Namespaces
Variants
Actions

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

From Encyclopedia of Mathematics
Jump to: navigation, search
(AUTOMATIC EDIT of page 1 out of 77 with 300 lines: Updated image/latex database (currently 22833 images latexified; order by Length, ascending: False.)
 
m (small changes)
 
(4 intermediate revisions by 2 users not shown)
Line 1: Line 1:
 
== List ==
 
== List ==
−
1. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008042.png ; $\left. \begin{array} { l } { \frac { d } { d t } \left( \begin{array} { c } { u } \\ { v } \end{array} \right) + \left( \begin{array} { c c } { 0 } & { - 1 } \\ { A } & { 0 } \end{array} \right) \left( \begin{array} { c } { u } \\ { v } \end{array} \right) = \left( \begin{array} { c } { 0 } \\ { f ( t ) } \end{array} \right) , \quad t \in [ 0 , T ] } \\ { \left( \begin{array} { c } { u ( 0 ) } \\ { v ( 0 ) } \end{array} \right) = \left( \begin{array} { c } { u _ { 0 } } \\ { u _ { 1 } } \end{array} \right) } \end{array} \right.$ ; confidence 0.315
+
1. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010139.png ; $3$ ; confidence 1.000
  
−
2. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011019.png ; $\alpha y = \left( \begin{array} { c c c c } { 0 } & { 0 } & { 0 } & { - i } \\ { 0 } & { 0 } & { i } & { 0 } \\ { 0 } & { - i } & { 0 } & { 0 } \\ { i } & { 0 } & { 0 } & { 0 } \end{array} \right) = \left( \begin{array} { c c } { 0 } & { \sigma y } \\ { \sigma y } & { 0 } \end{array} \right) , \alpha _ { z } = \left( \begin{array} { c c c c } { 0 } & { 0 } & { 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } \\ { 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { 0 } & { 0 } \end{array} \right) = \left( \begin{array} { c c } { 0 } & { \sigma _ { z } } \\ { \sigma _ { z } } & { 0 } \end{array} \right)$ ; confidence 0.089
+
2. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010134.png ; $( 4 n + 3 )$ ; confidence 1.000
  
−
3. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130030/o13003033.png ; $\lambda _ { 3 } = \left( \begin{array} { c c c } { 1 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } \end{array} \right) , \lambda _ { 4 } = \left( \begin{array} { c c c } { 0 } & { 0 } & { 1 } \\ { 0 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 0 } \end{array} \right) , \lambda _ { 5 } = \left( \begin{array} { c c c } { 0 } & { 0 } & { - i } \\ { 0 } & { 0 } & { 0 } \\ { i } & { 0 } & { 0 } \end{array} \right) , \lambda _ { 6 } = \left( \begin{array} { c c c } { 0 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 1 } \\ { 0 } & { 1 } & { 0 } \end{array} \right)$ ; confidence 0.458
+
3. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010115.png ; $11$ ; confidence 1.000
  
−
4. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120080/k12008079.png ; $= \frac { 1 } { ( 2 \pi i ) ^ { n } } \int _ { \partial \Omega } \sum _ { | \alpha | + \beta = n - 1 } ( \prod _ { j = 0 } ^ { m } \frac { \langle \rho ^ { \prime } ( \xi ) , z - p _ { j } \rangle } { \langle \rho ^ { \prime } ( \xi ) , \xi - p _ { j } \rangle } ) \times \times \frac { f ( \xi ) \partial \rho ( \xi ) \wedge ( \overline { \partial } \partial \rho ( \xi ) ) ^ { n - 1 } } { \langle \rho ^ { \prime } ( \xi ) , \xi - p \rangle ^ { \alpha } \langle \rho ^ { \prime } ( \xi ) , \xi - z \rangle ^ { \beta + 1 } }$ ; confidence 0.071
+
4. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001094.png ; $n + 2$ ; confidence 1.000
  
−
5. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520163.png ; $J ( f ) = \left\| \begin{array} { c c c c c c } { a } & { 1 } & { \square } & { \square } & { \square } & { 0 } \\ { \square } & { \cdot } & { \square } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { . } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { . } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { \square } & { . } & { 1 } \\ { 0 } & { \square } & { \square } & { \square } & { \square } & { a } \end{array} \right\|$ ; confidence 0.082
+
5. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010118.png ; $4 n + 3$ ; confidence 1.000
  
−
6. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008073.png ; $\left[ \begin{array} { c c } { E _ { 1 } } & { E _ { 2 } } \\ { E _ { 3 } } & { E _ { 4 } } \end{array} \right] \left[ \begin{array} { c } { x _ { i } ^ { k } + 1 , j } \\ { x _ { i , j + 1 } ^ { v } } \end{array} \right] = \left[ \begin{array} { c c } { A _ { 1 } } & { A _ { 2 } } \\ { A _ { 3 } } & { A _ { 4 } } \end{array} \right] \left[ \begin{array} { c } { x _ { i j } ^ { k } } \\ { x _ { i j } ^ { y } } \end{array} \right] + \left[ \begin{array} { c } { B _ { 1 } } \\ { B _ { 2 } } \end{array} \right] u _ { j }$ ; confidence 0.133
+
6. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t120010129.png ; $15$ ; confidence 1.000
  
−
7. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520141.png ; $N _ { 2 } = \left| \begin{array} { c c c c c } { . } & { \square } & { \square } & { \square } & { 0 } \\ { \square } & { . } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { L ( e _ { j } ^ { n _ { i j } } ) } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { . } & { \square } \\ { \square } & { \square } & { \square } & { \square } & { \square } \\ { 0 } & { \square } & { \square } & { \square } & { . } \end{array} \right|$ ; confidence 0.323
+
7. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001091.png ; $\mathcal Z$ ; confidence 1.000
  
−
8. 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
+
8. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001074.png ; $2$ ; confidence 1.000
  
−
9. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d12023020.png ; $\Delta = \frac { 1 } { \mathfrak { c } 0 } \left( \begin{array} { c c c } { \mathfrak { c } ^ { 2 } - \mathfrak { c } _ { 1 } ^ { 2 } } & { \square } & { \mathfrak { c } _ { 1 } \mathfrak { w } - \mathfrak { c } _ { 1 } \mathfrak { c } _ { 2 } } \\ { \mathfrak { c } _ { 1 } \mathfrak { c } _ { 0 } - \mathfrak { c } _ { 1 } \mathfrak { c } _ { 2 } } & { \square } & { \mathfrak { c } _ { 0 } ^ { 2 } - \mathfrak { c } _ { 2 } ^ { 2 } } \end{array} \right)$ ; confidence 0.064
+
9. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/a13013092.png ; $( 2 \times 2 )$ ; confidence 1.000
  
−
10. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020036.png ; $\left( \begin{array} { c c c c } { 1 } & { 2 } & { 3 } & { 4 } \\ { 5 } & { 6 } & { 7 } & { \square } \\ { 8 } & { \square } & { \square } & { \square } \\ { 9 } & { \square } & { \square } & { \square } \end{array} \right) = \left( \begin{array} { c c c c } { 4 } & { 2 } & { 1 } & { 3 } \\ { 6 } & { 5 } & { 7 } & { \square } \\ { 8 } & { \square } & { \square } & { \square } \\ { 9 } & { \square } & { \square } & { \square } \end{array} \right) \neq$ ; confidence 0.635
+
10. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120220/a12022025.png ; $Y = L ^ { 1 } ( \mu )$ ; confidence 1.000
  
−
11. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020057.png ; $\left( \begin{array} { c c c c } { 9 } & { 2 } & { 3 } & { 6 } \\ { 7 } & { 1 } & { 4 } & { \square } \\ { 5 } & { \square } & { \square } & { \square } \\ { 8 } & { \square } & { \square } & { \square } \end{array} \right) = \left( \begin{array} { c c c c } { 8 } & { 4 } & { 1 } & { 3 } \\ { 7 } & { 6 } & { 5 } & { \square } \\ { 2 } & { \square } & { \square } & { \square } \\ { 9 } & { \square } & { \square } & { \square } \end{array} \right)$ ; confidence 0.460
+
11. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240348.png ; $( r - q ) \times p$ ; confidence 1.000
  
−
12. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020037.png ; $\left( \begin{array} { c c c c } { 9 } & { 2 } & { 3 } & { 6 } \\ { 7 } & { 1 } & { 4 } & { \square } \\ { 8 } & { \square } & { \square } & { \square } \\ { 9 } & { \square } & { \square } & { \square } \end{array} \right) = \left( \begin{array} { c c c c } { 2 } & { 3 } & { 9 } & { 6 } \\ { 4 } & { 1 } & { 7 } & { \square } \\ { 8 } & { \square } & { \square } & { \square } \\ { 9 } & { \square } & { \square } & { \square } \end{array} \right)$ ; confidence 0.519
+
12. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240424.png ; $( 1 \times p )$ ; confidence 1.000
  
−
13. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a1200801.png ; $\left. \begin{array}{l}{ \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } = \sum _ { i , j = 1 } ^ { m } \frac { \partial } { \partial x _ { i } } \{ \alpha _ { j } , ( x ) \frac { \partial u } { \partial x _ { j } } \} + c ( x ) u + f ( x , t ) }\\{ ( x , t ) \in \Omega \times [ 0 , T ] }\\{ u ( x , 0 ) = u _ { 0 } ( x ) , \frac { \partial u } { \partial t } ( x , 0 ) = u _ { 1 } ( x ) , x \in \Omega }\end{array} \right.$ ; confidence 0.050
+
13. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240423.png ; $q \times 1$ ; confidence 1.000
  
−
14. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120010/t12001089.png ; $\left. \begin{array} { c c c c c } { \square } & { \square } & { C ( S ) } & { \square } & { \square } \\ { \square } & { \swarrow } & { \square } & { \searrow } & { \square } \\ { Z } & { \square } & { \downarrow } & { \square } & { S } \\ { \square } & { \searrow } & { \square } & { \swarrow } & { \square } \\ { \square } & { \square } & { O } & { \square } & { \square } \end{array} \right.$ ; confidence 0.059
+
14. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240375.png ; $( n - r ) F$ ; confidence 1.000
  
−
15. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520127.png ; $N _ { 1 } = \left\| \begin{array} { c c c c c } { L ( d _ { q + 1 } ) } & { \square } & { \square } & { \square } & { 0 } \\ { \square } & { . } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { . } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { . } & { \square } \\ { 0 } & { \square } & { \square } & { \square } & { L ( d _ { n } ) } \end{array} \right\|$ ; confidence 0.330
+
15. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420110.png ; $f$ ; confidence 1.000
  
−
16. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130090/c13009030.png ; $\frac { d C _ { j } } { d x } ( x _ { k } ) = \left\{ \begin{array} { l l } { \frac { 1 } { 6 } ( 1 + 2 N ^ { 2 } ) } & { \text { for } j = k = 0 } \\ { - \frac { 1 } { 6 } ( 1 + 2 N ^ { 2 } ) } & { \text { for } j = k = N } \\ { - \frac { x _ { j } } { 2 ( 1 - x _ { j } ^ { 2 } ) } } & { \text { for } j = k , 0 < j < N } \\ { ( - 1 ) ^ { j + k } \frac { \tau _ { k } } { \tau _ { j } ( x _ { k } - x _ { j } ) } } & { \text { for } j \neq k } \end{array} \right.$ ; confidence 0.518
+
16. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a13004067.png ; $\psi \in \Gamma$ ; confidence 1.000
  
−
17. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520175.png ; $J = \left\| \begin{array} { c c c c c } { . } & { \square } & { \square } & { \square } & { 0 } \\ { \square } & { . } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { J ( e _ { i } ^ { n _ { i j } } ) } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { . } & { \square } \\ { 0 } & { \square } & { \square } & { \square } & { . } \end{array} \right\|$ ; confidence 0.252
+
17. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018084.png ; $10 ^ { 16 }$ ; confidence 1.000
  
−
18. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120200/s12020023.png ; $\left. \begin{array} { l l l l l l l l l } { 1 } & { 2 } & { 3 } & { 4 } & { } & { 9 } & { 2 } & { 3 } & { 6 } \\ { 5 } & { 6 } & { 7 } & { \square } & { \text { and } } & { 7 } & { 1 } & { 4 } & { \square } \\ { 8 } & { \square } & { \square } & { \square } & { } & { 5 } & { \square } & { \square } & { \square } \\ { 9 } & { \square } & { \square } & { \square } & { } & { 8 } & { \square } & { \square } \end{array} \right.$ ; confidence 0.233
+
18. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110420/a110420166.png ; $2 n$ ; confidence 1.000
  
−
19. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130260/a1302603.png ; $\alpha _ { N } = \sum _ { k = 0 } ^ { n } \left( \begin{array} { c } { n + k } \\ { k } \end{array} \right) ^ { 2 } \left( \begin{array} { c } { n } \\ { k } \end{array} \right) ^ { 2 } , \quad b _ { n } = \sum _ { k = 0 } ^ { n } \left( \begin{array} { c } { n + k } \\ { k } \end{array} \right) \left( \begin{array} { c } { n } \\ { k } \end{array} \right) ^ { 2 }$ ; confidence 0.107
+
19. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032031.png ; $p < .5$ ; confidence 1.000
  
