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(AUTOMATIC EDIT of page 12 out of 77 with 300 lines: Updated image/latex database (currently 22833 images latexified; order by Length, ascending: False.)
 
(AUTOMATIC EDIT of page 12 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/a/a130/a130220/a13022046.png ; $E _ { C } ( X ) \subset \square _ { R } \operatorname { Mod } ( X , C )$ ; confidence 0.726
+
1. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021010.png ; $L ( u ) = 0$ ; confidence 0.995
  
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2. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027024.png ; $x _ { n } \in X _ { n } , Q _ { n } f \in Y _ { n } , T _ { n } = ( Q _ { n } T ) | x _ { n }$ ; confidence 0.686
+
2. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b120210123.png ; $l ( w _ { 1 } ) = l ( w _ { 2 } ) + 1$ ; confidence 0.995
  
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3. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130280/a13028017.png ; $L = \frac { 1 } { 2 } ( 2 \pi ) ^ { - 1 / 2 } \Gamma ( \frac { 1 } { 4 } ) ^ { 2 }$ ; confidence 0.999
+
3. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130100/z13010073.png ; $\forall x$ ; confidence 0.995
  
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4. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120280/a120280167.png ; $\pi ( \alpha _ { t } ( \alpha ) ) = U _ { t } \pi ( \alpha ) U _ { t } ^ { * }$ ; confidence 0.907
+
4. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m13018062.png ; $y \wedge x = 0$ ; confidence 0.995
  
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5. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021031.png ; $\delta _ { k } ( X \otimes X _ { 1 } \wedge \ldots \wedge X _ { k } ) =$ ; confidence 0.333
+
5. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130040/w13004033.png ; $\sum _ { j = 1 } ^ { 3 } \omega _ { j } ^ { 2 } = 0$ ; confidence 0.995
  
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6. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b120210129.png ; $w = w _ { 1 } \leftarrow \ldots \leftarrow w _ { k } = w ^ { \prime }$ ; confidence 0.778
+
6. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035760/e0357601.png ; $\{ T _ { t } \}$ ; confidence 0.995
  
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7. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120030/b1200306.png ; $f ( x ) = \sum _ { n \in Z } \sum _ { m \in Z } c _ { n , m } ( f ) g _ { n , m } ( x )$ ; confidence 0.097
+
7. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060109.png ; $\xi _ { 1 } \lambda _ { 1 } + \xi _ { 2 } \lambda _ { 2 }$ ; confidence 0.995
  
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8. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b13003043.png ; $\operatorname { Ker } ( y ) = \{ x \in V ^ { \sigma } : Q _ { y } x = 0 \}$ ; confidence 0.709
+
8. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008045.png ; $D ( A ) \times V$ ; confidence 0.995
  
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9. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040159.png ; $| x | | y | | _ { X ^ { \prime } } \leq ( 1 + \epsilon ) \| f \| _ { L _ { 1 } }$ ; confidence 0.337
+
9. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130190/b13019043.png ; $O ( T / M )$ ; confidence 0.995
  
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10. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130070/b1300703.png ; $BS ( m , n ) = \{ \alpha , b | \alpha ^ { - 1 } b ^ { m } \alpha = b ^ { n } \}$ ; confidence 0.215
+
10. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120030/a12003016.png ; $f ( x ) = \int _ { 0 } ^ { \infty } e ^ { x t } d \mu ( t )$ ; confidence 0.995
  
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11. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b110220175.png ; $z _ { D } : B ^ { m } ( X ) \rightarrow H _ { M } ^ { 2 m + 1 } ( X / R , R ( m + 1 ) )$ ; confidence 0.647
+
11. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l120100153.png ; $\gamma \geq 1 / 2$ ; confidence 0.995
  
−
12. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b130200100.png ; $\mathfrak { g } ^ { \alpha } \times \mathfrak { g } ^ { - \alpha }$ ; confidence 0.916
+
12. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018033.png ; $i = 0,1,2$ ; confidence 0.995
  
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13. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120440/b12044066.png ; $B ^ { H } = \{ \alpha \in B : h ^ { - 1 } a h = \text { afor all } h \in H \}$ ; confidence 0.405
+
13. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120230/m12023013.png ; $t \in ( 0 , T )$ ; confidence 0.995
  
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14. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120490/b1204903.png ; $\operatorname { lim } _ { x \rightarrow \infty } m ( E _ { x } ) = 0$ ; confidence 0.317
+
14. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130030/z13003047.png ; $( Z f ) ( t , w ) = ( Z f ) ( - t , - w )$ ; confidence 0.995
  
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15. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026050.png ; $\operatorname { deg } _ { B } [ F ( , \lambda ) , U _ { \lambda } , y ]$ ; confidence 0.892
+
15. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f12015038.png ; $B \in B ( Y , Z )$ ; confidence 0.995
  
−
16. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120520/b12052043.png ; $b _ { n + 1 } = \frac { f ( x _ { n } + 1 ) - f ( x _ { n } ) } { x _ { n } + 1 - x _ { n } }$ ; confidence 0.929
+
16. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011036.png ; $z = m l - b / 2$ ; confidence 0.995
  
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17. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120550/b12055053.png ; $b _ { p } ( x ) = \operatorname { sup } _ { \gamma } b _ { \gamma } ( x )$ ; confidence 0.970
+
17. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130030/z13003056.png ; $f ( t ) = O ( ( 1 + | t | ) ^ { - 1 - \epsilon } )$ ; confidence 0.995
  
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18. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020030/c02003034.png ; $\cup _ { N = 1 } ^ { \infty } V ^ { n } = \cup _ { N = 1 } ^ { \infty } U ^ { n }$ ; confidence 0.294
+
18. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d13018042.png ; $\| f - f g h \| \leq \| f - f g \| + \| f g - f g h \|$ ; confidence 0.995
  
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19. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130040/c13004022.png ; $G = Cl _ { 2 } ( \frac { 1 } { 2 } \pi ) = - Cl _ { 2 } ( \frac { 3 } { 2 } \pi ) =$ ; confidence 0.914
+
19. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110010/l11001034.png ; $f ( x ) \preceq g ( x )$ ; confidence 0.995
  
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20. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130100/c13010037.png ; $\int ( f _ { 1 } + f _ { 2 } ) d m = ( C ) \int f _ { 1 } d m + ( C ) \int f _ { 2 } d m$ ; confidence 0.680
+
20. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130220/m13022035.png ; $V _ { - 1 } = \rho _ { 1 }$ ; confidence 0.995
  
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21. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130140/c13014049.png ; $p _ { l , j } ^ { k } = | \{ z \in X : ( x , z ) \in R ; \& ( z , y ) \in R _ { j } \} |$ ; confidence 0.087
+
21. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032079.png ; $s , t \geq 0$ ; confidence 0.995
  
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22. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180224.png ; $S ^ { 2 } E \otimes S ^ { 2 } E \rightarrow A ^ { 2 } E \otimes A ^ { 2 } E$ ; confidence 0.452
+
22. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w12011062.png ; $u \mapsto ( u , \psi ) \varphi$ ; confidence 0.995
  
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23. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026043.png ; $\| U ^ { x } - u ^ { n } \| \leq \| U ^ { 0 } - u ^ { 0 } \| + O ( h ^ { 2 } + k ^ { 2 } )$ ; confidence 0.348
+
23. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c120300113.png ; $A$ ; confidence 0.995
  
−
24. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030270/d0302709.png ; $| f ( x ) - V _ { n , p } ( f , x ) | \leq 2 \frac { n + 1 } { p + 1 } E _ { n - p } ( f )$ ; confidence 0.955
+
24. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120050/k12005059.png ; $B = 0$ ; confidence 0.995
  
−
25. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030270/d03027035.png ; $K _ { n , p } ( t ) = \frac { 1 } { p + 1 } \sum _ { k = n - p } ^ { n } D _ { k } ( t ) =$ ; confidence 0.583
+
25. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120270/a12027014.png ; $W ( \rho ) = \prod W _ { P } ( \rho )$ ; confidence 0.995
  
−
26. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120070/d1200709.png ; $a _ { 1 } \sigma _ { 1 } ( u ) + \ldots + a _ { t } \sigma _ { t } ( u ) \neq 0$ ; confidence 0.871
+
26. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110650/b1106504.png ; $f : R \rightarrow R$ ; confidence 0.995
  
−
27. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120160/d12016069.png ; $\| f \| \neq \operatorname { dist } ( f , L _ { 1 } ( S ) + L _ { 1 } ( T ) )$ ; confidence 0.846
+
27. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120550/b1205507.png ; $d ( \gamma ( t ) , \gamma ( 0 ) ) = t$ ; confidence 0.995
  
−
28. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130130/d1301307.png ; $x = r \operatorname { sin } \theta \operatorname { cos } \phi$ ; confidence 0.941
+
28. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c130070121.png ; $g = \frac { ( n - 1 ) ( n - 2 ) } { 2 } - \sum \delta ( P )$ ; confidence 0.995
  
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29. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130130/d1301308.png ; $y = r \operatorname { sin } \theta \operatorname { sin } \phi$ ; confidence 0.944
+
29. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055780/k0557801.png ; $F ( \tau ) = \int _ { 0 } ^ { \infty } K _ { i \tau } ( x ) f ( x ) d x$ ; confidence 0.995
  
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30. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110220/d11022029.png ; $L y = ( \frac { d } { d x } + r _ { x } ) \dots ( \frac { d } { d x } + r _ { 1 } ) y$ ; confidence 0.303
+
30. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430110.png ; $\beta \alpha = q ^ { 2 } \alpha \beta$ ; confidence 0.995
  
−
31. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d13018088.png ; $\operatorname { lim } _ { n \rightarrow \infty } f g _ { n } = f$ ; confidence 0.784
+
31. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046020/h04602054.png ; $( 1 - P C ) ^ { - 1 }$ ; confidence 0.995
  
−
32. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120260/d12026014.png ; $E f ( X _ { n } ) \rightarrow E f ( w ) , \quad n \rightarrow \infty$ ; confidence 0.753
+
32. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130130/r13013010.png ; $\tau = \sigma ( A ) \backslash \sigma$ ; confidence 0.995
  
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33. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d12028059.png ; $\operatorname { grad } \Phi ^ { m } | _ { \partial D _ { m } } \neq 0$ ; confidence 0.491
+
33. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c1202607.png ; $h = 1 / J$ ; confidence 0.995
  
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34. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029075.png ; $f ( q _ { n } ) q _ { n } > c _ { 1 } ( \varphi ( q _ { n } ) / q _ { n } ) ^ { c _ { 2 } }$ ; confidence 0.840
+
34. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096900/v096900166.png ; $\zeta \mapsto \| T ( \zeta ) \|$ ; confidence 0.995
  
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35. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e12007026.png ; $( \varphi | _ { k } ^ { V } M ) ( z ) = v ( M ) ( cz + d ) ^ { - k } \varphi ( M z )$ ; confidence 0.197
+
35. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130220/a13022011.png ; $s : C \rightarrow B$ ; confidence 0.995
  
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36. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e0350009.png ; $B ( \zeta , \alpha ) = \{ x \in X : \rho ( x , \zeta ) \leq \alpha \}$ ; confidence 0.906
+
36. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054019.png ; $x y x ^ { - 1 } y ^ { - 1 }$ ; confidence 0.995
  
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37. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120140/e12014053.png ; $s \left( \begin{array} { l } { v } \\ { t } \end{array} \right)$ ; confidence 0.733
+
37. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130050/h13005040.png ; $( t )$ ; confidence 0.995
  
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38. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120180/e12018018.png ; $\operatorname { sign } ( M ) = \int _ { M } L ( M , g ) - \eta _ { D } ( 0 )$ ; confidence 0.973
+
38. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026056.png ; $[ f , \Omega , y ] \neq 0$ ; confidence 0.995
  
−
39. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e12026051.png ; $F ( t , \nu ) = \{ P ( \theta , t , \nu ) : \theta \in \Theta ( \mu ) \}$ ; confidence 0.542
+
39. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130020/m1300203.png ; $\int ( F _ { A } , F _ { A } ) + ( D _ { A } \phi , D _ { A } \phi ) - \lambda ( 1 - \| \phi \| ^ { 2 } ) ^ { 2 }$ ; confidence 0.995
  
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40. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130070/f1300702.png ; $F ( 2 , m ) = \{ x _ { 1 } , \dots , x _ { m } | x _ { i } x _ { i } + 1 = x _ { i } + 2 \}$ ; confidence 0.299
+
40. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120240/f12024082.png ; $x ( t + \theta ) : = \phi ( t + \theta )$ ; confidence 0.995
  
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41. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040490/f04049010.png ; $x = [ ( \nu _ { 1 } - 2 ) / \nu _ { 1 } ] \cdot [ \nu _ { 2 } / ( \nu _ { 2 } + 2 ) ]$ ; confidence 0.649
+
41. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030060/d0300609.png ; $\{ t > 0 , \square - \infty < x < \infty \}$ ; confidence 0.995
  
−
42. https://www.encyclopediaofmath.org/legacyimages/f/f040/f040490/f04049011.png ; $\frac { \nu _ { 2 } } { \nu _ { 2 } - 2 } \quad \text { for } \nu _ { 2 } > 2$ ; confidence 0.510
+
42. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120210/s12021015.png ; $\pi : S ^ { 3 } \rightarrow S ^ { 2 }$ ; confidence 0.995
  
−
43. 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
+
43. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027055.png ; $T ( x ) = g$ ; confidence 0.995
  
−
44. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011089.png ; $f ( x ) = \sum _ { \sigma } F _ { \sigma } ( x + i \Gamma _ { \sigma } 0 )$ ; confidence 0.989
+
44. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120370/b12037051.png ; $C _ { \Omega } ( f )$ ; confidence 0.995
  
−
45. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011055.png ; $g ( \xi ) = F [ f ] = \sum _ { k = 1 } ^ { M } G _ { k } ( \xi + i \Delta _ { k } 0 )$ ; confidence 0.957
+
45. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130050/a130050191.png ; $\partial ( A ) = \operatorname { log } _ { p } \operatorname { card } ( A )$ ; confidence 0.995
  
−
46. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f1202104.png ; $\alpha ^ { [ n ] } ( z ) = \sum _ { i = 0 } ^ { \infty } a _ { i } ^ { n } z ^ { i }$ ; confidence 0.253
+
46. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a1302705.png ; $( X , Y )$ ; confidence 0.995
  
−
47. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f1202101.png ; $L = \sum _ { n = 0 } ^ { N } a ^ { [ n ] } ( z ) z ^ { n } ( \frac { d } { d z } ) ^ { n }$ ; confidence 0.841
+
47. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130100/c13010039.png ; $( X , A , m )$ ; confidence 0.995
  
−
48. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f12021090.png ; $= a ^ { 2 } o ( \lambda - \lambda _ { 1 } ) ( \lambda - \lambda _ { 2 } )$ ; confidence 0.556
+
48. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120170/s12017037.png ; $f ( d ) < 0$ ; confidence 0.995
  
−
49. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120240/f12024027.png ; $\dot { x } ( t ) = f ( t , x ( t - h _ { 1 } ( t ) ) , \ldots , x ( t - h _ { k } ( t ) )$ ; confidence 0.506
+
49. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e13007038.png ; $f \in C ^ { \infty } [ N , N + M ]$ ; confidence 0.995
  
