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(AUTOMATIC EDIT of page 3 out of 77 with 300 lines: Updated image/latex database (currently 22833 images latexified; order by Length, ascending: False.)
 
(AUTOMATIC EDIT of page 3 out of 77 with 300 lines: Updated image/latex database (currently 22833 images latexified; order by Confidence, ascending: False.)
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== List ==
 
== List ==
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1. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i13004025.png ; $\sum _ { n = 0 } ^ { \infty } \{ \sum _ { m = 1 } ^ { \infty } [ \sum _ { k = m 2 ^ { n } } ^ { ( m + 1 ) 2 ^ { n } - 1 } | \Delta d _ { k } | ] ^ { 2 } \} ^ { 1 / 2 } < \infty$ ; confidence 0.350
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1. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011370/a01137071.png ; $f ( x ) = 0$ ; confidence 1.000
  
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2. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130020/j13002055.png ; $2 ^ { n } \operatorname { exp } \{ - \left( \begin{array} { c } { n / 100 } \\ { 3 } \end{array} \right) p ^ { 3 } + O ( n ^ { 4 } p ^ { 5 } ) \} = o ( 1 )$ ; confidence 0.844
+
2. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120170/b12017027.png ; $( 1 + | \xi | ^ { 2 } ) ^ { - \alpha / 2 }$ ; confidence 1.000
  
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3. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130130/p1301309.png ; $M ( S _ { n } ) \cong \left\{ \begin{array} { l l } { Z _ { 2 } } & { \text { if } n \geq 4 } \\ { \{ e \} } & { \text { if } n < 4 } \end{array} \right.$ ; confidence 0.301
+
3. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130160/b13016056.png ; $f \in C ( X , \tau )$ ; confidence 1.000
  
−
4. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130110/r13011025.png ; $\Phi ( u ) : = \sum _ { n = 1 } ^ { \infty } \pi n ^ { 2 } ( 2 \pi n ^ { 2 } e ^ { 4 \lambda } - 3 ) \operatorname { exp } ( 5 u - \pi n ^ { 2 } e ^ { 4 \lambda } )$ ; confidence 0.730
+
4. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093560/t09356011.png ; $f ( x ) < + \infty$ ; confidence 1.000
  
−
5. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130450/s13045011.png ; $r s = \frac { n ( n ^ { 2 } - 1 ) - 6 \sum _ { i = 1 } ^ { n } ( R _ { i } - S _ { i } ) ^ { 2 } - 6 ( T + U ) } { \sqrt { n ( n ^ { 2 } - 1 ) - 12 T } \sqrt { n ( n ^ { 2 } - 1 ) - 12 U } }$ ; confidence 0.907
+
5. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110890/b11089065.png ; $0 < \beta < 1$ ; confidence 1.000
  
−
6. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026039.png ; $t \rightarrow \int _ { 0 } ^ { t } ( \partial _ { s } ^ { * } + \partial _ { s } ) 1 d s = S ^ { - 1 } ( \int _ { 0 } ^ { t } ( D _ { s } ^ { * } + D _ { s } ) \Omega d s )$ ; confidence 0.455
+
6. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130070/m13007040.png ; $d = 2,3$ ; confidence 1.000
  
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7. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064019.png ; $\frac { 1 } { n } \sum _ { k = 1 } ^ { n } f ( \lambda _ { k } ^ { ( n ) } ) = \frac { 1 } { 2 \pi } \int _ { 0 } ^ { 2 \pi } f ( a ( e ^ { i \theta } ) ) d \theta + o ( 1 )$ ; confidence 0.899
+
7. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e120070103.png ; $P ( k )$ ; confidence 1.000
  
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8. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140118.png ; $[ X ] \mapsto \chi _ { R } ( [ X ] ) = \sum _ { m = 0 } ^ { \infty } ( - 1 ) ^ { m } \operatorname { dim } _ { K } \operatorname { Ext } _ { R } ^ { m } ( X , X )$ ; confidence 0.116
+
8. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c12018050.png ; $( p , q ) = ( n , 0 )$ ; confidence 1.000
  
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9. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t12014044.png ; $T _ { \phi } = \operatorname { dim } \operatorname { Ker } T _ { \phi } - \operatorname { dim } \operatorname { Ker } T _ { \phi } ^ { * } = 0$ ; confidence 0.871
+
9. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120040/v12004058.png ; $\chi ^ { \prime } ( G ) = \chi ( L ( G ) )$ ; confidence 1.000
  
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10. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110134.png ; $\operatorname { sup } _ { ( x , \xi ) \in R ^ { 2 n } , } | D _ { x } ^ { \alpha } D _ { \xi } ^ { \beta } \alpha ( x , \xi , h ) | h ^ { m - | \beta | } < \infty$ ; confidence 0.214
+
10. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180317.png ; $R ( g )$ ; confidence 1.000
  
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11. 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
+
11. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130070/m1300708.png ; $\{ 0 \} \cup [ m _ { 0 } , \infty )$ ; confidence 1.000
  
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12. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010104.png ; $\operatorname { Sp } ( n + 1 ) / \operatorname { Sp } ( n ) , \quad \operatorname { Sp } ( n + 1 ) / \operatorname { Sp } ( n ) \times Z _ { 2 }$ ; confidence 0.901
+
12. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120270/a12027093.png ; $W ( \rho ) = \pm 1$ ; confidence 1.000
  
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13. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a1201808.png ; $T _ { n } = \frac { S _ { n } S _ { n + 2 } - S _ { n + 1 } ^ { 2 } } { S _ { n + 2 } - 2 S _ { n + 1 } + S _ { n } } = S _ { n } - \frac { \Delta S _ { n } } { \Delta ^ { 2 } S _ { n } }$ ; confidence 0.785
+
13. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840380.png ; $- \frac { d ^ { 2 } y } { d x ^ { 2 } } + q y - \lambda y = f$ ; confidence 1.000
  
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14. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120020/b12002019.png ; $\frac { n ^ { 1 / 4 } } { ( \operatorname { log } n ) ^ { 1 / 2 } } \| \alpha _ { n } + \beta _ { n } \| \stackrel { d } { \rightarrow } \| B \| ^ { 1 / 2 }$ ; confidence 0.344
+
14. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130070/m13007033.png ; $\{ p : p ^ { 0 } > 0 , | p ^ { 2 } - m ^ { 2 } | < \epsilon \}$ ; confidence 1.000
  
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15. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120360/b12036011.png ; $P _ { l } = \frac { \operatorname { exp } ( - \epsilon _ { l } / k _ { B } T ) } { \sum _ { l } \operatorname { exp } ( - \epsilon _ { l } / k _ { B } T ) }$ ; confidence 0.423
+
15. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b130300109.png ; $B ( m , n , \infty )$ ; confidence 1.000
  
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16. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008025.png ; $\sum _ { l = 0 } ^ { n } a _ { n - 1 } \left[ \begin{array} { c } { A _ { 1 } ^ { m - i } } \\ { A _ { 2 } A _ { 1 } ^ { m - i - 1 } } \end{array} \right] = 0 _ { m n }$ ; confidence 0.605
+
16. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f120080200.png ; $B ( K ) = B ( G )$ ; confidence 1.000
  
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17. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c13016024.png ; $\phi \equiv ( x _ { 1 } \vee x _ { 2 } ) \wedge ( \overline { x _ { 2 } } \vee \overline { x _ { 3 } } ) \wedge ( \overline { x _ { 1 } } \vee x _ { 3 } )$ ; confidence 0.984
+
17. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230121.png ; $d ( z , w )$ ; confidence 1.000
  
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18. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026081.png ; $\frac { U _ { h } ^ { n + 1 } - U _ { h } ^ { n } } { k } = \frac { 1 } { 2 } F _ { h } ( t _ { n } , U _ { h } ^ { n } ) + \frac { 1 } { 2 } F _ { h } ( t _ { n } + 1 , U _ { h } ^ { n + 1 } )$ ; confidence 0.347
+
18. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120050/f12005060.png ; $( 1,1,1 )$ ; confidence 1.000
  
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19. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d13008096.png ; $= \{ z \in D : \operatorname { liminf } _ { W \rightarrow X } [ K _ { D } ( z , w ) - K _ { D } ( z 0 , w ) ] < \frac { 1 } { 2 } \operatorname { log } R \}$ ; confidence 0.205
+
19. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022063.png ; $\rho = \rho ( T )$ ; confidence 1.000
  
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20. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d1301109.png ; $( c \frac { \hbar } { c } \vec { \alpha } . \vec { \nabla } + \vec { \beta } m 0 c ^ { 2 } ) \Phi = i \hbar \frac { \partial \Phi } { \partial t }$ ; confidence 0.531
+
20. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120110/a12011011.png ; $b + 1$ ; confidence 1.000
  
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21. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130170/d13017054.png ; $\sum _ { k = 1 } ^ { \infty } e ^ { - \lambda _ { k } t } \approx \frac { A } { 4 \pi t } + \frac { L } { 8 \sqrt { \pi t } } + \frac { 1 } { 6 } ( 1 - r ) + O ( t )$ ; confidence 0.678
+
21. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004039.png ; $\gamma = ( \partial D ) \backslash \Gamma$ ; confidence 1.000
  
−
22. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130050/h1300505.png ; $\frac { \partial u } { \partial t } = \frac { \partial ^ { 3 } } { \partial x ^ { 3 } } ( \frac { 1 } { \sqrt { u } } ) , - \infty < x < \infty , t > 0$ ; confidence 0.996
+
22. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a1200802.png ; $u ( x , t ) = 0$ ; confidence 1.000
  
−
23. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006035.png ; $\equiv ( z - E _ { 0 } - \int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle | ^ { 2 } } { z - \lambda } d \lambda ) ( \phi , G ( z ) \phi ) = 1$ ; confidence 0.869
+
23. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120490/b12049030.png ; $A , B \in \Sigma$ ; confidence 1.000
  
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24. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140163.png ; $( F f ) ( z ) = \sum _ { j = 1 } ^ { n } ( z _ { j } \frac { \partial f ( z ) } { \partial z _ { j } } + z _ { j } \frac { \partial f ( z ) } { \partial z _ { j } } )$ ; confidence 0.386
+
24. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027020.png ; $R ( t )$ ; confidence 1.000
  
−
25. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068170/o06817011.png ; $\operatorname { lim } _ { n \rightarrow \infty } P \{ \int _ { 0 } ^ { 1 } Z _ { n } ^ { 2 } ( t ) d t < \lambda \} = P \{ \omega ^ { 2 } < \lambda \} =$ ; confidence 0.694
+
25. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110210/b11021056.png ; $p \neq 2$ ; confidence 1.000
  
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26. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005023.png ; $\left\{ \begin{array}{l}{ ( T - z I ) x = K J \varphi _ { - } }\\{ \varphi _ { + } = \varphi _ { - } - 2 i K ^ { * } x _ { } }\end{array} \right.$ ; confidence 0.118
+
26. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130030/z13003053.png ; $h ( t ) = \int _ { - \infty } ^ { \infty } R ( t - s ) f ( s ) d s$ ; confidence 1.000
  
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27. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006014.png ; $\frac { 1 } { i } ( A _ { 1 } - A _ { 1 } ^ { * } ) = \Phi ^ { * } \sigma _ { 1 } \Phi , \frac { 1 } { i } ( A _ { 2 } - A _ { 2 } ^ { * } ) = \Phi ^ { * } \sigma _ { 2 } \Phi$ ; confidence 0.964
+
27. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120030/t12003038.png ; $U ^ { \prime } = f ( U )$ ; confidence 1.000
  
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28. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130370/s13037014.png ; $\| \lambda \| = \operatorname { sup } _ { 0 \leq s < t \leq 1 } | \operatorname { log } \{ ( t - s ) ^ { - 1 } ( \lambda ( t ) - \lambda ( s ) ) \} |$ ; confidence 0.876
+
28. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e12026067.png ; $\theta _ { 2 } = - 1 / \sigma ^ { 2 }$ ; confidence 1.000
  
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29. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230153.png ; $( X A _ { 1 } X ^ { \prime } , \ldots , X A _ { s } X ^ { \prime } ) \sim L _ { s } ^ { ( 1 ) } ( f _ { 1 } , \frac { n _ { 1 } } { 2 } , \ldots , \frac { n _ { s } } { 2 } )$ ; confidence 0.226
+
29. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130130/w13013029.png ; $W \geq 4 \pi$ ; confidence 1.000
  
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30. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011032.png ; $w ( m , l ) = \frac { d \Phi } { d z } = - \frac { i \Gamma } { 2 \pi } [ \operatorname { cotan } \frac { \pi z } { l } - \frac { 1 } { z - m l } ] \equiv 0$ ; confidence 0.991
+
30. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c130070162.png ; $r ( 0,0 ) = 0$ ; confidence 1.000
  
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31. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011040.png ; $\| H ( u , v ) \| _ { L } 2 _ { \langle R ^ { 2 n } \rangle } = \| u \| _ { L } 2 _ { \langle R ^ { n } } \rangle \| v \| _ { L } 2 _ { \langle R ^ { n } } \rangle$ ; confidence 0.089
+
31. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030240/d03024026.png ; $f ( x ) = \operatorname { sgn } x$ ; confidence 1.000
  
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32. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130220/a13022062.png ; $0 \rightarrow \square _ { R } \operatorname { Mod } ( ? , A ) \rightarrow \square _ { R } \operatorname { Mod } ( ? , B ) \rightarrow$ ; confidence 0.807
+
32. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130490/s1304904.png ; $r ( p ) = 0$ ; confidence 1.000
  
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33. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023045.png ; $CF ( \zeta - z , w ) = \frac { ( n - 1 ) ! \sum _ { k = 1 } ^ { n } ( - 1 ) ^ { k - 1 } w _ { k } d w [ k ] \wedge d \zeta } { \langle w , \zeta - z \rangle ^ { n } }$ ; confidence 0.453
+
33. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027016.png ; $N ( t )$ ; confidence 1.000
  
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34. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130020/b1300209.png ; $\operatorname { lim } \{ \| x ^ { n } \| ^ { 1 / n } \} = \operatorname { max } \{ | \lambda | : \lambda \in \operatorname { sp } ( J , x ) \}$ ; confidence 0.370
+
34. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120170/f12017023.png ; $N ( r )$ ; confidence 1.000
  
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35. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e120120130.png ; $H \equiv - \frac { \partial ^ { 2 } } { \partial \theta . \partial \theta } \int f ( \theta , \phi ) d \phi | _ { \theta = \theta ^ { * } }$ ; confidence 0.919
+
35. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f12015079.png ; $i ( A ) = + \infty$ ; confidence 1.000
  
−
36. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e035000135.png ; $\operatorname { lim } _ { k \rightarrow \infty } \frac { S ( T ^ { k } , a f ( \epsilon ) ^ { k } ) } { k } = 2 H _ { \epsilon } ^ { \prime } ( \xi )$ ; confidence 0.824
+
36. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120100/b12010046.png ; $F ( t ) = U ( t ) F ( 0 )$ ; confidence 1.000
  
−
37. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e120260132.png ; $\pi _ { v , p } ( d \theta ) = A ( m , p ) ( L _ { \mu } ( \theta ) ) ^ { - p } \operatorname { exp } \langle \theta , v \rangle \alpha ( d \theta )$ ; confidence 0.272
+
37. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007070.png ; $( e - d )$ ; confidence 1.000
  
−
38. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130040/f1300404.png ; $\operatorname { Tr } [ \operatorname { Aexp } ( - i \hbar ^ { - 1 } H ( t ) ) ] = \sum _ { k = 1 } ^ { N } a _ { 0 } ( x _ { k } ) d _ { k } e ^ { b _ { k } } + O ( h )$ ; confidence 0.385
+
38. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130090/p13009035.png ; $\xi \in \partial \Omega$ ; confidence 1.000
  
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39. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g13004048.png ; $\operatorname { lim } _ { r \rightarrow 0 } \frac { H ^ { m } ( \{ y \in E \cap B ( x , r ) : \quad > \text { dist } ( y - x , V ) > } { > s | y - x | } ) = 0$ ; confidence 0.092
+
39. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a130070130.png ; $> 10 ^ { 5 }$ ; confidence 1.000
  
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40. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130050/k13005023.png ; $N \rightarrow \infty , \sigma \rightarrow 0 , \frac { 1 } { \lambda } = \operatorname { lim } ( \pi \sigma ^ { 2 } N ) \in ] 0 , \infty$ ; confidence 0.979
+
40. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130120/a13012057.png ; $\lambda > 1$ ; confidence 1.000
  
−
41. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005016.png ; $\frac { J - W _ { \Theta } ( z ) J W _ { \Theta } ( w ) ^ { * } } { z - \overline { w } } = 2 i K ^ { * } ( T - z I ) ^ { - 1 } ( T ^ { * } - \overline { w } l ) ^ { - 1 } K$ ; confidence 0.826
+
41. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016068.png ; $F ( r )$ ; confidence 1.000
  
−
42. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083360/s0833606.png ; $J _ { n } = \frac { z ^ { n } } { 2 ^ { \pi + 1 } \pi i } \int _ { - \infty } ^ { ( 0 + ) } t ^ { - n - 1 } \operatorname { exp } ( t - \frac { z ^ { 2 } } { 4 t } ) d t$ ; confidence 0.985
+
42. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061050/l06105076.png ; $F ( E ) = f ( E )$ ; confidence 1.000
  
−
43. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023050.png ; $\frac { \Gamma _ { p } [ \frac { \delta + n + p - 1 } { 2 } ] } { ( 2 \pi ) ^ { n } p / 2 | \Sigma | ^ { n / 2 } \Gamma _ { p } [ \frac { \delta + p - 1 } { 2 } ] }$ ; confidence 0.236
+
43. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065029.png ; $H ^ { 2 } ( \mu )$ ; confidence 1.000
  
−
44. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s12034025.png ; $SH ^ { * } ( M , \omega , L _ { 1 } , L _ { 2 } ) \otimes SH ^ { * } ( M , \omega , L _ { 2 } , L _ { 3 } ) \rightarrow SH ^ { * } ( M , \omega , L _ { 1 } , L _ { 3 } )$ ; confidence 0.434
+
44. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120190/l1201905.png ; $- B$ ; confidence 1.000
  
