Namespaces
Variants
Actions

Difference between revisions of "User:Maximilian Janisch/latexlist/latex/1"

From Encyclopedia of Mathematics
Jump to: navigation, search
(AUTOMATIC EDIT of page 1 out of 11 with 300 lines: Updated image/latex database (currently 3083 images latexified; order by Confidence, ascending: False.)
(AUTOMATIC EDIT of page 1 out of 11 with 300 lines: Updated image/latex database (currently 3083 images latexified; order by Confidence, ascending: False.)
Line 96: Line 96:
 
48. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001029.png ; $C ( S )$ ; confidence 0.946
 
48. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001029.png ; $C ( S )$ ; confidence 0.946
  
−
49. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200104.png ; $$m$$ ; confidence 0.499
+
49. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200104.png ; $m$ ; confidence 0.499
  
 
50. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001053.png ; $\{ \xi ^ { 1 } , \xi ^ { 2 } , \xi ^ { 3 } \}$ ; confidence 1.000
 
50. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001053.png ; $\{ \xi ^ { 1 } , \xi ^ { 2 } , \xi ^ { 3 } \}$ ; confidence 1.000
Line 102: Line 102:
 
51. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001099.png ; $_ { \nabla } ( G / K )$ ; confidence 0.326
 
51. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001099.png ; $_ { \nabla } ( G / K )$ ; confidence 0.326
  
−
52. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001094.png ; $$n + 2$$ ; confidence 1.000
+
52. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001094.png ; $n + 2$ ; confidence 1.000
  
 
53. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010118.png ; $4 n + 3$ ; confidence 1.000
 
53. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010118.png ; $4 n + 3$ ; confidence 1.000
Line 116: Line 116:
 
58. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001046.png ; $\lambda = \operatorname { dim } ( \delta ) - 1$ ; confidence 0.702
 
58. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001046.png ; $\lambda = \operatorname { dim } ( \delta ) - 1$ ; confidence 0.702
  
−
59. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010101.png ; $$Z = G / U ( 1 ) . K$$ ; confidence 0.948
+
59. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010101.png ; $Z = G / U ( 1 ) . K$ ; confidence 0.948
  
−
60. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200109.png ; $$1$$ ; confidence 0.742
+
60. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200109.png ; $1$ ; confidence 0.742
  
 
61. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010116.png ; $\operatorname { dim } ( O ) = 4$ ; confidence 0.996
 
61. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010116.png ; $\operatorname { dim } ( O ) = 4$ ; confidence 0.996
Line 142: Line 142:
 
71. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010121.png ; $S = SU ( m ) / S ( U ( m - 2 ) \times U ( 1 ) )$ ; confidence 0.541
 
71. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010121.png ; $S = SU ( m ) / S ( U ( m - 2 ) \times U ( 1 ) )$ ; confidence 0.541
  
−
72. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010158.png ; $$T ^ { n }$$ ; confidence 0.616
+
72. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010158.png ; $T ^ { n }$ ; confidence 0.616
  
 
73. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001019.png ; $( C ( S ) , \overline { g } )$ ; confidence 0.418
 
73. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001019.png ; $( C ( S ) , \overline { g } )$ ; confidence 0.418
Line 152: Line 152:
 
76. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010138.png ; $D$ ; confidence 0.661
 
76. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010138.png ; $D$ ; confidence 0.661
  
−
77. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001011.png ; $$\xi = I ( \partial _ { r } )$$ ; confidence 0.869
+
77. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001011.png ; $\xi = I ( \partial _ { r } )$ ; confidence 0.869
  
−
78. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010107.png ; $$n \geq 0$$ ; confidence 0.996
+
78. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010107.png ; $n \geq 0$ ; confidence 0.996
  
 
79. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001061.png ; $\Gamma \subset SU ( 2 )$ ; confidence 0.951
 
79. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001061.png ; $\Gamma \subset SU ( 2 )$ ; confidence 0.951
Line 166: Line 166:
 
83. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001077.png ; $\xi ( \tau )$ ; confidence 0.999
 
83. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001077.png ; $\xi ( \tau )$ ; confidence 0.999
  
−
84. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010133.png ; $$S ( p ) = U ( 1 ) _ { p } \backslash U ( n + 2 ) / U ( n )$$ ; confidence 0.916
+
84. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010133.png ; $S ( p ) = U ( 1 ) _ { p } \backslash U ( n + 2 ) / U ( n )$ ; confidence 0.916
  
 
85. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200108.png ; $1 > 1$ ; confidence 0.983
 
85. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t1200108.png ; $1 > 1$ ; confidence 0.983
Line 196: Line 196:
 
98. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a0100204.png ; $\{ E _ { n _ { 1 } } \ldots n _ { k } \}$ ; confidence 0.382
 
98. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a0100204.png ; $\{ E _ { n _ { 1 } } \ldots n _ { k } \}$ ; confidence 0.382
  
−
99. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a01002013.png ; $$\sigma \delta$$ ; confidence 0.999
+
99. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010020/a01002013.png ; $\sigma \delta$ ; confidence 0.999
  
 
100. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010080/a01008023.png ; $A _ { x _ { 1 } } ^ { \prime } \ldots x _ { k } = A _ { 1 } \cap \ldots \cap A _ { x _ { 1 } } \ldots x _ { k }$ ; confidence 0.061
 
100. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010080/a01008023.png ; $A _ { x _ { 1 } } ^ { \prime } \ldots x _ { k } = A _ { 1 } \cap \ldots \cap A _ { x _ { 1 } } \ldots x _ { k }$ ; confidence 0.061
Line 224: Line 224:
 
112. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420163.png ; $\theta = 1 - \theta$ ; confidence 0.998
 
112. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420163.png ; $\theta = 1 - \theta$ ; confidence 0.998
  
−
113. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420118.png ; $$H$$ ; confidence 0.998
+
113. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420118.png ; $H$ ; confidence 0.998
  
 
114. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042090.png ; $n > 0$ ; confidence 0.998
 
114. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a11042090.png ; $n > 0$ ; confidence 0.998
Line 346: Line 346:
 
173. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013075.png ; $( g )$ ; confidence 0.981
 
173. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013075.png ; $( g )$ ; confidence 0.981
  
−
174. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013023.png ; $$= \operatorname { exp } ( x P _ { 0 } z + \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } ) g ( z ) . . \operatorname { exp } ( - x P _ { 0 } z - \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { \gamma } )$$ ; confidence 0.382
+
174. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013023.png ; $= \operatorname { exp } ( x P _ { 0 } z + \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { r } ) g ( z ) . . \operatorname { exp } ( - x P _ { 0 } z - \sum _ { r = 1 } ^ { \infty } Q _ { 0 } z ^ { \gamma } )$ ; confidence 0.382
  
 
175. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013026.png ; $( 1 )$ ; confidence 0.515
 
175. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013026.png ; $( 1 )$ ; confidence 0.515
Line 354: Line 354:
 
177. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013078.png ; $q ^ { ( l ) } = 2 i \frac { \tau _ { l } + 1 } { \tau _ { l } } , r ^ { ( l ) } = - 2 i \frac { \tau _ { l } - 1 } { \tau _ { l } }$ ; confidence 0.315
 
177. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013078.png ; $q ^ { ( l ) } = 2 i \frac { \tau _ { l } + 1 } { \tau _ { l } } , r ^ { ( l ) } = - 2 i \frac { \tau _ { l } - 1 } { \tau _ { l } }$ ; confidence 0.315
  
−
178. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a130130100.png ; $$A K N S$$ ; confidence 0.971
+
178. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a130130100.png ; $A K N S$ ; confidence 0.971
  
 
179. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013025.png ; $C ^ { \infty } ( s ^ { 1 } , SL _ { 2 } ( C ) )$ ; confidence 0.430
 
179. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013025.png ; $C ^ { \infty } ( s ^ { 1 } , SL _ { 2 } ( C ) )$ ; confidence 0.430
Line 364: Line 364:
 
182. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013053.png ; $P ^ { ( l ) } = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) z + \left( \begin{array} { c c } { 0 } & { q ^ { ( l ) } } \\ { r ^ { ( l ) } } & { 0 } \end{array} \right)$ ; confidence 0.416
 
182. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013053.png ; $P ^ { ( l ) } = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) z + \left( \begin{array} { c c } { 0 } & { q ^ { ( l ) } } \\ { r ^ { ( l ) } } & { 0 } \end{array} \right)$ ; confidence 0.416
  
−
183. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013021.png ; $$h$$ ; confidence 0.644
+
183. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013021.png ; $h$ ; confidence 0.644
  
 
184. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013046.png ; $\frac { \partial } { \partial t _ { k } } F _ { i j } = \frac { \partial } { \partial t _ { i } } F _ { j k }$ ; confidence 0.932
 
184. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013046.png ; $\frac { \partial } { \partial t _ { k } } F _ { i j } = \frac { \partial } { \partial t _ { i } } F _ { j k }$ ; confidence 0.932
Line 398: Line 398:
 
199. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013016.png ; $8$ ; confidence 0.804
 
199. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013016.png ; $8$ ; confidence 0.804
  
−
200. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013085.png ; $$L$$ ; confidence 0.550
+
200. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013085.png ; $L$ ; confidence 0.550
  
 
201. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013054.png ; $t _ { n }$ ; confidence 0.933
 
201. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013054.png ; $t _ { n }$ ; confidence 0.933
Line 418: Line 418:
 
209. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013044.png ; $F _ { j k } =$ ; confidence 0.626
 
209. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013044.png ; $F _ { j k } =$ ; confidence 0.626
  
−
210. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013045.png ; $$= \frac { 1 } { 2 } \operatorname { Tr } ( \sum _ { r = 0 } ^ { j } ( j - r ) Q _ { r } Q _ { k + j - r } + \frac { 1 } { 2 } \sum _ { r = 0 } ^ { j } ( r - k ) Q _ { r } Q _ { k + j - r } )$$ ; confidence 0.240
+
210. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013045.png ; $= \frac { 1 } { 2 } \operatorname { Tr } ( \sum _ { r = 0 } ^ { j } ( j - r ) Q _ { r } Q _ { k + j - r } + \frac { 1 } { 2 } \sum _ { r = 0 } ^ { j } ( r - k ) Q _ { r } Q _ { k + j - r } )$ ; confidence 0.240
  
 
211. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013090.png ; $N$ ; confidence 0.183
 
211. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013090.png ; $N$ ; confidence 0.183
Line 428: Line 428:
 
214. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013069.png ; $\tau ( t ) = ( \tau _ { l } ( t ) ) _ { l \in Z }$ ; confidence 0.585
 
214. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013069.png ; $\tau ( t ) = ( \tau _ { l } ( t ) ) _ { l \in Z }$ ; confidence 0.585
  
−
215. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013091.png ; $$L : = P _ { 0 } \frac { d } { d x } + P _ { 1 } = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) \frac { d } { d x } + \left( \begin{array} { c c } { 0 } & { q } \\ { r } & { 0 } \end{array} \right)$$ ; confidence 0.711
+
215. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013091.png ; $L : = P _ { 0 } \frac { d } { d x } + P _ { 1 } = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) \frac { d } { d x } + \left( \begin{array} { c c } { 0 } & { q } \\ { r } & { 0 } \end{array} \right)$ ; confidence 0.711
  
