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14. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011970/a01197023.png ; $\lambda _ { k }$ ; confidence 0.761
 
14. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011970/a01197023.png ; $\lambda _ { k }$ ; confidence 0.761
  
−
15. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001041.png ; $\{ \xi ^ { \alpha } , \eta ^ { \alpha } , \Phi ^ { \alpha } \} \alpha = 1,2,3$ ; confidence 0.761
+
15. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001041.png ; $\{ \xi ^ { a } , \eta ^ { a } , \Phi ^ { a } \}_{a = 1,2,3}$ ; confidence 1.000
  
 
16. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021180/c021180103.png ; $S_r$ ; confidence 1.000
 
16. https://www.encyclopediaofmath.org/legacyimages/c/c021/c021180/c021180103.png ; $S_r$ ; confidence 1.000
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25. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051470/i051470126.png ; $a ^ { - 1 }$ ; confidence 0.761
 
25. https://www.encyclopediaofmath.org/legacyimages/i/i051/i051470/i051470126.png ; $a ^ { - 1 }$ ; confidence 0.761
  
−
26. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s120320114.png ; $U = ( U , {\cal O ( U )} , \text { ev } )$ ; confidence 1.000
+
26. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120320/s120320114.png ; ${\cal U} = ( U , {\cal O ( U )} , \text { ev } )$ ; confidence 1.000
  
 
27. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027046.png ; $T _ { n } : X _ { n } \rightarrow Y _ { n }$ ; confidence 1.000
 
27. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027046.png ; $T _ { n } : X _ { n } \rightarrow Y _ { n }$ ; confidence 1.000
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28. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023053.png ; $\Omega _ { r } = r \Omega$ ; confidence 0.761
 
28. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023053.png ; $\Omega _ { r } = r \Omega$ ; confidence 0.761
  
−
29. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140102.png ; $q R : {\bf Z} ^ { n } \rightarrow \bf Z$ ; confidence 1.000
+
29. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140102.png ; $q_R : {\bf Z} ^ { n } \rightarrow \bf Z$ ; confidence 1.000
  
 
30. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012200/a012200122.png ; $G \subset {\bf R} ^ { n }$ ; confidence 1.000
 
30. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012200/a012200122.png ; $G \subset {\bf R} ^ { n }$ ; confidence 1.000
  
−
31. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s12034040.png ; $- \operatorname{ id }$ ; confidence 1.000
+
31. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120340/s12034040.png ; $- \operatorname{ Id }$ ; confidence 1.000
  
 
32. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130310/a13031070.png ; $( {\cal Q} _ { 2 } , \mu _ { 2 } )$ ; confidence 1.000
 
32. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130310/a13031070.png ; $( {\cal Q} _ { 2 } , \mu _ { 2 } )$ ; confidence 1.000
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35. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140119.png ; $i , l = 1 , \dots , n$ ; confidence 0.760
 
35. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140119.png ; $i , l = 1 , \dots , n$ ; confidence 0.760
  
−
36. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w1201107.png ; $( x . \xi ) ^ { w } = ( x . D _ { x } + D _ { x } x ) / 2$ ; confidence 0.760
+
36. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w1201107.png ; $( x . \xi ) ^ { w } = ( x . D _ { x } + D _ { x } .x ) / 2$ ; confidence 1.000
  
 
37. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f12023035.png ; $\operatorname { Der }\Omega ( M ) = \oplus _ { k } \operatorname { Der } _ { k } \Omega ( M )$ ; confidence 1.000
 
37. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f12023035.png ; $\operatorname { Der }\Omega ( M ) = \oplus _ { k } \operatorname { Der } _ { k } \Omega ( M )$ ; confidence 1.000
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41. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120280/a12028072.png ; $\rho \otimes x ( A ) = \langle A x , \rho \rangle$ ; confidence 0.760
 
41. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120280/a12028072.png ; $\rho \otimes x ( A ) = \langle A x , \rho \rangle$ ; confidence 0.760
  
−
42. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087029.png ; $operatorname{Ab}$ ; confidence 1.000
+
42. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087029.png ; $\operatorname{Ab}$ ; confidence 1.000
  
 
43. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120520/b12052022.png ; $F ^ { \prime } ( x _ { c } ) s = - F ( x _ { c } )$ ; confidence 0.760
 
43. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120520/b12052022.png ; $F ^ { \prime } ( x _ { c } ) s = - F ( x _ { c } )$ ; confidence 0.760
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46. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130310/a13031098.png ; $\cal N E X P$ ; confidence 1.000
 
46. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130310/a13031098.png ; $\cal N E X P$ ; confidence 1.000
  
−
47. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c1202106.png ; $( {\cal X , A} _ { N } )$ ; confidence 0.760
+
47. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c1202106.png ; $( {\cal X , A} _ { n } )$ ; confidence 1.000
  
 
48. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c120210111.png ; $\theta _ { n } = \theta + h / \sqrt { n }$ ; confidence 0.760
 
48. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c120210111.png ; $\theta _ { n } = \theta + h / \sqrt { n }$ ; confidence 0.760
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56. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082320/r08232070.png ; $a, b \leq c \leq d , e$ ; confidence 1.000
 
56. https://www.encyclopediaofmath.org/legacyimages/r/r082/r082320/r08232070.png ; $a, b \leq c \leq d , e$ ; confidence 1.000
  
−
57. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008051.png ; $= \frac { d \operatorname { ln } g ( R ; m , s ) } { d m } \frac { d \operatorname { ln } g ( L ; m , s ) } { d s }$ ; confidence 0.759
+
57. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008051.png ; $= \frac { d \operatorname { ln } g ( R ; m , s ) } { d m } \frac { d \operatorname { ln } g ( L ; m , s ) } { d s }.$ ; confidence 0.759
  
 
58. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110400/c11040014.png ; ${\cal C} ( G )$ ; confidence 1.000
 
58. https://www.encyclopediaofmath.org/legacyimages/c/c110/c110400/c11040014.png ; ${\cal C} ( G )$ ; confidence 1.000
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66. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001033.png ; $Z ^ { - 1 } ( \tilde{x} ( z ) ) = x ( n )$ ; confidence 1.000
 
66. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130010/z13001033.png ; $Z ^ { - 1 } ( \tilde{x} ( z ) ) = x ( n )$ ; confidence 1.000
  
−
67. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120050/b12005014.png ; $f : U \rightarrow \cal C$ ; confidence 1.000
+
67. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120050/b12005014.png ; $f : U \rightarrow \bf C$ ; confidence 1.000
  
 
68. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026049.png ; $y \notin F ( \partial U )$ ; confidence 0.759
 
68. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130260/b13026049.png ; $y \notin F ( \partial U )$ ; confidence 0.759
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70. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130250/c13025010.png ; $\beta ^ { T } = ( \beta _ { 1 } , \dots , \beta _ { p } )$ ; confidence 0.759
 
70. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130250/c13025010.png ; $\beta ^ { T } = ( \beta _ { 1 } , \dots , \beta _ { p } )$ ; confidence 0.759
  
−
71. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520355.png ; $( \exists g ) ( \forall \phi ) ( \exists f ) ( \forall x _ { 1 } , \dots , x _ { n } )$ ; confidence 0.759
+
71. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520355.png ; $( \exists g ) ( \forall \phi ) ( \exists f ) ( \forall x _ { 1 } , \dots , x _ { n } ):$ ; confidence 1.000
  
 
72. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020176.png ; $H _ { 0 } ^ { 2 }$ ; confidence 0.759
 
72. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020176.png ; $H _ { 0 } ^ { 2 }$ ; confidence 0.759
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78. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029068.png ; $f ( q ) = O ( 1 / q ^ { 2 } )$ ; confidence 0.758
 
78. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029068.png ; $f ( q ) = O ( 1 / q ^ { 2 } )$ ; confidence 0.758
  