−
50. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130030/g13003035.png ; $( u _ { \lambda } - v _ { \lambda } ) _ { \lambda \in \Lambda } \in Z$ ; confidence 0.987
+
50. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120170/s1201709.png ; $F ( A , d ) \subseteq A$ ; confidence 0.995
  
−
51. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g130040199.png ; $\operatorname { spt } ( \| \nu \| ) \cap B ( a , ( 1 - \epsilon ) R )$ ; confidence 0.919
+
51. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020197.png ; $x ^ { ( k ) }$ ; confidence 0.995
  
−
52. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g13006021.png ; $r _ { i } ( A ) : = \sum _ { j = 1 \atop j \neq i } ^ { n } | \alpha _ { i , j } |$ ; confidence 0.165
+
52. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p12017078.png ; $1 < p < \infty$ ; confidence 0.995
  
−
53. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g120040175.png ; $| a _ { \alpha } | \leq C ^ { | \alpha | + 1 } , \alpha \in Z _ { + } ^ { n }$ ; confidence 0.375
+
53. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130100/p130100150.png ; $f \in H ^ { \infty } ( \Delta )$ ; confidence 0.995
  
−
54. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120030/h1200302.png ; $E ( \varphi ) = \frac { 1 } { 2 } \int _ { M } | d \varphi | ^ { 2 } v _ { g }$ ; confidence 0.797
+
54. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015048.png ; $Z ( p \times n )$ ; confidence 0.995
  
−
55. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130070/h13007060.png ; $a _ { i 1 } f _ { 1 } + \ldots + a _ { i l } f _ { l } = b _ { i } , i = 1 , \ldots , m$ ; confidence 0.200
+
55. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b13029081.png ; $s = \operatorname { dim } _ { A } M$ ; confidence 0.995
  
−
56. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130010/i13001055.png ; $\lambda _ { s } > \operatorname { max } \{ \lambda _ { s } + 1,1 \}$ ; confidence 0.743
+
56. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120090/l120090126.png ; $( T M , T ^ { * } M )$ ; confidence 0.995
  
−
57. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006014.png ; $\delta ( - k ) = - \delta ( k ) , k \in R , \quad \delta ( \infty ) = 0$ ; confidence 0.973
+
57. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023064.png ; $d v$ ; confidence 0.995
  
−
58. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007039.png ; $M : = \{ \theta : \theta \in C ^ { 3 } , \theta . \theta = k ^ { 2 } 0 \}$ ; confidence 0.823
+
58. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s130510133.png ; $\gamma ( u ) = \infty$ ; confidence 0.995
  
−
59. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090141.png ; $\lambda _ { p } ( k _ { \infty } / k ) = \mu _ { p } ( k _ { \infty } / k ) = 0$ ; confidence 0.539
+
59. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130130/f13013030.png ; $\phi \circ f = \phi$ ; confidence 0.995
  
−
60. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130030/j13003022.png ; $E \times E \times E \rightarrow E , ( x , y , z ) \mapsto \{ x y z \}$ ; confidence 0.726
+
60. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026083.png ; $g ( \partial B [ R ] ) \subset B$ ; confidence 0.995
  
−
61. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j130040116.png ; $P _ { K } ( v , z ) = v ^ { 2 c } \sum _ { c _ { i } , j } ( v ^ { 2 } - 1 ) ^ { i } z ^ { j }$ ; confidence 0.384
+
61. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110010/f11001039.png ; $0 \leq n x \leq y$ ; confidence 0.995
  
−
62. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j130040121.png ; $P _ { K } ( v , z ) \operatorname { mod } ( ( ( v ^ { 2 } - 1 ) , z ) ^ { k + 1 } )$ ; confidence 0.846
+
62. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120090/k12009029.png ; $( f ^ { * } g ) ( x ) =$ ; confidence 0.995
  
−
63. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j1300404.png ; $v ^ { - 1 } P _ { L _ { + } } ( v , z ) - v P _ { L - } ( v , z ) = z P _ { L _ { 0 } } ( v , z )$ ; confidence 0.654
+
63. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120140/b1201401.png ; $\sigma ( z ) S ( z ) \equiv \omega ( z ) ( \operatorname { mod } z ^ { 2 t } )$ ; confidence 0.995
  
−
64. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007034.png ; $\phi _ { \omega } ( z ) = \frac { | z - \omega | ^ { 2 } } { 1 - | z | ^ { 2 } }$ ; confidence 0.996
+
64. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043330/g04333095.png ; $\lambda \rightarrow 0$ ; confidence 0.995
  
−
65. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007054.png ; $\angle \operatorname { lim } _ { z \rightarrow \omega } F ( z )$ ; confidence 0.880
+
65. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p130070102.png ; $h ( z , w ) - \operatorname { log } \| z - w \| \leq$ ; confidence 0.995
  
−
66. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120040/k1200407.png ; $\Lambda _ { T _ { R } } ( a , x ) = ( \frac { a + a ^ { - 1 } - x } { x } ) ^ { n - 1 }$ ; confidence 0.415
+
66. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b11022015.png ; $n = \operatorname { dim } ( X )$ ; confidence 0.995
  
−
67. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120100/k12010022.png ; $\left( \begin{array} { c } { n j } \\ { 2 } \end{array} \right)$ ; confidence 0.718
+
67. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120170/s12017021.png ; $X = \{ X \}$ ; confidence 0.995
  
−
68. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840382.png ; $\alpha ( \lambda ) y ( 0 ) + \beta ( \lambda ) y ^ { \prime } ( 0 ) = 0$ ; confidence 0.982
+
68. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130050/e13005012.png ; $L ( \alpha , \beta )$ ; confidence 0.995
  
−
69. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840204.png ; $K \rightarrow ( T _ { 21 } + T _ { 22 } K ) ( T _ { 11 } + T _ { 12 } K ) ^ { - 1 }$ ; confidence 0.980
+
69. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130050/d13005028.png ; $G F ( q )$ ; confidence 0.995
  
−
70. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120130/k1201301.png ; $\int _ { x } ^ { b } p ( x ) f ( x ) d x \approx Q _ { 2 } i _ { ( n + 1 ) - 1 } [ f ] =$ ; confidence 0.339
+
70. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130140/w13014014.png ; $( 0 ) = 1$ ; confidence 0.995
  
−
71. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130070/k1300702.png ; $h _ { t } + h _ { X \times X x } + h _ { X X } + \frac { 1 } { 2 } h _ { X } ^ { 2 } = 0$ ; confidence 0.053
+
71. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130090/b13009010.png ; $u ( x , 0 ) = g ( x )$ ; confidence 0.995
  
−
72. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055070/k05507011.png ; $H ^ { 1 } ( M , C ) \cong A ^ { 1 } \oplus \overline { A } \square ^ { 1 }$ ; confidence 0.776
+
72. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120050/f12005057.png ; $\operatorname { deg } f \geq 4$ ; confidence 0.995
  
−
73. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110020/l110020130.png ; $M \subseteq N \Rightarrow M ^ { \perp } \supseteq N ^ { \perp }$ ; confidence 0.986
+
73. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a12006081.png ; $( t , u ) \in [ 0 , T ] \times W$ ; confidence 0.995
  
−
74. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110030/l11003018.png ; $| \mu | = \operatorname { sup } ( \mu , - \mu ) \in ca ( \Omega , F )$ ; confidence 0.907
+
74. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025830/c02583048.png ; $| u ( e ^ { i t } ) | = 1$ ; confidence 0.995
  
−
75. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120030/l12003036.png ; $K ( H ^ { * } \operatorname { Map } ( Z , Y ) , H ^ { * } X ) \rightarrow$ ; confidence 0.972
+
75. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011023.png ; $\Phi ( z ) = - \frac { i \Gamma } { 2 \pi } \operatorname { log } ( z - z _ { j } )$ ; confidence 0.995
  
−
76. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130010/l13001029.png ; $S _ { N } ( f ; x ) = \sum _ { k \backslash k < N } \hat { f } ( k ) e ^ { i k x }$ ; confidence 0.164
+
76. 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
  
−
77. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130010/l13001035.png ; $C _ { 1 } N ^ { ( n - 1 ) / 2 } \leq \| S _ { N } \| \leq C _ { 2 } N ^ { ( n - 1 ) / 2 }$ ; confidence 0.630
+
77. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120010/z12001091.png ; $W _ { 1 } ( m )$ ; confidence 0.995
  
−
78. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120080/l12008040.png ; $M _ { k } = \partial / \partial x + i x ^ { k } \partial / \partial y$ ; confidence 0.911
+
78. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035490/e03549048.png ; $J ( \tau )$ ; confidence 0.995
  
−
79. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l120100104.png ; $K _ { E } ( V ) = \sqrt { V _ { - } } ( - \Delta + E ) ^ { - 1 } \sqrt { V _ { - } }$ ; confidence 0.993
+
79. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011051.png ; $\{ \chi _ { k } ( z ) \}$ ; confidence 0.995
  
−
80. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060030/l06003038.png ; $\Pi ( \alpha ) = 2 \operatorname { arctan } ( e ^ { - \alpha / k } )$ ; confidence 0.786
+
80. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130050/e13005019.png ; $u ( x , y ) =$ ; confidence 0.995
  
−
81. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003079.png ; $\{ ( \vec { x } _ { 1 } , y _ { 1 } ) , \dots , ( \vec { x } _ { n } , y _ { n } ) \}$ ; confidence 0.721
+
81. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120200/d12020028.png ; $A \in B ( H ( G ) )$ ; confidence 0.995
  
−
82. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015057.png ; $\frac { 1 } { ( 2 \pi ) ^ { n p / 2 } | \Sigma | ^ { n / 2 } | \Psi | ^ { p / 2 } }$ ; confidence 0.913
+
82. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130290/f130290150.png ; $( X , L , \tau )$ ; confidence 0.995
  
−
83. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120230/m12023041.png ; $d f _ { t } = t ^ { - 1 } ( I - R _ { t } ) = ( ( \partial f ) ^ { - 1 } + t I ) ^ { - 1 }$ ; confidence 0.775
+
83. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120250/d1202503.png ; $f [ U ]$ ; confidence 0.995
  
−
84. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m1302506.png ; $\langle f u , \varphi \rangle = \langle u , f \varphi \rangle$ ; confidence 0.975
+
84. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130190/m13019011.png ; $L ( p ) > 0$ ; confidence 0.995
  
−
85. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066630/n066630131.png ; $u | _ { \partial \Omega } \in H _ { 2 } ^ { 1 / 2 } ( \partial \Omega )$ ; confidence 0.732
+
85. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120030/y12003035.png ; $D _ { A } \phi = 0$ ; confidence 0.995
  
−
86. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520373.png ; $\Lambda \equiv ( \lambda _ { 1 } , \dots , \lambda _ { n } ) \neq 0$ ; confidence 0.741
+
86. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b13029059.png ; $1 \leq i \leq d$ ; confidence 0.995
  
−
87. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006052.png ; $\overline { \gamma } = \tilde { \gamma } ^ { \prime \prime }$ ; confidence 0.147
+
87. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i130060104.png ; $\varphi _ { + } ( k ) = f ( k )$ ; confidence 0.995
  
−
88. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120050/o12005050.png ; $\psi ( v ) = \operatorname { sup } _ { x > 0 } \{ u v - \varphi ( u ) \}$ ; confidence 0.141
+
88. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130090/b13009013.png ; $u ( x , t ) = \phi ( x - v t - c )$ ; confidence 0.995
  
−
89. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120050/o12005067.png ; $\int _ { 0 } ^ { \infty } \psi ( f ^ { * } ( s ) / w ( s ) ) w ( s ) d s < \infty$ ; confidence 0.905
+
89. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012071.png ; $f \in A ^ { * }$ ; confidence 0.995
  
−
90. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130090/p13009015.png ; $\omega _ { n } = \frac { 2 \pi ^ { n / 2 } } { \Gamma ( \frac { n } { 2 } ) }$ ; confidence 0.504
+
90. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120120/h1201207.png ; $\nabla : X \rightarrow Y$ ; confidence 0.995
  
−
91. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p1301404.png ; $\hat { f } ( \alpha , p ) = \int _ { \operatorname { lap } } f ( x ) d s$ ; confidence 0.370
+
91. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c12001053.png ; $E \times C$ ; confidence 0.995
  
−
92. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p12017040.png ; $\hat { X } = X \oplus 0 \in \operatorname { ker } \delta _ { A , B }$ ; confidence 0.252
+
92. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120050/i12005090.png ; $e ( T , V )$ ; confidence 0.995
  
−
93. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130020/q13002050.png ; $\hat { f } | x , 1 , w \rangle \rightarrow | x , 1 - f ( x ) , w \rangle$ ; confidence 0.677
+
93. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k055840278.png ; $c ( A ) \subset \{ 0 \}$ ; confidence 0.995
  
−
94. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q12007063.png ; $\delta : s | _ { 2 } \rightarrow s | _ { 2 } \otimes s \dot { l } _ { 2 }$ ; confidence 0.185
+
94. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120170/s12017023.png ; $d _ { i } = 1,0 , - 1$ ; confidence 0.995
  
−
95. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130090/r1300904.png ; $a = ( \alpha _ { 1 } , \dots , a _ { n } ) \in R ^ { n } \backslash \{ 0 \}$ ; confidence 0.222
+
95. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130190/m13019045.png ; $M _ { 0 } ( z ) = f _ { 0 } ( z )$ ; confidence 0.995
  
−
96. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010018.png ; $0 \rightarrow X \rightarrow Y \rightarrow Z \rightarrow 0$ ; confidence 0.929
+
96. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026019.png ; $d [ f , M , N ]$ ; confidence 0.995
  
−
97. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130020/s13002036.png ; $U ^ { + } \partial M = \{ v \in S N : \langle v , N _ { x } \rangle > 0 \}$ ; confidence 0.298
+
97. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120140/p12014015.png ; $\theta > 2$ ; confidence 0.995
  
−
98. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004014.png ; $H ^ { L } = \{ z \in H : \operatorname { Im } z > L \} \text { for } L > 0$ ; confidence 0.977
+
98. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030075.png ; $n \geq 2 ^ { 48 }$ ; confidence 0.995
  
−
99. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004014.png ; $s _ { \lambda } = \frac { a _ { \lambda } + \delta } { a _ { \delta } }$ ; confidence 0.307
+
99. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c130070260.png ; $( V _ { 1 } , E _ { 1 } , F _ { 1 } )$ ; confidence 0.995
  
−
100. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120050/s12005066.png ; $K s ( w , z ) = [ 1 - S ( z ) \overline { S ( w ) } ] / ( 1 - z \overline { w } )$ ; confidence 0.443
+
100. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015098.png ; $\Omega , A , P$ ; confidence 0.995
  
−
101. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130370/s1303707.png ; $\| x \| = \operatorname { sup } _ { 0 } \leq t \leq 1 \quad | x ( t ) |$ ; confidence 0.574
+
101. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022100/c0221005.png ; $\Gamma ( \alpha )$ ; confidence 0.995
  
−
102. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120160/s12016028.png ; $X ^ { i } = \{ x _ { 1 } ^ { i } , \ldots , x ^ { i m _ { i } } \} \subset [ 0,1 ]$ ; confidence 0.490
+
102. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d1301808.png ; $g \in A ( X )$ ; confidence 0.995
  
