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(AUTOMATIC EDIT of page 6 out of 77 with 300 lines: Updated image/latex database (currently 22833 images latexified; order by Length, ascending: False.)
 
(AUTOMATIC EDIT of page 6 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/z/z130/z130080/z13008049.png ; $= - n ( n + 2 + 2 \alpha ) f , D = z \frac { \partial } { \partial z } + z \frac { \partial } { \partial z }$ ; confidence 0.987
+
1. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120140/b1201406.png ; $\operatorname { deg } S ( z ) < 2 t$ ; confidence 0.999
  
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2. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013028.png ; $\phi _ { - } ( x , t , z ) = \operatorname { exp } ( \sum _ { i = 1 } ^ { \infty } \chi _ { i } ( x , t ) z ^ { - i } )$ ; confidence 0.963
+
2. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c120170166.png ; $2 k - 1$ ; confidence 0.999
  
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3. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040754.png ; $_ { R } , \mathfrak { M } ( r ) = \operatorname { mng } _ { P \cup R } , \mathfrak { M } ( \varphi _ { r } )$ ; confidence 0.815
+
3. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120270/a12027011.png ; $\Lambda ( s , \rho )$ ; confidence 0.999
  
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4. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007095.png ; $\frac { \partial u } { \partial t } = L ( t , x , D _ { x } ) u + f ( t , x ) \text { in } [ 0 , T ] \times \Omega$ ; confidence 0.831
+
4. https://www.encyclopediaofmath.org/legacyimages/g/g045/g045090/g045090232.png ; $G ( z , w ) =$ ; confidence 0.999
  
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5. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060102.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { P ^ { \# } ( n ) } { G ^ { \# } ( n ) } = \lambda$ ; confidence 0.751
+
5. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060050/l06005032.png ; $( m < n )$ ; confidence 0.999
  
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6. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008050.png ; $\frac { d \operatorname { ln } g ( L ; m , s ) } { d m } \frac { d \operatorname { ln } g ( R ; m , s ) } { d s }$ ; confidence 0.495
+
6. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007083.png ; $A ( \alpha ^ { \prime } , \alpha )$ ; confidence 0.999
  
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7. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110320/a1103208.png ; $+ h \sum _ { j = 1 } ^ { i - 1 } A _ { j } ( h T ) [ f ( t _ { m } + c _ { j } h , u _ { m + 1 } ^ { ( j ) } ) - T u _ { n j } ^ { ( j ) } + 1 ]$ ; confidence 0.207
+
7. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f120150178.png ; $\Gamma ( A ) > 0$ ; confidence 0.999
  
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8. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016070.png ; $S _ { t } = \omega ( 1 - \lambda ) + \lambda S _ { t - 1 } + c _ { 1 } u _ { t } + \mu _ { t } - \lambda \mu _ { t - 1 }$ ; confidence 0.412
+
8. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120110/a12011018.png ; $A ( 1 , n ) = n + 2$ ; confidence 0.999
  
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9. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032042.png ; $E _ { \theta } ( N ) = \frac { P _ { \theta } ( S _ { N } = K ) K - P _ { \theta } ( S _ { N } = - J ) J } { 2 \theta - 1 }$ ; confidence 0.641
+
9. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130190/b1301908.png ; $\alpha = \operatorname { log } M / \operatorname { log } T \in ( 0,1 )$ ; confidence 0.999
  
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10. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110660/b11066014.png ; $\| f \| _ { * } = \operatorname { sup } _ { Q } \frac { 1 } { | Q | } \int _ { Q } | f ( t ) - f _ { Q } | d t < \infty$ ; confidence 0.901
+
10. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120160/b12016070.png ; $n = 4,5,6$ ; confidence 0.999
  
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11. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009037.png ; $( 1 + \alpha ^ { 2 } ) \frac { d \tau } { \tau } = ( p _ { S } ( \xi , \tau ) - \alpha i ) \frac { d \xi } { \xi }$ ; confidence 0.647
+
11. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130050/e13005021.png ; $+ \frac { \Gamma ( 1 - \alpha - \beta ) } { 2 \Gamma ( 1 - \alpha ) \Gamma ( 1 - \beta ) } ( y - x ) ^ { t - \alpha - \beta }$ ; confidence 0.999
  
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12. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120160/b1201609.png ; $x _ { j } ^ { \prime } = \sum _ { i , k } p _ { i k } , j _ { i } x _ { k } , \quad x _ { i } \geq 0 , \sum _ { i } x _ { i } = 1$ ; confidence 0.343
+
12. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007090.png ; $m < n$ ; confidence 0.999
  
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13. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120510/b12051059.png ; $H _ { + } = H _ { c } + \frac { y y ^ { T } } { y ^ { T } s } - \frac { ( H _ { c } s ) ( H _ { c } s ) ^ { T } } { s ^ { T } H _ { c } s }$ ; confidence 0.956
+
13. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120280/a120280110.png ; $x \neq 0$ ; confidence 0.999
  
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14. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c13016061.png ; $\operatorname { lim } _ { n \rightarrow \infty } t ( n ) ( \operatorname { log } t ( n ) ) / s ( n ) = 0$ ; confidence 0.906
+
14. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120050/k12005057.png ; $q \leq r ( d + 1 )$ ; confidence 0.999
  
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15. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180159.png ; $g ^ { - 1 } ( \theta \otimes \varphi ) = \langle \theta , \gamma ^ { - 1 } ( \varphi ) \rangle \in R$ ; confidence 0.653
+
15. https://www.encyclopediaofmath.org/legacyimages/p/p072/p072890/p07289018.png ; $( n \times p )$ ; confidence 0.999
  
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16. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180240.png ; $g ^ { - 1 } \{ p _ { 1 } , p _ { 2 } ; \ldots ; p _ { 4 m - 1 } , p _ { 4 m } \} ( W ( g ) \otimes \ldots \otimes W ( g ) )$ ; confidence 0.422
+
16. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008020.png ; $( A B )$ ; confidence 0.999
  
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17. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023064.png ; $= \sum _ { i = 0 } ^ { p - 1 } L ( x _ { i } ) L ^ { * } ( x _ { i } ) - \sum _ { i = 0 } ^ { q - 1 } L ( y _ { i } ) L ^ { * } ( y _ { i } )$ ; confidence 0.584
+
17. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120050/b12005034.png ; $\{ f \in H ^ { \infty } ( B _ { E } ) :$ ; confidence 0.999
  
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18. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012065.png ; $\propto \| \Sigma \| ^ { - 1 / 2 } [ \nu + ( y - \mu ) ^ { T } \Sigma ^ { - 1 } ( y - \mu ) ] ^ { - ( \nu + p ) / 2 }$ ; confidence 0.904
+
18. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013380/a0133806.png ; $\lambda \in R$ ; confidence 0.999
  
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19. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e03500092.png ; $H _ { \epsilon } ^ { \prime \prime } ( X ) = \operatorname { inf } \{ H ( U ) : U \in A _ { \epsilon } \}$ ; confidence 0.867
+
19. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e120070108.png ; $\beta ( f )$ ; confidence 0.999
  
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20. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023058.png ; $E ( L ) = \frac { \partial L } { \partial y } - D ( \frac { \partial L } { \partial y ^ { \prime } } )$ ; confidence 0.989
+
20. https://www.encyclopediaofmath.org/legacyimages/r/r081/r081490/r08149043.png ; $V ( \lambda )$ ; confidence 0.999
  
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21. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f1300909.png ; $\alpha ( x ) = \frac { x + ( x ^ { 2 } + 4 ) ^ { 1 / 2 } } { 2 } , \beta ( x ) = \frac { x - ( x ^ { 2 } + 4 ) ^ { 1 / 2 } } { 2 }$ ; confidence 0.989
+
21. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130160/f13016031.png ; $\Gamma ( \xi \oplus \eta )$ ; confidence 0.999
  
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22. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f130100137.png ; $T = c _ { 1 } \lambda ^ { p } ( \delta _ { x _ { 1 } } ) + \ldots + c _ { n } \lambda ^ { p } ( \delta _ { x _ { n } } )$ ; confidence 0.835
+
22. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t130050164.png ; $\lambda \in B _ { 4 }$ ; confidence 0.999
  
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23. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120090/f12009037.png ; $| f ( \zeta ) | \leq C _ { \epsilon } \operatorname { exp } ( H _ { K } ( \zeta ) + \epsilon | \zeta | )$ ; confidence 0.990
+
23. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011092.png ; $U \backslash \Omega$ ; confidence 0.999
  
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24. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f13024045.png ; $\left( \begin{array} { r r } { 0 } & { 0 } \\ { - \varepsilon K ( c , d ) } & { 0 } \end{array} \right)$ ; confidence 0.448
+
24. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005041.png ; $\| ( \lambda - A ( t ) ) ^ { - 1 } \| \leq M / ( 1 + | \lambda | )$ ; confidence 0.999
  
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25. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g130040141.png ; $F _ { K } ( S _ { 1 } , S _ { 2 } ) = \operatorname { inf } \{ M ( U ) + M ( V ) : U + \partial V = S _ { 1 } - S _ { 2 } \}$ ; confidence 0.655
+
25. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016056.png ; $( p _ { 1 } \times n _ { 1 } )$ ; confidence 0.999
  
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26. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g12004083.png ; $\Sigma _ { P } = \{ ( x , \xi ) \in \Omega \times ( R ^ { n } \backslash \{ 0 \} ) : p _ { m } ( x , \xi ) = 0 \}$ ; confidence 0.632
+
26. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130020/s13002034.png ; $N = \partial M$ ; confidence 0.999
  
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27. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110010/h1100101.png ; $M ( f ) = \operatorname { lim } _ { x \rightarrow \infty } \frac { 1 } { x } \cdot \sum _ { n < x } f ( n )$ ; confidence 0.532
+
27. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120110/h12011021.png ; $B ( 0 , r / 2 )$ ; confidence 0.999
  
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28. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120110/h12011040.png ; $S _ { n + 1 } = \{ z \in C ^ { n + 1 } : \operatorname { Im } z _ { n + 1 } > \sum ^ { n _ { j = 1 } } | z _ { j } | ^ { 2 } \}$ ; confidence 0.163
+
28. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030240/d03024029.png ; $f ( 2 k + 1 ) ( 0 )$ ; confidence 0.999
  
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29. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i130030181.png ; $\phi _ { * } ( \text { ind } ( D ) ) = ( - 1 ) ^ { n } ( 2 \pi i ) ^ { - m } ( Ch ( [ a ] ) T ( M ) f ^ { * } \phi ) [ T ^ { * } M ]$ ; confidence 0.164
+
29. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120240/b12024015.png ; $A ( \overline { U } , V )$ ; confidence 0.999
  
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30. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i1300408.png ; $bv = \{ d = \{ d _ { k } \} : \| \alpha \| _ { bv } = \sum _ { k = 0 } ^ { \infty } | \Delta d _ { k } | < \infty \}$ ; confidence 0.358
+
30. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020237.png ; $( \overline { \lambda } , \overline { \mu } )$ ; confidence 0.999
  
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31. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i1200407.png ; $b _ { 0 } P = \{ ( \zeta _ { 1 } , \dots , \zeta _ { n } ) : | \zeta _ { j } - a _ { j } | = r _ { j } , j = 1 , \dots , n \}$ ; confidence 0.718
+
31. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004080.png ; $s ( L )$ ; confidence 0.999
  
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32. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005068.png ; $S : = \{ r _ { + } ( k ) , i k _ { j } , ( m _ { j } ^ { + } ) ^ { 2 } : 1 \leq j \leq J , k _ { j } > 0 , m _ { j } ^ { + } > 0 , k > 0 \}$ ; confidence 0.873
+
32. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120200/w1202007.png ; $R [ f ] = ( r , f )$ ; confidence 0.999
  
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33. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i130060172.png ; $+ \int _ { \frac { x + y } { 2 } } ^ { \infty } d s \int _ { 0 } ^ { \frac { y - x } { 2 } } q ( s - t ) A ( s - t , s + t ) d t$ ; confidence 0.831
+
33. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110250/c1102505.png ; $( p , q )$ ; confidence 0.999
  
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34. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090217.png ; $( L ( k ^ { \prime } ) / k _ { \infty } ^ { \prime } ) \cong \text { varprojlim } A _ { n } ( k ^ { \prime } )$ ; confidence 0.661
+
34. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059024.png ; $M [ L ] > 0$ ; confidence 0.999
  
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35. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j12002098.png ; $\leq 2 E [ X _ { 0 } ] + 2 E [ X _ { \infty } \operatorname { log } + \frac { X _ { \infty } } { E [ X _ { 0 } ] } ]$ ; confidence 0.541
+
35. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022420/c02242020.png ; $\alpha , \beta > - 1$ ; confidence 0.999
  
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36. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j12002077.png ; $X = M ^ { 1 } - \operatorname { lim } _ { N \rightarrow \infty } \sum _ { n = - N } ^ { n = N } c _ { n } A ^ { n }$ ; confidence 0.947
+
36. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120070/k1200705.png ; $R ( t ) \in L ( V )$ ; confidence 0.999
  
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37. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020184.png ; $U _ { t } ^ { 1 } U _ { t } ^ { 2 } - \int _ { 0 } ^ { t } \nabla u _ { 1 } ( B _ { s } ) \cdot \nabla u _ { 2 } ( B _ { s } ) d s$ ; confidence 0.735
+
37. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130120/a1301201.png ; $D = ( V , B )$ ; confidence 0.999
  
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38. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055070/k05507010.png ; $H ^ { 2 r } ( M , C ) \neq 0 \quad \text { if } r = 1 , \dots , \frac { 1 } { 2 } \operatorname { dim } _ { C } M$ ; confidence 0.432
+
38. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120010/z12001063.png ; $W _ { 1 } ( 1 )$ ; confidence 0.999
  
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39. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120010/l12001050.png ; $\left\{ \begin{array} { c } { m } \\ { \lceil \frac { m + 1 } { 2 } \rceil } \end{array} \right\}$ ; confidence 0.282
+
39. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120030/l12003091.png ; $\tau ( R ^ { * } )$ ; confidence 0.999
  
−
40. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l13008018.png ; $- \mathfrak { c } _ { 1 } + \mathfrak { c } _ { 3 } d ^ { \nu } \operatorname { log } ( \rho / | \omega | )$ ; confidence 0.515
+
40. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130010/k13001036.png ; $( \vec { D } )$ ; confidence 0.999
  
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41. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170293.png ; $0 \rightarrow P _ { n } \rightarrow \ldots \rightarrow P _ { 0 } \rightarrow Z \rightarrow 0$ ; confidence 0.777
+
41. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007012.png ; $Y ^ { 2 } = X ^ { 3 }$ ; confidence 0.999
  
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42. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l12017044.png ; $\langle \alpha , b | \alpha = [ \alpha ^ { p } , b ^ { \gamma } ] , b = [ \alpha ^ { r } , b ^ { s } ] \rangle$ ; confidence 0.320
+
42. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130170/d13017035.png ; $| \Omega |$ ; confidence 0.999
  
−
43. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130020/m13002030.png ; $\phi = ( \frac { 1 } { \operatorname { tanh } r } - \frac { 1 } { r } ) \frac { x _ { i } } { r } \sigma _ { i }$ ; confidence 0.982
+
43. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120120/h120120134.png ; $f \cup g = m ( f \otimes g ) \Delta$ ; confidence 0.999
  
−
44. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120100/n12010048.png ; $\sum _ { i = 0 } ^ { k } \alpha _ { i } y _ { m + i } = h \sum _ { i = 0 } ^ { k } \beta _ { i } f ( x _ { m } + i , y _ { m + i } )$ ; confidence 0.143
+
44. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007039.png ; $( 1 / ( 1 + k ) ) \omega$ ; confidence 0.999
  
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45. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001080.png ; $A ( \alpha ^ { \prime } , \alpha , k ) \equiv - \frac { C } { 4 \pi } , \text { if } \Gamma u = u , k a \ll 1$ ; confidence 0.857
+
45. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043028.png ; $h \rightarrow ( h , h )$ ; confidence 0.999
  
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46. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p13007081.png ; $= \operatorname { sup } \{ \int _ { K } M ( u ) d V : u \in \operatorname { PSH } ( \Omega ) , 0 < u < 1 \}$ ; confidence 0.932
+
46. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046020/h04602043.png ; $R \in H ^ { \infty }$ ; confidence 0.999
  
−
47. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p13007046.png ; $f ( z _ { 1 } , z _ { 2 } ) = ( | z _ { 1 } | ^ { 2 } - \frac { 1 } { 2 } ) ^ { 2 } = ( | z _ { 2 } | ^ { 2 } - \frac { 1 } { 2 } ) ^ { 2 }$ ; confidence 0.998
+
47. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130030/n13003034.png ; $- T \Delta w ( x , y )$ ; confidence 0.999
  