−
79. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120520/b12052038.png ; $B _ { + } = B _ { c } + \frac { ( y - B _ { c } s ) s ^ { T } } { s ^ { T } s }$ ; confidence 0.758
+
79. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120520/b12052038.png ; $B _ { + } = B _ { c } + \frac { ( y - B _ { c } s ) s ^ { T } } { s ^ { T } s }.$ ; confidence 0.758
  
 
80. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b120420128.png ; $\operatorname{SL} _ { q } ( 2 )$ ; confidence 1.000
 
80. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120420/b120420128.png ; $\operatorname{SL} _ { q } ( 2 )$ ; confidence 1.000
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86. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005081.png ; $\mu = \frac { y ^ { T } H y . s ^ { T } B s } { ( s ^ { T } y ) ^ { 2 } }.$ ; confidence 1.000
 
86. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120050/q12005081.png ; $\mu = \frac { y ^ { T } H y . s ^ { T } B s } { ( s ^ { T } y ) ^ { 2 } }.$ ; confidence 1.000
  
−
87. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130030/g13003041.png ; ${\cal I} _ { 0 } = \{ ( u _ { j } ) _ { j \in \bf N }$ ; confidence 1.000
+
87. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130030/g13003041.png ; ${\cal I} _ { 0 } = \{ ( u _ { j } ) _ { j \in \bf N }$ ; confidence 1.000 NOTE: the parentesis remains open
  
 
88. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005066.png ; $\operatorname { Ker } D _ { A } / \operatorname { Ran } D _ { A } = \operatorname { Ker } A \oplus ({\cal X} / \operatorname { Ran } A )$ ; confidence 1.000
 
88. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005066.png ; $\operatorname { Ker } D _ { A } / \operatorname { Ran } D _ { A } = \operatorname { Ker } A \oplus ({\cal X} / \operatorname { Ran } A )$ ; confidence 1.000
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99. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002073.png ; $\varphi ( n ) = n - \frac { n } { p _ { 1 } } - \ldots - \frac { n } { p _ { k } } +$ ; confidence 0.757
 
99. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130020/i13002073.png ; $\varphi ( n ) = n - \frac { n } { p _ { 1 } } - \ldots - \frac { n } { p _ { k } } +$ ; confidence 0.757
  
−
100. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c12021082.png ; $\tilde{L}^'$ ; confidence 1.000
+
100. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c12021082.png ; $\tilde{ \cal L}'$ ; confidence 1.000
  
 
101. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130290/a13029082.png ; $Q _ { id } = Q \times S ^ { 1 } \rightarrow \Sigma \times S ^ { 1 }$ ; confidence 0.757
 
101. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130290/a13029082.png ; $Q _ { id } = Q \times S ^ { 1 } \rightarrow \Sigma \times S ^ { 1 }$ ; confidence 0.757
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121. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120350/s12035012.png ; $Z ^ { t - 1 } = \{ y ( t - 1 ) , u ( t - 1 ) , \dots , y ( 0 ) , u ( 0 ) \}:$ ; confidence 0.756
 
121. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120350/s12035012.png ; $Z ^ { t - 1 } = \{ y ( t - 1 ) , u ( t - 1 ) , \dots , y ( 0 ) , u ( 0 ) \}:$ ; confidence 0.756
  
−
122. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011096.png ; $- \frac { 1 } { k + d n _ { k } }_{..} [ ( i + d ) \mu ( i , m ) - ( i + d + 1 ) \mu ( i + 1 , m ) ] = 0.$ ; confidence 1.000
+
122. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011096.png ; $- \frac { 1 } { k + d n _ { k } } {..} [ ( i + d ) \mu ( i , m ) - ( i + d + 1 ) \mu ( i + 1 , m ) ] = 0.$ ; confidence 1.000
  
 
123. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032086.png ; $k \operatorname { log } m \leq i \operatorname { log } n < ( k + 1 ) \operatorname { log } m$ ; confidence 1.000
 
123. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032086.png ; $k \operatorname { log } m \leq i \operatorname { log } n < ( k + 1 ) \operatorname { log } m$ ; confidence 1.000
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125. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086360/s086360140.png ; $k = 0 , \pm 1 , \pm 2 , \ldots$ ; confidence 0.756
 
125. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086360/s086360140.png ; $k = 0 , \pm 1 , \pm 2 , \ldots$ ; confidence 0.756
  
−
126. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120240/s12024036.png ; $E * ( )$ ; confidence 1.000
+
126. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120240/s12024036.png ; ${\bf E} * ( )$ ; confidence 1.000
  
 
127. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700010.png ; $( \lambda x M ) \in \Lambda$ ; confidence 0.756
 
127. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l05700010.png ; $( \lambda x M ) \in \Lambda$ ; confidence 0.756
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130. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012074.png ; $t | \leq \pi$ ; confidence 0.756
 
130. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130120/b13012074.png ; $t | \leq \pi$ ; confidence 0.756
  
−
131. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030060/d03006010.png ; $\frac { \partial ^ { 2 } u ( t , x ) } { \partial t ^ { 2 } } - a ^ { 2 } \frac { \partial ^ { 2 } u ( t , x ) } { \partial x ^ { 2 } } = f ( t , x )$ ; confidence 0.756
+
131. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030060/d03006010.png ; $\frac { \partial ^ { 2 } u ( t , x ) } { \partial t ^ { 2 } } - a ^ { 2 } \frac { \partial ^ { 2 } u ( t , x ) } { \partial x ^ { 2 } } = f ( t , x ),$ ; confidence 0.756
  
 
132. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021073.png ; $( s _ { 1 } , \dots , s _ { k } , I _ { m } )$ ; confidence 1.000
 
132. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021073.png ; $( s _ { 1 } , \dots , s _ { k } , I _ { m } )$ ; confidence 1.000
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135. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120090/i1200901.png ; $( M ^ { 2 n } , \omega )$ ; confidence 0.756
 
135. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120090/i1200901.png ; $( M ^ { 2 n } , \omega )$ ; confidence 0.756
  
−
136. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013012.png ; $( L _ { 1 } , L _ { 2 } ) = ( S _ { 1 } \Lambda S _ { 1 } ^ { - 1 } , S _ { 2 } \Lambda ^ { t } S _ { 2 } ^ { - 1 } )$ ; confidence 0.756
+
136. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013012.png ; $( L _ { 1 } , L _ { 2 } ) = ( S _ { 1 } \Lambda S _ { 1 } ^ { - 1 } , S _ { 2 } \Lambda ^ { t } S _ { 2 } ^ { - 1 } );$ ; confidence 0.756
  
 
137. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007013.png ; $u \in {\bf Z} G$ ; confidence 1.000
 
137. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130070/z13007013.png ; $u \in {\bf Z} G$ ; confidence 1.000
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152. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064058.png ; $\hat{k}$ ; confidence 1.000
 
152. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130640/s13064058.png ; $\hat{k}$ ; confidence 1.000
  
−
153. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a130070129.png ; $n = 1.3 .5 . . ( 2 k - 1 )$ ; confidence 0.755
+
153. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a130070129.png ; $n = 1.3 .5 ... ( 2 k - 1 )$ ; confidence 1.000
  
 
154. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130070/w13007037.png ; $| \gamma | = r + \sum _ { j = 1 } ^ { s } p _ { j }$ ; confidence 0.755
 
154. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130070/w13007037.png ; $| \gamma | = r + \sum _ { j = 1 } ^ { s } p _ { j }$ ; confidence 0.755
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157. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130050/d1300501.png ; $m \geq 4$ ; confidence 1.000
 
157. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130050/d1300501.png ; $m \geq 4$ ; confidence 1.000
  