−
103. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120170/s1201702.png ; $F : X \times D \rightarrow 2 ^ { X } \backslash \{ \emptyset \}$ ; confidence 0.979
+
103. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009098.png ; $g \in L ^ { 2 } ( [ 0,1 ] ^ { n } )$ ; confidence 0.995
  
−
104. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130490/s13049042.png ; $\nabla ( A ) : = \{ q \in N _ { k } + 1 : q > \text { pfor some } p \in A \}$ ; confidence 0.244
+
104. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022039.png ; $\gamma _ { l } = m$ ; confidence 0.995
  
−
105. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051062.png ; $\{ G _ { 1 } = ( V _ { 1 } , E _ { 1 } ) , \dots , G _ { m } = ( V _ { m } , E _ { m } ) \}$ ; confidence 0.467
+
105. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i130030137.png ; $W = S \otimes E$ ; confidence 0.995
  
−
106. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120240/s12024032.png ; $E = \{ E _ { n } | \sigma : \Sigma : E _ { n } \rightarrow E _ { n } + 1 \}$ ; confidence 0.557
+
106. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130130/m13013088.png ; $( r , r )$ ; confidence 0.995
  
−
107. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026066.png ; $t \rightarrow \int _ { 0 } ^ { t } ( A _ { s } ^ { * } + A _ { s } ) \Omega d s$ ; confidence 0.996
+
107. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120050/k12005063.png ; $q \leq 2 d r$ ; confidence 0.995
  
−
108. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s120340158.png ; $\alpha _ { H } ( \mathfrak { Y } ) - \alpha _ { H } ( \overline { x } )$ ; confidence 0.243
+
108. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130130/f13013029.png ; $f : F \rightarrow F$ ; confidence 0.995
  
−
109. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065024.png ; $\delta _ { \mu } = \operatorname { exp } \{ c _ { \mu } / ( 4 \pi ) \}$ ; confidence 0.774
+
109. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120290/s1202901.png ; $( G , \tau )$ ; confidence 0.995
  
−
110. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120150/t12015045.png ; $\eta \in A ^ { \prime } \rightarrow \pi ^ { \prime } ( \eta ) \xi$ ; confidence 0.988
+
110. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l057000128.png ; $\sigma , \tau \in T$ ; confidence 0.995
  
−
111. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020042.png ; $g _ { 1 } ( k ) = \sum _ { j = 1 } ^ { n } b _ { j } ^ { \prime } ( k ) z _ { j } ^ { k }$ ; confidence 0.986
+
111. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015017.png ; $\mu$ ; confidence 0.995
  
−
112. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200197.png ; $1 = | z _ { 1 } | \geq \ldots \geq | z _ { k _ { 1 } } | \geq \delta _ { 1 } >$ ; confidence 0.665
+
112. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008065.png ; $m ^ { 2 }$ ; confidence 0.995
  
−
113. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005084.png ; $= ( m - n ) L ( m + n ) + \frac { 1 } { 12 } ( m ^ { 3 } - m ) \delta _ { n + m , 0 } c$ ; confidence 0.870
+
113. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120388.png ; $f ^ { * } ( z )$ ; confidence 0.995
  
−
114. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120040/v12004015.png ; $\Delta ( G ) \leq \chi ^ { \prime } ( G ) \leq \Delta ( G ) + \mu ( G )$ ; confidence 0.991
+
114. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010012.png ; $\gamma > 1 / 2$ ; confidence 0.995
  
−
115. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110124.png ; $= 2 ^ { 2 n } \int \int e ^ { - 4 i \pi [ X - Y , X - Z ] _ { a } ( Y ) b ( Z ) d Y d Z }$ ; confidence 0.362
+
115. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120050/i12005069.png ; $m ( n ; T , V )$ ; confidence 0.995
  
−
116. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080199.png ; $\frac { d f } { d t _ { s } } = \kappa \partial _ { s } f + \{ H _ { s } , f \}$ ; confidence 0.947
+
116. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014070/a0140703.png ; $1$ ; confidence 0.995
  
−
117. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008010.png ; $\theta _ { i } = \kappa _ { i } + \omega _ { i } + \hat { \theta } _ { i }$ ; confidence 0.977
+
117. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130160/b13016022.png ; $\operatorname { Re } ( f | _ { K } ) = 0$ ; confidence 0.995
  
−
118. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080214.png ; $L = \partial ^ { n + 1 } - q _ { 1 } \partial ^ { n - 1 } - \ldots - q _ { n }$ ; confidence 0.921
+
118. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120020/s1200209.png ; $\partial _ { t } L = \frac { 1 } { 2 } \nabla ^ { 2 } L$ ; confidence 0.995
  
−
119. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009073.png ; $H _ { k } ( x ) = ( - 1 ) ^ { n } e ^ { x ^ { 2 } / 2 } D _ { x } ^ { k } e ^ { - x ^ { 2 } / 2 }$ ; confidence 0.339
+
119. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b12022082.png ; $H ( f , \xi ) = f _ { 0 } \operatorname { ln } f _ { 0 }$ ; confidence 0.995
  
−
120. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021071.png ; $A A ^ { T } = A ^ { T } A = ( \sum _ { i = 1 } ^ { k } s _ { i } x _ { i } ^ { 2 } ) I _ { n }$ ; confidence 0.907
+
120. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120440/b12044040.png ; $\chi ( B _ { i } ) = 0$ ; confidence 0.995
  
−
121. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120010/y12001030.png ; $R = \sum _ { s = 1 } ^ { n } a _ { s } \otimes b _ { s } \in A \otimes _ { k } A$ ; confidence 0.640
+
121. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120100/a12010080.png ; $J _ { \lambda } = ( I + \lambda A ) ^ { - 1 }$ ; confidence 0.995
  
−
122. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007035.png ; $G = \langle \alpha \rangle \times \langle \dot { b } \rangle$ ; confidence 0.295
+
122. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e12006063.png ; $J ^ { 1 } ( J ^ { 1 } Y \rightarrow M )$ ; confidence 0.995
  
−
123. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007081.png ; $\operatorname { diag } ( \gamma _ { 1 } , \ldots , \gamma _ { N } )$ ; confidence 0.422
+
123. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013077.png ; $\frac { d F } { d t } = - \varepsilon F ( 1 - \gamma F ^ { p } )$ ; confidence 0.995
  
−
124. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011056.png ; $\frac { 1 } { n } G _ { p , n } \stackrel { \omega } { \rightarrow } G$ ; confidence 0.577
+
124. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r130070140.png ; $( f , g ) _ { H } = ( F , G ) _ { H }$ ; confidence 0.995
  
−
125. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240272.png ; $q ^ { - 1 } \sum _ { i = 1 } ^ { q } ( z _ { i } - \zeta _ { i } ) ^ { 2 } / MS _ { e }$ ; confidence 0.500
+
125. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130100/p130100140.png ; $K = \{ ( z , w ) : z \in T , w \in K _ { z } \}$ ; confidence 0.995
  
−
126. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007057.png ; $A _ { \alpha } ( x ) = o ( \frac { x } { \operatorname { log } x } )$ ; confidence 0.911
+
126. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021053.png ; $\lambda \in P ^ { + }$ ; confidence 0.995
  
−
127. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110300/a11030033.png ; $[ \theta ( d v _ { \alpha } ) ] = K _ { n _ { \alpha } } [ f _ { \alpha } ]$ ; confidence 0.709
+
127. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130190/c13019034.png ; $( N ^ { \prime } , L ^ { \prime } )$ ; confidence 0.995
  
−
128. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a120160160.png ; $\sum _ { i = 1 } ^ { S } \sum _ { t = 1 } ^ { T } n _ { t } q _ { i t } f ( y _ { i t } )$ ; confidence 0.492
+
128. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016045.png ; $A ( t ) = [ f ( u ( t ) ) + \beta ( X ( t ) - X ( t - \tau ) ) ] [ N _ { 0 } - A ( t ) ]$ ; confidence 0.995
  
−
129. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016045.png ; $A ( t ) = [ f ( u ( t ) ) + \beta ( X ( t ) - X ( t - \tau ) ) ] [ N _ { 0 } - A ( t ) ]$ ; confidence 0.995
+
129. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017330/b01733052.png ; $A ( D )$ ; confidence 0.995
  
−
130. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120270/a1202708.png ; $\rho : \operatorname { Gal } ( N / K ) \rightarrow G l _ { n } ( C )$ ; confidence 0.512
+
130. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b120400137.png ; $H ^ { i } ( G / B , \xi )$ ; confidence 0.995
  
−
131. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120270/a120270119.png ; $\rho : G \rightarrow S p _ { 2 n } ( C ) \rightarrow G k _ { 2 n } ( C )$ ; confidence 0.226
+
131. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120010/f12001012.png ; $U = Y$ ; confidence 0.995
  
−
132. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130300/a13030065.png ; $\{ \alpha \in A : \alpha . \Im ( T ) = \Im ( T ) , \alpha = \{ 0 \} \}$ ; confidence 0.281
+
132. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m1302508.png ; $\delta ( x )$ ; confidence 0.995
  
−
133. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130310/a13031028.png ; $\hat { \mu } ( X _ { i } ) = \sum _ { X _ { j } \leq X _ { i } } \mu ( X _ { j } )$ ; confidence 0.905
+
133. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m12003060.png ; $F _ { \sigma } ( x ) = \Phi ( x / \sigma )$ ; confidence 0.995
  
−
134. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b12004085.png ; $\int _ { 0 } ^ { t } f ^ { * } ( s ) d s \leq \int _ { 0 } ^ { t } g ^ { * } ( s ) d s$ ; confidence 0.851
+
134. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020034.png ; $\{ t \}$ ; confidence 0.995
  
−
135. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130060/b13006017.png ; $\| A \| _ { 1 } = \operatorname { max } _ { i } \sum _ { j } | a _ { i j } |$ ; confidence 0.759
+
135. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k05584083.png ; $L \subset K$ ; confidence 0.995
  
−
136. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120080/b12008025.png ; $\operatorname { log } \operatorname { log } ( 1 / \epsilon )$ ; confidence 0.998
+
136. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020078.png ; $c = c ( m )$ ; confidence 0.995
  
−
137. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130090/b13009024.png ; $u _ { t } - \Delta u _ { t } + \operatorname { div } \varphi ( u ) = 0$ ; confidence 0.997
+
137. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170186.png ; $\operatorname { dim } ( K - L ) \leq 2$ ; confidence 0.995
  
−
138. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120340/b12034063.png ; $\sum _ { k = 0 } ^ { \infty } | \mathfrak { c } _ { k } z ^ { k } | < 2 f ( 0 )$ ; confidence 0.572
+
138. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010180/a01018051.png ; $\alpha = 0$ ; confidence 0.995
  
−
139. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b13020095.png ; $\operatorname { dim } \mathfrak { g } ^ { \pm } \alpha _ { i } = 1$ ; confidence 0.567
+
139. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g120040112.png ; $1 < s < m / ( m - 1 )$ ; confidence 0.995
  
−
140. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130200/b130200166.png ; $V = \oplus _ { \lambda \in \mathfrak { h } ^ { * } } V ^ { \lambda }$ ; confidence 0.097
+
140. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015010/b0150102.png ; $\phi _ { n } : B _ { n } \rightarrow B O _ { n }$ ; confidence 0.995
  
−
141. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b120420103.png ; $\Psi _ { V , W } ( v \otimes w ) = \beta ( | v | , | w | ) w \varnothing$ ; confidence 0.173
+
141. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110020/b11002049.png ; $( B u , u ) < 0$ ; confidence 0.995
  
−
142. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042065.png ; $V ^ { \prime } : \underline { 1 } \rightarrow V \otimes V ^ { * }$ ; confidence 0.903
+
142. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035550/e03555032.png ; $\pi : X \rightarrow B$ ; confidence 0.995
  
−
143. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043069.png ; $\Psi ( y \bigotimes x ) = q x \otimes y + ( q ^ { 2 } - 1 ) y \otimes x$ ; confidence 0.342
+
143. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031280/d03128074.png ; $f , g : X \rightarrow Y$ ; confidence 0.995
  
−
144. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430113.png ; $\gamma \delta = \delta \gamma + ( 1 - q ^ { - 2 } ) \gamma \alpha$ ; confidence 0.998
+
144. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120250/s12025029.png ; $\sqrt { 1 - x ^ { 2 } } h \in C [ - 1,1 ]$ ; confidence 0.995
  
−
145. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022081.png ; $| u ( x ) | \leq C \sum _ { j = 0 } ^ { 2 } \rho ^ { j - N / p } | u | _ { p , j , T }$ ; confidence 0.723
+
145. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120120/n12012035.png ; $( x )$ ; confidence 0.995
  
−
146. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022051.png ; $| F ( u ) | \leq C \sum _ { j = 0 } ^ { m } \rho ^ { j - N / p } | u | _ { p , j , T }$ ; confidence 0.557
+
146. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110500/a11050074.png ; $K = Q$ ; confidence 0.995
  
−
147. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007036.png ; $H ^ { n } ( C , M ) = \operatorname { lim } _ { L } \leftarrow ^ { n } M$ ; confidence 0.186
+
147. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b130300144.png ; $2 k$ ; confidence 0.995
  
−
148. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008038.png ; $A = [ A , A _ { 2 } ] \in C ^ { \operatorname { max } } \times ( m n + p )$ ; confidence 0.091
+
148. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120110/a12011027.png ; $T ( i , n ) = T ( i - 1 , T ( i , n - 1 ) ) \text { for } i \geq 1 , n \geq 2$ ; confidence 0.995
  
−
149. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130080/c13008010.png ; $\sigma _ { \mathfrak { P } } = [ \frac { L / K } { \mathfrak { P } } ]$ ; confidence 0.975
+
149. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180389.png ; $M \times \{ 1 \} \times \{ 0 \} \subset M \times ( 0 , \infty ) \times ( - 1 + 1 )$ ; confidence 0.995
  
−
150. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120160/c12016019.png ; $r _ { j j } = ( a _ { j j } - \sum _ { k = 1 } ^ { j - 1 } r _ { k j } ^ { 2 } ) ^ { 1 / 2 }$ ; confidence 0.394
+
150. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120280/s1202802.png ; $X = ( X , x _ { 0 } )$ ; confidence 0.995
  
−
151. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130100/c13010035.png ; $( f _ { 1 } ( x ) - f _ { 1 } ( y ) ) \cdot ( f _ { 2 } ( x ) - f _ { 2 } ( y ) ) \geq 0$ ; confidence 0.943
+
151. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062220/m06222071.png ; $( h , m , n ) ^ { k }$ ; confidence 0.995
  
−
152. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c12017024.png ; $K _ { R } \equiv \{ x \in R ^ { n } : r ; ( x ) \geq 0 , j = 1 , \ldots , m \}$ ; confidence 0.268
+
152. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130230/m130230106.png ; $\operatorname { dim } X = 3$ ; confidence 0.995
  
−
153. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c120170170.png ; $\tau ( \sum a _ { i j } z ^ { i } z ^ { j } ) = \sum a _ { i j } \gamma _ { i j }$ ; confidence 0.188
+
153. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006017.png ; $( P )$ ; confidence 0.995
  
