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== List ==
 
== List ==
1. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057020/l05702053.png ; $\operatorname { Gal } ( \overline { k } _ { S } / k )$ ; confidence 0.400
+
1. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057020/l05702053.png ; $\operatorname { Gal } ( \overline { k } _ { s } / k )$ ; confidence 0.400
  
 
2. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007046.png ; $f ( x ) = ( 2 \pi ) ^ { - 2 n } \int _ { {\bf R} ^ { 2 n } } e ^ { i x \xi } \hat { f } ( \xi ) d \xi$ ; confidence 0.400
 
2. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w12007046.png ; $f ( x ) = ( 2 \pi ) ^ { - 2 n } \int _ { {\bf R} ^ { 2 n } } e ^ { i x \xi } \hat { f } ( \xi ) d \xi$ ; confidence 0.400
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4. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q1200104.png ; $\varphi _ { 1 } ( f ) , \dots , \varphi _ { n } ( f )$ ; confidence 0.400
 
4. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120010/q1200104.png ; $\varphi _ { 1 } ( f ) , \dots , \varphi _ { n } ( f )$ ; confidence 0.400
  
5. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009060.png ; $R = {\cal O} [ [ \Gamma ] ] = \text { varprojlim } O [ \Gamma / \Gamma ^ { p ^ { n } } ]$ ; confidence 0.400
+
5. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i13009060.png ; $R = {\cal O} [ [ \Gamma ] ] = \text { varprojlim } {\cal O} [ \Gamma / \Gamma ^ { p ^ { n } } ]$ ; confidence 0.400
  
 
6. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012084.png ; $c _ { t } ^ { \prime } \geq c _ { t }$ ; confidence 0.400
 
6. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012084.png ; $c _ { t } ^ { \prime } \geq c _ { t }$ ; confidence 0.400
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11. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130010/f13001053.png ; $O ^ { \sim }$ ; confidence 0.399
 
11. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130010/f13001053.png ; $O ^ { \sim }$ ; confidence 0.399
  
12. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t120070118.png ; $+ \frac { 1 } { 2 } ( 2 ^ { 12 } \frac { \eta ^ { 24 } ( q ) } { \eta ( q ^ { 1 / 2 } ) ^ { 24 } } - 2 ^ { 12 } \frac { \eta ( q ^ { 2 } ) ^ { 24 } \eta ( q ^ { 1 / 2 } ) ^ { 24 } } { \eta ( q ) ^ { 48 } } ),$ ; confidence 0.399
+
12. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120070/t120070118.png ; $+ \frac { 1 } { 2 } \left( 2 ^ { 12 } \frac { \eta ^ { 24 } ( q ) } { \eta ( q ^ { 1 / 2 } ) ^ { 24 } } - 2 ^ { 12 } \frac { \eta ( q ^ { 2 } ) ^ { 24 } \eta ( q ^ { 1 / 2 } ) ^ { 24 } } { \eta ( q ) ^ { 48 } } \right),$ ; confidence 0.399
  
 
13. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c1202104.png ; $P _ { n } ( A _ { n } ) \rightarrow 0$ ; confidence 0.399
 
13. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c1202104.png ; $P _ { n } ( A _ { n } ) \rightarrow 0$ ; confidence 0.399
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27. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110490/a11049023.png ; $F ^ { \prime }$ ; confidence 0.398
 
27. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110490/a11049023.png ; $F ^ { \prime }$ ; confidence 0.398
  
28. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g1200409.png ; $\operatorname { max } _ { x \in X } | \partial ^ { \alpha } f ( x ) | \leq C ^ { | \alpha | + 1 } ( | \alpha ! | ) ^ { s },$ ; confidence 0.398
+
28. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g1200409.png ; $\operatorname { max } _ { x \in K } | \partial ^ { \alpha } f ( x ) | \leq C ^ { | \alpha | + 1 } ( | \alpha ! | ) ^ { s },$ ; confidence 0.398
  
 
29. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i120080136.png ; $w ( \{ S _ { i } \} \rightarrow \{ S _ { i } ^ { \prime } \} )$ ; confidence 0.398
 
29. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i120080136.png ; $w ( \{ S _ { i } \} \rightarrow \{ S _ { i } ^ { \prime } \} )$ ; confidence 0.398
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30. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012034.png ; $g _ { j } = \sum _ { i = 1 } ^ { M } f _ { i } h _ {i j } , j = 1 , \ldots , N,$ ; confidence 0.398
 
30. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012034.png ; $g _ { j } = \sum _ { i = 1 } ^ { M } f _ { i } h _ {i j } , j = 1 , \ldots , N,$ ; confidence 0.398
  
31. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w1201804.png ; $\operatorname{E} W ^ { ( N ) } ( t ) W ^ { ( N ) } ( s ) = \prod _ { i = 1 } ^ { N } t _ { i } \bigwedge s _ { i },$ ; confidence 0.398
+
31. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w1201804.png ; $\mathsf{E} W ^ { ( N ) } ( t ) W ^ { ( N ) } ( s ) = \prod _ { i = 1 } ^ { N } t _ { i } \bigwedge s _ { i },$ ; confidence 0.398
  
32. https://www.encyclopediaofmath.org/legacyimages/r/r110/r110110/r11011028.png ; $x _ { 1 } \prec \ldots \prec x _ { \alpha } \prec . .$ ; confidence 0.398
+
32. https://www.encyclopediaofmath.org/legacyimages/r/r110/r110110/r11011028.png ; $x _ { 1 } \prec \ldots \prec x _ { \alpha } \prec \dots$ ; confidence 0.398
  
 
33. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012270/a01227058.png ; $S _ { 2 }$ ; confidence 0.398
 
33. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012270/a01227058.png ; $S _ { 2 }$ ; confidence 0.398
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36. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130010/r13001010.png ; $b _ { j } = a _ { j } |_{x _ { 0 } = 1 / f} f ^ { \mu }$ ; confidence 0.398
 
36. https://www.encyclopediaofmath.org/legacyimages/r/r130/r130010/r13001010.png ; $b _ { j } = a _ { j } |_{x _ { 0 } = 1 / f} f ^ { \mu }$ ; confidence 0.398
  
37. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a1201304.png ; $\operatorname{E} _ { \theta } [ H ( \theta , X ) ] = 0 , \quad \text { if } \theta = \theta ^ { * },$ ; confidence 0.398
+
37. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120130/a1201304.png ; $\mathsf{E} _ { \theta } [ H ( \theta , X ) ] = 0 , \quad \text { if } \theta = \theta ^ { * },$ ; confidence 0.398
  
 
38. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120490/b12049010.png ; $\operatorname { lim } _ { n \rightarrow \infty } m _ { i } ( E _ { n } ) = 0$ ; confidence 0.397
 
38. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120490/b12049010.png ; $\operatorname { lim } _ { n \rightarrow \infty } m _ { i } ( E _ { n } ) = 0$ ; confidence 0.397
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43. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230130.png ; $[ K , L ] ( X _ { 1 } , \dots , X _ { k + 1 } ) =$ ; confidence 0.397
 
43. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230130.png ; $[ K , L ] ( X _ { 1 } , \dots , X _ { k + 1 } ) =$ ; confidence 0.397
  
44. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180198.png ; $A ( g ) = \frac { 1 } { n - 2 } ( \operatorname { Ric } ( g ) - \frac { 1 } { 2 } \frac { S ( g ) } { n - 1 } g ) \in \operatorname{S} ^ { 2 } \cal E$ ; confidence 0.397
+
44. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180198.png ; $A ( g ) = \frac { 1 } { n - 2 } \left( \operatorname { Ric } ( g ) - \frac { 1 } { 2 } \frac { S ( g ) } { n - 1 } g \right) \in \mathsf{S} ^ { 2 } \cal E$ ; confidence 0.397
  
 
45. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520490.png ; $\Omega = \text{const}$ ; confidence 0.397
 
45. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520490.png ; $\Omega = \text{const}$ ; confidence 0.397
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71. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130070/h13007063.png ; $K [ X _ { 1 } , \dots , X _ { n } ]$ ; confidence 0.394
 
71. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130070/h13007063.png ; $K [ X _ { 1 } , \dots , X _ { n } ]$ ; confidence 0.394
  
72. 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
+
72. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120160/c12016019.png ; $r _ { j j } = \left( a _ { j j } - \sum _ { k = 1 } ^ { j - 1 } r _ { k j } ^ { 2 } \right) ^ { 1 / 2 }$ ; confidence 0.394
  
73. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023270/c0232707.png ; $\overline{A} \subset \overline { B }$ ; confidence 0.394
+
73. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023270/c0232707.png ; $\overline{A} \subseteq \overline { B }$ ; confidence 0.394
  
 
74. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180380.png ; $M \subset {\bf R} ^ { n }$ ; confidence 0.394
 
74. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180380.png ; $M \subset {\bf R} ^ { n }$ ; confidence 0.394
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80. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d130060126.png ; $T \subseteq X$ ; confidence 0.394
 
80. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d130060126.png ; $T \subseteq X$ ; confidence 0.394
  
81. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k12012065.png ; $\int _ { - \infty } ^ { \infty } [ \frac { - \operatorname { ln } F _ { \text{ac} } ^ { \prime } ( x ) } { 1 + x ^ { 2 } } ] d x < \infty ,$ ; confidence 0.394
+
81. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k12012065.png ; $\int _ { - \infty } ^ { \infty } \left[ \frac { - \operatorname { ln } F _ { \text{ac} } ^ { \prime } ( x ) } { 1 + x ^ { 2 } } \right] d x < \infty ,$ ; confidence 0.394
  
 
82. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b120400125.png ; $\delta : = ( 1 / 2 ) \sum _ { \alpha \in S ^ { + } } \alpha \in {\frak h} _ {\bf R } ^ { * }$ ; confidence 0.394
 
82. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120400/b120400125.png ; $\delta : = ( 1 / 2 ) \sum _ { \alpha \in S ^ { + } } \alpha \in {\frak h} _ {\bf R } ^ { * }$ ; confidence 0.394
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102. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020171.png ; $\tilde{u}_1$ ; confidence 0.392
 
102. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d120020171.png ; $\tilde{u}_1$ ; confidence 0.392
  
103. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007019.png ; $| \frac { \partial U ( t , s ) } { \partial t } \| \leq \frac { C } { t - s } , \quad s , t \in [ 0 , T ], $ ; confidence 0.392 NOTE: why is there a single bar on the left and a double bar on the right?
+
103. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120070/a12007019.png ; $\| \frac { \partial U ( t , s ) } { \partial t } \| \leq \frac { C } { t - s } , \quad s , t \in [ 0 , T ], $ ; confidence 0.392 NOTE: why is there a single bar on the left and a double bar on the right?
  
 
104. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110139.png ; $r _ { N } ( a , b ) \in S _ { \text{scl} } ^ { m _ { 1 }  + m _ { 2 } - N}$ ; confidence 0.392
 
104. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110139.png ; $r _ { N } ( a , b ) \in S _ { \text{scl} } ^ { m _ { 1 }  + m _ { 2 } - N}$ ; confidence 0.392
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116. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o13008055.png ; $q _ { 1 } ( x )$ ; confidence 0.391
 
116. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130080/o13008055.png ; $q _ { 1 } ( x )$ ; confidence 0.391
  
117. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230171.png ; $\sum _ { | \alpha | = 0 } ^ { k } ( \frac { \partial L } { \partial y _ { \alpha } ^ { a }}  \circ \sigma ^ { k }  ) ( \frac { \partial } { \partial x } ) ^ { \alpha } ( Z ^ { a } \circ \sigma ) \Delta.$ ; confidence 0.391
+
117. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230171.png ; $\sum _ { | \alpha | = 0 } ^ { k } \left( \frac { \partial L } { \partial y _ { \alpha } ^ { a }}  \circ \sigma ^ { k }  \right) ( \frac { \partial } { \partial x } ) ^ { \alpha } ( Z ^ { a } \circ \sigma ) \Delta.$ ; confidence 0.391
  
 
118. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130040/z13004024.png ; $K _ { 7  , 11}$ ; confidence 0.391
 
118. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130040/z13004024.png ; $K _ { 7  , 11}$ ; confidence 0.391
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119. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064037.png ; $E ( a ) = \operatorname { det } T ( a ) T ( a ^ { - 1 } )$ ; confidence 0.391
 
119. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064037.png ; $E ( a ) = \operatorname { det } T ( a ) T ( a ^ { - 1 } )$ ; confidence 0.391
  
120. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002036.png ; $\operatorname{P} ( A _ { 1 } \cup \ldots \cup A _ { n } )$ ; confidence 0.391
+
120. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002036.png ; $\mathsf{P} ( A _ { 1 } \cup \ldots \cup A _ { n } )$ ; confidence 0.391
  
 
121. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110254.png ; $q _ { \alpha } \in S ( \tilde { h } ^ { - 1 } , \tilde{g} )$ ; confidence 0.391
 
121. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110254.png ; $q _ { \alpha } \in S ( \tilde { h } ^ { - 1 } , \tilde{g} )$ ; confidence 0.391
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131. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b120220103.png ; $t _ { n  + 1} - t _ { n } \sim \varepsilon$ ; confidence 0.390
 
131. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120220/b120220103.png ; $t _ { n  + 1} - t _ { n } \sim \varepsilon$ ; confidence 0.390
  
132. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520395.png ; $y _ { i } = z _ { 1 } ^ { \alpha _ { i 1 } } \ldots z _ { n } ^ { \alpha _ { i n } } , \quad i = 1 , \dots , n$ ; confidence 0.390
+
132. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520395.png ; $y _ { i } = z _ { 1 } ^ { \alpha _ { i 1 } } \ldots z _ { n } ^ { \alpha _ { i n } } , \quad i = 1 , \dots , n,$ ; confidence 0.390
  
 
133. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031380/d031380221.png ; $\bf I$ ; confidence 0.390
 
133. https://www.encyclopediaofmath.org/legacyimages/d/d031/d031380/d031380221.png ; $\bf I$ ; confidence 0.390
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144. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l12012033.png ; $\hat { K } _ { \text{p} }$ ; confidence 0.389
 
144. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120120/l12012033.png ; $\hat { K } _ { \text{p} }$ ; confidence 0.389
  
145. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130050/f13005026.png ; $\| \sum _ { j = 1 } ^ { m } w _ { j } . \frac { p _ { j } - p _ { i } } { \| p _ { j } - p _ { i } \| } \| > w _ { i } , i \neq j,$ ; confidence 0.389
+
145. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130050/f13005026.png ; $\left\| \sum _ { j = 1 } ^ { m } w _ { j } . \frac { p _ { j } - p _ { i } } { \| p _ { j } - p _ { i } \| } \right\| > w _ { i } , i \neq j,$ ; confidence 0.389
  
 
146. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022440/c022440108.png ; $\{ u _ { i } \}$ ; confidence 0.389
 
146. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022440/c022440108.png ; $\{ u _ { i } \}$ ; confidence 0.389
  
147. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t09408033.png ; $\square \ldots \rightarrow \pi _ { n + 1 } ( X ; A , B , ^* ) \stackrel { \partial } { \rightarrow } \pi _ { n } ( A , A \bigcap B , ^* )$ ; confidence 0.389
+
147. https://www.encyclopediaofmath.org/legacyimages/t/t094/t094080/t09408033.png ; $\square \ldots \rightarrow \pi _ { n + 1 } ( X ; A , B , ^* ) \stackrel { \partial } { \rightarrow } \pi _ { n } ( A , A \bigcap B , ^* ) \rightarrow $ ; confidence 0.389
  
148. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110470/c11047044.png ; $F *$ ; confidence 0.389
+
148. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110470/c11047044.png ; $F_{*}$ ; confidence 0.389
  
149. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c1301604.png ; $S \subset \Sigma ^ {\color{blue} * }$ ; confidence 0.389
+
149. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c1301604.png ; $S \subseteq \Sigma ^ {\color{blue} * }$ ; confidence 0.389
  
 
150. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240224.png ; $z_1 , \dots ,z_n$ ; confidence 0.389
 
150. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240224.png ; $z_1 , \dots ,z_n$ ; confidence 0.389
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158. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130060/w13006030.png ; ${\cal V} _ { g , n }$ ; confidence 0.388
 
158. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130060/w13006030.png ; ${\cal V} _ { g , n }$ ; confidence 0.388
  
159. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240508.png ; $\operatorname{E} ( {\bf Z} _ { 13 } ) = 0$ ; confidence 0.388
+
159. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240508.png ; $\mathsf{E} ( {\bf Z} _ { 13 } ) = 0$ ; confidence 0.388
  
 
160. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c120010109.png ; $a \in \partial E$ ; confidence 0.388
 
160. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c120010109.png ; $a \in \partial E$ ; confidence 0.388
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164. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130190/c13019056.png ; $e_{k + 1} , \ldots , e _ { n }$ ; confidence 0.387
 
164. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130190/c13019056.png ; $e_{k + 1} , \ldots , e _ { n }$ ; confidence 0.387
  
165. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030037.png ; $a _ { k l } ( y ) \xi _ { k } \xi _ { l } \geq \alpha | \xi | ^ { 2 }$ ; confidence 0.387
+
165. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030037.png ; $a _ { k \text{l} } ( y ) \xi _ { k } \xi _ { \text{l} } \geq \alpha | \xi | ^ { 2 }$ ; confidence 0.387
  
 
166. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130310/a130310110.png ; $\sum _ { | X | \geq n } \mu ( X ) \frac { T ^ { - 1 } ( \operatorname { time } _ {\cal  A } ( X ) ) } { | X | } \leq \sum _ { | X | \geq n } \mu ( X ),$ ; confidence 0.387
 
166. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130310/a130310110.png ; $\sum _ { | X | \geq n } \mu ( X ) \frac { T ^ { - 1 } ( \operatorname { time } _ {\cal  A } ( X ) ) } { | X | } \leq \sum _ { | X | \geq n } \mu ( X ),$ ; confidence 0.387
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175. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130230/m13023043.png ; $R _ { j } = {\bf R} _ { \geq 0 } v_j$ ; confidence 0.386
 
175. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130230/m13023043.png ; $R _ { j } = {\bf R} _ { \geq 0 } v_j$ ; confidence 0.386
  
176. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140163.png ; $( F f ) ( z ) = \sum _ { j = 1 } ^ { n } ( z _ { j } \frac { \partial f ( z ) } { \partial z _ { j } } + \bar{z} _ { j } \frac { \partial f ( z ) } { \partial \bar{z} _ { j } } )$ ; confidence 0.386
+
176. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140163.png ; $( F f ) ( z ) = \sum _ { j = 1 } ^ { n } \left( z _ { j } \frac { \partial f ( z ) } { \partial z _ { j } } + \bar{z} _ { j } \frac { \partial f ( z ) } { \partial \bar{z} _ { j } } \right).$ ; confidence 0.386
  
 
177. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004038.png ; $X _ { g } ^ { * } = {\color{blue} \cup} _ { r \leq g } X _ { r }$ ; confidence 0.386
 
177. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130040/s13004038.png ; $X _ { g } ^ { * } = {\color{blue} \cup} _ { r \leq g } X _ { r }$ ; confidence 0.386
Line 368: Line 368:
 
184. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043320/g0433206.png ; $a _ { s t }$ ; confidence 0.386
 
184. https://www.encyclopediaofmath.org/legacyimages/g/g043/g043320/g0433206.png ; $a _ { s t }$ ; confidence 0.386
  
185. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008038.png ; $\operatorname{E} [ W _ { p } ] _ { \text{NP} } =$ ; confidence 0.386
+
185. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008038.png ; $\mathsf{E} [ W _ { p } ] _ { \text{NP} } =$ ; confidence 0.386
  
 
186. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l13008034.png ; $c_1 \operatorname{deg} I + c _ { 2 } \operatorname{log} \operatorname{ht} I$ ; confidence 0.386
 
186. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l13008034.png ; $c_1 \operatorname{deg} I + c _ { 2 } \operatorname{log} \operatorname{ht} I$ ; confidence 0.386
Line 410: Line 410:
 
205. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d12030055.png ; $d r = L ^ { * } r + \langle f ^ { - 1 } ( t , Y ( t ) ) g ( t , X ( t ) , Y ( t ) ) , d Y ( t ) \rangle  { r },$ ; confidence 0.385
 
205. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d12030055.png ; $d r = L ^ { * } r + \langle f ^ { - 1 } ( t , Y ( t ) ) g ( t , X ( t ) , Y ( t ) ) , d Y ( t ) \rangle  { r },$ ; confidence 0.385
  
206. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011031.png ; $\gamma _ { 1 } ^ { 2 } = 1 , \gamma _ { 2 } ^ { 2 } = \gamma _ { 3 } ^ { 2 } = \gamma _ { 4 } ^ { 2 } = - 1$ ; confidence 0.385
+
206. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011031.png ; $\gamma _ { 1 } ^ { 2 } = 1 , \gamma _ { 2 } ^ { 2 } = \gamma _ { 3 } ^ { 2 } = \gamma _ { 4 } ^ { 2 } = - 1,$ ; confidence 0.385
  
 
207. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d13018089.png ; $f \in I _ { E }$ ; confidence 0.385
 
207. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130180/d13018089.png ; $f \in I _ { E }$ ; confidence 0.385
  
208. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120020/t1200204.png ; $( F ^ {\bf Z } , {\cal B} ^ {\bf Z } , \operatorname{P} )$ ; confidence 0.385
+
208. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120020/t1200204.png ; $( F ^ {\bf Z } , {\cal B} ^ {\bf Z } , \mathsf{P} )$ ; confidence 0.385
  
 
209. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011380/a011380139.png ; $\frak B$ ; confidence 0.385
 
209. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011380/a011380139.png ; $\frak B$ ; confidence 0.385
Line 426: Line 426:
 
213. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b01747062.png ; $l_i$ ; confidence 0.384
 
213. https://www.encyclopediaofmath.org/legacyimages/b/b017/b017470/b01747062.png ; $l_i$ ; confidence 0.384
  
214. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230147.png ; $X A X ^ { \prime } \sim L _ { 1 } ^ { ( 1 ) } ( f _ { 1 } , \frac { { k } } { 2 } ),$ ; confidence 0.384
+
214. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120230/s120230147.png ; $X A X ^ { \prime } \sim L _ { 1 } ^ { ( 1 ) } \left( f _ { 1 } , \frac { { k } } { 2 } \right),$ ; confidence 0.384
  
 
215. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120270/m12027045.png ; $c_{i j k}$ ; confidence 0.384
 
215. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120270/m12027045.png ; $c_{i j k}$ ; confidence 0.384
Line 434: Line 434:
 
217. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120240/e12024044.png ; $E ( {\bf Q} )$ ; confidence 0.384
 
217. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120240/e12024044.png ; $E ( {\bf Q} )$ ; confidence 0.384
  
218. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130040/o13004014.png ; $\operatorname { lim } _ { \varepsilon \downarrow 0 } \frac { \mu _ { \varepsilon } ^ { X } ( \phi ) } { \mu _ { \varepsilon } ^ { X } ( \psi ) }$ ; confidence 0.384
+
218. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130040/o13004014.png ; $\operatorname { lim } _ { \varepsilon \downarrow 0 } \frac { \mu _ { \varepsilon } ^ { x } ( \phi ) } { \mu _ { \varepsilon } ^ { x } ( \psi ) }$ ; confidence 0.384
  
 
219. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012039.png ; $\sum _ { j } g _ { j }  = \sum _ { i } f _ { i } = \sum _ { j } h _ { i j } = 1$ ; confidence 0.384
 
219. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012039.png ; $\sum _ { j } g _ { j }  = \sum _ { i } f _ { i } = \sum _ { j } h _ { i j } = 1$ ; confidence 0.384
Line 442: Line 442:
 
221. 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
 
221. 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
  
222. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n12002072.png ; $\int _ { E } \operatorname { log } ( d \operatorname{P} / d \mu ) d \operatorname{P}$ ; confidence 0.384
+
222. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n12002072.png ; $\int _ { E } \operatorname { log } ( d \mathsf{P} / d \mu ) d \mathsf{P}$ ; confidence 0.384
  
223. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120030/h12003018.png ; $\tau ( \varphi ) ^ { \alpha } ( x ) = g ^ { i j } ( x ) ( \frac { \partial ^ { 2 } \varphi ^ { \alpha } } { \partial x ^ { i } \partial x ^ { j } } - \square ^ { M } \Gamma _ { i j } ^ { k } ( x ) \frac { \partial \varphi ^ { \alpha } } { \partial x ^ { k } } + + \square ^ { N } \Gamma _ { \beta \gamma } ^ { \alpha } ( \varphi ( x ) ) \frac { \partial \varphi \beta } { \partial x ^ { i } } \frac { \partial \varphi ^ { \gamma } } { \partial x ^ { j } } ),$ ; confidence 0.384
+
223. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120030/h12003018.png ; $\tau ( \varphi ) ^ { \alpha } ( x ) = g ^ { i j } ( x ) \left( \frac { \partial ^ { 2 } \varphi ^ { \alpha } } { \partial x ^ { i } \partial x ^ { j } } - \square ^ { M } \Gamma _ { i j } ^ { k } ( x ) \frac { \partial \varphi ^ { \alpha } } { \partial x ^ { k } } + + \square ^ { N } \Gamma _ { \beta \gamma } ^ { \alpha } ( \varphi ( x ) ) \frac { \partial \varphi \beta } { \partial x ^ { i } } \frac { \partial \varphi ^ { \gamma } } { \partial x ^ { j } } \right),$ ; confidence 0.384
  
 
224. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005080.png ; $V_{( n )} = 0$ ; confidence 0.384
 
224. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005080.png ; $V_{( n )} = 0$ ; confidence 0.384
Line 458: Line 458:
 
229. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120050/b12005020.png ; $( P _ { n } ) = ( P _ { n } ( z _ { 0 } ) )$ ; confidence 0.383
 
229. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120050/b12005020.png ; $( P _ { n } ) = ( P _ { n } ( z _ { 0 } ) )$ ; confidence 0.383
  
230. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120340/b12034031.png ; $\sum _ { \alpha } \operatorname { sup } _ { D _ { r } } | c _ { \alpha } z ^ { \alpha } | < 1$ ; confidence 0.383
+
230. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120340/b12034031.png ; $\sum _ { \alpha } \operatorname { sup } _ { D _ { r } } | c _ { \alpha } z ^ { \alpha } | < 1,$ ; confidence 0.383
  
 
231. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520243.png ; $\bar { A } _ { i j }$ ; confidence 0.383
 
231. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520243.png ; $\bar { A } _ { i j }$ ; confidence 0.383
  
232. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c1202805.png ; $X *$ ; confidence 0.383
+
232. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120280/c1202805.png ; $X_{*}$ ; confidence 0.383
  
 
233. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130120/h13012011.png ; $x \in G_1$ ; confidence 0.383
 
233. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130120/h13012011.png ; $x \in G_1$ ; confidence 0.383
Line 474: Line 474:
 
237. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m130250102.png ; $H ^ { s } ( {\bf R} ^ { n } )$ ; confidence 0.382
 
237. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130250/m130250102.png ; $H ^ { s } ( {\bf R} ^ { n } )$ ; confidence 0.382
  
238. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018068.png ; $r _ { 1 } ( t , s ) = \prod _ { i = 1 } ^ { N } ( t _ { i } \bigwedge s _ { i } - t _ { i } s _ { i } )$ ; confidence 0.382
+
238. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120180/w12018068.png ; $r _ { 1 } ( t , s ) = \prod _ { i = 1 } ^ { N } ( t _ { i } \bigwedge s _ { i } - t _ { i } s _ { i } ),$ ; confidence 0.382
  
 
239. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a0100204.png ; $\{ E _ { n _ { 1 }  \ldots n _ { k } }\}$ ; confidence 0.382
 
239. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a0100204.png ; $\{ E _ { n _ { 1 }  \ldots n _ { k } }\}$ ; confidence 0.382
  
240. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013023.png ; $= \operatorname { exp } ( x P _ { 0 } z + \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } ) g ( z ) . . \operatorname { exp } ( - x P _ { 0 } z - \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } ),$ ; confidence 0.382
+
240. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013023.png ; $= \operatorname { exp } \left( x P _ { 0 } z + \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } \right) g ( z ) . . \operatorname { exp } \left( - x P _ { 0 } z - \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } \right),$ ; confidence 0.382
  
 
241. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010222.png ; $E_i$ ; confidence 0.382
 
241. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a110010222.png ; $E_i$ ; confidence 0.382
Line 498: Line 498:
 
249. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c130160141.png ; $\operatorname{ATIME} [ n ^ { O ( 1 ) } ] = \operatorname { PSPACE }$ ; confidence 0.381
 
249. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130160/c130160141.png ; $\operatorname{ATIME} [ n ^ { O ( 1 ) } ] = \operatorname { PSPACE }$ ; confidence 0.381
  
250. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180122.png ; ${\cal E} \overset{\approx}{\to} {\cal E} {* * }$ ; confidence 0.381
+
250. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180122.png ; ${\cal E} \overset{\approx}{\to} {\cal E} _ {* * }$ ; confidence 0.381
  
251. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054017.png ; $( x _ { i j } ( a ) , x _ { k l } ( b ) ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } i \neq 1 , j \neq k }, \\ { x _ { il } ( a b ) } & { \text { if } i \neq 1 , j = k }. \end{array} \right.$ ; confidence 0.381
+
251. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054017.png ; $( x _ { i j } ( a ) , x _ { k \text{l} } ( b ) ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } i \neq \text{l} , j \neq k }, \\ { x _ { i \text{l} } ( a b ) } & { \text { if } i \neq \text{l} , j = k }. \end{array} \right.$ ; confidence 0.381
  
252. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040405.png ; ${\bf P} _ { U }\bf K$ ; confidence 0.381
+
252. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040405.png ; ${\bf P} _ { \text{U} } \mathsf{K}$ ; confidence 0.381
  
 
253. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005092.png ; $v _ { n } = v / z ^ { n }$ ; confidence 0.381
 
253. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005092.png ; $v _ { n } = v / z ^ { n }$ ; confidence 0.381
Line 532: Line 532:
 
266. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120240/f12024053.png ; $J _ { t }$ ; confidence 0.380
 
266. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120240/f12024053.png ; $J _ { t }$ ; confidence 0.380
  
267. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007062.png ; $H ^ { n } ( {\cal C} , M ) = \operatorname { Ext } _ { Z {\bf C} } ^ { n } ( {\cal Z} , M )$ ; confidence 0.380
+
267. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007062.png ; $H ^ { n } ( {\cal C} , M ) = \operatorname { Ext } _ { Z {\bf C} } ^ { n } ( {\cal Z} , M ),$ ; confidence 0.380
  
 
268. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007043.png ; $\underline{\operatorname{lim}} \leftarrow$ ; confidence 0.380
 
268. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120070/c12007043.png ; $\underline{\operatorname{lim}} \leftarrow$ ; confidence 0.380
  
269. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013043.png ; $\frac { d N ^ { i } } { d t } = \lambda _ { ( i ) } N ^ { i } ( 1 - \frac { N ^ { i } } { K _ { ( i ) } } ) , \quad i = 1 , \ldots , n$ ; confidence 0.380
+
269. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013043.png ; $\frac { d N ^ { i } } { d t } = \lambda _ { ( i ) } N ^ { i } \left( 1 - \frac { N ^ { i } } { K _ { ( i ) } } \right) , \quad i = 1 , \ldots , n,$ ; confidence 0.380
  
 
270. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g120040136.png ; $G ^ { 3 }$ ; confidence 0.380
 
270. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g120040136.png ; $G ^ { 3 }$ ; confidence 0.380
Line 556: Line 556:
 
278. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d13006041.png ; $j_1 , \dots , j _ { k }$ ; confidence 0.380
 
278. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130060/d13006041.png ; $j_1 , \dots , j _ { k }$ ; confidence 0.380
  
279. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018084.png ; ${\bf Alg} : \text{ ``logics"}\to \text{``pairs of classes of algebras"}$ ; confidence 0.380
+
279. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130180/a13018084.png ; ${\bf Alg} : \text{ ''logics"}\to \text{''pairs of classes of algebras"}$ ; confidence 0.380
  
 
280. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044980/g04498039.png ; $v _ { j }$ ; confidence 0.380
 
280. https://www.encyclopediaofmath.org/legacyimages/g/g044/g044980/g04498039.png ; $v _ { j }$ ; confidence 0.380

Latest revision as of 21:21, 10 May 2020

List

1. l05702053.png ; $\operatorname { Gal } ( \overline { k } _ { s } / k )$ ; confidence 0.400

2. w12007046.png ; $f ( x ) = ( 2 \pi ) ^ { - 2 n } \int _ { {\bf R} ^ { 2 n } } e ^ { i x \xi } \hat { f } ( \xi ) d \xi$ ; confidence 0.400

3. c130160150.png ; $\operatorname{PH} = \operatorname{ATIMEALT} [ n ^ { O ( 1 ) } , O ( 1 ) ]$ ; confidence 0.400

4. q1200104.png ; $\varphi _ { 1 } ( f ) , \dots , \varphi _ { n } ( f )$ ; confidence 0.400

5. i13009060.png ; $R = {\cal O} [ [ \Gamma ] ] = \text { varprojlim } {\cal O} [ \Gamma / \Gamma ^ { p ^ { n } } ]$ ; confidence 0.400

6. a12012084.png ; $c _ { t } ^ { \prime } \geq c _ { t }$ ; confidence 0.400

7. c13016052.png ; $\operatorname{DSPACE}[t(n)]$ ; confidence 0.399

8. n06663080.png ; $h \in {\bf R} ^ { n }$ ; confidence 0.399

9. a11033032.png ; $\tilde { N }$ ; confidence 0.399

10. l12010063.png ; $L _ { 0 , n } ^ { 1 }$ ; confidence 0.399

11. f13001053.png ; $O ^ { \sim }$ ; confidence 0.399

12. t120070118.png ; $+ \frac { 1 } { 2 } \left( 2 ^ { 12 } \frac { \eta ^ { 24 } ( q ) } { \eta ( q ^ { 1 / 2 } ) ^ { 24 } } - 2 ^ { 12 } \frac { \eta ( q ^ { 2 } ) ^ { 24 } \eta ( q ^ { 1 / 2 } ) ^ { 24 } } { \eta ( q ) ^ { 48 } } \right),$ ; confidence 0.399

13. c1202104.png ; $P _ { n } ( A _ { n } ) \rightarrow 0$ ; confidence 0.399

14. b12014038.png ; $r _ { i - 2} ( z ) = q _ { i } ( z ) r _ { i - 1} ( z ) + r _ { i } ( z ) , \quad i = 1,2 ,\dots .$ ; confidence 0.399

15. w13009017.png ; $h _ { j } \in H$ ; confidence 0.399

16. i13006054.png ; $k \in {\bf R}_+$ ; confidence 0.399

17. h1300201.png ; $A = \{ a _ { 1 } , \dots , a _ { q } \}$ ; confidence 0.399

18. n067520322.png ; $( x _ { 1 } , \dots , x _ { n } ) \in M ^ { n }$ ; confidence 0.399

19. b13029016.png ; $M / \mathfrak { q } M$ ; confidence 0.399

20. n067520157.png ; $\lambda - a_i$ ; confidence 0.399

21. l06004028.png ; $( - 1 ) ^ { n } f ( - z ) f ( z ) = a _ { 0 } ^ { 2 } \prod _ { i = 1 } ^ { n } ( z ^ { 2 } - r _ { i } ^ { 2 } )$ ; confidence 0.399

22. l12004068.png ; $w _ { 2 } = ( 1 - c ) / 2$ ; confidence 0.399

23. w12011069.png ; ${\bf R} _ { \xi } ^ { n }$ ; confidence 0.398

24. a110610189.png ; $\partial$ ; confidence 0.398

25. a13004099.png ; $\psi \in S$ ; confidence 0.398

26. b12002014.png ; $\alpha _ { n } + \beta _ { n }$ ; confidence 0.398

27. a11049023.png ; $F ^ { \prime }$ ; confidence 0.398

28. g1200409.png ; $\operatorname { max } _ { x \in K } | \partial ^ { \alpha } f ( x ) | \leq C ^ { | \alpha | + 1 } ( | \alpha ! | ) ^ { s },$ ; confidence 0.398

29. i120080136.png ; $w ( \{ S _ { i } \} \rightarrow \{ S _ { i } ^ { \prime } \} )$ ; confidence 0.398