−
158. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006055.png ; $= \int _ { 0 } ^ { \infty } | ( V \phi | \lambda ) | ^ { 2 } ( \frac { 1 } { \zeta - \lambda - i \epsilon } - \frac { 1 } { \zeta - \lambda + i \epsilon } ) d \lambda =;$ ; confidence 1.000
+
158. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006055.png ; $= \int _ { 0 } ^ { \infty } | ( V \phi | \lambda ) | ^ { 2 } ( \frac { 1 } { \zeta - \lambda - i \epsilon } - \frac { 1 } { \zeta - \lambda + i \epsilon } ) d \lambda =$ ; confidence 1.000
  
 
159. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016730/b0167303.png ; $s = 1,2 , \dots,$ ; confidence 1.000
 
159. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016730/b0167303.png ; $s = 1,2 , \dots,$ ; confidence 1.000
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181. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005048.png ; $Y ( v , x ) \bf 1$ ; confidence 1.000
 
181. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v13005048.png ; $Y ( v , x ) \bf 1$ ; confidence 1.000
  
−
182. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017017.png ; $K _ { j } \in {\bf R} ^ { n \times n } , K _ { 0 } = l , \sum _ { j = 0 } ^ { \infty } \| K _ { j } \| ^ { 2 } < \infty ,$ ; confidence 1.000
+
182. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017017.png ; $K _ { j } \in {\bf R} ^ { n \times n } , K _ { 0 } = I , \sum _ { j = 0 } ^ { \infty } \| K _ { j } \| ^ { 2 } < \infty ,$ ; confidence 1.000
  
 
183. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120190/e120190110.png ; $m \in S$ ; confidence 0.753
 
183. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120190/e120190110.png ; $m \in S$ ; confidence 0.753
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186. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015036.png ; $n / 2$ ; confidence 1.000
 
186. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015036.png ; $n / 2$ ; confidence 1.000
  
−
187. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020198.png ; $k _ { \vartheta } ( z ) = \frac { 1 - | z | ^ { 2 } } { | z - e ^ { i \vartheta | ^ { 2 } } }$ ; confidence 0.753
+
187. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020198.png ; $k _ { \vartheta } ( z ) = \frac { 1 - | z | ^ { 2 } } { | z - e ^ { i \vartheta }|^ 2 }.$ ; confidence 1.000
  
 
188. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059610/l0596103.png ; $q = ( {\bf r} _ { 1 } , \dots , {\bf r} _ { N } )$ ; confidence 1.000
 
188. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059610/l0596103.png ; $q = ( {\bf r} _ { 1 } , \dots , {\bf r} _ { N } )$ ; confidence 1.000
Line 404: Line 404:
 
202. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130030/q1300306.png ; $\alpha | 0 \rangle + \beta | 1 \rangle$ ; confidence 0.752
 
202. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130030/q1300306.png ; $\alpha | 0 \rangle + \beta | 1 \rangle$ ; confidence 0.752
  
−
203. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130060/m1300607.png ; $\operatorname{deg}_{x_m}\alpha _ { 1 } \geq d ^ { m - 1 } ( d - 1 )$ ; confidence 0.752
+
203. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130060/m1300607.png ; $\operatorname{deg}_{x_m} a _ { 1 } \geq d ^ { m - 1 } ( d - 1 )$ ; confidence 0.752
  
 
204. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q120070143.png ; ${\cal R} : G _ { q } \rightarrow U _ { q } ( {\frak g} )$ ; confidence 1.000
 
204. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q120070143.png ; ${\cal R} : G _ { q } \rightarrow U _ { q } ( {\frak g} )$ ; confidence 1.000
Line 464: Line 464:
 
232. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007045.png ; $A ( \alpha ^ { \prime } , \alpha_0 , k )$ ; confidence 1.000
 
232. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130070/i13007045.png ; $A ( \alpha ^ { \prime } , \alpha_0 , k )$ ; confidence 1.000
  
−
233. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006028.png ; $\sigma _ { 1 } = \frac { 1 } { i } ( A _ { 1 } - A _ { 1 } ^ { * } ) | _ { E } , \sigma _ { 2 } = \frac { 1 } { i } ( A _ { 2 } - A _ { 2 } ^ { * } ) | _ { \cal E } , \gamma = \frac { 1 } { i } ( A _ { 1 } A _ { 2 } ^ { * } - A _ { 2 } A _ { 1 } ^ { * } ) | _ { \cal E } , \tilde { \gamma } = \frac { 1 } { i } ( A _ { 2 } ^ { * } A _ { 1 } - A _ { 1 } ^ { * } A _ { 2 } ) | _ { \cal E }$ ; confidence 1.000
+
233. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006028.png ; $\sigma _ { 1 } = \frac { 1 } { i } ( A _ { 1 } - A _ { 1 } ^ { * } ) | _ {\cal E } , \sigma _ { 2 } = \frac { 1 } { i } ( A _ { 2 } - A _ { 2 } ^ { * } ) | _ { \cal E } , \gamma = \frac { 1 } { i } ( A _ { 1 } A _ { 2 } ^ { * } - A _ { 2 } A _ { 1 } ^ { * } ) | _ { \cal E } , \tilde { \gamma } = \frac { 1 } { i } ( A _ { 2 } ^ { * } A _ { 1 } - A _ { 1 } ^ { * } A _ { 2 } ) | _ { \cal E }$ ; confidence 1.000
  
 
234. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004073.png ; $f _ { i + 1 / 2 } = f ( u _ { i + 1 / 2 } ^ { n + 1 / 2 } );$ ; confidence 0.751
 
234. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004073.png ; $f _ { i + 1 / 2 } = f ( u _ { i + 1 / 2 } ^ { n + 1 / 2 } );$ ; confidence 0.751
Line 522: Line 522:
 
261. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023047.png ; $d \zeta = d \zeta _ { 1 } \wedge \ldots \wedge d \zeta _ { n }$ ; confidence 0.749
 
261. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023047.png ; $d \zeta = d \zeta _ { 1 } \wedge \ldots \wedge d \zeta _ { n }$ ; confidence 0.749
  
−
262. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040127.png ; $\psi^'$ ; confidence 1.000
+
262. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040127.png ; $\psi '$ ; confidence 1.000
  
 
263. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005076.png ; $r_+ ( k ) = O ( 1 / k )$ ; confidence 1.000
 
263. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005076.png ; $r_+ ( k ) = O ( 1 / k )$ ; confidence 1.000
Line 568: Line 568:
 
284. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p1201707.png ; $\operatorname{ker} \delta _ { A , B } = \{ X \in B ( H ) : \delta _ { A , B } ( X ) = 0 \}$ ; confidence 1.000
 
284. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120170/p1201707.png ; $\operatorname{ker} \delta _ { A , B } = \{ X \in B ( H ) : \delta _ { A , B } ( X ) = 0 \}$ ; confidence 1.000
  
−
285. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110500/a11050055.png ; $\alpha \in K$ ; confidence 0.748
+
285. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110500/a11050055.png ; $a \in K$ ; confidence 1.000
  
 
286. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012330/a01233028.png ; $l\geq  0$ ; confidence 1.000
 
286. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012330/a01233028.png ; $l\geq  0$ ; confidence 1.000
Line 590: Line 590:
 
295. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120260/a120260127.png ; $A \{ X _ { 1 } , \dots , X _ { s _ { i } } \}$ ; confidence 0.747
 
295. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120260/a120260127.png ; $A \{ X _ { 1 } , \dots , X _ { s _ { i } } \}$ ; confidence 0.747
  
−
296. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k05584061.png ; $\| G | ^ { 1 / 2 } x \|$ ; confidence 0.747
+
296. https://www.encyclopediaofmath.org/legacyimages/k/k055/k055840/k05584061.png ; $\| |G | ^ { 1 / 2 } x \|$ ; confidence 1.000
  