−
45. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s12034026.png ; $SH ^ { k } ( M , \omega , \phi _ { 1 } ) \otimes SH ^ { k } ( M , \omega , \phi _ { 2 } ) \rightarrow SH ^ { k } ( M , \omega , \phi _ { 2 } . \phi _ { 1 } )$ ; confidence 0.238
+
45. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120090/k12009017.png ; $F ( \tau ) =$ ; confidence 1.000
  
−
46. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064014.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { \operatorname { det } T _ { n } ( \alpha ) } { G ( \alpha ) ^ { N } } = E ( \alpha )$ ; confidence 0.614
+
46. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009025.png ; $f ( z , 1 ) = z$ ; confidence 1.000
  
−
47. https://www.encyclopediaofmath.org/legacyimages/u/u130/u130020/u13002015.png ; $( \int _ { - \infty } ^ { \infty } ( x - a ) ^ { 2 } | f ( x ) | ^ { 2 } d x ) ( \int _ { - \infty } ^ { \infty } ( y - b ) ^ { 2 } | \hat { f } ( y ) | ^ { 2 } d y ) \geq$ ; confidence 0.917
+
47. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010018.png ; $- A$ ; confidence 1.000
  
−
48. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v13007063.png ; $\operatorname { ln } ( 1 - \lambda ) = \frac { 1 } { \pi } \int _ { 0 } ^ { 1 } \frac { \theta ( s ^ { \prime } ) } { s ^ { \prime } } d s ^ { \prime }$ ; confidence 0.997
+
48. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c120010149.png ; $\zeta \in \partial \Omega$ ; confidence 1.000
  
−
49. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430112.png ; $\beta \gamma = \gamma \beta + ( 1 - q ^ { - 2 } ) \alpha ( \delta - \alpha ) , \delta \beta = \beta \delta + ( 1 - q ^ { - 2 } ) \alpha \beta$ ; confidence 0.947
+
49. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130070/m1300704.png ; $M = \sqrt { P _ { \mu } P ^ { \mu } }$ ; confidence 1.000
  
−
50. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001032.png ; $\frac { \partial v } { \partial t } - 6 v ^ { 2 } \frac { \partial v } { \partial x } + \frac { \partial ^ { 3 } v } { \partial x ^ { 3 } } = 0$ ; confidence 0.944
+
50. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130120/a13012013.png ; $3 - ( 4 \mu , 2 \mu , \mu - 1 )$ ; confidence 1.000
  
−
51. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130040/c13004031.png ; $\sum _ { k = 1 } ^ { \infty } \frac { \zeta ( 2 k ) } { k ( 2 k + 1 ) 2 ^ { 4 k } } = \operatorname { log } ( \frac { \pi } { 2 } ) - 1 + \frac { 2 G } { \pi }$ ; confidence 0.948
+
51. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r13008062.png ; $m ( t ) > 0$ ; confidence 1.000
  
−
52. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120110/d12011010.png ; $\operatorname { lim } _ { n \rightarrow \infty } \operatorname { sup } f ( \sum _ { j \in I } \sum _ { j \in I } \sum _ { [ 1 , n ] } x _ { j } )$ ; confidence 0.657
+
52. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840259.png ; $c ( A )$ ; confidence 1.000
  
−
53. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130170/d13017046.png ; $\sum _ { i = 1 } ^ { k } \lambda _ { i } \geq \frac { n } { n + 2 } \frac { 4 \pi ^ { 2 } k ^ { 1 + 2 / n } } { ( C _ { n } | \Omega | ) ^ { 2 / n } } k = 1,2 , \ldots$ ; confidence 0.496
+
53. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011840/a0118407.png ; $F ( s )$ ; confidence 1.000
  
−
54. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f13009096.png ; $H _ { n + 1 } ^ { ( k ) } ( x ) = \sum \frac { ( n _ { 1 } + \ldots + n _ { k } ) ! } { n _ { 1 } ! \ldots n _ { k } ! } x _ { 1 } ^ { n _ { 1 } } \ldots x _ { k } ^ { n _ { k } }$ ; confidence 0.364
+
54. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026230/c0262305.png ; $0 < r < 1$ ; confidence 1.000
  
−
55. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005058.png ; $F + ( x ) = \sum _ { j = 1 } ^ { J } ( m _ { j } ^ { + } ) ^ { 2 } e ^ { - k _ { j } x } + \frac { 1 } { 2 \pi } \int _ { - \infty } ^ { \infty } r _ { + } ( k ) e ^ { i k x } d k$ ; confidence 0.334
+
55. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065022.png ; $\delta _ { \mu }$ ; confidence 1.000
  
−
56. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130020/j13002015.png ; $\Delta = \frac { 1 } { 2 } \sum _ { A \neq B , A } \sum _ { B \neq \emptyset } E ( I _ { A } I _ { B } ) , \overline { \Delta } = \lambda + 2 \Delta$ ; confidence 0.546
+
56. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061050/l06105058.png ; $f ^ { - 1 } ( \{ x \} )$ ; confidence 1.000
  
−
57. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130020/k13002020.png ; $\tau _ { n } = \frac { c - d } { c + d } = \frac { S } { \left( \begin{array} { l } { n } \\ { 2 } \end{array} \right) } = \frac { 2 S } { n ( n - 1 ) }$ ; confidence 0.400
+
57. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130070/w13007044.png ; $\theta ( \alpha , \alpha ) = 1$ ; confidence 1.000
  
−
58. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120070/m1200705.png ; $m ( P ) = \int _ { 0 } ^ { 1 } \ldots \int _ { 0 } ^ { 1 } \operatorname { log } | P ( e ^ { i t } 1 , \ldots , e ^ { i t _ { n } } ) | d t _ { 1 } \ldots d t _ { n }$ ; confidence 0.291
+
58. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120110/h12011054.png ; $( k , k - 1 )$ ; confidence 1.000
  
−
59. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130060/n13006017.png ; $\mu _ { k } = \operatorname { sup } \operatorname { inf } \frac { \int _ { \Omega } ( \nabla u ) ^ { 2 } d x } { \int _ { \Omega } u ^ { 2 } d x }$ ; confidence 0.951
+
59. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120510/b12051017.png ; $\beta \in ( 0,1 )$ ; confidence 1.000
  
−
60. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060188.png ; $( \sigma _ { 2 } \frac { \partial } { \partial t _ { 1 } } - \sigma _ { 1 } \frac { \partial } { \partial t _ { 2 } } + \tilde { \gamma } ) v = 0$ ; confidence 0.190
+
60. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s130620101.png ; $\mu$ ; confidence 1.000
  
−
61. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120350/s1203506.png ; $\left\{ \begin{array} { l } { d x ( t ) = A x ( t ) d t + B u ( t ) d t + d w ( t ) } \\ { d y ( t ) = C x ( t ) d t + D u ( t ) d t + d v ( t ) } \end{array} \right.$ ; confidence 0.850
+
61. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090770/s09077034.png ; $y ( 0 ) = 0$ ; confidence 1.000
  
−
62. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t12007012.png ; $\Gamma _ { 0 } ( p ) + = \langle \Gamma _ { 0 } ( p ) , \left( \begin{array} { c c } { 0 } & { - 1 } \\ { p } & { 0 } \end{array} \right) \rangle$ ; confidence 0.962
+
62. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120100/i12010026.png ; $f ( t ) = ( K t ^ { 2 } + A t + B ) / 2 > 0$ ; confidence 1.000
  
−
63. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110146.png ; $( a \circ b ) ( x , \xi ) = \sum _ { | \alpha | < N } \frac { 1 } { \alpha ! } D _ { \xi } ^ { \alpha } a \partial _ { x } ^ { \alpha } b + t _ { N } ( a , b )$ ; confidence 0.305
+
63. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f120080126.png ; $B ( G ) = M A ( G )$ ; confidence 1.000
  
−
64. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a12006077.png ; $\left\{ \begin{array} { l } { \frac { d u } { d t } + A ( t , u ) u = f ( t , u ) , \quad t \in [ 0 , T ] } \\ { u ( 0 ) = u _ { 0 } } \end{array} \right.$ ; confidence 0.586
+
64. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074140/p074140164.png ; $p = 1,2$ ; confidence 1.000
  
−
65. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b12004055.png ; $q _ { X } = \operatorname { lim } _ { s \rightarrow 0 + } \frac { \operatorname { log } s } { \operatorname { log } \| D _ { s } \| _ { X } }$ ; confidence 0.248
+
65. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032058.png ; $F ( s , t ) = F ( t , s )$ ; confidence 1.000
  
−
66. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031066.png ; $S _ { R } ^ { \delta } ( f ) ( x ) = \sum _ { m \backslash | \leq R } ( 1 - \frac { | m | ^ { 2 } } { R ^ { 2 } } ) ^ { \delta } e ^ { 2 \pi i x m } \hat { f } ( m )$ ; confidence 0.191
+
66. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120080/w12008051.png ; $\Omega ( u )$ ; confidence 1.000
  
−
67. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c120080115.png ; $= \left\{ \begin{array} { l l } { I _ { n } , } & { p = q = 0 } \\ { 0 , } & { p \neq 0 \text { or } / \text { and } q \neq 0 } \end{array} \right.$ ; confidence 0.363
+
67. https://www.encyclopediaofmath.org/legacyimages/r/r120/r120020/r12002011.png ; $f ( \dot { q } )$ ; confidence 1.000
  
−
68. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180222.png ; $h . k = ( \theta \otimes \varphi - \varphi \otimes \theta ) \otimes ( \theta \otimes \varphi - \varphi \otimes \theta ) \in$ ; confidence 0.438
+
68. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200208.png ; $\phi ( z ) = 1$ ; confidence 1.000
  
−
69. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120030/d1200306.png ; $\operatorname { lim } _ { x \rightarrow \infty } f ( x _ { x } ) = f ( x ) = \operatorname { lim } _ { x \rightarrow \infty } f ( y _ { x } )$ ; confidence 0.428
+
69. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d12030044.png ; $f = g ^ { T } g$ ; confidence 1.000
  
−
70. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120050/d12005039.png ; $f ( x ) = \left\{ \begin{array} { l l } { \operatorname { sin } \frac { 1 } { x } , } & { x \neq 0 } \\ { a , } & { x = 0 } \end{array} \right.$ ; confidence 0.571
+
70. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b13003031.png ; $\sigma = \pm$ ; confidence 1.000
  
−
71. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e120120108.png ; $\operatorname { log } \int f ( \theta ^ { ( t + 1 ) } , \phi ) d \phi \geq \operatorname { log } \int f ( \theta ^ { ( t ) } , \phi ) d \phi$ ; confidence 0.976
+
71. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120110/a12011028.png ; $T ( i , 2 ) = 4$ ; confidence 1.000
  
−
72. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003080.png ; $( \Lambda ^ { \bullet } ( \mathfrak { g } / \mathfrak { k } ) , A ( \Gamma \backslash G ( R ) ) \otimes M _ { C } ) \rightleftharpoons$ ; confidence 0.119
+
72. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130010/g13001085.png ; $\gamma + \delta$ ; confidence 1.000
  
−
73. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e03500095.png ; $I _ { \epsilon } ( X ) = \operatorname { lim } _ { n \rightarrow \infty } \frac { 1 } { n } H _ { \epsilon } ^ { \prime \prime } ( X ^ { n } )$ ; confidence 0.963
+
73. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e12026053.png ; $F ( \mu )$ ; confidence 1.000
  
−
74. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130050/e1300509.png ; $\sum _ { n \in Z } \frac { [ \lambda + \alpha ; n ] [ \mu - n + 1 ; n ] } { [ \mu - n + \beta ; n ] [ \lambda + 1 ; n ] } x ^ { \lambda + x } y ^ { \mu - x }$ ; confidence 0.249
+
74. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070158.png ; $R ( L ) = H$ ; confidence 1.000
  
−
75. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230155.png ; $\frac { d } { d t } A ( \sigma _ { t } ) | _ { t = 0 } = \frac { d } { d t } \int _ { N } \sigma ^ { k ^ { * } } \phi _ { t } ^ { k ^ { * } } ( L \Delta ) | _ { t = 0 } =$ ; confidence 0.198
+
75. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130270/b1302703.png ; $\sigma ( \pi ( T ) )$ ; confidence 1.000
  
−
76. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e12026052.png ; $P ( \theta , t , \nu ) ( d \omega ) = \frac { 1 } { L _ { \mu } ( \theta ) } \operatorname { exp } \{ \theta , t ( \omega ) \} \nu ( d \omega )$ ; confidence 0.534
+
76. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022038.png ; $| \gamma | = m$ ; confidence 1.000
  
−
77. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055780/k05578014.png ; $\times \int _ { 0 } ^ { \alpha } [ K _ { i \tau } ( \alpha ) I _ { i \tau } ( x ) - I _ { i \tau } ( \alpha ) K _ { i \tau } ( x ) ] f ( x ) \frac { d x } { x }$ ; confidence 0.502
+
77. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120060/m12006011.png ; $P = P ( \rho , T )$ ; confidence 1.000
  
−
78. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130060/k13006034.png ; $\Delta ( F ) : = \{ Y \in \left( \begin{array} { c } { [ n ] } \\ { k - 1 } \end{array} \right) : Y \subset \text { Xfor someX } \in F \}$ ; confidence 0.462
+
78. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027065.png ; $\phi ( 0 ) = 0$ ; confidence 1.000
  
−
79. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060020/l06002016.png ; $L ( x ) = x \operatorname { ln } 2 - \frac { 1 } { 2 } \sum _ { k = 1 } ^ { \infty } ( - 1 ) ^ { k - 1 } \frac { \operatorname { sin } 2 k x } { k ^ { 2 } }$ ; confidence 0.977
+
79. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c120010126.png ; $A ^ { \prime } ( E )$ ; confidence 1.000
  
−
80. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r130080119.png ; $| u ( y ) | = | \sum _ { j = 1 } ^ { \infty } \lambda _ { j } ^ { 1 / 2 } v _ { j } \varphi _ { j } ( x ) | < c \Lambda \| v \| _ { 0 } = c \Lambda \| u \| _ { + }$ ; confidence 0.738
+
80. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120160/l12016014.png ; $\Omega U ( n )$ ; confidence 1.000
  
−
81. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130370/s1303705.png ; $x ( t + ) = x ( t ) \text { for allo } \leq t < 1 , x ( t - ) = \operatorname { lim } _ { s \uparrow t } x ( s ) \text { exists for all } 0 < t \leq 1$ ; confidence 0.118
+
81. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004025.png ; $( \Gamma \cap P ) \backslash H ^ { 1 }$ ; confidence 1.000
  
−
82. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130500/s13050019.png ; $\nabla ( A ) : = \{ Y \in \left( \begin{array} { l } { [ n ] } \\ { l + 1 } \end{array} \right) : Y \supset \text { Xfor someX } \in A \}$ ; confidence 0.359
+
82. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074520/p0745203.png ; $A B \subseteq P$ ; confidence 1.000
  
−
83. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064072.png ; $\operatorname { lim } _ { \tau \rightarrow \infty } \frac { \operatorname { det } ( I + W _ { \tau } ( k ) ) } { G ( a ) ^ { \tau } } = E ( a )$ ; confidence 0.634
+
83. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016055.png ; $P ( t )$ ; confidence 1.000
  
−
84. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020084.png ; $M _ { 2 } = \operatorname { min } _ { z _ { j } } \operatorname { max } _ { k = 2 , \ldots , n + 1 } | s _ { k } | \leq 2 ( n + 1 ) ^ { 2 } e ^ { - \theta n }$ ; confidence 0.289
+
84. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130070/t1300709.png ; $g ^ { \prime } ( 0 ) > 0$ ; confidence 1.000
  
−
85. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008095.png ; $d S = \sum _ { 1 } ^ { M } T _ { n } d \hat { \Omega } _ { n } = \sum _ { 1 } ^ { M } T _ { n } d \Omega _ { n } + \sum _ { 1 } ^ { g } \alpha _ { j } d \omega _ { j }$ ; confidence 0.722
+
85. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840318.png ; $H ( t ) \geq 0$ ; confidence 1.000
  
−
86. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008081.png ; $y = \Lambda ^ { N } ( w - \frac { 1 } { w } ) , P = \lambda ^ { N } - \sum _ { 2 } ^ { N } u _ { k } \lambda ^ { N - k } = \Lambda ^ { N } ( w + \frac { 1 } { w } )$ ; confidence 0.988
+
86. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s12034059.png ; $c _ { 1 } ( A ) = 0$ ; confidence 1.000
  
−
87. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001027.png ; $x ( \infty ) = \operatorname { lim } _ { n \rightarrow \infty } x ( n ) = \operatorname { lim } _ { z \rightarrow 1 } ( z - 1 ) Z ( x ( n ) )$ ; confidence 0.837
+
87. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070154.png ; $H = R ( L )$ ; confidence 1.000
  
−
88. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007037.png ; $3 ^ { 2 } \cdot 5 ^ { 2 } \cdot 11,3 ^ { 5 } \cdot 5 ^ { 2 } \cdot 13,3 ^ { 4 } \cdot 5 ^ { 2 } \cdot 13 ^ { 2 } , 3 ^ { 3 } \cdot 5 ^ { 3 } \cdot 13 ^ { 2 }$ ; confidence 0.589
+
88. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120080/w1200808.png ; $\Omega ( q , p )$ ; confidence 1.000
  
−
89. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007059.png ; $< x \operatorname { exp } ( - \frac { 1 } { 25 } ( \operatorname { log } x \operatorname { log } \operatorname { log } x ) ^ { 1 / 2 } )$ ; confidence 0.935
+
89. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a12006059.png ; $B ( t )$ ; confidence 1.000
  