−
48. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p13014052.png ; $D ( x _ { 0 } ) : = \operatorname { lim } _ { t \rightarrow + 0 } [ f ( x _ { 0 } + t n _ { 0 } ) - f ( x - t n _ { 0 } ) ]$ ; confidence 0.848
+
48. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130120/p13012030.png ; $\sigma ( K ) = - 2$ ; confidence 0.999
  
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49. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120030/q12003045.png ; $\psi = ( \text { id } \otimes \varphi ) \circ L : A \rightarrow \operatorname { Fun } _ { q } ( G )$ ; confidence 0.524
+
49. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a130070131.png ; $> 20162$ ; confidence 0.999
  
−
50. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s120040106.png ; $\operatorname { ch } ( \chi ) = \frac { 1 } { n ! } \sum _ { | \mu | = n } k _ { \mu } \chi _ { \mu } p _ { \mu }$ ; confidence 0.928
+
50. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046010/h04601058.png ; $\tau ( W , M _ { 0 } ) = 0$ ; confidence 0.999
  
−
51. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020069.png ; $S ^ { \lambda } = \operatorname { span } \{ e _ { t } : t _ { a } \lambda \square \text { tableau } \}$ ; confidence 0.051
+
51. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007042.png ; $\xi \in R ^ { 3 }$ ; confidence 0.999
  
−
52. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051052.png ; $N _ { n } = \{ u \in V : n = \operatorname { min } m , F ( u ) \cap \cup _ { i < m } P _ { i } \neq \emptyset \}$ ; confidence 0.729
+
52. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032099.png ; $F ( m ^ { 1 / p } , n ^ { 1 / p } ) = ( n + m ) ^ { 1 / p }$ ; confidence 0.999
  
−
53. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w12009096.png ; $\ldots \times \mathfrak { S } _ { \{ \lambda _ { 1 } + \ldots + \lambda _ { n - 1 } + 1 , \ldots , r \} }$ ; confidence 0.259
+
53. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060030/l0600302.png ; $A ^ { \prime } A$ ; confidence 0.999
  
−
54. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080164.png ; $Y ( \gamma ) = \psi ( z _ { 0 } , z _ { 0 } ) | _ { \gamma } = P \operatorname { exp } ( \oint _ { \gamma } A )$ ; confidence 0.794
+
54. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120130/b12013091.png ; $\| \varphi \| _ { p } = 1$ ; confidence 0.999
  
−
55. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z130110132.png ; $\frac { \mu _ { N } ( x ) } { M } \stackrel { P } { \rightarrow } \int _ { 0 } ^ { 1 } u ( 1 - u ) ^ { x - 1 } F ( d x )$ ; confidence 0.567
+
55. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031930/d031930128.png ; $\Delta u = 0$ ; confidence 0.999
  
−
56. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050212.png ; $\sum _ { n \leq x } \alpha ( n ) = A _ { 1 } x + O ( \sqrt { x } ) \quad \text { as } x \rightarrow \infty$ ; confidence 0.331
+
56. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130100/t13010053.png ; $\Gamma ( B )$ ; confidence 0.999
  
−
57. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007082.png ; $A ( 0 ) u _ { 0 } + f ( 0 ) - \frac { d } { d t } A ( t ) ^ { - 1 } | _ { t = 0 } A ( 0 ) u _ { 0 } \in \overline { D ( A ( 0 ) ) }$ ; confidence 0.704
+
57. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120100/b12010047.png ; $U ( t )$ ; confidence 0.999
  
−
58. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016046.png ; $A ( t _ { 0 } ) = A _ { 0 } , \dot { X } ( t ) = [ N ( X ( t ) , A ( t ) , t ) - X ( t ) ] \operatorname { exp } ( - k P ( t ) )$ ; confidence 0.365
+
58. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010180/a01018053.png ; $\sigma > 0$ ; confidence 0.999
  
−
59. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130120/a13012028.png ; $k = s \mu , v = s ^ { 2 } \mu , \lambda = \frac { s \mu - 1 } { \mu - 1 } , r = \frac { s ^ { 2 } \mu - 1 } { \mu - 1 }$ ; confidence 0.996
+
59. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096040/v09604020.png ; $s ( r ) \equiv r$ ; confidence 0.999
  
−
60. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009016.png ; $\frac { \partial f ( z , t ) } { \partial t } = - f ( z , t ) \frac { 1 + k f ( z , t ) } { 1 - \dot { k } f ( z , t ) }$ ; confidence 0.781
+
60. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130040/c1300408.png ; $\beta ( z ) : = \frac { 1 } { 2 } [ \psi ( \frac { 1 } { 2 } z + \frac { 1 } { 2 } ) - \psi ( \frac { 1 } { 2 } z ) ] =$ ; confidence 0.999
  
−
61. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b110220194.png ; $CH ^ { p } ( X ) ^ { 0 } = \operatorname { Ker } ( CH ^ { p } ( X ) \rightarrow H ^ { 2 p } B ( X _ { C } , Q ( p ) ) )$ ; confidence 0.124
+
61. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120280/s12028026.png ; $D ^ { 2 } X \approx X$ ; confidence 0.999
  
−
62. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130190/b13019025.png ; $U ( f ; M _ { 1 } , M _ { 2 } ; H _ { 1 } , H _ { 2 } ) = \sum _ { h } \frac { S ( h f ^ { \prime } ; M _ { 1 } , M _ { 2 } ) } { h }$ ; confidence 0.777
+
62. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120290/c12029045.png ; $w : R \rightarrow P$ ; confidence 0.999
  
−
63. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130230/b13023041.png ; $\operatorname { rist } _ { G } ( n ) = \langle \operatorname { rist } _ { G } ( u ) : | u | = n \rangle$ ; confidence 0.469
+
63. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e1200601.png ; $p : Y \rightarrow M$ ; confidence 0.999
  
−
64. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130040/c1300408.png ; $\beta ( z ) : = \frac { 1 } { 2 } [ \psi ( \frac { 1 } { 2 } z + \frac { 1 } { 2 } ) - \psi ( \frac { 1 } { 2 } z ) ] =$ ; confidence 0.999
+
64. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030054.png ; $\phi = \phi ( y ; \eta )$ ; confidence 0.999
  
−
65. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008037.png ; $\Delta ( A _ { 1 } ) = \sum _ { i = 0 } ^ { m } ( I _ { m } \otimes D _ { m - i } ) A _ { 1 } ^ { i } = 0 ( D _ { 0 } = I _ { n } )$ ; confidence 0.459
+
65. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007031.png ; $n ( n - 1 ) / 2 - 1 - ( n - 1 ) ( n - 2 ) / 2 = n - 2$ ; confidence 0.999
  
−
66. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008087.png ; $\left. \begin{array} { l l } { E _ { 1 } } & { E _ { 2 } } \\ { E _ { 3 } } & { E _ { 4 } } \end{array} \right.$ ; confidence 0.730
+
66. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120020/c12002072.png ; $m ( x ^ { \prime } )$ ; confidence 0.999
  
−
67. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180492.png ; $\mathfrak { g } = t ^ { 2 } \sum _ { i , j } \mathfrak { g } _ { i j } ( x , t ) d x ^ { i } \bigotimes d x ^ { j } +$ ; confidence 0.413
+
67. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120140/e120140101.png ; $( ( \neg \varphi \rightarrow \varphi ) \rightarrow \varphi ) = 1$ ; confidence 0.999
  
−
68. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c120210127.png ; $\int _ { A } \operatorname { exp } ( h ^ { \prime } \Delta _ { N } ^ { * } ( \theta ) ) d P _ { n , \theta }$ ; confidence 0.635
+
68. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005082.png ; $\theta = 1$ ; confidence 0.999
  
−
69. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120270/c12027015.png ; $\omega = \operatorname { inf } _ { p \in \Omega } \frac { Vol ( \Omega _ { p } ) } { \alpha ( n - 1 ) }$ ; confidence 0.663
+
69. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005076.png ; $\theta = \theta ^ { k }$ ; confidence 0.999
  
−
70. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030028.png ; $( H ^ { \otimes r } , H ^ { \otimes r + k } ) \rightarrow ( H ^ { \otimes r + 1 } , H ^ { \otimes r + 1 + k } )$ ; confidence 0.600
+
70. 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
  
−
71. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120110/d12011032.png ; $\operatorname { lim } _ { i \rightarrow \infty } x _ { i _ { i } } n _ { j } = 0 \text { for all } j \in N$ ; confidence 0.311
+
71. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130010/d1300101.png ; $h ( x , y )$ ; confidence 0.999
  
−
72. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230107.png ; $C _ { l } = ( \frac { u _ { i } v _ { j } ^ { * } } { f _ { i } - a _ { j } ^ { * } } ) , u _ { i } , v _ { i } \in C ^ { 1 \times r }$ ; confidence 0.648
+
72. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013029.png ; $\phi _ { + } = \operatorname { exp } ( \sum _ { j = 1 } ^ { \infty } \phi _ { j } ( x , t ) z ^ { j } )$ ; confidence 0.999
  
−
73. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130040/e13004036.png ; $= ( \Omega _ { + } - 1 ) ( g - \mathfrak { g } ) \psi ( t ) + ( \Omega _ { + } - 1 ) g \mathfrak { v } \psi ( t )$ ; confidence 0.087
+
73. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120190/e120190160.png ; $W ^ { + } ( h _ { 1 } , h _ { 2 } , p )$ ; confidence 0.999
  
−
74. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230175.png ; $\sigma ^ { 2 k ^ { * } } [ E ( L ) ( Z ^ { 2 k } ) ] = \sigma ^ { k + 1 ^ { * } } [ \Omega ( d L \Delta ) ( Z ^ { k + 1 } ) ]$ ; confidence 0.758
+
74. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120180/d12018068.png ; $L ^ { 4 } ( X , m )$ ; confidence 0.999
  
−
75. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130160/f13016044.png ; $\leq \operatorname { max } \{ \mu ( M , P ) + Kdim ( R / P ) : P \in j - \operatorname { Spec } ( R ) \}$ ; confidence 0.315
+
75. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004046.png ; $\rho ^ { \prime }$ ; confidence 0.999
  
−
76. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120140/f12014014.png ; $\frac { 1 } { \lambda } = \operatorname { sup } \frac { | D ( h ) - D ^ { * } ( h ) | } { D ( h ) + D ^ { * } ( h ) }$ ; confidence 0.998
+
76. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043390/g04339011.png ; $h \rightarrow \delta f ( x _ { 0 } , h )$ ; confidence 0.999
  
−
77. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130030/g130030109.png ; $\tau _ { \varepsilon } ( x ) = \frac { \varepsilon } { \pi } ( x ^ { 2 } + \varepsilon ^ { 2 } ) ^ { - 1 }$ ; confidence 0.795
+
77. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120090/l12009042.png ; $\Gamma ( T M )$ ; confidence 0.999
  
−
78. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g130060120.png ; $: = \{ B = [ b _ { i } , j ] : b _ { i , i } = a _ { i , i } , \text { and } r _ { i } ( B ) = r _ { i } ( A ) , 1 \leq i \leq n \}$ ; confidence 0.207
+
78. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010038.png ; $n = 6,7,8$ ; confidence 0.999
  
−
79. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130050/h13005041.png ; $\frac { d ^ { 2 } \psi } { d x ^ { 2 } } + [ \lambda \rho ( x , t ) - u ( x , t ) ] \psi = 0 , - \infty < x < \infty$ ; confidence 0.993
+
79. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055480/k0554805.png ; $\phi ( x , t )$ ; confidence 0.999
  
−
80. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090224.png ; $Y = \operatorname { Gal } ( M ( k ^ { \prime } ) / k _ { \infty } ^ { \prime } ) \otimes Z _ { p } [ \chi ]$ ; confidence 0.898
+
80. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120050/f12005053.png ; $f = T ^ { 2 } + T + \beta$ ; confidence 0.999
  
−
81. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090223.png ; $X = \operatorname { Gal } ( L ( k ^ { \prime } ) / k _ { \infty } ^ { \prime } ) \otimes Z _ { p } [ \chi ]$ ; confidence 0.772
+
81. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014120/a01412076.png ; $n ( n - 1 ) / 2$ ; confidence 0.999
  
−
82. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010023.png ; $\approx ( 2 \pi ) ^ { - n } \int _ { R ^ { n } \times R ^ { n } } [ p ^ { 2 } + V ( x ) ] _ { - } ^ { \gamma } d p d x =$ ; confidence 0.680
+
82. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020740/c020740261.png ; $\alpha = \beta$ ; confidence 0.999
  
−
83. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130100/l13010033.png ; $f _ { s l } ( x ) : = - \frac { 1 } { 4 \pi } \int _ { S ^ { 1 } } \hat { f } _ { p p } ( \alpha , \alpha x ) d \alpha$ ; confidence 0.254
+
83. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040490/f04049045.png ; $F = \sigma _ { 2 } ^ { 2 } s _ { 1 } ^ { 2 } / \sigma _ { 1 } ^ { 2 } s _ { 2 } ^ { 2 }$ ; confidence 0.999
  
−
84. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120070/m12007062.png ; $m ( P ) > c _ { 1 } ( \operatorname { log } \operatorname { log } d / \operatorname { log } d ) ^ { 3 }$ ; confidence 0.987
+
84. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130130/z13013042.png ; $z = \operatorname { exp } ( i \theta _ { 0 } )$ ; confidence 0.999
  
−
85. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m13011037.png ; $\frac { \partial \phi } { \partial t } = ( \frac { \partial \phi ( x , t ) } { \partial t } ) | _ { x }$ ; confidence 0.960
+
85. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060040/l06004010.png ; $f _ { k + 1 } ( z )$ ; confidence 0.999
  
−
86. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015065.png ; $\frac { 1 } { \beta _ { p } ( \alpha , b ) } | U | ^ { \alpha - ( p + 1 ) / 2 } | I _ { p } - U | ^ { \phi - ( p + 1 ) / 2 }$ ; confidence 0.250
+
86. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020090.png ; $1 + \theta + \operatorname { log } \theta = 0$ ; confidence 0.999
  
−
87. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520310.png ; $A = \sum _ { m , n \geq 0 } \int K _ { q , m } ( x _ { 1 } , \ldots , x _ { n } ; y _ { 1 } , \ldots , y _ { m } ) \times$ ; confidence 0.178
+
87. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130070/w13007027.png ; $( \alpha _ { k } | \beta _ { l } ) = 0$ ; confidence 0.999
  
−
88. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001020.png ; $v ( x , \alpha , k ) = \frac { e ^ { i k r } } { r } A ( \alpha ^ { \prime } , \alpha , k ) + o ( \frac { 1 } { r } )$ ; confidence 0.871
+
88. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031030.png ; $( n - 1 - 2 \delta ) / 2 n < 1 / p < ( n + 1 + 2 \delta ) / 2 n$ ; confidence 0.999
  
−
89. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068170/o0681706.png ; $E e ^ { i t \omega ^ { 2 } } = \prod _ { k = 1 } ^ { \infty } ( 1 - \frac { 2 i t } { \pi ^ { 2 } k ^ { 2 } } ) ^ { - 1 / 2 }$ ; confidence 0.848
+
89. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120210/e12021031.png ; $| z | \neq 1$ ; confidence 0.999
  
−
90. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p12017013.png ; $\operatorname { ker } \delta _ { A , B } \subseteq \operatorname { ker } \delta _ { A , B } ^ { * }$ ; confidence 0.231
+
90. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g130060124.png ; $\sigma ( \Omega ( A ) )$ ; confidence 0.999
  
−
91. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007068.png ; $( f , g ) : = ( \sum _ { j = 1 } ^ { J } K ( x , y _ { j } ) c _ { j } , \sum _ { m = 1 } ^ { M } K ( x , z _ { m } ) \beta _ { m } ) =$ ; confidence 0.871
+
91. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130070/f1300707.png ; $F ( 2 , m )$ ; confidence 0.999
  
−
92. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130110/s13011026.png ; $\partial _ { n } \ldots \partial _ { 1 } \mathfrak { S } _ { w _ { n + 1 } } = \mathfrak { S } _ { w _ { n } }$ ; confidence 0.260
+
92. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e12006066.png ; $[ \Gamma , [ \Gamma , \Gamma ] ] = 0$ ; confidence 0.999
  
−
93. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130110/s1301104.png ; $H ^ { * } ( F _ { n } , Z ) \simeq Z [ x _ { 1 } , \dots , x _ { n } ] / Z ^ { + } [ x _ { 1 } , \dots , x _ { n } ] ^ { S _ { n } }$ ; confidence 0.353
+
93. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120220/s12022062.png ; $\operatorname { det } ( \Delta )$ ; confidence 0.999
  
−
94. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120050/s1200507.png ; $S _ { n + 1 } ( z ) = \frac { 1 } { z } \frac { S _ { n } ( z ) - S _ { n } ( 0 ) } { 1 - S _ { n } ( 0 ) S _ { n } ( z ) } , n \geq 0$ ; confidence 0.660
+
94. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150149.png ; $p p _ { i } + ( 1 - p ) ( 1 - p _ { i } )$ ; confidence 0.999
  