 
297. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m13018020.png ; $g ( x ) = \sum _ { y : y \geq x } f ( y ) \Leftrightarrow f ( x ) = \sum _ { y : y \geq x } \mu ( x , y ) g ( y ).$ ; confidence 0.747
 
297. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m13018020.png ; $g ( x ) = \sum _ { y : y \geq x } f ( y ) \Leftrightarrow f ( x ) = \sum _ { y : y \geq x } \mu ( x , y ) g ( y ).$ ; confidence 0.747

Revision as of 16:18, 28 April 2020

List

1. a12026040.png ; $\tilde { y } \in A ^ { S }$ ; confidence 1.000

2. c13007085.png ; $d > 1$ ; confidence 0.762

3. e0353108.png ; $\{ \omega \}$ ; confidence 0.762

4. l120100142.png ; $p = n / ( n - 2 )$ ; confidence 1.000

5. b12027048.png ; $\operatorname { lim } _ { t \rightarrow \infty } ( U ( t + h ) - U ( t ) ) = \frac { h } { \operatorname{E} X _ { 1 } }$ ; confidence 1.000

6. l13005018.png ; ${\bf s} ^ { ( k ) }$ ; confidence 1.000

7. r13013018.png ; $P _ { \sigma }$ ; confidence 0.762

8. m12003078.png ; $e = y - \overset{\rightharpoonup} { x } ^ { t } \overset{\rightharpoonup} { \theta }$ ; confidence 1.000

9. m120100142.png ; $( \tilde { G } , \tilde{c} ) / \Lambda$ ; confidence 1.000

10. c02691097.png ; $2 \epsilon$ ; confidence 0.761

11. g130040202.png ; $\operatorname { dist } ( T _ { x } , T _ { y } ) \leq C ( r | x - y | ) ^ { 1 - \epsilon }$ ; confidence 0.761

12. l12013066.png ; $p \notin S$ ; confidence 0.761

13. c12018021.png ; $N \subset M$ ; confidence 0.761

14. a01197023.png ; $\lambda _ { k }$ ; confidence 0.761

15. t12001041.png ; $\{ \xi ^ { a } , \eta ^ { a } , \Phi ^ { a } \}_{a = 1,2,3}$ ; confidence 1.000

16. c021180103.png ; $S_r$ ; confidence 1.000

17. c130160154.png ; $( \operatorname { log } n ) ^ { O ( 1 ) }$ ; confidence 0.761

18. z12002013.png ; $F _ { n _ { 1 } }$ ; confidence 1.000

19. c12029053.png ; $\operatorname { Ker } ( \partial )$ ; confidence 0.761

20. j13003025.png ; $z \mapsto \{ a b z \}$ ; confidence 0.761

21. m1202308.png ; $( 2 t ) ^ { - 1 } \| . \| ^ { 2 }$ ; confidence 0.761

22. d1201507.png ; $d , e \in D$ ; confidence 0.761

23. g12004047.png ; $( x ^ { 0 } , \xi ^ { 0 } ) \in \Omega \times ( {\bf R} ^ { n } \backslash \{ 0 \} )$ ; confidence 1.000

24. m12023052.png ; $- f _ { t } + ( 2 t ) ^ { - 1 } \| . \| ^ { 2 }$ ; confidence 0.761

25. i051470126.png ; $a ^ { - 1 }$ ; confidence 0.761

26. s120320114.png ; ${\cal U} = ( U , {\cal O ( U )} , \text { ev } )$ ; confidence 1.000

27. a13027046.png ; $T _ { n } : X _ { n } \rightarrow Y _ { n }$ ; confidence 1.000

28. a12023053.png ; $\Omega _ { r } = r \Omega$ ; confidence 0.761

29. t130140102.png ; $q_R : {\bf Z} ^ { n } \rightarrow \bf Z$ ; confidence 1.000

30. a012200122.png ; $G \subset {\bf R} ^ { n }$ ; confidence 1.000

31. s12034040.png ; $- \operatorname{ Id }$ ; confidence 1.000

32. a13031070.png ; $( {\cal Q} _ { 2 } , \mu _ { 2 } )$ ; confidence 1.000

33. w130080212.png ; ${\cal M} _ { g , n } + 1$ ; confidence 1.000

34. d12012021.png ; $U \cal C$ ; confidence 1.000

35. m130140119.png ; $i , l = 1 , \dots , n$ ; confidence 0.760

36. w1201107.png ; $( x . \xi ) ^ { w } = ( x . D _ { x } + D _ { x } .x ) / 2$ ; confidence 1.000

37. f12023035.png ; $\operatorname { Der }\Omega ( M ) = \oplus _ { k } \operatorname { Der } _ { k } \Omega ( M )$ ; confidence 1.000

38. j1300709.png ; $\operatorname { Hol }( \Delta )$ ; confidence 1.000

39. l13001051.png ; $\| S_{NB} \| \leq CN^ { ( n - 1 ) / 2 }$ ; confidence 1.000

40. s12026065.png ; $\{ A_t , A _ { s } ^ { * } \} = \delta ( t - s ) , \{ A _ { t } , A _ { s } \} = \{ A _ { t } ^ { * } , A _ { s } ^ { * } \} = 0.$ ; confidence 1.000

41. a12028072.png ; $\rho \otimes x ( A ) = \langle A x , \rho \rangle$ ; confidence 0.760

42. b11087029.png ; $\operatorname{Ab}$ ; confidence 1.000

43. b12052022.png ; $F ^ { \prime } ( x _ { c } ) s = - F ( x _ { c } )$ ; confidence 0.760

44. b1200405.png ; $X \subset L ^ { 0 } ( \mu )$ ; confidence 0.760

45. b13007044.png ; $a ^ { - 1 } b ^ { k } a$ ; confidence 0.760

46. a13031098.png ; $\cal N E X P$ ; confidence 1.000

47. c1202106.png ; $( {\cal X , A} _ { n } )$ ; confidence 1.000

48. c120210111.png ; $\theta _ { n } = \theta + h / \sqrt { n }$ ; confidence 0.760

49. l120170308.png ; $X \times I ^ { 2 }$ ; confidence 0.760

50. f040230178.png ; $f _ { 1 } , \dots , f _ { k }$ ; confidence 0.760

51. a130240517.png ; ${\bf V} _ { j j ^ { \prime } } = {\bf Z} _ { 3 j } ^ { \prime } {\bf Z} _ { 3 j }$ ; confidence 0.760

52. s12035028.png ; $= \lambda \operatorname { lim } _ { N \rightarrow \infty } \sum _ { t = 1 } ^ { N } \operatorname{E} \frac { \partial } { \partial \theta } f ( Z ^ { t - 1 } , t , \theta ) ( \frac { \partial } { \partial \theta } f ( Z ^ { t - 1 } , t , \theta ) ) ^ { T }$ ; confidence 1.000

53. r13016035.png ; ${\cal R = C} ^ { \infty } ( \Omega ) / {\cal I} _ { S }$ ; confidence 1.000

54. m13023019.png ; $Z_2$ ; confidence 1.000

55. c02211046.png ; $j , r = 1 , \dots , m$ ; confidence 0.759

56. r08232070.png ; $a, b \leq c \leq d , e$ ; confidence 1.000

57. a13008051.png ; $= \frac { d \operatorname { ln } g ( R ; m , s ) } { d m } \frac { d \operatorname { ln } g ( L ; m , s ) } { d s }.$ ; confidence 0.759

58. c11040014.png ; ${\cal C} ( G )$ ; confidence 1.000

59. n067520244.png ; $d _ { i } \times d _ { j }$ ; confidence 0.759

60. f13019043.png ; $O ( N ^ { 2 d } )$ ; confidence 0.759

61. t120060106.png ; $\rho _ { \text { atom } } ^ { \text{TF} }$ ; confidence 1.000