 
216. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013076.png ; $P ^ { ( l ) }$ ; confidence 0.869
 
216. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013076.png ; $P ^ { ( l ) }$ ; confidence 0.869
Line 498: Line 498:
 
249. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022037.png ; $r _ { ess } ( T )$ ; confidence 0.259
 
249. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022037.png ; $r _ { ess } ( T )$ ; confidence 0.259
  
−
250. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022013.png ; $$T : X \rightarrow Y$$ ; confidence 0.863
+
250. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022013.png ; $T : X \rightarrow Y$ ; confidence 0.863
  
 
251. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022011.png ; $X = 1 ^ { p }$ ; confidence 0.914
 
251. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022011.png ; $X = 1 ^ { p }$ ; confidence 0.914
Line 570: Line 570:
 
285. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240545.png ; $2$ ; confidence 0.985
 
285. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240545.png ; $2$ ; confidence 0.985
  
−
286. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240141.png ; $$c$$ ; confidence 0.324
+
286. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240141.png ; $c$ ; confidence 0.324
  
 
287. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240308.png ; $\hat { \eta } _ { \Omega } = X \hat { \beta }$ ; confidence 0.485
 
287. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240308.png ; $\hat { \eta } _ { \Omega } = X \hat { \beta }$ ; confidence 0.485

Revision as of 11:41, 1 September 2019

List

1. a13001017.png ; $3 + 5$ ; confidence 0.136

2. a1300107.png ; $A , B , C \in C$ ; confidence 0.982

3. a1300103.png ; $( - ) ^ { * } : C ^ { 0 p } \rightarrow C$ ; confidence 0.505

4. a1300109.png ; $s = s ( ( A ^ { * } ) ^ { ( B ^ { * } ) } , ( B ^ { * } ) ^ { ( C ^ { * } ) } )$ ; confidence 0.907

5. a13001014.png ; $R el$ ; confidence 0.544

6. a1300104.png ; $d ( A , B ) : B ^ { A } \cong A ^ { * } B ^ { * }$ ; confidence 0.988

7. a1300105.png ; $4$ ; confidence 0.531

8. a13001015.png ; $S ^ { * } = S$ ; confidence 0.463

9. a13001016.png ; $B ^ { A } \cong ( A ^ { * } \otimes B )$ ; confidence 0.992

10. a1300106.png ; $B$ ; confidence 0.895

11. a1300102.png ; $C$ ; confidence 0.838

12. t12001048.png ; $( S , g )$ ; confidence 0.978

13. t120010139.png ; $3$ ; confidence 1.000

14. t120010117.png ; $D$ ; confidence 0.538

15. t12001030.png ; $5$ ; confidence 0.885

16. t12001056.png ; $F _ { 3 }$ ; confidence 0.996

17. t12001095.png ; $\operatorname { dim } ( S ) = 4 n + 3$ ; confidence 0.958

18. t120010140.png ; $\geq 7$ ; confidence 0.562

19. t120010134.png ; $( 4 n + 3 )$ ; confidence 1.000

20. t12001082.png ; $Z = S \nmid F _ { \tau }$ ; confidence 0.763

21. t12001041.png ; $\{ \xi ^ { \alpha } , \eta ^ { \alpha } , \Phi ^ { \alpha } \} \alpha = 1,2,3$ ; confidence 0.761

22. t120010159.png ; $4 n$ ; confidence 0.999

23. t120010109.png ; $m > 3$ ; confidence 0.916

24. t120010141.png ; $7$ ; confidence 0.937

25. t12001038.png ; $\eta ^ { \alpha } ( Y ) = g ( \xi ^ { \alpha } , Y )$ ; confidence 0.932

26. t120010135.png ; $S ( p )$ ; confidence 0.693

27. t120010148.png ; $T ^ { 2 } \times SO ( 3 )$ ; confidence 0.990

28. t12001034.png ; $SO ( 3 )$ ; confidence 0.940

29. t12001039.png ; $\Phi ^ { \alpha } ( Y ) = \nabla _ { Y } \xi ^ { \alpha }$ ; confidence 0.798

30. t120010125.png ; $\dot { i } \leq n$ ; confidence 0.190

31. t12001022.png ; $n \geq 1$ ; confidence 0.967

32. t12001035.png ; $SU ( 2 )$ ; confidence 0.811

33. t120010115.png ; $11$ ; confidence 1.000

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

35. t120010105.png ; $SU ( m ) / S ( U ( m - 2 ) \times U ( 1 ) ) , SO ( k ) / SO ( k - 4 ) \times Sp ( 1 )$ ; confidence 0.164

36. t12001057.png ; $0$ ; confidence 0.311

37. t12001021.png ; $m = 4 n + 3$ ; confidence 0.997

38. t12001088.png ; $\hat { v } ^ { ( S ) }$ ; confidence 0.182

39. t120010130.png ; $b _ { 2 } \neq b _ { 6 }$ ; confidence 0.994

40. t12001020.png ; $\operatorname { Sp } ( ( m + 1 ) / 4 )$ ; confidence 0.694

41. t12001072.png ; $\xi ( \tau ) = \tau _ { 1 } \xi ^ { 1 } + \tau _ { 2 } \xi ^ { 2 } + \tau _ { 3 } \xi ^ { 3 }$ ; confidence 0.998

42. t12001081.png ; $U ( 1 ) _ { \tau } \subset \operatorname { SU } ( 2 )$ ; confidence 0.671