−
95. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130410/s13041041.png ; $\sum _ { j = n - k } ^ { n + 1 } b _ { n , j } P _ { j } ( x ) = \sum _ { j = n - k } ^ { n + 1 } \beta _ { n + 1 , j } Q _ { j } ( x )$ ; confidence 0.708
+
95. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130130/d13013054.png ; $A ^ { \pm } = \frac { n } { 2 } ( \pm 1 - \operatorname { cos } \theta ) d \phi$ ; confidence 0.999
  
−
96. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064036.png ; $G ( \alpha ) = \operatorname { exp } ( [ \operatorname { log } \operatorname { det } a ] _ { 0 } )$ ; confidence 0.685
+
96. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120200/b12020015.png ; $\theta H ^ { 2 } = \{ \theta ( z ) f ( z ) : f \in H ^ { 2 } \}$ ; confidence 0.999
  
−
97. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v12002035.png ; $f ^ { * } : \overline { H } \square ^ { * } ( Y , G ) \rightarrow \overline { H } \square ^ { * } ( X , G )$ ; confidence 0.481
+
97. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026042.png ; $\phi : [ 0,1 ] \rightarrow ( L ^ { 2 } )$ ; confidence 0.999
  
−
98. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020133.png ; $\Lambda ( F ) = \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \operatorname { tr } ( r * n \circ t * n ^ { - 1 } )$ ; confidence 0.358
+
98. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005067.png ; $\phi = \phi ^ { k }$ ; confidence 0.999
  
−
99. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v12002043.png ; $f ^ { * } : \overline { H } \square ^ { q } ( Y , G ) \rightarrow \overline { H } \square ^ { q } ( X , G )$ ; confidence 0.481
+
99. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046010/h04601066.png ; $\tau ( W , M _ { 0 } )$ ; confidence 0.999
  
−
100. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090259.png ; $\mathfrak { B } = \{ e _ { \pm } \alpha , h _ { \beta } : \alpha \in \Phi ^ { + } , \beta \in \Sigma \}$ ; confidence 0.381
+
100. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b130200196.png ; $\epsilon ( s ) = 0$ ; confidence 0.999
  
−
101. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011021.png ; $= | t | ^ { - n } \int \int e ^ { - 2 i \pi t ^ { - 1 } y \cdot \eta } _ { \alpha ( x + y , \xi + \eta ) d y d \eta }$ ; confidence 0.344
+
101. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510112.png ; $\gamma ( u ) = \gamma ( v )$ ; confidence 0.999
  
−
102. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008060.png ; $\frac { \Omega _ { x } } { \partial T _ { m } } = \frac { \partial \Omega _ { m } } { \partial T _ { N } }$ ; confidence 0.071
+
102. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120170/s12017015.png ; $F ( A , d )$ ; confidence 0.999
  
−
103. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001057.png ; $= \frac { - 4 z } { z + 2 } + \frac { 4 z } { ( z + 2 ) ^ { 2 } } - \frac { 3 z } { ( z + 2 ) ^ { 3 } } + \frac { 4 z } { z + 3 }$ ; confidence 0.999
+
103. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005022.png ; $U ( t , r ) U ( r , s ) = U ( t , s )$ ; confidence 0.999
  
−
104. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z130110144.png ; $\mu _ { N } \rightarrow \infty \quad \text { but } \frac { \mu _ { \aleph } } { n } \rightarrow 0$ ; confidence 0.229
+
104. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120060/w12006013.png ; $T _ { A } f ( \varphi ) ( g ) = \varphi ( g \circ f )$ ; confidence 0.999
  
−
105. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040337.png ; $\operatorname { tg } E ( \lambda x _ { 0 } , \ldots , x _ { x } - 1 , \lambda y 0 , \ldots , y _ { n } - 1 )$ ; confidence 0.167
+
105. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130070/h13007052.png ; $D + r D$ ; confidence 0.999
  
−
106. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050224.png ; $\sum _ { n \leq x } G ( n ) = A _ { G } x ^ { \delta } + O ( x ^ { \eta } ) \text { as } x \rightarrow \infty$ ; confidence 0.597
+
106. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130070/f13007030.png ; $n = 4,5,6,8,12$ ; confidence 0.999
  
−
107. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120110/a12011017.png ; $A ( i , 0 ) = A ( i - 1,1 ) \text { for } i \geq 1 , A ( i , n ) = A ( i - 1 , A ( i , n - 1 ) ) \text { for } i \geq 1 , n$ ; confidence 0.921
+
107. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130120/h1301207.png ; $d ( h ( x y ) , h ( x ) h ( y ) ) < \delta$ ; confidence 0.999
  
−
108. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110320/a11032011.png ; $+ h \sum _ { j = 1 } ^ { s } B _ { j } ( h T ) [ f ( t _ { m } + c _ { j } h , u _ { m + 1 } ^ { ( j ) } ) - T u _ { m j } ^ { ( j ) } + 1 ]$ ; confidence 0.083
+
108. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027068.png ; $\phi ( t ) \rightarrow \infty$ ; confidence 0.999
  
−
109. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018056.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { S _ { n + 1 } - S } { S _ { n } - S } = \lambda$ ; confidence 0.571
+
109. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120070/g12007019.png ; $m \equiv 1,2$ ; confidence 0.999
  
−
110. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180125.png ; $\exists b _ { i } : b = \{ b _ { 0 } , \dots , b _ { i } - 1 , b _ { i } , b _ { i } + 1 , \dots , b _ { p } - 1 \} \in R \}$ ; confidence 0.084
+
110. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007059.png ; $f \in B ( D _ { A } ( \alpha , \infty ) )$ ; confidence 0.999
  
−
111. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130290/a13029045.png ; $HF _ { * } ^ { \text { inst } } ( Y , P _ { Y } ) \cong HF _ { * } ^ { \text { symp } } ( M ( P ) , L _ { 0 } , L _ { 1 } )$ ; confidence 0.183
+
111. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031049.png ; $f = 0$ ; confidence 0.999
  
−
112. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120100/b12010039.png ; $= F _ { N } ( X _ { 1 } ( - t , x _ { 1 } , \ldots , x _ { N } ) , \ldots , X _ { N } ( - t , x _ { 1 } , \ldots , x _ { N } ) )$ ; confidence 0.275
+
112. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008051.png ; $\frac { d ^ { 2 } u } { d t ^ { 2 } } + A ( t ) u = f ( t ) , t \in [ 0 , T ]$ ; confidence 0.999
  
−
113. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110660/b11066032.png ; $H f ( x ) = \operatorname { lim } _ { \epsilon } \lfloor 0 \int _ { | t | > \epsilon } f ( x - t ) / t d t$ ; confidence 0.520
+
113. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120060/b12006011.png ; $\frac { \partial ^ { 2 } w } { \partial z \partial z } + \epsilon \frac { n ( n + 1 ) } { ( 1 + \epsilon z z ) ^ { 2 } } w = 0$ ; confidence 0.999
  
−
114. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430173.png ; $\Delta f = 1 \bigotimes f + x \bigotimes \partial _ { q , x } f + y \otimes \partial _ { q , y } f +$ ; confidence 0.239
+
114. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016033.png ; $( q \times q )$ ; confidence 0.999
  
−
115. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c120010162.png ; $f ( z ) = \sum _ { k = 1 } ^ { \infty } \frac { c _ { k } } { ( 1 + \langle z , \alpha _ { k } \rangle ) ^ { n } }$ ; confidence 0.698
+
115. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120510/b12051090.png ; $d = H _ { 0 } ^ { - 1 } d$ ; confidence 0.999
  
−
116. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023096.png ; $P = ( \frac { u _ { i } u _ { j } ^ { * } - v _ { i } v _ { j } ^ { * } } { 1 - f _ { i } f _ { j } ^ { * } } ) _ { i , j = 0 } ^ { n - 1 }$ ; confidence 0.936
+
116. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058970/l05897018.png ; $0 < \rho < 1$ ; confidence 0.999
  
−
117. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003056.png ; $\operatorname { Eis } ( \omega ) = \sum _ { \gamma \in \Gamma / \Gamma _ { P } } \gamma \omega$ ; confidence 0.810
+
117. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o130010156.png ; $\theta , \theta ^ { \prime } \in M$ ; confidence 0.999
  
−
118. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230143.png ; $A ( \sigma ) = \int _ { M } L \circ \sigma ^ { k } \Delta = \int _ { M } \sigma ^ { k ^ { * } } ( L \Delta )$ ; confidence 0.612
+
118. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031036.png ; $( n - 1 - 2 \delta ) / 2 n < 1 / p < ( n - 1 + 2 \delta ) / 2 n$ ; confidence 0.999
  
−
119. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120040/f1200407.png ; $f ^ { c ( \varphi ) } ( w ) = \operatorname { sup } _ { x \in X } \{ \varphi ( x , w ) - f ( x ) \} ( w \in W )$ ; confidence 0.324
+
119. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010047.png ; $R ( I + A ) = X$ ; confidence 0.999
  
−
120. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f1202304.png ; $[ . , ] : \Omega ^ { k } ( M ; T M ) \times \Omega ^ { l } ( M ; T M ) \rightarrow \Omega ^ { k + l } ( M ; T M )$ ; confidence 0.407
+
120. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046080/h0460806.png ; $H ^ { T }$ ; confidence 0.999
  
−
121. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120010/g12001013.png ; $\int _ { - \infty } ^ { \infty } ( G _ { b } ^ { \alpha } f ) ( \omega ) d \dot { b } = \hat { f } ( \omega )$ ; confidence 0.739
+
121. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t09408025.png ; $\Omega ( X ; A , B )$ ; confidence 0.999
  
−
122. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g120040173.png ; $\sum _ { \alpha \in Z ^ { n } } \frac { \alpha _ { \alpha } } { ( | \alpha | ! ) ^ { s - 1 } } x ^ { \alpha }$ ; confidence 0.157
+
122. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110300/a11030026.png ; $( T V , d )$ ; confidence 0.999
  
−
123. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120120/h120120159.png ; $T ( \nabla ) _ { \infty } : ( T ( H ( Y ) ) , \partial _ { \infty } ) \rightarrow \overline { B } ( Y )$ ; confidence 0.991
+
123. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110410/c11041059.png ; $0 , \infty ]$ ; confidence 0.999
  
−
124. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120010/i12001020.png ; $\operatorname { sup } _ { x \neq y \in \Omega } | u ( x ) - u ( y ) | ( \sigma | x - y | ) ^ { - 1 } < \infty$ ; confidence 0.972
+
124. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130040/r13004058.png ; $\frac { 1 } { \mu _ { 2 } ( \Omega ) } + \frac { 1 } { \mu _ { 3 } ( \Omega ) } \geq \frac { 2 A } { \pi p _ { 1 } ^ { 2 } }$ ; confidence 0.999
  
−
125. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008079.png ; $Z = \sum _ { S _ { 1 } = \pm 1 } | s _ { 1 } | P ^ { N } | S _ { 1 } \rangle = \lambda _ { + } ^ { N } + \lambda ^ { N }$ ; confidence 0.081
+
125. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f120150177.png ; $\Phi _ { + } ( X , Y )$ ; confidence 0.999
  
−
126. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j12002096.png ; $E [ X _ { 0 } ] + E [ X _ { \infty } \operatorname { log } + \frac { X _ { \infty } } { E [ X _ { 0 } ] } ] \leq$ ; confidence 0.435
+
126. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120040/k12004034.png ; $11257$ ; confidence 0.999
  
−
127. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020204.png ; $\int _ { I } | \varphi - \varphi _ { I } | ^ { 2 } \frac { d \vartheta } { 2 \pi } \leq c _ { 1 } ^ { 2 } | I |$ ; confidence 0.284
+
127. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009046.png ; $\sqrt { n ! }$ ; confidence 0.999
  
−
128. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120080/k12008046.png ; $S _ { r } = \{ ( v _ { 0 } , \dots , v _ { r } ) \in R ^ { r + 1 } : v _ { j } \geq 0 , \sum _ { j = 0 } ^ { r } v _ { j } = 1 \}$ ; confidence 0.419
+
128. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110010/f11001052.png ; $y \in A ^ { + }$ ; confidence 0.999
  
−
129. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004075.png ; $\hat { a } _ { i } ^ { + } = u _ { i } ^ { n } + \frac { \Delta t } { \Delta x } ( f _ { i } ^ { n } - f _ { i + 1 } ^ { n } )$ ; confidence 0.323
+
129. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120030/c12003027.png ; $g ( t ) = f ( t , u ( t ) )$ ; confidence 0.999
  
−
130. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130010/l13001060.png ; $C _ { 1 } \operatorname { ln } ^ { n } N \leq \| S _ { N B } \| \leq C _ { 2 } \operatorname { ln } ^ { n } N$ ; confidence 0.826
+
130. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096030/v0960305.png ; $z ( t ) = \int _ { 0 } ^ { t } x ( \tau ) d \tau$ ; confidence 0.999
  
−
131. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006079.png ; $\langle \lambda | f ( z ) ) = \frac { 1 } { \lambda - z } \langle \lambda | V \phi ) ( \phi , f ( z ) )$ ; confidence 0.836
+
131. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130050/n13005031.png ; $( s , r , \mu )$ ; confidence 0.999
  
−
132. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016023.png ; $A X B + C \sim E _ { q , n } ( A M B + C , ( A \Sigma A ^ { \prime } ) \otimes ( B ^ { \prime } \Phi B ) , \psi )$ ; confidence 0.628
+
132. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130030/n13003040.png ; $w ( x , y ) = 0$ ; confidence 0.999
  
−
133. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120240/m1202409.png ; $\psi [ 1 ] = \psi - \frac { \varphi \Omega ( \varphi , \psi ) } { \Omega ( \varphi , \varphi ) }$ ; confidence 0.985
+
133. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005050.png ; $U ( t , s )$ ; confidence 0.999
  
−
134. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120050/o12005082.png ; $\operatorname { sup } _ { \lambda > 0 } \varphi ^ { \prime } ( a u ) / \varphi ^ { \prime } ( u ) < 1$ ; confidence 0.083
+
134. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007028.png ; $= ( p + p ^ { \prime } , q + q ^ { \prime } , t + t ^ { \prime } + \frac { 1 } { 2 } ( p q ^ { \prime } - q p ^ { \prime } ) )$ ; confidence 0.999
  
−
135. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004074.png ; $s _ { \lambda } = \frac { 1 } { n ! } \sum _ { | \mu | = n } k _ { \mu } \chi _ { \mu } ^ { \lambda } p _ { \mu }$ ; confidence 0.708
+
135. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130250/b13025065.png ; $\frac { 1 } { \operatorname { sin } ^ { 2 } \omega } = \frac { 1 } { \operatorname { sin } ^ { 2 } \alpha } + \frac { 1 } { \operatorname { sin } ^ { 2 } \beta } + \frac { 1 } { \operatorname { sin } ^ { 2 } \gamma }$ ; confidence 0.999
  
−
136. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510150.png ; $D = \{ u \in V : \sigma ( u ) = \infty ( K ) , 0 \notin K \} , N = \{ u \in V : 0 < \sigma ( u ) < \infty \} U$ ; confidence 0.790
+
136. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010220/a0102206.png ; $2 p$ ; confidence 0.999
  
−
137. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s13062016.png ; $( \operatorname { cos } \alpha ) y ( 0 ) + ( \operatorname { sin } \alpha ) y ^ { \prime } ( 0 ) = 0$ ; confidence 0.820
+
137. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130130/r1301307.png ; $\sigma \subset \sigma ( A )$ ; confidence 0.999
  
−
138. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s130620162.png ; $y ( x , \lambda ) = \frac { \operatorname { sin } x } { 1 + ( 2 x - \operatorname { sin } 2 x ) ^ { 2 } }$ ; confidence 0.997
+
138. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032780/d03278014.png ; $G \subset R ^ { 2 }$ ; confidence 0.999
  
−
139. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s12032016.png ; $[ x , y ] = - ( - 1 ) ^ { p ( x ) p ( y ) } [ y , x ] , [ x , [ y , z ] ] = [ [ x , y ] , z ] + ( - 1 ) ^ { p ( x ) p ( y ) } [ y , [ x , z ] ]$ ; confidence 0.989
+
139. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a120050125.png ; $A ( t , u )$ ; confidence 0.999
  
−
140. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065054.png ; $S _ { k + 1 } ( z ) = z ^ { - 1 } \frac { S _ { k } ( z ) - S _ { k } ( 0 ) } { 1 - \overline { S } _ { k } ( 0 ) S _ { k } ( z ) }$ ; confidence 0.545
+
140. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g120040179.png ; $\sigma = 1 / ( s - 1 ) > 0$ ; confidence 0.999
  