−
20. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130010/d1300106.png ; $\left( \begin{array} { c c c c } { h ( x _ { 1 } , y _ { 1 } ) } & { h ( x _ { 1 } , y _ { 2 } ) } & { \dots } & { h ( x _ { 1 } , y _ { n } ) } \\ { h ( x _ { 2 } , y _ { 1 } ) } & { h ( x _ { 2 } , y _ { 2 } ) } & { \dots } & { h ( x _ { 2 } , y _ { n } ) } \\ { \vdots } & { \vdots } & { \ddots } & { \vdots } \\ { h ( x _ { n } , y _ { 1 } ) } & { h ( x _ { n } , y _ { 2 } ) } & { \dots } & { h ( x _ { n } , y _ { n } ) } \end{array} \right)$ ; confidence 0.609
+
20. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021067.png ; $\Theta( L ( \lambda ) )$ ; confidence 1.000
  
−
21. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086020/s08602038.png ; $\left. \begin{array}{l}{ \Phi ^ { + } ( t _ { 0 } ) = \frac { 1 } { 2 \pi i } \int _ { \Gamma } \frac { \phi ( t ) d t } { t - t _ { 0 } } + ( 1 - \frac { \beta } { 2 \pi } ) \phi ( t _ { 0 } ) }\\{ \Phi ^ { - } ( t _ { 0 } ) = \frac { 1 } { 2 \pi i } \int \frac { \phi ( t ) d t } { t - t _ { 0 } } - \frac { \beta } { 2 \pi } \phi ( t _ { 0 } ) , 0 \leq \beta \leq 2 \pi }\end{array} \right.$ ; confidence 0.166
+
21. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015400/b01540048.png ; $s ( z )$ ; confidence 1.000
  
−
22. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120020/i1200209.png ; $\times [ \frac { \operatorname { sin } \frac { \pi \mu } { 2 } } { \operatorname { cosh } \frac { \pi \tau } { 2 } } \operatorname { Re } J _ { i \tau } ( x ) - \frac { \operatorname { cos } \frac { \pi \mu } { 2 } } { \operatorname { sinh } \frac { \pi \tau } { 2 } } \operatorname { Im } J _ { i \tau } ( x ) ] , f ( x ) = \frac { 2 ^ { - \mu } } { \pi ^ { 2 } x } x$ ; confidence 0.660
+
22. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130190/b1301906.png ; $F ( x ) = f ( M x )$ ; confidence 1.000
  
−
23. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009052.png ; $\frac { m } { 1 + \alpha ^ { 2 } } \{ \int _ { 0 } ^ { z } \frac { p _ { 1 } ( s ) - p _ { 0 } ( s ) } { s ^ { 1 - \frac { m } { 1 + \alpha i } } } e ^ { \frac { m } { 1 + \alpha ^ { 2 } } \int _ { 0 } ^ { s } \frac { p _ { 0 } ( t ) - 1 } { t } d t } d s + \frac { 1 + \alpha ^ { 2 } } { m } z ^ { \frac { m } { 1 + \alpha i } } e ^ { \frac { m } { 1 + \alpha ^ { 2 } } } \int _ { 0 } ^ { z } \frac { p _ { 0 } ( t ) - 1 } { t } d t$ ; confidence 0.115
+
23. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180506.png ; $N = N \times \{ 1 \} \times \{ 0 \}$ ; confidence 1.000
  
−
24. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130190/m13019048.png ; $M _ { n } ( z ) = \left( \begin{array} { c c c } { \langle f _ { 0 } , f _ { 0 } \rangle } & { \dots } & { \langle f _ { 0 } , f _ { n } \rangle } \\ { \vdots } & { \square } & { \vdots } \\ { \langle f _ { n - 1 } , f _ { 0 } \rangle } & { \dots } & { \langle f _ { n - 1 } , f _ { n } \rangle } \\ { f _ { 0 } ( z ) } & { \dots } & { f _ { n } ( z ) } \end{array} \right)$ ; confidence 0.156
+
24. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120300/c12030069.png ; $n = \infty$ ; confidence 1.000
  
−
25. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430115.png ; $\Delta \left( \begin{array} { c c } { \alpha } & { \beta } \\ { \gamma } & { \delta } \end{array} \right) = \left( \begin{array} { c c } { \alpha } & { \beta } \\ { \gamma } & { \delta } \end{array} \right) \otimes \left( \begin{array} { c c } { \alpha } & { \beta } \\ { \gamma } & { \delta } \end{array} \right)$ ; confidence 0.279
+
25. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110220/a110220101.png ; $R ( f )$ ; confidence 1.000
  
−
26. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130060/k13006012.png ; $m = \left( \begin{array} { c } { a _ { k } } \\ { k } \end{array} \right) + \left( \begin{array} { c } { \alpha _ { k } - 1 } \\ { k - 1 } \end{array} \right) + \ldots + \left( \begin{array} { c } { \alpha _ { 2 } } \\ { 2 } \end{array} \right) + \left( \begin{array} { c } { \alpha _ { 1 } } \\ { 1 } \end{array} \right)$ ; confidence 0.307
+
26. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130050/d13005022.png ; $m - 2 r$ ; confidence 1.000
  
−
27. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130500/s1305006.png ; $\left( \begin{array} { l } { n } \\ { 0 } \end{array} \right) < \ldots < \left( \begin{array} { c } { n } \\ { \lfloor n / 2 \rfloor } \end{array} \right) = \left( \begin{array} { c } { n } \\ { \lceil n / 2 \rceil } \end{array} \right) > \ldots > \left( \begin{array} { l } { n } \\ { n } \end{array} \right)$ ; confidence 0.251
+
27. https://www.encyclopediaofmath.org/legacyimages/a/a012/a012250/a01225011.png ; $R > 0$ ; confidence 1.000
  
−
28. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013051.png ; $\left. \begin{array}{l}{ \frac { d N ^ { 1 } } { d t } = \lambda _ { ( 1 ) } N ^ { 1 } ( 1 - \frac { N ^ { 1 } } { K _ { ( 1 ) } } - \delta _ { ( 1 ) } \frac { N ^ { 2 } } { K _ { ( 1 ) } } ) }\\{ \frac { d N ^ { 2 } } { d t } = \lambda _ { ( 2 ) } N ^ { 2 } ( 1 - \frac { N ^ { 2 } } { K _ { ( 2 ) } } - \delta _ { ( 2 ) } \frac { N ^ { 1 } } { K _ { ( 2 ) } } ) }\end{array} \right.$ ; confidence 0.089
+
28. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120180/d12018084.png ; $C ( G )$ ; confidence 1.000
  
−
29. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120270/m12027042.png ; $\left\{ \begin{array} { l } { x _ { 1 } ^ { 3 } + \sum _ { i + j + k \leq 2 } a _ { j k } x _ { 1 } ^ { i } x _ { 2 } ^ { j } x _ { 3 } ^ { k } = 0 } \\ { x _ { 2 } ^ { 3 } + \sum _ { i + j + k \leq 2 } b _ { j k } x _ { 1 } ^ { i } x _ { 2 } ^ { j } x _ { 3 } ^ { k } = 0 } \\ { x _ { 3 } ^ { 3 } + \sum _ { i + j + k \leq 2 } c _ { i j k } x _ { 1 } ^ { i } x _ { 2 } ^ { j } x _ { 3 } ^ { k } = 0 } \end{array} \right.$ ; confidence 0.094
+
29. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029018.png ; $f ( q ) = 1 / ( \sqrt { 5 } q ^ { 2 } )$ ; confidence 1.000
  
−
30. https://www.encyclopediaofmath.org/legacyimages/s/s086/s086020/s08602017.png ; $\left.\begin{array} { r l } { \Phi ^ { + } ( t _ { 0 } ) } & { = \frac { 1 } { 2 \pi i } \int _ { \Gamma } \frac { \phi ( t ) d t } { t - t _ { 0 } } + \frac { 1 } { 2 } \phi ( t _ { 0 } ) } \\ { \Phi ^ { - } ( t _ { 0 } ) } & { = \frac { 1 } { 2 \pi i } \int _ { \Gamma } \frac { \phi ( t ) d t } { t - t _ { 0 } } - \frac { 1 } { 2 } \phi ( t _ { 0 } ) } \end{array} \right\}$ ; confidence 0.187
+
30. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120150/e12015070.png ; $\lambda _ { 1 } = \lambda _ { 2 }$ ; confidence 1.000
  
−
31. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130030/o13003034.png ; $\lambda _ { 7 } = \left( \begin{array} { c c c } { 0 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { - i } \\ { 0 } & { i } & { 0 } \end{array} \right) , \lambda _ { 8 } = \left( \begin{array} { c c c } { \frac { 1 } { \sqrt { 3 } } } & { 0 } & { 0 } \\ { 0 } & { \frac { 1 } { \sqrt { 3 } } } & { 0 } \\ { 0 } & { 0 } & { \frac { - 2 } { \sqrt { 3 } } } \end{array} \right)$ ; confidence 0.724
+
31. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120100/f12010041.png ; $( 8 \times 8 )$ ; confidence 1.000
  
−
32. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120060/b12006014.png ; $\frac { 1 } { \operatorname { sin } ^ { 2 } \vartheta } \cdot \frac { \partial ^ { 2 } Y } { \partial \varphi ^ { 2 } } + \frac { 1 } { \operatorname { sin } \vartheta } \cdot \frac { \partial } { \partial \vartheta } ( \operatorname { sin } \vartheta \cdot \frac { \partial Y } { \partial \vartheta } ) +$ ; confidence 0.972
+
32. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f12015010.png ; $R ( A )$ ; confidence 1.000
  
−
33. https://www.encyclopediaofmath.org/legacyimages/v/v110/v110060/v11006010.png ; $[ u , v ] \equiv \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } \frac { \partial ^ { 2 } v } { \partial y ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial y ^ { 2 } } \frac { \partial ^ { 2 } v } { \partial x ^ { 2 } } - 2 \frac { \partial ^ { 2 } u } { \partial x \partial y } \frac { \partial ^ { 2 } v } { \partial x \partial y }$ ; confidence 0.995
+
33. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120030/g12003011.png ; $3 n + 2$ ; confidence 1.000
  
−
34. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a12017038.png ; $\left. \begin{array} { l } { p _ { t } ( \alpha , t ) + p _ { \alpha } ( \alpha , t ) + \mu ( \alpha , S ( t ) ) p ( \alpha , t ) = 0 } \\ { p ( 0 , t ) = \int ^ { + \infty } \beta ( \sigma , s ( t ) ) p ( \sigma , t ) d \sigma } \\ { p ( \alpha , 0 ) = p 0 } \\ { S ( t ) = \int \gamma ( \sigma ) p ( \sigma , t ) d \sigma } \end{array} \right.$ ; confidence 0.169
+
34. https://www.encyclopediaofmath.org/legacyimages/c/c026/c026010/c026010588.png ; $J ( \alpha )$ ; confidence 1.000
  
−
35. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120070/l1200705.png ; $L = \left( \begin{array} { c c c c c } { m _ { 1 } } & { m _ { 2 } } & { \ldots } & { \ldots } & { m _ { k } } \\ { p _ { 1 } } & { 0 } & { \ldots } & { \ldots } & { 0 } \\ { 0 } & { p _ { 2 } } & { 0 } & { \ldots } & { 0 } \\ { \vdots } & { \square } & { \ddots } & { \square } & { \vdots } \\ { 0 } & { \ldots } & { 0 } & { p _ { k - 1 } } & { 0 } \end{array} \right)$ ; confidence 0.442
+
35. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130090/i130090151.png ; $p < 12000000$ ; confidence 1.000
  
−
36. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016034.png ; $u = \left\{ \begin{array} { c c } { \overline { u } } & { \text { for } \frac { i T } { k } \leq t < ( i + \alpha ) \frac { T } { k } } \\ { } & { 0 \leq i \leq k - 1 } \\ { 0 } & { \text { for } ( i + \alpha ) \frac { T } { k } \leq t \leq ( i + 1 ) \frac { T } { k } } \\ { } & { \text { and fort } = T ; 0 \leq i \leq k - 1 } \end{array} \right.$ ; confidence 0.115
+
36. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130010/k13001019.png ; $T ( s )$ ; confidence 1.000
  
−
37. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008064.png ; $= \left( \begin{array} { c c } { \frac { d A ( t ) ^ { 1 / 2 } } { d t } A ( t ) ^ { - 1 / 2 } } & { i A ( t ) ^ { 1 / 2 } } \\ { i A ( t ) ^ { 1 / 2 } } & { 0 } \end{array} \right) \left( \begin{array} { c } { v _ { 0 } } \\ { v _ { 1 } } \end{array} \right) + \left( \begin{array} { c } { 0 } \\ { f ( t ) } \end{array} \right) , t \in [ 0 , T ]$ ; confidence 0.535
+
37. https://www.encyclopediaofmath.org/legacyimages/l/l061/l061050/l0610509.png ; $f ^ { \prime } ( x ) = 0$ ; confidence 1.000
  