−
154. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026062.png ; $\| U ^ { n } \| _ { \infty } \leq C \| U ^ { 0 } \| _ { \infty } , 1 \leq n$ ; confidence 0.140
+
154. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110670/a11067024.png ; $L ^ { 1 } ( G )$ ; confidence 0.995
  
−
155. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026047.png ; $\| \Delta V \| ^ { 2 } = \sum _ { j = 1 } ^ { J } h | \Delta V _ { j } | ^ { 2 }$ ; confidence 0.953
+
155. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030025.png ; $| B ( m , 2 ) |$ ; confidence 0.995
  
−
156. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130260/c13026030.png ; $\langle [ A ] , \phi \} = \int _ { \operatorname { reg } A } \phi$ ; confidence 0.642
+
156. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120160/f12016040.png ; $( \lambda I - T )$ ; confidence 0.995
  
−
157. https://www.encyclopediaofmath.org/legacyimages/d/d110/d110080/d11008057.png ; $[ L : K ] \geq \sum _ { l = 1 } ^ { m } e ( w _ { l } | v ) \cdot f ( w _ { l } | w )$ ; confidence 0.157
+
157. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120190/l12019046.png ; $X _ { A } ( t , z )$ ; confidence 0.995
  
−
158. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d13006016.png ; $\operatorname { Pl } ( A ) = 1 - \operatorname { Bel } ( \Xi - A )$ ; confidence 0.575
+
158. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b120210132.png ; $( w _ { 1 } , w _ { 2 } )$ ; confidence 0.995
  
−
159. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d1300608.png ; $\operatorname { Bel } ( A _ { 1 } \cup \ldots \cup A _ { k } ) \geq$ ; confidence 0.831
+
159. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010128.png ; $b _ { 2 } \neq b _ { 4 }$ ; confidence 0.995
  
−
160. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120020/e12002061.png ; $\pi _ { n } ( X , Y ) = [ \Sigma ^ { n } X , Y ] \cong [ X , \Omega ^ { n } Y ]$ ; confidence 0.900
+
160. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240142.png ; $m \times 1$ ; confidence 0.995
  
−
161. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e03500060.png ; $B ( y _ { i } , \epsilon ) \cap B ( y _ { j } , \epsilon ) = \emptyset$ ; confidence 0.951
+
161. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040442.png ; $h ^ { - 1 } ( F _ { 0 } )$ ; confidence 0.995
  
−
162. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120160/e12016050.png ; $J ^ { \prime } \mapsto M ^ { \prime t } J ^ { \prime } M ^ { \prime }$ ; confidence 0.705
+
162. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016064.png ; $\lambda < 1$ ; confidence 0.995
  
−
163. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120240/e120240132.png ; $\left[ \begin{array} { l } { 1 } \\ { 8 } \end{array} \right]$ ; confidence 0.209
+
163. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030087.png ; $T _ { 1 } ( H )$ ; confidence 0.995
  
−
164. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130010/f13001036.png ; $\operatorname { gcd } ( \alpha ^ { ( q ^ { i } - 1 ) / 2 } - 1 , f _ { i } )$ ; confidence 0.799
+
164. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024790/c02479065.png ; $f ( \zeta )$ ; confidence 0.995
  
−
165. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f1300906.png ; $U _ { m + n } ( x ) = U _ { m + 1 } ( x ) U _ { n } ( x ) + U _ { m } ( x ) U _ { n - 1 } ( x )$ ; confidence 0.917
+
165. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004062.png ; $\operatorname { cr } ( K )$ ; confidence 0.995
  
−
166. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f13009052.png ; $P ( N _ { k } = n + k ) = \frac { U _ { n + 1 } ^ { ( k ) } } { 2 ^ { n + k } } , n = 0,1$ ; confidence 0.314
+
166. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120080/k12008015.png ; $K _ { p } ( f ) ( p _ { i } ) = f ( p _ { i } )$ ; confidence 0.995
  
−
167. https://www.encyclopediaofmath.org/legacyimages/f/f110/f110160/f110160128.png ; $\psi _ { \mathfrak { A } } ^ { l + 1 } \overline { \mathfrak { a } }$ ; confidence 0.393
+
167. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058480/l05848075.png ; $L ( H )$ ; confidence 0.995
  
−
168. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230117.png ; $- ( - 1 ) ^ { ( q + k _ { 1 } ) k _ { 2 } } L ( K _ { 2 } ) \omega \wedge K _ { 1 } +$ ; confidence 0.704
+
168. https://www.encyclopediaofmath.org/legacyimages/t/t092/t092810/t092810205.png ; $\beta ( M )$ ; confidence 0.995
  
−
169. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130290/f13029025.png ; $L ^ { X } = \{ \alpha : X \rightarrow L , \text { aa function } \}$ ; confidence 0.729
+
169. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m130110120.png ; $D \phi / D t$ ; confidence 0.995
  
−
170. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130010/g13001087.png ; $\omega ^ { c } + \omega ^ { d } = \omega ^ { c } ( 1 + \omega ^ { d - c } )$ ; confidence 0.708
+
170. https://www.encyclopediaofmath.org/legacyimages/v/v110/v110060/v11006010.png ; $[ u , v ] \equiv \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } \frac { \partial ^ { 2 } v } { \partial y ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial y ^ { 2 } } \frac { \partial ^ { 2 } v } { \partial x ^ { 2 } } - 2 \frac { \partial ^ { 2 } u } { \partial x \partial y } \frac { \partial ^ { 2 } v } { \partial x \partial y }$ ; confidence 0.995
  
−
171. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120050/g1200501.png ; $\frac { \partial \psi } { \partial t } = L _ { R } \psi + N ( \psi )$ ; confidence 0.989
+
171. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120310/b12031037.png ; $1 / p \leq ( n - 1 - 2 \delta ) / 2 n$ ; confidence 0.995
  
−
172. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043390/g0433905.png ; $\delta f ( x _ { 0 } , h ) = \frac { d } { d t } f ( x _ { 0 } + t h ) | _ { t = 0 } =$ ; confidence 0.673
+
172. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080151.png ; $\mu \in \Omega ^ { - 1,1 } ( \Sigma _ { g } )$ ; confidence 0.995
  
−
173. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046010/h046010135.png ; $\tau ( W \times P , M _ { 0 } \times P ) = \tau ( W , M _ { 0 } ) \chi ( P )$ ; confidence 0.988
+
173. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130040/j13004039.png ; $( ( v - v ^ { 3 } ) / z + v z ) ^ { 3 }$ ; confidence 0.995
  
−
174. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130030/h13003060.png ; $g ( z ) = r ( z ) + \sum _ { i = 1 } ^ { \infty } s _ { 2 m + i } z ^ { - ( 2 m + i ) }$ ; confidence 0.632
+
174. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016360/b0163604.png ; $a , b , c , d$ ; confidence 0.995
  
−
175. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130060/h13006014.png ; $T _ { n } T _ { m } = \sum _ { d } \sum _ { d ( n , m ) } d ^ { k - 1 } T _ { m n / d } 2$ ; confidence 0.203
+
175. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c12028046.png ; $\gamma \rho$ ; confidence 0.995
  
−
176. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120120/h12012082.png ; $\nabla _ { \infty } = \nabla - \phi \Sigma _ { \infty } \nabla$ ; confidence 0.989
+
176. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g130040168.png ; $\| \nu \| ( A ) = \nu ( A \times G ( n , m ) )$ ; confidence 0.995
  
−
177. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i13004039.png ; $| x | ^ { \lambda } \operatorname { exp } ( - A | x | ^ { - \alpha } )$ ; confidence 0.959
+
177. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130190/f13019013.png ; $\frac { 1 } { 2 N } \operatorname { sin } N ( x - x _ { j } ) \operatorname { cot } \frac { ( x - x _ { j } ) } { 2 }$ ; confidence 0.995
  
−
178. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006090.png ; $\operatorname { dim } ( G ) = \operatorname { Idim } ( P _ { G } )$ ; confidence 0.666
+
178. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120010/m1200105.png ; $T : X \supset D ( T ) \rightarrow 2 ^ { X }$ ; confidence 0.995
  
−
179. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i130060171.png ; $A ( x , y ) = \frac { 1 } { 2 } \int _ { ( x + y ) / 2 } ^ { \infty } q ( t ) d t +$ ; confidence 0.982
+
179. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120080/f12008037.png ; $\varphi ( g ) = ( \xi , \eta ) ( g ) : = ( \pi ( g ) \xi , \eta )$ ; confidence 0.995
  
−
180. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008048.png ; $m _ { s } = \operatorname { lim } _ { H \rightarrow 0 } m ( T , H ) > 0$ ; confidence 0.630
+
180. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120010/y120010141.png ; $= R ( y , z ) _ { 23 } R ( x , z ) _ { 13 } R ( x , y ) _ { 12 }$ ; confidence 0.995
  
−
181. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009061.png ; $\Gamma / \Gamma ^ { p m } \rightarrow \Gamma / \Gamma ^ { p , R }$ ; confidence 0.050
+
181. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230105.png ; $F = \operatorname { diag } \{ f _ { i } \}$ ; confidence 0.995
  
−
182. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007036.png ; $E ( k , \omega ) = \{ z \in \Delta : \phi _ { \omega } ( z ) \leq k \}$ ; confidence 0.994
+
182. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120190/l12019042.png ; $V ( t , x ) = x ^ { * } P ( t ) x$ ; confidence 0.995
  
−
183. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130020/k13002016.png ; $\left( \begin{array} { l } { n } \\ { 2 } \end{array} \right)$ ; confidence 0.969
+
183. https://www.encyclopediaofmath.org/legacyimages/l/l058/l058770/l058770109.png ; $G \times M \rightarrow M$ ; confidence 0.995
  
−
184. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l057000149.png ; $\Gamma \vdash ( \lambda x . M ) : ( \sigma \rightarrow \tau )$ ; confidence 0.396
+
184. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a1303206.png ; $H _ { 0 } : \theta = 0$ ; confidence 0.995
  
−
185. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120030/l12003071.png ; $T _ { E } ( M \otimes _ { F } p ) = T _ { E } M \otimes _ { F } p ^ { T } _ { E } N$ ; confidence 0.290
+
185. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051950/i05195052.png ; $( x _ { k } , y _ { k } )$ ; confidence 0.995
  
−
186. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130010/l13001011.png ; $\hat { f } ( k ) = ( 2 \pi ) ^ { - n } \int _ { T ^ { n } } f ( x ) e ^ { - i k x } d x$ ; confidence 0.256
+
186. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520411.png ; $2 ^ { - k } \operatorname { log } \omega _ { k } ^ { - 1 } < \infty$ ; confidence 0.995
  
−
187. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l13008032.png ; $\nu : = \operatorname { min } \{ \operatorname { dim } l , n \}$ ; confidence 0.781
+
187. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a120070125.png ; $( t , v )$ ; confidence 0.995
  
−
188. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l120120202.png ; $\prod _ { p ^ { \prime } \in S ^ { \prime } } G ( K _ { p ^ { \prime } } )$ ; confidence 0.409
+
188. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120020/w12002014.png ; $c ( x , y ) = d ^ { p } ( x , y )$ ; confidence 0.995
  
−
189. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120160/l1201602.png ; $\Omega G = \{ \gamma : S ^ { 1 } \rightarrow G : \gamma ( 1 ) = 1 \}$ ; confidence 0.984
+
189. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120010/f12001023.png ; $\pi _ { 1 } ( X , * )$ ; confidence 0.995
  
−
190. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120090/m12009043.png ; $( P ( D ) ( \phi ) ) _ { \Delta } ( \xi ) = P ( \xi ) \hat { \phi } ( \xi )$ ; confidence 0.235
+
190. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120140/b12014048.png ; $b ( z ) = z ^ { 2 t }$ ; confidence 0.995
  
−
191. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120240/m1202407.png ; $( \psi [ 1 ] \varphi ) y = \varphi ^ { 2 } ( \psi \varphi ^ { - 1 } ) y$ ; confidence 0.582
+
191. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130490/s13049015.png ; $r ( P ) : = \operatorname { max } \{ r ( p ) : p \in P \}$ ; confidence 0.995
  
−
192. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120010/n1200104.png ; $( M , g ) = ( R ^ { 2 } \backslash \{ 0 \} , 2 / ( u ^ { 2 } + v ^ { 2 } ) d u d v )$ ; confidence 0.712
+
192. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v12002057.png ; $H ^ { k } ( f ^ { - 1 } ( y ) , G ) \neq 0$ ; confidence 0.995
  
−
193. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520398.png ; $z _ { j } = z _ { i } f ( z _ { 1 } , \dots , z _ { k } ) , \quad i = 1 , \dots , n$ ; confidence 0.402
+
193. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120500/b1205004.png ; $Z _ { 0 } : = \{ t : W _ { t } = 0 \}$ ; confidence 0.995
  
−
194. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520435.png ; $\dot { v } _ { i } = \tilde { \psi } _ { i } ( V ) , \quad i = 1 , \dots , n$ ; confidence 0.387
+
194. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b11022092.png ; $Y = X \backslash X$ ; confidence 0.995
  
−
195. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006053.png ; $\overline { \gamma } ^ { \prime } = \gamma ^ { \prime \prime }$ ; confidence 0.247
+
195. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120200/b12020059.png ; $y ( n ) = c x ( n ) + d u ( n )$ ; confidence 0.995
  
−
196. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130130/p13013030.png ; $\lambda = ( \lambda _ { 1 } , \dots , \lambda _ { r } ( \lambda ) )$ ; confidence 0.450
+
196. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b12015025.png ; $\frac { 1 } { 1 + \sqrt { n } } ( x \sqrt { n } + \frac { 1 } { 2 } )$ ; confidence 0.995
  
−
197. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p1201708.png ; $\delta _ { A } \subseteq \operatorname { ker } \delta _ { A } *$ ; confidence 0.620
+
197. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120510/b12051064.png ; $\nabla ^ { 2 } f ( x ^ { * } )$ ; confidence 0.995
  
−
198. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008066.png ; $\left[ \begin{array} { l } { 1 } \\ { 1 } \end{array} \right]$ ; confidence 0.187
+
198. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120050/g12005033.png ; $f _ { c } ( y )$ ; confidence 0.995
  
−
199. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130070/r13007074.png ; $= \sum _ { j = 1 } ^ { J } K ( y , y _ { j } ) c _ { j } = f ( y ) , \forall y \in E$ ; confidence 0.910
+
199. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015041.png ; $f _ { X , Y } ( X , Y ) = f _ { X } ( X ) f _ { Y } ( Y )$ ; confidence 0.995
  
−
200. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130140/s1301408.png ; $Q ( r , s ) = q r q _ { s } + 2 \sum _ { i = 1 } ^ { s } ( - 1 ) ^ { i } q + i q _ { s } - i$ ; confidence 0.165
+
200. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002012.png ; $U _ { 1 } = \{ u _ { 1 } \geq 0 : g ( u _ { 1 } ) > - \infty \}$ ; confidence 0.995
  
−
201. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120040/s12004071.png ; $p _ { \lambda } = p _ { \lambda _ { 1 } } \cdots p _ { \lambda _ { l } }$ ; confidence 0.606
+
201. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120110/k12011020.png ; $u ( x , y , t )$ ; confidence 0.995
  
−
202. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130450/s13045061.png ; $= 12 \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { 1 } [ C _ { X , Y } ( u , v ) - u v ] d u d v$ ; confidence 0.487
+
202. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024230/c024230146.png ; $P = N P$ ; confidence 0.995
  