43. t120010123.png ; $\sum _ { k = 1 } ^ { n } k ( n + 1 - k ) ( n + 1 - 2 k ) b _ { 2 k } = 0$ ; confidence 0.782

44. t12001028.png ; $\{ I ^ { 1 } , R ^ { 2 } , \hat { P } \}$ ; confidence 0.143

45. t12001060.png ; $S ^ { 3 } / \Gamma$ ; confidence 0.633

46. t12001098.png ; $k$ ; confidence 0.208

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

48. t12001029.png ; $C ( S )$ ; confidence 0.946

49. t1200104.png ; $m$ ; confidence 0.499

50. t12001053.png ; $\{ \xi ^ { 1 } , \xi ^ { 2 } , \xi ^ { 3 } \}$ ; confidence 1.000

51. t12001099.png ; $_ { \nabla } ( G / K )$ ; confidence 0.326

52. t12001094.png ; $n + 2$ ; confidence 1.000

53. t120010118.png ; $4 n + 3$ ; confidence 1.000

54. t120010129.png ; $15$ ; confidence 1.000

55. t12001014.png ; $5$ ; confidence 0.574

56. t12001075.png ; $s ^ { 2 }$ ; confidence 0.942

57. t12001040.png ; $\alpha = 1,2,3$ ; confidence 0.734

58. t12001046.png ; $\lambda = \operatorname { dim } ( \delta ) - 1$ ; confidence 0.702

59. t120010101.png ; $Z = G / U ( 1 ) . K$ ; confidence 0.948

60. t1200109.png ; $1$ ; confidence 0.742

61. t120010116.png ; $\operatorname { dim } ( O ) = 4$ ; confidence 0.996

62. t120010114.png ; $\operatorname { im } ( S ) = 7$ ; confidence 0.799

63. t1200106.png ; $U ( ( m + 1 ) / 2 )$ ; confidence 0.997

64. t12001079.png ; $F _ { \tau } \subset F _ { 3 } \subset S$ ; confidence 0.996

65. t12001026.png ; $\xi ^ { \mathscr { L } } = I ^ { \mathscr { L } } ( \partial _ { r } )$ ; confidence 0.127

66. t120010106.png ; $G _ { 2 } / \operatorname { Sp } ( 1 ) , \quad F _ { 4 } / \operatorname { Sp } ( 3 ) , E _ { 6 } / SU ( 6 ) , \quad E _ { 7 } / \operatorname { Spin } ( 12 ) , \quad E _ { 8 } / E _ { 7 }$ ; confidence 0.614

67. t12001032.png ; $g ( \xi ^ { \alpha } , \xi ^ { b } ) = \delta _ { \alpha b }$ ; confidence 0.989

68. t120010136.png ; $p = ( p _ { 1 } , \dots , p _ { n } + 2 )$ ; confidence 0.447

69. t120010100.png ; $O = G / \operatorname { Sp } ( 1 ) . K$ ; confidence 0.187

70. t12001091.png ; $z$ ; confidence 1.000

71. t120010121.png ; $S = SU ( m ) / S ( U ( m - 2 ) \times U ( 1 ) )$ ; confidence 0.541

72. t120010158.png ; $T ^ { n }$ ; confidence 0.616

73. t12001019.png ; $( C ( S ) , \overline { g } )$ ; confidence 0.418

74. t120010108.png ; $Sp ( 0 )$ ; confidence 0.378

75. t12001064.png ; $s ^ { 3 }$ ; confidence 0.948

76. t120010138.png ; $D$ ; confidence 0.661

77. t12001011.png ; $\xi = I ( \partial _ { r } )$ ; confidence 0.869

78. t120010107.png ; $n \geq 0$ ; confidence 0.996

79. t12001061.png ; $\Gamma \subset SU ( 2 )$ ; confidence 0.951

80. t120010124.png ; $b _ { 2 } i + 1 ( S ) = 0$ ; confidence 0.920

81. t1200107.png ; $m = 2 i + 1$ ; confidence 0.871

82. t12001033.png ; $[ \xi ^ { \alpha } , \xi ^ { b } ] = 2 \epsilon _ { \alpha b c } \xi ^ { c }$ ; confidence 0.322

83. t12001077.png ; $\xi ( \tau )$ ; confidence 0.999

84. t120010133.png ; $S ( p ) = U ( 1 ) _ { p } \backslash U ( n + 2 ) / U ( n )$ ; confidence 0.916

85. t1200108.png ; $1 > 1$ ; confidence 0.983

86. t120010120.png ; $b _ { 2 } ( s ) \leq 1$ ; confidence 0.580

87. t12001085.png ; $0$ ; confidence 0.355

88. t12001078.png ; $1$ ; confidence 0.998

89. t12001074.png ; $2$ ; confidence 1.000

90. t12001071.png ; $\tau _ { 1 } ^ { 2 } + \tau _ { 3 } ^ { 2 } + \tau _ { 3 } ^ { 2 } = 1$ ; confidence 0.974

91. t120010147.png ; $T ^ { 2 } \times \operatorname { Sp } ( 1 )$ ; confidence 0.987

92. t1200105.png ; $( C ( S ) , \overline { g } ) = ( R _ { + } \times S , d \nu ^ { 2 } + r ^ { 2 } g )$ ; confidence 0.265

93. t120010110.png ; $k > 7$ ; confidence 0.997

94. t120010104.png ; $\operatorname { Sp } ( n + 1 ) / \operatorname { Sp } ( n ) , \quad \operatorname { Sp } ( n + 1 ) / \operatorname { Sp } ( n ) \times Z _ { 2 }$ ; confidence 0.901