30. e12012034.png ; $g _ { j } = \sum _ { i = 1 } ^ { M } f _ { i } h _ {i j } , j = 1 , \ldots , N,$ ; confidence 0.398

31. w1201804.png ; $\mathsf{E} W ^ { ( N ) } ( t ) W ^ { ( N ) } ( s ) = \prod _ { i = 1 } ^ { N } t _ { i } \bigwedge s _ { i },$ ; confidence 0.398

32. r11011028.png ; $x _ { 1 } \prec \ldots \prec x _ { \alpha } \prec \dots$ ; confidence 0.398

33. a01227058.png ; $S _ { 2 }$ ; confidence 0.398

34. t130140105.png ; $r_{i, j} = | L \cap e _ { j } I e _ { i } |$ ; confidence 0.398

35. w12010037.png ; $F - O _ { n }$ ; confidence 0.398

36. r13001010.png ; $b _ { j } = a _ { j } |_{x _ { 0 } = 1 / f} f ^ { \mu }$ ; confidence 0.398

37. a1201304.png ; $\mathsf{E} _ { \theta } [ H ( \theta , X ) ] = 0 , \quad \text { if } \theta = \theta ^ { * },$ ; confidence 0.398

38. b12049010.png ; $\operatorname { lim } _ { n \rightarrow \infty } m _ { i } ( E _ { n } ) = 0$ ; confidence 0.397

39. l120170191.png ; $\tau \in \operatorname{Wh} ( \pi )$ ; confidence 0.397

40. c13016018.png ; $\operatorname{NTIME} [t( n )]$ ; confidence 0.397

41. l057000152.png ; $\vdash ( \lambda x y . x ) : ( \sigma \rightarrow ( \tau \rightarrow \sigma ) )$ ; confidence 0.397

42. n067520464.png ; $\tilde {\cal A } = {\cal A} \cap K$ ; confidence 0.397

43. f120230130.png ; $[ K , L ] ( X _ { 1 } , \dots , X _ { k + 1 } ) =$ ; confidence 0.397

44. c120180198.png ; $A ( g ) = \frac { 1 } { n - 2 } \left( \operatorname { Ric } ( g ) - \frac { 1 } { 2 } \frac { S ( g ) } { n - 1 } g \right) \in \mathsf{S} ^ { 2 } \cal E$ ; confidence 0.397

45. n067520490.png ; $\Omega = \text{const}$ ; confidence 0.397

46. r1101105.png ; $x \preceq y \Rightarrow x z \preceq y z.$ ; confidence 0.397

47. s12017039.png ; $f ( d ) = \sum d _ { i }$ ; confidence 0.397

48. i12004031.png ; $= {\bf C}^ { n }$ ; confidence 0.397

49. z130110131.png ; $M _ { k } = \sum _ { i = 1 } ^ { k } M _ { i k }$ ; confidence 0.396

50. t13005080.png ; $\sigma _ { \text{p} }$ ; confidence 0.396

51. o13008011.png ; $x \in {\bf R} _ { + } , \psi _ { m } ( 0 , k ) = 1 , \psi _ { m } ^ { \prime } ( 0 , k ) = 0.$ ; confidence 0.396

52. l057000149.png ; $\Gamma \vdash ( \lambda x . M ) : ( \sigma \rightarrow \tau )$ ; confidence 0.396

53. c021620116.png ; $D ^ { n }$ ; confidence 0.396

54. c12002044.png ; $\widehat { ( I ^ { \alpha } f ) } ( \xi ) = | \xi | ^ { - \alpha } \hat { f } ( \xi )$ ; confidence 0.396

55. a12022033.png ; $S$ ; confidence 0.396

56. a11042079.png ; $\psi$ ; confidence 0.396

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

58. w12011028.png ; $( a ^ { w } u , v ) = \int \int a ( x , \xi ) {\cal H} ( u , v ) ( x , \xi ) d x d \xi, $ ; confidence 0.396

59. a01021070.png ; $P _ { 2 }$ ; confidence 0.396

60. a13018062.png ; ${\bf C A} _ { n }$ ; confidence 0.396

61. c120180147.png ; $g : \otimes ^ { 2 } \cal E * \rightarrow R$ ; confidence 0.396

62. b13001097.png ; $X = {\cal H} _ { n }$ ; confidence 0.395

63. t120060118.png ; $\text{(const)} \int _ { {\bf R} ^ { 3 } } | \nabla \sqrt { \rho ( x ) } | ^ { 2 } d x$ ; confidence 0.395

64. m130180167.png ; $M \backslash a$ ; confidence 0.395

65. t120050118.png ; $x \in \Sigma ^ { i _ { 1 } } ( f )$ ; confidence 0.395

66. b11022050.png ; $i \in \bf N$ ; confidence 0.395

67. c13016032.png ; $\operatorname{SAT} \in \operatorname{NP}$ ; confidence 0.395

68. z13007059.png ; $\operatorname{diag} (g_1, \dots , g _ { n } )$ ; confidence 0.395

69. t120070100.png ; $v _ { n } 1 = 0$ ; confidence 0.395

70. m130260195.png ; $S A W ^ { * }$ ; confidence 0.395

71. h13007063.png ; $K [ X _ { 1 } , \dots , X _ { n } ]$ ; confidence 0.394

72. c12016019.png ; $r _ { j j } = \left( a _ { j j } - \sum _ { k = 1 } ^ { j - 1 } r _ { k j } ^ { 2 } \right) ^ { 1 / 2 }$ ; confidence 0.394

73. c0232707.png ; $\overline{A} \subseteq \overline { B }$ ; confidence 0.394

74. c120180380.png ; $M \subset {\bf R} ^ { n }$ ; confidence 0.394

75. e1202003.png ; $( x _ { i 1 } , \ldots , x _ { i r } )$ ; confidence 0.394

76. b12005021.png ; $f ( z ) = \sum _ { n = 0 } ^ { \infty } P _ { n } ( z - z _ { 0 } )$ ; confidence 0.394

77. e035000118.png ; ${\cal H} _ { \epsilon } ^ { \prime \prime }$ ; confidence 0.394

78. o13005090.png ; $x _ { n } = x / z ^ { n }$ ; confidence 0.394

79. w120110208.png ; $\Delta p _ { j } \Delta q_j \sim h _ { j } ^ { - 1 } \geq 1$ ; confidence 0.394

80. d130060126.png ; $T \subseteq X$ ; confidence 0.394

81. k12012065.png ; $\int _ { - \infty } ^ { \infty } \left[ \frac { - \operatorname { ln } F _ { \text{ac} } ^ { \prime } ( x ) } { 1 + x ^ { 2 } } \right] d x < \infty ,$ ; confidence 0.394

82. b120400125.png ; $\delta : = ( 1 / 2 ) \sum _ { \alpha \in S ^ { + } } \alpha \in {\frak h} _ {\bf R } ^ { * }$ ; confidence 0.394

83. b1200206.png ; $\Gamma _ { n } ^ { - 1 }$ ; confidence 0.394

84. f110160128.png ; $\psi _ { \mathfrak { A } } ^ { l + 1 } \overline { { a } }$ ; confidence 0.393

85. c13014016.png ; $A \circ B = ( a _ { i , j} b _ { i , j} )$ ; confidence 0.393

86. c130070226.png ; $\mathfrak { R } ( C _ { 2 } )$ ; confidence 0.393

87. b13029085.png ; $\varphi _ { M } ^ { i } : \operatorname { Ext } _ { A } ^ { i } ( A / \mathfrak { m } , M ) \rightarrow H _ {\frak m } ^ { i } ( M ) = \operatorname { lim } _ { n \rightarrow \infty } \operatorname { Ext } _ { A } ^ { i } ( A / \mathfrak { m } ^ { n } , M )$ ; confidence 0.393

88. a1103408.png ; $\theta _ { i }$ ; confidence 0.393

89. b13020083.png ; $\mathfrak { g } ^ { \alpha }$ ; confidence 0.393

90. b13026010.png ; $\frac { 1 } { \operatorname{vol} S ^ { n - 1 } } \int _ { \partial K } f ^ { * } \omega,$ ; confidence 0.393

91. f12005028.png ; $y ^ { q ^ { r } } \phi_f ( x / y ) - z ^ { p } = 0,$ ; confidence 0.393

92. w12011036.png ; $a \in {\cal S} ^ { \prime } ( {\bf R} ^ { 2 n } )$ ; confidence 0.393

93. w12005062.png ; ${\bf R} ^ { m } \rightarrow {\bf R} ^ { k }$ ; confidence 0.393

94. a01012057.png ; $k = 0,1 , \dots ,$ ; confidence 0.393

95. d030700109.png ; $s_0$ ; confidence 0.393

96. n067520364.png ; $x _ { i } = \xi _ { i } ( y _ { i } , \ldots , y _ { n } ) , \quad i = 1 , \ldots , n,$ ; confidence 0.393

97. i130090229.png ; $Y^{\chi}$ ; confidence 0.393

98. b015350206.png ; $\Lambda _ { n }$ ; confidence 0.393

99. k1201103.png ; $2 . \frac { \partial ^ { 2 } } { \partial x ^ { 2 } } \operatorname { log } \tau,$ ; confidence 0.393

100. a11050066.png ; ${\bf x} = ( x _ { 1 } , \ldots , x _ { n } )$ ; confidence 0.393

101. a130040281.png ; $x \rightarrow y$ ; confidence 0.392

102. d120020171.png ; $\tilde{u}_1$ ; confidence 0.392

103. a12007019.png ; $\| \frac { \partial U ( t , s ) } { \partial t } \| \leq \frac { C } { t - s } , \quad s , t \in [ 0 , T ], $ ; confidence 0.392 NOTE: why is there a single bar on the left and a double bar on the right?