−
203. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130450/s13045027.png ; $\rho _ { S } = \operatorname { corr } [ F _ { X } ( X ) , F _ { Y } ( Y ) ] =$ ; confidence 0.853
+
203. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007050.png ; $f \in L ^ { \infty } ( 0 , T ; X )$ ; confidence 0.995
  
−
204. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120250/s12025028.png ; $\operatorname { log } h / \sqrt { 1 - x ^ { 2 } } \in L _ { 1 } [ - 1,1 ]$ ; confidence 0.998
+
204. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e12006060.png ; $J ^ { 1 } \Gamma ( \Gamma ( Y ) )$ ; confidence 0.995
  
−
205. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120280/s1202808.png ; $E = \{ E _ { n } , \sigma : \Sigma E _ { n } \rightarrow E _ { n } + 1 \}$ ; confidence 0.659
+
205. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120030/t12003040.png ; $\Psi : U ^ { \prime } \rightarrow V ^ { \prime }$ ; confidence 0.995
  
−
206. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s120320112.png ; $\operatorname { Ber } ( T ^ { st } ) = \operatorname { Ber } ( T )$ ; confidence 0.855
+
206. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l057000179.png ; $( b , \beta ) \in B$ ; confidence 0.995
  
−
207. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130040/t13004040.png ; $y _ { n } ^ { * } ( x ) = \tau \sum _ { k = 0 } ^ { n } c _ { k } ^ { n } Q _ { k } ( x )$ ; confidence 0.909
+
207. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120290/c12029064.png ; $\mu : M \rightarrow P$ ; confidence 0.995
  
−
208. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005050.png ; $\sigma _ { T } ( A , X ) = \{ \lambda \in C ^ { n } : K ( A - \lambda , X )$ ; confidence 0.747
+
208. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030019.png ; $\phi : B ( m , n ) \rightarrow G$ ; confidence 0.995
  
−
209. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014069.png ; $M _ { i j } ^ { \beta } \in M _ { v _ { j } \times v _ { i } } ( K ) _ { \beta }$ ; confidence 0.705
+
209. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120070/k1200709.png ; $X ^ { \prime \prime } ( t ) + R ( t ) \circ X ( t ) = 0$ ; confidence 0.995
  
−
210. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014026.png ; $X = ( X _ { i } , \phi _ { \beta } ) _ { j \in Q _ { 0 } , } \beta \in Q _ { 1 }$ ; confidence 0.354
+
210. https://www.encyclopediaofmath.org/legacyimages/m/m062/m062500/m0625002.png ; $\mu ( A )$ ; confidence 0.995
  
−
211. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013025.png ; $W _ { 1 } = S _ { 1 } e ^ { \sum _ { 1 } ^ { \infty } x _ { k } \Lambda ^ { k } }$ ; confidence 0.873
+
211. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120050/e12005021.png ; $( u , v ) \in \Omega ^ { * } \times \Omega ^ { * }$ ; confidence 0.995
  
−
212. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130150/t13015031.png ; $D = \{ z \in C ^ { n } : | z _ { 1 } | ^ { 2 } + \ldots + | z _ { n } | ^ { 2 } < 1 \}$ ; confidence 0.917
+
212. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020061.png ; $M _ { 1 } ( k ) = 1$ ; confidence 0.995
  
−
213. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200225.png ; $G _ { 2 } ( r ) = \sum _ { j = 1 } ^ { n } b _ { j } \phi ( z _ { j } ) z _ { j } ^ { k }$ ; confidence 0.908
+
213. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120440/b12044073.png ; $B ^ { G } = T _ { H } ^ { G } ( B ^ { H } )$ ; confidence 0.995
  
−
214. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200166.png ; $G _ { 2 } ( k ) = \sum _ { j = 1 } ^ { n } b _ { j } \phi ( z _ { j } ) z _ { j } ^ { k }$ ; confidence 0.985
+
214. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180271.png ; $( - 1 ) ^ { p } \in \{ - 1 , + 1 \}$ ; confidence 0.995
  
−
215. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v130050119.png ; $( v ) = \sum _ { i \geq 0 } ( - 1 ) ^ { i + n + 1 } D ^ { ( i ) } ( v _ { n + i } ( u ) )$ ; confidence 0.551
+
215. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d13018034.png ; $A ( \hat { G } ) \cong L ^ { 1 } ( G )$ ; confidence 0.995
  
−
216. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v1300504.png ; $\sum _ { n \geq - 1 } ( \operatorname { dim } V _ { n } ^ { n } ) q ^ { n }$ ; confidence 0.271
+
216. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120160/l12016027.png ; $f : S ^ { 2 } \rightarrow G$ ; confidence 0.995
  
−
217. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v120020181.png ; $F : \overline { D } \square ^ { n + 1 } \rightarrow K ( E ^ { n + 1 } )$ ; confidence 0.986
+
217. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130130/f13013036.png ; $F \rightarrow M$ ; confidence 0.995
  
−
218. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v12002081.png ; $\operatorname { rd } \gamma ( M _ { k } ( f ) ) \leq n - 2 - \dot { k }$ ; confidence 0.294
+
218. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130200/a13020020.png ; $A \circ B = ( A B + B A ) / 2$ ; confidence 0.995
  
−
219. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080122.png ; $T _ { n } = T _ { n } T _ { 1 } ^ { - 1 } , \hat { u } _ { k } = T _ { 1 } ^ { k } u _ { k }$ ; confidence 0.236
+
219. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012250/a01225027.png ; $\nu = 1$ ; confidence 0.995
  
−
220. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008057.png ; $d \tilde { \Omega } = d \lambda + O ( \lambda ^ { - 2 } ) d \lambda$ ; confidence 0.433
+
220. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010053.png ; $( i , \alpha ) ^ { \prime }$ ; confidence 0.995
  
−
221. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130140/w13014015.png ; $\operatorname { sinc } ( x ) = x ^ { - 1 } \operatorname { sin } x$ ; confidence 0.992
+
221. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120010/w12001048.png ; $W _ { N }$ ; confidence 0.995
  
−
222. https://www.encyclopediaofmath.org/legacyimages/y/y120/y120010/y1200108.png ; $\tau _ { U , V } : U \otimes _ { k } V \rightarrow V \otimes _ { k } U$ ; confidence 0.905
+
222. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a12006061.png ; $L ( X )$ ; confidence 0.995
  
−
223. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z130110126.png ; $E \frac { \mu _ { N } ( x ) } { M } \rightarrow \frac { 1 } { x ( x + 1 ) }$ ; confidence 0.777
+
223. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120190/d1201907.png ; $E ( f ) = \int _ { \Omega } | \nabla f | ^ { 2 } d x$ ; confidence 0.995
  
−
224. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240461.png ; $f ( t ) = \beta _ { 0 } + \beta _ { 1 } t + \ldots + \beta _ { k } t ^ { k }$ ; confidence 0.991
+
224. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c12001022.png ; $H ^ { 0 } ( E ) = Z , \quad H ^ { p } ( E ) = 0 , p > 0$ ; confidence 0.995
  
−
225. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040627.png ; $\langle F m _ { P } , \operatorname { mod } e l s s _ { P } \rangle$ ; confidence 0.080
+
225. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020017.png ; $p ( t ) \in F [ t ]$ ; confidence 0.995
  
−
226. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040228.png ; $\Gamma \approx \Delta \vDash _ { K } \varphi \approx \psi$ ; confidence 0.556
+
226. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012054.png ; $y _ { j } ^ { j } > 0$ ; confidence 0.995
  
−
227. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040331.png ; $\operatorname { Id } E ( x , x ) \text { and } x , E ( x , y ) | _ { D } y$ ; confidence 0.093
+
227. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005077.png ; $k \rightarrow \pm \infty$ ; confidence 0.995
  
−
228. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a12006034.png ; $u ( t ) = e ^ { - t A } u _ { 0 } + \int _ { 0 } ^ { t } e ^ { - ( t - s ) A } f ( s ) d s$ ; confidence 0.579
+
228. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d13018097.png ; $A ( T ^ { 2 } )$ ; confidence 0.995
  
−
229. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007083.png ; $H ( x ) > ( 1 - \varepsilon ) ( \operatorname { log } x ) ^ { 2 }$ ; confidence 0.997
+
229. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130140/w13014012.png ; $r ( \pm 1 ) = 1 / 2$ ; confidence 0.995
  
−
230. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a130180126.png ; $\pi _ { i } : \square ^ { n } U \rightarrow \square ^ { ( n - 1 ) } U$ ; confidence 0.693
+
230. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130050/n13005018.png ; $r \leq \frac { s ^ { 2 } \mu - 1 } { \mu - 1 }$ ; confidence 0.995
  
−
231. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120280/a120280141.png ; $S _ { E } = \{ \omega \in \hat { G } : E + \omega \subseteq E \}$ ; confidence 0.881
+
231. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032026.png ; $H _ { 0 } : \theta = p$ ; confidence 0.995
  
−
232. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130290/a13029082.png ; $Q _ { id } = Q \times S ^ { 1 } \rightarrow \Sigma \times S ^ { 1 }$ ; confidence 0.757
+
232. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120160/f12016038.png ; $\sigma ( T ) \cap G$ ; confidence 0.995
  
−
233. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120100/b1201004.png ; $x _ { i } \equiv ( q _ { i } , p _ { i } ) \in R ^ { \nu } \times R ^ { \nu }$ ; confidence 0.666
+
233. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130260/m130260156.png ; $b ^ { 2 } = b$ ; confidence 0.995
  
−
234. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021048.png ; $\overline { D } _ { k } = U ( a ) \otimes U ( p ) \wedge ^ { k } ( a / p )$ ; confidence 0.194
+
234. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f13010076.png ; $C V _ { p } ( G )$ ; confidence 0.995
  
−
235. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120020/b12002012.png ; $\Gamma _ { n } ^ { - 1 } ( t ) = 2 t - \Gamma _ { n } ( t ) + o ( n ^ { - 1 / 2 } )$ ; confidence 0.698
+
235. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043088.png ; $E _ { 2 } ^ { 2 } E _ { 1 } + E _ { 1 } E _ { 2 } ^ { 2 } - ( q + q ^ { - 1 } ) E _ { 2 } E _ { 1 } E _ { 2 } = 0$ ; confidence 0.995
  
−
236. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b13003045.png ; $V ^ { \sigma \langle y \rangle } / \operatorname { Ker } ( y )$ ; confidence 0.366
+
236. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130090/p1300901.png ; $f : D \rightarrow R$ ; confidence 0.995
  
−
237. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130030/b13003042.png ; $\| x z \| ^ { \prime } \leq \| x \| ^ { \prime } \| z \| ^ { \prime }$ ; confidence 0.680
+
237. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130100/r13010025.png ; $\tau _ { A } ^ { j }$ ; confidence 0.995
  
−
238. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120060/b12006019.png ; $\Delta _ { 3 } U = \frac { \partial ^ { 2 } U } { \partial t ^ { 2 } }$ ; confidence 0.996
+
238. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005024.png ; $\alpha \mapsto f ( x ^ { k } + \alpha d ^ { k } )$ ; confidence 0.995
  
−
239. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b110220166.png ; $= \operatorname { dim } H _ { D } ^ { i + 1 } ( X _ { / R } , R ( i + 1 - m ) )$ ; confidence 0.131
+
239. https://www.encyclopediaofmath.org/legacyimages/a/a014/a014320/a01432014.png ; $n \neq 2$ ; confidence 0.995
  
−
240. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012073.png ; $\Delta _ { \varepsilon } ( t ) = ( 1 - | t | / \varepsilon ) _ { + }$ ; confidence 0.515
+
240. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005027.png ; $f ( x , k )$ ; confidence 0.995
  
−
241. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120290/b12029031.png ; $\varepsilon _ { X } ^ { C U } ( g ) = \varepsilon _ { X } ^ { C U } ( f )$ ; confidence 0.833
+
241. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120110/d1201104.png ; $f ( x ) - f ( y ) \leq f ( x + y ) \leq f ( x ) + f ( y ) , x , y \in S$ ; confidence 0.995
  
−
242. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030037.png ; $\alpha _ { k 1 } ( y ) \xi _ { k } \xi _ { 1 } \geq \alpha | \xi | ^ { 2 }$ ; confidence 0.387
+
242. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018011.png ; $m ( . )$ ; confidence 0.995
  
−
243. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b12040061.png ; $\mathfrak { b } = \mathfrak { h } \oplus \mathfrak { n } ^ { + }$ ; confidence 0.932
+
243. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e12006075.png ; $[ Q , \Gamma ]$ ; confidence 0.995
  
−
244. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b12040059.png ; $n ^ { + } = \oplus _ { \alpha \in S } + \mathfrak { g } _ { \alpha }$ ; confidence 0.489
+
244. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120070/m12007015.png ; $M ( P ) \leq L ( P ) \leq 2 ^ { d } M ( P )$ ; confidence 0.995
  
−
245. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b12042031.png ; $\Psi _ { V , W } \otimes _ { Z } = \Psi _ { V , Z } \circ \Psi _ { V , W }$ ; confidence 0.418
+
245. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120060/v1200609.png ; $B _ { 2 n } = N _ { 2 n } / D _ { 2 n }$ ; confidence 0.995
  
−
246. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430119.png ; $\Psi ( \alpha \bigotimes \beta ) = q \beta \otimes \alpha$ ; confidence 0.230
+
246. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130070/j13007040.png ; $k / ( 1 + k )$ ; confidence 0.995
  
−
247. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430166.png ; $\Delta f = 1 \bigotimes f + x \varnothing \partial _ { q } f +$ ; confidence 0.195
+
247. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020072.png ; $\operatorname { dim } X < + \infty$ ; confidence 0.995
  
−
248. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026025.png ; $f : \overline { \Omega } \subset R ^ { N } \rightarrow R ^ { X }$ ; confidence 0.143
+
248. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061150/l06115021.png ; $\xi _ { i } ( 0 ) = 0$ ; confidence 0.995
  
−
249. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026010.png ; $\frac { 1 } { vol S ^ { n - 1 } } \int _ { \partial K } f ^ { * } \omega$ ; confidence 0.393
+
249. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130280/a13028014.png ; $\theta _ { i } ( v )$ ; confidence 0.995
  
−
250. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120530/b1205306.png ; $( f \mapsto \int K ( t , . ) f ( t ) d \mu ( t ) = T f ) \in L ^ { p } ( \nu )$ ; confidence 0.489
+
250. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007044.png ; $v ( \alpha , \theta )$ ; confidence 0.995
  
−
251. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030048.png ; $\alpha = 1 + ( m - 1 ) 3 ^ { C _ { m } ^ { 1 } + C _ { m } ^ { 2 } + C _ { m } ^ { 3 } }$ ; confidence 0.765
+
251. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093560/t09356033.png ; $\mathfrak { M } _ { f }$ ; confidence 0.995
  
−
252. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130010/c1300107.png ; $F = N _ { V } \int _ { V } ( f _ { 0 } ( c ) + \kappa | \nabla c | ^ { 2 } ) d V$ ; confidence 0.772
+
252. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120080/l12008048.png ; $( x ^ { k + 1 } / ( k + 1 ) + i y )$ ; confidence 0.995
  