−
38. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c120210122.png ; $L [ \Lambda _ { n } ( \theta ) | P _ { n , \theta } ] \Rightarrow N ( - \frac { 1 } { 2 } h ^ { \prime } \Gamma ( \theta ) h , h ^ { \prime } \Gamma ( \theta ) h ) , L [ \Lambda _ { n } ( \theta ) | P _ { n , \theta _ { n } } ] \Rightarrow N ( \frac { 1 } { 2 } h ^ { \prime } \Gamma ( \theta ) h , h ^ { \prime } \Gamma ( \theta ) h )$ ; confidence 0.889
+
38. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130070/n13007025.png ; $m ( B ) = 0$ ; confidence 1.000
  
−
39. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f13009036.png ; $\left. \begin{array}{l}{ U _ { 0 } ^ { ( k ) } ( x ) = 0 }\\{ U _ { 1 } ^ { ( k ) } ( x ) = 1 }\\{ U _ { n } ^ { ( k ) } ( x ) = \sum _ { j = 1 } ^ { n } x ^ { k - j } U _ { n - j } ^ { ( k ) } ( x ) , \quad n = 2 , \ldots , k }\\{ U _ { n } ^ { ( k ) } ( x ) = \sum _ { j = 1 } ^ { k } x ^ { k - j } U _ { n - j } ^ { ( k ) } ( x ) }\\{ n = k + 1 , k + 2 , \ldots }\end{array} \right.$ ; confidence 0.136
+
39. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520368.png ; $\phi _ { i } ( 0 ) = 0$ ; confidence 1.000
  
−
40. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b1200108.png ; $B _ { i } ( x _ { 1 } , x _ { 2 } , u , \frac { \partial u } { \partial x _ { 1 } } , \frac { \partial u } { \partial x _ { 2 } } : x _ { 1 } ^ { \prime } , x _ { 2 } ^ { \prime } , u ^ { \prime } , \frac { \partial u ^ { \prime } } { \partial x _ { 1 } ^ { \prime } } , \frac { \partial u ^ { \prime } } { \partial x _ { 2 } ^ { \prime } } ) = 0$ ; confidence 0.851
+
40. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120130/p1201308.png ; $\theta$ ; confidence 1.000
  
−
41. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059032.png ; $Q _ { 2 n } ( z ) = \frac { 1 } { H _ { 2 n } ^ { ( - 2 n ) } } \left| \begin{array} { c c c c } { c _ { - 2 n } } & { \cdots } & { c _ { - 1 } } & { z ^ { - n } } \\ { \vdots } & { \square } & { \vdots } & { \vdots } \\ { c _ { - 1 } } & { \cdots } & { c _ { 2 n - 2 } } & { z ^ { n - 1 } } \\ { 0 } & { \cdots } & { c _ { 2 n - 1 } } & { z ^ { n } e n d } \end{array} \right|$ ; confidence 0.239
+
41. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020280/c020280124.png ; $E ( \lambda )$ ; confidence 1.000
  
−
42. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002053.png ; $( LD ) v ^ { * } = \left\{ \begin{array} { c l } { \operatorname { max } } & { q } \\ { s.t. } & { q \leq c ^ { T } x ^ { ( k ) } + u _ { 1 } ^ { T } ( A _ { 1 } x ^ { ( k ) } - b _ { 1 } ) } \\ { } & { \forall k \in P } \\ { 0 \leq } & { c ^ { T } x ^ { ( k ) } + u _ { 1 } ^ { T } A _ { 1 } x ^ { ( k ) } , \forall k \in R } \\ { u _ { 1 } \geq 0 } \end{array} \right.$ ; confidence 0.111
+
42. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090131.png ; $\Delta ( \lambda ) ^ { \mu }$ ; confidence 1.000
  
−
43. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130590/s13059034.png ; $Q _ { 2 n + 1 } ( z ) = \frac { - 1 } { H _ { 2 n + 1 } ^ { ( - 2 n ) } } \left| \begin{array} { c c c c } { c - 2 n - 1 } & { \cdots } & { c - 1 } & { z ^ { - n - 1 } } \\ { \vdots } & { \square } & { \vdots } & { \vdots } \\ { c - 1 } & { \cdots } & { c _ { 2 n - 1 } } & { z ^ { n - 1 } } \\ { 0 } & { \cdots } & { c _ { 2 n } } & { z ^ { n } e n d } \end{array} \right|$ ; confidence 0.116
+
43. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130090/w13009083.png ; $\iota( g ) = g ^ { \prime }$ ; confidence 1.000
  
−
44. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046020/h04602032.png ; $\left[ \begin{array} { l } { Y _ { 1 } } \\ { Y _ { 2 } } \end{array} \right] = \left[ \begin{array} { c c } { \frac { 1 } { 1 - P C } } & { \frac { P } { 1 - P C } } \\ { \frac { C } { 1 - P C } } & { \frac { 1 } { 1 - P C } } \end{array} \right] \left[ \begin{array} { l } { X _ { 1 } } \\ { X _ { 2 } } \end{array} \right]$ ; confidence 0.295
+
44. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120110/p12011022.png ; $3$ ; confidence 1.000
  
−
45. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120160/m12016027.png ; $X = \left( \begin{array} { l } { X _ { 1 } } \\ { X _ { 2 } } \end{array} \right) , M = \left( \begin{array} { c } { M _ { 1 } } \\ { M _ { 2 } } \end{array} \right) , \Sigma = \left( \begin{array} { l l } { \Sigma _ { 11 } } & { \Sigma _ { 12 } } \\ { \Sigma _ { 21 } } & { \Sigma _ { 22 } } \end{array} \right)$ ; confidence 0.335
+
45. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110010/a11001057.png ; $10$ ; confidence 1.000
  
−
46. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032091.png ; $\frac { k } { k + 1 } \frac { \operatorname { log } a _ { \mathfrak { W } } } { \operatorname { log } m } \leq \frac { \operatorname { log } a _ { \mathfrak { N } } } { \operatorname { log } n } \leq \frac { k + 1 } { k } \frac { \operatorname { log } a _ { \mathfrak { N } } } { \operatorname { log } m }$ ; confidence 0.050
+
46. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a01160016.png ; $- 1$ ; confidence 1.000
  
−
47. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130060/h13006066.png ; $= \{ \left( \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right) \in SL ( 2 , Z ) : \left( \begin{array} { c c } { \alpha } & { b } \\ { c } & { d } \end{array} \right) \equiv \left( \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) ( \operatorname { mod } n ) \}$ ; confidence 0.062
+
47. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025440/c02544045.png ; $3 \times 3$ ; confidence 1.000
  
−
48. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008099.png ; $y = \left\{ \begin{array} { l l } { ( \frac { c } { \alpha - x } ) ^ { k + 1 } } & { \text { for } x \in ( - \infty , \alpha - c ] } \\ { 1 } & { \text { for } x \in [ \alpha - c , \alpha - c + b ] } \\ { ( \frac { b - c } { x - \alpha } ) ^ { k + 1 } } & { \text { for } x \in [ \alpha - c + b , \infty ] } \end{array} \right.$ ; confidence 0.297
+
48. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120110/p1201103.png ; $15$ ; confidence 1.000
  
−
49. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i12004020.png ; $= \sum _ { j = 1 } ^ { n } ( - 1 ) ^ { j - 1 } ( \overline { \zeta _ { j } } - \overline { z _ { j } } ) d \overline { \zeta _ { 1 } } \wedge \ldots \wedge [ d \overline { \zeta _ { j } } ] \wedge \ldots \wedge d \overline { \zeta _ { n } } , \omega ( \zeta ) = d \zeta _ { 1 } \wedge \cdots \wedge d \zeta _ { n }$ ; confidence 0.388
+
49. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a130070132.png ; $10 ^ { 4 }$ ; confidence 1.000
  
−
50. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130070/p13007048.png ; $u ( z _ { 1 } , z _ { 2 } ) = \left\{ \begin{array} { c l } { 0 } & { \text { if } | z _ { 1 } | ^ { 2 } , | z _ { 2 } | ^ { 2 } < \frac { 1 } { 2 } } \\ { \operatorname { max } \{ ( | z _ { 1 } | ^ { 2 } - \frac { 1 } { 2 } ) ^ { 2 } , } & { ( | z _ { 2 } | ^ { 2 } - \frac { 1 } { 2 } ) ^ { 2 } \} } \\ { \text { elsewhere on } D } \end{array} \right.$ ; confidence 0.287
+
50. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007016.png ; $100$ ; confidence 1.000
  
−
51. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120360/b12036025.png ; $= \frac { \operatorname { exp } ( - \frac { ( p _ { x } ^ { 2 } + p _ { y } ^ { 2 } + p _ { z } ^ { 2 } ) } { 2 m k _ { B } T } ) d p _ { x } d p _ { y } d p _ { z } } { \int \int \int _ { - \infty } ^ { \infty } \operatorname { exp } ( \frac { - ( p _ { x } ^ { 2 } + p _ { y } ^ { 2 } + p _ { z } ^ { 2 } ) } { 2 m k _ { B } T } ) d p _ { x } d p _ { y } d p _ { z } }$ ; confidence 0.216
+
51. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011480/a01148042.png ; $x ^ { 2 } + 1$ ; confidence 1.000
  
−
52. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230171.png ; $\left( \begin{array} { c } { 0 } \\ { G _ { i + 1 } } \end{array} \right) = Z _ { i } G _ { i } \Theta _ { i } \left( \begin{array} { c c } { 1 } & { 0 } \\ { 0 } & { 0 } \end{array} \right) + G _ { i } \Theta _ { i } \left( \begin{array} { c c } { 0 } & { 0 } \\ { 0 } & { I _ { p + q - 1 } } \end{array} \right)$ ; confidence 0.337
+
52. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120120/e12012092.png ; $( t + 1 )$ ; confidence 1.000
  
−
53. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130110/s13011014.png ; $\left. \begin{array} { l } { \partial _ { i } ^ { 2 } = 0 } \\ { \partial _ { i } \partial _ { j } = \partial _ { j } \partial _ { i } \text { if } | i - j | > 1 } \\ { \partial _ { i } \partial _ { i + 1 } \partial _ { i } = \partial _ { i + 1 } \partial _ { i } \partial _ { i + 1 } } \end{array} \right.$ ; confidence 0.719
+
53. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040163.png ; $24$ ; confidence 1.000
  
−
54. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130190/f13019022.png ; $\frac { d ^ { 2 } C _ { j } } { d x ^ { 2 } } ( x _ { i } ) = \left\{ \begin{array} { l l } { - \frac { 2 N ^ { 2 } + 1 } { 6 } } & { \text { for } i = j } \\ { \frac { 1 } { 2 } \frac { ( - 1 ) ^ { i + j + 1 } } { \operatorname { sin } ^ { 2 } \frac { x _ { i } - x _ { j } } { 2 } } } & { \text { for } i \neq j } \end{array} \right.$ ; confidence 0.706
+
54. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011380/a011380171.png ; $1 + 1$ ; confidence 1.000
  
−
55. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008076.png ; $P \equiv \left( \begin{array} { c c } { \operatorname { exp } ( \frac { J + H } { k _ { B } T } ) } & { \operatorname { exp } ( \frac { - J } { k _ { B } T } ) } \\ { \operatorname { exp } ( \frac { - J } { k _ { B } T } ) } & { \operatorname { exp } ( \frac { J - H } { k _ { B } T } ) } \end{array} \right)$ ; confidence 0.635
+
55. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130140/a13014045.png ; $\sqrt { 2 }$ ; confidence 1.000
  
−
56. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120010/o12001033.png ; $\left. \begin{array} { l } { \operatorname { Re } ( \nabla p _ { 0 } + b ) = 0 } \\ { \Lambda _ { 1 } C ( \theta _ { r } ) ( \frac { \partial \theta _ { 0 } } { \partial t } + \nabla \theta _ { 0 } v _ { 0 } ) = \Delta \theta _ { 0 } } \\ { \operatorname { div } v _ { 0 } = 0 } \end{array} \right.$ ; confidence 0.567
+
56. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s13062082.png ; $f ( \lambda )$ ; confidence 1.000
  
−
57. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006028.png ; $\sigma _ { 1 } = \frac { 1 } { i } ( A _ { 1 } - A _ { 1 } ^ { * } ) | _ { E } , \sigma _ { 2 } = \frac { 1 } { i } ( A _ { 2 } - A _ { 2 } ^ { * } ) | _ { E } , \gamma = \frac { 1 } { i } ( A _ { 1 } A _ { 2 } ^ { * } - A _ { 2 } A _ { 1 } ^ { * } ) | _ { E } , \tilde { \gamma } = \frac { 1 } { i } ( A _ { 2 } ^ { * } A _ { 1 } - A _ { 1 } ^ { * } A _ { 2 } ) | _ { E }$ ; confidence 0.751
+
57. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041140/f0411402.png ; $( - \infty , + \infty )$ ; confidence 1.000
  
−
58. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130130/z1301307.png ; $[ \partial _ { r r } + \frac { 2 } { r } \partial _ { r } + \frac { 1 } { r ^ { 2 } } \partial _ { \theta \theta } + \frac { \operatorname { ctan } \theta } { r ^ { 2 } } \partial _ { \theta } + \frac { 1 } { r ^ { 2 } \operatorname { sin } ^ { 2 } \theta } \partial _ { \varphi \varphi } ] H = 0$ ; confidence 0.318
+
58. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120340/b12034062.png ; $f ( 0 ) > 0$ ; confidence 1.000
  