104. w120110139.png ; $r _ { N } ( a , b ) \in S _ { \text{scl} } ^ { m _ { 1 } + m _ { 2 } - N}$ ; confidence 0.392

105. i130090219.png ; $\tilde{g} \in \operatorname { Gal } ( L ( k ^ { \prime } ) / k )$ ; confidence 0.392

106. n12010058.png ; $Y _ { m } = ( y _ { m + k - 1} , \ldots , y _ { m } ) ^ { T }$ ; confidence 0.392

107. f12021084.png ; $l = 0 , \dots , n _ { j } - 1$ ; confidence 0.392

108. a13018027.png ; $\operatorname{Fm} _ { \tau }$ ; confidence 0.392

109. g12003016.png ; $\int _ { - 1 } ^ { 1 } p ( x ) P _ { n } ( x ) E _ { n + 1 } ( x ) x ^ { k } d x = 0 , \quad k = 0 , \dots , n, $ ; confidence 0.392

110. a012090101.png ; $K ^ { 2 }$ ; confidence 0.392

111. b12044028.png ; $R G = B _ { 1 } \bigoplus \ldots \bigoplus B _ { n }.$ ; confidence 0.392

112. t120200101.png ; $\operatorname { max } _ { k = m + 1 , \ldots , m + n } | g ( k ) | \geq \frac { 1 } { 3 } | g ( 0 ) | \prod _ { j = 1 } ^ { n } \frac { | z _ { j } | - \operatorname { exp } ( - 1 / m ) } { | z _ { j } | + 1 }.$ ; confidence 0.392

113. z12002037.png ; $F _ { m - n + 1}$ ; confidence 0.392

114. t12006094.png ; $\operatorname { lim } _ { Z \rightarrow \infty } \frac { E ^ { \text{TF} } ( \lambda Z ) } { E ^ { \text{Q} } ( \lambda Z ) } = 1.$ ; confidence 0.392

115. d12030037.png ; $\mu_Y$ ; confidence 0.391

116. o13008055.png ; $q _ { 1 } ( x )$ ; confidence 0.391

117. e120230171.png ; $\sum _ { | \alpha | = 0 } ^ { k } \left( \frac { \partial L } { \partial y _ { \alpha } ^ { a }} \circ \sigma ^ { k } \right) ( \frac { \partial } { \partial x } ) ^ { \alpha } ( Z ^ { a } \circ \sigma ) \Delta.$ ; confidence 0.391

118. z13004024.png ; $K _ { 7 , 11}$ ; confidence 0.391

119. s13064037.png ; $E ( a ) = \operatorname { det } T ( a ) T ( a ^ { - 1 } )$ ; confidence 0.391

120. i13002036.png ; $\mathsf{P} ( A _ { 1 } \cup \ldots \cup A _ { n } )$ ; confidence 0.391

121. w120110254.png ; $q _ { \alpha } \in S ( \tilde { h } ^ { - 1 } , \tilde{g} )$ ; confidence 0.391

122. f12020016.png ; $v _ { 1 } , \dots , v _ { n + 1 }$ ; confidence 0.391

123. g130040194.png ; $a \in \operatorname { spt } \nu$ ; confidence 0.390

124. i130090105.png ; $k _ { n }$ ; confidence 0.390

125. l12005027.png ; $\| f ^ { * } g \| \leq \| f \| \| g \|$ ; confidence 0.390

126. a130040181.png ; $a \in G$ ; confidence 0.390

127. l1201504.png ; $[ ., . ] : A \times A \rightarrow A$ ; confidence 0.390

128. m12009026.png ; $P ( D ) ( E ^ { * } g ) = ( P ( D ) ( E ) ) ^ { * } g = \delta _ { 0 } * g = g.$ ; confidence 0.390

129. i13003023.png ; $\operatorname{ind} ( P ) = ( - 1 ) ^ { n } \operatorname{Ch} ( [ a ] ) {\cal T} ( M ) [ T ^ { * } M ],$ ; confidence 0.390

130. d03202025.png ; $\xi_ { 0 }$ ; confidence 0.390

131. b120220103.png ; $t _ { n + 1} - t _ { n } \sim \varepsilon$ ; confidence 0.390

132. n067520395.png ; $y _ { i } = z _ { 1 } ^ { \alpha _ { i 1 } } \ldots z _ { n } ^ { \alpha _ { i n } } , \quad i = 1 , \dots , n,$ ; confidence 0.390

133. d031380221.png ; $\bf I$ ; confidence 0.390

134. b11002023.png ; $\operatorname { sup } _ { \| v \| \leq 1 } | b ( u , v ) | \geq \| u \| , \forall u \in U,$ ; confidence 0.390

135. s13051072.png ; ${\bf V} = \{ ( u _ { 1 } , \dots , u _ { m } ) : u _ { i } \in V _ { i } , i \in \{ 1 , \dots , m \} \};$ ; confidence 0.390

136. a01292076.png ; $\phi_n$ ; confidence 0.390

137. d130180103.png ; $g \in J _ { E } ^ { \circ }$ ; confidence 0.389

138. a0109703.png ; $O$ ; confidence 0.389

139. l110020119.png ; $M ^ { \perp } = \{ x \in G : | x | \wedge | m | = e \text { for all } m \in M \}$ ; confidence 0.389

140. a12023066.png ; $q_j$ ; confidence 0.389

141. w120090137.png ; ${\bf Z} \Lambda ( n )$ ; confidence 0.389

142. b12021057.png ; $U ( {\frak n} )$ ; confidence 0.389

143. r13007058.png ; $v _ { j } \lambda _ { j } ^ { 1 / 2 } = u _ { j }$ ; confidence 0.389

144. l12012033.png ; $\hat { K } _ { \text{p} }$ ; confidence 0.389

145. f13005026.png ; $\left\| \sum _ { j = 1 } ^ { m } w _ { j } . \frac { p _ { j } - p _ { i } } { \| p _ { j } - p _ { i } \| } \right\| > w _ { i } , i \neq j,$ ; confidence 0.389

146. c022440108.png ; $\{ u _ { i } \}$ ; confidence 0.389

147. t09408033.png ; $\square \ldots \rightarrow \pi _ { n + 1 } ( X ; A , B , ^* ) \stackrel { \partial } { \rightarrow } \pi _ { n } ( A , A \bigcap B , ^* ) \rightarrow $ ; confidence 0.389

148. c11047044.png ; $F_{*}$ ; confidence 0.389

149. c1301604.png ; $S \subseteq \Sigma ^ {\color{blue} * }$ ; confidence 0.389

150. a130240224.png ; $z_1 , \dots ,z_n$ ; confidence 0.389

151. e12024012.png ; ${\bf Z} / p ^ { m }$ ; confidence 0.389

152. d12002065.png ; $| P |$ ; confidence 0.388

153. f04195089.png ; $\Delta ^ { n }$ ; confidence 0.388

154. l12007059.png ; $c r ^ { t } w$ ; confidence 0.388

155. s120320121.png ; $a \in \cal O ( U )$ ; confidence 0.388

156. t13021037.png ; $R ( x ; a _ { 0 } , \dots , a _ { N } ) = \sum _ { n } r _ { n } ( a _ { 0 } , \dots , a _ { N } ) \phi _ { n } ( x )$ ; confidence 0.388

157. i12004020.png ; $= \sum _ { j = 1 } ^ { n } ( - 1 ) ^ { j - 1 } ( \overline { \zeta _ { j } } - \overline { z _ { j } } ) d \overline { \zeta _ { 1 } } \bigwedge \ldots \bigwedge [ d \overline { \zeta _ { j } } ] \bigwedge \ldots \bigwedge d \overline { \zeta _ { n } } , \omega ( \zeta ) = d \zeta _ { 1 } \bigwedge \cdots \bigwedge d \zeta _ { n },$ ; confidence 0.388

158. w13006030.png ; ${\cal V} _ { g , n }$ ; confidence 0.388

159. a130240508.png ; $\mathsf{E} ( {\bf Z} _ { 13 } ) = 0$ ; confidence 0.388

160. c120010109.png ; $a \in \partial E$ ; confidence 0.388

161. b12044089.png ; $a ( g h ) = g ^ { - 1 } a h$ ; confidence 0.388

162. a12016010.png ; $C _ { i j } ( t )$ ; confidence 0.388

163. b12034032.png ; $D _ { r } = r . D$ ; confidence 0.388

164. c13019056.png ; $e_{k + 1} , \ldots , e _ { n }$ ; confidence 0.387

165. b12030037.png ; $a _ { k \text{l} } ( y ) \xi _ { k } \xi _ { \text{l} } \geq \alpha | \xi | ^ { 2 }$ ; confidence 0.387