−
90. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009035.png ; $\frac { 1 } { p _ { 2 } ( \xi , \tau ) + \alpha i } = \frac { p _ { S } ( \xi , \tau ) } { 1 + \alpha ^ { 2 } } - \frac { \alpha i } { 1 + \alpha ^ { 2 } }$ ; confidence 0.385
+
90. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120110/n12011065.png ; $\eta ( y )$ ; confidence 1.000
  
−
91. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b1301205.png ; $A ^ { * } = \{ f : \| f \| _ { A } ^ { * } = \sum _ { k = 0 } ^ { \infty } \operatorname { sup } _ { k \leq p | < \infty } | \hat { f } ( m ) | < \infty \}$ ; confidence 0.134
+
91. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074160/p074160147.png ; $| z | > R$ ; confidence 1.000
  
−
92. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027092.png ; $\operatorname { lim } _ { t \rightarrow \infty } a ( t ) = \frac { \int _ { 0 } ^ { \infty } b ( u ) d u } { \int _ { 0 } ^ { \infty } u d F ( u ) }$ ; confidence 0.842
+
92. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120150/s12015078.png ; $( X \backslash \Omega ) \geq 1$ ; confidence 1.000
  
−
93. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031094.png ; $S _ { R } ^ { \delta } f ( x ) = \sum _ { \lambda _ { k } \leq R } ( 1 - \frac { \lambda _ { k } } { R } ) ^ { \delta } ( f , \phi _ { k } ) \phi _ { k } ( x )$ ; confidence 0.541
+
93. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f12015030.png ; $A \in \Phi ( X , Y )$ ; confidence 1.000
  
−
94. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020220.png ; $x = \sum _ { k \in P ^ { \prime } } \overline { \lambda } _ { k } x ^ { ( k ) } + \sum _ { k \in R ^ { \prime } } \overline { \mu } _ { k } x ^ { ( k ) }$ ; confidence 0.248
+
94. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520239.png ; $R ( A , B )$ ; confidence 1.000
  
−
95. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003048.png ; $H ^ { \bullet } ( \partial ( \Gamma \backslash X ) , \tilde { M } ) = H ^ { 0 } \oplus H ^ { 1 } \rightleftarrows Q ^ { k } \oplus Q ^ { h }$ ; confidence 0.109
+
95. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130140/w13014020.png ; $H ( 0 ) = 1 / 2$ ; confidence 1.000
  
−
96. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120140/e12014067.png ; $q \left( \begin{array} { l } { v } \\ { s } \end{array} \right) = r \left( \begin{array} { l } { v } \\ { t } \end{array} \right)$ ; confidence 0.717
+
96. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022570/c02257023.png ; $y = y ^ { \prime }$ ; confidence 1.000
  
−
97. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040490/f04049021.png ; $P \{ F _ { \nu _ { 1 } , \nu _ { 2 } } < x \} = B _ { \nu _ { 1 } } / 2 , \nu _ { 2 } / 2 ( \frac { ( \nu _ { 1 } / \nu _ { 2 } ) x } { 1 + ( \nu _ { 1 } / \nu _ { 2 } ) x } )$ ; confidence 0.734
+
97. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120160/d12016024.png ; $f ^ { * } - f$ ; confidence 1.000
  
−
98. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008025.png ; $F = - \frac { k _ { B } T \operatorname { ln } Z } { N } , \quad Z = \operatorname { Tr } \operatorname { exp } ( - \frac { H } { k _ { B } T } )$ ; confidence 0.706
+
98. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130030/n1300302.png ; $u ( 0 , t ) = u ( \pi , t ) = 0$ ; confidence 1.000
  
−
99. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m13011074.png ; $v = \frac { \partial } { \partial t } ( x ^ { 0 } + u ) | _ { x ^ { 0 } } = ( \frac { \partial u } { \partial t } ) | _ { x ^ { 0 } } = \frac { D u } { D t }$ ; confidence 0.932
+
99. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c12021069.png ; $\int \operatorname { exp } \lambda d L = 1$ ; confidence 1.000
  
−
100. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066630/n06663028.png ; $\| \Delta _ { h _ { i } } ^ { 1 } f _ { x _ { i } } ^ { ( r _ { i } ^ { * } ) } \| _ { L _ { p } ( \Omega _ { W _ { i } } | ) } \leq M _ { i } | h _ { i } | ^ { \alpha _ { i } }$ ; confidence 0.057
+
100. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b1300301.png ; $V = ( V ^ { + } , V ^ { - } )$ ; confidence 1.000
  
−
101. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060180.png ; $( \xi _ { 1 } \frac { \partial } { \partial t _ { 1 } } + \xi _ { 2 } \frac { \partial } { \partial t _ { 2 } } ) \langle f , f \rangle _ { H } =$ ; confidence 0.977
+
101. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120210/t12021060.png ; $\phi ( E )$ ; confidence 1.000
  
−
102. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082320/r08232051.png ; $\operatorname { lim } _ { r \rightarrow 1 } \int _ { 0 } ^ { 2 \pi } | f ( r e ^ { i \theta } ) - f ( e ^ { i \theta } ) | ^ { \delta } d \theta = 0$ ; confidence 0.920
+
102. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006074.png ; $\operatorname { dim } ( P ) \leq \operatorname { max } \{ 2 , | A | \}$ ; confidence 1.000
  
−
103. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064025.png ; $T ( a ) = \operatorname { Ran } ( \alpha ) \cup \{ z \notin \operatorname { Ran } ( \alpha ) : \text { wind } ( \alpha - z ) \neq 0 \}$ ; confidence 0.339
+
103. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007017.png ; $n > 0$ ; confidence 1.000
  
−
104. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t12014062.png ; $\sigma ( T _ { \phi } ) = \operatorname { conv } ( R ( \phi ) ) = [ \operatorname { essinf } \phi , \operatorname { esssup } \phi ]$ ; confidence 0.775
+
104. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120030/q12003044.png ; $\varphi ( 1 ) = 1$ ; confidence 1.000
  
−
105. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020012.png ; $\operatorname { inf } _ { z _ { j } } \operatorname { max } _ { k \in S } \frac { | \sum _ { j = 1 } ^ { n } b _ { j } z _ { j } ^ { k } | } { M _ { d } ( k ) }$ ; confidence 0.252
+
105. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001023.png ; $\frac { \partial ^ { 2 } u } { \partial \xi \partial \eta } = \operatorname { sin } ( u )$ ; confidence 1.000
  
−
106. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200144.png ; $\frac { k = m + 1 , \ldots , m + | g ( k ) | } { \sum _ { j = 1 } ^ { N } | b _ { j } z _ { j } ^ { k } | } \geq \frac { 1 } { n } ( \frac { \delta } { 2 } ) ^ { n - 1 }$ ; confidence 0.341
+
106. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130030/z13003022.png ; $[ - b , b ]$ ; confidence 1.000
  
−
107. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a12013044.png ; $R ( \theta ^ { * } ) = \sum _ { n = - \infty } ^ { \infty } \operatorname { cov } ( H ( \theta ^ { * } , X _ { n } ) , H ( \theta ^ { * } , X _ { 0 } ) )$ ; confidence 0.963
+
107. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520135.png ; $\lambda E - A$ ; confidence 1.000
  
−
108. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130250/b13025064.png ; $\operatorname { cot } \omega = \operatorname { cot } \alpha + \operatorname { cot } \beta + \operatorname { cot } \gamma$ ; confidence 0.991
+
108. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029020.png ; $q ^ { 2 } f ( q )$ ; confidence 1.000
  
−
109. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c1200707.png ; $C ^ { n } ( C , M ) = \prod _ { \langle \alpha _ { 1 } , \ldots , \alpha _ { N } \rangle } M ( \operatorname { codom } \alpha _ { n } ) , n > 0$ ; confidence 0.202
+
109. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005074.png ; $B = H ^ { - 1 }$ ; confidence 1.000
  
−
110. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c120210117.png ; $\Lambda _ { n } ( \theta ) - h ^ { \prime } \Delta _ { n } ( \theta ) \rightarrow - \frac { 1 } { 2 } h ^ { \prime } \Gamma ( \theta ) h$ ; confidence 0.843
+
110. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110380/b11038016.png ; $d \mu$ ; confidence 1.000
  
−
111. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130250/c13025052.png ; $\hat { A } ( t | \beta ) = \int _ { 0 , t } \frac { 1 } { \sum _ { k = 1 } ^ { n } l _ { k } ( s - ) e ^ { Z _ { k } ^ { T } ( s - ) \beta } } d \overline { N } ( s )$ ; confidence 0.138
+
111. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018067.png ; $[ 0,1 ] ^ { N }$ ; confidence 1.000
  
−
112. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120160/e12016016.png ; $\int ( R _ { k } + \frac { 1 } { 2 } f ^ { - 2 } h ^ { \alpha \beta } \partial _ { \alpha } E \partial _ { \beta } \overline { E } ) d \mu _ { R }$ ; confidence 0.509
+
112. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130060/h13006065.png ; $\Gamma ( n ) =$ ; confidence 1.000
  
−
113. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130050/e13005033.png ; $E _ { q } ( \alpha , \beta ) = [ \theta _ { x } + \alpha ] _ { q } [ \partial _ { y } ] _ { q } - [ \theta _ { y } + \beta ] [ \partial _ { x } ] _ { q }$ ; confidence 0.722
+
113. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130130/w13013066.png ; $W = \int H ^ { 2 } d A$ ; confidence 1.000
  
−
114. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130050/e13005014.png ; $E ( \alpha , \beta ) = \partial _ { x } \partial _ { y } - \frac { \beta } { x - y } \partial _ { x } + \frac { \alpha } { x - y } \partial y$ ; confidence 0.825
+
114. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p130070112.png ; $z \rightarrow \partial \Omega$ ; confidence 1.000
  
−
115. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120020/h12002012.png ; $\operatorname { inf } \{ \| \phi \| _ { \infty } : \phi \in L ^ { \infty } , \hat { \phi } ( j ) = \alpha _ { j } \text { for } j \geq 0 \}$ ; confidence 0.959
+
115. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031024.png ; $( 1 - 2 \delta ) / 4 < 1 / p < ( 3 + 2 \delta ) / 4$ ; confidence 1.000
  
−
116. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055780/k0557807.png ; $= \frac { 2 } { \pi ^ { 2 } x _ { 0 } } \int _ { 0 } ^ { \infty } K _ { i \tau } ( x _ { 0 } ) \tau \operatorname { sinh } \pi \tau F ( \tau ) d \tau$ ; confidence 0.854
+
116. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120020/w1200209.png ; $W ( P , Q )$ ; confidence 1.000
  
−
117. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003096.png ; $\operatorname { IF } ( ( \vec { x } _ { 0 } , y _ { 0 } ) ; T , H _ { \vec { \theta } } ) = \eta ( \vec { x } _ { 0 } , e _ { 0 } ) M ^ { - 1 } \vec { x } _ { 0 }$ ; confidence 0.466
+
117. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032057.png ; $F ( 0 , t ) = t$ ; confidence 1.000
  
−
118. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083360/s0833603.png ; $- \frac { \operatorname { sin } n \pi } { \pi } \int _ { 0 } ^ { \infty } e ^ { - n \theta - z \operatorname { sinh } \theta } d \theta$ ; confidence 0.965
+
118. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042059.png ; $( i , i + 1 )$ ; confidence 1.000
  
−
119. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064016.png ; $E ( \alpha ) = \operatorname { exp } ( \sum _ { k = 1 } ^ { \infty } k [ \operatorname { log } a ] _ { k } [ \operatorname { log } a ] - k )$ ; confidence 0.720
+
119. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006071.png ; $T ( z ) = V + V G ( z ) V$ ; confidence 1.000
  
−
120. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020071.png ; $\operatorname { max } _ { j = 1 , \ldots , n - m + 1 } | s _ { j } | \geq m ( \frac { 1 } { 2 } + \frac { m } { 8 n } + \frac { 3 m ^ { 2 } } { 64 n ^ { 2 } } )$ ; confidence 0.610
+
120. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031076.png ; $\delta > ( n - 1 ) / 2$ ; confidence 1.000
  
−
121. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011039.png ; $\Phi ( z ) = - \frac { i \Gamma } { 2 \pi } [ \operatorname { log } \operatorname { sin } ( \frac { \pi } { l } ( z - \frac { i b } { 2 } ) ) +$ ; confidence 0.830
+
121. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120240/a12024030.png ; $( p , p )$ ; confidence 1.000
  
−
122. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008023.png ; $d \omega _ { 1 } ( \lambda ) = \frac { \prod _ { i = 1 } ^ { g } ( \lambda - \alpha _ { i } ) } { \sqrt { R _ { g } ( \lambda ) } } d \lambda \sim$ ; confidence 0.401
+
122. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120140/d12014040.png ; $( n , q - 1 ) = 1$ ; confidence 1.000
  
−
123. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040346.png ; $= \{ \langle \alpha , b \rangle \in A ^ { 2 } : \epsilon ^ { A } ( \alpha , b ) \in \text { Ffor all } \epsilon ( x , y ) \in E ( x , y ) \}$ ; confidence 0.459
+
123. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520102.png ; $\lambda E - B$ ; confidence 1.000
  
−
124. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007058.png ; $x \operatorname { exp } ( - 8 ( \operatorname { log } x \operatorname { log } \operatorname { log } x ) ^ { 1 / 2 } ) < A _ { 2 } ( x ) <$ ; confidence 0.852
+
124. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120020/z12002010.png ; $100 = 89 + 8 + 3,1111 = 987 + 89 + 34 + 1$ ; confidence 1.000
  
−
125. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180134.png ; $\mathfrak { R } d _ { n } ( U ) = \{ \mathfrak { P } ( \square ^ { n } U ) , \mathfrak { c } _ { 0 } , \ldots , \mathfrak { c } _ { n } - 1 , Id \}$ ; confidence 0.077
+
125. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021070.png ; $\lambda = \lambda _ { 2 }$ ; confidence 1.000
  
−
126. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020037.png ; $\delta _ { T } = \operatorname { sup } _ { x \in X } \operatorname { dim } \operatorname { lin } \{ x , T x , T ^ { 2 } x , \ldots \} = N$ ; confidence 0.674
+
126. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006076.png ; $G = ( V , E )$ ; confidence 1.000
  
−
127. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b130120102.png ; $\int _ { 0 } ^ { 1 } \omega ( f ^ { \prime } ; t ) _ { p } ( \operatorname { ln } \frac { 1 } { t } ) ^ { - 1 / p ^ { \prime } } t ^ { - 1 } d t < \infty$ ; confidence 0.729
+
127. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n06752025.png ; $B = C A D$ ; confidence 1.000
  
−
128. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001027.png ; $\frac { \partial u ^ { \prime } ( \xi ^ { \prime } ( \xi , \eta ) , \eta ^ { \prime } ( \xi , \eta ) ) } { \partial \eta ^ { \prime } } =$ ; confidence 0.993
+
128. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016680/b01668015.png ; $H ( t )$ ; confidence 1.000
  
−
129. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008058.png ; $\Delta ( \lambda , \mu ) = \operatorname { det } [ E \lambda - A \mu ] = \sum _ { i = 0 } ^ { n } a _ { i , n - i } \lambda ^ { i } \mu ^ { n - i }$ ; confidence 0.406
+
129. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130040/e1300405.png ; $U ( t ) \psi ( 0 ) = \psi ( t )$ ; confidence 1.000
  
−
130. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120140/e12014099.png ; $[ ( \varphi \rightarrow \psi ) \rightarrow ( ( \psi \rightarrow \chi ) \rightarrow ( \varphi \rightarrow \chi ) ) ] = 1$ ; confidence 0.997
+
130. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120040/a12004011.png ; $t > 0$ ; confidence 1.000
  
−
131. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i1300504.png ; $u _ { - } = \left\{ \begin{array} { l } { e ^ { - i k x } + r _ { - } ( k ) e ^ { - i k x } } \\ { t - ( k ) e ^ { i k x } , \quad x } \end{array} \right.$ ; confidence 0.602
+
131. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120020/c12002070.png ; $\mu \equiv \mu ( x )$ ; confidence 1.000
  
−
132. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130010/m13001033.png ; $v _ { MAP } = \operatorname { arg } \operatorname { max } _ { v _ { j } \in V } \prod _ { i } P ( \alpha _ { i } | v _ { j } ) \cdot P ( v _ { j } )$ ; confidence 0.242
+
132. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130190/b13019033.png ; $\rho ( f ^ { \prime } ) = [ f ^ { \prime } ] - f ^ { \prime } + \frac { 1 } { 2 }$ ; confidence 1.000
  
−
133. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140109.png ; $\frac { \pi ^ { n } } { n \operatorname { vol } ( D _ { 1 } ) } \int _ { \partial D _ { 1 } } f ( \zeta ) \nu ( \zeta - \alpha ) = f ( \alpha )$ ; confidence 0.405
+
133. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015065.png ; $X = B ( 0,1 )$ ; confidence 1.000
  
−
134. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120100/n12010052.png ; $\sum _ { l = 0 } ^ { k } \alpha _ { i } y _ { m + i } = h f ( \sum _ { i = 0 } ^ { k } \beta _ { i } x _ { m + i } , \sum _ { i = 0 } ^ { k } \beta _ { i } y _ { m + i } )$ ; confidence 0.166
+
134. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030041.png ; $\lambda = \lambda ( \eta )$ ; confidence 1.000
  
−
135. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130030/o13003041.png ; $f _ { j k l } = \frac { - i } { 4 } \operatorname { Tr } [ ( \lambda _ { j } \lambda _ { k } - \lambda _ { k } \lambda _ { j } ) \lambda _ { l } ]$ ; confidence 0.632
+
135. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130040/o1300404.png ; $A = \frac { 1 } { 2 } \Delta + b$ ; confidence 1.000
  
−
136. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130040/o13004015.png ; $\operatorname { exp } [ \int _ { 0 } ^ { T } L ( \dot { \phi } ( s ) , \phi ( s ) ) d s - \int _ { 0 } ^ { T } L ( \dot { \psi } ( s ) , \psi ( s ) ) d s ]$ ; confidence 0.987
+
136. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n12002031.png ; $F ( \mu ^ { \prime } )$ ; confidence 1.000
  