−
59. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a1200601.png ; $\left. \begin{array} { c } { \frac { \partial u } { \partial t } + \sum _ { j = 1 } ^ { m } \alpha _ { j } ( x ) \frac { \partial u } { \partial x _ { j } } + c ( x ) u = f ( x , t ) } \\ { ( x , t ) \in \Omega \times [ 0 , T ] } \\ { u ( x , 0 ) = u _ { 0 } ( x ) , \quad x \in \Omega } \end{array} \right.$ ; confidence 0.387
+
59. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060186.png ; $f ( 0,0 )$ ; confidence 1.000
  
−
60. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004063.png ; $- \frac { 1 } { \langle \rho ^ { \prime } , \zeta \} ^ { N } } \sum _ { | \alpha | = 0 } ^ { m } \frac { ( | \alpha | + n - 1 ) ! } { \alpha _ { 1 } ! \ldots \alpha _ { N } ! } ( \frac { \rho ^ { \prime } ( \zeta ) } { \langle \rho ^ { \prime } , \zeta \rangle } ) ^ { \alpha } z ^ { \alpha } \sigma$ ; confidence 0.140
+
60. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110250/b11025029.png ; $g ( t )$ ; confidence 1.000
  
−
61. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009045.png ; $\frac { m } { 1 + \alpha ^ { 2 } } \int _ { z } ^ { \xi } \frac { p _ { 0 } ( s ) - \alpha i } { s } d s \int _ { z } ^ { \xi } \frac { p _ { 1 } ( s ) - p _ { 0 } ( s ) } { s } \frac { \frac { m } { 1 + \alpha ^ { 2 } } \int _ { z } ^ { s } \frac { p _ { 0 } ( t ) - \alpha i } { t } d t } { t } d s - \frac { 1 + \alpha ^ { 2 } } { m } \}$ ; confidence 0.055
+
61. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130140/a13014041.png ; $\sqrt { 3 }$ ; confidence 1.000
  
−
62. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120140/e120140107.png ; $( \exists x \varphi ( x ) ) = \varphi \left( \begin{array} { c } { x } \\ { \varepsilon x \varphi } \end{array} \right) \text { and } ( \forall x \varphi ( x ) ) = \varphi \left( \begin{array} { c } { x } \\ { \varepsilon x ( \neg \varphi ) } \end{array} \right)$ ; confidence 0.647
+
62. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011180/a0111801.png ; $( 1,1 )$ ; confidence 1.000
  
−
63. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059610/l0596105.png ; $\frac { \partial w _ { N } } { \partial t } = \{ H , w _ { N } \} _ { cl } \equiv \sum _ { i = 1 } ^ { N } ( \frac { \partial H } { \partial r _ { i } } \frac { \partial w _ { N } } { \partial p _ { i } } - \frac { \partial w _ { N } } { \partial r _ { i } } \frac { \partial H } { \partial p _ { i } } )$ ; confidence 0.810
+
63. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040145.png ; $18$ ; confidence 1.000
  
−
64. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130060/k13006047.png ; $\partial _ { k } ( m ) = \left( \begin{array} { c } { \alpha _ { k } } \\ { k - 1 } \end{array} \right) + \left( \begin{array} { c } { \alpha _ { k } - 1 } \\ { k - 2 } \end{array} \right) + \ldots + \left( \begin{array} { c } { \alpha _ { 1 } } \\ { 0 } \end{array} \right)$ ; confidence 0.529
+
64. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130020/o13002021.png ; $180$ ; confidence 1.000
  
−
65. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/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
+
65. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023220/c02322014.png ; $( - 1,1 )$ ; confidence 1.000
  
−
66. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120020/i1200206.png ; $\times G _ { p + 2 , q } ^ { m , n + 2 } \left( \begin{array} { c } { 1 - \mu + i \tau , 1 - \mu - i \tau , ( \alpha _ { p } ) } \\ { ( \beta _ { q } ) } \end{array} \right) , f ( x ) = \frac { 1 } { \pi ^ { 2 } } \int _ { 0 } ^ { \infty } \tau \operatorname { sinh } ( 2 \pi \tau ) F ( \tau ) d \tau$ ; confidence 0.438
+
66. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130020/o13002022.png ; $41$ ; confidence 1.000
  
−
67. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200235.png ; $c _ { m , n } = \left\{ \begin{array} { l l } { 2 ^ { 1 - n } ( \frac { n + k } { 4 e ( m + n + k ) } ) ^ { n + k } } & { \text { if } \frac { m } { m + n + k } \geq \rho } \\ { \rho ^ { m } 2 ^ { 1 - n } ( \frac { 1 - \rho } { 4 } ) ^ { n + k } } & { \text { if } \frac { m } { m + n + k } < \rho } \end{array} \right.$ ; confidence 0.301
+
67. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012031.png ; $( 1,4 )$ ; confidence 1.000
  
−
68. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120010/w12001019.png ; $= \left\{ \begin{array} { l l } { \sum _ { - n \leq i \leq - 1 } f ( i ) g ( i + n ) , } & { n = - m > 0 } \\ { - \sum _ { n \leq i \leq - 1 } f ( i - n ) g ( i ) , } & { n = - m < 0 } \\ { 0 , } & { \left\{ \begin{array} { l } { n + m \neq 0 } \\ { n = m = 0 } \end{array} \right.} \end{array} \right.$ ; confidence 0.261
+
68. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018091.png ; $23$ ; confidence 1.000
  
−
69. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008047.png ; $+ \frac { d } { d m } \operatorname { ln } g ( L ; m , s ) \frac { d m } { d s } + \frac { d } { d s } \operatorname { ln } g ( L ; m , s ) = 0 , - \frac { d } { d s } \operatorname { ln } \alpha ( s ) = - \frac { d } { d R } \operatorname { ln } \frac { f ( R ) } { g ( R ; m , s ) } \frac { d R } { d s }$ ; confidence 0.940
+
69. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007017.png ; $( - 1,0 )$ ; confidence 1.000
  
−
70. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011018.png ; $\alpha _ { X } = \left( \begin{array} { l l l l } { 0 } & { 0 } & { 0 } & { 1 } \\ { 0 } & { 0 } & { 1 } & { 0 } \\ { 0 } & { 1 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 0 } & { 0 } \end{array} \right) = \left( \begin{array} { l l } { 0 } & { \sigma _ { x } } \\ { \sigma _ { x } } & { 0 } \end{array} \right)$ ; confidence 0.193
+
70. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b1200904.png ; $f ( 0 ) = 0$ ; confidence 1.000
  
−
71. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t120140164.png ; $\Lambda = \left( \begin{array} { c c c c } { z ^ { k _ { 1 } } } & { 0 } & { \ldots } & { 0 } \\ { 0 } & { z ^ { k } 2 } & { \ldots } & { 0 } \\ { \vdots } & { \vdots } & { \ddots } & { \vdots } \\ { 0 } & { 0 } & { \ldots } & { z ^ { k _ { R } } } \end{array} \right) , k _ { 1 } , \ldots , k _ { N } \in Z$ ; confidence 0.145
+
71. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007061.png ; $- 8$ ; confidence 1.000
  
−
72. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130060/i130060168.png ; $| \frac { \partial A ( x , y ) } { \partial x } + \frac { 1 } { 4 } q ( \frac { x + y } { 2 } ) | \leq c \sigma ( x ) \sigma ( \frac { x + y } { 2 } ) , | \frac { \partial A ( x , y ) } { \partial y } + \frac { 1 } { 4 } q ( \frac { x + y } { 2 } ) | \leq c \sigma ( x ) \sigma ( \frac { x + y } { 2 } )$ ; confidence 0.958
+
72. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011830/a01183015.png ; $\{ 0,1 \}$ ; confidence 1.000
  
−
73. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001097.png ; $C = \alpha _ { 12 } - \mu _ { 0 } \beta _ { 21 } \operatorname { cos } \theta + \mu _ { 0 } \beta _ { 31 } \operatorname { sin } \theta , D = \alpha _ { 11 } + \mu _ { 0 } \beta _ { 22 } \operatorname { cos } \theta - \mu _ { 0 } \beta _ { 32 } \operatorname { sin } \theta$ ; confidence 0.936
+
73. https://www.encyclopediaofmath.org/legacyimages/q/q130/q130030/q13003028.png ; $( 4 \times 4 )$ ; confidence 1.000
  
−
74. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a1201707.png ; $\left\{ \begin{array} { l } { p t ( \alpha , t ) + p _ { x } ( \alpha , t ) + \mu ( \alpha ) p ( \alpha , t ) = 0 } \\ { p ( 0 , t ) = \int _ { 0 } ^ { + \infty } \beta ( \alpha ) p ( \alpha , t ) d \alpha } \\ { p ( \alpha , 0 ) = p _ { 0 } ( \alpha ) \geq 0 } \end{array} \right.$ ; confidence 0.099
+
74. https://www.encyclopediaofmath.org/legacyimages/v/v096/v096030/v09603022.png ; $164$ ; confidence 1.000
  
−
75. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013056.png ; $\left. \begin{array}{l}{ N _ { * } ^ { 1 } = \frac { K _ { ( 1 ) } - \delta _ { ( 1 ) } K _ { ( 2 ) } } { 1 - \delta _ { ( 1 ) } \delta _ { ( 2 ) } } }\\{ N _ { * } ^ { 2 } = \frac { K _ { ( 2 ) } - \delta _ { ( 2 ) } K _ { ( 1 ) } } { 1 - \delta _ { ( 1 ) } \delta _ { ( 2 ) } } }\end{array} \right.$ ; confidence 0.545
+
75. https://www.encyclopediaofmath.org/legacyimages/f/f041/f041470/f04147017.png ; $\bar{\lambda}$ ; confidence 1.000
  
−
76. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120060/b1200609.png ; $\frac { \partial } { \partial z } = \frac { 1 } { 2 } ( \frac { \partial } { \partial x } - i \frac { \partial } { \partial y } ) , \frac { \partial } { \partial z } = \frac { 1 } { 2 } ( \frac { \partial } { \partial x } + i \frac { \partial } { \partial y } )$ ; confidence 0.984
+
76. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120050/d1200507.png ; $f ( y )$ ; confidence 1.000
  
−
77. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120050/l12005024.png ; $\frac { 1 } { 2 \sqrt { 2 \pi } } \int _ { 0 } ^ { \infty } \int _ { 0 } ^ { \infty } \operatorname { exp } ( - \frac { 1 } { 2 } ( \frac { x u } { v } + \frac { x v } { u } + \frac { u v } { x } ) ) \times \times ( \frac { 1 } { x } + \frac { 1 } { u } + \frac { 1 } { v } ) f ( u ) g ( v ) d u d v$ ; confidence 0.341
+
77. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090217.png ; $\nabla ( \lambda )$ ; confidence 1.000
  
−
78. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m130110113.png ; $( \frac { \partial \phi } { \partial t } ) | _ { x _ { k } ^ { 0 } } = \frac { D \phi } { D t } , ( \frac { \partial \phi } { \partial t } ) | _ { x _ { i } } = \frac { \partial \phi } { \partial t } , ( \frac { \partial x _ { i } } { \partial t } ) | _ { x _ { k } ^ { 0 } } = v _ { i }$ ; confidence 0.340
+
78. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120030/a12003018.png ; $[ 0 , \infty )$ ; confidence 1.000
  
−
79. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120010/o12001037.png ; $\left. \begin{array} { l } { \nabla p _ { 1 } = \nabla p _ { 2 } = 0 } \\ { \frac { \partial v _ { 0 } } { \partial t } + [ \nabla v _ { 0 } ] v _ { 0 } = \frac { 1 } { Re } \Delta v _ { 0 } + \operatorname { Re } \nabla p _ { 3 } + \theta _ { 0 } b } \end{array} \right.$ ; confidence 0.316
+
79. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120010/l12001041.png ; $( 2 \times 4 )$ ; confidence 1.000
  
−
80. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430117.png ; $S \left( \begin{array} { c c } { \alpha } & { \beta } \\ { \gamma } & { \delta } \end{array} \right) = \left( \begin{array} { c c } { q ^ { 2 } \delta + ( 1 - q ^ { 2 } ) \alpha } & { - q ^ { 2 } \beta } \\ { - q ^ { 2 } \gamma } & { \alpha } \end{array} \right)$ ; confidence 0.875
+
80. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130070/k13007034.png ; $256$ ; confidence 1.000
  
−
81. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011015.png ; $\left\{ \begin{array} { l l } { \alpha _ { i } \alpha _ { j } + \alpha _ { j } \alpha _ { i } = 0 } & { \text { fori, } j \in \{ x , y , z \} , i \neq j } \\ { \alpha _ { i } \beta + \beta \alpha _ { i } = 0 } & { \text { for } i , j \in \{ x , y , z \} } \end{array} \right.$ ; confidence 0.152
+
81. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120360/b12036043.png ; $( 1 + 1 )$ ; confidence 1.000
  
−
82. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140140.png ; $= ( 2 \pi i ) ^ { 1 - n } \int _ { \Delta _ { N } } d t \int _ { S } ( F _ { N } f ) \times \times ( ( 1 - t _ { 2 } - \ldots - t _ { n } ) ( z , \zeta ) , \frac { t _ { 2 } } { \zeta _ { 2 } } ( z , \zeta ) , \ldots , \frac { t _ { n } } { \zeta _ { n } } ( z , \zeta ) ) \frac { d \zeta } { \zeta }$ ; confidence 0.073
+
82. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130090/c1300908.png ; $[ - 1,1 ]$ ; confidence 1.000
  