166. a130310110.png ; $\sum _ { | X | \geq n } \mu ( X ) \frac { T ^ { - 1 } ( \operatorname { time } _ {\cal A } ( X ) ) } { | X | } \leq \sum _ { | X | \geq n } \mu ( X ),$ ; confidence 0.387

167. n067520435.png ; $\dot { v } _ { i } = \tilde { \psi } _ { i } ( V ) , \quad i = 1 , \dots , n,$ ; confidence 0.387

168. t120070150.png ; ${ j}_g = 1 / q + a _ { 1 } ( g ) q +\dots$ ; confidence 0.387

169. f12021059.png ; $i = 1 , \dots , \nu$ ; confidence 0.387

170. e12015025.png ; $\bar{x} \square ^ { i } ( t ) = x ^ { i } ( t ) + \xi ^ { i } ( t ) \eta,$ ; confidence 0.387

171. t13021042.png ; $h = ( b - a ) / N$ ; confidence 0.387

172. a1200601.png ; $\left. \begin{cases} { \frac { \partial u } { \partial t } + \sum _ { j = 1 } ^ { m } a _ { j } ( x ) \frac { \partial u } { \partial x _ { j } } + c ( x ) u = f ( x , t ) }, \\ { ( x , t ) \in \Omega \times [ 0 , T ] }, \\ { u ( x , 0 ) = u _ { 0 } ( x ) , \quad x \in \Omega, } \end{cases} \right.$ ; confidence 0.387

173. s13045076.png ; $\phi_S$ ; confidence 0.387

174. e13006038.png ; ${\cal C} ( Z \times _ { S } Y , X ) \cong {\cal C} ( Z , {\cal C} ( Y , X ) )$ ; confidence 0.387

175. m13023043.png ; $R _ { j } = {\bf R} _ { \geq 0 } v_j$ ; confidence 0.386

176. m130140163.png ; $( F f ) ( z ) = \sum _ { j = 1 } ^ { n } \left( z _ { j } \frac { \partial f ( z ) } { \partial z _ { j } } + \bar{z} _ { j } \frac { \partial f ( z ) } { \partial \bar{z} _ { j } } \right).$ ; confidence 0.386

177. s13004038.png ; $X _ { g } ^ { * } = {\color{blue} \cup} _ { r \leq g } X _ { r }$ ; confidence 0.386

178. t13021026.png ; $( u , v ) = \int _ { a } ^ { b } u ( x ) v ( x ) \rho ( x ) d x$ ; confidence 0.386

179. b12052072.png ; $\{ B _ { n } \}$ ; confidence 0.386

180. t120200216.png ; $K = k _ { 1 } + \ldots + k _ { n }$ ; confidence 0.386

181. c02563024.png ; $T ^ { t }$ ; confidence 0.386

182. f12011047.png ; $\operatorname { Im } z$ ; confidence 0.386

183. a120260126.png ; $A ( X _ { 1 } , \dots , X _ { s _ { i } } )$ ; confidence 0.386

184. g0433206.png ; $a _ { s t }$ ; confidence 0.386

185. q12008038.png ; $\mathsf{E} [ W _ { p } ] _ { \text{NP} } =$ ; confidence 0.386

186. l13008034.png ; $c_1 \operatorname{deg} I + c _ { 2 } \operatorname{log} \operatorname{ht} I$ ; confidence 0.386

187. b13006043.png ; $| E |$ ; confidence 0.386

188. l12011020.png ; $\| A \| \| A ^ { - 1 } \|$ ; confidence 0.386

189. i12008098.png ; $[ S _ { i } ( S _ { i - 1 } + S _ { i + 1 } ) ]$ ; confidence 0.386

190. s13054064.png ; $\{ a , b \} = d a / a \wedge d b / b$ ; confidence 0.386

191. w1300402.png ; $X : M \rightarrow {\bf R} ^ { n }$ ; confidence 0.386

192. t13005027.png ; $A \equiv ( A _ { 1 } , \dots , A _ { n } )$ ; confidence 0.385

193. c13009026.png ; $L _ { i , j } u _ { j } = f _ { i }$ ; confidence 0.385

194. c130160140.png ; $\operatorname{ASPACE}[\operatorname{log} n] = P$ ; confidence 0.385

195. s12004045.png ; $\lambda = e _ { \lambda _ { 1 } } \cdots e _ { \lambda _ { l } }$ ; confidence 0.385

196. q12007013.png ; $H ^ { \otimes 2 }$ ; confidence 0.385

197. s120230130.png ; $\frac { \pi ^ { n p / 2 } } { \Gamma _ { p } ( n / 2 ) } | S | ^ { ( n - p - 1 ) / 2 } f ( S ) , \quad S > 0.$ ; confidence 0.385

198. a12027080.png ; $r _ { P } : K _ { P } ^ { * } / K _ { P } ^ { * 2 } \rightarrow C ^ { * }$ ; confidence 0.385

199. w120090107.png ; $\operatorname{sg} ( \pi )$ ; confidence 0.385

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

201. b12009035.png ; $\frac { 1 } { p _ { 2 } ( \xi , \tau ) + a i } = \frac { p _ { 3 } ( \xi , \tau ) } { 1 + a ^ { 2 } } - \frac { a i } { 1 + a ^ { 2 } }$ ; confidence 0.385

202. p07310063.png ; $W _ { k }$ ; confidence 0.385

203. d12003076.png ; $f _ { I \cap P }$ ; confidence 0.385

204. f1300404.png ; $\operatorname { Tr } [ A \operatorname { exp } ( - i h ^ { - 1 } H ( t ) ) ] = \sum _ { k = 1 } ^ { n } a _ { 0 } ( x _ { k } ) d _ { k } e ^ { b _ { k } } + O ( h ).$ ; confidence 0.385

205. d12030055.png ; $d r = L ^ { * } r + \langle f ^ { - 1 } ( t , Y ( t ) ) g ( t , X ( t ) , Y ( t ) ) , d Y ( t ) \rangle { r },$ ; confidence 0.385

206. d13011031.png ; $\gamma _ { 1 } ^ { 2 } = 1 , \gamma _ { 2 } ^ { 2 } = \gamma _ { 3 } ^ { 2 } = \gamma _ { 4 } ^ { 2 } = - 1,$ ; confidence 0.385

207. d13018089.png ; $f \in I _ { E }$ ; confidence 0.385

208. t1200204.png ; $( F ^ {\bf Z } , {\cal B} ^ {\bf Z } , \mathsf{P} )$ ; confidence 0.385

209. a011380139.png ; $\frak B$ ; confidence 0.385

210. h13002013.png ; $w _ { i } ^ { l } = a _ { l }$ ; confidence 0.385

211. a12010054.png ; $X ^ { * }$ ; confidence 0.384

212. q12007053.png ; ${\bf C} [ [ \hbar ] ]$ ; confidence 0.384

213. b01747062.png ; $l_i$ ; confidence 0.384

214. s120230147.png ; $X A X ^ { \prime } \sim L _ { 1 } ^ { ( 1 ) } \left( f _ { 1 } , \frac { { k } } { 2 } \right),$ ; confidence 0.384

215. m12027045.png ; $c_{i j k}$ ; confidence 0.384

216. a13024066.png ; $y _ { i j k } = \mu + \alpha _ { i } + \beta _ { j } + \gamma _ { i j } + e _ { i j k },$ ; confidence 0.384

217. e12024044.png ; $E ( {\bf Q} )$ ; confidence 0.384

218. o13004014.png ; $\operatorname { lim } _ { \varepsilon \downarrow 0 } \frac { \mu _ { \varepsilon } ^ { x } ( \phi ) } { \mu _ { \varepsilon } ^ { x } ( \psi ) }$ ; confidence 0.384

219. e12012039.png ; $\sum _ { j } g _ { j } = \sum _ { i } f _ { i } = \sum _ { j } h _ { i j } = 1$ ; confidence 0.384

220. c13001037.png ; $c _ { \beta }$ ; confidence 0.384

221. j130040116.png ; $P _ { K } ( v , z ) = v ^ { 2 c } \sum c _ { i, j } ( v ^ { 2 } - 1 ) ^ { i } z ^ { j }$ ; confidence 0.384

222. n12002072.png ; $\int _ { E } \operatorname { log } ( d \mathsf{P} / d \mu ) d \mathsf{P}$ ; confidence 0.384

223. h12003018.png ; $\tau ( \varphi ) ^ { \alpha } ( x ) = g ^ { i j } ( x ) \left( \frac { \partial ^ { 2 } \varphi ^ { \alpha } } { \partial x ^ { i } \partial x ^ { j } } - \square ^ { M } \Gamma _ { i j } ^ { k } ( x ) \frac { \partial \varphi ^ { \alpha } } { \partial x ^ { k } } + + \square ^ { N } \Gamma _ { \beta \gamma } ^ { \alpha } ( \varphi ( x ) ) \frac { \partial \varphi \beta } { \partial x ^ { i } } \frac { \partial \varphi ^ { \gamma } } { \partial x ^ { j } } \right),$ ; confidence 0.384

224. v13005080.png ; $V_{( n )} = 0$ ; confidence 0.384

225. c12017069.png ; $1, Z , \bar{Z} , Z ^ { 2 } , \bar{Z} Z , Z ^ { 2 } , \ldots , Z ^ { n } , \ldots , \bar{Z} ^ { n }$ ; confidence 0.384