95. t12001097.png ; $SO ( 4 n + 3 )$ ; confidence 0.906

96. a0100206.png ; $t$ ; confidence 0.637

97. a0100205.png ; $P = \cup _ { n _ { 1 } , \ldots , n _ { k } , \ldots } \cap _ { k = 1 } ^ { \infty } E _ { n _ { 1 } } \square \ldots x _ { k }$ ; confidence 0.192

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

99. a01002013.png ; $\sigma \delta$ ; confidence 0.999

100. a01008023.png ; $A _ { x _ { 1 } } ^ { \prime } \ldots x _ { k } = A _ { 1 } \cap \ldots \cap A _ { x _ { 1 } } \ldots x _ { k }$ ; confidence 0.061

101. a0100808.png ; $x _ { 1 } , \ldots , A _ { x _ { 1 } } \ldots x _ { k } , \ldots ,$ ; confidence 0.104

102. a0100805.png ; $\{ A _ { n _ { 1 } } \ldots n _ { k } \}$ ; confidence 0.200

103. a0100807.png ; $A _ { x } _ { 1 } \ldots x _ { k } x _ { k + 1 } \subset A _ { x _ { 1 } } \ldots x _ { k }$ ; confidence 0.139

104. a01008024.png ; $M$ ; confidence 0.626

105. a0100803.png ; $x$ ; confidence 0.475

106. a110420123.png ; $\pi$ ; confidence 0.772

107. a110420169.png ; $K$ ; confidence 0.738

108. a110420153.png ; $K _ { 0 } ( B ) ^ { + }$ ; confidence 0.993

109. a11042060.png ; $K _ { 1 }$ ; confidence 0.970

110. a110420164.png ; $C ( S ^ { 2 n } )$ ; confidence 0.540

111. a110420108.png ; $\tau ( x y ) = \tau ( y x )$ ; confidence 0.993

112. a110420163.png ; $\theta = 1 - \theta$ ; confidence 0.998

113. a110420118.png ; $H$ ; confidence 0.998

114. a11042090.png ; $n > 0$ ; confidence 0.998

115. a11042070.png ; $K _ { 0 } ( \varphi ) = \alpha$ ; confidence 0.993

116. a11042086.png ; $z \in G$ ; confidence 0.715

117. a110420112.png ; $f : G \rightarrow R$ ; confidence 0.996

118. a11042095.png ; $C ^ { * }$ ; confidence 0.866

119. a11042050.png ; $( K _ { 0 } ( A ) , K _ { 0 } ( A ) ^ { + } , \Sigma ( A ) )$ ; confidence 0.990

120. a110420127.png ; $D$ ; confidence 0.683

121. a110420138.png ; $I \mapsto I$ ; confidence 0.782

122. a110420149.png ; $K _ { 0 } ( \varphi ) : K _ { 0 } ( A ) \rightarrow K _ { 0 } ( B )$ ; confidence 0.977

123. a110420113.png ; $f ( G ^ { + } ) \subseteq R ^ { + }$ ; confidence 1.000

124. a110420128.png ; $h$ ; confidence 0.307

125. a11042064.png ; $( K _ { 0 } ( A ) , K _ { 0 } ( A ) ^ { + } , \Sigma ( A ) )$ ; confidence 0.990

126. a11042053.png ; $K _ { 0 } ( A )$ ; confidence 0.745

127. a110420117.png ; $H ^ { + } = G ^ { + } \cap H$ ; confidence 0.999

128. a11042063.png ; $\square ^ { * }$ ; confidence 0.982

129. a110420150.png ; $K _ { 0 } ( \varphi )$ ; confidence 0.924

130. a11042084.png ; $x _ { 1 } , x _ { 2 } , y _ { 1 } , y _ { 2 } \in G$ ; confidence 0.943

131. a11042088.png ; $( G , G ^ { + } )$ ; confidence 1.000

132. a11042079.png ; $25$ ; confidence 0.396

133. a110420162.png ; $\theta = \theta ^ { \prime }$ ; confidence 0.994

134. a110420121.png ; $y \leq x$ ; confidence 0.998

135. a11042066.png ; $\alpha : K _ { 0 } ( A ) \rightarrow K _ { 0 } ( B )$ ; confidence 0.991

136. a11042067.png ; $\alpha ( K _ { 0 } ( A ) ^ { + } ) = K _ { 0 } ( B ) ^ { + }$ ; confidence 0.997

137. a11042055.png ; $K _ { 0 } ( A ) ^ { + }$ ; confidence 0.988

138. a11042077.png ; $K _ { 0 } ( \varphi ) = K _ { 0 } ( \psi )$ ; confidence 0.842

139. a110420161.png ; $A _ { \theta } \cong A _ { \theta }$ ; confidence 0.999

140. a110420110.png ; $f$ ; confidence 1.000

141. a11042089.png ; $\geq 0$ ; confidence 1.000

142. a11042078.png ; $4$ ; confidence 0.978

143. a110420166.png ; $2 n$ ; confidence 1.000

144. a11042068.png ; $\alpha ( \Sigma ( A ) ) = \Sigma ( B )$ ; confidence 0.988

145. a11042069.png ; $\varphi : A \rightarrow B$ ; confidence 0.999

146. a11042072.png ; $\alpha ( \Sigma ( A ) ) \subseteq \Sigma ( B )$ ; confidence 0.978

147. a11042087.png ; $x _ { i } \leq z \leq y _ { j }$ ; confidence 0.967

148. a110420154.png ; $K _ { 0 }$ ; confidence 0.936

149. a110420137.png ; $\tau \mapsto K _ { 0 } ( \tau )$ ; confidence 0.994

150. a11042091.png ; $x \in G$ ; confidence 0.737

151. a110420126.png ; $K _ { 0 } ( \tau ) ( [ p ] _ { 0 } - [ q ] _ { 0 } ) = \tau ( p ) - \tau ( q )$ ; confidence 0.889