−
137. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060184.png ; $\frac { \partial ^ { 2 } f } { \partial t _ { 1 } \partial t _ { 2 } } = \frac { \partial ^ { 2 } f } { \partial t _ { 2 } \partial t _ { 1 } }$ ; confidence 0.999
+
137. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030036.png ; $B ( m , 4 )$ ; confidence 1.000
  
−
138. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006058.png ; $p ( \lambda _ { 1 } , \lambda _ { 2 } ) = \operatorname { det } ( \lambda _ { 1 } \sigma _ { 2 } - \lambda _ { 2 } \sigma _ { 1 } + \gamma )$ ; confidence 0.998
+
138. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130120/z13012023.png ; $0 \leq \sigma \leq ( 1 / n ) \operatorname { tan } ^ { 2 } ( \pi / 2 n )$ ; confidence 1.000
  
−
139. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120020/q12002043.png ; $\operatorname { Fun } _ { q } ( M ) \rightarrow \operatorname { Fun } _ { q } ( M ) \otimes \operatorname { Fun } _ { q } ( SU ( n ) )$ ; confidence 0.482
+
139. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f12015090.png ; $\beta ( A + T ) \leq \beta ( A )$ ; confidence 1.000
  
−
140. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008057.png ; $E [ W ] _ { \operatorname { exh } } = \frac { \delta ^ { 2 } } { 2 r } + \frac { P \lambda \dot { b } ^ { ( 2 ) } + r ( P - \rho ) } { 2 ( 1 - \rho ) }$ ; confidence 0.202
+
140. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070178.png ; $f ( x ) \in R ( L )$ ; confidence 1.000
  
−
141. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130140/r13014028.png ; $f ( x ) \mapsto ( S ^ { \alpha } f ) ( x ) = \int _ { | \xi | \leq 1 } \hat { f ( \xi ) } ( 1 - | \xi | ^ { 2 } ) ^ { \alpha } e ^ { 2 \pi i x . \xi } d \xi$ ; confidence 0.223
+
141. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b110220211.png ; $i + 1 < 2 j$ ; confidence 1.000
  
−
142. https://www.encyclopediaofmath.org/legacyimages/s/s083/s083360/s0833602.png ; $J _ { n } ( z ) = \frac { 1 } { \pi } \int _ { 0 } ^ { \pi } \operatorname { cos } ( n \theta - z \operatorname { sin } \theta ) d \theta +$ ; confidence 0.516
+
142. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120030/t12003030.png ; $V = \Phi ( U )$ ; confidence 1.000
  
−
143. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059040.png ; $\frac { F _ { 1 } z } { 1 + G _ { 1 } z } \square _ { + } \frac { F _ { 2 } z } { 1 + G _ { 2 } z } \square _ { + } \frac { F _ { 3 } } { 1 + G _ { 3 } z } \square$ ; confidence 0.097
+
143. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130280/a13028021.png ; $s _ { 0 } = 1 / 2$ ; confidence 1.000
  
−
144. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200133.png ; $\geq 2 ( \frac { \delta _ { 1 } - \delta _ { 2 } } { 12 e } ) ^ { N } \operatorname { min } _ { j = k , \ldots , l } | b _ { 1 } + \ldots + b _ { j } |$ ; confidence 0.076
+
144. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032052.png ; $F : [ 0 , \infty ) ^ { 2 } \rightarrow [ 0 , \infty )$ ; confidence 1.000
  
−
145. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120190/w1201906.png ; $\psi _ { W } ( x , p , t ) = \int _ { R ^ { 3 N } } e ^ { i p z / \hbar } \overline { \psi } ( x + \frac { z } { 2 } , t ) \psi ( x - \frac { z } { 2 } , t ) d z$ ; confidence 0.345
+
145. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040360.png ; $\Omega F$ ; confidence 1.000
  
−
146. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001010.png ; $\delta _ { k } ( n ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } n = k } \\ { 0 } & { \text { if } n \neq k } \end{array} \right.$ ; confidence 0.980
+
146. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110160/a11016093.png ; $b = 0$ ; confidence 1.000
  
−
147. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130080/z13008036.png ; $= \frac { ( \alpha + 1 ) _ { k + l } } { ( \alpha + 1 ) _ { k } ( \alpha + 1 ) _ { l } } z ^ { k } z ^ { l } F ( - k , - l ; - k - l - \alpha ; \frac { 1 } { 2 z } )$ ; confidence 0.273
+
147. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120250/s12025018.png ; $h ( x ) = \sqrt { 1 - x ^ { 2 } }$ ; confidence 1.000
  
−
148. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040231.png ; $E ( \Gamma , \Delta ) = \{ \epsilon _ { i } ( \gamma , \delta ) : \gamma \approx \delta \in \Gamma \approx \Delta , i \in I \}$ ; confidence 0.992
+
148. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130120/z13012028.png ; $\sigma > ( 1 / n ) \operatorname { tan } ^ { 2 } ( \pi / 2 n )$ ; confidence 1.000
  
−
149. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040591.png ; $S _ { P } = \langle P , \operatorname { Mod } _ { S _ { P } } , \operatorname { mng } _ { S _ { P } } , \operatorname { Fod } e l s _ { P } \}$ ; confidence 0.056
+
149. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130140/r1301409.png ; $U \cap \sigma ( R ) = \{ \lambda \}$ ; confidence 1.000
  
−
150. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040241.png ; $\Gamma \dagger _ { D } \varphi \text { iff } K ( \Gamma ) \approx L ( \Gamma ) \vDash _ { K } K ( \varphi ) \approx L ( \varphi )$ ; confidence 0.254
+
150. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032110/d03211065.png ; $t < 0$ ; confidence 1.000
  
−
151. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a12006045.png ; $\| ( \lambda + A ( t _ { k } ) ) ^ { - 1 } \ldots ( \lambda + A ( t _ { 1 } ) ) ^ { - 1 } \| _ { L ( X ) } \leq \frac { M } { ( \lambda - \beta ) ^ { k } }$ ; confidence 0.617
+
151. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120140/d12014054.png ; $( n , 2 ) = 1$ ; confidence 1.000
  
−
152. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015010/b01501037.png ; $B O _ { n } = \operatorname { lim } _ { r \rightarrow \infty } \operatorname { inf } \operatorname { Gras } _ { n } ( R ^ { r + n } )$ ; confidence 0.744
+
152. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130110/c1301106.png ; $\sigma \geq 0$ ; confidence 1.000
  
−
153. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031062.png ; $G _ { \delta } = ( 2 / \pi ) \operatorname { sup } _ { x > 0 } \int _ { 0 } ^ { 1 } ( 1 - t ^ { 2 } ) ^ { \delta } \operatorname { sin } x t d t / t$ ; confidence 0.931
+
153. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f12015023.png ; $i ( A ) = \alpha ( A ) - \beta ( A )$ ; confidence 1.000
  
−
154. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001025.png ; $\frac { \partial u ^ { \prime } ( \xi ^ { \prime } ( \xi , \eta ) , \eta ^ { \prime } ( \xi , \eta ) ) } { \partial \xi ^ { \prime } } =$ ; confidence 0.993
+
154. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120090/m12009017.png ; $P ( D ) ( E ) = \delta _ { 0 }$ ; confidence 1.000
  
−
155. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120150/d12015027.png ; $= ( 2 ^ { 2 t + 2 } \frac { 2 ^ { 2 t } - 1 } { 3 } , 2 ^ { 2 t - 1 } \frac { 2 ^ { 2 t + 1 } + 1 } { 3 } , 2 ^ { 2 t - 1 } \frac { 2 ^ { 2 t - 1 } + 1 } { 3 } , 2 ^ { 4 t - 2 } )$ ; confidence 0.940
+
155. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130120/z13012010.png ; $\xi > 1$ ; confidence 1.000
  
−
156. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d12030047.png ; $E [ \gamma ( X ( t ) ) | \sigma ( Y ( u , u \leq t ) ] = \frac { E _ { \mu _ { X } } [ \gamma ( X ( t ) ) \psi ( t ) ] } { E _ { \mu _ { X } } [ \psi ( t ) ] }$ ; confidence 0.213
+
156. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g130040186.png ; $\epsilon \in ( 0,1 )$ ; confidence 1.000
  
−
157. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012030.png ; $L ( \theta | Y _ { 0 b s } ) = \int _ { M ( Y _ { \text { aug } } ) = Y _ { \text { obs } } } L ( \theta | Y _ { \text { aug } } ) d Y _ { \text { aug } }$ ; confidence 0.135
+
157. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a130080106.png ; $U \leq b ( X )$ ; confidence 1.000
  
−
158. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e03500080.png ; $H _ { \epsilon } ^ { \prime } ( \xi ) = \operatorname { inf } \{ I ( \xi , \xi ^ { \prime } ) : \xi ^ { \prime } \in W _ { \epsilon } \}$ ; confidence 0.589
+
158. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130160/b13016072.png ; $f ( x ) \neq f ( y )$ ; confidence 1.000
  
−
159. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120160/e12016045.png ; $J = \frac { 1 } { f } \left( \begin{array} { c c } { 1 } & { - \psi } \\ { - \psi } & { \psi ^ { 2 } + r ^ { 2 } f ^ { 2 } } \end{array} \right)$ ; confidence 0.916
+
159. https://www.encyclopediaofmath.org/legacyimages/r/r077/r077540/r0775408.png ; $[ 0 , + \infty ]$ ; confidence 1.000
  
−
160. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120040/f12004030.png ; $f ^ { \Delta ( \varphi ) } ( w ) = \operatorname { sup } _ { x \in X } \operatorname { min } \{ \varphi ( x , w ) , - f ( x ) \} ( w \in W )$ ; confidence 0.403
+
160. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130410/s13041013.png ; $\mu _ { 0 } = \mu _ { 1 }$ ; confidence 1.000
  
−
161. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f13009044.png ; $U _ { n + 1 } ^ { ( k ) } ( x ) = \sum \frac { ( n _ { 1 } + \ldots + n _ { k } ) ! } { n _ { 1 } ! \ldots n _ { k } ! } x ^ { k ( x _ { 1 } + \ldots + n _ { k } ) - n }$ ; confidence 0.481
+
161. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006063.png ; $p ( \lambda _ { 1 } , \lambda _ { 2 } )$ ; confidence 1.000
  
−
162. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f120210111.png ; $p _ { i } ( z ) z ^ { \lambda } = \sum _ { n = 0 } ^ { N } \alpha ^ { n _ { i } } z ^ { n } ( \frac { \partial } { \partial z } ) ^ { n } z ^ { \lambda }$ ; confidence 0.120
+
162. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120050/f12005043.png ; $x ^ { 2 } - y ^ { 2 } = z ^ { 2 }$ ; confidence 1.000
  
−
163. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f12023028.png ; $\Omega ( M ) = \oplus _ { k \geq 0 } \Omega ^ { k } ( M ) = \oplus _ { k = 0 } ^ { \operatorname { dim } M } \Gamma ( \bigwedge T ^ { * } M )$ ; confidence 0.683
+
163. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130050/r13005014.png ; $( G )$ ; confidence 1.000
  
−
164. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120050/g12005052.png ; $\frac { \partial A } { \partial \tau } = A + ( 1 + i \alpha ) \frac { \partial ^ { 2 } A } { \partial \xi ^ { 2 } } - ( 1 + i b ) A | A | ^ { 2 }$ ; confidence 0.737
+
164. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060040/l06004022.png ; $\leq n - p$ ; confidence 1.000
  
−
165. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120110/h12011038.png ; $\operatorname { limsup } _ { k \rightarrow \infty } | \int _ { \Gamma } \frac { f ( \xi ) } { \xi ^ { k + 1 } } d \xi | ^ { 1 / k } \leq 1$ ; confidence 0.992
+
165. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110670/b110670111.png ; $A C$ ; confidence 1.000
  
−
166. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i13003056.png ; $\operatorname { ind } _ { g } ( P ) = ( - 1 ) ^ { n } \operatorname { Ch } ( [ a | _ { T ^ { * } M ^ { g } } ] ) T ( M ^ { g } ) L ( N , g ) [ T ^ { * } M ^ { g } ]$ ; confidence 0.103
+
166. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f12008039.png ; $( \xi , \xi )$ ; confidence 0.999
  
−
167. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i13004026.png ; $( N + 1 ) ^ { - 1 } \| \sum _ { k = 0 } ^ { N } c _ { k } D _ { k } \| _ { L } \leq \operatorname { max } _ { 0 \leq k \leq N } | \mathfrak { c } _ { k } |$ ; confidence 0.066
+
167. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840269.png ; $E ( \Delta )$ ; confidence 0.999
  
−
168. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i12004033.png ; $f ( z ) = \int _ { \partial D } f ( \zeta ) K _ { BM } ( \zeta , z ) - \int _ { D } \overline { \partial } f ( \zeta ) / K _ { BM } ( \zeta , z )$ ; confidence 0.838
+
168. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130070/h13007018.png ; $B ( m , D , n )$ ; confidence 0.999
  
−
169. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061050/l06105073.png ; $F ( E ) = \{ t \in T : \text { there is an } \square \omega \in \Omega \square \text { such that } \square ( \omega , t ) \in F \}$ ; confidence 0.693
+
169. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130070/f1300708.png ; $m = 1,2,3,4,5,7$ ; confidence 0.999
  
−
170. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m13025067.png ; $\operatorname { lim } _ { \varepsilon \rightarrow 0 } ( u ^ { * } \rho _ { \varepsilon } ) ( v ^ { * } \sigma _ { \varepsilon } )$ ; confidence 0.979
+
170. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110890/b11089067.png ; $\beta = 1 / 2$ ; confidence 0.999
  
−
171. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130130/p13013063.png ; $\zeta _ { \lambda } ^ { \lambda } = i ^ { ( n - r ( \lambda ) + 1 ) / 2 } \sqrt { ( \lambda _ { 1 } \ldots \lambda _ { r ( \lambda ) } ) / 2 }$ ; confidence 0.359
+
171. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f12015040.png ; $\alpha ( B ) < \infty$ ; confidence 0.999
  
−
172. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r13008022.png ; $\sum _ { i , j = 1 } ^ { n } K ( x _ { i } , x _ { j } ) t _ { j } \overline { t } _ { i } \geq 0 , \forall x _ { i } , y _ { j } \in E , \forall t \in C ^ { n }$ ; confidence 0.693
+
172. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029069.png ; $f ( q ) \geq 0$ ; confidence 0.999
  
−
173. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130340/s13034035.png ; $\ldots \subset C _ { 3 } \subset \ldots \subset C _ { 2 } \subset \ldots \subset C _ { 1 } \subset \ldots \subset C _ { 0 } = R K$ ; confidence 0.609
+
173. https://www.encyclopediaofmath.org/legacyimages/e/e036/e036440/e03644014.png ; $x < 0$ ; confidence 0.999
  
−
174. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005066.png ; $\operatorname { Ker } D _ { A } / \operatorname { Ran } D _ { A } = \operatorname { Ker } A \oplus ( X / \operatorname { Ran } A )$ ; confidence 0.758
+
174. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009078.png ; $P ( T )$ ; confidence 0.999
  
−
175. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120190/w12019043.png ; $F = ( 2 \pi \hbar ) ^ { - 6 N } \int _ { R ^ { 3 N } \times R ^ { 3 N } } e ^ { i ( \sigma X + r P ) / \hbar } \phi ( \sigma , \tau ) d \sigma d \tau$ ; confidence 0.648
+
175. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i1300505.png ; $r ( k )$ ; confidence 0.999
  
−
176. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021061.png ; $x _ { , j } = \left\{ \begin{array} { l l } { 1 , } & { \text { if } i + j = m + 1 } \\ { 0 } & { \text { otherwise } } \end{array} \right.$ ; confidence 0.156
+
176. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k12012041.png ; $\int _ { 0 } ^ { \infty } \frac { - \operatorname { ln } f ( x ^ { 2 } ) } { 1 + x ^ { 2 } } d x = \infty$ ; confidence 0.999
  
−
177. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z130100119.png ; $V _ { 0 } = \emptyset ; V _ { \alpha } = \cup _ { \beta < \alpha } P ( V _ { \beta + 1 } ) ; \text { and } V = \cup _ { \alpha } V _ { \alpha }$ ; confidence 0.704
+
177. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120060/w12006046.png ; $( n , r )$ ; confidence 0.999
  
−
178. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a120050129.png ; $\frac { \partial u } { \partial t } + \sum _ { j = 1 } ^ { m } \alpha _ { j } ( t , u ) \frac { \partial u } { \partial x _ { j } } = f ( t , u )$ ; confidence 0.931
+
178. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059140/l05914040.png ; $x ( 0 ) = 0$ ; confidence 0.999
  
−
179. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a12006036.png ; $\left\{ \begin{array} { l l } { \frac { d u } { d t } + A ( t ) u = f ( t ) , } & { t \in [ 0 , T ] } \\ { u ( 0 ) = u _ { 0 } } \end{array} \right.$ ; confidence 0.432
+
179. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120060/d12006013.png ; $D ^ { \pm } f = f - \sigma ^ { \pm } T ^ { \pm 1 } ( f )$ ; confidence 0.999
  
−
180. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a12013052.png ; $\overline { \theta } _ { n } = \overline { \theta } _ { n - 1 } + \frac { 1 } { n } ( \theta _ { n - 1 } - \overline { \theta } _ { n - 1 } )$ ; confidence 0.827
+
180. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026010/c026010570.png ; $( \Omega , F )$ ; confidence 0.999
  
−
181. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040103.png ; $\| x ^ { \prime } \| _ { X ^ { \prime } } = \operatorname { sup } \{ \int _ { \Omega } | x x ^ { \prime } | d \mu : \| x \| _ { X } \leq 1 \}$ ; confidence 0.746
+
181. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d1203002.png ; $( Y ( t ) , t \geq 0 )$ ; confidence 0.999
  
−
182. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042010.png ; $( \phi \otimes \text { id } ) \Psi _ { V , W } = \Psi _ { V , Z } ( \text { id } \varnothing \phi ) , \forall \phi : W \rightarrow Z$ ; confidence 0.381
+
182. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010990/a01099011.png ; $k \neq 0$ ; confidence 0.999
  