−
141. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006011.png ; $= \frac { 3 } { 5 } \gamma \int _ { R ^ { 3 } } \rho ( x ) ^ { 5 / 3 } d x - \int _ { R ^ { 3 } } V ( x ) \rho ( x ) d x +$ ; confidence 0.644
+
141. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004018.png ; $M = \Gamma$ ; confidence 0.999
  
−
142. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013030.png ; $= \oint _ { z = \infty } \tau _ { n + 1 } ( x , y - [ z ] ) \tau _ { m } ( x ^ { \prime } , y ^ { \prime } + [ z ] ) x$ ; confidence 0.883
+
142. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120040/h12004025.png ; $\eta < \lambda$ ; confidence 0.999
  
−
143. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020063.png ; $R _ { n } = \operatorname { min } _ { z _ { j } } \operatorname { max } _ { k = 1 , \ldots , n } | s _ { k } |$ ; confidence 0.225
+
143. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120210/s1202108.png ; $E ( \lambda , D _ { Y } )$ ; confidence 0.999
  
−
144. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130040/w13004038.png ; $N = \frac { 1 } { | g | ^ { 2 } + 1 } ( 2 \operatorname { Re } g , 2 \operatorname { Im } g , | g | ^ { 2 } - 1 )$ ; confidence 0.511
+
144. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013080.png ; $p \in ( 1 / 2,3 / 2 )$ ; confidence 0.999
  
−
145. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110221.png ; $\operatorname { sup } _ { X \in \Phi } \| \alpha ^ { ( k ) } ( X ) \| _ { G _ { X } } m ( X ) ^ { - 1 } < \infty$ ; confidence 0.564
+
145. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054024.png ; $\pi : H \rightarrow G$ ; confidence 0.999
  
−
146. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011059.png ; $A ( u , v ) ( \xi , x ) = \int u ( z - \frac { x } { 2 } ) \nabla ( z + \frac { x } { 2 } ) e ^ { - 2 i \pi z . \xi } d z$ ; confidence 0.810
+
146. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l1300805.png ; $| \omega | \geq 1$ ; confidence 0.999
  
−
147. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009058.png ; $\| \varphi \| _ { L ^ { 2 } ( \mu ) } ^ { 2 } = \sum _ { n = 0 } ^ { \infty } n ! | f _ { n } | _ { H } ^ { 2 } \otimes$ ; confidence 0.404
+
147. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d13008016.png ; $\xi \in \partial \Delta$ ; confidence 0.999
  
−
148. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001045.png ; $K _ { i } = \operatorname { lim } _ { z \rightarrow z _ { i } } [ ( z - z _ { i } ) \frac { h ( z ) } { g ( z ) } ]$ ; confidence 0.946
+
148. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d12028093.png ; $A ( U ^ { \prime } )$ ; confidence 0.999
  
−
149. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130030/z13003066.png ; $\hat { f } ( - 2 \pi w ) = \frac { 1 } { \sqrt { 2 \pi } } \int _ { 0 } ^ { 1 } e ^ { - 2 \pi i w t } ( Z f ) ( t , w ) d t$ ; confidence 0.757
+
149. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093560/t09356039.png ; $s ( x , y ) = \phi ( y ^ { * } x )$ ; confidence 0.999
  
−
150. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011033.png ; $G _ { n } ( f ( k , n ) ) = \operatorname { max } \{ k ^ { \prime } : f _ { ( k ^ { \prime } , n ) } = f ( k , n ) \}$ ; confidence 0.516
+
150. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200206.png ; $( r ) \geq$ ; confidence 0.999
  
−
151. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040541.png ; $h ( \psi ^ { i } ) \in C ( \{ h ( \varphi _ { 0 } ^ { i } ) , \ldots , h ( \varphi _ { n _ { i } - 1 } ^ { i } ) \} )$ ; confidence 0.325
+
151. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n06752072.png ; $K = F [ \lambda ]$ ; confidence 0.999
  
−
152. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005053.png ; $| \frac { \partial } { \partial t } U ( t , s ) \| \leq \frac { C } { t - s } , \quad 0 \leq s < t \leq T$ ; confidence 0.766
+
152. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008045.png ; $\alpha ( s ) = \frac { f ( L ( s ) ) } { g ( L ( s ) ; m ( s ) , s ) } = \frac { f ( R ( s ) ) } { g ( R ( s ) ; m ( s ) , s ) }$ ; confidence 0.999
  
−
153. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008045.png ; $\alpha ( s ) = \frac { f ( L ( s ) ) } { g ( L ( s ) ; m ( s ) , s ) } = \frac { f ( R ( s ) ) } { g ( R ( s ) ; m ( s ) , s ) }$ ; confidence 0.999
+
153. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110280/a11028056.png ; $\chi ( G )$ ; confidence 0.999
  
−
154. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018018.png ; $L ( \tau ) = \langle Fm _ { \tau } , Mod _ { \tau } , F _ { \tau } , mng _ { \tau } , t _ { \tau } \rangle$ ; confidence 0.140
+
154. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m13011024.png ; $\phi = \phi ( x , t )$ ; confidence 0.999
  
−
155. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130200/a13020013.png ; $\langle x y z \rangle - \langle z y x \rangle = \langle z x y \rangle - \langle x z y \rangle$ ; confidence 0.728
+
155. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006028.png ; $- k ^ { 2 } j$ ; confidence 0.999
  
−
156. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012080.png ; $\operatorname { lim } _ { \varepsilon \rightarrow 0 } \| f V _ { \varepsilon } \| _ { A } * = 0$ ; confidence 0.931
+
156. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120050/f12005017.png ; $\operatorname { gcd } ( n , p ) \neq 1$ ; confidence 0.999
  
−
157. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130250/b13025014.png ; $\angle \Omega ^ { \prime } B A = \angle \Omega ^ { \prime } C B = \angle \Omega ^ { \prime } A C$ ; confidence 0.997
+
157. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130220/m1302201.png ; $196884 = 196883 + 1$ ; confidence 0.999
  
−
158. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b13029058.png ; $( \alpha _ { 1 } , \dots , a _ { i - 1 } ) : \alpha _ { i } = ( \alpha _ { 1 } , \dots , \alpha _ { i - 1 } ) : m$ ; confidence 0.141
+
158. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023045.png ; $p + q = r$ ; confidence 0.999
  
−
159. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130050/c13005040.png ; $\operatorname { Aut } ( G , S ) = \{ \sigma \in \operatorname { Aut } ( G ) : S ^ { \sigma } = S \}$ ; confidence 0.331
+
159. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230133.png ; $R _ { 12 } = I = R _ { 21 }$ ; confidence 0.999
  
−
160. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007026.png ; $\left( \begin{array} { c } { m + 2 } \\ { 2 } \end{array} \right) = \frac { ( m + 2 ) ( m + 1 ) } { 2 }$ ; confidence 0.990
+
160. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006026.png ; $[ L ( x ) , U ( x ) ]$ ; confidence 0.999
  
−
161. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180180.png ; $g ^ { - 1 } \{ p , q , r , s \} = g ^ { - 1 } \{ p , q \} g ^ { - 1 } \{ r , s \} = g ^ { - 1 } \{ r , s \} g ^ { - 1 } \{ p , q \}$ ; confidence 0.996
+
161. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120150/d12015037.png ; $( v , n ) > 1$ ; confidence 0.999
  
−
162. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120310/c12031054.png ; $e _ { \lambda } ^ { ran } ( F _ { d } ) = \operatorname { inf } _ { Q _ { n } } e ^ { ran } ( Q _ { n } , F _ { d } )$ ; confidence 0.160
+
162. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025830/c02583050.png ; $m _ { T } ( T ) = 0$ ; confidence 0.999
  
−
163. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002046.png ; $= \operatorname { min } _ { k \in P } c ^ { T } x ^ { ( k ) } + u _ { 1 } ^ { T } ( A _ { 1 } x ^ { ( k ) } - b _ { 1 } )$ ; confidence 0.488
+
163. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120110/a12011032.png ; $T ( 2 , n )$ ; confidence 0.999
  
−
164. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120110/d12011033.png ; $\operatorname { lim } _ { i \rightarrow \infty } \sum _ { j = 1 } ^ { \infty } x _ { i j } x _ { j } = 0$ ; confidence 0.142
+
164. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016022.png ; $B ( n \times m )$ ; confidence 0.999
  
−
165. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120160/d12016060.png ; $\| f \| \neq \operatorname { dist } ( f , C ( S ) \otimes \pi _ { k } ( T ) + \pi ( S ) \otimes C ( T ) )$ ; confidence 0.736
+
165. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023029.png ; $\Omega = \{ \zeta : \psi ( \zeta ) < 0 \}$ ; confidence 0.999
  
−
166. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120160/e12016046.png ; $\partial _ { r } ( r J ^ { - 1 } \partial _ { r } J ) + \partial _ { z } ( r J ^ { - 1 } \partial _ { z } J ) = 0$ ; confidence 0.648
+
166. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m13018051.png ; $x \geq y > 0$ ; confidence 0.999
  
−
167. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e12026012.png ; $L _ { \mu } ( \theta ) = \int _ { E } \operatorname { exp } \langle \theta , x \rangle \mu ( d x )$ ; confidence 0.740
+
167. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086520/s086520150.png ; $\phi \in H ^ { \infty }$ ; confidence 0.999
  
−
168. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f120110200.png ; $C _ { \delta } = \{ z : | \operatorname { Im } z | < \delta ( | \operatorname { Re } _ { z | } + 1 ) \}$ ; confidence 0.519
+
168. https://www.encyclopediaofmath.org/legacyimages/a/a013/a013000/a01300017.png ; $R ( z )$ ; confidence 0.999
  
−
169. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021069.png ; $= \frac { ( n _ { 1 } + l ) ! } { ! ! } ( \operatorname { log } z ) ^ { l } z ^ { \lambda _ { 2 } } + \ldots$ ; confidence 0.665
+
169. https://www.encyclopediaofmath.org/legacyimages/v/v110/v110060/v1100603.png ; $\nu \in ( - 1,1 / 2 )$ ; confidence 0.999
  
−
170. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f12023033.png ; $D ( \varphi \wedge \psi ) = D ( \varphi ) \wedge \psi + ( - 1 ) ^ { k l } \varphi \wedge D ( \psi )$ ; confidence 0.995
+
170. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p130070123.png ; $\operatorname { log } \operatorname { tanh } C ( z , w ) \leq W ( z , w ) \leq$ ; confidence 0.999
  
−
171. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g13004046.png ; $\operatorname { limsup } _ { r \rightarrow 0 } \frac { H ^ { m } ( E \cap B ( x , r ) ) } { r ^ { m } } > 0$ ; confidence 0.556
+
171. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120020/h120020158.png ; $| \nu ( t ) - \nu ( - t ) | \leq 2$ ; confidence 0.999
  
−
172. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120020/h12002085.png ; $s _ { j } ( T ) = \operatorname { inf } \{ \| T - R \| : \operatorname { rank } R \leq j \} , j \geq 0$ ; confidence 0.936
+
172. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011910/a01191025.png ; $A \cap B$ ; confidence 0.999
  
−
173. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002022.png ; $S _ { k } = \left( \begin{array} { c } { n } \\ { k } \end{array} \right) \frac { ( n - k ) ! } { n ! }$ ; confidence 0.636
+
173. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e120070133.png ; $H ^ { 1 }$ ; confidence 0.999
  
−
174. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090145.png ; $\lambda _ { p } ( k _ { \infty } / k ) = \mu _ { p } ( k _ { \infty } / k ) = \nu _ { p } ( k _ { \infty } / k ) = 0$ ; confidence 0.839
+
174. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008023.png ; $F ( T , H )$ ; confidence 0.999
  
−
175. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020216.png ; $\alpha \leq \frac { 1 } { | l _ { j } | } \int _ { I _ { j } } | u ( \vartheta ) | d \vartheta < 2 \alpha$ ; confidence 0.721
+
175. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003023.png ; $\int \Psi ( x , T ( G ) ) d G ( x ) = 0$ ; confidence 0.999
  
−
176. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007066.png ; $\angle \operatorname { lim } _ { z \rightarrow \omega } F ( z ) = \eta \in \partial \Delta$ ; confidence 0.934
+
176. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120170/s12017010.png ; $A \in X$ ; confidence 0.999
  
−
177. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130010/k1300107.png ; $\langle L _ { + } \rangle = A \langle L _ { 0 } \rangle + A ^ { - 1 } \langle L _ { \infty } \rangle$ ; confidence 0.405
+
177. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025830/c02583015.png ; $T = T _ { 0 } \otimes T _ { 1 }$ ; confidence 0.999
  
−
178. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130010/k13001035.png ; $f ( \vec { D } ( A ) ) = ( - A ^ { 3 } ) ^ { - \operatorname { Tait } ( \vec { D } ) } \langle D \rangle$ ; confidence 0.497
+
178. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130230/a13023047.png ; $U + V$ ; confidence 0.999
  
−
179. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010050.png ; $| e _ { 1 } | ^ { \gamma } \leq L _ { \gamma , n } ^ { 1 } \int _ { R ^ { n } } V _ { - } ( x ) ^ { \gamma + n / 2 } d x$ ; confidence 0.311
+
179. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a1200602.png ; $u ( x , t ) \in P ( x ) , \quad ( x , t ) \in \partial \Omega \times [ 0 , T ]$ ; confidence 0.999
  
−
180. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003039.png ; $V ( T , F _ { \theta } ) = \int \operatorname { IF } ( x ; T , F _ { \theta } ) ^ { 2 } d F _ { \theta } ( x )$ ; confidence 0.919
+
180. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050222.png ; $\eta < \delta$ ; confidence 0.999
  
−
181. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m13011062.png ; $v _ { i } = - \frac { D _ { x _ { i } } } { D t } = ( \frac { \partial x _ { i } } { \partial t } ) | _ { x _ { k } 0 }$ ; confidence 0.154
+
181. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130280/b13028054.png ; $B ( 2 n )$ ; confidence 0.999
  
−
182. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140147.png ; $d \zeta / \zeta = d \zeta _ { 2 } / \zeta _ { 2 } \wedge \ldots \wedge d \zeta _ { n } / \zeta _ { n }$ ; confidence 0.740
+
182. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c130070174.png ; $2 \delta ( P )$ ; confidence 0.999
  
−
183. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m13018020.png ; $g ( x ) = \sum _ { y : y \geq x } f ( y ) \Leftrightarrow f ( x ) = \sum _ { y : y \geq x } \mu ( x , y ) g ( y )$ ; confidence 0.747
+
183. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017057.png ; $\int _ { - \pi } ^ { \pi } \operatorname { log } \operatorname { det } f ( \lambda ) d \lambda > - \infty$ ; confidence 0.999
  
−
184. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m13018019.png ; $g ( x ) = \sum _ { y : y \leq x } f ( y ) \Leftrightarrow f ( x ) = \sum _ { y : y \leq x } g ( y ) \mu ( y , x )$ ; confidence 0.855
+
184. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r13008034.png ; $R ( K ) = H$ ; confidence 0.999
  
−
185. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o130010132.png ; $\operatorname { sup } _ { \alpha ^ { \prime } , \alpha \in S ^ { 2 } } | A _ { 1 } - A _ { 2 } | < \delta$ ; confidence 0.959
+
185. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e120120118.png ; $\int f ( \theta , \phi ) d \phi$ ; confidence 0.999
  
−
186. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p13007024.png ; $M f = \operatorname { det } ( \frac { \partial ^ { 2 } f } { \partial z _ { i } \partial z _ { j } } )$ ; confidence 0.974
+
186. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031930/d031930178.png ; $\zeta = \xi + i \eta$ ; confidence 0.999
  
−
187. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007047.png ; $= c \sum _ { j = 1 } ^ { \infty } ( A \varphi _ { j } , \varphi _ { j } ) _ { 0 } = c \Lambda ^ { 2 } < \infty$ ; confidence 0.984
+
187. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110660/b11066024.png ; $p < \infty$ ; confidence 0.999
  
−
188. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070104.png ; $\| f \| _ { 1 } ^ { 2 } = \operatorname { lim } _ { n \rightarrow \infty } \| f _ { n } \| _ { 1 } ^ { 2 } =$ ; confidence 0.590
+
188. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021029.png ; $m \leq 40$ ; confidence 0.999
  
−
189. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r13008051.png ; $K _ { D } ( z , \zeta ) = \sum _ { j = 1 } ^ { \infty } \phi _ { j } ( z ) \overline { \phi _ { j } ( \zeta ) }$ ; confidence 0.978
+
189. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120100/f12010052.png ; $\tau ( n ) \neq 0$ ; confidence 0.999
  
−
190. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086020/s0860209.png ; $| \phi ( t _ { 1 } ) - \phi ( t _ { 2 } ) | \leq C | t _ { 1 } - t _ { 2 } | ^ { \alpha } , \quad 0 < \alpha \leq 1$ ; confidence 0.970
+
190. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120030/h1200308.png ; $\tau ( \varphi ) = 0$ ; confidence 0.999
  
