  
212. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093670/t09367085.png ; $r < | w | < 1$ ; confidence 0.982
+
212. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130010/k13001041.png ; $A | D _ { + } \rangle - A ^ { - 1 } \langle D _ { - } \} = ( A ^ { 2 } - A ^ { - 2 } ) \langle D _ { 0 } \}$ ; confidence 0.230
  
213. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093670/t09367092.png ; $d s _ { é } = \frac { | d z | } { 1 + | z | ^ { 2 } }$ ; confidence 0.470
+
213. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065160/m06516021.png ; $\operatorname { ess } \operatorname { sup } _ { X } | f ( x ) | = \operatorname { lim } _ { n \rightarrow \infty } ( \frac { \int | f ( x ) | ^ { n } d M _ { X } } { \int _ { X } d M _ { x } } )$ ; confidence 0.229
  
214. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093670/t09367039.png ; $\operatorname { lim } _ { \epsilon \rightarrow 0 } d ( E _ { \epsilon } ) = d ( E )$ ; confidence 0.993
+
214. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093160/t09316053.png ; $\sum _ { k = 1 } ^ { \infty } p _ { 1 } ( x _ { k } ) p _ { 2 } ( y _ { k } ) \leq p _ { 1 } \overline { Q } p _ { 2 } ( u ) + \epsilon$ ; confidence 0.229
  
215. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093710/t0937107.png ; $x = f ( \alpha )$ ; confidence 0.993
+
215. https://www.encyclopediaofmath.org/legacyimages/e/e037/e037040/e03704050.png ; $n + = n - = n$ ; confidence 0.228
  
216. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093770/t09377057.png ; $\mathfrak { A } f ( x ) = \operatorname { lim } _ { U ! x } [ \frac { E _ { x } f ( x _ { \tau } ) - f ( x ) } { E _ { x } \tau } ]$ ; confidence 0.104
+
216. https://www.encyclopediaofmath.org/legacyimages/x/x120/x120010/x120010101.png ; $\operatorname { Aut } ( R ) / \operatorname { ln } n ( R ) \cong H$ ; confidence 0.228
  
217. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093770/t09377067.png ; $\mathfrak { A } f$ ; confidence 0.742
+
217. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110410/c11041043.png ; $C X Y$ ; confidence 0.226
  
218. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093770/t09377043.png ; $R ^ { 0 } f$ ; confidence 0.999
+
218. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073530/p07353041.png ; $t ^ { i _ { 1 } } \cdots \dot { d p } = \operatorname { det } \| x _ { i } ^ { i _ { k } } \|$ ; confidence 0.226
  
219. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093770/t09377039.png ; $g = R ^ { \alpha } f$ ; confidence 0.864
+
219. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110250/c1102508.png ; $20$ ; confidence 0.225
  
220. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093860/t09386023.png ; $P ( S )$ ; confidence 0.765
+
220. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025700/c02570021.png ; $I \rightarrow \cup _ { i \in l } J _ { i }$ ; confidence 0.225
  
221. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093890/t09389045.png ; $o ( N ) / N \rightarrow 0$ ; confidence 0.792
+
221. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026450/c02645033.png ; $\sum _ { K \in \mathscr { K } } \lambda _ { K } \chi _ { K } ( i ) = \chi _ { I } ( i ) \quad \text { for all } i \in I$ ; confidence 0.223
  
222. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093900/t093900196.png ; $T _ { 23 } n ( \operatorname { cos } \pi \omega )$ ; confidence 0.946
+
222. https://www.encyclopediaofmath.org/legacyimages/m/m063/m063710/m06371091.png ; $n _ { 1 } < n _ { 2 } .$ ; confidence 0.222
  
223. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093900/t09390073.png ; $g _ { n } ( \Omega )$ ; confidence 0.875
+
223. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043470/g0434707.png ; $\nabla _ { \theta } : H _ { \delta R } ^ { 1 } ( X / K ) \rightarrow H _ { \partial R } ^ { 1 } ( X / K )$ ; confidence 0.221
  
224. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093900/t093900115.png ; $l \mu \frac { \partial W ^ { k } } { \partial x } + ( 1 - c ) W ^ { k } = c ( \Phi _ { 0 } ^ { k } - \phi _ { 0 } ^ { k } )$ ; confidence 0.308
+
224. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012460/a012460130.png ; $X \equiv 0$ ; confidence 0.220
  
225. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093900/t093900146.png ; $Q _ { n } W ^ { k } = P _ { n } c ( W ^ { k } + \Phi _ { 0 } ^ { k } - \phi _ { 0 } ^ { k } )$ ; confidence 0.976
+
225. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080740/r0807408.png ; $x _ { n m _ { n } } \rightarrow ( 0 )$ ; confidence 0.220
  
226. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093900/t093900154.png ; $g _ { k } = ( 1 + y _ { k } ) / 2$ ; confidence 0.953
+
226. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240383.png ; $H ^ { \prime }$ ; confidence 0.219
  
227. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093980/t0939808.png ; $V = f ^ { - 1 } ( X )$ ; confidence 1.000
+
227. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110270/b11027042.png ; $P ( s S ) = P ( S )$ ; confidence 0.219
  
228. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093990/t09399044.png ; $Q _ { 1 } \cup \square \ldots \cup Q _ { m }$ ; confidence 0.878
+
228. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031750/d03175051.png ; $Z _ { h }$ ; confidence 0.217
  
229. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094000/t09400030.png ; $f ( x ) = g ( y )$ ; confidence 1.000
+
229. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087420/s087420178.png ; $\mathfrak { A } _ { \infty } = \overline { U _ { V \subset R ^ { 3 } } } A ( \mathcal { H } _ { V } )$ ; confidence 0.216
  
230. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130210/t13021052.png ; $2 / ( 3 N / 2 )$ ; confidence 0.990
+
230. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058430/l058430107.png ; $g ^ { \prime } / ( 1 - u ) g ^ { \prime } = \overline { g }$ ; confidence 0.215
  
231. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094240/t09424015.png ; $\frac { a _ { 0 } } { 4 } x ^ { 2 } - \sum _ { k = 1 } ^ { \infty } \frac { a _ { k } \operatorname { cos } k x + b _ { k } \operatorname { sin } k x } { k ^ { 2 } }$ ; confidence 0.667
+
231. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015660/b01566071.png ; $\nu = a + x + 2 [ \frac { n - t - x - \alpha } { 2 } ] + 1$ ; confidence 0.213
  
232. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094300/t094300134.png ; $\operatorname { Fix } ( T ) \subset \mathfrak { R }$ ; confidence 0.710
+
232. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044340/g044340202.png ; $\xi _ { p } \in ( \nu F ^ { m } ) p$ ; confidence 0.212
  
233. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094300/t09430077.png ; $\left. \begin{array} { c c c } { T A } & { \stackrel { T f } { S } } & { T B } \\ { \alpha \downarrow } & { \square } & { \downarrow \beta } \\ { A } & { \vec { f } } & { B } \end{array} \right.$ ; confidence 0.204
+
233. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031730/d03173088.png ; $| u - v | \leq \operatorname { inf } _ { w ^ { \prime } \in K } | u - w |$ ; confidence 0.210
  
234. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094420/t09442025.png ; $\overline { U } / \partial \overline { U }$ ; confidence 0.976
+
234. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082070/r08207022.png ; $R _ { i l k } ^ { q } = - R _ { k l } ^ { q }$ ; confidence 0.210
  
235. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094440/t09444040.png ; $u _ { m } = u ( M _ { m } )$ ; confidence 0.360
+
235. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031280/d031280129.png ; $f : X ^ { \cdot } \rightarrow Y$ ; confidence 0.209
  
236. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200142.png ; $m > - 1$ ; confidence 0.998
+
236. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031470/d0314706.png ; $| \hat { b } _ { n } | = 1$ ; confidence 0.209
  
237. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200179.png ; $\operatorname { Re } G _ { 1 } ( r ) \geq B$ ; confidence 0.984
+
237. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013042.png ; $X _ { i } \in \operatorname { sl } _ { 2 } ( C )$ ; confidence 0.209
  
238. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094530/t094530109.png ; $\sum ( k _ { i } - 1 )$ ; confidence 0.930
+
238. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001098.png ; $k$ ; confidence 0.208
  
239. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094540/t09454051.png ; $\{ \omega _ { n } ^ { + } ( V ) \}$ ; confidence 0.949
+
239. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014310/a01431097.png ; $| x$ ; confidence 0.207
  
240. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094600/t09460022.png ; $f _ { 0 } \neq 0$ ; confidence 0.997
+
240. https://www.encyclopediaofmath.org/legacyimages/f/f042/f042060/f042060121.png ; $\mathfrak { g } \otimes \mathfrak { g } \rightarrow U \mathfrak { g } \otimes U \mathfrak { g } \otimes U _ { \mathfrak { g } }$ ; confidence 0.207
  
241. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094600/t0946003.png ; $\alpha \geq A _ { 0 }$ ; confidence 0.904
+
241. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010600/a01060019.png ; $H _ { \hat { j } }$ ; confidence 0.205
  
242. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094650/t09465038.png ; $\forall v \phi$ ; confidence 0.989
+
242. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016650/b0166503.png ; $2 \int \int _ { G } ( x \frac { \partial y } { \partial u } \frac { \partial y } { \partial v } ) d u d v = \oint _ { \partial G } ( x y d y )$ ; confidence 0.204
  
243. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094650/t09465066.png ; $\in M$ ; confidence 0.717
+
243. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031380/d031380296.png ; $\sum _ { \sim } D _ { n + 1 } ^ { 0 }$ ; confidence 0.204
  
244. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094650/t09465036.png ; $( \phi \& \psi )$ ; confidence 0.997
+
244. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094300/t09430077.png ; $\left. \begin{array} { c c c } { T A } & { \stackrel { T f } { S } } & { T B } \\ { \alpha \downarrow } & { \square } & { \downarrow \beta } \\ { A } & { \vec { f } } & { B } \end{array} \right.$ ; confidence 0.204
  
245. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094660/t09466060.png ; $\{ f ( z ) \}$ ; confidence 1.000
+
245. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020740/c020740146.png ; $\alpha \rightarrow \dot { b }$ ; confidence 0.200
  
246. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094660/t09466020.png ; $\phi ( z ) = \frac { 1 - z ^ { 2 } } { z } f ( z ) \in C$ ; confidence 0.993
+
246. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010080/a0100805.png ; $\{ A _ { n _ { 1 } } \ldots n _ { k } \}$ ; confidence 0.200
  
247. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095070/u09507044.png ; $T ( X ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } X = 1 } \\ { 0 } & { \text { if } X \geq 2 } \end{array} \right.$ ; confidence 0.976
+
247. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012970/a012970198.png ; $\hat { W } \square _ { \infty } ^ { \gamma }$ ; confidence 0.199
  
248. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095210/u0952109.png ; $f _ { \alpha } ( x ) \geq - c$ ; confidence 0.977
+
248. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033420/d03342015.png ; $\sigma _ { k }$ ; confidence 0.198
  
249. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095230/u09523081.png ; $\{ d f _ { n } / d x \}$ ; confidence 0.954
+
249. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092470/t092470182.png ; $e _ { v } \leq \mathfrak { e } _ { v } + 1$ ; confidence 0.197
  
250. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095290/u09529039.png ; $t \rightarrow t + w z$ ; confidence 0.466
+
250. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120190/e12019037.png ; $l _ { x }$ ; confidence 0.196
  
251. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095290/u09529022.png ; $w = \operatorname { sin }$ ; confidence 0.905
+
251. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023150/c02315041.png ; $f : S ^ { m } \rightarrow S ^ { n }$ ; confidence 0.195
  
252. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095400/u09540011.png ; $( g - 1 ) ^ { n } = 0$ ; confidence 0.996
+
252. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059160/l059160187.png ; $\dot { u } = A _ { n } u$ ; confidence 0.195
  
253. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095410/u09541013.png ; $U _ { n } ( K )$ ; confidence 0.987
+
253. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120010/e1200103.png ; $A \stackrel { f } { \rightarrow } B = A \stackrel { é } { \rightarrow } f [ A ] \stackrel { m } { \rightarrow } B$ ; confidence 0.193
  
254. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095410/u09541052.png ; $g ^ { p } = e$ ; confidence 0.978
+
254. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083330/s0833306.png ; $\phi _ { \mathscr { A } } ( . )$ ; confidence 0.193
  
255. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095440/u09544022.png ; $O ( \epsilon _ { N } )$ ; confidence 0.478
+
255. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a0100205.png ; $P = \cup _ { n _ { 1 } , \ldots , n _ { k } , \ldots } \cap _ { k = 1 } ^ { \infty } E _ { n _ { 1 } } \square \ldots x _ { k }$ ; confidence 0.192
  
256. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095440/u09544020.png ; $U ( \epsilon )$ ; confidence 0.998
+
256. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015390/b01539020.png ; $\rho ( \theta , \delta ) = \int _ { Y } L ( \theta , \delta ( x ) ) P _ { \theta } ( d x )$ ; confidence 0.192
  
257. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095620/u09562096.png ; $\sum _ { k = 1 } ^ { \infty } | \alpha _ { k } | ^ { 2 } = \frac { 1 } { 2 \pi } \int _ { 0 } ^ { 2 \pi } | f ( e ^ { i t } ) | ^ { 2 } d t \leq 1$ ; confidence 0.986
+
257. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110490/c1104902.png ; $\sqrt { 2 }$ ; confidence 0.191
  
258. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095630/u09563071.png ; $U : B \rightarrow A$ ; confidence 0.544
+
258. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010011.png ; $\left\{ \begin{array} { l l } { \gamma \geq \frac { 1 } { 2 } } & { \text { forn } = 1 } \\ { \gamma > 0 } & { \text { forn } = 2 } \\ { \gamma \geq 0 } & { \text { forn } \geq 3 } \end{array} \right.$ ; confidence 0.191
  
259. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095680/u09568015.png ; $( n \geq 0 )$ ; confidence 1.000
+
259. https://www.encyclopediaofmath.org/legacyimages/p/p110/p110120/p110120432.png ; $\operatorname { limsup } _ { n \rightarrow + \infty } \frac { 1 } { n } \operatorname { log } + P _ { N } ( f ) \geq h ( f )$ ; confidence 0.191
  
260. https://www.encyclopediaofmath.org/legacyimages/u/u095/u095820/u09582023.png ; $v ( x ) \geq f ( x )$ ; confidence 0.996
+
260. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080190/r08019038.png ; $\{ f ^ { t } | \Sigma _ { X } \} _ { t \in R }$ ; confidence 0.191
  
261. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096020/v096020116.png ; $f ( z ) \in K$ ; confidence 0.998
+
261. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010125.png ; $\dot { i } \leq n$ ; confidence 0.190
  
262. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096020/v096020108.png ; $\lambda \leq 0.5$ ; confidence 0.968
+
262. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074710/p07471055.png ; $g _ { 0 } g ^ { \prime } \in G$ ; confidence 0.189
  
263. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096020/v096020147.png ; $( f ) \subseteq V ( f )$ ; confidence 0.998
+
263. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026010/c026010308.png ; $v _ { ( E ) } = v$ ; confidence 0.188
  
264. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096040/v0960408.png ; $s ( r )$ ; confidence 0.997
+
264. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010100.png ; $O = G / \operatorname { Sp } ( 1 ) . K$ ; confidence 0.187
  
265. https://www.encyclopediaofmath.org/legacyimages/v/v110/v110020/v11002046.png ; $x \in Y ( u )$ ; confidence 0.570
+
265. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030060/d03006013.png ; $+ \frac { 1 } { 2 \alpha } \int _ { x - w t } ^ { x + c t } \psi ( \xi ) d \xi + \frac { 1 } { 2 } [ \phi ( x + a t ) + \phi ( x - a t ) ]$ ; confidence 0.187
  
266. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096350/v0963509.png ; $( a + b ) + c = a + ( b + c )$ ; confidence 0.946
+
266. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046370/h04637012.png ; $\int _ { \alpha } ^ { b } \theta ^ { p } ( x ) d x \leq 2 ( \frac { p } { p - 1 } ) ^ { p } \int _ { a } ^ { b } f ^ { p } ( x ) d x$ ; confidence 0.187
  
267. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096350/v09635084.png ; $a \perp b$ ; confidence 0.521
+
267. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c12001098.png ; $\rho _ { j \overline { k } } = \partial ^ { 2 } \rho / \partial z _ { j } \partial z _ { k }$ ; confidence 0.185
  
268. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096350/v09635060.png ; $\left. \begin{array} { l l l } { \alpha _ { 1 } } & { \alpha _ { 2 } } & { \alpha _ { 3 } } \\ { b _ { 1 } } & { b _ { 2 } } & { b _ { 3 } } \\ { c _ { 1 } } & { c _ { 2 } } & { c _ { 3 } } \end{array} \right| = 0$ ; confidence 0.378
+
268. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043780/g043780231.png ; $\overline { h } ( X ) = \operatorname { lim } _ { h } h ^ { * } ( X _ { \alpha } )$ ; confidence 0.185
  
269. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v09638081.png ; $u ^ { * } ( \pi )$ ; confidence 0.996
+
269. https://www.encyclopediaofmath.org/legacyimages/p/p073/p073460/p07346086.png ; $P ^ { \perp } = \cap _ { v \in P } v ^ { \perp } = \emptyset$ ; confidence 0.185
  
270. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v096380113.png ; $\pi ^ { \prime } \oplus \theta ^ { \prime }$ ; confidence 0.992
+
270. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023530/c023530133.png ; $\Pi ^ { N } \tau$ ; confidence 0.183
  
271. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v09638042.png ; $G ^ { k } ( V ) \times V$ ; confidence 0.950
+
271. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120250/s1202506.png ; $h _ { n } = \int _ { a } ^ { b } x ^ { n } h ( x ) d x$ ; confidence 0.183
  
272. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v096380128.png ; $w : \xi \oplus \zeta \rightarrow \pi$ ; confidence 0.996
+
272. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013090.png ; $N$ ; confidence 0.183
  
273. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v09638089.png ; $\pi : B \rightarrow G ^ { k } ( V )$ ; confidence 0.258
+
273. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025970/c02597042.png ; $e ^ { i } ( e _ { j } ) = \delta _ { j } ^ { s }$ ; confidence 0.182
  
274. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096380/v09638020.png ; $X ^ { \prime } \cap \pi ^ { - 1 } ( b )$ ; confidence 0.999
+
274. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001088.png ; $\hat { v } ^ { ( S ) }$ ; confidence 0.182
  
275. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096450/v09645016.png ; $+ \frac { 1 } { N ! } \int _ { t _ { 0 } } ^ { t } ( t - \tau ) ^ { N _ { r } ( N + 1 ) } ( \tau ) d \tau$ ; confidence 0.696
+
275. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043280/g0432804.png ; $\hat { K } _ { i }$ ; confidence 0.180
  
276. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130060/v13006019.png ; $j \in ( 1 / 2 ) Z$ ; confidence 0.983
+
276. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043340/g04334048.png ; $\sum _ { \Sigma } ^ { 3 } \square ^ { i \alpha } \neq 0$ ; confidence 0.180
  
277. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v130050114.png ; $1 _ { n } ( w ) = 0$ ; confidence 0.957
+
277. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011970/a01197046.png ; $U - \text { a.p. } \subset S ^ { p } - \text { a.p. } \subset W ^ { p } - \text { a.p. } \subset B ^ { p } - \text { a.p. } \quad p \geq 1$ ; confidence 0.179
  
278. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v1200207.png ; $f ^ { * } : H ^ { * } ( Y ) \rightarrow H ^ { * } ( X )$ ; confidence 0.997
+
278. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120460/b12046037.png ; $( \oplus _ { b } G _ { E B } b )$ ; confidence 0.179
  
279. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020197.png ; $H ^ { n } ( S ^ { n } )$ ; confidence 0.629
+
279. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120040/n1200405.png ; $A _ { i \psi }$ ; confidence 0.179
  
280. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020220.png ; $\delta ^ { * } \circ ( t - r ) ^ { * } \beta _ { 1 } = k ( t ^ { * } \square ^ { - 1 } \beta _ { 3 } )$ ; confidence 0.259
+
280. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072850/p0728502.png ; $_ { k }$ ; confidence 0.179
  
281. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020184.png ; $F : S ^ { n } \rightarrow K ( E ^ { n + 1 } \backslash \theta )$ ; confidence 0.783
+
281. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030620/d03062019.png ; $\alpha \in C \cup \{ \infty \}$ ; confidence 0.176
  
282. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020188.png ; $t ^ { * } : H ^ { N } ( S ^ { N } ) \rightarrow H ^ { N } ( \Gamma _ { S ^ { n } } )$ ; confidence 0.119
+
282. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013083.png ; $C$ ; confidence 0.175
  
283. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v12002064.png ; $d _ { k } = rd _ { Y } M _ { k }$ ; confidence 0.623
+
283. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110160/c11016063.png ; $( a b \alpha ) ^ { \alpha } = \alpha ^ { \alpha } b ^ { \alpha } \alpha ^ { \alpha }$ ; confidence 0.173
  
284. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096650/v0966506.png ; $n \geq 12$ ; confidence 0.886
+
284. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013033.png ; $\phi - ^ { 1 } ( \frac { \partial } { \partial x } - P _ { 0 z } ) \phi _ { - } = \frac { \partial } { \partial x } - P$ ; confidence 0.173
  
285. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096670/v09667018.png ; $P ^ { 2 r - k }$ ; confidence 0.936
+
285. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021470/c02147033.png ; $\tilde { Y } \square _ { j } ^ { ( k ) } \in Y _ { j }$ ; confidence 0.172
  
286. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096740/v0967406.png ; $v _ { \nu } ( t _ { 0 } ) = 0$ ; confidence 0.996
+
286. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110240/h11024025.png ; $n _ { s } + n _ { u } = n$ ; confidence 0.172
  
287. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096770/v0967704.png ; $F : \Omega \times R ^ { n } \times R ^ { n } \times S ^ { n } \rightarrow R$ ; confidence 0.909
+
287. https://www.encyclopediaofmath.org/legacyimages/r/r080/r080680/r08068010.png ; $x \frac { \operatorname { lim } _ { x \rightarrow D } u ( x ) = f ( y _ { 0 } ) } { x \in D }$ ; confidence 0.172
  
288. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v13007046.png ; $q e ^ { ( - i \theta ) }$ ; confidence 0.903
+
288. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087030/s08703096.png ; $\operatorname { max } _ { n \atop n } \| u ^ { n } \| _ { H } \leq e ^ { C _ { 1 } T } \{ \| \phi \| _ { H } + C _ { 0 } \sum _ { n } \tau \| f ^ { n + 1 } \| _ { H } \}$ ; confidence 0.172
  
289. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v1300709.png ; $\vec { V }$ ; confidence 0.987
+
289. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033570/d0335708.png ; $\sum _ { i \in I } \prod _ { j \in J ( i ) } \alpha _ { i j } = \prod _ { \phi \in \Phi } \sum _ { i \in I } \alpha _ { i \phi ( i ) }$ ; confidence 0.170
  
290. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096870/v09687032.png ; $\tau _ { j } < 0$ ; confidence 0.887
+
290. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110680/a11068093.png ; $L f \theta$ ; confidence 0.169
  
291. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011059.png ; $2 i$ ; confidence 0.747
+
291. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a13024067.png ; $e _ { j k }$ ; confidence 0.169
  
292. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011069.png ; $\theta = 2 \pi$ ; confidence 0.999
+
292. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087270/s08727063.png ; $V _ { x } 0 ( \lambda ) \sim \operatorname { exp } [ i \lambda S ( x ^ { 0 } ) ] \sum _ { k = 0 } ^ { \infty } ( \sum _ { l = 0 } ^ { N } \alpha _ { k l } \lambda ^ { - r _ { k } } ( \operatorname { ln } \lambda ) ^ { l } \}$ ; confidence 0.167
  
293. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011064.png ; $U = \frac { \Gamma } { 2 l } \operatorname { tanh } \frac { \pi b } { l } = \frac { \Gamma } { 2 l \sqrt { 2 } }$ ; confidence 0.768
+
293. https://www.encyclopediaofmath.org/legacyimages/s/s087/s087790/s08779013.png ; $RP ^ { \infty }$ ; confidence 0.165
  
294. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900234.png ; $\Pi I _ { \lambda }$ ; confidence 0.300
+
294. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010105.png ; $SU ( m ) / S ( U ( m - 2 ) \times U ( 1 ) ) , SO ( k ) / SO ( k - 4 ) \times Sp ( 1 )$ ; confidence 0.164
  
295. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v09690074.png ; $\phi ( U T U ^ { - 1 } ) = \phi ( T )$ ; confidence 0.999
+
295. https://www.encyclopediaofmath.org/legacyimages/m/m065/m065030/m06503013.png ; $\tilde { y } = \alpha _ { 21 } x + \alpha _ { 22 } y + \alpha _ { 23 } z + b$ ; confidence 0.163
  
296. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900232.png ; $III _ { 0 }$ ; confidence 0.560
+
296. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013058.png ; $s = \sum _ { i > 0 } C \lambda ^ { i } \left( \begin{array} { c c } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) \oplus \sum _ { i > 0 } C \lambda ^ { - i } \left( \begin{array} { c c } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) \oplus C _ { i }$ ; confidence 0.161
  
297. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900125.png ; $P \sim P _ { 1 }$ ; confidence 0.999
+
297. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050790/i05079039.png ; $| \alpha _ { 1 } + \ldots + \alpha _ { n } | \leq | \alpha _ { 1 } | + \ldots + | \alpha _ { n } |$ ; confidence 0.160
  
298. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900122.png ; $Q = U U ^ { * }$ ; confidence 0.977
+
298. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240407.png ; $M _ { E } = \sum _ { i j k } ( y _ { i j k } - y _ { i j . } ) ^ { \prime } ( y _ { i j k } - y _ { i j } )$ ; confidence 0.159
  
299. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900124.png ; $P _ { 1 } \in A$ ; confidence 0.996
+
299. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013013.png ; $\frac { \partial } { \partial t _ { m } } P - \frac { \partial } { \partial x } Q ^ { ( m ) } + [ P , Q ^ { ( r ) } ] = 0 \Leftrightarrow$ ; confidence 0.156
  
300. https://www.encyclopediaofmath.org/legacyimages/w/w097/w097030/w09703012.png ; $\overline { \sum _ { g } n ( g ) g } = \sum w ( g ) n ( g ) g ^ { - 1 }$ ; confidence 0.832
+
300. https://www.encyclopediaofmath.org/legacyimages/z/z099/z099250/z09925023.png ; $001 c 23 + c 02 c 31 + c 03 c 12 \neq 0$ ; confidence 0.156

Revision as of 11:46, 1 September 2019

List

1. l11014014.png ; $\tilde { y } ( x ) = \operatorname { exp } ( - \epsilon ) f ( x \operatorname { exp } ( - \epsilon ) )$ ; confidence 0.405

2. s120340135.png ; $\alpha _ { H } ( \tilde { x } _ { + } ) - \alpha _ { H } ( \tilde { x } _ { - } ) = 1$ ; confidence 0.404

3. a130240452.png ; $P$ ; confidence 0.403

4. c020740324.png ; $( \alpha _ { e } ) _ { é \in E }$ ; confidence 0.403

5. c02518096.png ; $T _ { s ( x ) } ( E ) = \Delta _ { s ( x ) } \oplus T _ { s ( x ) } ( F _ { x } )$ ; confidence 0.402

6. i05226072.png ; $Z \in G$ ; confidence 0.401

7. a13013036.png ; $\partial / \partial x = \partial / \partial t _ { 1 }$ ; confidence 0.401

8. p07283021.png ; $\epsilon _ { i j } ^ { k }$ ; confidence 0.400

9. l060090100.png ; $\operatorname { dim } Z \cap \overline { S _ { k + q + 1 } } ( F | _ { X \backslash Z } ) \leq k$ ; confidence 0.399

10. i0521507.png ; $\forall x ( P ( x ) \vee \neg P ( x ) ) \wedge \neg \neg \neg x P ( x ) \supset \exists x P ( x )$ ; confidence 0.397

11. a12022033.png ; $5$ ; confidence 0.396

12. a11042079.png ; $25$ ; confidence 0.396

13. b12050014.png ; $M _ { t } : = \operatorname { sup } _ { s \leq t } W _ { s }$ ; confidence 0.396

14. r081560116.png ; $R _ { V } = \frac { 1 } { ( 2 \pi i ) ^ { n } } \int _ { \sigma _ { V } } f ( z ) d z$ ; confidence 0.396

15. c02718064.png ; $H ( K )$ ; confidence 0.395

16. d030020144.png ; $\operatorname { gr } D _ { X }$ ; confidence 0.395

17. e11008028.png ; $P _ { n } ( f ) = \int _ { S } f d P _ { n } = \frac { 1 } { n } \sum _ { i = 1 } ^ { n } f ( X _ { i } )$ ; confidence 0.394

18. t0935701.png ; $x = \pm \alpha \operatorname { ln } \frac { \alpha + \sqrt { \alpha ^ { 2 } - y ^ { 2 } } } { y } - \sqrt { \alpha ^ { 2 } - y ^ { 2 } }$ ; confidence 0.391

19. c022780377.png ; $1 B S G$ ; confidence 0.389

20. a130240508.png ; $E ( Z _ { 13 } ) = 0$ ; confidence 0.388

21. d03233041.png ; $r : h \rightarrow f ( x _ { 0 } + h ) - f ( x _ { 0 } ) - h _ { 0 } ( h )$ ; confidence 0.388

22. t13004015.png ; $( n + 1 ) a _ { n + 1 } + \alpha _ { n } = \tau$ ; confidence 0.385

23. b11099015.png ; $P _ { \alpha }$ ; confidence 0.384

24. f04132023.png ; $v _ { 0 } ^ { k }$ ; confidence 0.384

25. c1202805.png ; $X *$ ; confidence 0.383

26. a0100204.png ; $\{ E _ { n _ { 1 } } \ldots n _ { k } \}$ ; confidence 0.382

27. a13013023.png ; $= \operatorname { exp } ( x P _ { 0 } z + \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } ) g ( z ) . . \operatorname { exp } ( - x P _ { 0 } z - \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { \gamma } )$ ; confidence 0.382

28. i05097047.png ; $F ( M ^ { k } ) \subset \nabla \square ^ { n }$ ; confidence 0.382

29. c02592019.png ; $631$ ; confidence 0.381

30. a1301307.png ; $Q$ ; confidence 0.380

31. s08778021.png ; $w ^ { \prime }$ ; confidence 0.380

32. v09635060.png ; $\left. \begin{array} { l l l } { \alpha _ { 1 } } & { \alpha _ { 2 } } & { \alpha _ { 3 } } \\ { b _ { 1 } } & { b _ { 2 } } & { b _ { 3 } } \\ { c _ { 1 } } & { c _ { 2 } } & { c _ { 3 } } \end{array} \right| = 0$ ; confidence 0.378

33. t120010108.png ; $Sp ( 0 )$ ; confidence 0.378

34. a130240236.png ; $n - r$ ; confidence 0.377

35. a12015019.png ; $( g )$ ; confidence 0.376

36. p110120321.png ; $4 x$ ; confidence 0.375

37. h0471603.png ; $H ( z ) = \sum _ { i = 1 } ^ { n } \sum _ { j = 1 } ^ { n } a _ { i j } z _ { i } z _ { j }$ ; confidence 0.374

38. k055850103.png ; $D _ { \alpha }$ ; confidence 0.374

39. a1301305.png ; $P = P _ { 0 } z + P _ { 1 } : = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) z + \left( \begin{array} { l l } { 0 } & { q } \\ { r } & { 0 } \end{array} \right)$ ; confidence 0.374

40. b01703046.png ; $\mathfrak { M } _ { n }$ ; confidence 0.373

41. c12008028.png ; $A _ { j } A _ { k l } = A _ { k l } A _ { j }$ ; confidence 0.372

42. i05302096.png ; $\beta _ { k } q _ { k + 1 } = A q _ { k } - \beta _ { k - 1 } q _ { k - 1 } - \alpha _ { k } q _ { k k }$ ; confidence 0.371

43. s0870309.png ; $f _ { h } \in U _ { k }$ ; confidence 0.371

44. f041060205.png ; $d _ { C } ^ { - 1 } = \operatorname { det } \left\| \begin{array} { c c } { \phi _ { \theta } \theta } & { \phi _ { \theta x } } \\ { \phi _ { y } \theta } & { \phi _ { y x } } \end{array} \right\|$ ; confidence 0.370

45. a13013099.png ; $z \in C$ ; confidence 0.369

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

47. a11041070.png ; $K _ { X } ^ { v } \otimes L ^ { i }$ ; confidence 0.368

48. f120150202.png ; $n \| < C$ ; confidence 0.368

49. p07566043.png ; $\partial _ { x } = \partial / \partial x$ ; confidence 0.368

50. p07519074.png ; $E _ { i j }$ ; confidence 0.366

51. d03233040.png ; $b _ { 0 }$ ; confidence 0.363

52. l13006070.png ; $\frac { 1 } { 4 n } \operatorname { max } \{ \alpha _ { i } : 0 \leq i \leq t \} \leq \Delta _ { 2 } \leq \frac { 1 } { 4 n } ( \sum _ { i = 0 } ^ { t } \alpha _ { i } + 2 )$ ; confidence 0.363

53. d03232015.png ; $u _ { R } ^ { k } ( x ) = \sum _ { i = 1 } ^ { n } u _ { i } a _ { i } ^ { k } ( x )$ ; confidence 0.362

54. s09067035.png ; $j _ { X } ^ { k } ( u )$ ; confidence 0.362

55. b01539040.png ; $E [ L ( \theta , d ) | x ]$ ; confidence 0.361

56. t09444040.png ; $u _ { m } = u ( M _ { m } )$ ; confidence 0.360

57. d032150132.png ; $\hat { V }$ ; confidence 0.359

58. c02095032.png ; $L u = \sum _ { | \alpha | \leq m } \alpha _ { \alpha } ( x ) \frac { \partial ^ { \alpha } u } { \partial x ^ { \alpha } } = f ( x )$ ; confidence 0.358

59. o13005087.png ; $v _ { n } \in G$ ; confidence 0.357

60. w120110269.png ; $g _ { 1 } = | d x | ^ { 2 } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } } \leq g = \frac { | d x | ^ { 2 } } { | x | ^ { 2 } } + \frac { | d \xi | ^ { 2 } } { | \xi | ^ { 2 } }$ ; confidence 0.357