−
83. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130050/g13005086.png ; $\left( \begin{array} { c c c c } { 1 } & { p _ { 0 } ^ { 1 } } & { \dots } & { p _ { 0 } ^ { k } } \\ { \vdots } & { \vdots } & { \ddots } & { \vdots } \\ { 1 } & { p _ { k } ^ { 1 } } & { \cdots } & { p _ { i k } ^ { k } } \end{array} \right) | _ { 1 \leq i _ { 0 } < \ldots < i _ { k } \leq n }$ ; confidence 0.059
+
83. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020540/c02054039.png ; $( p - 1 )$ ; confidence 1.000
  
−
84. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120010/l1200106.png ; $M = \left( \begin{array} { c c c } { 1 } & { - 1 } & { 0 } \\ { 1 } & { 1 } & { - 1 } \\ { 1 } & { 1 } & { 1 } \end{array} \right) , \quad N = \left( \begin{array} { c c c c } { 1 } & { 1 } & { 1 } & { - 1 } \\ { 1 } & { 1 } & { - 1 } & { 1 } \\ { 1 } & { - 1 } & { 1 } & { 1 } \end{array} \right)$ ; confidence 0.981
+
84. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c1200405.png ; $( 2 n - 1 )$ ; confidence 1.000
  
−
85. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008065.png ; $g ( x ; m , s ) = \left\{ \begin{array} { l l } { \frac { 1 } { 2 s } \operatorname { exp } ( \frac { x - m } { s } ) } & { \text { for } x \leq m } \\ { \frac { 1 } { 2 s } \operatorname { exp } ( \frac { m - x } { s } ) } & { \text { for } x \geq m } \end{array} \right.$ ; confidence 0.804
+
85. https://www.encyclopediaofmath.org/legacyimages/h/h047/h047040/h04704018.png ; $( 0,2 )$ ; confidence 1.000
  
−
86. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130050/h13005042.png ; $\frac { \partial u } { \partial t } = - 2 \frac { \partial ^ { 3 } } { \partial x ^ { 3 } } ( \frac { 1 } { \sqrt { u } } ) + 6 u ^ { 2 } \frac { \partial } { \partial y } [ u ^ { - 1 } \partial ^ { - 1 } x \frac { \partial } { \partial y } ( \frac { 1 } { \sqrt { u } } ) ]$ ; confidence 0.957
+
86. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020026.png ; $p ( t )$ ; confidence 1.000
  
−
87. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120070/q120070116.png ; $\Delta \left( \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right) = \left( \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right) \otimes \left( \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right)$ ; confidence 0.420
+
87. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018062.png ; $\lambda \neq 0$ ; confidence 1.000
  
−
88. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130100/w13010019.png ; $\operatorname { Var } | W ^ { \alpha } ( t ) | \asymp \left\{ \begin{array} { l l } { t , } & { d = 1 } \\ { \frac { t ^ { 2 } } { \operatorname { log } ^ { 4 } t } , } & { d = 2 } \\ { \operatorname { tlog } t , } & { d = 3 } \\ { t , } & { d \geq 4 } \end{array} \right.$ ; confidence 0.128
+
88. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051013.png ; $g ( u ) =$ ; confidence 1.000
  
−
89. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i120080104.png ; $m = \frac { \operatorname { exp } ( \frac { H _ { eff } } { k _ { B } T } ) - \operatorname { exp } ( - \frac { H _ { eff } } { k _ { B } T } ) } { \operatorname { exp } ( \frac { H _ { eff } } { k _ { B } T } ) + \operatorname { exp } ( - \frac { H _ { eff } } { k _ { B } T } ) } =$ ; confidence 0.908
+
89. https://www.encyclopediaofmath.org/legacyimages/d/d033/d033400/d0334002.png ; $f ( t ) = 0$ ; confidence 1.000
  
−
90. https://www.encyclopediaofmath.org/legacyimages/g/g110/g110120/g1101206.png ; $\lambda _ { 1 } = \left( \begin{array} { l l l } { 0 } & { 1 } & { 0 } \\ { 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } \end{array} \right) , \lambda _ { 2 } = \left( \begin{array} { c c c } { 0 } & { - i } & { 0 } \\ { i } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } \end{array} \right)$ ; confidence 0.766
+
90. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130580/s13058044.png ; $4 \times 4$ ; confidence 1.000
  
−
91. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006037.png ; $\mathfrak { V } ^ { \prime \prime } = ( A _ { 1 } ^ { \prime \prime } , A _ { 2 } ^ { \prime \prime } , H ^ { \prime \prime } , \Phi ^ { \prime \prime } , E , \sigma _ { 1 } , \sigma _ { 2 } , \gamma ^ { \prime \prime } , \tilde { \gamma } ^ { \prime \prime } )$ ; confidence 0.589
+
91. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130020/b13002048.png ; $( 3 \times 3 )$ ; confidence 1.000
  
−
92. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008058.png ; $E [ W ] _ { gated } = \frac { \delta ^ { 2 } } { 2 r } + \frac { P \lambda b ^ { ( 2 ) } + r ( P + \rho ) } { 2 ( 1 - \rho ) } , E [ W ] _ { lim } = \frac { \delta ^ { 2 } } { 2 r } + \frac { P \lambda b ^ { ( 2 ) } + r ( P + \rho ) + P \lambda \delta ^ { 2 } } { 2 ( 1 - \rho - P \lambda r ) }$ ; confidence 0.089
+
92. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120060/d12006031.png ; $2 + 1$ ; confidence 1.000
  
−
93. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200105.png ; $\operatorname { max } _ { 1 \leq k \leq 4 } \left( \begin{array} { c } { \operatorname { max } } \\ { n + r - 1 } \\ { r } \end{array} \right) g ( k ) | \geq | g ( 0 ) | ( 2 e \left( \begin{array} { c } { n + r - 1 } \\ { r } \end{array} \right) ) ^ { - 1 / r }$ ; confidence 0.330
+
93. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140128.png ; $2 n ^ { 2 }$ ; confidence 1.000
  
−
94. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120060/m1200604.png ; $\frac { \partial \vec { v } } { \partial t } + ( \vec { v } \nabla ) \vec { v } = - \frac { 1 } { \rho } \nabla P - \frac { 1 } { 4 \pi \rho } [ \vec { B } \times \operatorname { rot } \vec { B } ] , \frac { \partial s } { \partial t } + \vec { v } \nabla s = 0$ ; confidence 0.889
+
94. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012039.png ; $( 3 \times 3 )$ ; confidence 1.000
  
−
95. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o13001096.png ; $A = \mu _ { 0 } \beta _ { 11 } + \alpha _ { 22 } \operatorname { cos } \theta - \alpha _ { 32 } \operatorname { sin } \theta , B = \alpha _ { 21 } \operatorname { cos } \theta - \alpha _ { 31 } \operatorname { sin } \theta - \mu _ { 0 } \beta _ { 12 }$ ; confidence 0.891
+
95. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120030/g1200309.png ; $3 n + 1$ ; confidence 1.000
  
−
96. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/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
+
96. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032110/d0321106.png ; $\mu > 0$ ; confidence 1.000
  
−
97. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004056.png ; $\left. \begin{array}{l}{ f _ { i + 1 / 2 } ^ { waf } = \frac { 1 } { \Delta x } \int _ { - \frac { 1 } { 2 } \Delta x } ^ { \frac { 1 } { 2 } \Delta x } f [ u _ { t + 1 / 2 } ( x , \frac { 1 } { 2 } \Delta t ) ] d x }\\{ - \frac { 1 } { 2 } \Delta x }\end{array} \right.$ ; confidence 0.090
+
97. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130410/s13041061.png ; $\sqrt { z ^ { 2 } - 1 } > 0$ ; confidence 1.000
  
−
98. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200117.png ; $\geq \frac { n } { 4 N ^ { 2 } / 2 } \operatorname { exp } ( - 30 n ( \frac { 1 } { \operatorname { log } ( N / n ) } + \frac { 1 } { \operatorname { log } ( N / m ) } ) ) \times \times \times \operatorname { min } _ { l \leq n } | \sum _ { j = 1 } ^ { l } b _ { j }$ ; confidence 0.300
+
98. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a1200604.png ; $\partial \Omega$ ; confidence 1.000
  
−
99. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z130110145.png ; $\frac { \mu _ { n } ( x ) } { \mu _ { n } } \rightarrow \frac { \int _ { - \infty } ^ { \infty } \alpha ^ { s ( x + \beta ) } e ^ { - \alpha ^ { s } } d N ( s ) } { \Gamma ( x + 1 ) \int _ { - \infty } ^ { \infty } \alpha ^ { s } ^ { \beta } e ^ { - \alpha ^ { s } } d N ( s ) }$ ; confidence 0.447
+
99. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012029.png ; $( 1,2 )$ ; confidence 1.000
  
−
100. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120040/e1200405.png ; $\left\{ \begin{array} { l } { L _ { x } ^ { 2 } L _ { x x } + 2 L _ { x } L _ { y } L _ { x y } + L _ { y } ^ { 2 } L _ { y y } = 0 } \\ { L _ { x } ^ { 3 } L _ { x x x } + 3 L _ { x } ^ { 2 } L _ { y } L _ { x x y } + 3 L _ { x } L _ { y } ^ { 2 } L _ { x y } y + L _ { y } ^ { 3 } L _ { y y y } < 0 } \end{array} \right.$ ; confidence 0.474
+
100. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130070/t1300708.png ; $g ( 0 ) = 0$ ; confidence 1.000
  
−
101. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120200/f1202007.png ; $\left( \begin{array} { c c c c } { 0 } & { \square } & { \square } & { - a _ { 0 } } \\ { 1 } & { \ddots } & { \square } & { - a _ { 1 } } \\ { \square } & { \ddots } & { 0 } & { \vdots } \\ { \square } & { \square } & { 1 } & { - a _ { n - 1 } } \end{array} \right)$ ; confidence 0.700
+
101. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120210/s12021022.png ; $\mu ( \lambda ) = \lambda$ ; confidence 1.000
  
−
102. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120200/f1202008.png ; $\left( \begin{array} { c c c c } { 0 } & { 1 } & { \square } & { \square } \\ { \square } & { \ddots } & { \ddots } & { \square } \\ { \square } & { \square } & { 0 } & { 1 } \\ { - a _ { 0 } } & { \cdots } & { \cdots } & { - a _ { n - 1 } } \end{array} \right)$ ; confidence 0.805
+
102. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018063.png ; $\lambda = 0$ ; confidence 1.000
  
−
103. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m120130106.png ; $\left. \begin{array} { l } { \frac { d N } { d t } = N ( - 2 \alpha N - \delta F + \lambda ) } \\ { \frac { d F } { d t } = F ( 2 \beta N + \gamma F ^ { p } - \varepsilon - \mu _ { 1 } L ) } \\ { \frac { d L } { d t } = \mu _ { 2 } L F - \nu L } \end{array} \right.$ ; confidence 0.937
+
103. https://www.encyclopediaofmath.org/legacyimages/g/g110/g110170/g1101706.png ; $\sqrt { t }$ ; confidence 1.000
  
−
104. https://www.encyclopediaofmath.org/legacyimages/l/l059/l059610/l05961011.png ; $\frac { d w _ { N } } { d t } = \frac { \partial w _ { N } } { \partial t } + \sum _ { i = 1 } ^ { N } ( \frac { \partial w _ { N } } { \partial r _ { i } } \frac { d r _ { i } } { d t } + \frac { \partial w _ { N } } { \partial p _ { i } } \frac { d p _ { i } } { d t } ) = 0$ ; confidence 0.716
+
104. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120210/w12021036.png ; $( - 1 , + 1 )$ ; confidence 1.000
  
−
105. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t130050153.png ; $( A ) = \operatorname { dim } \operatorname { Ker } D _ { A } ^ { 0 } - \operatorname { dim } ( \operatorname { Ker } D _ { A } ^ { 1 } / \operatorname { Ran } D _ { A } ^ { 0 } ) + \operatorname { dim } ( X / \operatorname { Ran } D _ { A } ^ { 1 } )$ ; confidence 0.752
+
105. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120140/b1201407.png ; $2 t + 1$ ; confidence 1.000
  
−
106. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120270/c12027017.png ; $\frac { \text { Vol } ( \partial \Omega ) } { \text { Vol } ( \Omega ) } \geq \frac { \mathfrak { c } _ { 1 } } { \operatorname { diam } \Omega } \cdot \omega , \quad \mathfrak { c } _ { 1 } = \frac { 2 \pi \alpha ( n - 1 ) } { \alpha ( n ) }$ ; confidence 0.087
+
106. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130100/p130100122.png ; $( 2 p + 1 )$ ; confidence 1.000
  
−
107. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120090/e12009017.png ; $F ^ { \mu \nu } = \left( \begin{array} { c c c c } { 0 } & { E _ { X } } & { E _ { y } } & { E _ { z } } \\ { - E _ { x } } & { 0 } & { H _ { z } } & { - H _ { y } } \\ { - E _ { y } } & { - H _ { z } } & { 0 } & { H _ { X } } \\ { - E _ { z } } & { H _ { y } } & { - H _ { X } } & { 0 } \end{array} \right)$ ; confidence 0.158
+
107. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120160/b12016041.png ; $f ^ { \prime } = f$ ; confidence 1.000
  