−
191. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059042.png ; $F _ { R } = \frac { H _ { X } ^ { ( - n ) } H _ { n } ^ { ( - n + 3 ) } } { H _ { n } ^ { ( - n + 2 ) } H _ { n - 1 } ^ { ( - n + 1 ) } }$ ; confidence 0.057
+
191. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120500/b12050012.png ; $W ^ { + } : = \{ | W _ { t } | : t \geq 0 \}$ ; confidence 0.999
  
−
192. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130070/w13007010.png ; $\operatorname { ch } V = \sum _ { \mu \in h ^ { * } } ( \operatorname { dim } V _ { \mu } ) e ^ { \mu }$ ; confidence 0.357
+
192. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120310/a120310106.png ; $B ( K ) / M ( K ) = C ( S )$ ; confidence 0.999
  
−
193. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009078.png ; $\{ \varphi _ { n _ { 1 } , n _ { 2 } , \ldots } : n _ { j } \geq 0 , n _ { 1 } + n _ { 2 } + \ldots = n , n \geq 0 \}$ ; confidence 0.183
+
193. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130080/r13008055.png ; $f ( z , z _ { 0 } ) = 0$ ; confidence 0.999
  
−
194. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120040/y1200405.png ; $\operatorname { lim } _ { j \rightarrow \infty } \int _ { \Omega } \varphi ( x , f j ( x ) ) d x =$ ; confidence 0.690
+
194. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011370/a011370125.png ; $f \in A$ ; confidence 0.999
  
−
195. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130030/z13003067.png ; $f ( 2 \pi t ) = \frac { 1 } { \sqrt { 2 \pi } } \int _ { 0 } ^ { 1 } e ^ { - 2 \pi i x t } ( Z \hat { f } ) ( x , t ) d x$ ; confidence 0.805
+
195. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023110/c023110102.png ; $p A = 0$ ; confidence 0.999
  
−
196. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005087.png ; $| \prod _ { j = 1 } ^ { k } ( \lambda - A ( t _ { j } ) ) ^ { - 1 } \| _ { X } \leq M ( \lambda - \beta ) ^ { - k }$ ; confidence 0.936
+
196. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l13006019.png ; $m = p$ ; confidence 0.999
  
−
197. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a12006028.png ; $D ( A ) = \{ u \in [ H ^ { 1 } ( \Omega ] ^ { p } : u ( x ) \in P ( x ) \text { a.e. on } \partial \Omega \}$ ; confidence 0.643
+
197. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001055.png ; $x ( 3 ) = 10$ ; confidence 0.999
  
−
198. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060117.png ; $G ^ { \# } ( n ) \sim C Z _ { G } ( q ^ { - 1 } ) q ^ { n } n ^ { - \alpha } \text { asn } \rightarrow \infty$ ; confidence 0.776
+
198. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015024.png ; $f _ { X , Y } ( X , Y )$ ; confidence 0.999
  
−
199. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110320/a11032023.png ; $B _ { j } ( z ) = \sum _ { l = 0 } ^ { \rho _ { s + 1 } } R _ { l + 1 } ^ { ( s + 1 ) } ( z ) \lambda _ { l j } ^ { ( s + 1 ) }$ ; confidence 0.113
+
199. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e120070138.png ; $1 \leq h \leq t - 1$ ; confidence 0.999
  
−
200. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110020/b11002024.png ; $\operatorname { sup } _ { \alpha \in U } | b ( u , v ) | > 0 , \forall v \in V \backslash \{ 0 \} )$ ; confidence 0.321
+
200. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010061.png ; $\gamma < 1$ ; confidence 0.999
  
−
201. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120340/b12034018.png ; $\frac { 1 } { 3 \sqrt { n } } < K _ { n } < \frac { 2 \sqrt { \operatorname { log } n } } { \sqrt { n } }$ ; confidence 0.996
+
201. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010097.png ; $H = - \Delta + V ( x )$ ; confidence 0.999
  
−
202. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020086.png ; $\mathfrak { g } _ { \pm } = \oplus _ { \alpha \in \Delta _ { \pm } } \mathfrak { g } ^ { \alpha }$ ; confidence 0.871
+
202. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001070.png ; $\tau = ( \tau _ { 1 } , \tau _ { 2 } , \tau _ { 3 } ) \in R ^ { 3 }$ ; confidence 0.999
  
−
203. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026030.png ; $\sum _ { x \in f ^ { - 1 } ( y ) } \operatorname { sign } \operatorname { det } f ^ { \prime } ( x )$ ; confidence 0.975
+
203. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120010/y120010121.png ; $R = R _ { V }$ ; confidence 0.999
  
−
204. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c130160156.png ; $NC = \text { ASPACETIME } [ \operatorname { log } n , ( \operatorname { log } n ) ^ { O ( 1 ) } ]$ ; confidence 0.357
+
204. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022059.png ; $f ^ { 0 } ( x , \xi ) = M ( u ^ { 0 } ( x ) , \xi )$ ; confidence 0.999
  
−
205. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c130160189.png ; $L \subseteq NL \subseteq NC \subseteq P \subseteq NP \subseteq PH \subseteq PSPACE$ ; confidence 0.906
+
205. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057630/l05763020.png ; $f ( t ) \leq g ( t )$ ; confidence 0.999
  
−
206. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c120210114.png ; $\Lambda _ { n } ( \theta ) = \operatorname { log } ( d P _ { n , \theta _ { n } } / P _ { n , \theta } )$ ; confidence 0.827
+
206. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040152.png ; $X ^ { 1 / 2 } ( X ^ { \prime } ) ^ { 1 / 2 } = L _ { 2 }$ ; confidence 0.999
  
−
207. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020229.png ; $\overline { x } = \sum _ { k \in R ^ { \prime } } \overline { \mu } _ { k } \overline { x } ^ { ( k ) }$ ; confidence 0.152
+
207. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120020/f12002013.png ; $Q ( 0 ) = 1$ ; confidence 0.999
  
−
208. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120310/d1203109.png ; $f ( T ) = \frac { 1 } { 2 \pi i } \int _ { \partial U } f ( \lambda ) ( \lambda - T ) ^ { - 1 } d \lambda$ ; confidence 0.982
+
208. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a120160109.png ; $1,160$ ; confidence 0.999
  
−
209. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120100/e12010035.png ; $f ^ { em } = 0 = \operatorname { div } t ^ { em } f - \frac { \partial G ^ { em f } } { \partial t }$ ; confidence 0.071
+
209. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001058.png ; $x ( n ) = ( \frac { 3 } { 4 } n ^ { 2 } - \frac { 11 } { 4 } n - 4 ) ( - 2 ) ^ { n } + 4 ( - 3 ) ^ { n }$ ; confidence 0.999
  
−
210. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023034.png ; $A ( \sigma ) = \int _ { M } L ( \sigma ^ { 1 } ( x ) ) d x = \int _ { M } L ( x , y ( x ) , y ^ { \prime } ( x ) ) d x$ ; confidence 0.319
+
210. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120150/t12015040.png ; $\pi ^ { \prime } ( \eta )$ ; confidence 0.999
  
−
211. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f120110218.png ; $O ( e ^ { - \varepsilon | \operatorname { Re } \cdot Z | - H _ { L } } ( \operatorname { Re } z ) )$ ; confidence 0.118
+
211. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120190/f1201906.png ; $g \in G \backslash H$ ; confidence 0.999
  
−
212. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120010/g1200105.png ; $g _ { \alpha } ( t ) = \frac { 1 } { 2 \sqrt { \pi \alpha } } e ^ { - t ^ { 2 } / ( 4 \alpha ) } , \alpha > 0$ ; confidence 0.919
+
212. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050295.png ; $k > 1$ ; confidence 0.999
  
−
213. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g13006043.png ; $( \lambda - \alpha _ { j } , i ) x _ { i } = \sum _ { j = 1 \atop j \neq i } ^ { n } \alpha _ { i , j } x _ { j }$ ; confidence 0.086
+
213. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110160/f110160109.png ; $i < j$ ; confidence 0.999
  
−
214. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006088.png ; $g ( t ) : = - \frac { 2 } { \pi } \int _ { 0 } ^ { \infty } \delta ( k ) \operatorname { sin } ( k t ) d k$ ; confidence 0.791
+
214. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065072.png ; $\alpha , \beta \in \{ - 1 / 2,1 / 2 \}$ ; confidence 0.999
  
−
215. https://www.encyclopediaofmath.org/legacyimages/i/i053/i053030/i0530309.png ; $d f ( t , X _ { t } ) = [ f _ { t } ^ { \prime } ( t , X _ { t } ) + \alpha ( t ) f _ { X } ^ { \prime } ( t , X _ { t } ) +$ ; confidence 0.983
+
215. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008020.png ; $L ^ { 2 } ( \Omega )$ ; confidence 0.999
  
−
216. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130030/j13003030.png ; $[ \alpha \square b ^ { * } , x \square y ^ { * } ] = \{ a b x \} \square y ^ { * } - x \square \{ y a b \}$ ; confidence 0.748
+
216. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031770/d03177065.png ; $\mu \rightarrow 0$ ; confidence 0.999
  
−
217. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120010/j1200109.png ; $\operatorname { deg } F = \operatorname { max } _ { i } \operatorname { deg } F _ { i } \leq 2$ ; confidence 0.934
+
217. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011480/a01148096.png ; $k - 1$ ; confidence 0.999
  
−
218. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004066.png ; $P _ { \varphi } ( D _ { 1 } * D _ { 2 } ) ( v ) = P _ { \varphi } ( D _ { 1 } ) ( v ) P _ { \varphi } ( D _ { 2 } ) ( v )$ ; confidence 0.491
+
218. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120020/a12002020.png ; $f : X \rightarrow Z$ ; confidence 0.999
  
−
219. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j130040115.png ; $\frac { P _ { 2 } ( v , z ) - \frac { v ^ { - 1 } - v } { z } } { z ( ( \frac { v ^ { - 1 } - v } { z } ) ^ { 2 } - 1 ) } = - v$ ; confidence 0.463
+
219. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120080/l12008013.png ; $L ( u ) = g$ ; confidence 0.999
  
−
220. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120080/k12008067.png ; $\kappa _ { p } ( f ) = K _ { p } ( \operatorname { Re } ( f ) ) + i K _ { p } ( \operatorname { Im } ( f ) )$ ; confidence 0.943
+
220. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015071.png ; $\lambda _ { 1 } \neq \lambda _ { 2 }$ ; confidence 0.999
  
−
221. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120100/k12010055.png ; $\bigwedge _ { j = 1 } ^ { m } \frac { d z _ { j } - d z _ { j } ^ { \prime } } { z _ { j } - z _ { j } ^ { \prime } }$ ; confidence 0.632
+
221. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130040/w1300405.png ; $z = u + i v$ ; confidence 0.999
  
−
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
+
222. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130160/b13016078.png ; $C ( X , \tau )$ ; confidence 0.999
  
−
223. 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
+
223. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130090/a13009029.png ; $k + 1$ ; confidence 0.999
  
−
224. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840335.png ; $L ( \lambda ) = \lambda ^ { n } I + \lambda ^ { n - 1 } B _ { n - 1 } + \ldots + \lambda B _ { 1 } + B _ { 0 }$ ; confidence 0.904
+
224. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200126.png ; $0 < \delta _ { 1 } < \delta _ { 2 } < n / ( m + n + 1 )$ ; confidence 0.998
  
−
225. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l1200409.png ; $u _ { i } ^ { n + 1 } = u _ { i } ^ { n } + \frac { \Delta t ^ { n } } { \Delta x } [ f _ { i - 1 / 2 } - f _ { i + 1 / 2 } ]$ ; confidence 0.830
+
225. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130130/w1301303.png ; $W = \int _ { \Sigma } H ^ { 2 } d A$ ; confidence 0.998
  
−
226. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120070/l12007016.png ; $\left( \begin{array} { c } { v _ { 1 } , t } \\ { \vdots } \\ { v _ { k , t } } \end{array} \right)$ ; confidence 0.522
+
226. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f120080157.png ; $B _ { p } ( X , X )$ ; confidence 0.998
  
−
227. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120230/m12023051.png ; $d f _ { t } ( x ) = 0 \Leftrightarrow \partial f ( x ) \ni 0 \Leftrightarrow f _ { t } ( x ) = f ( x )$ ; confidence 0.974
+
227. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010051.png ; $( i + 1 , x )$ ; confidence 0.998
  
−
228. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001042.png ; $f ( x ) = \frac { 1 } { ( 2 \pi ) ^ { 3 / 2 } } \int _ { R ^ { 3 } } \hat { f } ( \xi ) u ( x , \xi ) d \xi , \xi : = k$ ; confidence 0.238
+
228. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120040/f12004016.png ; $W = X ^ { * }$ ; confidence 0.998
  
−
229. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130020/o13002018.png ; $D = \operatorname { liminf } _ { x \rightarrow \infty } M ( r _ { 1 } , r _ { 2 } ) ^ { 1 / n } \geq 22$ ; confidence 0.322
+
229. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c1201806.png ; $( M , \lambda g )$ ; confidence 0.998
  
−
230. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005075.png ; $B _ { new } = B - \frac { B s s ^ { T } B } { s ^ { T } B s } + \frac { y y ^ { T } } { y ^ { T } s } + \theta . w w ^ { T }$ ; confidence 0.463
+
230. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011490/a011490140.png ; $y ( x )$ ; confidence 0.998
  
−
231. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130110/s13011045.png ; $\mathfrak { S } _ { \mathfrak { d } } = \mathfrak { x } _ { \mathfrak { l } } ^ { \mathfrak { W } }$ ; confidence 0.089
+
231. https://www.encyclopediaofmath.org/legacyimages/i/i050/i050790/i05079032.png ; $x = 2$ ; confidence 0.998
  
−
232. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130410/s13041035.png ; $T _ { N } ( x ) = \sum _ { j = n - k } ^ { n + 1 } \frac { b _ { n } , j } { j } P _ { j } ^ { \prime } ( x ) , n \geq k + 1$ ; confidence 0.181
+
232. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120060/o12006052.png ; $C ^ { \infty } ( \Omega ) \cap W ^ { k } E _ { \Phi } ( \Omega )$ ; confidence 0.998
  
−
233. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s12032095.png ; $\operatorname { str } ( T ) = \operatorname { tr } P - ( - 1 ) ^ { p ( S ) } \operatorname { tr } S$ ; confidence 0.889
+
233. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020021.png ; $\lambda = ( 4,3,1,1 )$ ; confidence 0.998
  
−
234. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065045.png ; $F _ { \mu } ( z ) = \frac { 1 } { 2 \pi } \int _ { - \pi } ^ { \pi } R ( e ^ { i \theta } , z ) d \mu ( \theta )$ ; confidence 0.237
+
234. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130410/s1304106.png ; $\lambda _ { i } \in R ^ { + }$ ; confidence 0.998
  
−
235. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065031.png ; $\operatorname { lim } _ { n \rightarrow \infty } \phi _ { n } ^ { * } ( z ) = D _ { \mu } ( z ) ^ { - 1 }$ ; confidence 0.757
+
235. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c12018039.png ; $r \geq 0$ ; confidence 0.998
  
−
236. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065025.png ; $c _ { \mu } = \int _ { - \pi } ^ { \pi } \operatorname { log } \mu ^ { \prime } ( \theta ) d \theta$ ; confidence 0.954
+
236. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e035000106.png ; $\pi ( A \times X ) = \pi ( X \times A ) = \mu ( A )$ ; confidence 0.998
  
−
237. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v1301108.png ; $\frac { b } { h } = \frac { 1 } { \pi } \operatorname { cosh } ^ { - 1 } \sqrt { 2 } \approx 0.2806$ ; confidence 0.980
+
237. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o13008060.png ; $f _ { 1 } - f _ { 2 } : = f$ ; confidence 0.998
  
−
238. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120050/w12005039.png ; $D _ { n } ^ { * } = R [ x _ { 1 } , \ldots , x _ { n } ] / \langle x _ { 1 } , \ldots , x _ { n } \rangle ^ { r + 1 }$ ; confidence 0.143
+
238. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034260/d03426069.png ; $i = 1,2,3$ ; confidence 0.998
  
−
239. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008026.png ; $\sqrt { \lambda } d \lambda + \text { (holomorphic), as } \lambda \rightarrow \infty$ ; confidence 0.492
+
239. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v12002026.png ; $f : ( X , X _ { 0 } ) \rightarrow ( Y , Y _ { 0 } )$ ; confidence 0.998
  
−
240. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009099.png ; $I _ { n } ( g ) = \int _ { [ 0,1 ] ^ { n } } g ( t _ { 1 } , \ldots , t _ { n } ) d B ( t _ { 1 } ) \ldots d B ( t _ { n } )$ ; confidence 0.258
+
240. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120040/a12004013.png ; $t \in ( 0 , \infty )$ ; confidence 0.998
  