61. b120210148.png ; $\mathfrak { p } \supset b$ ; confidence 0.356

62. m063760111.png ; $0 \rightarrow A \rightarrow B \stackrel { sp } { \rightarrow } \pi * C \rightarrow 0$ ; confidence 0.355

63. t12001085.png ; $0$ ; confidence 0.355

64. a13013088.png ; $t$ ; confidence 0.354

65. a11063032.png ; $\rho _ { 0 n + } = \operatorname { sin } A$ ; confidence 0.354

66. w09779041.png ; $\pi _ { 4 n - 1 } ( S ^ { 2 n } ) \rightarrow \pi _ { 4 n } ( S ^ { 2 n + 1 } )$ ; confidence 0.354

67. a1301303.png ; $P _ { 1 } = \left( \begin{array} { c c c } { 0 } & { \square } & { q } \\ { r } & { \square } & { 0 } \end{array} \right) , Q _ { 2 } = \left( \begin{array} { c c } { - \frac { i } { 2 } q r } & { \frac { i } { 2 } q x } \\ { - \frac { i } { 2 } r _ { x } } & { \frac { i } { 2 } q r } \end{array} \right)$ ; confidence 0.352

68. w09751010.png ; $m _ { k } = \dot { k }$ ; confidence 0.352

69. m06546014.png ; $( \alpha \vee ( b . e ) ) : e = ( \alpha : e ) \vee b$ ; confidence 0.351

70. l05872090.png ; $l _ { k } ( A )$ ; confidence 0.348

71. a130240276.png ; $\leq F _ { \alpha ; q , x - \gamma }$ ; confidence 0.345

72. s0876903.png ; $f _ { h } ( t ) = \frac { 1 } { h } \int _ { t - k / 2 } ^ { t + k / 2 } f ( u ) d u = \frac { 1 } { h } \int _ { - k / 2 } ^ { k / 2 } f ( t + v ) d v$ ; confidence 0.345

73. c02572034.png ; $y _ { 0 } = A _ { x }$ ; confidence 0.344

74. l06031040.png ; $R = \{ \alpha \in K : \operatorname { mod } _ { K } ( \alpha ) \leq 1 \}$ ; confidence 0.342

75. t093150743.png ; $\left. \begin{array} { c c c } { B _ { i } } & { \stackrel { h _ { i } } { \rightarrow } } & { A _ { i } } \\ { g _ { i } \downarrow } & { \square } & { \downarrow f _ { i } } \\ { B } & { \vec { f } } & { A } \end{array} \right.$ ; confidence 0.342

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

77. n06711048.png ; $\phi _ { i } / \partial x _ { Y }$ ; confidence 0.338

78. m06236012.png ; $T _ { i j }$ ; confidence 0.337

79. g043780168.png ; $T _ { \nu }$ ; confidence 0.336

80. i050230379.png ; $\| f \| _ { \Lambda _ { p } ^ { r } ( R ^ { n } ) } \leq K$ ; confidence 0.335

81. l057050123.png ; $c \rightarrow N$ ; confidence 0.335

82. l05715031.png ; $\mu$ ; confidence 0.335

83. s085400325.png ; $\tilde { f } : \Delta ^ { n + 1 } \rightarrow E$ ; confidence 0.333

84. c11047054.png ; $h : H \rightarrow ( C \bigotimes T M ) / ( H \oplus \overline { H } )$ ; confidence 0.332

85. c1202808.png ; $F T op$ ; confidence 0.332

86. r08250032.png ; $\| u - P _ { n } u \| _ { A } \rightarrow 0$ ; confidence 0.332

87. l05751032.png ; $\Delta ( \alpha _ { 1 } \ldots i _ { p } d x ^ { i _ { 1 } } \wedge \ldots \wedge d x ^ { i p } ) =$ ; confidence 0.331

88. c020740394.png ; $( \alpha \circ \beta ) ( c ) _ { d x } = \sum _ { b } \alpha ( b ) _ { a } \beta ( c ) _ { b }$ ; confidence 0.330

89. c120180420.png ; $C ^ { \infty } ( \tilde { N } )$ ; confidence 0.330

90. m06222011.png ; $\Delta \lambda _ { i } ^ { \alpha }$ ; confidence 0.329

91. r08221030.png ; $o = e K$ ; confidence 0.327

92. t12001099.png ; $_ { \nabla } ( G / K )$ ; confidence 0.326

93. b1104407.png ; $\overline { \Xi } \epsilon = 0$ ; confidence 0.326

94. a130240141.png ; $c$ ; confidence 0.324

95. n067520141.png ; $N _ { 2 } = \left| \begin{array} { c c c c c } { . } & { \square } & { \square } & { \square } & { 0 } \\ { \square } & { . } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { L ( e _ { j } ^ { n _ { i j } } ) } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { . } & { \square } \\ { \square } & { \square } & { \square } & { \square } & { \square } \\ { 0 } & { \square } & { \square } & { \square } & { . } \end{array} \right|$ ; confidence 0.323

96. f04162020.png ; $X _ { i } \cap X _ { j } =$ ; confidence 0.322

97. s08764086.png ; $n ( O _ { x } ) = 0$ ; confidence 0.322

98. t12001033.png ; $[ \xi ^ { \alpha } , \xi ^ { b } ] = 2 \epsilon _ { \alpha b c } \xi ^ { c }$ ; confidence 0.322

99. a130240339.png ; $\Sigma _ { 1 } = X _ { 4 } ^ { \prime } \Sigma X _ { 4 }$ ; confidence 0.322

100. b11088033.png ; $P _ { I } ^ { f } : C ^ { \infty } \rightarrow L$ ; confidence 0.321

101. k11003029.png ; $\frac { x ^ { \rho + 1 } f ( x ) } { \int _ { x } ^ { x } t ^ { \sigma } f ( t ) d t } \rightarrow \sigma + \rho + 1 \quad ( x \rightarrow \infty )$ ; confidence 0.320

102. h04702011.png ; $F _ { n } ( x ) = ( x _ { 1 } ^ { 2 } + \ldots + x _ { y } ^ { 2 } ) ^ { 1 / 2 }$ ; confidence 0.316

103. o12001037.png ; $\left. \begin{array} { l } { \nabla p _ { 1 } = \nabla p _ { 2 } = 0 } \\ { \frac { \partial v _ { 0 } } { \partial t } + [ \nabla v _ { 0 } ] v _ { 0 } = \frac { 1 } { Re } \Delta v _ { 0 } + \operatorname { Re } \nabla p _ { 3 } + \theta _ { 0 } b } \end{array} \right.$ ; confidence 0.316

104. a13013078.png ; $q ^ { ( l ) } = 2 i \frac { \tau _ { l } + 1 } { \tau _ { l } } , r ^ { ( l ) } = - 2 i \frac { \tau _ { l } - 1 } { \tau _ { l } }$ ; confidence 0.315

105. b12015024.png ; $x = \frac { 1 } { n } \sum _ { j = 1 } ^ { n } x$ ; confidence 0.315

106. c024100277.png ; $\partial _ { r }$ ; confidence 0.315

107. w12010028.png ; $\nabla _ { i g j k } = \gamma _ { i } g _ { j k }$ ; confidence 0.315

108. a0143102.png ; $e$ ; confidence 0.314

109. e12023045.png ; $\therefore M \rightarrow F$ ; confidence 0.313

110. j05405048.png ; $\theta _ { 3 } ( v \pm \frac { 1 } { 2 } \tau ) = e ^ { - i \pi \tau / 4 } \cdot e ^ { - i \pi v } \cdot \theta _ { 2 } ( v )$ ; confidence 0.312

111. p07340055.png ; $M ^ { 0 }$ ; confidence 0.312

112. t12001057.png ; $0$ ; confidence 0.311

113. k05552082.png ; $\Gamma 20$ ; confidence 0.310

114. q07683071.png ; $p _ { m } = ( \sum _ { j = 0 } ^ { m } A _ { j } ) ^ { - 1 }$ ; confidence 0.310

115. f04215011.png ; $\left. \begin{array} { l l } { F _ { 1 } ( A ) } & { \frac { F _ { 1 } ( \alpha ) } { \rightarrow } } & { F _ { 1 } ( B ) } \\ { \phi _ { A } \downarrow } & { \square } & { \downarrow \phi _ { B } } \\ { F _ { 2 } ( A ) } & { \vec { F _ { 2 } ( \alpha ) } } & { F _ { 2 } ( B ) } \end{array} \right.$ ; confidence 0.308

116. t093900115.png ; $l \mu \frac { \partial W ^ { k } } { \partial x } + ( 1 - c ) W ^ { k } = c ( \Phi _ { 0 } ^ { k } - \phi _ { 0 } ^ { k } )$ ; confidence 0.308