−
253. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120030/c12003014.png ; $h _ { K } ( t ) = \operatorname { sup } \{ \| f ( t , x ) \| : x \in K \}$ ; confidence 0.850
+
253. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080188.png ; $\omega ^ { 0 } = ( \delta v , \delta u )$ ; confidence 0.995
  
−
254. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180305.png ; $R ( \nabla ) \otimes 1 : S ^ { 2 } E \rightarrow \otimes ^ { 4 } E$ ; confidence 0.956
+
254. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120500/b12050049.png ; $= \operatorname { exp } ( - x \sqrt { 2 u } )$ ; confidence 0.995
  
−
255. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c12018067.png ; $g = ( \theta \otimes \varphi + \varphi \otimes \theta ) / 2$ ; confidence 0.994
+
255. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150109.png ; $\delta \in N \cup \{ 0 \}$ ; confidence 0.995
  
−
256. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120230/c12023022.png ; $X ^ { ( r ) } \rightarrow X ^ { \perp } \rightarrow X ^ { ( r - 1 ) }$ ; confidence 0.600
+
256. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130010/c13001033.png ; $\sqrt { \kappa }$ ; confidence 0.995
  
−
257. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030280/d0302807.png ; $V _ { n } ( f , x ) = \int _ { - \pi } ^ { \pi } f ( x + t ) \tau _ { n } ( t ) d t$ ; confidence 0.719
+
257. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020430/c02043012.png ; $A ( f )$ ; confidence 0.995
  
−
258. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120110/d12011034.png ; $\operatorname { lim } _ { i \rightarrow \infty } x _ { i i } = 0$ ; confidence 0.938
+
258. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120270/b12027082.png ; $\{ b ( t ) : n h \leq t < ( n + 1 ) h \}$ ; confidence 0.995
  
−
259. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120140/d12014016.png ; $( x ^ { 2 } - 4 a ) y ^ { \prime \prime } + x y ^ { \prime } - n ^ { 2 } y = 0$ ; confidence 0.927
+
259. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120010/e1200106.png ; $m : f [ A ] \rightarrow B$ ; confidence 0.995
  
−
260. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d1301106.png ; $( p _ { x } ^ { 2 } + p _ { y } ^ { 2 } + p _ { z } ^ { 2 } ) + m _ { 0 } ^ { 2 } c ^ { 2 } =$ ; confidence 0.755
+
260. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120020/v12002013.png ; $H _ { q } ( M , G ) = 0$ ; confidence 0.995
  
−
261. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130170/d13017067.png ; $\lambda _ { 1 } ( \Omega ) \geq \frac { a } { r _ { \Omega } ^ { 2 } }$ ; confidence 0.502
+
261. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120030/l12003052.png ; $( Z , Y )$ ; confidence 0.995
  
−
262. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120060/e12006051.png ; $[ \Gamma X _ { 1 } , \Gamma X _ { 2 } ] - \Gamma ( [ X _ { 1 } , X _ { 2 } ] )$ ; confidence 0.962
+
262. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016062.png ; $\Sigma = A A ^ { \prime }$ ; confidence 0.995
  
−
263. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120070/e12007061.png ; $F ( z ) = ( 1 / k ! ) \int _ { i } ^ { z } f ( \tau ) ( z - \tau ) ^ { k } d \tau$ ; confidence 0.799
+
263. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120260/s12026030.png ; $D _ { t } : \Gamma ^ { + } \rightarrow ( L ^ { 2 } )$ ; confidence 0.995
  
−
264. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130040/e13004035.png ; $( \Omega _ { + } - 1 ) \psi ( t ) = ( \Omega _ { + } - 1 ) g \psi ( t ) =$ ; confidence 0.997
+
264. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130110/v13011062.png ; $A = \frac { 1 } { 2 } \theta ( 2 \pi - \theta ) - \frac { \pi ^ { 2 } } { \operatorname { cosh } ^ { 2 } ( \pi b / l ) } = 0$ ; confidence 0.995
  
−
265. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120210/e12021038.png ; $\operatorname { ind } _ { F } ( \operatorname { log } | z | ) = 1$ ; confidence 0.665
+
265. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022360/c02236040.png ; $p + q = n$ ; confidence 0.995
  
−
266. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120260/e12026020.png ; $F = F ( \mu ) = \{ P ( \theta , \mu ) : \theta \in \Theta ( \mu ) \}$ ; confidence 0.697
+
266. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021620/c021620355.png ; $\lambda _ { 0 } = 1$ ; confidence 0.995
  
−
267. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e13007016.png ; $h ( n ) \overline { h ( n ) } \equiv 1 ( \operatorname { mod } q )$ ; confidence 0.997
+
267. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009076.png ; $( \pi )$ ; confidence 0.995
  
−
268. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130070/e13007088.png ; $\sum _ { i = 1 } ^ { k } m _ { i } ^ { k } = \sum _ { i = 1 } ^ { k } n _ { i } ^ { k }$ ; confidence 0.709
+
268. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120150/t12015059.png ; $\{ \Delta ^ { \alpha } : \alpha \in C \}$ ; confidence 0.995
  
−
269. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120040/f1200408.png ; $( + \infty ) - ( + \infty ) = - \infty - ( - \infty ) = - \infty$ ; confidence 0.999
+
269. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130120/w13012018.png ; $d ( x , A _ { \lambda } ) \rightarrow d ( x , A )$ ; confidence 0.995
  
−
270. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f1301005.png ; $( ( k _ { N } ) _ { N = 1 } ^ { \infty } , ( l _ { N } ) _ { N = 1 } ^ { \infty } )$ ; confidence 0.208
+
270. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006061.png ; $\kappa = 2 J + 1$ ; confidence 0.995
  
−
271. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120110/f12011061.png ; $\Delta _ { \sigma } = \{ x \in R ^ { n } : \sigma _ { j } x _ { j } > 0 \}$ ; confidence 0.304
+
271. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w130080150.png ; $( \overline { \partial } + \overline { A } ) \psi = 0$ ; confidence 0.995
  
−
272. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f13024020.png ; $\langle x , y \rangle = - \varepsilon \langle y , x \rangle$ ; confidence 0.751
+
272. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n12002066.png ; $m \in M _ { F }$ ; confidence 0.995
  
−
273. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130280/f13028023.png ; $\mu _ { A x } ( z ) = \operatorname { sup } _ { z = A x } \mu _ { A } ( A )$ ; confidence 0.125
+
273. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026043.png ; $\Omega _ { 2 } \subset \Omega$ ; confidence 0.995
  
−
274. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g13006039.png ; $| x _ { i } | = \operatorname { max } _ { 1 \leq j \leq n } | x _ { j } |$ ; confidence 0.233
+
274. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110030/l11003088.png ; $A \in F$ ; confidence 0.995
  
−
275. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g12004067.png ; $\Gamma \subset \Omega \times ( R ^ { n } \backslash \{ 0 \} )$ ; confidence 0.627
+
275. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130040/r13004045.png ; $\frac { \partial u } { \partial n } = 0$ ; confidence 0.995
  
−
276. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120020/h12002078.png ; $\{ f \in H ^ { \infty } : \| \phi - f \| _ { L } \infty \leq \rho \}$ ; confidence 0.933
+
276. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120010/o12001034.png ; $O ( \varepsilon )$ ; confidence 0.995
  
−
277. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130050/h13005015.png ; $\int _ { - \infty } ^ { \infty } ( 1 + | x | ) | u ( x , 0 ) | d x < \infty$ ; confidence 0.991
+
277. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130050/e1300508.png ; $\phi ( \lambda , \mu ; \alpha , \beta ; x , y ) =$ ; confidence 0.995
  
−
278. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130030/i130030113.png ; $c : T ^ { * } M \cong T M \rightarrow \operatorname { End } ( W )$ ; confidence 0.361
+
278. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130130/w13013020.png ; $\chi ( \Sigma )$ ; confidence 0.995
  
−
279. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120020/i1200201.png ; $F ( \tau ) = \int _ { 0 } ^ { \infty } W _ { \mu , i \tau } ( x ) f ( x ) d x$ ; confidence 0.977
+
279. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a1302409.png ; $( n \times 1 )$ ; confidence 0.995
  
−
280. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006018.png ; $\operatorname { ldim } ( P ) \leq \operatorname { dim } ( P )$ ; confidence 0.977
+
280. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p13007082.png ; $E \subset \Omega$ ; confidence 0.995
  
−
281. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006031.png ; $\operatorname { ldim } ( P ) \leq \operatorname { dim } ( Q )$ ; confidence 0.902
+
281. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005049.png ; $\int _ { - \infty } ^ { \infty } | f ( x , i k _ { j } ) | ^ { 2 } d x = ( m _ { j } ^ { + } ) ^ { - 2 }$ ; confidence 0.995
  
−
282. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120060/i12006055.png ; $\operatorname { ldim } ( P ) = \operatorname { dim } ( C ( P ) )$ ; confidence 0.936
+
282. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130050/q13005028.png ; $M = \lambda ( K ) : = [ \mu ^ { - 1 } ( \pi K / 2 ) ] ^ { - 2 } - 1$ ; confidence 0.995
  
−
283. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005062.png ; $\{ r _ { + } ( k ) , i k _ { j } , ( m _ { j } ^ { + } ) ^ { 2 } : 1 \leq j \leq J \}$ ; confidence 0.949
+
283. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130050/r13005021.png ; $G = V _ { 4 } = \{ ( 1 ) , ( 12 ) ( 34 ) , ( 13 ) ( 24 ) , ( 14 ) ( 23 ) \}$ ; confidence 0.995
  
−
284. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i130060163.png ; $f ( x , k ) = e ^ { i k x } + \int _ { x } ^ { \infty } A ( x , y ) e ^ { i k y } d y$ ; confidence 0.951
+
284. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120210/t12021020.png ; $t ( M ; 1,1 )$ ; confidence 0.995
  
−
285. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i13006048.png ; $A ( x , y ) + F ( x , y ) + \int _ { x } ^ { \infty } A ( x , s ) F ( s + y ) d s = 0$ ; confidence 0.997
+
285. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008092.png ; $1 \leq p \leq P - 1$ ; confidence 0.995
  
−
286. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008096.png ; $\chi = ( k _ { B } T ) ^ { - 1 } \operatorname { exp } ( 2 J / k _ { B } T )$ ; confidence 0.993
+
286. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120010/z12001078.png ; $p ^ { m - 1 }$ ; confidence 0.995
  
−
287. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090194.png ; $G _ { \chi } ( T ) = \pi ^ { \mu } \chi g _ { \chi } ( T ) u _ { \chi } ( T )$ ; confidence 0.558
+
287. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120110/h12011022.png ; $f \in C ( B ( 0 , r ) )$ ; confidence 0.995
  
−
288. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130020/j13002048.png ; $P ( X = 0 ) \leq \frac { \operatorname { var } ( X ) } { \lambda }$ ; confidence 0.691
+
288. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130220/b13022073.png ; $p > N$ ; confidence 0.995
  
−
289. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020178.png ; $U _ { t } ^ { j } = u _ { j } ( B _ { \operatorname { min } } ( t , \tau ) )$ ; confidence 0.638
+
289. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130140/s1301407.png ; $r , s \geq 0$ ; confidence 0.995
  
−
290. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120110/k1201107.png ; $\frac { \partial } { \partial t _ { j } } L = [ ( L ^ { j } ) _ { + } , L ]$ ; confidence 0.925
+
290. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p13014027.png ; $p = \alpha x$ ; confidence 0.995
  
−
291. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120110/k1201101.png ; $( u _ { t } + 6 u u _ { X } + u _ { X X X } ) _ { X } + 3 \sigma ^ { 2 } u _ { y } y = 0$ ; confidence 0.534
+
291. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120150/t12015076.png ; $\Delta ^ { i t }$ ; confidence 0.995
  
−
292. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120050/k12005072.png ; $f ^ { * } f * O _ { X } ( m q ( H + \lambda ( K _ { X } + B ) ) ) \rightarrow$ ; confidence 0.816
+
292. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c120170143.png ; $( p q ) ( Z , Z ) = 0$ ; confidence 0.995
  
−
293. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k1201201.png ; $K : = \int \frac { - \operatorname { ln } f ( . ) } { 1 + x ^ { 2 } } d x$ ; confidence 0.620
+
293. https://www.encyclopediaofmath.org/legacyimages/l/l060/l060030/l06003022.png ; $A A ^ { \prime }$ ; confidence 0.995
  
−
294. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055080/k05508017.png ; $\overline { ( h _ { \mu \nu } ) } \square ^ { T } = ( h _ { \mu \nu } )$ ; confidence 0.938
+
294. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046020/h04602031.png ; $Y _ { 1 } = X _ { 1 } + P Y _ { 2 } , \quad Y _ { 2 } = X _ { 2 } + C Y _ { 1 }$ ; confidence 0.995
  
−
295. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057020/l05702022.png ; $Z _ { l } ( m ) _ { X } = ( \mu _ { l ^ { 2 } , X } ^ { \otimes m } ) _ { n \in N }$ ; confidence 0.104
+
295. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018074.png ; $| t | = \sqrt { \sum _ { k = 1 } ^ { N } t _ { k } ^ { 2 } }$ ; confidence 0.995
  
−
296. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110020/l11002058.png ; $e \preceq \mathfrak { c } _ { i } \preceq \mathfrak { b } _ { i }$ ; confidence 0.143
+
296. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120200/b12020058.png ; $x ( n + 1 ) = A x ( n ) + b u ( n )$ ; confidence 0.995
  
−
297. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120030/l12003056.png ; $H ^ { * } \operatorname { Map } ( B E , X ) \approx T _ { E } H ^ { * } X$ ; confidence 0.989
+
297. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040762.png ; $\Sigma ( P , R ^ { \prime } )$ ; confidence 0.995
  
−
298. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l120100140.png ; $\| \rho \| _ { L ^ { p } ( R ^ { 2 } ) } \leq B _ { p } m ^ { - 2 / p } N ^ { 1 / p }$ ; confidence 0.919
+
298. https://www.encyclopediaofmath.org/legacyimages/t/t093/t093560/t09356035.png ; $\mathfrak { M } _ { f } \cap A ^ { + }$ ; confidence 0.995
  
−
299. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130060/l13006068.png ; $N _ { 2 } ^ { * } = \operatorname { min } _ { i } \{ m _ { i } + p _ { i } \}$ ; confidence 0.815
+
299. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180220.png ; $\theta \in E$ ; confidence 0.995
  
−
300. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130100/l13010070.png ; $b ( x , t , \alpha ) t _ { + } ^ { n - 1 } + b ( x , - t , - \alpha ) t ^ { n - 1 }$ ; confidence 0.688
+
300. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030057.png ; $A ( \eta )$ ; confidence 0.995

Revision as of 00:10, 13 February 2020

List

1. f12021010.png ; $L ( u ) = 0$ ; confidence 0.995

2. b120210123.png ; $l ( w _ { 1 } ) = l ( w _ { 2 } ) + 1$ ; confidence 0.995

3. z13010073.png ; $\forall x$ ; confidence 0.995

4. m13018062.png ; $y \wedge x = 0$ ; confidence 0.995

5. w13004033.png ; $\sum _ { j = 1 } ^ { 3 } \omega _ { j } ^ { 2 } = 0$ ; confidence 0.995