62. c120180393.png ; $q _ { 1 } + \ldots + q _ { m }$ ; confidence 0.759

63. a12022010.png ; $X = c_0$ ; confidence 1.000

64. b13006017.png ; $\| A \| _ { 1 } = \operatorname { max } _ { i } \sum _ { j } | a _ { i j } |,$ ; confidence 0.759

65. l13001080.png ; $C _ { 1 } N ^ { n + ( n - 1 ) / 2 } \leq \| S _ { H _ { N } } \| \leq C _ { 2 } N ^ { n + ( n - 1 ) / 2 }$ ; confidence 0.759

66. z13001033.png ; $Z ^ { - 1 } ( \tilde{x} ( z ) ) = x ( n )$ ; confidence 1.000

67. b12005014.png ; $f : U \rightarrow \bf C$ ; confidence 1.000

68. b13026049.png ; $y \notin F ( \partial U )$ ; confidence 0.759

69. j13003031.png ; $a \square a ^ { * }$ ; confidence 1.000

70. c13025010.png ; $\beta ^ { T } = ( \beta _ { 1 } , \dots , \beta _ { p } )$ ; confidence 0.759

71. n067520355.png ; $( \exists g ) ( \forall \phi ) ( \exists f ) ( \forall x _ { 1 } , \dots , x _ { n } ):$ ; confidence 1.000

72. j120020176.png ; $H _ { 0 } ^ { 2 }$ ; confidence 0.759

73. b13002018.png ; $\| x \| ^ { 2 } \leq \| x ^ { 2 } + y ^ { 2 } \|$ ; confidence 0.759

74. c02327011.png ; $\overline { p } = p$ ; confidence 0.759

75. d12028052.png ; $D ; \subset {\bf C} ^ { 1 }$ ; confidence 1.000

76. p12017070.png ; $\delta _ { A , B } ( X ) \in I$ ; confidence 0.758

77. b12043047.png ; $[ m ] _ { q } ! = [ m ] _ { q } [ m - 1 ] _ { q } \ldots [ 1 ] _ { q }$ ; confidence 0.758

78. d12029068.png ; $f ( q ) = O ( 1 / q ^ { 2 } )$ ; confidence 0.758

79. b12052038.png ; $B _ { + } = B _ { c } + \frac { ( y - B _ { c } s ) s ^ { T } } { s ^ { T } s }.$ ; confidence 0.758

80. b120420128.png ; $\operatorname{SL} _ { q } ( 2 )$ ; confidence 1.000

81. a13022050.png ; $S _ { C } ( D ) = k$ ; confidence 0.758

82. j12001053.png ; $F \in \operatorname { Aut } _ { R } R [ X ]$ ; confidence 0.758

83. c0232702.png ; $A \rightarrow \overline { A },$ ; confidence 0.758

84. q13005091.png ; $z _ { 2 } \neq z _ { 3 }$ ; confidence 0.758

85. y1200404.png ; $f _ { j } : \Omega \rightarrow {\bf R} ^ { d }$ ; confidence 1.000

86. q12005081.png ; $\mu = \frac { y ^ { T } H y . s ^ { T } B s } { ( s ^ { T } y ) ^ { 2 } }.$ ; confidence 1.000

87. g13003041.png ; ${\cal I} _ { 0 } = \{ ( u _ { j } ) _ { j \in \bf N }$ ; confidence 1.000 NOTE: the parentesis remains open

88. t13005066.png ; $\operatorname { Ker } D _ { A } / \operatorname { Ran } D _ { A } = \operatorname { Ker } A \oplus ({\cal X} / \operatorname { Ran } A )$ ; confidence 1.000

89. e120230175.png ; $\sigma ^ { 2 k ^ { * } } [ {\cal E} ( L ) ( Z ^ { 2 k } ) ] = \sigma ^ { k + 1 ^ { * } } [ \Omega ( d L \Delta ) ( Z ^ { k + 1 } ) ],$ ; confidence 1.000

90. a13018024.png ; $\operatorname{Mod}_{\cal L}$ ; confidence 1.000

91. i130060186.png ; $S ( k ) = f ( - k ) / f ( k )$ ; confidence 0.758

92. a13012058.png ; $s > 2$ ; confidence 0.758

93. g12004098.png ; $d_ {x , \xi} p _ { m } ( x , \xi )$ ; confidence 1.000

94. l05754062.png ; $C _ { + }$ ; confidence 0.758

95. g120040117.png ; $G ^ { S }$ ; confidence 0.758

96. f120110107.png ; ${\cal Q} [ K ]$ ; confidence 1.000

97. f12004027.png ; $X \times W$ ; confidence 0.757

98. a01246092.png ; $f = ( f _ { 1 } , \dots , f _ { n } )$ ; confidence 0.757

99. i13002073.png ; $\varphi ( n ) = n - \frac { n } { p _ { 1 } } - \ldots - \frac { n } { p _ { k } } +$ ; confidence 0.757

100. c12021082.png ; $\tilde{ \cal L}'$ ; confidence 1.000

101. a13029082.png ; $Q _ { id } = Q \times S ^ { 1 } \rightarrow \Sigma \times S ^ { 1 }$ ; confidence 0.757

102. b1300206.png ; $\operatorname { sp } ( J , x )$ ; confidence 0.757

103. n12012014.png ; $x \in \Sigma ^ { * }$ ; confidence 0.757

104. k1101403.png ; ${\cal L}_0$ ; confidence 1.000

105. a130180122.png ; $R \subseteq \square ^ { n } U$ ; confidence 0.757

106. z13003066.png ; $\hat { f } ( - 2 \pi w ) = \frac { 1 } { \sqrt { 2 \pi } } \int _ { 0 } ^ { 1 } e ^ { - 2 \pi i w t } ( Z f ) ( t , w ) d t,$ ; confidence 0.757

107. d130080141.png ; $\operatorname { Ker } ( I - F ^ { \prime } ( c ) ) \bigoplus \operatorname { Im } ( I - F ^ { \prime } ( c ) ) = X$ ; confidence 1.000

108. f1302102.png ; $f \in L _ { \text{C} } ^ { 1 } ( G )$ ; confidence 1.000

109. h1201106.png ; $\Gamma \cup \text { int } ( \Gamma ) \subset \Omega$ ; confidence 0.757

110. b110220184.png ; $L ^ { * } ( h ^ { 2 } ( X ) , s ) _ { s = 1 }$ ; confidence 0.757

111. d12011018.png ; $\sum _ { j \in I } f ( x _ { i j } ) < \infty$ ; confidence 0.757

112. d03383074.png ; $S _ { \mu }$ ; confidence 0.757

113. b01533015.png ; $d < b$ ; confidence 0.757

114. g13002011.png ; $e ^ { z _ { 1 } + z _ { 2 } } = e ^ { z _ { 1 } } e ^ { z _ { 2 } }$ ; confidence 0.757

115. z13008032.png ; $k , l \in {\bf N} _ { 0 }$ ; confidence 1.000

116. q12005059.png ; $H _ { k + 1 } = H _ { k } + \beta _ { k } u ^ { k } ( u ^ { k } ) ^ { T } + \gamma _ { k } v ^ { k } ( v ^ { k } ) ^ { T }$ ; confidence 0.757

117. s13065031.png ; $\operatorname { lim } _ { n \rightarrow \infty } \phi _ { n } ^ { * } ( z ) = D _ { \mu } ( z ) ^ { - 1 }$ ; confidence 0.757

118. a13006064.png ; $G _ { R }$ ; confidence 0.757

119. l1100107.png ; $\preceq$ ; confidence 1.000

120. p1301207.png ; $s ( D )$ ; confidence 0.756

121. s12035012.png ; $Z ^ { t - 1 } = \{ y ( t - 1 ) , u ( t - 1 ) , \dots , y ( 0 ) , u ( 0 ) \}:$ ; confidence 0.756