−
183. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001031.png ; $\frac { \partial u } { \partial t } + 6 u \frac { \partial u } { \partial x } + \frac { \partial ^ { 3 } u } { \partial x ^ { 3 } } = 0$ ; confidence 0.998
+
183. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k12012024.png ; $\int _ { - \infty } ^ { \infty } \frac { - \operatorname { ln } f ( x ) } { 1 + x ^ { 2 } } d x < \infty$ ; confidence 0.999
  
−
184. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026029.png ; $( L _ { h k } V ) _ { j } ^ { n + 1 } = \frac { V _ { j } ^ { n + 1 } - V _ { j } ^ { n } } { k } - \delta ^ { 2 } ( \frac { V _ { j } ^ { n + 1 } + V _ { j } ^ { n } } { 2 } )$ ; confidence 0.374
+
184. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031540/d0315402.png ; $G \times G$ ; confidence 0.999
  
−
185. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120310/c12031045.png ; $n ( \epsilon , F _ { d } ) \leq K . d ^ { p } . \epsilon ^ { - \gamma } , \quad \forall d = 1,2 , \dots , \forall \epsilon \in ( 0,1 ]$ ; confidence 0.163
+
185. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130120/a13012030.png ; $( s , \mu )$ ; confidence 0.999
  
−
186. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030280/d0302804.png ; $\operatorname { lim } _ { x \rightarrow \infty } [ a _ { 0 } + \frac { n } { n + 1 } a _ { 1 } + \frac { n ( n - 1 ) } { ( n + 1 ) ( n + 2 ) } a _ { 2 }$ ; confidence 0.512
+
186. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011300/a011300153.png ; $\mu = 1$ ; confidence 0.999
  
−
187. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d1300609.png ; $\sum _ { I \subseteq \{ 1 , \ldots , k \} , I \neq \emptyset } ( - 1 ) ^ { | | | + 1 } \operatorname { Bel } ( \cap _ { i \in I } A _ { i } )$ ; confidence 0.180
+
187. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130020/m13002052.png ; $4 k - 1$ ; confidence 0.999
  
−
188. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120140/d12014081.png ; $E _ { n } ( x , a ) = \sum _ { i = 0 } ^ { | n / 2 | } \left( \begin{array} { c } { n - i } \\ { i } \end{array} \right) ( - a ) ^ { i } x ^ { n - 2 i }$ ; confidence 0.153
+
188. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009024.png ; $f = f ( z , \tau )$ ; confidence 0.999
  
−
189. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120140/e120140103.png ; $( \varphi \rightarrow \varphi \left( \begin{array} { c } { x } \\ { \varepsilon x \varphi } \end{array} \right) ) = 1$ ; confidence 0.826
+
189. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110670/b110670129.png ; $( m - 1 )$ ; confidence 0.999
  
−
190. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130010/i13001030.png ; $\overline { d } _ { \chi } ^ { G } ( A ) : = d _ { \chi } ^ { G } ( A ) / \chi ( \text { id } ) = d _ { \chi } ^ { G } ( A ) / d _ { \chi } ^ { G } ( I _ { n } )$ ; confidence 0.731
+
190. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120070/m1200706.png ; $M ( P ) = \operatorname { exp } ( m ( P ) )$ ; confidence 0.999
  
−
191. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006045.png ; $\{ \operatorname { Pred } ( x ) , x \in X _ { P } \} \cup \{ \operatorname { Pred } \operatorname { Succ } ( x ) , x \in X _ { P } \}$ ; confidence 0.274
+
191. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a12013036.png ; $h ( \theta ) = 0$ ; confidence 0.999
  
−
192. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j130040111.png ; $\equiv - \operatorname { lk } ( L ) v ( \frac { v ^ { - 1 } - v } { z } ) ^ { \operatorname { com } ( L ) - 2 } \operatorname { mod } ( z )$ ; confidence 0.939
+
192. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031670/d03167026.png ; $( \xi , \eta , \zeta )$ ; confidence 0.999
  
−
193. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130020/m13002037.png ; $\frac { d T _ { 1 } } { d s } = [ T _ { 2 } , T _ { 3 } ] , \frac { d T _ { 2 } } { d s } = [ T _ { 3 } , T _ { 1 } ] , \frac { d T _ { 3 } } { d s } = [ T _ { 1 } , T _ { 2 } ]$ ; confidence 0.926
+
193. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005083.png ; $\rho ( A ( t ) ) \supset ( \beta , \infty )$ ; confidence 0.999
  
−
194. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130220/m13022031.png ; $\Gamma _ { 0 } ( 2 ) ^ { + } : = \{ \Gamma _ { 0 } ( 2 ) , \left( \begin{array} { c c } { 0 } & { - 1 } \\ { 2 } & { 0 } \end{array} \right) \}$ ; confidence 0.769
+
194. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043330/g04333028.png ; $( m + 1 )$ ; confidence 0.999
  
−
195. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060187.png ; $( \sigma _ { 2 } \frac { \partial } { \partial t _ { 1 } } - \sigma _ { 1 } \frac { \partial } { \partial t _ { 2 } } + \gamma ) u = 0$ ; confidence 0.449
+
195. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510127.png ; $\gamma ( u ) = \gamma ^ { \prime } ( u )$ ; confidence 0.999
  
−
196. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p13007090.png ; $= \operatorname { sup } \{ h ( z ) : \quad h ( \zeta ) - \operatorname { log } \| \zeta - w \| = O ( 1 ) ( \zeta \rightarrow w ) \}$ ; confidence 0.779
+
196. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b13003013.png ; $V ^ { + } = V ^ { - }$ ; confidence 0.999
  
−
197. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130040/r13004073.png ; $\frac { \lambda _ { 2 } ( \Omega ) } { \lambda _ { 1 } ( \Omega ) } \leq \frac { j _ { \Re / 2,1 } ^ { 2 } } { j _ { \aleph / 2 - 1,1 } ^ { 2 } }$ ; confidence 0.243
+
197. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o130010160.png ; $\theta ^ { \prime } \in M$ ; confidence 0.999
  
−
198. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120160/s12016030.png ; $\| f \| _ { k } = \operatorname { max } \{ \| D ^ { \alpha } f \| _ { L _ { \infty } } : \alpha \in N _ { 0 } ^ { d } , \alpha _ { i } \leq k \}$ ; confidence 0.553
+
198. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033280/d03328015.png ; $\{ x \}$ ; confidence 0.999
  
−
199. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013041.png ; $W _ { n } = \operatorname { span } _ { C } \{ \frac { \partial ^ { k } \Psi _ { 1 , n } ( x , z ) } { \partial x _ { 1 } } : k = 0,1 , \ldots \}$ ; confidence 0.732
+
199. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120040/v1200407.png ; $\Delta ( G ) \leq \chi ^ { \prime } ( G )$ ; confidence 0.999
  
−
200. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096030/v09603011.png ; $\epsilon x ^ { \prime } = y - x + \frac { x ^ { 3 } } { 3 } , \quad y ^ { \prime } = - x , \quad \square ^ { \prime } = \frac { d } { d \tau }$ ; confidence 0.539
+
200. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130260/a1302606.png ; $\zeta ( 2 ) = \pi ^ { 2 } / 6$ ; confidence 0.999
  
−
201. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z13010086.png ; $\forall x \forall v _ { 1 } \ldots \forall v _ { n } \exists y \forall v ( v \in y \leftrightarrow ( v \in x / \not \varphi ) )$ ; confidence 0.115
+
201. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110110/m1101105.png ; $0 \leq m \leq p$ ; confidence 0.999
  
−
202. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120020/z12002044.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { F _ { n } + 1 } { F _ { n } } = \frac { 1 } { 2 } ( \sqrt { 5 } + 1 ) \simeq 1.618$ ; confidence 0.544
+
202. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020230/c02023032.png ; $\leq n - 2$ ; confidence 0.999
  
−
203. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013052.png ; $q ^ { ( l + 1 ) } = - ( q ^ { ( l ) } ) ^ { 2 } r ^ { ( l ) } + q ^ { ( l ) } \operatorname { log } ( q ^ { ( l ) } ) , r ^ { ( l + 1 ) } = \frac { 1 } { q ^ { ( l ) } }$ ; confidence 0.906
+
203. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120060/k12006044.png ; $E + D$ ; confidence 0.999
  
−
204. 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
+
204. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e13007084.png ; $( p , p + 1 / 2 )$ ; confidence 0.999
  
−
205. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020041.png ; $\{ f ( t ) \} _ { ( k ; t _ { i } ) } = \sum _ { m = 0 } ^ { k } \frac { ( t - t _ { i } ) ^ { m } } { m ! } \frac { d ^ { m } f ( t ) } { d t ^ { m } } | _ { t = t _ { i } }$ ; confidence 0.370
+
205. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007097.png ; $f ^ { \prime } ( X ^ { \prime } , Y ^ { \prime } ) = 0$ ; confidence 0.999
  
−
206. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040150.png ; $( X _ { 0 } ^ { 1 - \theta } X _ { 1 } ^ { \theta } ) ^ { \prime } = ( X _ { 0 } ^ { \prime } ) ^ { 1 - \theta } ( X _ { 1 } ^ { \prime } ) ^ { \theta }$ ; confidence 0.985
+
206. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130070/n13007012.png ; $m ( A \cup B ) - m ( B )$ ; confidence 0.999
  
−
207. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120340/b12034060.png ; $\sum _ { 0 } ^ { \infty } | f _ { n } | \operatorname { sup } _ { U } | \varphi _ { n } ( z ) | \leq \operatorname { sup } _ { K } | f ( z ) |$ ; confidence 0.934
+
207. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026055.png ; $k h ^ { - 2 } \leq 1$ ; confidence 0.999
  
−
208. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120050/c12005017.png ; $f \rightarrow \frac { 1 } { 2 \pi } \int _ { 0 } ^ { 2 \pi } \operatorname { Re } \frac { e ^ { i t } + z } { e ^ { t t } - z } f ( e ^ { i t } ) d t$ ; confidence 0.641
+
208. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130050/r13005027.png ; $\Omega = G$ ; confidence 0.999
  
−
209. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130110/c13011012.png ; $f ^ { \circ } ( x ; v ) : = \operatorname { liminf } _ { y \rightarrow x , t } \operatorname { lo } \frac { f ( y + t v ) - f ( y ) } { t }$ ; confidence 0.055
+
209. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c1202603.png ; $[ 0,1 ] \times [ 0 , T ]$ ; confidence 0.999
  
−
210. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180363.png ; $= g ^ { - 1 } \{ p _ { 1 } , p _ { 2 } ; \ldots ; p _ { 4 m - 1 } , p _ { 4 m } \} ( W ( g ) \otimes \ldots \otimes W ( g ) ) \in \in C ^ { \infty } ( M )$ ; confidence 0.307
+
210. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120150/t12015017.png ; $\pi ( \xi )$ ; confidence 0.999
  
−
211. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130160/f13016035.png ; $\mu _ { R } ( M ) \leq \operatorname { max } \{ \mu ( M , P ) : P \in \operatorname { Spec } ( R ) \} + \operatorname { Kdim } ( R )$ ; confidence 0.743
+
211. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110210/b1102107.png ; $d ( x , y )$ ; confidence 0.999
  
−
212. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f1201108.png ; $\| \varphi \| = \operatorname { sup } _ { | \operatorname { maz } } | \varphi ( z ) | e ^ { \delta | \operatorname { Re } z | }$ ; confidence 0.125
+
212. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m13018027.png ; $\mu ( m , n )$ ; confidence 0.999
  
−
213. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g13004096.png ; $\operatorname { lim } _ { i \rightarrow \infty } c _ { i } \int \phi ( \frac { y - x } { r _ { i } } ) d \mu ( y ) = \int \phi ( y ) d \nu$ ; confidence 0.860
+
213. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130070/b13007014.png ; $\pi ( m ) = \pi ( n )$ ; confidence 0.999
  
−
214. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120050/g12005039.png ; $\psi - \psi _ { 0 } = \varepsilon A ( \xi , \tau ) f _ { C } ( y ) e ^ { i ( \langle k _ { C } , x \rangle + \mu _ { C } t ) } + \text { c.c. } +$ ; confidence 0.057
+
214. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f120150142.png ; $A \in \Phi _ { - } ( X , Y )$ ; confidence 0.999
  
−
215. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130050/h1300507.png ; $\frac { \partial u } { \partial t } + u \frac { \partial u } { \partial x } + \frac { \partial ^ { 3 } u } { \partial x ^ { 3 } } = 0$ ; confidence 0.997
+
215. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015018.png ; $G = M ( n )$ ; confidence 0.999
  
−
216. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020106.png ; $| \{ \vartheta \in I : | \varphi ( e ^ { i \vartheta } ) - \varphi _ { I } | \geq \lambda \} | \leq C e ^ { - \gamma \lambda } | I |$ ; confidence 0.547
+
216. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900189.png ; $T ( \zeta ) \in A ( \zeta )$ ; confidence 0.999
  
−
217. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020119.png ; $\int _ { \partial D } \operatorname { exp } ( \varepsilon | \varphi ( e ^ { i \vartheta } ) - \varphi _ { I } | ) d \vartheta$ ; confidence 0.495
+
217. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i120080115.png ; $\beta = 1 / 8$ ; confidence 0.999
  
−
218. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m130110137.png ; $\frac { D v } { D t } = \frac { \partial v } { \partial t } + \frac { 1 } { 2 } \nabla v ^ { 2 } + ( \operatorname { curl } v ) \times v$ ; confidence 0.796
+
218. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007060.png ; $- ( \sqrt { 6 } + \varepsilon )$ ; confidence 0.999
  
−
219. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120230/m12023030.png ; $\frac { \partial u ( t , x ) } { \partial t } + \frac { 1 } { 2 } \| d _ { \chi } u ( t , x ) \| ^ { 2 } = 0 , \quad ( t , x ) \in ( 0 , T ) \times H$ ; confidence 0.545
+
219. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060174.png ; $f = f ( t _ { 1 } , t _ { 2 } )$ ; confidence 0.999
  
−
220. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m13025072.png ; $\operatorname { lim } _ { \varepsilon \rightarrow 0 } ( u ^ { * } \rho _ { \varepsilon } ) ( v ^ { * } \rho _ { \varepsilon } )$ ; confidence 0.965
+
220. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c12001047.png ; $T ( F )$ ; confidence 0.999
  
−
221. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130030/o13003040.png ; $d _ { j k l } = \frac { 1 } { 4 } \operatorname { Tr } [ ( \gamma _ { j } \gamma _ { k } + \lambda _ { k } \lambda _ { j } ) \lambda _ { l } ]$ ; confidence 0.723
+
221. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120050/o12005023.png ; $w ( t ) \equiv 1$ ; confidence 0.999
  
−
222. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064053.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { \operatorname { det } T _ { n } ( a ) } { G ( b ) ^ { n } n ^ { \Omega } } = E$ ; confidence 0.483
+
222. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k12012025.png ; $\int _ { - \infty } ^ { \infty } \frac { - \operatorname { ln } f ( x ) } { 1 + x ^ { 2 } } d x = \infty$ ; confidence 0.999
  
−
223. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t09408034.png ; $\rightarrow \pi _ { n } ( X , B , * ) \rightarrow \pi _ { n } ( X ; A , B , x _ { 0 } ) \stackrel { \partial } { \rightarrow } \ldots$ ; confidence 0.195
+
223. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120060/o12006014.png ; $| \Omega | < \infty$ ; confidence 0.999
  
−
224. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020036.png ; $\operatorname { inf } _ { z _ { j } } \operatorname { max } _ { k \in S } \frac { \operatorname { Re } g _ { 2 } ( k ) } { M _ { d } ( k ) }$ ; confidence 0.419
+
224. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130250/b1302508.png ; $\angle \Omega B C$ ; confidence 0.999
  
−
225. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005068.png ; $x _ { 0 } ^ { - 1 } \delta ( \frac { x _ { 1 } - x _ { 2 } } { x _ { 0 } } ) = \sum _ { n \in Z } \frac { ( x _ { 1 } - x _ { 2 } ) ^ { n } } { x _ { 0 } ^ { n + 1 } } =$ ; confidence 0.587
+
225. https://www.encyclopediaofmath.org/legacyimages/p/p074/p074520/p07452021.png ; $F = L \backslash P$ ; confidence 0.999
  
−
226. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090122.png ; $\operatorname { diag } ( t _ { 1 } , \ldots , t _ { n } ) \mapsto t _ { 1 } ^ { \lambda _ { 1 } } \ldots t _ { n } ^ { \lambda _ { n } } \in K$ ; confidence 0.507
+
226. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016430/b01643030.png ; $x = - 1$ ; confidence 0.999
  
−
227. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120190/w12019030.png ; $= \sum _ { k , l } A _ { k l } \int _ { R ^ { 3 N } } e ^ { i p z / \hbar } u _ { l k } ( x - \frac { z } { 2 } ) \overline { u } / ( x + \frac { z } { 2 } ) d z$ ; confidence 0.340
+
227. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520292.png ; $A = U ^ { - 1 } K _ { \rho } U$ ; confidence 0.999
  
−
228. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013051.png ; $F _ { j k } = \frac { \partial } { \partial t _ { j } } \frac { \partial } { \partial t _ { k } } \operatorname { log } ( \tau )$ ; confidence 0.976
+
228. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066960/n0669609.png ; $n + \lambda$ ; confidence 0.999
  
−
229. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023049.png ; $\operatorname { grad } \psi = ( \partial \psi / \partial \zeta _ { 1 } , \dots , \partial \psi / \partial \zeta _ { N } )$ ; confidence 0.302
+
229. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025470/c02547040.png ; $2 n + 1$ ; confidence 0.999
  
−
230. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027088.png ; $\operatorname { lim } _ { \overline { A } } a _ { n } = \frac { \sum _ { 0 } ^ { \infty } b _ { j } } { \sum _ { 0 } ^ { \infty } j p _ { j } }$ ; confidence 0.177
+
230. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011300/a01130057.png ; $( n - 2 )$ ; confidence 0.999
  