6. e0357601.png ; $\{ T _ { t } \}$ ; confidence 0.995

7. o130060109.png ; $\xi _ { 1 } \lambda _ { 1 } + \xi _ { 2 } \lambda _ { 2 }$ ; confidence 0.995

8. a12008045.png ; $D ( A ) \times V$ ; confidence 0.995

9. b13019043.png ; $O ( T / M )$ ; confidence 0.995

10. a12003016.png ; $f ( x ) = \int _ { 0 } ^ { \infty } e ^ { x t } d \mu ( t )$ ; confidence 0.995

11. l120100153.png ; $\gamma \geq 1 / 2$ ; confidence 0.995

12. a12018033.png ; $i = 0,1,2$ ; confidence 0.995

13. m12023013.png ; $t \in ( 0 , T )$ ; confidence 0.995

14. z13003047.png ; $( Z f ) ( t , w ) = ( Z f ) ( - t , - w )$ ; confidence 0.995

15. f12015038.png ; $B \in B ( Y , Z )$ ; confidence 0.995

16. v13011036.png ; $z = m l - b / 2$ ; confidence 0.995

17. z13003056.png ; $f ( t ) = O ( ( 1 + | t | ) ^ { - 1 - \epsilon } )$ ; confidence 0.995

18. d13018042.png ; $\| f - f g h \| \leq \| f - f g \| + \| f g - f g h \|$ ; confidence 0.995

19. l11001034.png ; $f ( x ) \preceq g ( x )$ ; confidence 0.995

20. m13022035.png ; $V _ { - 1 } = \rho _ { 1 }$ ; confidence 0.995

21. b12032079.png ; $s , t \geq 0$ ; confidence 0.995

22. w12011062.png ; $u \mapsto ( u , \psi ) \varphi$ ; confidence 0.995

23. c120300113.png ; $A$ ; confidence 0.995

24. k12005059.png ; $B = 0$ ; confidence 0.995

25. a12027014.png ; $W ( \rho ) = \prod W _ { P } ( \rho )$ ; confidence 0.995

26. b1106504.png ; $f : R \rightarrow R$ ; confidence 0.995

27. b1205507.png ; $d ( \gamma ( t ) , \gamma ( 0 ) ) = t$ ; confidence 0.995

28. c130070121.png ; $g = \frac { ( n - 1 ) ( n - 2 ) } { 2 } - \sum \delta ( P )$ ; confidence 0.995

29. k0557801.png ; $F ( \tau ) = \int _ { 0 } ^ { \infty } K _ { i \tau } ( x ) f ( x ) d x$ ; confidence 0.995

30. b120430110.png ; $\beta \alpha = q ^ { 2 } \alpha \beta$ ; confidence 0.995

31. h04602054.png ; $( 1 - P C ) ^ { - 1 }$ ; confidence 0.995

32. r13013010.png ; $\tau = \sigma ( A ) \backslash \sigma$ ; confidence 0.995

33. c1202607.png ; $h = 1 / J$ ; confidence 0.995

34. v096900166.png ; $\zeta \mapsto \| T ( \zeta ) \|$ ; confidence 0.995

35. a13022011.png ; $s : C \rightarrow B$ ; confidence 0.995

36. s13054019.png ; $x y x ^ { - 1 } y ^ { - 1 }$ ; confidence 0.995

37. h13005040.png ; $( t )$ ; confidence 0.995

38. b13026056.png ; $[ f , \Omega , y ] \neq 0$ ; confidence 0.995

39. m1300203.png ; $\int ( F _ { A } , F _ { A } ) + ( D _ { A } \phi , D _ { A } \phi ) - \lambda ( 1 - \| \phi \| ^ { 2 } ) ^ { 2 }$ ; confidence 0.995

40. f12024082.png ; $x ( t + \theta ) : = \phi ( t + \theta )$ ; confidence 0.995

41. d0300609.png ; $\{ t > 0 , \square - \infty < x < \infty \}$ ; confidence 0.995

42. s12021015.png ; $\pi : S ^ { 3 } \rightarrow S ^ { 2 }$ ; confidence 0.995

43. a13027055.png ; $T ( x ) = g$ ; confidence 0.995

44. b12037051.png ; $C _ { \Omega } ( f )$ ; confidence 0.995

45. a130050191.png ; $\partial ( A ) = \operatorname { log } _ { p } \operatorname { card } ( A )$ ; confidence 0.995

46. a1302705.png ; $( X , Y )$ ; confidence 0.995

47. c13010039.png ; $( X , A , m )$ ; confidence 0.995

48. s12017037.png ; $f ( d ) < 0$ ; confidence 0.995

49. e13007038.png ; $f \in C ^ { \infty } [ N , N + M ]$ ; confidence 0.995

50. s1201709.png ; $F ( A , d ) \subseteq A$ ; confidence 0.995

51. d120020197.png ; $x ^ { ( k ) }$ ; confidence 0.995

52. p12017078.png ; $1 < p < \infty$ ; confidence 0.995

53. p130100150.png ; $f \in H ^ { \infty } ( \Delta )$ ; confidence 0.995

54. m12015048.png ; $Z ( p \times n )$ ; confidence 0.995

55. b13029081.png ; $s = \operatorname { dim } _ { A } M$ ; confidence 0.995

56. l120090126.png ; $( T M , T ^ { * } M )$ ; confidence 0.995

57. a12023064.png ; $d v$ ; confidence 0.995

58. s130510133.png ; $\gamma ( u ) = \infty$ ; confidence 0.995

59. f13013030.png ; $\phi \circ f = \phi$ ; confidence 0.995

60. b13026083.png ; $g ( \partial B [ R ] ) \subset B$ ; confidence 0.995

61. f11001039.png ; $0 \leq n x \leq y$ ; confidence 0.995

62. k12009029.png ; $( f ^ { * } g ) ( x ) =$ ; confidence 0.995

63. b1201401.png ; $\sigma ( z ) S ( z ) \equiv \omega ( z ) ( \operatorname { mod } z ^ { 2 t } )$ ; confidence 0.995

64. g04333095.png ; $\lambda \rightarrow 0$ ; confidence 0.995

65. p130070102.png ; $h ( z , w ) - \operatorname { log } \| z - w \| \leq$ ; confidence 0.995

66. b11022015.png ; $n = \operatorname { dim } ( X )$ ; confidence 0.995

67. s12017021.png ; $X = \{ X \}$ ; confidence 0.995

68. e13005012.png ; $L ( \alpha , \beta )$ ; confidence 0.995

69. d13005028.png ; $G F ( q )$ ; confidence 0.995

70. w13014014.png ; $( 0 ) = 1$ ; confidence 0.995

71. b13009010.png ; $u ( x , 0 ) = g ( x )$ ; confidence 0.995

72. f12005057.png ; $\operatorname { deg } f \geq 4$ ; confidence 0.995

73. a12006081.png ; $( t , u ) \in [ 0 , T ] \times W$ ; confidence 0.995

74. c02583048.png ; $| u ( e ^ { i t } ) | = 1$ ; confidence 0.995

75. v13011023.png ; $\Phi ( z ) = - \frac { i \Gamma } { 2 \pi } \operatorname { log } ( z - z _ { j } )$ ; confidence 0.995

76. f12023033.png ; $D ( \varphi \wedge \psi ) = D ( \varphi ) \wedge \psi + ( - 1 ) ^ { k l } \varphi \wedge D ( \psi )$ ; confidence 0.995

77. z12001091.png ; $W _ { 1 } ( m )$ ; confidence 0.995

78. e03549048.png ; $J ( \tau )$ ; confidence 0.995

79. f12011051.png ; $\{ \chi _ { k } ( z ) \}$ ; confidence 0.995

80. e13005019.png ; $u ( x , y ) =$ ; confidence 0.995

81. d12020028.png ; $A \in B ( H ( G ) )$ ; confidence 0.995

82. f130290150.png ; $( X , L , \tau )$ ; confidence 0.995

83. d1202503.png ; $f [ U ]$ ; confidence 0.995

84. m13019011.png ; $L ( p ) > 0$ ; confidence 0.995

85. y12003035.png ; $D _ { A } \phi = 0$ ; confidence 0.995

86. b13029059.png ; $1 \leq i \leq d$ ; confidence 0.995

87. i130060104.png ; $\varphi _ { + } ( k ) = f ( k )$ ; confidence 0.995

88. b13009013.png ; $u ( x , t ) = \phi ( x - v t - c )$ ; confidence 0.995

89. b13012071.png ; $f \in A ^ { * }$ ; confidence 0.995

90. h1201207.png ; $\nabla : X \rightarrow Y$ ; confidence 0.995

91. c12001053.png ; $E \times C$ ; confidence 0.995

92. i12005090.png ; $e ( T , V )$ ; confidence 0.995

93. k055840278.png ; $c ( A ) \subset \{ 0 \}$ ; confidence 0.995

94. s12017023.png ; $d _ { i } = 1,0 , - 1$ ; confidence 0.995

95. m13019045.png ; $M _ { 0 } ( z ) = f _ { 0 } ( z )$ ; confidence 0.995

96. b13026019.png ; $d [ f , M , N ]$ ; confidence 0.995

97. p12014015.png ; $\theta > 2$ ; confidence 0.995

98. b13030075.png ; $n \geq 2 ^ { 48 }$ ; confidence 0.995

99. c130070260.png ; $( V _ { 1 } , E _ { 1 } , F _ { 1 } )$ ; confidence 0.995

100. b12015098.png ; $\Omega , A , P$ ; confidence 0.995

101. c0221005.png ; $\Gamma ( \alpha )$ ; confidence 0.995

102. d1301808.png ; $g \in A ( X )$ ; confidence 0.995

103. w13009098.png ; $g \in L ^ { 2 } ( [ 0,1 ] ^ { n } )$ ; confidence 0.995

104. b13022039.png ; $\gamma _ { l } = m$ ; confidence 0.995

105. i130030137.png ; $W = S \otimes E$ ; confidence 0.995

106. m13013088.png ; $( r , r )$ ; confidence 0.995

107. k12005063.png ; $q \leq 2 d r$ ; confidence 0.995

108. f13013029.png ; $f : F \rightarrow F$ ; confidence 0.995

109. s1202901.png ; $( G , \tau )$ ; confidence 0.995

110. l057000128.png ; $\sigma , \tau \in T$ ; confidence 0.995

111. p12015017.png ; $\mu$ ; confidence 0.995

112. c12008065.png ; $m ^ { 2 }$ ; confidence 0.995

113. d034120388.png ; $f ^ { * } ( z )$ ; confidence 0.995

114. l12010012.png ; $\gamma > 1 / 2$ ; confidence 0.995

115. i12005069.png ; $m ( n ; T , V )$ ; confidence 0.995

116. a0140703.png ; $1$ ; confidence 0.995

117. b13016022.png ; $\operatorname { Re } ( f | _ { K } ) = 0$ ; confidence 0.995

118. s1200209.png ; $\partial _ { t } L = \frac { 1 } { 2 } \nabla ^ { 2 } L$ ; confidence 0.995

119. b12022082.png ; $H ( f , \xi ) = f _ { 0 } \operatorname { ln } f _ { 0 }$ ; confidence 0.995

120. b12044040.png ; $\chi ( B _ { i } ) = 0$ ; confidence 0.995

121. a12010080.png ; $J _ { \lambda } = ( I + \lambda A ) ^ { - 1 }$ ; confidence 0.995

122. e12006063.png ; $J ^ { 1 } ( J ^ { 1 } Y \rightarrow M )$ ; confidence 0.995

123. m12013077.png ; $\frac { d F } { d t } = - \varepsilon F ( 1 - \gamma F ^ { p } )$ ; confidence 0.995

124. r130070140.png ; $( f , g ) _ { H } = ( F , G ) _ { H }$ ; confidence 0.995

125. p130100140.png ; $K = \{ ( z , w ) : z \in T , w \in K _ { z } \}$ ; confidence 0.995

126. b12021053.png ; $\lambda \in P ^ { + }$ ; confidence 0.995

127. c13019034.png ; $( N ^ { \prime } , L ^ { \prime } )$ ; confidence 0.995

128. a12016045.png ; $A ( t ) = [ f ( u ( t ) ) + \beta ( X ( t ) - X ( t - \tau ) ) ] [ N _ { 0 } - A ( t ) ]$ ; confidence 0.995

129. b01733052.png ; $A ( D )$ ; confidence 0.995

130. b120400137.png ; $H ^ { i } ( G / B , \xi )$ ; confidence 0.995

131. f12001012.png ; $U = Y$ ; confidence 0.995

132. m1302508.png ; $\delta ( x )$ ; confidence 0.995

133. m12003060.png ; $F _ { \sigma } ( x ) = \Phi ( x / \sigma )$ ; confidence 0.995

134. s12020034.png ; $\{ t \}$ ; confidence 0.995

135. k05584083.png ; $L \subset K$ ; confidence 0.995

136. t12020078.png ; $c = c ( m )$ ; confidence 0.995

137. l120170186.png ; $\operatorname { dim } ( K - L ) \leq 2$ ; confidence 0.995

138. a01018051.png ; $\alpha = 0$ ; confidence 0.995

139. g120040112.png ; $1 < s < m / ( m - 1 )$ ; confidence 0.995

140. b0150102.png ; $\phi _ { n } : B _ { n } \rightarrow B O _ { n }$ ; confidence 0.995

141. b11002049.png ; $( B u , u ) < 0$ ; confidence 0.995

142. e03555032.png ; $\pi : X \rightarrow B$ ; confidence 0.995

143. d03128074.png ; $f , g : X \rightarrow Y$ ; confidence 0.995

144. s12025029.png ; $\sqrt { 1 - x ^ { 2 } } h \in C [ - 1,1 ]$ ; confidence 0.995

145. n12012035.png ; $( x )$ ; confidence 0.995

146. a11050074.png ; $K = Q$ ; confidence 0.995

147. b130300144.png ; $2 k$ ; confidence 0.995

148. a12011027.png ; $T ( i , n ) = T ( i - 1 , T ( i , n - 1 ) ) \text { for } i \geq 1 , n \geq 2$ ; confidence 0.995

149. c120180389.png ; $M \times \{ 1 \} \times \{ 0 \} \subset M \times ( 0 , \infty ) \times ( - 1 + 1 )$ ; confidence 0.995

150. s1202802.png ; $X = ( X , x _ { 0 } )$ ; confidence 0.995

151. m06222071.png ; $( h , m , n ) ^ { k }$ ; confidence 0.995

152. m130230106.png ; $\operatorname { dim } X = 3$ ; confidence 0.995

153. i12006017.png ; $( P )$ ; confidence 0.995

154. a11067024.png ; $L ^ { 1 } ( G )$ ; confidence 0.995

155. b13030025.png ; $| B ( m , 2 ) |$ ; confidence 0.995

156. f12016040.png ; $( \lambda I - T )$ ; confidence 0.995

157. l12019046.png ; $X _ { A } ( t , z )$ ; confidence 0.995

158. b120210132.png ; $( w _ { 1 } , w _ { 2 } )$ ; confidence 0.995

159. t120010128.png ; $b _ { 2 } \neq b _ { 4 }$ ; confidence 0.995

160. a130240142.png ; $m \times 1$ ; confidence 0.995

161. a130040442.png ; $h ^ { - 1 } ( F _ { 0 } )$ ; confidence 0.995

162. a12016064.png ; $\lambda < 1$ ; confidence 0.995

163. c12030087.png ; $T _ { 1 } ( H )$ ; confidence 0.995

164. c02479065.png ; $f ( \zeta )$ ; confidence 0.995

165. j13004062.png ; $\operatorname { cr } ( K )$ ; confidence 0.995

166. k12008015.png ; $K _ { p } ( f ) ( p _ { i } ) = f ( p _ { i } )$ ; confidence 0.995