−
108. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a12017014.png ; $p ( \alpha , t ) = \left\{ \begin{array} { l l } { p _ { 0 } ( \alpha - t ) \frac { \Pi ( \alpha ) } { \Pi ( \alpha - t ) } } & { \text { if } \alpha \geq t } \\ { b ( t - \alpha ) \Pi ( \alpha ) } & { \text { if } \alpha < t } \end{array} \right.$ ; confidence 0.451
+
108. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012033.png ; $( 2,4 )$ ; confidence 1.000
  
−
109. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g13004016.png ; $H ^ { m } ( E ) = \operatorname { sup } _ { \delta > 0 } \operatorname { inf } \{ c _ { m } \sum _ { i } | E _ { i } | ^ { m } : \quad \begin{array} { c } { E \subset \cup _ { i } E _ { i } } \\ { | E _ { i } | < \delta \text { for alli } } \end{array} \}$ ; confidence 0.095
+
109. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110670/b11067055.png ; $( 2 n + 1 )$ ; confidence 1.000
  
−
110. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008081.png ; $P = \left( \begin{array} { c c } { \lambda _ { + } } & { 0 } \\ { 0 } & { \lambda _ { - } } \end{array} \right) , \quad P ^ { N } = \left( \begin{array} { c c } { \lambda _ { + } ^ { N } } & { 0 } \\ { 0 } & { \lambda ^ { N } } \end{array} \right)$ ; confidence 0.901
+
110. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130050/n13005037.png ; $\mu > 1$ ; confidence 1.000
  
−
111. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120100/k1201008.png ; $\sum _ { m = 0 } ^ { \infty } \frac { 1 } { ( 2 \pi i ) ^ { m / 3 } } \int _ { T } \sum _ { P = \{ ( z _ { j } , z _ { j } ^ { \prime } ) \} } ( - 1 ) ^ { \perp } D _ { P } \bigwedge _ { j = 1 } ^ { m } \frac { d z _ { j } - d z _ { j } ^ { \prime } } { z _ { j } - z _ { j } ^ { \prime } }$ ; confidence 0.129
+
111. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057780/l05778081.png ; $30$ ; confidence 1.000
  
−
112. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120050/s12005024.png ; $\left( \begin{array} { c c c c } { S _ { 0 } } & { 0 } & { \ldots } & { 0 } \\ { S _ { 1 } } & { S _ { 0 } } & { \ldots } & { 0 } \\ { \vdots } & { \vdots } & { \ddots } & { \vdots } \\ { S _ { n - 1 } } & { S _ { n - 2 } } & { \ldots } & { S _ { 0 } } \end{array} \right)$ ; confidence 0.600
+
112. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120170/l120170246.png ; $\operatorname{max}( 3 , n )$ ; confidence 1.000
  
−
113. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130290/b13029085.png ; $\varphi _ { M } ^ { i } : \operatorname { Ext } _ { A } ^ { i } ( A / \mathfrak { m } , M ) \rightarrow H _ { m } ^ { i } ( M ) = \operatorname { lim } _ { n \rightarrow \infty } \operatorname { Ext } _ { A } ^ { i } ( A / \mathfrak { m } ^ { n } , M )$ ; confidence 0.393
+
113. https://www.encyclopediaofmath.org/legacyimages/d/d032/d032240/d032240214.png ; $( 1,0 )$ ; confidence 1.000
  
−
114. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d12002011.png ; $( S ) g ( \overline { u } _ { 1 } ) = \left\{ \begin{array} { c l } { \operatorname { min } } & { c ^ { T } x + \overline { u } ^ { T } ( A _ { 1 } x - b _ { 1 } ) } \\ { \text { s.t. } } & { A _ { 2 } x \leq b _ { 2 } } \\ { x } & { \geq 0 } \end{array} \right.$ ; confidence 0.060
+
114. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025830/c0258308.png ; $\{ 0 \}$ ; confidence 1.000
  
−
115. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120040/i12004019.png ; $K _ { BM } ( \zeta , z ) = \frac { ( n - 1 ) ! } { ( 2 \pi i ) ^ { n } } \frac { \omega _ { \zeta } ^ { \prime } ( \overline { \zeta } - z ) \wedge \omega ( \zeta ) } { | \zeta - z | ^ { 2 n } } , \omega _ { \zeta } ^ { \prime } ( \overline { \zeta } - z )$ ; confidence 0.289
+
115. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a120160137.png ; $13$ ; confidence 1.000
  
−
116. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120040/l12004082.png ; $f _ { l + 1 / 2 } ^ { \operatorname { mac } } = \left\{ \begin{array} { l } { \frac { 1 } { 2 } ( \hat { f } _ { i } ^ { + } + f _ { l + 1 } ^ { n } ) } \\ { \text { or } } \\ { \frac { 1 } { 2 } ( \hat { f } _ { i + 1 } ^ { - } + f _ { l } ^ { n } ) } \end{array} \right.$ ; confidence 0.206
+
116. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011800/a01180083.png ; $( i + 1 )$ ; confidence 1.000
  
−
117. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120360/b12036032.png ; $w ( i , j , k , l ) = w \left( \begin{array} { c c c } { \square } & { l } & { \square } \\ { i } & { + } & { k } \\ { \square } & { j } & { \square } \end{array} \right) = \operatorname { exp } ( - \frac { \epsilon ( i , j , k , l ) } { k _ { B } T } )$ ; confidence 0.405
+
117. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012025.png ; $( 2,3 )$ ; confidence 1.000
  
−
118. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003025.png ; $\Omega ^ { \bullet } ( \tilde { M } _ { C } ) \rightleftarrows \operatorname { Hom } _ { K _ { \infty } } ( \Lambda ^ { \bullet } ( \mathfrak { g } / \mathfrak { k } ) , C _ { \infty } ( \Gamma \backslash G ( R ) \otimes M _ { C } ) )$ ; confidence 0.185
+
118. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130120/a13012041.png ; $4 \mu$ ; confidence 1.000
  
−
119. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130190/f13019021.png ; $\frac { d C _ { j } } { d x } ( x _ { i } ) = \left\{ \begin{array} { l l } { 0 } & { \text { for } i = j } \\ { \frac { 1 } { 2 } ( - 1 ) ^ { i + j } \operatorname { cot } \frac { x _ { i } - x _ { j } } { 2 } } & { \text { for } i \neq j } \end{array} \right.$ ; confidence 0.674
+
119. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011600/a01160062.png ; $\pm 1$ ; confidence 1.000
  
−
120. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130110/m130110112.png ; $( \frac { \partial \phi } { \partial t } ) | _ { x _ { k } 0 } = ( \frac { \partial \phi } { \partial t } ) | _ { x _ { i } } + ( \frac { \partial \phi } { \partial x _ { i } } ) | _ { t } ( \frac { \partial x _ { i } } { \partial t } ) | _ { x _ { k } 0 }$ ; confidence 0.179
+
120. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120330/s12033023.png ; $( 4 n - 1,2 n - 1 , n - 1 )$ ; confidence 1.000
  
−
121. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015015.png ; $\{ s \in S : \left( \begin{array} { c c c } { x _ { 11 } ( s _ { 11 } ) } & { \dots } & { x _ { 1 n } ( s _ { 1 n } ) } \\ { \vdots } & { \square } & { \vdots } \\ { x _ { p 1 } ( s _ { p 1 } ) } & { \dots } & { x _ { p n } ( s _ { p n } ) } \end{array} \right) \in B \}$ ; confidence 0.303
+
121. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a120160175.png ; $\alpha \in ( 0,1 )$ ; confidence 1.000
  
−
122. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130230/a13023041.png ; $\operatorname { cos } \alpha = \operatorname { sup } \left\{ \begin{array} { r l } { u \in U } & { V ^ { \perp } } \\ { \langle u , v \rangle : } & { v \in V \cap U ^ { \perp } } \\ { \| u \| , \| v \| \leq 1 } \end{array} \right\}$ ; confidence 0.100
+
122. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b1200905.png ; $f ^ { \prime } ( 0 ) = 1$ ; confidence 1.000
  
−
123. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120170/m12017011.png ; $\operatorname { det } \left( \begin{array} { c c c } { 1 } & { \ldots } & { I } \\ { X _ { 1 } } & { \ldots } & { X _ { n } } \\ { \vdots } & { \ldots } & { \vdots } \\ { X _ { 1 } ^ { n - 1 } } & { \ldots } & { X _ { n } ^ { n - 1 } } \end{array} \right)$ ; confidence 0.148
+
123. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w120070123.png ; $( 2 + 1 )$ ; confidence 1.000
  
−
124. https://www.encyclopediaofmath.org/legacyimages/m/m110/m110110/m1101104.png ; $= \frac { 1 } { 2 \pi i } \int _ { L } \frac { \prod _ { j = 1 } ^ { m } \Gamma ( b _ { j } - s ) \prod _ { j = 1 } ^ { n } \Gamma ( 1 - a _ { j } + s ) } { \prod _ { j = m + 1 } ^ { q } \Gamma ( 1 - b _ { j } + s ) \prod _ { j = n + 1 } ^ { p } \Gamma ( a _ { j } - s ) } x ^ { s } d s$ ; confidence 0.471
+
124. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120030/a1200308.png ; $f ( - x )$ ; confidence 1.000
  
−
125. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120020/o12002010.png ; $\times \int _ { - \infty } ^ { \infty } \tau | \Gamma ( c - \alpha + \frac { i \tau } { 2 } ) | ^ { 2 } \times \times \square _ { 2 } F _ { 1 } ( \alpha + \frac { i \tau } { 2 } , a - \frac { i \tau } { 2 } ; c ; - \frac { 1 } { x } ) f ( \tau ) d \tau$ ; confidence 0.140
+
125. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120240/a12024025.png ; $( p - 1 , p - 1 )$ ; confidence 1.000
  
−
126. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120350/s12035028.png ; $= \lambda \operatorname { lim } _ { N \rightarrow \infty } \sum _ { t = 1 } ^ { N } E \frac { \partial } { \partial \theta } f ( Z ^ { t - 1 } , t , \theta ) ( \frac { \partial } { \partial \theta } f ( Z ^ { t - 1 } , t , \theta ) ) ^ { T }$ ; confidence 0.760
+
126. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110060/a11006014.png ; $\Omega \times \Omega$ ; confidence 1.000
  
−
127. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120010/o1200104.png ; $\operatorname { div } v = \frac { f ^ { \prime } ( \theta ) } { f ( \theta ) } ( \frac { \partial \theta } { \partial t } + \nabla \theta y ) = \alpha ( \theta ) ( \frac { \partial \theta } { \partial t } + \nabla \theta y )$ ; confidence 0.575
+
127. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130100/l13010047.png ; $| \xi | > R$ ; confidence 1.000
  
−
128. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008073.png ; $\left. \begin{array} { c } { ( \frac { d ^ { 2 } u } { d t ^ { 2 } } , v ) _ { L ^ { 2 } } + a ( u , v ) = ( f ( t ) , v ) _ { L ^ { 2 } } } \\ { \text { a.e.t } \in [ 0 , T ] , v \in V } \\ { u ( 0 ) = u _ { 0 } , \frac { d u } { d t } ( 0 ) = u _ { 1 } } \end{array} \right.$ ; confidence 0.217
+
128. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130220/m13022024.png ; $194$ ; confidence 1.000
  
−
129. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130140/s13014037.png ; $\lambda = \square \left. \begin{array} { l l l } { \bullet } & { \bullet } & { \bullet } \\ { \lambda = } & { \square \bullet } & { \bullet } & { \square } \\ { \square } & { \square } & { \bullet } \end{array} \right.$ ; confidence 0.116
+
129. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022420/c02242033.png ; $( - \infty , \infty )$ ; confidence 1.000
  
−
130. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130100/w13010015.png ; $E | W ^ { \alpha } ( t ) | \sim \left\{ \begin{array} { l l } { \sqrt { \frac { 8 t } { \pi } } , } & { d = 1 } \\ { \frac { 2 \pi t } { \operatorname { log } t } , } & { d = 2 } \\ { \kappa _ { \alpha } t , } & { d \geq 3 } \end{array} \right.$ ; confidence 0.110
+
130. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090670/s09067014.png ; $( f ^ { \prime } , g ^ { \prime } )$ ; confidence 1.000
  
−
131. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130080/a13008057.png ; $g ( x ; m , s ) = \left\{ \begin{array} { l l } { \frac { 1 } { s } - \frac { m - x } { s ^ { 2 } } } & { \text { if } m - s \leq x \leq m } \\ { \frac { 1 } { s } - \frac { x - m } { s ^ { 2 } } } & { \text { if } m \leq x \leq m + s } \end{array} \right.$ ; confidence 0.945
+
131. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018085.png ; $\operatorname { ln } 2$ ; confidence 1.000
  
−
132. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120020/c12002025.png ; $\int _ { 0 } ^ { \infty } \frac { f ^ { * } \mu _ { t } } { t } d t \equiv \operatorname { lim } _ { \epsilon \rightarrow 0 , \rho \rightarrow \infty } \int _ { \epsilon } ^ { \rho } \frac { f ^ { * } \mu _ { t } } { t } d t = c _ { \mu } f$ ; confidence 0.478
+
132. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120300/d1203007.png ; $Y ( 0 ) = 0$ ; confidence 1.000
  