−
231. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130270/b13027063.png ; $0 \rightarrow \operatorname { Ext } _ { 2 } ^ { 1 } ( K _ { 0 } ( A ) , Z ) \rightarrow \operatorname { Ext } ( A ) \rightarrow$ ; confidence 0.466
+
231. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067280/n06728054.png ; $M ( \lambda )$ ; confidence 0.999
  
−
232. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120510/b12051081.png ; $H _ { + } ^ { - 1 } = ( I - \frac { s y ^ { T } } { y ^ { T } s } ) H _ { c } ^ { - 1 } ( I - \frac { y s ^ { T } } { y ^ { T } s } ) + \frac { s s ^ { T } } { y ^ { T } s }$ ; confidence 0.648
+
232. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110280/a11028022.png ; $k = - 1$ ; confidence 0.999
  
−
233. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001017.png ; $\frac { d ^ { 2 } u } { d t ^ { 2 } } = \operatorname { sin } ( u ) , \quad \frac { d ^ { 2 } v } { d t ^ { 2 } } = \operatorname { sinh } ( v )$ ; confidence 0.991
+
233. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230117.png ; $d ( z , w ) = 1 - z w ^ { * }$ ; confidence 0.999
  
−
234. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008031.png ; $= \Lambda ^ { m } + D _ { 1 } \Lambda ^ { m - 1 } + \ldots + D _ { m - 1 } \Lambda + D _ { m } , D _ { k } \in C ^ { n \times n } , k = 1 , \ldots , m$ ; confidence 0.523
+
234. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012060.png ; $f ( \theta ) = \int f ( \theta , \phi ) d \phi$ ; confidence 0.999
  
−
235. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120160/c12016043.png ; $\Pi ^ { T } A \Pi = R ^ { T } R , \quad R = \left( \begin{array} { c c } { R _ { 11 } } & { R _ { 12 } } \\ { 0 } & { 0 } \end{array} \right)$ ; confidence 0.987
+
235. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130150/c13015037.png ; $\Lambda = ( 0 , \infty )$ ; confidence 0.999
  
−
236. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120250/c1202504.png ; $\mu ( x ) = \left( \begin{array} { l l } { \mu _ { 11 } } & { \mu _ { 12 } } \\ { \mu _ { 21 } } & { \mu _ { 22 } } \end{array} \right) =$ ; confidence 0.548
+
236. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007021.png ; $[ A , B ] = A B - B A$ ; confidence 0.999
  
−
237. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030060/d03006010.png ; $\frac { \partial ^ { 2 } u ( t , x ) } { \partial t ^ { 2 } } - a ^ { 2 } \frac { \partial ^ { 2 } u ( t , x ) } { \partial x ^ { 2 } } = f ( t , x )$ ; confidence 0.756
+
237. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047010/h04701017.png ; $h ( x ) = \operatorname { exp } ( - x ^ { 2 } )$ ; confidence 0.999
  
−
238. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012093.png ; $w _ { i } ^ { ( t + 1 ) } = E ( q _ { i } | y _ { i } , \mu ^ { ( t ) } , \Sigma ^ { ( t ) } ) = \frac { \nu + p } { \nu + d _ { i } ^ { ( t ) } } , i = 1 , \dots , n$ ; confidence 0.208
+
238. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120270/a12027084.png ; $\{ \pm 1 \}$ ; confidence 0.999
  
−
239. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e120070127.png ; $n \overline { H } ^ { 1 } = \operatorname { dim } C ^ { 0 } ( \Gamma , k + 2 , v ) + \operatorname { dim } C ^ { 0 } ( \Gamma , k + 2 , v )$ ; confidence 0.101
+
239. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130100/w13010031.png ; $\operatorname { lim } _ { t \rightarrow \infty } f ( t ) = \infty$ ; confidence 0.999
  
−
240. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120100/e12010018.png ; $w ^ { em } = J . E + \frac { \partial P } { \partial t } E - M \cdot \frac { \partial B } { \partial t } + \nabla \cdot ( v ( P . E ) )$ ; confidence 0.154
+
240. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130120/h13012026.png ; $0 \leq p < 1$ ; confidence 0.999
  
−
241. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f12023011.png ; $= \varphi \wedge \psi \otimes [ X , Y ] + \varphi \wedge L _ { X } \psi \otimes Y - L _ { Y } \varphi \wedge \psi \otimes X +$ ; confidence 0.423
+
241. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016022.png ; $u ( t )$ ; confidence 0.999
  
−
242. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g130060127.png ; $\sigma ( \Omega ( A ) ) \subseteq \cup _ { i , j = 1 \atop j \neq j } ^ { n } K _ { i j } ( A ) \subseteq \cup _ { i = 1 } ^ { n } G _ { i } ( A )$ ; confidence 0.105
+
242. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110010/l110010101.png ; $( A , P )$ ; confidence 0.999
  
−
243. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110010/h11001024.png ; $\operatorname { exp } ( - \sum _ { p \leq x } \frac { 1 } { p } \cdot ( 1 - \operatorname { Re } ( f ( p ) p ^ { - i \alpha _ { 0 } } ) ) )$ ; confidence 0.700
+
243. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021076.png ; $( B , \delta )$ ; confidence 0.999
  
−
244. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i12004069.png ; $s _ { r } ( \zeta , z ) = ( \partial r / \partial \zeta _ { 1 } ( \zeta ) , \ldots , \partial r / \partial \zeta _ { n } ( \zeta ) )$ ; confidence 0.465
+
244. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b130220110.png ; $\{ x \} \cup B$ ; confidence 0.999
  
−
245. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006092.png ; $( l + H _ { x } ) \Gamma _ { x } : = \Gamma _ { x } ( t , s ) + \int _ { 0 } ^ { x } H ( t - u ) \Gamma _ { x } ( u , s ) d u = H ( t - s ) , 0 \leq t , s \leq x$ ; confidence 0.293
+
245. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110070/c1100707.png ; $| z | < 1$ ; confidence 0.999
  
−
246. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008070.png ; $\operatorname { exp } \{ \frac { 1 } { k _ { B } T } \sum _ { l = 1 } ^ { N } [ J S _ { i } S _ { + 1 } + \frac { H } { 2 } ( S _ { i } + S _ { + 1 } ) ] \} =$ ; confidence 0.367
+
246. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f120150169.png ; $\mu ( A ) > 0$ ; confidence 0.999
  
−
247. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007073.png ; $\angle \operatorname { lim } _ { z \rightarrow \omega } F ( z ) = \omega , \text { and } \angle F ^ { \prime } ( \omega ) < 1$ ; confidence 0.668
+
247. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016970/b0169703.png ; $\sigma = 1$ ; confidence 0.999
  
−
248. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120140/l12014027.png ; $q ( T ) p ( T ) \leq \operatorname { dim } \operatorname { ker } q ( T ) + \operatorname { dim } \operatorname { ker } p ( T )$ ; confidence 0.980
+
248. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023023.png ; $F \in H ( D ) \cap C ( D \cup \Gamma )$ ; confidence 0.999
  
−
249. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130020/m13002029.png ; $A = ( \frac { 1 } { \operatorname { sinh } r } - \frac { 1 } { r } ) \epsilon _ { i j k } \frac { x _ { j } } { r } \sigma _ { k } d x _ { i }$ ; confidence 0.768
+
249. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130020/h13002032.png ; $A ^ { N }$ ; confidence 0.999
  
−
250. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p13014058.png ; $\psi ( \gamma ) = \frac { 2 } { \pi ^ { 2 } \gamma } + O ( \frac { 1 } { \gamma ^ { 3 } } ) \text { as } \gamma \rightarrow + \infty$ ; confidence 0.633
+
250. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009053.png ; $w ( z ) =$ ; confidence 0.999
  
−
251. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120220/s12022066.png ; $\operatorname { det } ( \Delta + z ) = \operatorname { exp } ( - \frac { \partial } { \partial s } \zeta ( s , z ) | _ { s = 0 } )$ ; confidence 0.604
+
251. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120020/z12002032.png ; $m \geq n \geq 2$ ; confidence 0.999
  
−
252. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s12023052.png ; $\frac { B _ { - } ( \delta + p - 1 ) / 2 ( \frac { 1 } { 4 } \Sigma T T ^ { \prime } ) } { \Gamma _ { p } [ \frac { 1 } { 2 } ( \delta + p - 1 ) ] }$ ; confidence 0.509
+
252. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130250/c13025050.png ; $A ( t ) = \int _ { 0 } ^ { t } \alpha ( s ) d s$ ; confidence 0.999
  
−
253. 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
+
253. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130070/n13007026.png ; $m ( A \cup B ) = m ( A )$ ; confidence 0.999
  
−
254. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t09408033.png ; $\square \ldots \rightarrow \pi _ { n + 1 } ( X ; A , B , * ) \stackrel { \partial } { \rightarrow } \pi _ { n } ( A , A \cap B , * )$ ; confidence 0.389
+
254. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120560/b12056013.png ; $\lambda _ { 1 } \leq 2 ( n - 1 ) \delta h + 10 h ^ { 2 }$ ; confidence 0.999
  
−
255. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v13007070.png ; $x = \frac { 1 - \lambda } { \pi } \operatorname { ln } \frac { 1 } { 2 } ( 1 + \operatorname { cos } \frac { \pi y } { \lambda } )$ ; confidence 0.782
+
255. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026058.png ; $s \in [ 0,1 ]$ ; confidence 0.999
  
−
256. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v13007056.png ; $k q ^ { \prime } s \frac { d } { d s } [ q ^ { \prime } s \frac { d \theta } { d s } ] + \operatorname { cos } \theta - q ^ { \prime } = 0$ ; confidence 0.975
+
256. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120210/t12021089.png ; $t ( T _ { 1 } ) = t ( T _ { 2 } )$ ; confidence 0.999
  
−
257. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090135.png ; $\chi _ { \lambda } = \sum _ { \mu \in \Lambda ( n ) } \operatorname { dim } _ { K } ( \Delta ( \lambda ) ^ { \mu } ) _ { e _ { \mu } }$ ; confidence 0.461
+
257. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a130080103.png ; $f ( L ) = f ( R )$ ; confidence 0.999
  
−
258. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010013.png ; $e ^ { - t A _ { X } } = \operatorname { lim } _ { n \rightarrow \infty } ( I + \frac { t } { n } A ) ^ { - n } x = S ( t ) x , \forall x \in X$ ; confidence 0.189
+
258. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b1203001.png ; $\eta \in R ^ { N }$ ; confidence 0.999
  
−
259. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130310/a130310110.png ; $\sum _ { | X | \geq n } \mu ( X ) \frac { T ^ { - 1 } ( \operatorname { time } _ { A } ( X ) ) } { | X | } \leq \sum _ { | X | \geq n } \mu ( X )$ ; confidence 0.387
+
259. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012970/a012970220.png ; $\gamma > 0$ ; confidence 0.999
  
−
260. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120020/b12002054.png ; $+ O ( \frac { ( \operatorname { log } n ) ^ { 1 / 2 } ( \operatorname { log } \operatorname { log } n ) ^ { 1 / 4 } } { n ^ { 3 / 4 } } )$ ; confidence 0.631
+
260. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130120/r1301209.png ; $[ 0 , u ] + [ 0 , v ] = [ 0 , u + v ]$ ; confidence 0.999
  
−
261. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120360/b12036014.png ; $P ( E _ { l } ) = \frac { \operatorname { exp } ( - E _ { l } / k _ { B } T ) } { \sum _ { l } \operatorname { exp } ( - E _ { l } / k _ { B } T ) }$ ; confidence 0.499
+
261. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w12009060.png ; $[ \lambda ]$ ; confidence 0.999
  
−
262. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007016.png ; $+ ( - 1 ) ^ { n + 1 } \operatorname { pr } ( \alpha _ { 2 } , \dots , \alpha _ { n + 1 } ) \} ( \alpha _ { 1 } , \dots , \alpha _ { n + 1 } )$ ; confidence 0.247
+
262. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120270/e12027022.png ; $\frac { \beta } { 2 } + \frac { 1 } { 4 } \leq s < \frac { \beta } { 2 } + \frac { 5 } { 4 }$ ; confidence 0.999
  
−
263. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c120170126.png ; $V ( z _ { 0 } , \dots , z _ { r } - 1 ) ( \rho _ { 0 } , \dots , \rho _ { r - 1 } ) ^ { T } = ( \gamma _ { 00 } , \dots , \gamma _ { 0 , r - 1 } ) ^ { T }$ ; confidence 0.356
+
263. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120030/w12003060.png ; $[ 0,1 ] ^ { \Gamma }$ ; confidence 0.999
  
−
264. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180276.png ; $\nabla ( \Theta \otimes \Phi ) = \nabla \Theta \otimes \Phi + \tau _ { p + 1 } ( \Theta \varnothing \nabla \Phi ) \in$ ; confidence 0.260
+
264. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008069.png ; $H ^ { 1 } ( \Omega ) \times H ^ { 1 } ( \Omega )$ ; confidence 0.999
  
−
265. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180352.png ; $= g ^ { - 1 } \{ 1,4 \} \nabla C ( g ) - g ^ { - 1 } \{ 1,3 ; 2,5 \} ( A ( g ) \otimes W ( g ) ) \subset \subset \otimes \square ^ { 2 } E$ ; confidence 0.099
+
265. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022065.png ; $m - 1$ ; confidence 0.999
  
−
266. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040490/f0404905.png ; $f _ { \nu _ { 1 } , \nu _ { 2 } } ( x ) = \frac { 1 } { B ( \nu _ { 1 } / 2 , \nu _ { 2 } / 2 ) } ( \frac { \nu _ { 1 } } { \nu _ { 2 } } ) ^ { \nu _ { 1 } / 2 }$ ; confidence 0.967
+
266. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130100/p130100109.png ; $P ( K ) = C ( K )$ ; confidence 0.999
  
−
267. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f13024047.png ; $[ \left( \begin{array} { c c } { Id } & { 0 } \\ { 0 } & { - Id } \end{array} \right) , L _ { \ell } ] = i L _ { i } ( - 2 \leq i \leq 2 )$ ; confidence 0.301
+
267. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130170/d13017014.png ; $\lambda _ { k } \rightarrow \infty$ ; confidence 0.999
  
−
268. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130010/i13001040.png ; $\operatorname { per } ( A ) \geq \operatorname { per } ( B ) \operatorname { per } ( D ) \geq \prod _ { i = 1 } ^ { n } a _ { i i }$ ; confidence 0.696
+
268. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s120040120.png ; $\mu \subseteq \lambda$ ; confidence 0.999
  
−
269. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007063.png ; $\angle \operatorname { lim } _ { z \rightarrow \omega } ( F ( z ) - \eta ) / ( z - \omega ) = \angle F ^ { \prime } ( \omega )$ ; confidence 0.912
+
269. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p12017047.png ; $0 < p \leq 1$ ; confidence 0.999
  
−
270. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l120120207.png ; $\alpha _ { 0 } : \cup _ { \mathfrak { p } ^ { \prime } \in S ^ { \prime } } G ( K _ { \mathfrak { p } ^ { \prime } } ) \rightarrow G$ ; confidence 0.239
+
270. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006022.png ; $d \lambda$ ; confidence 0.999
  
−
271. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520316.png ; $a ( f ) = \int _ { M } a ( x ) f ( x ) d \sigma ( x ) , \quad \alpha ^ { * } ( f ) = \int _ { M } a ^ { * } ( x ) \overline { f } ( x ) d \sigma ( x )$ ; confidence 0.180
+
271. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009054.png ; $\varphi \in L ^ { 2 } ( \mu )$ ; confidence 0.999
  
−
272. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005081.png ; $\left.\begin{array} { c c } { T } & { ( I - T T ^ { * } ) ^ { 1 / 2 } } \\ { ( I - T ^ { * } T ) ^ { 1 / 2 } } & { T ^ { * } } \end{array} \right\}$ ; confidence 0.169
+
272. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023270/c02327028.png ; $r ( A ) < | A |$ ; confidence 0.999
  
−
273. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060119.png ; $S ( \lambda ) = I _ { E } - i \Phi ( \xi _ { 1 } A _ { 1 } + \xi _ { 2 } A _ { 2 } - \xi _ { 1 } \lambda _ { 1 } - \xi _ { 2 } \lambda _ { 2 } ) ^ { - 1 }$ ; confidence 0.459
+
273. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120250/a12025045.png ; $d = k - n + 2$ ; confidence 0.999
  
−
274. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060105.png ; $\mathfrak { E } ( \lambda ) = \operatorname { ker } ( \lambda _ { 1 } \sigma _ { 2 } - \lambda _ { 2 } \sigma _ { 1 } + \gamma )$ ; confidence 0.252
+
274. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022420/c02242038.png ; $\alpha > - 1$ ; confidence 0.999
  
−
275. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082320/r08232032.png ; $J ( \rho ) = J ( \rho ; x _ { 0 } , u ) = \frac { 1 } { \sigma _ { N } ( \rho ) } \int _ { S _ { R } ( x _ { 0 } , \rho ) } u ( y ) d \sigma _ { N } ( y )$ ; confidence 0.275
+
275. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120130/p12013025.png ; $\lambda > 0$ ; confidence 0.999
  
−
276. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130020/s13002049.png ; $\operatorname { Vol } ( \overline { U M } ) = C _ { 1 } ( n ) \int _ { U ^ { + } \partial N } l ( v ) \langle v , N _ { x } \rangle d v d x$ ; confidence 0.421
+
276. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120200/b12020054.png ; $\theta ( e ^ { i t } )$ ; confidence 0.999
  
−
277. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t120070117.png ; $= \frac { 1 } { 2 } ( \frac { \Theta _ { \Delta } ( q ) } { \eta ( q ) ^ { 24 } } + \frac { \eta ( q ) ^ { 24 } } { \eta ( q ^ { 2 } ) ^ { 24 } } ) +$ ; confidence 0.904
+
277. https://www.encyclopediaofmath.org/legacyimages/c/c027/c027370/c0273701.png ; $R ( X , Y )$ ; confidence 0.999
  