167. l05848075.png ; $L ( H )$ ; confidence 0.995

168. t092810205.png ; $\beta ( M )$ ; confidence 0.995

169. m130110120.png ; $D \phi / D t$ ; confidence 0.995

170. v11006010.png ; $[ u , v ] \equiv \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } \frac { \partial ^ { 2 } v } { \partial y ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial y ^ { 2 } } \frac { \partial ^ { 2 } v } { \partial x ^ { 2 } } - 2 \frac { \partial ^ { 2 } u } { \partial x \partial y } \frac { \partial ^ { 2 } v } { \partial x \partial y }$ ; confidence 0.995

171. b12031037.png ; $1 / p \leq ( n - 1 - 2 \delta ) / 2 n$ ; confidence 0.995

172. w130080151.png ; $\mu \in \Omega ^ { - 1,1 } ( \Sigma _ { g } )$ ; confidence 0.995

173. j13004039.png ; $( ( v - v ^ { 3 } ) / z + v z ) ^ { 3 }$ ; confidence 0.995

174. b0163604.png ; $a , b , c , d$ ; confidence 0.995

175. c12028046.png ; $\gamma \rho$ ; confidence 0.995

176. g130040168.png ; $\| \nu \| ( A ) = \nu ( A \times G ( n , m ) )$ ; confidence 0.995

177. f13019013.png ; $\frac { 1 } { 2 N } \operatorname { sin } N ( x - x _ { j } ) \operatorname { cot } \frac { ( x - x _ { j } ) } { 2 }$ ; confidence 0.995

178. m1200105.png ; $T : X \supset D ( T ) \rightarrow 2 ^ { X }$ ; confidence 0.995

179. f12008037.png ; $\varphi ( g ) = ( \xi , \eta ) ( g ) : = ( \pi ( g ) \xi , \eta )$ ; confidence 0.995

180. y120010141.png ; $= R ( y , z ) _ { 23 } R ( x , z ) _ { 13 } R ( x , y ) _ { 12 }$ ; confidence 0.995

181. d120230105.png ; $F = \operatorname { diag } \{ f _ { i } \}$ ; confidence 0.995

182. l12019042.png ; $V ( t , x ) = x ^ { * } P ( t ) x$ ; confidence 0.995

183. l058770109.png ; $G \times M \rightarrow M$ ; confidence 0.995

184. a1303206.png ; $H _ { 0 } : \theta = 0$ ; confidence 0.995

185. i05195052.png ; $( x _ { k } , y _ { k } )$ ; confidence 0.995

186. n067520411.png ; $2 ^ { - k } \operatorname { log } \omega _ { k } ^ { - 1 } < \infty$ ; confidence 0.995

187. a120070125.png ; $( t , v )$ ; confidence 0.995

188. w12002014.png ; $c ( x , y ) = d ^ { p } ( x , y )$ ; confidence 0.995

189. f12001023.png ; $\pi _ { 1 } ( X , * )$ ; confidence 0.995

190. b12014048.png ; $b ( z ) = z ^ { 2 t }$ ; confidence 0.995

191. s13049015.png ; $r ( P ) : = \operatorname { max } \{ r ( p ) : p \in P \}$ ; confidence 0.995

192. v12002057.png ; $H ^ { k } ( f ^ { - 1 } ( y ) , G ) \neq 0$ ; confidence 0.995

193. b1205004.png ; $Z _ { 0 } : = \{ t : W _ { t } = 0 \}$ ; confidence 0.995

194. b11022092.png ; $Y = X \backslash X$ ; confidence 0.995

195. b12020059.png ; $y ( n ) = c x ( n ) + d u ( n )$ ; confidence 0.995

196. b12015025.png ; $\frac { 1 } { 1 + \sqrt { n } } ( x \sqrt { n } + \frac { 1 } { 2 } )$ ; confidence 0.995

197. b12051064.png ; $\nabla ^ { 2 } f ( x ^ { * } )$ ; confidence 0.995

198. g12005033.png ; $f _ { c } ( y )$ ; confidence 0.995

199. m12015041.png ; $f _ { X , Y } ( X , Y ) = f _ { X } ( X ) f _ { Y } ( Y )$ ; confidence 0.995

200. d12002012.png ; $U _ { 1 } = \{ u _ { 1 } \geq 0 : g ( u _ { 1 } ) > - \infty \}$ ; confidence 0.995

201. k12011020.png ; $u ( x , y , t )$ ; confidence 0.995

202. c024230146.png ; $P = N P$ ; confidence 0.995

203. a12007050.png ; $f \in L ^ { \infty } ( 0 , T ; X )$ ; confidence 0.995

204. e12006060.png ; $J ^ { 1 } \Gamma ( \Gamma ( Y ) )$ ; confidence 0.995

205. t12003040.png ; $\Psi : U ^ { \prime } \rightarrow V ^ { \prime }$ ; confidence 0.995

206. l057000179.png ; $( b , \beta ) \in B$ ; confidence 0.995

207. c12029064.png ; $\mu : M \rightarrow P$ ; confidence 0.995

208. b13030019.png ; $\phi : B ( m , n ) \rightarrow G$ ; confidence 0.995

209. k1200709.png ; $X ^ { \prime \prime } ( t ) + R ( t ) \circ X ( t ) = 0$ ; confidence 0.995

210. m0625002.png ; $\mu ( A )$ ; confidence 0.995

211. e12005021.png ; $( u , v ) \in \Omega ^ { * } \times \Omega ^ { * }$ ; confidence 0.995

212. t12020061.png ; $M _ { 1 } ( k ) = 1$ ; confidence 0.995

213. b12044073.png ; $B ^ { G } = T _ { H } ^ { G } ( B ^ { H } )$ ; confidence 0.995

214. c120180271.png ; $( - 1 ) ^ { p } \in \{ - 1 , + 1 \}$ ; confidence 0.995

215. d13018034.png ; $A ( \hat { G } ) \cong L ^ { 1 } ( G )$ ; confidence 0.995

216. l12016027.png ; $f : S ^ { 2 } \rightarrow G$ ; confidence 0.995

217. f13013036.png ; $F \rightarrow M$ ; confidence 0.995

218. a13020020.png ; $A \circ B = ( A B + B A ) / 2$ ; confidence 0.995

219. a01225027.png ; $\nu = 1$ ; confidence 0.995

220. r13010053.png ; $( i , \alpha ) ^ { \prime }$ ; confidence 0.995

221. w12001048.png ; $W _ { N }$ ; confidence 0.995

222. a12006061.png ; $L ( X )$ ; confidence 0.995

223. d1201907.png ; $E ( f ) = \int _ { \Omega } | \nabla f | ^ { 2 } d x$ ; confidence 0.995

224. c12001022.png ; $H ^ { 0 } ( E ) = Z , \quad H ^ { p } ( E ) = 0 , p > 0$ ; confidence 0.995

225. a12020017.png ; $p ( t ) \in F [ t ]$ ; confidence 0.995

226. a12012054.png ; $y _ { j } ^ { j } > 0$ ; confidence 0.995

227. i13005077.png ; $k \rightarrow \pm \infty$ ; confidence 0.995

228. d13018097.png ; $A ( T ^ { 2 } )$ ; confidence 0.995

229. w13014012.png ; $r ( \pm 1 ) = 1 / 2$ ; confidence 0.995

230. n13005018.png ; $r \leq \frac { s ^ { 2 } \mu - 1 } { \mu - 1 }$ ; confidence 0.995

231. a13032026.png ; $H _ { 0 } : \theta = p$ ; confidence 0.995

232. f12016038.png ; $\sigma ( T ) \cap G$ ; confidence 0.995

233. m130260156.png ; $b ^ { 2 } = b$ ; confidence 0.995

234. f13010076.png ; $C V _ { p } ( G )$ ; confidence 0.995

235. b12043088.png ; $E _ { 2 } ^ { 2 } E _ { 1 } + E _ { 1 } E _ { 2 } ^ { 2 } - ( q + q ^ { - 1 } ) E _ { 2 } E _ { 1 } E _ { 2 } = 0$ ; confidence 0.995

236. p1300901.png ; $f : D \rightarrow R$ ; confidence 0.995

237. r13010025.png ; $\tau _ { A } ^ { j }$ ; confidence 0.995

238. q12005024.png ; $\alpha \mapsto f ( x ^ { k } + \alpha d ^ { k } )$ ; confidence 0.995

239. a01432014.png ; $n \neq 2$ ; confidence 0.995

240. i13005027.png ; $f ( x , k )$ ; confidence 0.995

241. d1201104.png ; $f ( x ) - f ( y ) \leq f ( x + y ) \leq f ( x ) + f ( y ) , x , y \in S$ ; confidence 0.995

242. w12018011.png ; $m ( . )$ ; confidence 0.995

243. e12006075.png ; $[ Q , \Gamma ]$ ; confidence 0.995

244. m12007015.png ; $M ( P ) \leq L ( P ) \leq 2 ^ { d } M ( P )$ ; confidence 0.995

245. v1200609.png ; $B _ { 2 n } = N _ { 2 n } / D _ { 2 n }$ ; confidence 0.995

246. j13007040.png ; $k / ( 1 + k )$ ; confidence 0.995

247. a12020072.png ; $\operatorname { dim } X < + \infty$ ; confidence 0.995

248. l06115021.png ; $\xi _ { i } ( 0 ) = 0$ ; confidence 0.995

249. a13028014.png ; $\theta _ { i } ( v )$ ; confidence 0.995

250. i13007044.png ; $v ( \alpha , \theta )$ ; confidence 0.995

251. t09356033.png ; $\mathfrak { M } _ { f }$ ; confidence 0.995

252. l12008048.png ; $( x ^ { k + 1 } / ( k + 1 ) + i y )$ ; confidence 0.995

253. w130080188.png ; $\omega ^ { 0 } = ( \delta v , \delta u )$ ; confidence 0.995

254. b12050049.png ; $= \operatorname { exp } ( - x \sqrt { 2 u } )$ ; confidence 0.995

255. b120150109.png ; $\delta \in N \cup \{ 0 \}$ ; confidence 0.995

256. c13001033.png ; $\sqrt { \kappa }$ ; confidence 0.995

257. c02043012.png ; $A ( f )$ ; confidence 0.995

258. b12027082.png ; $\{ b ( t ) : n h \leq t < ( n + 1 ) h \}$ ; confidence 0.995

259. e1200106.png ; $m : f [ A ] \rightarrow B$ ; confidence 0.995

260. v12002013.png ; $H _ { q } ( M , G ) = 0$ ; confidence 0.995

261. l12003052.png ; $( Z , Y )$ ; confidence 0.995

262. m12016062.png ; $\Sigma = A A ^ { \prime }$ ; confidence 0.995

263. s12026030.png ; $D _ { t } : \Gamma ^ { + } \rightarrow ( L ^ { 2 } )$ ; confidence 0.995

264. v13011062.png ; $A = \frac { 1 } { 2 } \theta ( 2 \pi - \theta ) - \frac { \pi ^ { 2 } } { \operatorname { cosh } ^ { 2 } ( \pi b / l ) } = 0$ ; confidence 0.995

265. c02236040.png ; $p + q = n$ ; confidence 0.995

266. c021620355.png ; $\lambda _ { 0 } = 1$ ; confidence 0.995

267. i13009076.png ; $( \pi )$ ; confidence 0.995

268. t12015059.png ; $\{ \Delta ^ { \alpha } : \alpha \in C \}$ ; confidence 0.995

269. w13012018.png ; $d ( x , A _ { \lambda } ) \rightarrow d ( x , A )$ ; confidence 0.995

270. i13006061.png ; $\kappa = 2 J + 1$ ; confidence 0.995

271. w130080150.png ; $( \overline { \partial } + \overline { A } ) \psi = 0$ ; confidence 0.995

272. n12002066.png ; $m \in M _ { F }$ ; confidence 0.995

273. b13026043.png ; $\Omega _ { 2 } \subset \Omega$ ; confidence 0.995

274. l11003088.png ; $A \in F$ ; confidence 0.995

275. r13004045.png ; $\frac { \partial u } { \partial n } = 0$ ; confidence 0.995

276. o12001034.png ; $O ( \varepsilon )$ ; confidence 0.995

277. e1300508.png ; $\phi ( \lambda , \mu ; \alpha , \beta ; x , y ) =$ ; confidence 0.995

278. w13013020.png ; $\chi ( \Sigma )$ ; confidence 0.995

279. a1302409.png ; $( n \times 1 )$ ; confidence 0.995

280. p13007082.png ; $E \subset \Omega$ ; confidence 0.995

281. i13005049.png ; $\int _ { - \infty } ^ { \infty } | f ( x , i k _ { j } ) | ^ { 2 } d x = ( m _ { j } ^ { + } ) ^ { - 2 }$ ; confidence 0.995

282. q13005028.png ; $M = \lambda ( K ) : = [ \mu ^ { - 1 } ( \pi K / 2 ) ] ^ { - 2 } - 1$ ; confidence 0.995

283. r13005021.png ; $G = V _ { 4 } = \{ ( 1 ) , ( 12 ) ( 34 ) , ( 13 ) ( 24 ) , ( 14 ) ( 23 ) \}$ ; confidence 0.995

284. t12021020.png ; $t ( M ; 1,1 )$ ; confidence 0.995

285. q12008092.png ; $1 \leq p \leq P - 1$ ; confidence 0.995

286. z12001078.png ; $p ^ { m - 1 }$ ; confidence 0.995

287. h12011022.png ; $f \in C ( B ( 0 , r ) )$ ; confidence 0.995

288. b13022073.png ; $p > N$ ; confidence 0.995

289. s1301407.png ; $r , s \geq 0$ ; confidence 0.995

290. p13014027.png ; $p = \alpha x$ ; confidence 0.995

291. t12015076.png ; $\Delta ^ { i t }$ ; confidence 0.995

292. c120170143.png ; $( p q ) ( Z , Z ) = 0$ ; confidence 0.995

293. l06003022.png ; $A A ^ { \prime }$ ; confidence 0.995

294. h04602031.png ; $Y _ { 1 } = X _ { 1 } + P Y _ { 2 } , \quad Y _ { 2 } = X _ { 2 } + C Y _ { 1 }$ ; confidence 0.995

295. w12018074.png ; $| t | = \sqrt { \sum _ { k = 1 } ^ { N } t _ { k } ^ { 2 } }$ ; confidence 0.995

296. b12020058.png ; $x ( n + 1 ) = A x ( n ) + b u ( n )$ ; confidence 0.995

297. a130040762.png ; $\Sigma ( P , R ^ { \prime } )$ ; confidence 0.995

298. t09356035.png ; $\mathfrak { M } _ { f } \cap A ^ { + }$ ; confidence 0.995

299. c120180220.png ; $\theta \in E$ ; confidence 0.995

300. b12030057.png ; $A ( \eta )$ ; confidence 0.995

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/12. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/12&oldid=44422
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