−
133. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f13024030.png ; $= \left( \begin{array} { c c } { L ( a , d ) - L ( c , b ) } & { K ( a , c ) } \\ { - \varepsilon K ( b , d ) } & { \varepsilon ( L ( d , a ) - L ( b , c ) ) } \end{array} \right) \left( \begin{array} { l } { e } \\ { f } \end{array} \right)$ ; confidence 0.292
+
133. https://www.encyclopediaofmath.org/legacyimages/c/c024/c024990/c02499012.png ; $[ - \pi , \pi ]$ ; confidence 1.000
  
−
134. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120170/m12017017.png ; $\operatorname { det } ( X _ { 1 } ) \ldots \operatorname { det } ( X _ { n } ) = ( - 1 ) ^ { n } \operatorname { det } ( A _ { n } ) , \operatorname { det } ( I - \lambda X _ { 1 } ) \ldots \operatorname { det } ( I - \lambda X _ { n } )$ ; confidence 0.776
+
134. https://www.encyclopediaofmath.org/legacyimages/s/s091/s091060/s09106032.png ; $\{ f , g \}$ ; confidence 1.000
  
−
135. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/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
+
135. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009027.png ; $| f | < 1$ ; confidence 1.000
  
−
136. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021073.png ; $( B , \delta ) : 0 \rightarrow B _ { r } \stackrel { \delta _ { r } } { \rightarrow } \ldots \stackrel { \delta _ { 1 } } { \rightarrow } B _ { 1 } \stackrel { \delta _ { 0 } } { \rightarrow } L ( \lambda ) \rightarrow 0$ ; confidence 0.151
+
136. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120100/f12010077.png ; $27$ ; confidence 1.000
  
−
137. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120020/b12002018.png ; $\operatorname { limsup } _ { n \rightarrow \infty } \frac { n ^ { 1 / 4 } } { ( \operatorname { log } n ) ^ { 1 / 2 } ( \operatorname { log } \operatorname { log } n ) ^ { 1 / 4 } } \| \alpha _ { n } + \beta _ { n } \| = 2 ^ { - 1 / 4 }$ ; confidence 0.470
+
137. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130010/i13001059.png ; $( 4 ^ { 2 } , 3 ^ { 2 } )$ ; confidence 1.000
  
−
138. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120050/g12005047.png ; $- \frac { 1 } { 2 } \sum _ { i , j = 1 } ^ { n } \frac { \partial ^ { 2 } \mu _ { 0 } } { \partial k _ { i } \partial \dot { k } _ { j } } ( k _ { c } , R _ { c } ) \frac { \partial ^ { 2 } A } { \partial \xi _ { i } \partial \xi _ { j } } + 1 A | A | ^ { 2 }$ ; confidence 0.456
+
138. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s130540120.png ; $\{ - 1 , - 1 \}$ ; confidence 1.000
  
−
139. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020177.png ; $E [ U _ { \infty } ^ { 1 } U _ { \infty } ^ { 2 } ] = \int _ { \partial D } u _ { 1 } u _ { 2 } \frac { d \vartheta } { 2 \pi } = \int _ { \partial D } v _ { 1 } v _ { 2 } \frac { d \vartheta } { 2 \pi } = E [ V _ { \infty } ^ { 1 } V _ { \infty } ^ { 2 } ]$ ; confidence 0.554
+
139. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120020/k12002011.png ; $( - 2 )$ ; confidence 1.000
  
−
140. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120010/o12001025.png ; $\left( \begin{array} { l } { v } \\ { \theta } \\ { p } \end{array} \right) = \sum _ { n = 0 } ^ { \infty } \varepsilon ^ { n } \left( \begin{array} { c } { v _ { n } } \\ { \theta _ { n } } \\ { p _ { n } } \end{array} \right)$ ; confidence 0.329
+
140. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012035.png ; $( 3,4 )$ ; confidence 1.000
  
−
141. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120120/d12012064.png ; $\left. \begin{array} { c c c } { \square } & { c _ { 2 } } & { \square } \\ { \square } & { \square } & { \searrow ^ { \phi _ { 2 } } } \\ { \square ^ { \phi _ { 1 } } } & { \nearrow } & { \vec { \phi _ { 3 } } } \end{array} \right.$ ; confidence 0.190
+
141. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016084.png ; $5$ ; confidence 1.000
  
−
142. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230126.png ; $\frac { ( - 1 ) ^ { k - 1 } } { ( k - 1 ) ! ( 1 - 1 ) ! 2 ! } \times \times \sum _ { \sigma } \operatorname { sign } \sigma \omega ( K ( [ X _ { \sigma 1 } , X _ { \sigma 2 } ] , X _ { \sigma 3 } , \ldots ) , X _ { \sigma ( k + 2 ) } , \ldots )$ ; confidence 0.852
+
142. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120030/m120030111.png ; $\rho ( 0 ) = 0$ ; confidence 1.000
  
−
143. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130050/i13005081.png ; $\alpha ( z ) : = \prod _ { j = 1 } ^ { J } \frac { z - i k _ { j } } { z + i k _ { j } } \operatorname { exp } \{ - \frac { 1 } { 2 \pi i } \int _ { - \infty } ^ { \infty } \frac { \operatorname { ln } ( 1 - | r _ { + } ( k ) | ^ { 2 } ) } { k - z } d k \}$ ; confidence 0.801
+
143. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120010/l12001056.png ; $m + 2$ ; confidence 1.000
  
−
144. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008034.png ; $\left\{ \begin{array}{l}{ m = - ( \frac { \partial F } { \partial H } ) _ { T } }\\{ \chi = ( \frac { \partial m } { \partial H } ) _ { T } }\\{ S = - ( \frac { \partial F } { \partial T } ) _ { H } }\end{array} \right.$ ; confidence 0.670
+
144. https://www.encyclopediaofmath.org/legacyimages/m/m064/m064590/m06459013.png ; $[ 0 , + \infty )$ ; confidence 1.000
  
−
145. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120270/c12027018.png ; $\frac { Vol ( \partial \Omega ) ^ { n } } { Vol ( \Omega ) ^ { n - 1 } } \geq \mathfrak { c } _ { 2 } \cdot \omega ^ { n + 1 } , \quad \mathfrak { c } _ { 2 } = \frac { \alpha ( n - 1 ) ^ { n } } { ( \frac { \alpha ( n ) } { 2 } ) ^ { n - 1 } }$ ; confidence 0.077
+
145. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145010.png ; $f ( x , y )$ ; confidence 1.000
  
−
146. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120020/i1200207.png ; $\times G _ { p + 2 , q } ^ { q - m , p - n + 2 } \left\{ \begin{array} { c } { | \mu + i \tau , \mu - i \tau , - ( \alpha _ { p } ^ { n + 1 } ) , - ( \alpha _ { n } ) } \\ { - ( \beta _ { q } ^ { m + 1 } ) , - ( \beta _ { m } ) } \end{array} \right\}$ ; confidence 0.103
+
146. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130270/a13027066.png ; $\phi ( t ) > 0$ ; confidence 1.000
  
−
147. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120110/n12011066.png ; $\eta ( y ) = \left\{ \begin{array} { l l } { \operatorname { sup } \{ \xi ( x ) : x \in R ^ { n } , \psi ( x ) = y \} , } & { \psi ^ { - 1 } ( y ) \neq \emptyset } \\ { 0 , } & { \psi ^ { - 1 } ( y ) = \emptyset } \end{array} \right.$ ; confidence 0.208
+
147. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012042.png ; $\{ 21 \}$ ; confidence 1.000
  
−
148. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230135.png ; $\frac { ( - 1 ) ^ { ( k - 1 ) l } } { ( k - 1 ) ! ( 1 - 1 ) ! 2 ! } \times \times \sum _ { \sigma } \operatorname { sign } \sigma K ( L ( [ X _ { \sigma 1 } , X _ { \sigma 2 } ] , X _ { \sigma 3 } , \ldots ) , X _ { \sigma ( 1 + 2 ) , \ldots } )$ ; confidence 0.149
+
148. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120110/p1201105.png ; $10$ ; confidence 1.000
  
−
149. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c12026057.png ; $V _ { j } ^ { n } \leq \operatorname { max } ( \operatorname { max } _ { 0 \leq j \leq J } V _ { j } ^ { 0 } , \operatorname { max } _ { 0 \leq m \leq n } V _ { 0 } ^ { m } , \operatorname { max } _ { 0 \leq m \leq n } V _ { j } ^ { m } )$ ; confidence 0.452
+
149. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005086.png ; $\lambda > \beta$ ; confidence 1.000
  
−
150. 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
+
150. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130220/m13022022.png ; $171$ ; confidence 1.000
  
−
151. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120300/b12030073.png ; $\sigma ( A ) = \sigma _ { Bloch } = \cup _ { m = 1 } ^ { \infty } [ \operatorname { min } _ { \eta \in Y ^ { \prime } } \lambda _ { m } ( \eta ) , \operatorname { max } _ { \eta \in Y ^ { \prime } } \lambda _ { m } ( \eta ) ]$ ; confidence 0.644
+
151. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k12012023.png ; $[ - 1 , + \infty ]$ ; confidence 1.000
  
−
152. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230189.png ; $S ( \phi ) = \sum _ { | \alpha | = 0 } ^ { k - 1 } S _ { \alpha i } ^ { \alpha } ( \phi ) \omega _ { \alpha } ^ { \alpha } \wedge ( \frac { \partial } { \partial x _ { i } } - ( \alpha x _ { 1 } \wedge \ldots \wedge d x _ { n } ) )$ ; confidence 0.107
+
152. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046910/h04691024.png ; $2 ( n + 1 )$ ; confidence 1.000
  
−
153. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230134.png ; $\frac { ( - 1 ) ^ { k - 1 } } { ( k - 1 ) ! ( 1 - 1 ) ! 2 ! } \times \times \sum _ { \sigma } \operatorname { sign } \sigma L ( K ( [ X _ { \sigma 1 } , X _ { \sigma 2 } ] , X _ { \sigma 3 } , \ldots ) , X _ { \sigma ( k + 2 ) } , \ldots ) +$ ; confidence 0.791
+
153. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068080/o0680802.png ; $10 ^ { 28 }$ ; confidence 1.000
  
−
154. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010046.png ; $L _ { \gamma , 1 } = \frac { 1 } { \sqrt { \pi } ( \gamma - \frac { 1 } { 2 } ) } \frac { \Gamma ( \gamma + 1 ) } { \Gamma ( \gamma + 1 / 2 ) } ( \frac { \gamma - \frac { 1 } { 2 } } { \gamma + \frac { 1 } { 2 } } ) ^ { \gamma + 1 / 2 }$ ; confidence 0.926
+
154. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007020.png ; $( t ^ { 2 } , t ^ { 3 } )$ ; confidence 1.000
  
−
155. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008092.png ; $= - J - k _ { B } \operatorname { Tn } \{ \operatorname { cosh } ( \frac { H } { k _ { B } T } ) + + [ \operatorname { sinh } ^ { 2 } ( \frac { H } { k _ { B } T } ) + \operatorname { exp } ( - \frac { 4 J } { k _ { B } T } ) ] ^ { 1 / 2 }$ ; confidence 0.503
+
155. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040158.png ; $f = x y$ ; confidence 1.000
  
−
156. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130010/o130010155.png ; $\tilde { \chi } ( \xi ) = \frac { 8 \pi } { \xi ^ { 2 } } \operatorname { lim } _ { \varepsilon \downarrow 0 } \int _ { S ^ { 2 } } A ( \theta ^ { \prime } , \alpha ) v _ { \varepsilon } ( \alpha , \theta ) d \alpha$ ; confidence 0.228
+
156. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130040/g130040157.png ; $G ( n , m )$ ; confidence 1.000
  
−
157. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013021.png ; $= ( \frac { e ^ { \sum _ { 1 } y _ { i } z ^ { - i } } \tau _ { n + 1 } ( x , y - [ z ] ) z ^ { n } } { \tau _ { n } ( x , y ) } | _ { n \in Z } , ( L _ { 1 } , L _ { 2 } ) ( \Psi _ { 1 } ( z ) , \Psi _ { 2 } ( z ) ) = ( z , z ^ { - 1 } ) ( \Psi _ { 1 } ( z ) , \Psi _ { 2 } ( z ) )$ ; confidence 0.149
+
157. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120250/a12025022.png ; $( q + 1 )$ ; confidence 1.000
  
−
158. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110138.png ; $\sum _ { 0 \leq k < N } 2 ^ { - k } \sum _ { | \alpha | + | \beta | = k } \frac { ( - 1 ) ^ { \beta | } } { \alpha ! \beta ! } D _ { \xi } ^ { \alpha } \partial _ { x } ^ { \beta } a D _ { \xi } ^ { \beta } \partial _ { x } ^ { \alpha } b$ ; confidence 0.150
+
158. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016050/b0160505.png ; $f ( \theta )$ ; confidence 1.000
  