−
278. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t12014055.png ; $R ( \phi ) \subset \sigma _ { e } ( T _ { \phi } ) \subset \sigma ( T _ { \phi } ) \subset \operatorname { conv } ( R ( \phi ) )$ ; confidence 0.936
+
278. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055070/k05507079.png ; $d = 10$ ; confidence 0.999
  
−
279. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200211.png ; $\operatorname { max } _ { k = 1 , \ldots , n } ( \frac { 1 } { n } | s _ { k } | ) ^ { 1 / k } > \frac { 1 } { 5 } > \frac { 1 } { 2 + \sqrt { 8 } }$ ; confidence 0.635
+
279. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120100/i1201008.png ; $R ( \pi ) = R ( X , Y )$ ; confidence 0.999
  
−
280. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200218.png ; $\operatorname { min } _ { r = m + 1 , \ldots , m + K } | G _ { 1 } ( r ) | \geq \frac { 1 } { P _ { m , K } } | \sum _ { j = 1 } ^ { n } P _ { j } ( 0 ) |$ ; confidence 0.350
+
280. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g13002056.png ; $\Gamma ( 1 / 4 )$ ; confidence 0.999
  
−
281. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110248.png ; $g x ( T ) = \frac { G _ { X } ( T ) } { H ( X ) [ 1 + \alpha ( X ) + H ( X ) ^ { 2 } \| \alpha ^ { \prime \prime } ( X ) \| ^ { 2 } G _ { X } ] ^ { 1 / 2 } }$ ; confidence 0.162
+
281. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f120150140.png ; $F _ { - } ( X , Y )$ ; confidence 0.999
  
−
282. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130040/z13004017.png ; $| \frac { n } { 2 } | \lfloor \frac { n - 1 } { 2 } \rfloor \lfloor \frac { m } { 2 } \rfloor \lfloor \frac { m - 1 } { 2 } \rfloor$ ; confidence 0.206
+
282. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p13014057.png ; $\psi ( + 0 ) = 1 / 2$ ; confidence 0.999
  
−
283. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008048.png ; $+ \frac { d } { d m } \operatorname { ln } g ( R ; m , s ) \frac { d m } { d s } + \frac { d } { d s } \operatorname { ln } g ( R ; m , s ) = 0$ ; confidence 0.979
+
283. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520230.png ; $( A , B ) \sim ( S A S ^ { - 1 } , S B )$ ; confidence 0.999
  
−
284. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a12017026.png ; $p ^ { * } ( \alpha , t ) = \omega e ^ { \lambda ^ { * } ( t - \alpha ) } \Pi ( \alpha ) = e ^ { \lambda ^ { * } t _ { w } ^ { * } ( \alpha ) }$ ; confidence 0.131
+
284. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061050/l06105082.png ; $P ( E ) = 0 \Rightarrow \lambda ( F ( E ) ) = 0$ ; confidence 0.999
  
−
285. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020043.png ; $\mathfrak { p } _ { i } ( t ) = q _ { i } ( t ) \prod _ { m = 1 , m \neq i } ^ { n } ( t - t _ { m } ) ^ { \gamma _ { m } } \quad ( i = 1 , \ldots , n )$ ; confidence 0.353
+
285. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024850/c02485061.png ; $A + B$ ; confidence 0.999
  
−
286. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b110220206.png ; $L ^ { * } ( h ^ { i } ( X ) , s ) _ { s = m } \equiv \operatorname { det } ( \Pi ) \cdot \operatorname { det } \langle . . \rangle$ ; confidence 0.138
+
286. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130060/h13006061.png ; $R ( X , D )$ ; confidence 0.999
  
−
287. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110260/b11026010.png ; $X ^ { \prime } = \sqrt { X ^ { 2 } + \hat { y } ^ { 2 } } e ^ { ( \operatorname { arctan } y / X + k \pi ) \rho / \omega } - X _ { H } + \Re$ ; confidence 0.068
+
287. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c130070161.png ; $M ( R ( P ) )$ ; confidence 0.999
  
−
288. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130110/b1301105.png ; $b _ { j } ^ { n } ( x ) : = \left( \begin{array} { c } { n } \\ { j } \end{array} \right) x ^ { j } ( 1 - x ) ^ { n - j } , j = 0 , \ldots , n$ ; confidence 0.444
+
288. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120030/d12003067.png ; $f ( x ) \in ( 0,1 ]$ ; confidence 0.999
  
−
289. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120180/b12018033.png ; $\forall x _ { 1 } \ldots \forall x _ { N } ( P _ { X 1 } \ldots x _ { N } \leftrightarrow \varphi ( x _ { 1 } , \ldots , x _ { N } ) )$ ; confidence 0.198
+
289. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004047.png ; $\gamma \cap \Gamma$ ; confidence 0.999
  
−
290. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022013.png ; $\partial _ { t } \int f \operatorname { ln } f d v + \operatorname { div } _ { X } \int v f \operatorname { ln } f d v \leq 0$ ; confidence 0.472
+
290. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004035.png ; $( 2 g ) \times ( 2 g )$ ; confidence 0.999
  
−
291. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130190/b13019015.png ; $S ^ { * } ( \frac { \alpha } { q } ) = \sum _ { k } e ( x ( h ) y ( \frac { \alpha } { q } ) ) \gamma ( h ) \delta ( \frac { \alpha } { q } )$ ; confidence 0.317
+
291. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040111.png ; $f ( x _ { n } ) \rightarrow 0$ ; confidence 0.999
  
−
292. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b12040071.png ; $\mathfrak { h } _ { R } \rightarrow \mathfrak { h } _ { R } ^ { * } : = \operatorname { hom } _ { R } ( \mathfrak { h } _ { R } , R )$ ; confidence 0.571
+
292. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007094.png ; $Y = X ^ { \prime } Y ^ { \prime }$ ; confidence 0.999
  
−
293. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130040/c1300406.png ; $\psi ( z ) : = \frac { d } { d z } \{ \operatorname { log } \Gamma ( z ) \} = \frac { \Gamma ^ { \prime } ( z ) } { \Gamma ( z ) }$ ; confidence 0.998
+
293. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034020/d0340203.png ; $F ( \xi )$ ; confidence 0.999
  
−
294. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130030/d13003024.png ; $0 < C _ { \psi } = 2 \pi \int _ { 0 } ^ { \infty } \frac { | \hat { \psi } ( \alpha \omega ) | ^ { 2 } } { \alpha } d \alpha < \infty$ ; confidence 0.655
+
294. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120060/v1200607.png ; $B _ { 1 } = - 1 / 2$ ; confidence 0.999
  
−
295. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120160/d12016014.png ; $( M _ { t } f ) ( s ) = \frac { 1 } { 2 } \operatorname { sup } _ { t } f ( s , t ) + \frac { 1 } { 2 } \operatorname { inf } _ { t } f ( s , t )$ ; confidence 0.930
+
295. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m130180107.png ; $\mu ( 0 , x ) \neq 0$ ; confidence 0.999
  
−
296. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120160/d12016013.png ; $( M _ { s } f ) ( t ) = \frac { 1 } { 2 } \operatorname { sup } _ { s } f ( s , t ) + \frac { 1 } { 2 } \operatorname { inf } _ { s } f ( s , t )$ ; confidence 0.838
+
296. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f13024017.png ; $\varepsilon = - 1$ ; confidence 0.999
  
−
297. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130050/e13005018.png ; $( y - x ) ^ { \alpha + \beta } ( \frac { \partial u } { \partial y } - \frac { \partial u } { \partial x } ) | _ { x = y } = \nu ( x )$ ; confidence 0.989
+
297. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n12002048.png ; $\alpha \in [ 1,2 )$ ; confidence 0.999
  
−
298. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130170/f1301706.png ; $\| u \| A _ { 2 } ( G ) = \operatorname { inf } \{ N _ { 2 } ( k ) N _ { 2 } ( l ) : k , l \in L _ { C } ^ { 2 } ( G ) , u = \overline { k } ^ { * } t \}$ ; confidence 0.142
+
298. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130190/a13019027.png ; $2 n - 2 m$ ; confidence 0.999
  
−
299. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021054.png ; $u _ { i l } = z ^ { \lambda _ { i } } \sum _ { j = 0 } ^ { l } \sum _ { k = 0 } ^ { \infty } b _ { j k } ( \operatorname { log } z ) ^ { j } z ^ { k }$ ; confidence 0.664
+
299. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l120100121.png ; $( - \Delta + E ) ^ { - 1 }$ ; confidence 0.999
  
−
300. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006046.png ; $F ( x ) : = \sum _ { j = 1 } ^ { J } s _ { j } e ^ { - k _ { j } x } + \frac { 1 } { 2 \pi } \int _ { - \infty } ^ { \infty } [ 1 - S ( k ) ] e ^ { i k x } d k$ ; confidence 0.646
+
300. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120260/d1202609.png ; $0 \leq t \leq 1$ ; confidence 0.999

Revision as of 00:10, 13 February 2020

List

1. a01137071.png ; $f ( x ) = 0$ ; confidence 1.000

2. b12017027.png ; $( 1 + | \xi | ^ { 2 } ) ^ { - \alpha / 2 }$ ; confidence 1.000

3. b13016056.png ; $f \in C ( X , \tau )$ ; confidence 1.000

4. t09356011.png ; $f ( x ) < + \infty$ ; confidence 1.000

5. b11089065.png ; $0 < \beta < 1$ ; confidence 1.000

6. m13007040.png ; $d = 2,3$ ; confidence 1.000

7. e120070103.png ; $P ( k )$ ; confidence 1.000

8. c12018050.png ; $( p , q ) = ( n , 0 )$ ; confidence 1.000

9. v12004058.png ; $\chi ^ { \prime } ( G ) = \chi ( L ( G ) )$ ; confidence 1.000

10. c120180317.png ; $R ( g )$ ; confidence 1.000

11. m1300708.png ; $\{ 0 \} \cup [ m _ { 0 } , \infty )$ ; confidence 1.000

12. a12027093.png ; $W ( \rho ) = \pm 1$ ; confidence 1.000

13. k055840380.png ; $- \frac { d ^ { 2 } y } { d x ^ { 2 } } + q y - \lambda y = f$ ; confidence 1.000

14. m13007033.png ; $\{ p : p ^ { 0 } > 0 , | p ^ { 2 } - m ^ { 2 } | < \epsilon \}$ ; confidence 1.000

15. b130300109.png ; $B ( m , n , \infty )$ ; confidence 1.000

16. f120080200.png ; $B ( K ) = B ( G )$ ; confidence 1.000

17. d120230121.png ; $d ( z , w )$ ; confidence 1.000

18. f12005060.png ; $( 1,1,1 )$ ; confidence 1.000

19. b13022063.png ; $\rho = \rho ( T )$ ; confidence 1.000

20. a12011011.png ; $b + 1$ ; confidence 1.000

21. c12004039.png ; $\gamma = ( \partial D ) \backslash \Gamma$ ; confidence 1.000

22. a1200802.png ; $u ( x , t ) = 0$ ; confidence 1.000

23. b12049030.png ; $A , B \in \Sigma$ ; confidence 1.000

24. b12027020.png ; $R ( t )$ ; confidence 1.000

25. b11021056.png ; $p \neq 2$ ; confidence 1.000

26. z13003053.png ; $h ( t ) = \int _ { - \infty } ^ { \infty } R ( t - s ) f ( s ) d s$ ; confidence 1.000

27. t12003038.png ; $U ^ { \prime } = f ( U )$ ; confidence 1.000

28. e12026067.png ; $\theta _ { 2 } = - 1 / \sigma ^ { 2 }$ ; confidence 1.000

29. w13013029.png ; $W \geq 4 \pi$ ; confidence 1.000

30. c130070162.png ; $r ( 0,0 ) = 0$ ; confidence 1.000

31. d03024026.png ; $f ( x ) = \operatorname { sgn } x$ ; confidence 1.000

32. s1304904.png ; $r ( p ) = 0$ ; confidence 1.000

33. b12027016.png ; $N ( t )$ ; confidence 1.000

34. f12017023.png ; $N ( r )$ ; confidence 1.000

35. f12015079.png ; $i ( A ) = + \infty$ ; confidence 1.000

36. b12010046.png ; $F ( t ) = U ( t ) F ( 0 )$ ; confidence 1.000

37. c13007070.png ; $( e - d )$ ; confidence 1.000

38. p13009035.png ; $\xi \in \partial \Omega$ ; confidence 1.000

39. a130070130.png ; $> 10 ^ { 5 }$ ; confidence 1.000

40. a13012057.png ; $\lambda > 1$ ; confidence 1.000

41. m12016068.png ; $F ( r )$ ; confidence 1.000

42. l06105076.png ; $F ( E ) = f ( E )$ ; confidence 1.000

43. s13065029.png ; $H ^ { 2 } ( \mu )$ ; confidence 1.000

44. l1201905.png ; $- B$ ; confidence 1.000

45. k12009017.png ; $F ( \tau ) =$ ; confidence 1.000

46. b12009025.png ; $f ( z , 1 ) = z$ ; confidence 1.000

47. a12010018.png ; $- A$ ; confidence 1.000

48. c120010149.png ; $\zeta \in \partial \Omega$ ; confidence 1.000

49. m1300704.png ; $M = \sqrt { P _ { \mu } P ^ { \mu } }$ ; confidence 1.000

50. a13012013.png ; $3 - ( 4 \mu , 2 \mu , \mu - 1 )$ ; confidence 1.000

51. r13008062.png ; $m ( t ) > 0$ ; confidence 1.000

52. k055840259.png ; $c ( A )$ ; confidence 1.000

53. a0118407.png ; $F ( s )$ ; confidence 1.000

54. c0262305.png ; $0 < r < 1$ ; confidence 1.000

55. s13065022.png ; $\delta _ { \mu }$ ; confidence 1.000

56. l06105058.png ; $f ^ { - 1 } ( \{ x \} )$ ; confidence 1.000

57. w13007044.png ; $\theta ( \alpha , \alpha ) = 1$ ; confidence 1.000

58. h12011054.png ; $( k , k - 1 )$ ; confidence 1.000

59. b12051017.png ; $\beta \in ( 0,1 )$ ; confidence 1.000

60. s130620101.png ; $\mu$ ; confidence 1.000

61. s09077034.png ; $y ( 0 ) = 0$ ; confidence 1.000

62. i12010026.png ; $f ( t ) = ( K t ^ { 2 } + A t + B ) / 2 > 0$ ; confidence 1.000

63. f120080126.png ; $B ( G ) = M A ( G )$ ; confidence 1.000

64. p074140164.png ; $p = 1,2$ ; confidence 1.000

65. b12032058.png ; $F ( s , t ) = F ( t , s )$ ; confidence 1.000

66. w12008051.png ; $\Omega ( u )$ ; confidence 1.000

67. r12002011.png ; $f ( \dot { q } )$ ; confidence 1.000

68. t120200208.png ; $\phi ( z ) = 1$ ; confidence 1.000

69. d12030044.png ; $f = g ^ { T } g$ ; confidence 1.000

70. b13003031.png ; $\sigma = \pm$ ; confidence 1.000

71. a12011028.png ; $T ( i , 2 ) = 4$ ; confidence 1.000

72. g13001085.png ; $\gamma + \delta$ ; confidence 1.000

73. e12026053.png ; $F ( \mu )$ ; confidence 1.000

74. r130070158.png ; $R ( L ) = H$ ; confidence 1.000

75. b1302703.png ; $\sigma ( \pi ( T ) )$ ; confidence 1.000

76. b13022038.png ; $| \gamma | = m$ ; confidence 1.000

77. m12006011.png ; $P = P ( \rho , T )$ ; confidence 1.000

78. a13027065.png ; $\phi ( 0 ) = 0$ ; confidence 1.000

79. c120010126.png ; $A ^ { \prime } ( E )$ ; confidence 1.000

80. l12016014.png ; $\Omega U ( n )$ ; confidence 1.000

81. s13004025.png ; $( \Gamma \cap P ) \backslash H ^ { 1 }$ ; confidence 1.000

82. p0745203.png ; $A B \subseteq P$ ; confidence 1.000

83. a12016055.png ; $P ( t )$ ; confidence 1.000

84. t1300709.png ; $g ^ { \prime } ( 0 ) > 0$ ; confidence 1.000

85. k055840318.png ; $H ( t ) \geq 0$ ; confidence 1.000

86. s12034059.png ; $c _ { 1 } ( A ) = 0$ ; confidence 1.000

87. r130070154.png ; $H = R ( L )$ ; confidence 1.000

88. w1200808.png ; $\Omega ( q , p )$ ; confidence 1.000

89. a12006059.png ; $B ( t )$ ; confidence 1.000

90. n12011065.png ; $\eta ( y )$ ; confidence 1.000

91. p074160147.png ; $| z | > R$ ; confidence 1.000

92. s12015078.png ; $( X \backslash \Omega ) \geq 1$ ; confidence 1.000

93. f12015030.png ; $A \in \Phi ( X , Y )$ ; confidence 1.000

94. n067520239.png ; $R ( A , B )$ ; confidence 1.000

95. w13014020.png ; $H ( 0 ) = 1 / 2$ ; confidence 1.000

96. c02257023.png ; $y = y ^ { \prime }$ ; confidence 1.000

97. d12016024.png ; $f ^ { * } - f$ ; confidence 1.000

98. n1300302.png ; $u ( 0 , t ) = u ( \pi , t ) = 0$ ; confidence 1.000

99. c12021069.png ; $\int \operatorname { exp } \lambda d L = 1$ ; confidence 1.000

100. b1300301.png ; $V = ( V ^ { + } , V ^ { - } )$ ; confidence 1.000

101. t12021060.png ; $\phi ( E )$ ; confidence 1.000

102. i12006074.png ; $\operatorname { dim } ( P ) \leq \operatorname { max } \{ 2 , | A | \}$ ; confidence 1.000