152. a110420122.png ; $y \in H$ ; confidence 0.503

153. a110420134.png ; $K _ { 0 } ( I ) \rightarrow K _ { 0 } ( A )$ ; confidence 0.923

154. a110420109.png ; $x , y \in A$ ; confidence 0.906

155. a11042092.png ; $x > 0$ ; confidence 0.700

156. a110420158.png ; $A _ { \theta }$ ; confidence 0.786

157. a11042065.png ; $( K _ { 0 } ( B ) , K _ { 0 } ( B ) ^ { + } , \Sigma ( B ) )$ ; confidence 0.997

158. a110420107.png ; $\tau : A \rightarrow C$ ; confidence 0.987

159. a110420133.png ; $i$ ; confidence 0.450

160. a11042075.png ; $\varphi , \psi : A \rightarrow B$ ; confidence 0.980

161. a11042056.png ; $\Sigma ( A )$ ; confidence 0.626

162. a110420119.png ; $x \in H ^ { + }$ ; confidence 0.518

163. a110420120.png ; $y \in G ^ { + }$ ; confidence 0.943

164. a110420143.png ; $1$ ; confidence 0.989

165. a11042085.png ; $x _ { i } \leq y _ { j }$ ; confidence 0.993

166. a110420160.png ; $K _ { 0 } ( B ) = Z + \theta Z$ ; confidence 0.898

167. a11042098.png ; $K _ { 1 } ( A ) = 0$ ; confidence 0.997

168. a110420125.png ; $( K _ { 0 } ( A ) , K _ { 0 } ( A ) ^ { + } )$ ; confidence 0.951

169. a13013088.png ; $t$ ; confidence 0.354

170. a13013059.png ; $i$ ; confidence 0.570

171. a13013037.png ; $SL _ { 2 } ( C )$ ; confidence 0.910

172. a13013039.png ; $Q = \sum _ { j = 0 } ^ { \infty } Q _ { j } z ^ { - j } , Q _ { j } = \left( \begin{array} { c c } { h _ { j } } & { e _ { j } } \\ { f _ { j } } & { - h _ { j } } \end{array} \right)$ ; confidence 0.875

173. a13013075.png ; $( g )$ ; confidence 0.981

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

175. a13013026.png ; $( 1 )$ ; confidence 0.515

176. a13013067.png ; $C [ t ] = C [ t _ { 1 } , t _ { 2 } , \ldots$ ; confidence 0.593

177. a13013078.png ; $q ^ { ( l ) } = 2 i \frac { \tau _ { l } + 1 } { \tau _ { l } } , r ^ { ( l ) } = - 2 i \frac { \tau _ { l } - 1 } { \tau _ { l } }$ ; confidence 0.315

178. a130130100.png ; $A K N S$ ; confidence 0.971

179. a13013025.png ; $C ^ { \infty } ( s ^ { 1 } , SL _ { 2 } ( C ) )$ ; confidence 0.430

180. a13013032.png ; $\phi$ ; confidence 0.476

181. a13013042.png ; $X _ { i } \in \operatorname { sl } _ { 2 } ( C )$ ; confidence 0.209

182. a13013053.png ; $P ^ { ( l ) } = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) z + \left( \begin{array} { c c } { 0 } & { q ^ { ( l ) } } \\ { r ^ { ( l ) } } & { 0 } \end{array} \right)$ ; confidence 0.416

183. a13013021.png ; $h$ ; confidence 0.644

184. a13013046.png ; $\frac { \partial } { \partial t _ { k } } F _ { i j } = \frac { \partial } { \partial t _ { i } } F _ { j k }$ ; confidence 0.932

185. a13013010.png ; $t = ( t _ { x } )$ ; confidence 0.458

186. a13013034.png ; $\phi _ { - } ^ { - 1 } \frac { \partial } { \partial t _ { \mu } } - Q _ { 0 } z ^ { \mu } \phi _ { - } = \frac { \partial } { \partial t _ { \mu } } - Q ^ { ( n ) }$ ; confidence 0.140

187. a13013083.png ; $C$ ; confidence 0.175

188. a13013066.png ; $5$ ; confidence 0.571

189. a13013055.png ; $L ( \Lambda _ { 0 } )$ ; confidence 0.993

190. a13013049.png ; $k$ ; confidence 0.504

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

192. a1301301.png ; $\left. \begin{array} { l } { i \frac { \partial } { \partial t } q ( x , t ) = i q t = - \frac { 1 } { 2 } q x x + q ^ { 2 } r } \\ { i \frac { \partial } { \partial t } r ( x , t ) = i r t = \frac { 1 } { 2 } r x - q r ^ { 2 } } \end{array} \right.$ ; confidence 0.260

193. a13013027.png ; $\phi = \phi _ { - } \phi _ { + }$ ; confidence 0.996

194. a1301302.png ; $\frac { \partial } { \partial t } P _ { 1 } - \frac { \partial } { \partial x } Q _ { 2 } + [ P _ { 1 } , Q _ { 2 } ] = 0$ ; confidence 0.971

195. a13013056.png ; $A _ { 1 } ^ { ( 1 ) }$ ; confidence 0.822

196. a13013070.png ; $( \tau _ { l } )$ ; confidence 0.726

197. a13013040.png ; $Q ^ { ( n ) } = \sum _ { j = 0 } ^ { n } Q _ { j } z ^ { n - j }$ ; confidence 0.991