−
241. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120190/w12019015.png ; $\rho = \sum \lambda _ { i } P _ { i } , \quad 0 \leq \lambda _ { i } \leq 1 , \sum \lambda _ { i } = 1$ ; confidence 0.991
+
241. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c12028069.png ; $\pi ( K \times L ) \rightarrow \pi ( K ) \otimes \pi ( L )$ ; confidence 0.998
  
−
242. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120010/y1200107.png ; $R _ { 13 } = ( 1 \otimes _ { k } \tau _ { V , V } ) ( R \otimes _ { k } 1 ) ( 1 \otimes _ { k } \tau _ { V , V } )$ ; confidence 0.752
+
242. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130250/c1302509.png ; $\beta = 0$ ; confidence 0.998
  
−
243. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050146.png ; $\zeta _ { G } ( z ) = \sum _ { x = 1 } ^ { \infty } G ( n ) n ^ { - z } = \sum _ { \alpha \in G } | a | ^ { - z } =$ ; confidence 0.334
+
243. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130250/b13025027.png ; $\gamma = \angle A C B$ ; confidence 0.998
  
−
244. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005039.png ; $S _ { \theta _ { 0 } } = \{ z \in C : \operatorname { larg } z | \leq \theta _ { 0 } \} \cup \{ 0 \}$ ; confidence 0.304
+
244. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120080/b12008025.png ; $\operatorname { log } \operatorname { log } ( 1 / \epsilon )$ ; confidence 0.998
  
−
245. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007019.png ; $| \frac { \partial U ( t , s ) } { \partial t } | | \leq \frac { C } { t - s } , \quad s , t \in [ 0 , T ]$ ; confidence 0.392
+
245. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023840/c02384052.png ; $A ^ { T }$ ; confidence 0.998
  
−
246. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008063.png ; $\frac { d } { d t } \left( \begin{array} { l } { v _ { 0 } } \\ { v _ { 1 } } \end{array} \right) =$ ; confidence 0.779
+
246. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030040.png ; $| B ( 4,4 ) | = 2 ^ { 422 }$ ; confidence 0.998
  
−
247. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a12017024.png ; $\int _ { 0 } ^ { + \infty } e ^ { - \lambda \alpha } \beta ( \alpha ) \Pi ( \alpha ) d \alpha = 1$ ; confidence 0.561
+
247. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n12002029.png ; $\mu ^ { \prime } \in M ( E )$ ; confidence 0.998
  
−
248. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130230/a1302308.png ; $\operatorname { lim } _ { n \rightarrow \infty } ( ( 1 - Q ) ( I - P ) ) ^ { n } f = ( I - P _ { U + V } ) f$ ; confidence 0.820
+
248. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030025.png ; $| \eta | ^ { 2 } = \lambda$ ; confidence 0.998
  
−
249. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023021.png ; $\alpha _ { k } = \int _ { \Gamma } \frac { f ( \zeta ) d \zeta } { \zeta ^ { k + 1 } } , \quad k = 0,1$ ; confidence 0.846
+
249. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a120070111.png ; $C ( \overline { \Omega } )$ ; confidence 0.998
  
−
250. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110660/b11066062.png ; $| K ( x , y ^ { \prime } ) - K ( x , y ) | \leq C | y ^ { \prime } - y | ^ { \gamma } | x - y | ^ { - n - \gamma }$ ; confidence 0.802
+
250. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f120080138.png ; $\Lambda _ { G } = 2 n - 1$ ; confidence 0.998
  
−
251. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b110220137.png ; $c ( i , m ) L ( i , m ) = \operatorname { det } _ { Q } r _ { D } ( H _ { M } ^ { i + 1 } ( X , Q ( i + 1 - m ) ) _ { Z } )$ ; confidence 0.157
+
251. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130050/h13005031.png ; $u ( x , 0 )$ ; confidence 0.998
  
−
252. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015058.png ; $\operatorname { lim } _ { n \rightarrow \infty } E _ { P } [ ( d _ { n } ^ { * } - d ^ { * } ) ^ { 2 } ] = 0$ ; confidence 0.582
+
252. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130070/f13007028.png ; $F ( 2,2 n )$ ; confidence 0.998
  
−
253. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b130120107.png ; $\omega ( f ^ { \prime } ; t ) _ { \infty } = O ( \operatorname { ln } \frac { 1 } { t } ) ^ { - 1 / 2 } )$ ; confidence 0.560
+
253. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520278.png ; $\int _ { - \infty } ^ { + \infty } | F ( \xi ) | ^ { 2 } d ( E _ { \xi } h _ { 0 } , h _ { 0 } ) < \infty$ ; confidence 0.998
  
−
254. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027048.png ; $\operatorname { lim } _ { t \rightarrow \infty } ( U ( t + h ) - U ( t ) ) = \frac { h } { E X _ { 1 } }$ ; confidence 0.762
+
254. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015063.png ; $\varepsilon \neq 0$ ; confidence 0.998
  
−
255. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032086.png ; $k \operatorname { log } m \leq i \operatorname { log } n < ( k + 1 ) \operatorname { log } r$ ; confidence 0.756
+
255. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016670/b016670116.png ; $t > 2$ ; confidence 0.998
  
−
256. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020070.png ; $\mathfrak { g } = \mathfrak { g } _ { + } \oplus \mathfrak { h } \oplus \mathfrak { g } _ { - }$ ; confidence 0.962
+
256. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007068.png ; $\operatorname { gcd } ( e , d ) = 1$ ; confidence 0.998
  
−
257. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026061.png ; $\operatorname { deg } _ { B } [ f , \Omega , y ] = \operatorname { deg } _ { B } [ f , \Omega , z ]$ ; confidence 0.962
+
257. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120200/d1202001.png ; $\sigma + i t$ ; confidence 0.998
  
−
258. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026058.png ; $\operatorname { deg } _ { B } [ f , \Omega , y ] = \operatorname { deg } _ { B } [ g , \Omega , y ]$ ; confidence 0.894
+
258. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120230/m12023045.png ; $d f _ { t } \rightarrow \partial f$ ; confidence 0.998
  
−
259. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c130070246.png ; $\nu _ { 1 } ( 2 g _ { 1 } - 2 ) + \mathfrak { D } _ { 1 } = \nu _ { 2 } ( 2 g _ { 2 } - 2 ) + \mathfrak { D } _ { 2 }$ ; confidence 0.968
+
259. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130060/h13006017.png ; $\tau ( m )$ ; confidence 0.998
  
−
260. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130130/c13013010.png ; $A = \frac { \partial Q } { \partial L } \cdot \frac { 1 } { 1 - \alpha } \dot { k } ^ { - \alpha }$ ; confidence 0.216
+
260. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z13010083.png ; $f ( y ) \in y$ ; confidence 0.998
  
−
261. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130190/c1301909.png ; $S = \operatorname { inv } ( N ) : = \{ x \in N : \varphi ( t , x ) \in \text { Nfor all } t \in R \}$ ; confidence 0.693
+
261. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130030/m13003033.png ; $J ( q )$ ; confidence 0.998
  
−
262. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030060/d03006011.png ; $u ( t , x ) | _ { t = 0 } = \phi ( x ) , \frac { \partial u ( t , x ) } { \partial t } | _ { t = 0 } = \psi ( x )$ ; confidence 0.969
+
262. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110010/l11001069.png ; $P \cap P = \{ 0 \}$ ; confidence 0.998
  
−
263. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020127.png ; $g ( \overline { u } _ { 1 } ) = c ^ { T } x ^ { ( l ) } + ( A _ { 1 } x ^ { ( l ) } - b _ { 1 } ) ^ { T } \overline { u }$ ; confidence 0.522
+
263. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120190/e120190195.png ; $\mu ( \Phi ) = \mu ( \Phi _ { 1 } ) + \mu ( \Phi _ { 2 } )$ ; confidence 0.998
  
−
264. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012094.png ; $d _ { i } ^ { ( t ) } = ( y _ { i } - \mu ^ { ( t ) } ) ^ { T } [ \Sigma ^ { ( t ) } ] ^ { - 1 } ( y _ { i } - \mu ^ { ( t ) } )$ ; confidence 0.846
+
264. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006086.png ; $\delta ( \infty ) = 0$ ; confidence 0.998
  
−
265. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120020/e12002046.png ; $( X \wedge Z , Y ) \approx \operatorname { map } * ( X , \operatorname { map } _ { * } ( Z , Y ) )$ ; confidence 0.089
+
265. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o13008021.png ; $h ( x ) \equiv 0$ ; confidence 0.998
  
−
266. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120100/e12010044.png ; $t ^ { em } = t ^ { em } + ( P \otimes E ^ { \prime } - B \otimes M ^ { \prime } + 2 ( M ^ { \prime } B ) 1 )$ ; confidence 0.275
+
266. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130070/t13007013.png ; $h ( w ) : = \operatorname { log } ( g ( w ) / w )$ ; confidence 0.998
  
−
267. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021083.png ; $= \frac { ( m _ { j } + l ) ! } { l ! } ( \operatorname { log } z ) ^ { l } z ^ { \lambda _ { j } } + \ldots$ ; confidence 0.700
+
267. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120040/m1200404.png ; $\vec { F } = q ( \vec { E } + \vec { v } \times \vec { B } )$ ; confidence 0.998
  
−
268. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130020/h13002080.png ; $( \alpha _ { 1 } , \alpha _ { 2 } , \dots , \alpha _ { q } \cup \gamma ^ { d } ) \in F ( S ^ { d } ) ^ { q }$ ; confidence 0.504
+
268. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006051.png ; $\mu ( Z ) = 0$ ; confidence 0.998
  
−
269. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110010/h11001017.png ; $S _ { f } ( \alpha ) = \sum _ { p } 1 / p \cdot ( 1 - \operatorname { Re } ( f ( p ) p ^ { - i \alpha } ) )$ ; confidence 0.571
+
269. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e13007058.png ; $+ O ( T ^ { 1 / 3 } ) + O ( N ^ { 2 } T ^ { - 1 / 2 } )$ ; confidence 0.998
  
−
270. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120020/h120020105.png ; $\int _ { D } | \psi ^ { ( n ) } ( \zeta ) | ^ { p } ( 1 - | \zeta | ) ^ { n p - 2 } d m _ { 2 } ( \zeta ) < \infty$ ; confidence 0.932
+
270. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022530/c02253040.png ; $\pi _ { 1 } ( M )$ ; confidence 0.998
  
−
271. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120020/h12002032.png ; $\operatorname { lim } _ { | | \rightarrow 0 } \frac { 1 } { | T | } \int _ { I } | f - f _ { I } | d m = 0$ ; confidence 0.276
+
271. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b12004038.png ; $g \in L ^ { 0 } ( \mu )$ ; confidence 0.998
  
−
272. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130010/i13001042.png ; $\overline { d } ( n ) ( A ) = \operatorname { per } ( A ) \geq \overline { d } _ { \lambda } ( A )$ ; confidence 0.524
+
272. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170109.png ; $p s - q r = \pm 1$ ; confidence 0.998
  
−
273. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006090.png ; $H ( t ) : = - \frac { 1 } { 2 \pi } \int _ { - \infty } ^ { \infty } ( | f ( k ) | ^ { - 2 } - 1 ) e ^ { - i k t } d k$ ; confidence 0.844
+
273. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008071.png ; $E , A$ ; confidence 0.998
  
−
274. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055070/k05507045.png ; $g = \sum g _ { \alpha \overline { \beta } } d z ^ { \alpha } \otimes d z \square ^ { \beta }$ ; confidence 0.694
+
274. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110440/c11044032.png ; $\alpha + \beta = 1$ ; confidence 0.998
  
−
275. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120020/l1200208.png ; $\phi _ { i j } : \phi _ { j } ( U _ { i } \cap U _ { j } ) \rightarrow \phi _ { i } ( U _ { i } \cap U _ { j } )$ ; confidence 0.906
+
275. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l057000129.png ; $( \sigma \rightarrow \tau ) \in T$ ; confidence 0.998
  
−
276. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l13006074.png ; $z _ { i } \equiv \alpha _ { i } z _ { i - 1 } + \ldots + a _ { i } z _ { i - r } ( \operatorname { mod } p )$ ; confidence 0.242
+
276. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015019.png ; $f _ { X } ( X ) \geq 0$ ; confidence 0.998
  
−
277. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120070/m12007013.png ; $M ( P ) = | \alpha _ { 0 } | \prod _ { k = 1 } ^ { \phi } \operatorname { max } ( | \alpha _ { k } | , 1 )$ ; confidence 0.169
+
277. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120080/l12008031.png ; $X + i Y$ ; confidence 0.998
  
−
278. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120190/m1201901.png ; $F ( \tau ) = \frac { \pi } { 2 } \int _ { 0 } ^ { \infty } P _ { ( i \tau - 1 ) / 2 } ( 2 x ^ { 2 } + 1 ) f ( x ) d x$ ; confidence 0.458
+
278. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012068.png ; $p ^ { * } > 0$ ; confidence 0.998
  
−
279. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130220/m13022050.png ; $\left( \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right) \in SL _ { 2 } ( Z )$ ; confidence 0.434
+
279. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130370/s1303701.png ; $D = D [ 0,1 ]$ ; confidence 0.998
  
−
280. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m13018035.png ; $g ( n ) = \sum _ { d | n } f ( d ) \Leftrightarrow f ( n ) = \sum _ { d | n } g ( d ) \mu ( \frac { n } { d } )$ ; confidence 0.878
+
280. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025830/c0258305.png ; $H = H _ { 1 }$ ; confidence 0.998
  
−
281. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120100/n12010059.png ; $\| Y _ { m } \| _ { G } ^ { 2 } = \sum _ { i , j = 1 } ^ { k } g j \langle y _ { m } + i - 1 , y _ { m } + j - 1 \rangle$ ; confidence 0.187
+
281. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130030/z13003026.png ; $f ( t ) = ( 2 \gamma ) ^ { 1 / 4 } \operatorname { exp } ( - \pi \gamma t ^ { 2 } ) , \gamma > 0$ ; confidence 0.998
  
−
282. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520441.png ; $\dot { u } _ { i } = \tilde { \psi } _ { i } ( U ) + \tilde { \phi } _ { i } ( U ) , \quad i = 1 , \ldots , n$ ; confidence 0.234
+
282. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020174.png ; $q \circ p ^ { - 1 }$ ; confidence 0.998
  
−
283. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o1300807.png ; $x \in R _ { + } , f _ { m } ( x , k ) = e ^ { i k x } + o ( 1 ) \operatorname { as } x \rightarrow + \infty$ ; confidence 0.151
+
283. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012960/a01296090.png ; $\alpha > 1 / 2$ ; confidence 0.998
  
−
284. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q120070136.png ; $R ( t ^ { i } \square j \otimes t ^ { k } \square l ) = R ^ { i } \square j \square ^ { k } \square l$ ; confidence 0.278
+
284. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120120/m120120103.png ; $u ^ { - 1 } R u = R$ ; confidence 0.998
  
−
285. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130040/r13004051.png ; $\mu _ { 2 } ( \Omega ) \leq ( \frac { 1 } { | \Omega | } ) ^ { 2 / n } C _ { n } ^ { 2 / n } p _ { n / 2,1 } ^ { 2 }$ ; confidence 0.369
+
285. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b130300160.png ; $G \cap B = \{ 1 \}$ ; confidence 0.998
  
−
286. https://www.encyclopediaofmath.org/legacyimages/r/r120/r120020/r12002017.png ; $M _ { 11 } ( q ) \ddot { q } _ { 1 } + M _ { 12 } ( q ) \ddot { q } _ { 2 } + F _ { 1 } ( q , \dot { q } ) = \tau _ { 1 }$ ; confidence 0.991
+
286. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120240/a12024041.png ; $( E , h )$ ; confidence 0.998
  
−
287. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120160/s12016027.png ; $H ( q , d ) = \cup _ { q - d + 1 \leq | p | \leq q } ( X ^ { j _ { 1 } } \times \ldots \times X ^ { j _ { d } } )$ ; confidence 0.106
+
287. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007064.png ; $\eta \in \partial \Delta$ ; confidence 0.998
  
−
288. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130530/s13053016.png ; $e = \frac { | U | } { | G | } ( \sum _ { b \in B } b ) ( \sum _ { w \in W } \operatorname { sign } ( w ) w )$ ; confidence 0.138
+
288. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016035.png ; $\frac { d A } { d t } = f ( u ) ( 1 - A ) - b A$ ; confidence 0.998
  
−
289. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026065.png ; $\{ A , A _ { s } ^ { * } \} = \delta ( t - s ) , \{ A _ { t } , A _ { s } \} = \{ A _ { t } ^ { * } , A _ { s } ^ { * } \} = 0$ ; confidence 0.760
+
289. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130130/s13013026.png ; $H ^ { 2 } ( \Gamma , U _ { L } )$ ; confidence 0.998
  