122. z13011096.png ; $- \frac { 1 } { k + d n _ { k } } {..} [ ( i + d ) \mu ( i , m ) - ( i + d + 1 ) \mu ( i + 1 , m ) ] = 0.$ ; confidence 1.000

123. b12032086.png ; $k \operatorname { log } m \leq i \operatorname { log } n < ( k + 1 ) \operatorname { log } m$ ; confidence 1.000

124. p13010018.png ; $P ( K ) ^ { * }$ ; confidence 0.756

125. s086360140.png ; $k = 0 , \pm 1 , \pm 2 , \ldots$ ; confidence 0.756

126. s12024036.png ; ${\bf E} * ( )$ ; confidence 1.000

127. l05700010.png ; $( \lambda x M ) \in \Lambda$ ; confidence 0.756

128. c12029052.png ; $G = \text { Coker } ( \partial )$ ; confidence 0.756

129. c13010018.png ; $A _ { i } \cap A _ { j } = \emptyset$ ; confidence 0.756

130. b13012074.png ; $t | \leq \pi$ ; confidence 0.756

131. d03006010.png ; $\frac { \partial ^ { 2 } u ( t , x ) } { \partial t ^ { 2 } } - a ^ { 2 } \frac { \partial ^ { 2 } u ( t , x ) } { \partial x ^ { 2 } } = f ( t , x ),$ ; confidence 0.756

132. w12021073.png ; $( s _ { 1 } , \dots , s _ { k } , I _ { m } )$ ; confidence 1.000

133. t12020095.png ; $( n / ( 2 e ( m + n ) ) ) ^ { n }$ ; confidence 0.756

134. f13029038.png ; ${\cal T} : L ^ { X } \rightarrow L$ ; confidence 1.000

135. i1200901.png ; $( M ^ { 2 n } , \omega )$ ; confidence 0.756

136. t12013012.png ; $( L _ { 1 } , L _ { 2 } ) = ( S _ { 1 } \Lambda S _ { 1 } ^ { - 1 } , S _ { 2 } \Lambda ^ { t } S _ { 2 } ^ { - 1 } );$ ; confidence 0.756

137. z13007013.png ; $u \in {\bf Z} G$ ; confidence 1.000

138. c0220803.png ; $x _ { S }$ ; confidence 0.756

139. d13018023.png ; $J _ { E } \subset I _ { E }$ ; confidence 0.755

140. a12015046.png ; $\operatorname{Ad}( G ) X$ ; confidence 1.000

141. c130070170.png ; ${\frak C} ( P )$ ; confidence 1.000

142. v130050104.png ; $( u , v ) \mapsto u _ { n } ( v )$ ; confidence 1.000

143. c12007093.png ; $F : {\cal C} ^ { * } \otimes _ { k } {\cal C} \rightarrow \operatorname{Ab}$ ; confidence 1.000

144. d1301106.png ; $( {\bf p} _ { x } ^ { 2 } + {\bf p} _ { y } ^ { 2 } + {\bf p} _ { z } ^ { 2 } ) + m _ { 0 } ^ { 2 } c ^ { 2 } =$ ; confidence 1.000

145. b12034074.png ; $\| f \| \leq 2 f ( z _ { 0 } )$ ; confidence 0.755

146. w12006085.png ; ${\cal T} _ { A } \xi$ ; confidence 1.000

147. i130030166.png ; $\phi * ( \text { ind } ( D ) )$ ; confidence 0.755

148. o13003046.png ; ${\bf N} ( X ) = \sum _ { j = 1 } ^ { 8 } X _ { j } ^ { 2 }$ ; confidence 1.000

149. m13013020.png ; $m _ { i j } = 0$ ; confidence 0.755

150. p12014039.png ; $E _ { r } = S \cup T$ ; confidence 0.755

151. i120050112.png ; $P _ { \theta } ( \| T _ { N } - \theta \| > \epsilon _ { N } )$ ; confidence 0.755

152. s13064058.png ; $\hat{k}$ ; confidence 1.000

153. a130070129.png ; $n = 1.3 .5 ... ( 2 k - 1 )$ ; confidence 1.000

154. w13007037.png ; $| \gamma | = r + \sum _ { j = 1 } ^ { s } p _ { j }$ ; confidence 0.755

155. j13003055.png ; $\{ x y z \} = x \circ ( y ^ { * } \circ z ) + z \circ ( y ^ { * } \circ x ) - ( x \circ z ) \circ y ^ { * }$ ; confidence 0.755

156. d11008037.png ; $\delta ( w | v )$ ; confidence 0.755

157. d1300501.png ; $m \geq 4$ ; confidence 1.000

158. l12006055.png ; $= \int _ { 0 } ^ { \infty } | ( V \phi | \lambda ) | ^ { 2 } ( \frac { 1 } { \zeta - \lambda - i \epsilon } - \frac { 1 } { \zeta - \lambda + i \epsilon } ) d \lambda =$ ; confidence 1.000

159. b0167303.png ; $s = 1,2 , \dots,$ ; confidence 1.000

160. f12024083.png ; $t + \theta < t_0$ ; confidence 1.000

161. l11002068.png ; $| x y | \preceq | x | | y | | x |$ ; confidence 0.754

162. c1202803.png ; $C _ { 2 } \rightarrow C _ { 1 } \underset{\rightarrow}{\rightarrow} C _ { 0 }$ ; confidence 1.000

163. g0433208.png ; $u \in C _ { 0 } ^ { \infty } ( G )$ ; confidence 0.754

164. w12001039.png ; $W _ { \infty }$ ; confidence 0.754

165. c12017046.png ; $K \subset \bf R$ ; confidence 1.000

166. t12007057.png ; $n \geq - 1$ ; confidence 1.000

167. w13009052.png ; $\theta _ { n } ( f ) = \varphi$ ; confidence 1.000

168. a130180148.png ; $\bf P$ ; confidence 1.000

169. d13008035.png ; $b \in \partial \Delta$ ; confidence 0.754

170. a130040615.png ; $h = \operatorname { mng } _ {{\cal S}_P, \mathfrak { N } } $ ; confidence 1.000

171. f04044029.png ; $a \leq 0$ ; confidence 0.754

172. b12010021.png ; $( [ {\cal L , A} ] F ) _ { n } ( X ) =$ ; confidence 1.000

173. d13017021.png ; $\{ \varphi _ { i } \} _ { l = 1 } ^ { k - 1 }$ ; confidence 0.754

174. p13013029.png ; $\operatorname{SP} ( n )$ ; confidence 1.000

175. c12031033.png ; $\| f \| ^ { 2 } = \sum _ { \alpha _ { l } \leq k } \| D ^ { \alpha } f \| ^ { 2 _{L _ { 2 }}},$ ; confidence 1.000

176. a013010149.png ; $A _ { p }$ ; confidence 1.000

177. b12012014.png ; $R ( t ) = R ( \gamma ^ { \prime } ( t ) , . ) \gamma ^ { \prime } ( t )$ ; confidence 0.754

178. c1202002.png ; $\xi = \operatorname{ker} \alpha$ ; confidence 1.000

179. s13054097.png ; $\{ a , b \} _ { \infty }$ ; confidence 0.753

180. m13007025.png ; $E_{[ m , s ]} A ( f ) \Omega \neq 0$ ; confidence 1.000

181. v13005048.png ; $Y ( v , x ) \bf 1$ ; confidence 1.000

182. w13017017.png ; $K _ { j } \in {\bf R} ^ { n \times n } , K _ { 0 } = I , \sum _ { j = 0 } ^ { \infty } \| K _ { j } \| ^ { 2 } < \infty ,$ ; confidence 1.000

183. e120190110.png ; $m \in S$ ; confidence 0.753

184. d120020161.png ; $X \neq \emptyset$ ; confidence 1.000

185. s12023088.png ; $\operatorname{P} ( | XX ^ { \prime } | \neq 0 ) = 1$ ; confidence 1.000