198. a1301304.png ; $8$ ; confidence 0.857

199. a13013016.png ; $8$ ; confidence 0.804

200. a13013085.png ; $L$ ; confidence 0.550

201. a13013054.png ; $t _ { n }$ ; confidence 0.933

202. a13013079.png ; $F _ { j k } ^ { ( l ) } : = \frac { \partial } { \partial t _ { j } } \frac { \partial } { \partial t _ { k } } \operatorname { log } ( \tau _ { l } )$ ; confidence 0.981

203. a13013028.png ; $\phi _ { - } ( x , t , z ) = \operatorname { exp } ( \sum _ { i = 1 } ^ { \infty } \chi _ { i } ( x , t ) z ^ { - i } )$ ; confidence 0.963

204. a130130103.png ; $K P$ ; confidence 0.846

205. a13013098.png ; $\pi$ ; confidence 0.434

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

207. a13013031.png ; $( \partial / \partial t _ { x } ) - Q _ { 0 } z ^ { x }$ ; confidence 0.284

208. a13013020.png ; $0.00$ ; confidence 0.237

209. a13013044.png ; $F _ { j k } =$ ; confidence 0.626

210. a13013045.png ; $= \frac { 1 } { 2 } \operatorname { Tr } ( \sum _ { r = 0 } ^ { j } ( j - r ) Q _ { r } Q _ { k + j - r } + \frac { 1 } { 2 } \sum _ { r = 0 } ^ { j } ( r - k ) Q _ { r } Q _ { k + j - r } )$ ; confidence 0.240

211. a13013090.png ; $N$ ; confidence 0.183

212. a13013047.png ; $i$ ; confidence 0.889

213. a13013024.png ; $g ( z )$ ; confidence 0.996

214. a13013069.png ; $\tau ( t ) = ( \tau _ { l } ( t ) ) _ { l \in Z }$ ; confidence 0.585

215. a13013091.png ; $L : = P _ { 0 } \frac { d } { d x } + P _ { 1 } = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) \frac { d } { d x } + \left( \begin{array} { c c } { 0 } & { q } \\ { r } & { 0 } \end{array} \right)$ ; confidence 0.711

216. a13013076.png ; $P ^ { ( l ) }$ ; confidence 0.869

217. a13013051.png ; $F _ { j k } = \frac { \partial } { \partial t _ { j } } \frac { \partial } { \partial t _ { k } } \operatorname { log } ( \tau )$ ; confidence 0.976

218. a13013052.png ; $q ^ { ( l + 1 ) } = - ( q ^ { ( l ) } ) ^ { 2 } r ^ { ( l ) } + q ^ { ( l ) } \operatorname { log } ( q ^ { ( l ) } ) , r ^ { ( l + 1 ) } = \frac { 1 } { q ^ { ( l ) } }$ ; confidence 0.906

219. a1301306.png ; $Q ^ { ( n ) } : = Q _ { 0 } z ^ { n } + Q _ { 1 } z ^ { n - 1 } \ldots Q _ { n }$ ; confidence 0.716

220. a13013036.png ; $\partial / \partial x = \partial / \partial t _ { 1 }$ ; confidence 0.401

221. a13013014.png ; $\Leftrightarrow [ \frac { \partial } { \partial x } - P , \frac { \partial } { \partial t _ { n } } - Q ^ { ( n ) } ] = 0$ ; confidence 0.947

222. a1301305.png ; $P = P _ { 0 } z + P _ { 1 } : = \left( \begin{array} { c c } { - i } & { 0 } \\ { 0 } & { i } \end{array} \right) z + \left( \begin{array} { l l } { 0 } & { q } \\ { r } & { 0 } \end{array} \right)$ ; confidence 0.374

223. a13013041.png ; $\sum _ { i = 0 } ^ { \infty } X _ { i } z ^ { - i }$ ; confidence 0.831

224. a13013096.png ; $P _ { 1 }$ ; confidence 0.674

225. a13013097.png ; $L ( \psi ) = z \psi$ ; confidence 0.998

226. a1301303.png ; $P _ { 1 } = \left( \begin{array} { c c c } { 0 } & { \square } & { q } \\ { r } & { \square } & { 0 } \end{array} \right) , Q _ { 2 } = \left( \begin{array} { c c } { - \frac { i } { 2 } q r } & { \frac { i } { 2 } q x } \\ { - \frac { i } { 2 } r _ { x } } & { \frac { i } { 2 } q r } \end{array} \right)$ ; confidence 0.352

227. a1301307.png ; $Q$ ; confidence 0.380

228. a13013058.png ; $s = \sum _ { i > 0 } C \lambda ^ { i } \left( \begin{array} { c c } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) \oplus \sum _ { i > 0 } C \lambda ^ { - i } \left( \begin{array} { c c } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) \oplus C _ { i }$ ; confidence 0.161

229. a13013095.png ; $12$ ; confidence 0.590

230. a13013035.png ; $Q _ { 0 } = P _ { 0 }$ ; confidence 0.896

231. a13013073.png ; $Q$ ; confidence 0.095

232. a13013099.png ; $z \in C$ ; confidence 0.369

233. a13013033.png ; $\phi - ^ { 1 } ( \frac { \partial } { \partial x } - P _ { 0 z } ) \phi _ { - } = \frac { \partial } { \partial x } - P$ ; confidence 0.173

234. a13013013.png ; $\frac { \partial } { \partial t _ { m } } P - \frac { \partial } { \partial x } Q ^ { ( m ) } + [ P , Q ^ { ( r ) } ] = 0 \Leftrightarrow$ ; confidence 0.156

235. a13013012.png ; $Q _ { 1 } = P _ { 1 }$ ; confidence 0.999

236. a13013030.png ; $( \partial / \partial x ) - P _ { 0 } z$ ; confidence 0.947