−
290. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s1306403.png ; $a _ { n } = \frac { 1 } { 2 \pi } \int _ { 0 } ^ { 2 \pi } a ( e ^ { i \theta } ) e ^ { - i n \theta } d \theta$ ; confidence 0.839
+
290. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096040/v09604010.png ; $\Psi ( p )$ ; confidence 0.998
  
−
291. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014044.png ; $X \mapsto \operatorname { dim } X = ( \operatorname { dim } _ { K } X _ { j } ) _ { j \in Q _ { 0 } }$ ; confidence 0.819
+
291. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110160/f110160188.png ; $P ( T , \omega )$ ; confidence 0.998
  
−
292. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140119.png ; $\operatorname { dim } _ { 1 } : K _ { 0 } ( \operatorname { mod } R ) \rightarrow Z ^ { Q _ { 0 } }$ ; confidence 0.287
+
292. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013022.png ; $\phi ( x , t , z ) =$ ; confidence 0.998
  
−
293. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120210/t12021078.png ; $t ( M ; x , y ) = \sum _ { S \subseteq E } ( \prod _ { e \in S } p ( e ) ) ( \prod _ { e \in S } ( 1 - p ( e ) ) )$ ; confidence 0.241
+
293. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080102.png ; $( T _ { n } , \alpha _ { j } )$ ; confidence 0.998
  
−
294. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120210/t12021039.png ; $\chi ( G ; \lambda ) = \lambda ^ { \ell ( G ) } ( - 1 ) ^ { v ( G ) - c ( G ) } t ( M _ { G } , 1 - \lambda , 0 )$ ; confidence 0.067
+
294. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120050/t120050104.png ; $r = 1,2,3,4$ ; confidence 0.998
  
−
295. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120020/w12002021.png ; $l _ { 1 } ( P , Q ) = \operatorname { sup } \{ \int f d ( P - Q ) : \operatorname { Lip } f \leq 1 \}$ ; confidence 0.358
+
295. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120220/s1202207.png ; $L ^ { 2 } ( E )$ ; confidence 0.998
  
−
296. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z13010064.png ; $\exists x ( \emptyset \in x \wedge \forall y ( y \in x \rightarrow y \cup \{ y \} \in x ) )$ ; confidence 0.260
+
296. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025830/c02583063.png ; $0 \leq s \leq \infty$ ; confidence 0.998
  
−
297. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011095.png ; $= \frac { ( 1 - \alpha ) } { \dot { k } + c m _ { k } } . [ ( i - 1 + c ) \mu ( i - 1 , m ) - ( i + c ) \mu ( i , m ) ] +$ ; confidence 0.299
+
297. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026048.png ; $V _ { 0 } = V _ { J } = 0$ ; confidence 0.998
  
−
298. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050215.png ; $\sum _ { n \leq x } S ( n ) = A _ { 2 } x + O ( \sqrt { x } ) \quad \text { as } x \rightarrow \infty$ ; confidence 0.344
+
298. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010910/a01091018.png ; $m = 1$ ; confidence 0.998
  
−
299. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050206.png ; $\sum _ { n \leq x } G _ { K } ( n ) = A _ { K } x + O ( x ^ { \eta } K ) \text { as } x \rightarrow \infty$ ; confidence 0.498
+
299. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064620/m06462050.png ; $\phi > 0$ ; confidence 0.998
  
−
300. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a13006075.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { P ^ { \# } ( n ) } { G ^ { \# } ( n ) } = 1$ ; confidence 0.848
+
300. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b11022073.png ; $A ( j )$ ; confidence 0.998

Revision as of 00:10, 13 February 2020

List

1. b1201406.png ; $\operatorname { deg } S ( z ) < 2 t$ ; confidence 0.999

2. c120170166.png ; $2 k - 1$ ; confidence 0.999

3. a12027011.png ; $\Lambda ( s , \rho )$ ; confidence 0.999

4. g045090232.png ; $G ( z , w ) =$ ; confidence 0.999

5. l06005032.png ; $( m < n )$ ; confidence 0.999

6. i13007083.png ; $A ( \alpha ^ { \prime } , \alpha )$ ; confidence 0.999

7. f120150178.png ; $\Gamma ( A ) > 0$ ; confidence 0.999

8. a12011018.png ; $A ( 1 , n ) = n + 2$ ; confidence 0.999

9. b1301908.png ; $\alpha = \operatorname { log } M / \operatorname { log } T \in ( 0,1 )$ ; confidence 0.999

10. b12016070.png ; $n = 4,5,6$ ; confidence 0.999

11. e13005021.png ; $+ \frac { \Gamma ( 1 - \alpha - \beta ) } { 2 \Gamma ( 1 - \alpha ) \Gamma ( 1 - \beta ) } ( y - x ) ^ { t - \alpha - \beta }$ ; confidence 0.999

12. a13007090.png ; $m < n$ ; confidence 0.999

13. a120280110.png ; $x \neq 0$ ; confidence 0.999

14. k12005057.png ; $q \leq r ( d + 1 )$ ; confidence 0.999

15. p07289018.png ; $( n \times p )$ ; confidence 0.999

16. i12008020.png ; $( A B )$ ; confidence 0.999

17. b12005034.png ; $\{ f \in H ^ { \infty } ( B _ { E } ) :$ ; confidence 0.999

18. a0133806.png ; $\lambda \in R$ ; confidence 0.999

19. e120070108.png ; $\beta ( f )$ ; confidence 0.999

20. r08149043.png ; $V ( \lambda )$ ; confidence 0.999

21. f13016031.png ; $\Gamma ( \xi \oplus \eta )$ ; confidence 0.999

22. t130050164.png ; $\lambda \in B _ { 4 }$ ; confidence 0.999

23. f12011092.png ; $U \backslash \Omega$ ; confidence 0.999

24. a12005041.png ; $\| ( \lambda - A ( t ) ) ^ { - 1 } \| \leq M / ( 1 + | \lambda | )$ ; confidence 0.999

25. m12016056.png ; $( p _ { 1 } \times n _ { 1 } )$ ; confidence 0.999

26. s13002034.png ; $N = \partial M$ ; confidence 0.999

27. h12011021.png ; $B ( 0 , r / 2 )$ ; confidence 0.999

28. d03024029.png ; $f ( 2 k + 1 ) ( 0 )$ ; confidence 0.999

29. b12024015.png ; $A ( \overline { U } , V )$ ; confidence 0.999

30. d120020237.png ; $( \overline { \lambda } , \overline { \mu } )$ ; confidence 0.999

31. j13004080.png ; $s ( L )$ ; confidence 0.999

32. w1202007.png ; $R [ f ] = ( r , f )$ ; confidence 0.999

33. c1102505.png ; $( p , q )$ ; confidence 0.999

34. s13059024.png ; $M [ L ] > 0$ ; confidence 0.999

35. c02242020.png ; $\alpha , \beta > - 1$ ; confidence 0.999

36. k1200705.png ; $R ( t ) \in L ( V )$ ; confidence 0.999

37. a1301201.png ; $D = ( V , B )$ ; confidence 0.999

38. z12001063.png ; $W _ { 1 } ( 1 )$ ; confidence 0.999

39. l12003091.png ; $\tau ( R ^ { * } )$ ; confidence 0.999

40. k13001036.png ; $( \vec { D } )$ ; confidence 0.999

41. c13007012.png ; $Y ^ { 2 } = X ^ { 3 }$ ; confidence 0.999

42. d13017035.png ; $| \Omega |$ ; confidence 0.999

43. h120120134.png ; $f \cup g = m ( f \otimes g ) \Delta$ ; confidence 0.999

44. j13007039.png ; $( 1 / ( 1 + k ) ) \omega$ ; confidence 0.999

45. b12043028.png ; $h \rightarrow ( h , h )$ ; confidence 0.999

46. h04602043.png ; $R \in H ^ { \infty }$ ; confidence 0.999

47. n13003034.png ; $- T \Delta w ( x , y )$ ; confidence 0.999

48. p13012030.png ; $\sigma ( K ) = - 2$ ; confidence 0.999

49. a130070131.png ; $> 20162$ ; confidence 0.999

50. h04601058.png ; $\tau ( W , M _ { 0 } ) = 0$ ; confidence 0.999

51. i13007042.png ; $\xi \in R ^ { 3 }$ ; confidence 0.999

52. b12032099.png ; $F ( m ^ { 1 / p } , n ^ { 1 / p } ) = ( n + m ) ^ { 1 / p }$ ; confidence 0.999

53. l0600302.png ; $A ^ { \prime } A$ ; confidence 0.999

54. b12013091.png ; $\| \varphi \| _ { p } = 1$ ; confidence 0.999

55. d031930128.png ; $\Delta u = 0$ ; confidence 0.999

56. t13010053.png ; $\Gamma ( B )$ ; confidence 0.999

57. b12010047.png ; $U ( t )$ ; confidence 0.999

58. a01018053.png ; $\sigma > 0$ ; confidence 0.999

59. v09604020.png ; $s ( r ) \equiv r$ ; confidence 0.999

60. c1300408.png ; $\beta ( z ) : = \frac { 1 } { 2 } [ \psi ( \frac { 1 } { 2 } z + \frac { 1 } { 2 } ) - \psi ( \frac { 1 } { 2 } z ) ] =$ ; confidence 0.999

61. s12028026.png ; $D ^ { 2 } X \approx X$ ; confidence 0.999

62. c12029045.png ; $w : R \rightarrow P$ ; confidence 0.999

63. e1200601.png ; $p : Y \rightarrow M$ ; confidence 0.999

64. b12030054.png ; $\phi = \phi ( y ; \eta )$ ; confidence 0.999

65. c13007031.png ; $n ( n - 1 ) / 2 - 1 - ( n - 1 ) ( n - 2 ) / 2 = n - 2$ ; confidence 0.999

66. c12002072.png ; $m ( x ^ { \prime } )$ ; confidence 0.999

67. e120140101.png ; $( ( \neg \varphi \rightarrow \varphi ) \rightarrow \varphi ) = 1$ ; confidence 0.999

68. q12005082.png ; $\theta = 1$ ; confidence 0.999

69. q12005076.png ; $\theta = \theta ^ { k }$ ; confidence 0.999

70. 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

71. d1300101.png ; $h ( x , y )$ ; confidence 0.999

72. a13013029.png ; $\phi _ { + } = \operatorname { exp } ( \sum _ { j = 1 } ^ { \infty } \phi _ { j } ( x , t ) z ^ { j } )$ ; confidence 0.999

73. e120190160.png ; $W ^ { + } ( h _ { 1 } , h _ { 2 } , p )$ ; confidence 0.999

74. d12018068.png ; $L ^ { 4 } ( X , m )$ ; confidence 0.999

75. c12004046.png ; $\rho ^ { \prime }$ ; confidence 0.999

76. g04339011.png ; $h \rightarrow \delta f ( x _ { 0 } , h )$ ; confidence 0.999

77. l12009042.png ; $\Gamma ( T M )$ ; confidence 0.999

78. r13010038.png ; $n = 6,7,8$ ; confidence 0.999

79. k0554805.png ; $\phi ( x , t )$ ; confidence 0.999

80. f12005053.png ; $f = T ^ { 2 } + T + \beta$ ; confidence 0.999

81. a01412076.png ; $n ( n - 1 ) / 2$ ; confidence 0.999

82. c020740261.png ; $\alpha = \beta$ ; confidence 0.999

83. f04049045.png ; $F = \sigma _ { 2 } ^ { 2 } s _ { 1 } ^ { 2 } / \sigma _ { 1 } ^ { 2 } s _ { 2 } ^ { 2 }$ ; confidence 0.999

84. z13013042.png ; $z = \operatorname { exp } ( i \theta _ { 0 } )$ ; confidence 0.999

85. l06004010.png ; $f _ { k + 1 } ( z )$ ; confidence 0.999

86. t12020090.png ; $1 + \theta + \operatorname { log } \theta = 0$ ; confidence 0.999

87. w13007027.png ; $( \alpha _ { k } | \beta _ { l } ) = 0$ ; confidence 0.999

88. b12031030.png ; $( n - 1 - 2 \delta ) / 2 n < 1 / p < ( n + 1 + 2 \delta ) / 2 n$ ; confidence 0.999

89. e12021031.png ; $| z | \neq 1$ ; confidence 0.999

90. g130060124.png ; $\sigma ( \Omega ( A ) )$ ; confidence 0.999

91. f1300707.png ; $F ( 2 , m )$ ; confidence 0.999

92. e12006066.png ; $[ \Gamma , [ \Gamma , \Gamma ] ] = 0$ ; confidence 0.999

93. s12022062.png ; $\operatorname { det } ( \Delta )$ ; confidence 0.999

94. b120150149.png ; $p p _ { i } + ( 1 - p ) ( 1 - p _ { i } )$ ; confidence 0.999

95. d13013054.png ; $A ^ { \pm } = \frac { n } { 2 } ( \pm 1 - \operatorname { cos } \theta ) d \phi$ ; confidence 0.999

96. b12020015.png ; $\theta H ^ { 2 } = \{ \theta ( z ) f ( z ) : f \in H ^ { 2 } \}$ ; confidence 0.999

97. s12026042.png ; $\phi : [ 0,1 ] \rightarrow ( L ^ { 2 } )$ ; confidence 0.999

98. q12005067.png ; $\phi = \phi ^ { k }$ ; confidence 0.999

99. h04601066.png ; $\tau ( W , M _ { 0 } )$ ; confidence 0.999

100. b130200196.png ; $\epsilon ( s ) = 0$ ; confidence 0.999

101. s130510112.png ; $\gamma ( u ) = \gamma ( v )$ ; confidence 0.999

102. s12017015.png ; $F ( A , d )$ ; confidence 0.999

103. a12005022.png ; $U ( t , r ) U ( r , s ) = U ( t , s )$ ; confidence 0.999

104. w12006013.png ; $T _ { A } f ( \varphi ) ( g ) = \varphi ( g \circ f )$ ; confidence 0.999

105. h13007052.png ; $D + r D$ ; confidence 0.999

106. f13007030.png ; $n = 4,5,6,8,12$ ; confidence 0.999

107. h1301207.png ; $d ( h ( x y ) , h ( x ) h ( y ) ) < \delta$ ; confidence 0.999

108. a13027068.png ; $\phi ( t ) \rightarrow \infty$ ; confidence 0.999

109. g12007019.png ; $m \equiv 1,2$ ; confidence 0.999

110. a12007059.png ; $f \in B ( D _ { A } ( \alpha , \infty ) )$ ; confidence 0.999

111. b12031049.png ; $f = 0$ ; confidence 0.999

112. a12008051.png ; $\frac { d ^ { 2 } u } { d t ^ { 2 } } + A ( t ) u = f ( t ) , t \in [ 0 , T ]$ ; confidence 0.999

113. b12006011.png ; $\frac { \partial ^ { 2 } w } { \partial z \partial z } + \epsilon \frac { n ( n + 1 ) } { ( 1 + \epsilon z z ) ^ { 2 } } w = 0$ ; confidence 0.999

114. m12016033.png ; $( q \times q )$ ; confidence 0.999

115. b12051090.png ; $d = H _ { 0 } ^ { - 1 } d$ ; confidence 0.999

116. l05897018.png ; $0 < \rho < 1$ ; confidence 0.999

117. o130010156.png ; $\theta , \theta ^ { \prime } \in M$ ; confidence 0.999

118. b12031036.png ; $( n - 1 - 2 \delta ) / 2 n < 1 / p < ( n - 1 + 2 \delta ) / 2 n$ ; confidence 0.999

119. a12010047.png ; $R ( I + A ) = X$ ; confidence 0.999

120. h0460806.png ; $H ^ { T }$ ; confidence 0.999

121. t09408025.png ; $\Omega ( X ; A , B )$ ; confidence 0.999

122. a11030026.png ; $( T V , d )$ ; confidence 0.999

123. c11041059.png ; $0 , \infty ]$ ; confidence 0.999

124. r13004058.png ; $\frac { 1 } { \mu _ { 2 } ( \Omega ) } + \frac { 1 } { \mu _ { 3 } ( \Omega ) } \geq \frac { 2 A } { \pi p _ { 1 } ^ { 2 } }$ ; confidence 0.999

125. f120150177.png ; $\Phi _ { + } ( X , Y )$ ; confidence 0.999

126. k12004034.png ; $11257$ ; confidence 0.999

127. w13009046.png ; $\sqrt { n ! }$ ; confidence 0.999

128. f11001052.png ; $y \in A ^ { + }$ ; confidence 0.999

129. c12003027.png ; $g ( t ) = f ( t , u ( t ) )$ ; confidence 0.999

130. v0960305.png ; $z ( t ) = \int _ { 0 } ^ { t } x ( \tau ) d \tau$ ; confidence 0.999