186. p12015036.png ; $n / 2$ ; confidence 1.000

187. j120020198.png ; $k _ { \vartheta } ( z ) = \frac { 1 - | z | ^ { 2 } } { | z - e ^ { i \vartheta }|^ 2 }.$ ; confidence 1.000

188. l0596103.png ; $q = ( {\bf r} _ { 1 } , \dots , {\bf r} _ { N } )$ ; confidence 1.000

189. d1200206.png ; $( \operatorname{PD} )$ ; confidence 1.000

190. a12026057.png ; $A ^ {\bf N }$ ; confidence 1.000

191. e12006030.png ; $T _ { y } Y = V _ { y } Y + \Gamma ( y )$ ; confidence 0.753

192. t13008012.png ; $V _ { t } = \mu _ { X + t} d t S - P d t +$ ; confidence 0.753

193. a01149074.png ; $x ^ { \prime }$ ; confidence 0.753

194. f13002013.png ; $c ^ { a } ( x ) c ^ { b } ( y ) = - c ^ { b } ( y ) c ^ { a } ( x )$ ; confidence 1.000

195. d12026014.png ; $\operatorname{E} f ( X _ { n } ) \rightarrow \operatorname{E} f ( w ) , \quad n \rightarrow \infty, $ ; confidence 1.000

196. g04339014.png ; $\delta f ( x _ { 0 } , h ) = f _ { G } ^ { \prime } ( x _ { 0 } ) h , \quad f _ { G } ^ { \prime } ( x _ { 0 } ) \in L ( X , Y ).$ ; confidence 0.752

197. t13014070.png ; $h _ { j } \in \operatorname{Gl} ( v _ { j } , K )$ ; confidence 1.000

198. c02189013.png ; $r = 2$ ; confidence 0.752

199. y1200107.png ; $R _ { 13 } = ( 1 \otimes _ { k } \tau _ { V , V } ) ( R \otimes _ { k } 1 ) ( 1 \otimes _ { k } \tau _ { V , V } )$ ; confidence 0.752

200. p12015051.png ; $\Delta$ ; confidence 0.752

201. a12005058.png ; $u \in C ( [ 0 , T ] ; X ) \cap C ^ { 1 } ( ( 0 , T ] ; X )$ ; confidence 0.752

202. q1300306.png ; $\alpha | 0 \rangle + \beta | 1 \rangle$ ; confidence 0.752

203. m1300607.png ; $\operatorname{deg}_{x_m} a _ { 1 } \geq d ^ { m - 1 } ( d - 1 )$ ; confidence 0.752

204. q120070143.png ; ${\cal R} : G _ { q } \rightarrow U _ { q } ( {\frak g} )$ ; confidence 1.000

205. k13007042.png ; $\operatorname{L} ^ { \infty }$ ; confidence 1.000

206. t130050153.png ; $\operatorname{index}( A ) = \operatorname { dim } \operatorname { Ker } D _ { A } ^ { 0 } - \operatorname { dim } ( \operatorname { Ker } D _ { A } ^ { 1 } / \operatorname { Ran } D _ { A } ^ { 0 } ) + \operatorname { dim } ( {\cal X} / \operatorname { Ran } D _ { A } ^ { 1 } )$ ; confidence 1.000

207. m130230103.png ; $- ( K _ { X } + B )$ ; confidence 0.752

208. b01731024.png ; $y_1$ ; confidence 1.000

209. i12006079.png ; $L _ { 1 } , \ldots , L _ { k }$ ; confidence 0.752

210. c130160165.png ; $( w \in S )$ ; confidence 0.752

211. s13036017.png ; ${\bf l}_t$ ; confidence 1.000

212. a01105026.png ; $f : X \rightarrow S$ ; confidence 0.752

213. a0113707.png ; $f ( a )$ ; confidence 0.752

214. i120080123.png ; $T / T _ { c } \rightarrow 1$ ; confidence 0.752

215. i13006057.png ; $s _ { j } > 0$ ; confidence 0.751

216. g12005029.png ; $R < R _ { c }$ ; confidence 0.751

217. a130060102.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { P ^ { \# } ( n ) } { G ^ { \# } ( n ) } = \lambda.$ ; confidence 0.751

218. c02245012.png ; $\xi _ { 1 }$ ; confidence 0.751

219. c120180328.png ; $\tau _ { 3 } : \otimes ^ { 3 } {\cal E} \rightarrow \otimes ^ { 3 } {\cal E}$ ; confidence 1.000

220. a010210120.png ; $\frak a$ ; confidence 1.000

221. z13011028.png ; $\Delta G _ { n } ( x ) \equiv \mu _ { n } ( x ) = \sum {\bf 1} _ { \{ f _ { i n } = x \} }$ ; confidence 1.000

222. a1302006.png ; $( x , y , z ) \rightarrow \langle x y z \rangle$ ; confidence 1.000

223. c13016074.png ; $\bar{S} = \Sigma ^ {\color{blue} * } - S$ ; confidence 1.000

224. s13050034.png ; $X = \{ \pi ( 1 ) , \ldots , \pi ( | X | ) \}$ ; confidence 0.751

225. e120260100.png ; $\operatorname{P} ( \theta , \mu _ { p _ { j } } )$ ; confidence 1.000

226. d12014023.png ; $D _ { n } ( x , 1 ) = u ^ { n } + u ^ { - n } = e ^ { i n \alpha } + e ^ { - i n \alpha } =$ ; confidence 1.000

227. a130240101.png ; $t$ ; confidence 0.751

228. h12015024.png ; $\operatorname { log } | \phi ( h ) | = \int \operatorname { log } | h | dm$ ; confidence 1.000

229. s13002038.png ; $l ( u ) = \operatorname { sup } \{ t \geq 0 : g_t ( u ) \text { is defined} \}$ ; confidence 1.000

230. p130100153.png ; $z \in T$ ; confidence 0.751

231. h13006012.png ; $T _ { n } f ( z ) = \sum _ { m = 0 } ^ { \infty } \gamma _ { n } ( m ) q ^ { m } ( z ),$ ; confidence 0.751

232. i13007045.png ; $A ( \alpha ^ { \prime } , \alpha_0 , k )$ ; confidence 1.000

233. o13006028.png ; $\sigma _ { 1 } = \frac { 1 } { i } ( A _ { 1 } - A _ { 1 } ^ { * } ) | _ {\cal E } , \sigma _ { 2 } = \frac { 1 } { i } ( A _ { 2 } - A _ { 2 } ^ { * } ) | _ { \cal E } , \gamma = \frac { 1 } { i } ( A _ { 1 } A _ { 2 } ^ { * } - A _ { 2 } A _ { 1 } ^ { * } ) | _ { \cal E } , \tilde { \gamma } = \frac { 1 } { i } ( A _ { 2 } ^ { * } A _ { 1 } - A _ { 1 } ^ { * } A _ { 2 } ) | _ { \cal E }$ ; confidence 1.000

234. l12004073.png ; $f _ { i + 1 / 2 } = f ( u _ { i + 1 / 2 } ^ { n + 1 / 2 } );$ ; confidence 0.751

235. f12010096.png ; $\operatorname{SL} ( 2 , O _ { K } )$ ; confidence 1.000

236. a13002017.png ; $\nu = \operatorname { lim } \sum _ { k = 0 } ^ { n - 1 } \frac { 1 } { n } \delta _ { T ^ { n } x }$ ; confidence 0.751

237. w120090298.png ; ${\frak b} ^ { + }$ ; confidence 1.000

238. h13006019.png ; $\tilde{T} _ { n } ( L ) = \sum L ^ { \prime }$ ; confidence 1.000