237. a13013048.png ; $i$ ; confidence 0.474

238. a13013043.png ; $F _ { j k }$ ; confidence 0.974

239. a13013093.png ; $P _ { n + 1 } = \sum _ { i = 0 } ^ { n + 1 } u _ { i } ( \frac { d } { d x } ) ^ { i }$ ; confidence 0.947

240. a1301308.png ; $s l _ { 2 }$ ; confidence 0.247

241. a13013092.png ; $( 2 \times 2 )$ ; confidence 1.000

242. a13013017.png ; $P$ ; confidence 0.462

243. a13013038.png ; $\frac { \partial } { \partial t _ { n } } Q = [ Q ^ { ( n ) } , Q ] , n \geq 1$ ; confidence 0.137

244. a13013074.png ; $T$ ; confidence 0.973

245. a12022026.png ; $L ^ { Y } ( X , Y )$ ; confidence 0.431

246. a12022034.png ; $0 \leq S \leq T \in L ( X )$ ; confidence 0.657

247. a1202206.png ; $\varepsilon \in X$ ; confidence 0.430

248. a12022022.png ; $Y$ ; confidence 0.894

249. a12022037.png ; $r _ { ess } ( T )$ ; confidence 0.259

250. a12022013.png ; $T : X \rightarrow Y$ ; confidence 0.863

251. a12022011.png ; $X = 1 ^ { p }$ ; confidence 0.914

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

253. a1202209.png ; $x | < e$ ; confidence 0.841

254. a1202207.png ; $| e | | < 1$ ; confidence 0.271

255. a12022039.png ; $S < T$ ; confidence 0.984

256. a12022042.png ; $r _ { e . s s } ( T ) \in \sigma _ { ess } ( T )$ ; confidence 0.088

257. a12022025.png ; $Y = L ^ { 1 } ( \mu )$ ; confidence 1.000

258. a12022033.png ; $5$ ; confidence 0.396

259. a12022038.png ; $S , T \in L ( X )$ ; confidence 0.814

260. a12022035.png ; $r ( S ) \leq r ( T )$ ; confidence 0.998

261. a12022036.png ; $\sigma _ { ess } ( T )$ ; confidence 0.490

262. a12022012.png ; $1 \leq p < \infty$ ; confidence 0.999

263. a12022031.png ; $0 \leq S \leq T$ ; confidence 0.838

264. a12022010.png ; $X = c 0$ ; confidence 0.759

265. a1202208.png ; $| x | | \leq 1$ ; confidence 0.929

266. a130240286.png ; $1 - \alpha$ ; confidence 0.993

267. a130240135.png ; $A$ ; confidence 0.952

268. a130240204.png ; $74$ ; confidence 0.550

269. a13024051.png ; $3$ ; confidence 0.891

270. a130240441.png ; $\beta _ { 1 } , \ldots , \beta _ { p }$ ; confidence 0.501

271. a130240336.png ; $Z = X \Gamma + F$ ; confidence 0.500

272. a130240339.png ; $\Sigma _ { 1 } = X _ { 4 } ^ { \prime } \Sigma X _ { 4 }$ ; confidence 0.322

273. a130240101.png ; $x$ ; confidence 0.751

274. a130240218.png ; $z = \Gamma y$ ; confidence 0.946

275. a13024048.png ; $s \times p$ ; confidence 0.642

276. a13024059.png ; $( i , j )$ ; confidence 0.935

277. a130240137.png ; $B$ ; confidence 0.651

278. a130240478.png ; $0$ ; confidence 0.969

279. a130240397.png ; $M _ { E }$ ; confidence 0.680

280. a130240527.png ; $( n$ ; confidence 0.239

281. a130240519.png ; $Z _ { 13 }$ ; confidence 0.481

282. a130240539.png ; $T _ { 1 }$ ; confidence 0.446

283. a130240452.png ; $P$ ; confidence 0.403

284. a130240446.png ; $j = 1 , \ldots , p$ ; confidence 0.616

285. a130240545.png ; $2$ ; confidence 0.985

286. a130240141.png ; $c$ ; confidence 0.324

287. a130240308.png ; $\hat { \eta } _ { \Omega } = X \hat { \beta }$ ; confidence 0.485

288. a130240106.png ; $t$ ; confidence 0.895

289. a130240516.png ; $R = V _ { 33 } ^ { - 1 } V _ { 32 }$ ; confidence 0.628

290. a130240276.png ; $\leq F _ { \alpha ; q , x - \gamma }$ ; confidence 0.345

291. a130240431.png ; $a ^ { \prime } \Theta$ ; confidence 0.987

292. a130240449.png ; $y _ { 1 } , \dots , y _ { j }$ ; confidence 0.424

293. a130240196.png ; $\sqrt { 3 }$ ; confidence 0.281

294. a130240399.png ; $X _ { 3 }$ ; confidence 0.593

295. a130240238.png ; $MS _ { e } = SS _ { e } / ( n - r )$ ; confidence 0.793

296. a130240152.png ; $X \beta$ ; confidence 0.414

297. a130240309.png ; $\sum _ { i j k } ( y _ { i j k } - \eta _ { i j } ) ^ { 2 }$ ; confidence 0.779

298. a130240444.png ; $N$ ; confidence 0.740

299. a130240371.png ; $Z _ { 1 } M _ { E } ^ { - 1 } Z _ { 1 } ^ { \prime }$ ; confidence 0.548

300. a130240500.png ; $2$ ; confidence 0.672

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/1. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/1&oldid=43808
Retrieved from "https://encyclopediaofmath.org/index.php?title=User:Maximilian_Janisch/latexlist/latex/1&oldid=43819"