117. d11011051.png ; $M _ { 1 } = H \cap _ { k \tau _ { S } } H ^ { \prime }$ ; confidence 0.307

118. i050230319.png ; $f \in S _ { y } ^ { \prime }$ ; confidence 0.307

119. a110420128.png ; $h$ ; confidence 0.307

120. b11082017.png ; $\pi _ { i } / ( \pi _ { i } + \pi _ { j } )$ ; confidence 0.304

121. r08279064.png ; $\operatorname { Pic } ( F ) \cong p ^ { * } \operatorname { Pic } ( C ) \oplus Z ^ { 5 }$ ; confidence 0.304

122. p07354050.png ; $P \{ X _ { v + 1 } = k + 1 | X _ { k } = k \} = \frac { b + k c } { b + r + n c } = \frac { p + k \gamma } { 1 + n \gamma }$ ; confidence 0.303

123. e03691017.png ; $a ^ { X } = e ^ { X \operatorname { ln } \alpha }$ ; confidence 0.301

124. s086940100.png ; $- \infty \leq w \leq + \infty$ ; confidence 0.301

125. c02110012.png ; $x \in \operatorname { Dom } A$ ; confidence 0.300

126. r08085028.png ; $e \omega ^ { r } f$ ; confidence 0.300

127. v096900234.png ; $\Pi I _ { \lambda }$ ; confidence 0.300

128. d120280147.png ; $\overline { U }$ ; confidence 0.299

129. l05774010.png ; $\operatorname { lim } _ { n \rightarrow \infty } \operatorname { sup } \frac { S _ { n } } { c _ { n } } = 1 \quad ( \alpha . s . )$ ; confidence 0.299

130. t09265033.png ; $\{ \partial f \rangle$ ; confidence 0.295

131. a0142305.png ; $\{ A \rangle$ ; confidence 0.294

132. p072430105.png ; $\phi _ { im }$ ; confidence 0.294

133. o07015054.png ; $\alpha ^ { n } < b ^ { n + 1 }$ ; confidence 0.291

134. r082160299.png ; $\{ \operatorname { exp } _ { m } ( \text { Cutval } ( \xi ) \xi ) \} = \text { Cutloc } ( m )$ ; confidence 0.291

135. d031380384.png ; $\sum _ { \mathfrak { D } _ { 1 } ^ { 1 } } ( E \times N ^ { N } )$ ; confidence 0.290

136. g04468049.png ; $t \circ \in E$ ; confidence 0.290

137. i05213037.png ; $\forall y \exists z ( \gamma ( y ) + 1 = \alpha ( g * \overline { \beta } ( z ) ) )$ ; confidence 0.288

138. a13023034.png ; $\| f _ { 1 } - P _ { U \cap V ^ { J } } f \| \leq c ^ { 2 l - 1 } \| f \|$ ; confidence 0.287

139. a0141905.png ; $x _ { y } + 1 = t$ ; confidence 0.287

140. f041940310.png ; $A \in \mathfrak { S }$ ; confidence 0.285

141. c02727013.png ; $j = \frac { 1728 g _ { 2 } ^ { 3 } } { g _ { 2 } ^ { 3 } - 27 g _ { 3 } ^ { 2 } }$ ; confidence 0.284

142. a13013031.png ; $( \partial / \partial t _ { x } ) - Q _ { 0 } z ^ { x }$ ; confidence 0.284

143. a130240196.png ; $\sqrt { 3 }$ ; confidence 0.281

144. a130040685.png ; $X \in X$ ; confidence 0.278

145. r082060102.png ; $f ^ { \mu } | _ { K }$ ; confidence 0.278

146. a130240191.png ; $X ^ { \prime } X \hat { \beta } = X ^ { \prime } y$ ; confidence 0.277

147. a130240430.png ; $a ^ { \prime } \Theta$ ; confidence 0.275

148. a13027051.png ; $\{ x _ { n j } ^ { \prime } \}$ ; confidence 0.273

149. g045090279.png ; $G _ { A B } ^ { ( c ) } ( t - t ^ { \prime } ) = \ll A ( t ) | B ( t ^ { \prime } ) \gg ( c ) \equiv \langle T _ { \eta } A ( t ) B ( t ^ { \prime } ) \rangle$ ; confidence 0.272

150. a01241063.png ; $s = s ^ { * } \cup ( s \backslash s ^ { * } ) ^ { * } U \ldots$ ; confidence 0.271

151. b016960150.png ; $99$ ; confidence 0.271

152. a1202207.png ; $| e | | < 1$ ; confidence 0.271

153. l05892067.png ; $Z y \rightarrow \infty$ ; confidence 0.270

154. f040230147.png ; $\sum _ { \nu = 1 } ^ { k - 1 } \frac { B _ { \nu } } { \nu ! } \{ f ^ { \langle \nu - 1 \rangle } ( n ) - f ^ { \langle \nu - 1 \rangle } ( 0 ) \} + \frac { B _ { k } } { k ! } \sum _ { x = 0 } ^ { n - 1 } f ^ { ( k ) } ( x + \theta )$ ; confidence 0.269

155. f12019010.png ; $N = \{ G \backslash ( \cup _ { x \in G } x ^ { - 1 } H x ) \} \cup \{ 1 \}$ ; confidence 0.269

156. c02157044.png ; $\chi \pi _ { \alpha }$ ; confidence 0.268

157. t1200105.png ; $( C ( S ) , \overline { g } ) = ( R _ { + } \times S , d \nu ^ { 2 } + r ^ { 2 } g )$ ; confidence 0.265

158. i130030178.png ; $h ( [ a ] )$ ; confidence 0.265

159. r08094048.png ; $\{ \alpha _ { n } \} _ { \aleph = 0 } ^ { \infty }$ ; confidence 0.264

160. l05911071.png ; $+ \sum _ { i = 1 } ^ { s } \| k _ { i k } [ u ] _ { k } - \{ l _ { i } u \} _ { i k } \| _ { \Phi _ { i k } } + \| p _ { i k } \phi _ { i } - \{ \phi _ { i } \} _ { i k } \| _ { \Phi _ { i k } }$ ; confidence 0.263

161. c023150187.png ; $\alpha : H ^ { n } ( : Z ) \rightarrow H ^ { n + 3 } ( : Z _ { 2 } )$ ; confidence 0.262

162. l057000153.png ; $+ ( \lambda x y \cdot y ) : ( \sigma \rightarrow ( \tau \rightarrow \tau ) )$ ; confidence 0.262

163. q07661044.png ; $\beta X = S \square x = \omega _ { \kappa } X$ ; confidence 0.261

164. a1301301.png ; $\left. \begin{array} { l } { i \frac { \partial } { \partial t } q ( x , t ) = i q t = - \frac { 1 } { 2 } q x x + q ^ { 2 } r } \\ { i \frac { \partial } { \partial t } r ( x , t ) = i r t = \frac { 1 } { 2 } r x - q r ^ { 2 } } \end{array} \right.$ ; confidence 0.260

165. a12022037.png ; $r _ { ess } ( T )$ ; confidence 0.259

166. a1201308.png ; $m$ ; confidence 0.259

167. s08777049.png ; $V _ { k } ( H ^ { n } ) = \frac { Sp ( n ) } { Sp ( n - k ) }$ ; confidence 0.259

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

169. v09638089.png ; $\pi : B \rightarrow G ^ { k } ( V )$ ; confidence 0.258

170. i05250054.png ; $L ^ { \prime }$ ; confidence 0.256

171. o06837057.png ; $x _ { C }$ ; confidence 0.256

172. p07370045.png ; $[ f _ { G } ]$ ; confidence 0.256

173. g044350101.png ; $D \Re \subset M$ ; confidence 0.255

174. a01071024.png ; $A = A _ { 1 } \cap \ldots \cap A _ { n }$ ; confidence 0.254

175. c027180124.png ; $7$ ; confidence 0.254

176. c12030053.png ; $\sum _ { i = 1 } ^ { n } S _ { i } S _ { i } ^ { * } < I$ ; confidence 0.253

177. i05298049.png ; $L ^ { \prime } ( T _ { x } M )$ ; confidence 0.252

178. q07680094.png ; $\tau _ { 0 } ^ { e ^ { 3 } }$ ; confidence 0.252

179. a01082073.png ; $X \in Ob \odot$ ; confidence 0.251

180. b12037092.png ; $\sum \frac { 1 } { 1 }$ ; confidence 0.251

181. a130240242.png ; $SS _ { H } = \sum _ { i = 1 } ^ { \Psi } z _ { i } ^ { 2 }$ ; confidence 0.251