226. l058510138.png ; $X \in \mathfrak { h }$ ; confidence 0.384

227. v1300601.png ; $\widehat{{\frak sl}(2)}$ ; confidence 0.384

228. a11032036.png ; $n _ { s }$ ; confidence 0.383

229. b12005020.png ; $( P _ { n } ) = ( P _ { n } ( z _ { 0 } ) )$ ; confidence 0.383

230. b12034031.png ; $\sum _ { \alpha } \operatorname { sup } _ { D _ { r } } | c _ { \alpha } z ^ { \alpha } | < 1,$ ; confidence 0.383

231. n067520243.png ; $\bar { A } _ { i j }$ ; confidence 0.383

232. c1202805.png ; $X_{*}$ ; confidence 0.383

233. h13012011.png ; $x \in G_1$ ; confidence 0.383

234. m130140141.png ; $\Delta _ { n } = \{ ( t _ { 2 } , \dots , t _ { n } ) : t _ { 2 } , \dots , t _ { n } \geq 0 , t _ { 2 } + \dots + t _ { n } \leq 1 \}$ ; confidence 0.383

235. c1202505.png ; $= \int _ { \xi \in {\bf R} ^ { 2 } } \left( \begin{array} { c c } { L _ { x } ^ { 2 } } & { L _ { x } L _ { y } } \\ { L _ { x } L _ { y } } & { L _ { y } ^ { 2 } } \end{array} \right) g ( x - \xi ; s ) d x,$ ; confidence 0.382

236. t12020032.png ; $\operatorname { inf } _ { z _ { j } } \operatorname { max } _ { k \in S } \frac { | g _ { 2 } ( k ) | } { M _ { d } ( k ) }$ ; confidence 0.382

237. m130250102.png ; $H ^ { s } ( {\bf R} ^ { n } )$ ; confidence 0.382

238. w12018068.png ; $r _ { 1 } ( t , s ) = \prod _ { i = 1 } ^ { N } ( t _ { i } \bigwedge s _ { i } - t _ { i } s _ { i } ),$ ; confidence 0.382

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

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

241. a110010222.png ; $E_i$ ; confidence 0.382

242. i13001033.png ; $\overline { d } _ { \chi } ^ { G } ( A ) \geq \operatorname { det } ( A ) = \overline { d } _ { ( 1 ^ { n } )} ( A ).$ ; confidence 0.382

243. l11004017.png ; $l = \{ . , e , ^{- 1} , \vee , \wedge \}$ ; confidence 0.382

244. l12013026.png ; $f _ { 1 } , \dots , f _ { m } \in {\bf Q} ( X _ { 1 } , \dots , X _ { n } )$ ; confidence 0.382

245. c12019051.png ; $c _ { q } = ( - 1 ) ^ { q } q ! / ( 2 q ) !$ ; confidence 0.382

246. s13048029.png ; ${\frak G} _ { D }$ ; confidence 0.382

247. a11058037.png ; $q_1$ ; confidence 0.381

248. k1300609.png ; $\{ a _ { 1 } + 1 , \dots , a _ { k } + 1 \}$ ; confidence 0.381

249. c130160141.png ; $\operatorname{ATIME} [ n ^ { O ( 1 ) } ] = \operatorname { PSPACE }$ ; confidence 0.381

250. c120180122.png ; ${\cal E} \overset{\approx}{\to} {\cal E} _ {* * }$ ; confidence 0.381

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

252. a130040405.png ; ${\bf P} _ { \text{U} } \mathsf{K}$ ; confidence 0.381

253. o13005092.png ; $v _ { n } = v / z ^ { n }$ ; confidence 0.381

254. f120110109.png ; $K = D ^ { n }$ ; confidence 0.381

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

256. s1202705.png ; $Q _ { n } [ f ] = \sum _ { v = 1 } ^ { n } a _ { v , n } f ( x _ { v , n } ),$ ; confidence 0.381

257. k12007011.png ; $C _ { 0 } ( t )$ ; confidence 0.381

258. t12019017.png ; $T ( n , k , r ) \geq \frac { n - k + 1 } { n - r + 1 } \left( \begin{array} { c } { n } \\ { r } \end{array} \right) / \left( \begin{array} { c } { k - 1 } \\ { r - 1 } \end{array} \right)$ ; confidence 0.381

259. b13022015.png ; $\partial T$ ; confidence 0.381

260. i13006060.png ; $\kappa = 2 J$ ; confidence 0.381

261. m13013063.png ; $i j$ ; confidence 0.381

262. t130140121.png ; $\operatorname{mod} R$ ; confidence 0.381

263. a01165043.png ; $r _ { j }$ ; confidence 0.381

264. b12042010.png ; $( \phi \bigotimes \text { id } ) \Psi _ { V , W } = \Psi _ { V , Z } ( \text { id } \bigotimes \phi ) , \forall \phi : W \rightarrow Z,$ ; confidence 0.381

265. s13041026.png ; $\langle p , q \rangle = \int _ {\bf R } p q d \mu _ { 0 } + \lambda \int _ {\bf R } p ^ { \prime } q ^ { \prime } d \mu _ { 1 },$ ; confidence 0.381

266. f12024053.png ; $J _ { t }$ ; confidence 0.380

267. c12007062.png ; $H ^ { n } ( {\cal C} , M ) = \operatorname { Ext } _ { Z {\bf C} } ^ { n } ( {\cal Z} , M ),$ ; confidence 0.380

268. c12007043.png ; $\underline{\operatorname{lim}} \leftarrow$ ; confidence 0.380

269. m12013043.png ; $\frac { d N ^ { i } } { d t } = \lambda _ { ( i ) } N ^ { i } \left( 1 - \frac { N ^ { i } } { K _ { ( i ) } } \right) , \quad i = 1 , \ldots , n,$ ; confidence 0.380

270. g120040136.png ; $G ^ { 3 }$ ; confidence 0.380

271. c12008064.png ; $M _ { m } ( P _ { n } )$ ; confidence 0.380

272. w1202106.png ; $H H ^ { T } = H ^ { T } H = n I _ { n }$ ; confidence 0.380

273. a13030094.png ; ${\bf l}^ { 1 } ( G )$ ; confidence 0.380

274. a1301307.png ; $Q_i$ ; confidence 0.380

275. a130040213.png ; $\operatorname{Alg} \operatorname{Mod}^ { *S } \operatorname{S} 5$ ; confidence 0.380

276. w12009024.png ; $0 \leq r \in \bf Z$ ; confidence 0.380

277. c13025012.png ; $z _ { k } ^ { T } ( t ) = ( z _ { k , 1 } ( t ) , \dots , z _ { k , p } ( t ) )$ ; confidence 0.380

278. d13006041.png ; $j_1 , \dots , j _ { k }$ ; confidence 0.380

279. a13018084.png ; ${\bf Alg} : \text{ ''logics"}\to \text{''pairs of classes of algebras"}$ ; confidence 0.380

280. g04498039.png ; $v _ { j }$ ; confidence 0.380

281. r0806501.png ; $y _ { t }$ ; confidence 0.380

282. s1300709.png ; $s \in S , u , v \in H , \phi : S \times H \rightarrow S,$ ; confidence 0.380

283. j13004024.png ; $P _ { 2 _ { 1 } } = \frac { v - v ^ { 3 } } { z } + v z.$ ; confidence 0.380

284. s12016019.png ; $| I _ { 1 } ( f ) - U ^ { i } ( f ) |$ ; confidence 0.379

285. a1302609.png ; $\operatorname { lcm } ( 1 , \ldots , n ) ^ { 3 }$ ; confidence 0.379

286. d11008053.png ; $w _ { 1 } , \dots , w _ { m }$ ; confidence 0.379

287. h13009033.png ; $G ^ { * } \mu$ ; confidence 0.379

288. a13030056.png ; $( \mathfrak { S } ( T R _ { 1 } \ldots R _ { n} ) : n \in \bf N )$ ; confidence 0.379

289. m13014023.png ; $r = r_2$ ; confidence 0.379

290. m06222062.png ; $P _ { n - 1 }$ ; confidence 0.379

291. m12021013.png ; $u \in S ^ { n - 1 } : = \{ v \in {\bf E} : \langle v , v \rangle = 1 \}$ ; confidence 0.379

292. c120210102.png ; $P _ { \theta }$ ; confidence 0.379

293. a130070106.png ; $d | n$ ; confidence 0.379

294. m130140100.png ; $H _ { 2n }$ ; confidence 0.379

295. f120110149.png ; $K \cap {\bf R} ^ { n }$ ; confidence 0.379

296. f120110157.png ; $G ( \zeta ) = O ( e ^ { \varepsilon | \zeta | + H _ { K } ( \operatorname { lm } \zeta ) } )$ ; confidence 0.379

297. l12012041.png ; $\hat { K } _ { \text{p} } = \bf R$ ; confidence 0.379

298. d0300902.png ; $R _ { \nu }$ ; confidence 0.379

299. b130290169.png ; $h _ { d } = \operatorname { rank } _ { A } M - \sum _ { i = 1 } ^ { d - 1 } \left( \begin{array} { c } { d - 1 } \\ { i - 1 } \end{array} \right) h _ { i }$ ; confidence 0.379

300. a12010035.png ; $X = \bf R$ ; confidence 0.378

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/64. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/64&oldid=45686