239. k12010021.png ; $( t _ { 1 } , \dots , t _ { m } )$ ; confidence 0.751

240. f13024020.png ; $\langle x , y \rangle = - \varepsilon \langle y , x \rangle$ ; confidence 0.751

241. d12026020.png ; $\operatorname{P} \{ X _ { n } \in G \} \rightarrow \operatorname{P} \{ w \in G \}.$ ; confidence 1.000

242. e120010110.png ; $( f _ { i } : X \rightarrow G A _ { i } ) _ { I }$ ; confidence 0.751

243. t13013047.png ; $\operatorname{Hom}_\Lambda ( T , . ) : \cal T \rightarrow Y$ ; confidence 1.000

244. h12005037.png ; $+ \frac { 4 } { 3 } \pi ^ { - 1 / 2 } \int _ { C _ { N } } \phi _ { ; m } \rho _ { ; m } d y.$ ; confidence 0.750

245. b120150138.png ; $k j \in {\bf N} \cup \{ 0 \}$ ; confidence 1.000

246. b12005010.png ; $P ( z ) = A ( z , \dots , z )$ ; confidence 0.750

247. a12022021.png ; $T$ ; confidence 0.750

248. i13006013.png ; $f ( k ) = | f ( k ) | e ^ { - i \delta ( k ) },$ ; confidence 0.750

249. b12014032.png ; $\omega ( \beta ) / \sigma ^ { \prime } ( \beta )$ ; confidence 1.000

250. f04098026.png ; $M ^ { 4 }$ ; confidence 0.750

251. b12023031.png ; $\Sigma \cal V$ ; confidence 1.000

252. q1300409.png ; $G.$ ; confidence 0.750

253. s12024040.png ; $H _ { * } ^ { S }$ ; confidence 1.000

254. a130240235.png ; $\operatorname{SS} _ { e } = \sum _ { i = r + 1 } ^ { n } z _ { i } ^ { 2 }$ ; confidence 1.000

255. w13004027.png ; $g = - \frac { \omega _ { 1 } + i \omega _ { 2 } } { \omega _ { 3 } } = \frac { \omega _ { 3 } } { \omega _ { 1 } - i \omega _ { 2 } } , \eta = g ^ { - 1 } \omega _ { 3 }.$ ; confidence 0.750

256. t12005095.png ; $\Sigma ^ { i _ { 1 } , \ldots , i _ { r } } ( V , W )$ ; confidence 0.750

257. m120120104.png ; $R C \subseteq R N \subseteq Q _ { s } ( R )$ ; confidence 0.750

258. m12003089.png ; $\overset{\rightharpoonup} { x }$ ; confidence 1.000

259. s13048058.png ; $M = G / G_0$ ; confidence 1.000

260. e12009023.png ; $F _ { ,\nu } ^ { \mu \nu } = S ^ { \mu }$ ; confidence 1.000

261. a12023047.png ; $d \zeta = d \zeta _ { 1 } \wedge \ldots \wedge d \zeta _ { n }$ ; confidence 0.749

262. a130040127.png ; $\psi '$ ; confidence 1.000

263. i13005076.png ; $r_+ ( k ) = O ( 1 / k )$ ; confidence 1.000

264. t12020085.png ; $\theta \approx 0.2784$ ; confidence 1.000

265. a12006027.png ; ${\cal A} u = \sum _ { j = 1 } ^ { m } a _ { j } ( x ) \frac { \partial u } { \partial x _ { j } } + c ( x ) u$ ; confidence 0.749

266. i13003072.png ; $T _ { \text{vert} } ^ { * } Y : = T ^ { * } Y / \pi ^ { * } ( T ^ { * } B )$ ; confidence 1.000

267. n067520492.png ; $\Lambda ( \lambda _ { 1 } , \dots , \lambda _ { n } )$ ; confidence 0.749

268. a12027059.png ; $\operatorname{Gal}( N / K )$ ; confidence 1.000

269. t12005026.png ; $x \in \Sigma ^ { i , j } ( f )$ ; confidence 0.749

270. e12014038.png ; $v _ { i } \in V$ ; confidence 0.749

271. j12002099.png ; $Y _ { t } = B _ { \operatorname { min } ( t , 1 )}$ ; confidence 1.000

272. k12004023.png ; $K _ { 1 } \# - K _ { 2 }$ ; confidence 0.749

273. f120150201.png ; $\{ x _ { n } \} \subset D ( A )$ ; confidence 0.748

274. i13006012.png ; $f ( 0 , k ) : = f ( k )$ ; confidence 0.748

275. n1300306.png ; $v _ { x x } = \lambda v$ ; confidence 0.748

276. b110420103.png ; $a ( x , \xi )$ ; confidence 1.000

277. a13006069.png ; ${\cal G} _ { 1 }$ ; confidence 1.000

278. m130180173.png ; $( M \backslash a , M , M / a )$ ; confidence 0.748

279. e12002093.png ; $\Sigma \Omega X \rightarrow X$ ; confidence 0.748

280. a12007046.png ; $u ^ { \prime } \in C ^ { \alpha } ( [ 0 , T ] ; X ) \cap B ( D _ { A } ( \alpha , \infty ) ),$ ; confidence 0.748

281. j13003030.png ; $[ a \square b ^ { * } , x \square y ^ { * } ] = \{ a b x \} \square y ^ { * } - x \square \{ y a b \}$ ; confidence 0.748

282. k12013026.png ; $p ( x ) = \sqrt { 1 - x ^ { 2 } } / \rho _ { m } ( x )$ ; confidence 0.748

283. b13016057.png ; $f | _ { K } \in A | _ { K }$ ; confidence 0.748

284. p1201707.png ; $\operatorname{ker} \delta _ { A , B } = \{ X \in B ( H ) : \delta _ { A , B } ( X ) = 0 \}$ ; confidence 1.000

285. a11050055.png ; $a \in K$ ; confidence 1.000

286. a01233028.png ; $l\geq 0$ ; confidence 1.000

287. b12052085.png ; $= - \prod _ { j = 0 } ^ { n - 1 } ( I - w _ { j } v _ { j } ^ { T } ) B _ { 0 } ^ { - 1 } F ( x _ { n } ).$ ; confidence 0.747

288. d0304107.png ; $a \geq 0$ ; confidence 0.747

289. t13005050.png ; $\sigma _ { T } ( A , {\cal X} ) = \{ \lambda \in C ^ { n } : K ( A - \lambda , {\cal X} ) \text{ is not exact}\}.$ ; confidence 1.000

290. c0235705.png ; $M \subset X$ ; confidence 0.747

291. b01556042.png ; $D ^ { * }$ ; confidence 0.747

292. n067520242.png ; $\overline { B } = S ^ { - 1 } B = ( \overline { b } _ { 1 } , \dots , \overline { b } _ { m } )$ ; confidence 0.747

293. d03033015.png ; $\gamma \rightarrow \int _ { \gamma } \omega$ ; confidence 0.747

294. b015350295.png ; $l_ { \infty }$ ; confidence 1.000

295. a120260127.png ; $A \{ X _ { 1 } , \dots , X _ { s _ { i } } \}$ ; confidence 0.747

296. k05584061.png ; $\| |G | ^ { 1 / 2 } x \|$ ; confidence 1.000

297. m13018020.png ; $g ( x ) = \sum _ { y : y \geq x } f ( y ) \Leftrightarrow f ( x ) = \sum _ { y : y \geq x } \mu ( x , y ) g ( y ).$ ; confidence 0.747

298. m12016054.png ; $\operatorname{rank} ( \Phi ) = n _ { 1 }$ ; confidence 1.000

299. b130300100.png ; $\psi _ { i - 1 } ( A _ { i } ^ { n } )$ ; confidence 0.747

300. s1200406.png ; $\lambda = ( \lambda _ { 1 } , \dots , \lambda _ { l } )$ ; confidence 0.747

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/43. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/43&oldid=45583
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