182. b11091027.png ; $\frac { \partial N _ { i } } { \partial t } + u _ { i } \nabla N _ { i } = G _ { i } - L _ { i }$ ; confidence 0.250

183. p07383050.png ; $E \subset X = R ^ { \prime }$ ; confidence 0.250

184. q07685043.png ; $E [ \tau _ { j } ^ { S } - \tau _ { j } ^ { \dot { e } } ] ^ { 2 + \gamma }$ ; confidence 0.250

185. d03319041.png ; $t _ { 8 } + 1 / 2 = t _ { n } + \tau / 2$ ; confidence 0.248

186. l12006043.png ; $\int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle ^ { 2 } } { \lambda } _ { d } \lambda < E _ { 0 }$ ; confidence 0.248

187. q07650033.png ; $3 r ( L _ { 1 } \cap L _ { 2 } ) = 3 _ { r } ( L _ { 1 } ) + 3 r ( L _ { 2 } )$ ; confidence 0.248

188. a1301308.png ; $s l _ { 2 }$ ; confidence 0.247

189. k0556303.png ; $| m K _ { V ^ { \prime } } | ^ { J }$ ; confidence 0.246

190. a110010217.png ; $1 / | y ^ { i } _ { x ^ { i } } ^ { * }$ ; confidence 0.245

191. e03517056.png ; $\| \hat { A } - A \| \leq \delta$ ; confidence 0.245

192. k05508019.png ; $\nu _ { 0 } \in C ^ { n }$ ; confidence 0.245

193. o070010110.png ; $X = \cup _ { \alpha } X _ { \alpha }$ ; confidence 0.245

194. t130140116.png ; $q R$ ; confidence 0.245

195. b11099011.png ; $V _ { Q }$ ; confidence 0.244

196. b110130209.png ; $v ( \lambda ) = ( y _ { 0 } + \lambda ^ { - 1 } y _ { - 1 } + \ldots + \lambda ^ { - p } y - p ) y _ { 0 } ^ { - 1 / 2 }$ ; confidence 0.241

197. a13013045.png ; $= \frac { 1 } { 2 } \operatorname { Tr } ( \sum _ { r = 0 } ^ { j } ( j - r ) Q _ { r } Q _ { k + j - r } + \frac { 1 } { 2 } \sum _ { r = 0 } ^ { j } ( r - k ) Q _ { r } Q _ { k + j - r } )$ ; confidence 0.240

198. a130240527.png ; $( n$ ; confidence 0.239

199. w09787060.png ; $\prod _ { \nu } : \prod _ { i \in I _ { \nu } } f _ { i } : = \sum _ { G } \prod _ { e \in G } < f _ { e _ { 1 } } f _ { e _ { 2 } } > : \prod _ { i \notin [ G ] } f _ { i : }$ ; confidence 0.238

200. a13013020.png ; $0.00$ ; confidence 0.237

201. c02645091.png ; $X _ { 1 }$ ; confidence 0.237

202. b01540091.png ; $\Psi _ { 1 } ( Y ) / \hat { q } ( Y ) \leq \psi ( Y ) \leq \Psi _ { 2 } ( Y ) / \hat { q } ( Y )$ ; confidence 0.236

203. h0470704.png ; $\alpha _ { i k } = \overline { a _ { k i } }$ ; confidence 0.235

204. j05405038.png ; $\theta _ { 2 } ( v \pm \tau ) = e ^ { - i \pi \tau } \cdot e ^ { - 2 i \pi v } \cdot \theta _ { 2 } ( v )$ ; confidence 0.234

205. s08317062.png ; $\tilde { D } = E \{ M | m = 0 \} = \frac { ( \sum _ { r = 1 } ^ { N - n } r \frac { C _ { N - r } ^ { n } } { C _ { N } ^ { n } } p _ { r } ) } { P \{ m = 0 \} }$ ; confidence 0.234

206. b11037052.png ; $= 0 \text { as. } \cdot P _ { \theta _ { 0 } } ]$ ; confidence 0.233

207. s091910121.png ; $T _ { i } = C A ^ { i } B ^ { i } B$ ; confidence 0.233

208. c02019023.png ; $C A$ ; confidence 0.232

209. d031380303.png ; $\Pi \stackrel { D } { 3 } = F _ { \sigma \delta }$ ; confidence 0.232

210. b01556018.png ; $D \times D \in \Gamma ^ { 2 }$ ; confidence 0.230

211. c022780328.png ; $im ( \Omega _ { S C } \rightarrow \Omega _ { O } )$ ; confidence 0.230

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

213. m06516021.png ; $\operatorname { ess } \operatorname { sup } _ { X } | f ( x ) | = \operatorname { lim } _ { n \rightarrow \infty } ( \frac { \int | f ( x ) | ^ { n } d M _ { X } } { \int _ { X } d M _ { x } } )$ ; confidence 0.229

214. t09316053.png ; $\sum _ { k = 1 } ^ { \infty } p _ { 1 } ( x _ { k } ) p _ { 2 } ( y _ { k } ) \leq p _ { 1 } \overline { Q } p _ { 2 } ( u ) + \epsilon$ ; confidence 0.229

215. e03704050.png ; $n + = n - = n$ ; confidence 0.228

216. x120010101.png ; $\operatorname { Aut } ( R ) / \operatorname { ln } n ( R ) \cong H$ ; confidence 0.228

217. c11041043.png ; $C X Y$ ; confidence 0.226

218. p07353041.png ; $t ^ { i _ { 1 } } \cdots \dot { d p } = \operatorname { det } \| x _ { i } ^ { i _ { k } } \|$ ; confidence 0.226

219. c1102508.png ; $20$ ; confidence 0.225

220. c02570021.png ; $I \rightarrow \cup _ { i \in l } J _ { i }$ ; confidence 0.225

221. c02645033.png ; $\sum _ { K \in \mathscr { K } } \lambda _ { K } \chi _ { K } ( i ) = \chi _ { I } ( i ) \quad \text { for all } i \in I$ ; confidence 0.223

222. m06371091.png ; $n _ { 1 } < n _ { 2 } .$ ; confidence 0.222

223. g0434707.png ; $\nabla _ { \theta } : H _ { \delta R } ^ { 1 } ( X / K ) \rightarrow H _ { \partial R } ^ { 1 } ( X / K )$ ; confidence 0.221

224. a012460130.png ; $X \equiv 0$ ; confidence 0.220

225. r0807408.png ; $x _ { n m _ { n } } \rightarrow ( 0 )$ ; confidence 0.220

226. a130240383.png ; $H ^ { \prime }$ ; confidence 0.219

227. b11027042.png ; $P ( s S ) = P ( S )$ ; confidence 0.219

228. d03175051.png ; $Z _ { h }$ ; confidence 0.217

229. s087420178.png ; $\mathfrak { A } _ { \infty } = \overline { U _ { V \subset R ^ { 3 } } } A ( \mathcal { H } _ { V } )$ ; confidence 0.216

230. l058430107.png ; $g ^ { \prime } / ( 1 - u ) g ^ { \prime } = \overline { g }$ ; confidence 0.215

231. b01566071.png ; $\nu = a + x + 2 [ \frac { n - t - x - \alpha } { 2 } ] + 1$ ; confidence 0.213

232. g044340202.png ; $\xi _ { p } \in ( \nu F ^ { m } ) p$ ; confidence 0.212

233. d03173088.png ; $| u - v | \leq \operatorname { inf } _ { w ^ { \prime } \in K } | u - w |$ ; confidence 0.210

234. r08207022.png ; $R _ { i l k } ^ { q } = - R _ { k l } ^ { q }$ ; confidence 0.210

235. d031280129.png ; $f : X ^ { \cdot } \rightarrow Y$ ; confidence 0.209

236. d0314706.png ; $| \hat { b } _ { n } | = 1$ ; confidence 0.209

237. a13013042.png ; $X _ { i } \in \operatorname { sl } _ { 2 } ( C )$ ; confidence 0.209

238. t12001098.png ; $k$ ; confidence 0.208

239. a01431097.png ; $| x$ ; confidence 0.207

240. f042060121.png ; $\mathfrak { g } \otimes \mathfrak { g } \rightarrow U \mathfrak { g } \otimes U \mathfrak { g } \otimes U _ { \mathfrak { g } }$ ; confidence 0.207

241. a01060019.png ; $H _ { \hat { j } }$ ; confidence 0.205

242. b0166503.png ; $2 \int \int _ { G } ( x \frac { \partial y } { \partial u } \frac { \partial y } { \partial v } ) d u d v = \oint _ { \partial G } ( x y d y )$ ; confidence 0.204

243. d031380296.png ; $\sum _ { \sim } D _ { n + 1 } ^ { 0 }$ ; confidence 0.204

244. t09430077.png ; $\left. \begin{array} { c c c } { T A } & { \stackrel { T f } { S } } & { T B } \\ { \alpha \downarrow } & { \square } & { \downarrow \beta } \\ { A } & { \vec { f } } & { B } \end{array} \right.$ ; confidence 0.204