131. n13005031.png ; $( s , r , \mu )$ ; confidence 0.999

132. n13003040.png ; $w ( x , y ) = 0$ ; confidence 0.999

133. a12005050.png ; $U ( t , s )$ ; confidence 0.999

134. w12007028.png ; $= ( p + p ^ { \prime } , q + q ^ { \prime } , t + t ^ { \prime } + \frac { 1 } { 2 } ( p q ^ { \prime } - q p ^ { \prime } ) )$ ; confidence 0.999

135. b13025065.png ; $\frac { 1 } { \operatorname { sin } ^ { 2 } \omega } = \frac { 1 } { \operatorname { sin } ^ { 2 } \alpha } + \frac { 1 } { \operatorname { sin } ^ { 2 } \beta } + \frac { 1 } { \operatorname { sin } ^ { 2 } \gamma }$ ; confidence 0.999

136. a0102206.png ; $2 p$ ; confidence 0.999

137. r1301307.png ; $\sigma \subset \sigma ( A )$ ; confidence 0.999

138. d03278014.png ; $G \subset R ^ { 2 }$ ; confidence 0.999

139. a120050125.png ; $A ( t , u )$ ; confidence 0.999

140. g120040179.png ; $\sigma = 1 / ( s - 1 ) > 0$ ; confidence 0.999

141. c12004018.png ; $M = \Gamma$ ; confidence 0.999

142. h12004025.png ; $\eta < \lambda$ ; confidence 0.999

143. s1202108.png ; $E ( \lambda , D _ { Y } )$ ; confidence 0.999

144. m12013080.png ; $p \in ( 1 / 2,3 / 2 )$ ; confidence 0.999

145. s13054024.png ; $\pi : H \rightarrow G$ ; confidence 0.999

146. l1300805.png ; $| \omega | \geq 1$ ; confidence 0.999

147. d13008016.png ; $\xi \in \partial \Delta$ ; confidence 0.999

148. d12028093.png ; $A ( U ^ { \prime } )$ ; confidence 0.999

149. t09356039.png ; $s ( x , y ) = \phi ( y ^ { * } x )$ ; confidence 0.999

150. t120200206.png ; $( r ) \geq$ ; confidence 0.999

151. n06752072.png ; $K = F [ \lambda ]$ ; confidence 0.999

152. a13008045.png ; $\alpha ( s ) = \frac { f ( L ( s ) ) } { g ( L ( s ) ; m ( s ) , s ) } = \frac { f ( R ( s ) ) } { g ( R ( s ) ; m ( s ) , s ) }$ ; confidence 0.999

153. a11028056.png ; $\chi ( G )$ ; confidence 0.999

154. m13011024.png ; $\phi = \phi ( x , t )$ ; confidence 0.999

155. i13006028.png ; $- k ^ { 2 } j$ ; confidence 0.999

156. f12005017.png ; $\operatorname { gcd } ( n , p ) \neq 1$ ; confidence 0.999

157. m1302201.png ; $196884 = 196883 + 1$ ; confidence 0.999

158. d12023045.png ; $p + q = r$ ; confidence 0.999

159. d120230133.png ; $R _ { 12 } = I = R _ { 21 }$ ; confidence 0.999

160. i12006026.png ; $[ L ( x ) , U ( x ) ]$ ; confidence 0.999

161. d12015037.png ; $( v , n ) > 1$ ; confidence 0.999

162. c02583050.png ; $m _ { T } ( T ) = 0$ ; confidence 0.999

163. a12011032.png ; $T ( 2 , n )$ ; confidence 0.999

164. m12016022.png ; $B ( n \times m )$ ; confidence 0.999

165. a12023029.png ; $\Omega = \{ \zeta : \psi ( \zeta ) < 0 \}$ ; confidence 0.999

166. m13018051.png ; $x \geq y > 0$ ; confidence 0.999

167. s086520150.png ; $\phi \in H ^ { \infty }$ ; confidence 0.999

168. a01300017.png ; $R ( z )$ ; confidence 0.999

169. v1100603.png ; $\nu \in ( - 1,1 / 2 )$ ; confidence 0.999

170. p130070123.png ; $\operatorname { log } \operatorname { tanh } C ( z , w ) \leq W ( z , w ) \leq$ ; confidence 0.999

171. h120020158.png ; $| \nu ( t ) - \nu ( - t ) | \leq 2$ ; confidence 0.999

172. a01191025.png ; $A \cap B$ ; confidence 0.999

173. e120070133.png ; $H ^ { 1 }$ ; confidence 0.999

174. i12008023.png ; $F ( T , H )$ ; confidence 0.999

175. m12003023.png ; $\int \Psi ( x , T ( G ) ) d G ( x ) = 0$ ; confidence 0.999

176. s12017010.png ; $A \in X$ ; confidence 0.999

177. c02583015.png ; $T = T _ { 0 } \otimes T _ { 1 }$ ; confidence 0.999

178. a13023047.png ; $U + V$ ; confidence 0.999

179. a1200602.png ; $u ( x , t ) \in P ( x ) , \quad ( x , t ) \in \partial \Omega \times [ 0 , T ]$ ; confidence 0.999

180. a130050222.png ; $\eta < \delta$ ; confidence 0.999

181. b13028054.png ; $B ( 2 n )$ ; confidence 0.999

182. c130070174.png ; $2 \delta ( P )$ ; confidence 0.999

183. w13017057.png ; $\int _ { - \pi } ^ { \pi } \operatorname { log } \operatorname { det } f ( \lambda ) d \lambda > - \infty$ ; confidence 0.999

184. r13008034.png ; $R ( K ) = H$ ; confidence 0.999

185. e120120118.png ; $\int f ( \theta , \phi ) d \phi$ ; confidence 0.999

186. d031930178.png ; $\zeta = \xi + i \eta$ ; confidence 0.999

187. b11066024.png ; $p < \infty$ ; confidence 0.999

188. w12021029.png ; $m \leq 40$ ; confidence 0.999

189. f12010052.png ; $\tau ( n ) \neq 0$ ; confidence 0.999

190. h1200308.png ; $\tau ( \varphi ) = 0$ ; confidence 0.999

191. b12050012.png ; $W ^ { + } : = \{ | W _ { t } | : t \geq 0 \}$ ; confidence 0.999

192. a120310106.png ; $B ( K ) / M ( K ) = C ( S )$ ; confidence 0.999

193. r13008055.png ; $f ( z , z _ { 0 } ) = 0$ ; confidence 0.999

194. a011370125.png ; $f \in A$ ; confidence 0.999

195. c023110102.png ; $p A = 0$ ; confidence 0.999

196. l13006019.png ; $m = p$ ; confidence 0.999

197. z13001055.png ; $x ( 3 ) = 10$ ; confidence 0.999

198. m12015024.png ; $f _ { X , Y } ( X , Y )$ ; confidence 0.999

199. e120070138.png ; $1 \leq h \leq t - 1$ ; confidence 0.999

200. l12010061.png ; $\gamma < 1$ ; confidence 0.999

201. l12010097.png ; $H = - \Delta + V ( x )$ ; confidence 0.999

202. t12001070.png ; $\tau = ( \tau _ { 1 } , \tau _ { 2 } , \tau _ { 3 } ) \in R ^ { 3 }$ ; confidence 0.999

203. y120010121.png ; $R = R _ { V }$ ; confidence 0.999

204. b12022059.png ; $f ^ { 0 } ( x , \xi ) = M ( u ^ { 0 } ( x ) , \xi )$ ; confidence 0.999

205. l05763020.png ; $f ( t ) \leq g ( t )$ ; confidence 0.999

206. b120040152.png ; $X ^ { 1 / 2 } ( X ^ { \prime } ) ^ { 1 / 2 } = L _ { 2 }$ ; confidence 0.999

207. f12002013.png ; $Q ( 0 ) = 1$ ; confidence 0.999

208. a120160109.png ; $1,160$ ; confidence 0.999

209. z13001058.png ; $x ( n ) = ( \frac { 3 } { 4 } n ^ { 2 } - \frac { 11 } { 4 } n - 4 ) ( - 2 ) ^ { n } + 4 ( - 3 ) ^ { n }$ ; confidence 0.999

210. t12015040.png ; $\pi ^ { \prime } ( \eta )$ ; confidence 0.999

211. f1201906.png ; $g \in G \backslash H$ ; confidence 0.999

212. a130050295.png ; $k > 1$ ; confidence 0.999

213. f110160109.png ; $i < j$ ; confidence 0.999

214. s13065072.png ; $\alpha , \beta \in \{ - 1 / 2,1 / 2 \}$ ; confidence 0.999

215. a12008020.png ; $L ^ { 2 } ( \Omega )$ ; confidence 0.999

216. d03177065.png ; $\mu \rightarrow 0$ ; confidence 0.999

217. a01148096.png ; $k - 1$ ; confidence 0.999

218. a12002020.png ; $f : X \rightarrow Z$ ; confidence 0.999

219. l12008013.png ; $L ( u ) = g$ ; confidence 0.999

220. e12015071.png ; $\lambda _ { 1 } \neq \lambda _ { 2 }$ ; confidence 0.999

221. w1300405.png ; $z = u + i v$ ; confidence 0.999

222. b13016078.png ; $C ( X , \tau )$ ; confidence 0.999

223. a13009029.png ; $k + 1$ ; confidence 0.999

224. t120200126.png ; $0 < \delta _ { 1 } < \delta _ { 2 } < n / ( m + n + 1 )$ ; confidence 0.998

225. w1301303.png ; $W = \int _ { \Sigma } H ^ { 2 } d A$ ; confidence 0.998

226. f120080157.png ; $B _ { p } ( X , X )$ ; confidence 0.998

227. r13010051.png ; $( i + 1 , x )$ ; confidence 0.998

228. f12004016.png ; $W = X ^ { * }$ ; confidence 0.998

229. c1201806.png ; $( M , \lambda g )$ ; confidence 0.998

230. a011490140.png ; $y ( x )$ ; confidence 0.998

231. i05079032.png ; $x = 2$ ; confidence 0.998

232. o12006052.png ; $C ^ { \infty } ( \Omega ) \cap W ^ { k } E _ { \Phi } ( \Omega )$ ; confidence 0.998

233. s12020021.png ; $\lambda = ( 4,3,1,1 )$ ; confidence 0.998

234. s1304106.png ; $\lambda _ { i } \in R ^ { + }$ ; confidence 0.998

235. c12018039.png ; $r \geq 0$ ; confidence 0.998

236. e035000106.png ; $\pi ( A \times X ) = \pi ( X \times A ) = \mu ( A )$ ; confidence 0.998

237. o13008060.png ; $f _ { 1 } - f _ { 2 } : = f$ ; confidence 0.998

238. d03426069.png ; $i = 1,2,3$ ; confidence 0.998

239. v12002026.png ; $f : ( X , X _ { 0 } ) \rightarrow ( Y , Y _ { 0 } )$ ; confidence 0.998

240. a12004013.png ; $t \in ( 0 , \infty )$ ; confidence 0.998

241. c12028069.png ; $\pi ( K \times L ) \rightarrow \pi ( K ) \otimes \pi ( L )$ ; confidence 0.998

242. c1302509.png ; $\beta = 0$ ; confidence 0.998

243. b13025027.png ; $\gamma = \angle A C B$ ; confidence 0.998

244. b12008025.png ; $\operatorname { log } \operatorname { log } ( 1 / \epsilon )$ ; confidence 0.998

245. c02384052.png ; $A ^ { T }$ ; confidence 0.998

246. b13030040.png ; $| B ( 4,4 ) | = 2 ^ { 422 }$ ; confidence 0.998

247. n12002029.png ; $\mu ^ { \prime } \in M ( E )$ ; confidence 0.998

248. b12030025.png ; $| \eta | ^ { 2 } = \lambda$ ; confidence 0.998

249. a120070111.png ; $C ( \overline { \Omega } )$ ; confidence 0.998

250. f120080138.png ; $\Lambda _ { G } = 2 n - 1$ ; confidence 0.998

251. h13005031.png ; $u ( x , 0 )$ ; confidence 0.998

252. f13007028.png ; $F ( 2,2 n )$ ; confidence 0.998

253. n067520278.png ; $\int _ { - \infty } ^ { + \infty } | F ( \xi ) | ^ { 2 } d ( E _ { \xi } h _ { 0 } , h _ { 0 } ) < \infty$ ; confidence 0.998

254. e12015063.png ; $\varepsilon \neq 0$ ; confidence 0.998

255. b016670116.png ; $t > 2$ ; confidence 0.998

256. c13007068.png ; $\operatorname { gcd } ( e , d ) = 1$ ; confidence 0.998

257. d1202001.png ; $\sigma + i t$ ; confidence 0.998

258. m12023045.png ; $d f _ { t } \rightarrow \partial f$ ; confidence 0.998

259. h13006017.png ; $\tau ( m )$ ; confidence 0.998

260. z13010083.png ; $f ( y ) \in y$ ; confidence 0.998

261. m13003033.png ; $J ( q )$ ; confidence 0.998

262. l11001069.png ; $P \cap P = \{ 0 \}$ ; confidence 0.998

263. e120190195.png ; $\mu ( \Phi ) = \mu ( \Phi _ { 1 } ) + \mu ( \Phi _ { 2 } )$ ; confidence 0.998

264. i13006086.png ; $\delta ( \infty ) = 0$ ; confidence 0.998

265. o13008021.png ; $h ( x ) \equiv 0$ ; confidence 0.998

266. t13007013.png ; $h ( w ) : = \operatorname { log } ( g ( w ) / w )$ ; confidence 0.998

267. m1200404.png ; $\vec { F } = q ( \vec { E } + \vec { v } \times \vec { B } )$ ; confidence 0.998

268. t12006051.png ; $\mu ( Z ) = 0$ ; confidence 0.998

269. e13007058.png ; $+ O ( T ^ { 1 / 3 } ) + O ( N ^ { 2 } T ^ { - 1 / 2 } )$ ; confidence 0.998

270. c02253040.png ; $\pi _ { 1 } ( M )$ ; confidence 0.998

271. b12004038.png ; $g \in L ^ { 0 } ( \mu )$ ; confidence 0.998

272. l120170109.png ; $p s - q r = \pm 1$ ; confidence 0.998

273. c12008071.png ; $E , A$ ; confidence 0.998

274. c11044032.png ; $\alpha + \beta = 1$ ; confidence 0.998

275. l057000129.png ; $( \sigma \rightarrow \tau ) \in T$ ; confidence 0.998

276. m12015019.png ; $f _ { X } ( X ) \geq 0$ ; confidence 0.998

277. l12008031.png ; $X + i Y$ ; confidence 0.998

278. a12012068.png ; $p ^ { * } > 0$ ; confidence 0.998

279. s1303701.png ; $D = D [ 0,1 ]$ ; confidence 0.998

280. c0258305.png ; $H = H _ { 1 }$ ; confidence 0.998

281. z13003026.png ; $f ( t ) = ( 2 \gamma ) ^ { 1 / 4 } \operatorname { exp } ( - \pi \gamma t ^ { 2 } ) , \gamma > 0$ ; confidence 0.998

282. v120020174.png ; $q \circ p ^ { - 1 }$ ; confidence 0.998

283. a01296090.png ; $\alpha > 1 / 2$ ; confidence 0.998

284. m120120103.png ; $u ^ { - 1 } R u = R$ ; confidence 0.998

285. b130300160.png ; $G \cap B = \{ 1 \}$ ; confidence 0.998

286. a12024041.png ; $( E , h )$ ; confidence 0.998

287. j13007064.png ; $\eta \in \partial \Delta$ ; confidence 0.998

288. a12016035.png ; $\frac { d A } { d t } = f ( u ) ( 1 - A ) - b A$ ; confidence 0.998

289. s13013026.png ; $H ^ { 2 } ( \Gamma , U _ { L } )$ ; confidence 0.998

290. v09604010.png ; $\Psi ( p )$ ; confidence 0.998

291. f110160188.png ; $P ( T , \omega )$ ; confidence 0.998

292. a13013022.png ; $\phi ( x , t , z ) =$ ; confidence 0.998

293. w130080102.png ; $( T _ { n } , \alpha _ { j } )$ ; confidence 0.998

294. t120050104.png ; $r = 1,2,3,4$ ; confidence 0.998

295. s1202207.png ; $L ^ { 2 } ( E )$ ; confidence 0.998

296. c02583063.png ; $0 \leq s \leq \infty$ ; confidence 0.998

297. c12026048.png ; $V _ { 0 } = V _ { J } = 0$ ; confidence 0.998

298. a01091018.png ; $m = 1$ ; confidence 0.998

299. m06462050.png ; $\phi > 0$ ; confidence 0.998

300. b11022073.png ; $A ( j )$ ; confidence 0.998

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/6. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/6&oldid=44416
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