103. c12007017.png ; $n > 0$ ; confidence 1.000

104. q12003044.png ; $\varphi ( 1 ) = 1$ ; confidence 1.000

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

106. z13003022.png ; $[ - b , b ]$ ; confidence 1.000

107. n067520135.png ; $\lambda E - A$ ; confidence 1.000

108. d12029020.png ; $q ^ { 2 } f ( q )$ ; confidence 1.000

109. q12005074.png ; $B = H ^ { - 1 }$ ; confidence 1.000

110. b11038016.png ; $d \mu$ ; confidence 1.000

111. w12018067.png ; $[ 0,1 ] ^ { N }$ ; confidence 1.000

112. h13006065.png ; $\Gamma ( n ) =$ ; confidence 1.000

113. w13013066.png ; $W = \int H ^ { 2 } d A$ ; confidence 1.000

114. p130070112.png ; $z \rightarrow \partial \Omega$ ; confidence 1.000

115. b12031024.png ; $( 1 - 2 \delta ) / 4 < 1 / p < ( 3 + 2 \delta ) / 4$ ; confidence 1.000

116. w1200209.png ; $W ( P , Q )$ ; confidence 1.000

117. b12032057.png ; $F ( 0 , t ) = t$ ; confidence 1.000

118. b12042059.png ; $( i , i + 1 )$ ; confidence 1.000

119. l12006071.png ; $T ( z ) = V + V G ( z ) V$ ; confidence 1.000

120. b12031076.png ; $\delta > ( n - 1 ) / 2$ ; confidence 1.000

121. a12024030.png ; $( p , p )$ ; confidence 1.000

122. d12014040.png ; $( n , q - 1 ) = 1$ ; confidence 1.000

123. n067520102.png ; $\lambda E - B$ ; confidence 1.000

124. z12002010.png ; $100 = 89 + 8 + 3,1111 = 987 + 89 + 34 + 1$ ; confidence 1.000

125. f12021070.png ; $\lambda = \lambda _ { 2 }$ ; confidence 1.000

126. i12006076.png ; $G = ( V , E )$ ; confidence 1.000

127. n06752025.png ; $B = C A D$ ; confidence 1.000

128. b01668015.png ; $H ( t )$ ; confidence 1.000

129. e1300405.png ; $U ( t ) \psi ( 0 ) = \psi ( t )$ ; confidence 1.000

130. a12004011.png ; $t > 0$ ; confidence 1.000

131. c12002070.png ; $\mu \equiv \mu ( x )$ ; confidence 1.000

132. b13019033.png ; $\rho ( f ^ { \prime } ) = [ f ^ { \prime } ] - f ^ { \prime } + \frac { 1 } { 2 }$ ; confidence 1.000

133. p12015065.png ; $X = B ( 0,1 )$ ; confidence 1.000

134. b12030041.png ; $\lambda = \lambda ( \eta )$ ; confidence 1.000

135. o1300404.png ; $A = \frac { 1 } { 2 } \Delta + b$ ; confidence 1.000

136. n12002031.png ; $F ( \mu ^ { \prime } )$ ; confidence 1.000

137. b13030036.png ; $B ( m , 4 )$ ; confidence 1.000

138. z13012023.png ; $0 \leq \sigma \leq ( 1 / n ) \operatorname { tan } ^ { 2 } ( \pi / 2 n )$ ; confidence 1.000

139. f12015090.png ; $\beta ( A + T ) \leq \beta ( A )$ ; confidence 1.000

140. r130070178.png ; $f ( x ) \in R ( L )$ ; confidence 1.000

141. b110220211.png ; $i + 1 < 2 j$ ; confidence 1.000

142. t12003030.png ; $V = \Phi ( U )$ ; confidence 1.000

143. a13028021.png ; $s _ { 0 } = 1 / 2$ ; confidence 1.000

144. b12032052.png ; $F : [ 0 , \infty ) ^ { 2 } \rightarrow [ 0 , \infty )$ ; confidence 1.000

145. a130040360.png ; $\Omega F$ ; confidence 1.000

146. a11016093.png ; $b = 0$ ; confidence 1.000

147. s12025018.png ; $h ( x ) = \sqrt { 1 - x ^ { 2 } }$ ; confidence 1.000

148. z13012028.png ; $\sigma > ( 1 / n ) \operatorname { tan } ^ { 2 } ( \pi / 2 n )$ ; confidence 1.000

149. r1301409.png ; $U \cap \sigma ( R ) = \{ \lambda \}$ ; confidence 1.000

150. d03211065.png ; $t < 0$ ; confidence 1.000

151. d12014054.png ; $( n , 2 ) = 1$ ; confidence 1.000

152. c1301106.png ; $\sigma \geq 0$ ; confidence 1.000

153. f12015023.png ; $i ( A ) = \alpha ( A ) - \beta ( A )$ ; confidence 1.000

154. m12009017.png ; $P ( D ) ( E ) = \delta _ { 0 }$ ; confidence 1.000

155. z13012010.png ; $\xi > 1$ ; confidence 1.000

156. g130040186.png ; $\epsilon \in ( 0,1 )$ ; confidence 1.000

157. a130080106.png ; $U \leq b ( X )$ ; confidence 1.000

158. b13016072.png ; $f ( x ) \neq f ( y )$ ; confidence 1.000

159. r0775408.png ; $[ 0 , + \infty ]$ ; confidence 1.000

160. s13041013.png ; $\mu _ { 0 } = \mu _ { 1 }$ ; confidence 1.000

161. o13006063.png ; $p ( \lambda _ { 1 } , \lambda _ { 2 } )$ ; confidence 1.000

162. f12005043.png ; $x ^ { 2 } - y ^ { 2 } = z ^ { 2 }$ ; confidence 1.000

163. r13005014.png ; $( G )$ ; confidence 1.000

164. l06004022.png ; $\leq n - p$ ; confidence 1.000

165. b110670111.png ; $A C$ ; confidence 1.000

166. f12008039.png ; $( \xi , \xi )$ ; confidence 0.999

167. k055840269.png ; $E ( \Delta )$ ; confidence 0.999

168. h13007018.png ; $B ( m , D , n )$ ; confidence 0.999

169. f1300708.png ; $m = 1,2,3,4,5,7$ ; confidence 0.999

170. b11089067.png ; $\beta = 1 / 2$ ; confidence 0.999

171. f12015040.png ; $\alpha ( B ) < \infty$ ; confidence 0.999

172. d12029069.png ; $f ( q ) \geq 0$ ; confidence 0.999

173. e03644014.png ; $x < 0$ ; confidence 0.999

174. i13009078.png ; $P ( T )$ ; confidence 0.999

175. i1300505.png ; $r ( k )$ ; confidence 0.999

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

177. w12006046.png ; $( n , r )$ ; confidence 0.999

178. l05914040.png ; $x ( 0 ) = 0$ ; confidence 0.999

179. d12006013.png ; $D ^ { \pm } f = f - \sigma ^ { \pm } T ^ { \pm 1 } ( f )$ ; confidence 0.999

180. c026010570.png ; $( \Omega , F )$ ; confidence 0.999

181. d1203002.png ; $( Y ( t ) , t \geq 0 )$ ; confidence 0.999

182. a01099011.png ; $k \neq 0$ ; confidence 0.999

183. k12012024.png ; $\int _ { - \infty } ^ { \infty } \frac { - \operatorname { ln } f ( x ) } { 1 + x ^ { 2 } } d x < \infty$ ; confidence 0.999

184. d0315402.png ; $G \times G$ ; confidence 0.999

185. a13012030.png ; $( s , \mu )$ ; confidence 0.999

186. a011300153.png ; $\mu = 1$ ; confidence 0.999

187. m13002052.png ; $4 k - 1$ ; confidence 0.999

188. b12009024.png ; $f = f ( z , \tau )$ ; confidence 0.999

189. b110670129.png ; $( m - 1 )$ ; confidence 0.999

190. m1200706.png ; $M ( P ) = \operatorname { exp } ( m ( P ) )$ ; confidence 0.999

191. a12013036.png ; $h ( \theta ) = 0$ ; confidence 0.999

192. d03167026.png ; $( \xi , \eta , \zeta )$ ; confidence 0.999

193. a12005083.png ; $\rho ( A ( t ) ) \supset ( \beta , \infty )$ ; confidence 0.999

194. g04333028.png ; $( m + 1 )$ ; confidence 0.999

195. s130510127.png ; $\gamma ( u ) = \gamma ^ { \prime } ( u )$ ; confidence 0.999

196. b13003013.png ; $V ^ { + } = V ^ { - }$ ; confidence 0.999

197. o130010160.png ; $\theta ^ { \prime } \in M$ ; confidence 0.999

198. d03328015.png ; $\{ x \}$ ; confidence 0.999

199. v1200407.png ; $\Delta ( G ) \leq \chi ^ { \prime } ( G )$ ; confidence 0.999

200. a1302606.png ; $\zeta ( 2 ) = \pi ^ { 2 } / 6$ ; confidence 0.999

201. m1101105.png ; $0 \leq m \leq p$ ; confidence 0.999

202. c02023032.png ; $\leq n - 2$ ; confidence 0.999

203. k12006044.png ; $E + D$ ; confidence 0.999

204. e13007084.png ; $( p , p + 1 / 2 )$ ; confidence 0.999

205. c13007097.png ; $f ^ { \prime } ( X ^ { \prime } , Y ^ { \prime } ) = 0$ ; confidence 0.999

206. n13007012.png ; $m ( A \cup B ) - m ( B )$ ; confidence 0.999

207. c12026055.png ; $k h ^ { - 2 } \leq 1$ ; confidence 0.999

208. r13005027.png ; $\Omega = G$ ; confidence 0.999

209. c1202603.png ; $[ 0,1 ] \times [ 0 , T ]$ ; confidence 0.999

210. t12015017.png ; $\pi ( \xi )$ ; confidence 0.999

211. b1102107.png ; $d ( x , y )$ ; confidence 0.999

212. m13018027.png ; $\mu ( m , n )$ ; confidence 0.999

213. b13007014.png ; $\pi ( m ) = \pi ( n )$ ; confidence 0.999

214. f120150142.png ; $A \in \Phi _ { - } ( X , Y )$ ; confidence 0.999

215. p12015018.png ; $G = M ( n )$ ; confidence 0.999

216. v096900189.png ; $T ( \zeta ) \in A ( \zeta )$ ; confidence 0.999

217. i120080115.png ; $\beta = 1 / 8$ ; confidence 0.999

218. a13007060.png ; $- ( \sqrt { 6 } + \varepsilon )$ ; confidence 0.999

219. o130060174.png ; $f = f ( t _ { 1 } , t _ { 2 } )$ ; confidence 0.999

220. c12001047.png ; $T ( F )$ ; confidence 0.999

221. o12005023.png ; $w ( t ) \equiv 1$ ; confidence 0.999

222. k12012025.png ; $\int _ { - \infty } ^ { \infty } \frac { - \operatorname { ln } f ( x ) } { 1 + x ^ { 2 } } d x = \infty$ ; confidence 0.999

223. o12006014.png ; $| \Omega | < \infty$ ; confidence 0.999

224. b1302508.png ; $\angle \Omega B C$ ; confidence 0.999

225. p07452021.png ; $F = L \backslash P$ ; confidence 0.999

226. b01643030.png ; $x = - 1$ ; confidence 0.999

227. n067520292.png ; $A = U ^ { - 1 } K _ { \rho } U$ ; confidence 0.999

228. n0669609.png ; $n + \lambda$ ; confidence 0.999

229. c02547040.png ; $2 n + 1$ ; confidence 0.999

230. a01130057.png ; $( n - 2 )$ ; confidence 0.999

231. n06728054.png ; $M ( \lambda )$ ; confidence 0.999

232. a11028022.png ; $k = - 1$ ; confidence 0.999

233. d120230117.png ; $d ( z , w ) = 1 - z w ^ { * }$ ; confidence 0.999

234. e12012060.png ; $f ( \theta ) = \int f ( \theta , \phi ) d \phi$ ; confidence 0.999

235. c13015037.png ; $\Lambda = ( 0 , \infty )$ ; confidence 0.999

236. w12007021.png ; $[ A , B ] = A B - B A$ ; confidence 0.999

237. h04701017.png ; $h ( x ) = \operatorname { exp } ( - x ^ { 2 } )$ ; confidence 0.999

238. a12027084.png ; $\{ \pm 1 \}$ ; confidence 0.999

239. w13010031.png ; $\operatorname { lim } _ { t \rightarrow \infty } f ( t ) = \infty$ ; confidence 0.999

240. h13012026.png ; $0 \leq p < 1$ ; confidence 0.999

241. a12016022.png ; $u ( t )$ ; confidence 0.999

242. l110010101.png ; $( A , P )$ ; confidence 0.999

243. b12021076.png ; $( B , \delta )$ ; confidence 0.999

244. b130220110.png ; $\{ x \} \cup B$ ; confidence 0.999

245. c1100707.png ; $| z | < 1$ ; confidence 0.999

246. f120150169.png ; $\mu ( A ) > 0$ ; confidence 0.999

247. b0169703.png ; $\sigma = 1$ ; confidence 0.999

248. a12023023.png ; $F \in H ( D ) \cap C ( D \cup \Gamma )$ ; confidence 0.999

249. h13002032.png ; $A ^ { N }$ ; confidence 0.999

250. b12009053.png ; $w ( z ) =$ ; confidence 0.999

251. z12002032.png ; $m \geq n \geq 2$ ; confidence 0.999

252. c13025050.png ; $A ( t ) = \int _ { 0 } ^ { t } \alpha ( s ) d s$ ; confidence 0.999

253. n13007026.png ; $m ( A \cup B ) = m ( A )$ ; confidence 0.999

254. b12056013.png ; $\lambda _ { 1 } \leq 2 ( n - 1 ) \delta h + 10 h ^ { 2 }$ ; confidence 0.999

255. s12026058.png ; $s \in [ 0,1 ]$ ; confidence 0.999

256. t12021089.png ; $t ( T _ { 1 } ) = t ( T _ { 2 } )$ ; confidence 0.999

257. a130080103.png ; $f ( L ) = f ( R )$ ; confidence 0.999

258. b1203001.png ; $\eta \in R ^ { N }$ ; confidence 0.999

259. a012970220.png ; $\gamma > 0$ ; confidence 0.999

260. r1301209.png ; $[ 0 , u ] + [ 0 , v ] = [ 0 , u + v ]$ ; confidence 0.999

261. w12009060.png ; $[ \lambda ]$ ; confidence 0.999

262. e12027022.png ; $\frac { \beta } { 2 } + \frac { 1 } { 4 } \leq s < \frac { \beta } { 2 } + \frac { 5 } { 4 }$ ; confidence 0.999

263. w12003060.png ; $[ 0,1 ] ^ { \Gamma }$ ; confidence 0.999

264. a12008069.png ; $H ^ { 1 } ( \Omega ) \times H ^ { 1 } ( \Omega )$ ; confidence 0.999

265. b13022065.png ; $m - 1$ ; confidence 0.999

266. p130100109.png ; $P ( K ) = C ( K )$ ; confidence 0.999

267. d13017014.png ; $\lambda _ { k } \rightarrow \infty$ ; confidence 0.999

268. s120040120.png ; $\mu \subseteq \lambda$ ; confidence 0.999

269. p12017047.png ; $0 < p \leq 1$ ; confidence 0.999

270. l12006022.png ; $d \lambda$ ; confidence 0.999

271. w13009054.png ; $\varphi \in L ^ { 2 } ( \mu )$ ; confidence 0.999

272. c02327028.png ; $r ( A ) < | A |$ ; confidence 0.999

273. a12025045.png ; $d = k - n + 2$ ; confidence 0.999

274. c02242038.png ; $\alpha > - 1$ ; confidence 0.999

275. p12013025.png ; $\lambda > 0$ ; confidence 0.999

276. b12020054.png ; $\theta ( e ^ { i t } )$ ; confidence 0.999

277. c0273701.png ; $R ( X , Y )$ ; confidence 0.999

278. k05507079.png ; $d = 10$ ; confidence 0.999

279. i1201008.png ; $R ( \pi ) = R ( X , Y )$ ; confidence 0.999

280. g13002056.png ; $\Gamma ( 1 / 4 )$ ; confidence 0.999

281. f120150140.png ; $F _ { - } ( X , Y )$ ; confidence 0.999

282. p13014057.png ; $\psi ( + 0 ) = 1 / 2$ ; confidence 0.999

283. n067520230.png ; $( A , B ) \sim ( S A S ^ { - 1 } , S B )$ ; confidence 0.999

284. l06105082.png ; $P ( E ) = 0 \Rightarrow \lambda ( F ( E ) ) = 0$ ; confidence 0.999

285. c02485061.png ; $A + B$ ; confidence 0.999

286. h13006061.png ; $R ( X , D )$ ; confidence 0.999

287. c130070161.png ; $M ( R ( P ) )$ ; confidence 0.999

288. d12003067.png ; $f ( x ) \in ( 0,1 ]$ ; confidence 0.999

289. c12004047.png ; $\gamma \cap \Gamma$ ; confidence 0.999

290. s13004035.png ; $( 2 g ) \times ( 2 g )$ ; confidence 0.999

291. b120040111.png ; $f ( x _ { n } ) \rightarrow 0$ ; confidence 0.999

292. c13007094.png ; $Y = X ^ { \prime } Y ^ { \prime }$ ; confidence 0.999

293. d0340203.png ; $F ( \xi )$ ; confidence 0.999

294. v1200607.png ; $B _ { 1 } = - 1 / 2$ ; confidence 0.999

295. m130180107.png ; $\mu ( 0 , x ) \neq 0$ ; confidence 0.999

296. f13024017.png ; $\varepsilon = - 1$ ; confidence 0.999

297. n12002048.png ; $\alpha \in [ 1,2 )$ ; confidence 0.999

298. a13019027.png ; $2 n - 2 m$ ; confidence 0.999

299. l120100121.png ; $( - \Delta + E ) ^ { - 1 }$ ; confidence 0.999

300. d1202609.png ; $0 \leq t \leq 1$ ; confidence 0.999

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/3. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/3&oldid=44491
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