245. c020740146.png ; $\alpha \rightarrow \dot { b }$ ; confidence 0.200

246. a0100805.png ; $\{ A _ { n _ { 1 } } \ldots n _ { k } \}$ ; confidence 0.200

247. a012970198.png ; $\hat { W } \square _ { \infty } ^ { \gamma }$ ; confidence 0.199

248. d03342015.png ; $\sigma _ { k }$ ; confidence 0.198

249. t092470182.png ; $e _ { v } \leq \mathfrak { e } _ { v } + 1$ ; confidence 0.197

250. e12019037.png ; $l _ { x }$ ; confidence 0.196

251. c02315041.png ; $f : S ^ { m } \rightarrow S ^ { n }$ ; confidence 0.195

252. l059160187.png ; $\dot { u } = A _ { n } u$ ; confidence 0.195

253. e1200103.png ; $A \stackrel { f } { \rightarrow } B = A \stackrel { é } { \rightarrow } f [ A ] \stackrel { m } { \rightarrow } B$ ; confidence 0.193

254. s0833306.png ; $\phi _ { \mathscr { A } } ( . )$ ; confidence 0.193

255. a0100205.png ; $P = \cup _ { n _ { 1 } , \ldots , n _ { k } , \ldots } \cap _ { k = 1 } ^ { \infty } E _ { n _ { 1 } } \square \ldots x _ { k }$ ; confidence 0.192

256. b01539020.png ; $\rho ( \theta , \delta ) = \int _ { Y } L ( \theta , \delta ( x ) ) P _ { \theta } ( d x )$ ; confidence 0.192

257. c1104902.png ; $\sqrt { 2 }$ ; confidence 0.191

258. l12010011.png ; $\left\{ \begin{array} { l l } { \gamma \geq \frac { 1 } { 2 } } & { \text { forn } = 1 } \\ { \gamma > 0 } & { \text { forn } = 2 } \\ { \gamma \geq 0 } & { \text { forn } \geq 3 } \end{array} \right.$ ; confidence 0.191

259. p110120432.png ; $\operatorname { limsup } _ { n \rightarrow + \infty } \frac { 1 } { n } \operatorname { log } + P _ { N } ( f ) \geq h ( f )$ ; confidence 0.191

260. r08019038.png ; $\{ f ^ { t } | \Sigma _ { X } \} _ { t \in R }$ ; confidence 0.191

261. t120010125.png ; $\dot { i } \leq n$ ; confidence 0.190

262. p07471055.png ; $g _ { 0 } g ^ { \prime } \in G$ ; confidence 0.189

263. c026010308.png ; $v _ { ( E ) } = v$ ; confidence 0.188

264. t120010100.png ; $O = G / \operatorname { Sp } ( 1 ) . K$ ; confidence 0.187

265. d03006013.png ; $+ \frac { 1 } { 2 \alpha } \int _ { x - w t } ^ { x + c t } \psi ( \xi ) d \xi + \frac { 1 } { 2 } [ \phi ( x + a t ) + \phi ( x - a t ) ]$ ; confidence 0.187

266. h04637012.png ; $\int _ { \alpha } ^ { b } \theta ^ { p } ( x ) d x \leq 2 ( \frac { p } { p - 1 } ) ^ { p } \int _ { a } ^ { b } f ^ { p } ( x ) d x$ ; confidence 0.187

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

268. g043780231.png ; $\overline { h } ( X ) = \operatorname { lim } _ { h } h ^ { * } ( X _ { \alpha } )$ ; confidence 0.185

269. p07346086.png ; $P ^ { \perp } = \cap _ { v \in P } v ^ { \perp } = \emptyset$ ; confidence 0.185

270. c023530133.png ; $\Pi ^ { N } \tau$ ; confidence 0.183

271. s1202506.png ; $h _ { n } = \int _ { a } ^ { b } x ^ { n } h ( x ) d x$ ; confidence 0.183

272. a13013090.png ; $N$ ; confidence 0.183

273. c02597042.png ; $e ^ { i } ( e _ { j } ) = \delta _ { j } ^ { s }$ ; confidence 0.182

274. t12001088.png ; $\hat { v } ^ { ( S ) }$ ; confidence 0.182

275. g0432804.png ; $\hat { K } _ { i }$ ; confidence 0.180

276. g04334048.png ; $\sum _ { \Sigma } ^ { 3 } \square ^ { i \alpha } \neq 0$ ; confidence 0.180

277. a01197046.png ; $U - \text { a.p. } \subset S ^ { p } - \text { a.p. } \subset W ^ { p } - \text { a.p. } \subset B ^ { p } - \text { a.p. } \quad p \geq 1$ ; confidence 0.179

278. b12046037.png ; $( \oplus _ { b } G _ { E B } b )$ ; confidence 0.179

279. n1200405.png ; $A _ { i \psi }$ ; confidence 0.179

280. p0728502.png ; $_ { k }$ ; confidence 0.179

281. d03062019.png ; $\alpha \in C \cup \{ \infty \}$ ; confidence 0.176

282. a13013083.png ; $C$ ; confidence 0.175

283. c11016063.png ; $( a b \alpha ) ^ { \alpha } = \alpha ^ { \alpha } b ^ { \alpha } \alpha ^ { \alpha }$ ; confidence 0.173

284. a13013033.png ; $\phi - ^ { 1 } ( \frac { \partial } { \partial x } - P _ { 0 z } ) \phi _ { - } = \frac { \partial } { \partial x } - P$ ; confidence 0.173

285. c02147033.png ; $\tilde { Y } \square _ { j } ^ { ( k ) } \in Y _ { j }$ ; confidence 0.172

286. h11024025.png ; $n _ { s } + n _ { u } = n$ ; confidence 0.172

287. r08068010.png ; $x \frac { \operatorname { lim } _ { x \rightarrow D } u ( x ) = f ( y _ { 0 } ) } { x \in D }$ ; confidence 0.172

288. s08703096.png ; $\operatorname { max } _ { n \atop n } \| u ^ { n } \| _ { H } \leq e ^ { C _ { 1 } T } \{ \| \phi \| _ { H } + C _ { 0 } \sum _ { n } \tau \| f ^ { n + 1 } \| _ { H } \}$ ; confidence 0.172

289. d0335708.png ; $\sum _ { i \in I } \prod _ { j \in J ( i ) } \alpha _ { i j } = \prod _ { \phi \in \Phi } \sum _ { i \in I } \alpha _ { i \phi ( i ) }$ ; confidence 0.170

290. a11068093.png ; $L f \theta$ ; confidence 0.169

291. a13024067.png ; $e _ { j k }$ ; confidence 0.169

292. s08727063.png ; $V _ { x } 0 ( \lambda ) \sim \operatorname { exp } [ i \lambda S ( x ^ { 0 } ) ] \sum _ { k = 0 } ^ { \infty } ( \sum _ { l = 0 } ^ { N } \alpha _ { k l } \lambda ^ { - r _ { k } } ( \operatorname { ln } \lambda ) ^ { l } \}$ ; confidence 0.167

293. s08779013.png ; $RP ^ { \infty }$ ; confidence 0.165

294. t120010105.png ; $SU ( m ) / S ( U ( m - 2 ) \times U ( 1 ) ) , SO ( k ) / SO ( k - 4 ) \times Sp ( 1 )$ ; confidence 0.164

295. m06503013.png ; $\tilde { y } = \alpha _ { 21 } x + \alpha _ { 22 } y + \alpha _ { 23 } z + b$ ; confidence 0.163

296. a13013058.png ; $s = \sum _ { i > 0 } C \lambda ^ { i } \left( \begin{array} { c c } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) \oplus \sum _ { i > 0 } C \lambda ^ { - i } \left( \begin{array} { c c } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) \oplus C _ { i }$ ; confidence 0.161

297. i05079039.png ; $| \alpha _ { 1 } + \ldots + \alpha _ { n } | \leq | \alpha _ { 1 } | + \ldots + | \alpha _ { n } |$ ; confidence 0.160

298. a130240407.png ; $M _ { E } = \sum _ { i j k } ( y _ { i j k } - y _ { i j . } ) ^ { \prime } ( y _ { i j k } - y _ { i j } )$ ; confidence 0.159

299. a13013013.png ; $\frac { \partial } { \partial t _ { m } } P - \frac { \partial } { \partial x } Q ^ { ( m ) } + [ P , Q ^ { ( r ) } ] = 0 \Leftrightarrow$ ; confidence 0.156

300. z09925023.png ; $001 c 23 + c 02 c 31 + c 03 c 12 \neq 0$ ; confidence 0.156

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/10. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/10&oldid=43828