−
159. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009057.png ; $= \{ \frac { \beta } { 1 + \alpha ^ { 2 } } \int _ { 0 } ^ { z } \frac { h ( \xi ) - \alpha i } { \xi ^ { 1 + \alpha \beta i / ( 1 + \alpha ^ { 2 } ) } } g ( \xi ) ^ { \beta / ( 1 + \alpha ^ { 2 } ) } d \xi \} ^ { ( 1 + \alpha i ) / \beta }$ ; confidence 0.175
+
159. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130020/s13002048.png ; $f ( u ) = 1$ ; confidence 1.000
  
−
160. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130250/b13025065.png ; $\frac { 1 } { \operatorname { sin } ^ { 2 } \omega } = \frac { 1 } { \operatorname { sin } ^ { 2 } \alpha } + \frac { 1 } { \operatorname { sin } ^ { 2 } \beta } + \frac { 1 } { \operatorname { sin } ^ { 2 } \gamma }$ ; confidence 0.999
+
160. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230156.png ; $( n - i ) \times ( n - i )$ ; confidence 1.000
  
−
161. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230133.png ; $+ \frac { ( - 1 ) ^ { k ! } } { ( k - 1 ) ! ! } \sum _ { \sigma } \operatorname { sign } \sigma \times \times K ( [ L ( X _ { \sigma 1 } , \ldots , X _ { \sigma 1 } ) , X _ { \sigma ( 1 + 1 ) } ] , X _ { \sigma ( 1 + 2 ) } , \ldots ) +$ ; confidence 0.107
+
161. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130110/d13011027.png ; $2 ^ { 4 }$ ; confidence 1.000
  
−
162. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015047.png ; $\left\{ \begin{array} { l } { \Delta u + \alpha u = 0 \quad \text { in } \Omega } \\ { \frac { \partial u } { \partial n } = 0 \text { and } u = 1 \quad \text { on } \partial \Omega } \end{array} \right.$ ; confidence 0.733
+
162. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012057.png ; $\lambda ( x , y )$ ; confidence 1.000
  
−
163. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130250/b13025055.png ; $\frac { \overline { \Omega } \Omega ^ { \prime } } { 2 \operatorname { sin } \omega } = \overline { O \Omega } = \overline { O \Omega ^ { \prime } } = R \sqrt { 1 - 4 \operatorname { sin } ^ { 2 } \omega }$ ; confidence 0.871
+
163. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057780/l05778080.png ; $20$ ; confidence 1.000
  
−
164. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001010.png ; $\frac { \partial ^ { 2 } u ^ { \prime } } { \partial x _ { 1 } ^ { \prime } \partial x _ { 2 } ^ { \prime } } - \frac { \partial ^ { 2 } u ^ { \prime } } { \partial x _ { 2 } ^ { \prime } \partial x _ { 1 } ^ { \prime } } = 0$ ; confidence 0.984
+
164. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c130070117.png ; $\delta ( P ) = 0$ ; confidence 1.000
  
−
165. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008088.png ; $\Delta ( z _ { 1 } , z _ { 2 } ) = \operatorname { det } \left[ \begin{array} { c c } { E _ { 1 } z _ { 1 } - A _ { 1 } } & { E _ { 2 } z _ { 2 } - A _ { 2 } } \\ { E _ { 3 } z _ { 1 } - A _ { 3 } } & { E _ { 4 } z _ { 2 } - A 4 } \end{array} \right] =$ ; confidence 0.515
+
165. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130030/h13003034.png ; $q ( 0 ) = 1$ ; confidence 1.000
  
−
166. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130080/i13008028.png ; $X ^ { \prime \prime } = L _ { 1 } ^ { \prime \prime } \cap L _ { 2 } ^ { \prime \prime } = L _ { 2 } ^ { \prime \prime } \cap L _ { 3 } ^ { \prime \prime } = L _ { 1 } ^ { \prime \prime } \cap L _ { 3 } ^ { \prime \prime }$ ; confidence 0.831
+
166. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018055.png ; $\lambda \neq 1$ ; confidence 1.000
  
−
167. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120190/m12019030.png ; $= \pi ^ { 2 } \sqrt { \frac { \pi } { 2 } } \int _ { 0 } ^ { \infty } \tau \frac { \operatorname { sinh } ( \pi \tau ) } { \operatorname { cosh } ^ { 3 } ( \pi \tau ) } P _ { i \tau - 1 / 2 } ( x ) F ( \tau ) G ( \tau ) d \tau$ ; confidence 0.627
+
167. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130060/a130060105.png ; $( 0,1 )$ ; confidence 1.000
  
−
168. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120130/t12013020.png ; $= ( \frac { e ^ { \sum _ { 1 } ^ { \infty } x _ { i } ^ { i } z ^ { i } } \tau _ { n } ( x - [ z ^ { - 1 } ] , y ) z ^ { n } } { \tau _ { n } ( x , y ) } | _ { n \in Z } , \Psi _ { 2 } ( z ) = e ^ { \sum _ { 1 } ^ { \infty } y _ { i } z ^ { - i } } S _ { 2 } \chi ( z ) =$ ; confidence 0.338
+
168. https://www.encyclopediaofmath.org/legacyimages/n/n130/n130070/n13007023.png ; $[ - \infty , \infty ]$ ; confidence 1.000
  
−
169. https://www.encyclopediaofmath.org/legacyimages/d/d130/d130080/d13008078.png ; $\operatorname { lim } _ { \mu \rightarrow \alpha } [ \rho ( \lambda , \mu ) - \rho ( 0 , \mu ) ] = \frac { 1 } { 2 } \operatorname { log } \frac { | 1 - \lambda \overline { a } ^ { 2 } } { 1 - | \lambda | ^ { 2 } }$ ; confidence 0.594
+
169. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t120200245.png ; $3 ( 4 )$ ; confidence 1.000
  
−
170. https://www.encyclopediaofmath.org/legacyimages/j/j130/j130020/j13002059.png ; $P ( X \leq \lambda - t ) \leq \operatorname { exp } ( - \frac { \phi ( - t / \lambda ) \lambda ^ { 2 } } { \overline { \Delta } } ) \leq \operatorname { exp } ( - \frac { t ^ { 2 } } { 2 \overline { \Delta } } )$ ; confidence 0.591
+
170. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120210/s12021024.png ; $\lambda \leq \mu$ ; confidence 1.000
  
−
171. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006070.png ; $\operatorname { det } ( \lambda _ { 1 } \sigma _ { 2 } - \lambda _ { 2 } \sigma _ { 1 } + \gamma ) = \operatorname { det } ( \lambda _ { 1 } \sigma _ { 2 } - \lambda _ { 2 } \sigma _ { 1 } + \overline { \gamma } )$ ; confidence 0.644
+
171. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012047.png ; $y = 0$ ; confidence 1.000
  
−
172. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120090/b12009054.png ; $= \{ \frac { m } { 1 + \alpha ^ { 2 } } \int _ { 0 } ^ { z } \frac { p _ { 1 } ( s ) - \alpha i } { s ^ { 1 - \frac { m } { 1 + \alpha i } } } e ^ { \frac { m } { 1 + \alpha ^ { 2 } } \int _ { 0 } ^ { s } \frac { p _ { 0 } ( t ) - 1 } { t } d t } d s \}$ ; confidence 0.221
+
172. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130180/m130180120.png ; $\mu ( 0,1 ) + 1$ ; confidence 1.000
  
−
173. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120230/d120230127.png ; $R = \left( \begin{array} { l l } { R _ { 11 } } & { R _ { 12 } } \\ { R _ { 21 } } & { R _ { 22 } } \end{array} \right) , F = \left( \begin{array} { l l } { F _ { 1 } } & { 0 } \\ { F _ { 2 } } & { F _ { 3 } } \end{array} \right)$ ; confidence 0.347
+
173. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120110/p12011020.png ; $4$ ; confidence 1.000
  
−
174. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120280/d120280149.png ; $\overline { u } ( z ) = \int _ { \partial D _ { m } } w ( \zeta ) \frac { \sum _ { k = 1 } ^ { n } ( - 1 ) ^ { k - 1 } ( \overline { \zeta } _ { k } - z _ { k } ) d \overline { \zeta } [ k ] \wedge d \zeta } { | \zeta - z | ^ { 2 n } }$ ; confidence 0.850
+
174. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130300/b13030064.png ; $n\geq 4381$ ; confidence 1.000
  
−
175. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230125.png ; $\frac { - 1 } { k ! ( 1 - 1 ) ! } \times \times \sum _ { \sigma } \operatorname { sign } \sigma \omega ( [ K ( X _ { \sigma 1 } , \ldots , X _ { \sigma k } ) , X _ { \sigma ( k + 1 ) } ] , X _ { \sigma ( k + 2 ) } , \ldots )$ ; confidence 0.504
+
175. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090206.png ; $\mu - \lambda$ ; confidence 1.000
  
−
176. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f12023052.png ; $\frac { 1 } { ( k + 1 ) ! ( 1 - 1 ) ! } \times \times \sum _ { \sigma \in S _ { k + 1 } } \operatorname { sign } \sigma . \omega ( K ( X _ { \sigma 1 } , \ldots , X _ { \sigma ( k + 1 ) } ) , X _ { \sigma ( k + 2 ) } , \ldots )$ ; confidence 0.423
+
176. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120130/w12013020.png ; $( A + i ) ^ { - 1 } - ( B + i ) ^ { - 1 }$ ; confidence 1.000
  
−
177. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001028.png ; $= - \frac { \partial u } { \partial \eta } + \frac { 2 } { \lambda } \operatorname { sin } ( \frac { u ( \xi , \eta ) - u ^ { \prime } ( \xi ^ { \prime } ( \xi , \eta ) , \eta ^ { \prime } ( \xi , \eta ) ) } { 2 } )$ ; confidence 0.967
+
177. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012041.png ; $\{ 1 ( 11 ) \}$ ; confidence 1.000
  
−
178. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008092.png ; $\left.\begin{array} { l l } { E _ { l } } & { 0 } \\ { E _ { 3 } } & { 0 } \end{array} \right] T _ { p , q - 1 } + \left[ \begin{array} { l l } { 0 } & { E _ { 2 } } \\ { 0 } & { E _ { 4 } } \end{array} \right] T _ { p - 1 , q } +$ ; confidence 0.596
+
178. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120250/a12025014.png ; $( q + 2 )$ ; confidence 1.000
  
−
179. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120030/h12003017.png ; $| d \varphi | ^ { 2 } ( x ) = g ^ { i j } ( x ) h _ { \alpha \beta } ( \varphi ( x ) ) \cdot \frac { \partial \varphi ^ { \alpha } } { \partial x ^ { i } } \frac { \partial \varphi ^ { \beta } } { \partial x ^ { j } }$ ; confidence 0.882
+
179. https://www.encyclopediaofmath.org/legacyimages/c/c020/c020850/c02085023.png ; $\mu = 0$ ; confidence 1.000
  
−
180. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120130/h12013050.png ; $\omega _ { 1 } * \omega _ { 2 } ( t ) = \left\{ \begin{array} { l l } { \omega _ { 1 } ( t ) } & { \text { for } 0 \leq t \leq 1 / 2 } \\ { \omega ( 2 t - 1 ) } & { \text { for } 1 / 2 \leq t \leq 1 } \end{array} \right.$ ; confidence 0.722
+
180. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120130/p12013050.png ; $[ 1 , \infty )$ ; confidence 1.000
  
−
181. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130050/o13005045.png ; $\Theta = \left( \begin{array} { c c c } { A } & { } & { K } & { J } \\ { \mathfrak { H } _ { + } \subset \mathfrak { H } \subset \mathfrak { H } _ { - } } & { \square } & { \mathfrak { E } } \end{array} \right)$ ; confidence 0.446
+
181. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130510/s13051015.png ; $g ( u ) = 0$ ; confidence 1.000
  
−
182. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230171.png ; $\sum _ { | \alpha | = 0 } ^ { k } ( \frac { \partial L } { \partial y _ { \alpha } ^ { \alpha } \circ \sigma ^ { k } } ) ( \frac { \partial } { \partial x } ) ^ { \alpha } ( Z ^ { \alpha } \circ \sigma ) \Delta$ ; confidence 0.391
+
182. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022920/c022920100.png ; $| \zeta | > 1$ ; confidence 1.000
  
−
183. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120060/l12006061.png ; $\operatorname { Im } h ^ { I I } ( z ) = \operatorname { Im } z ( \int _ { 0 } ^ { \infty } \frac { | ( V \phi | \lambda \rangle | ^ { 2 } } { | z - \lambda | ^ { 2 } } d \lambda ) + 2 \pi \operatorname { Re } W ( z )$ ; confidence 0.861
+
183. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s130620135.png ; $\lambda,$ ; confidence 1.000
  
−
184. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120020/o12002016.png ; $= 8 \pi ^ { 2 } \int _ { - \infty } ^ { \infty } \tau \operatorname { sinh } ( \pi \tau ) | \frac { \Gamma ( c - a + \frac { i \tau } { 2 } ) } { \Gamma ( a + \frac { i \tau } { 2 } ) } | ^ { 2 } | f ( \tau ) | ^ { 2 } d \tau$ ; confidence 0.436
+
184. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120110/p12011012.png ; $120$ ; confidence 1.000
  
−
185. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120320/b12032093.png ; $\frac { 1 } { p } : = \frac { \operatorname { log } a _ { \mathfrak { M } } } { \operatorname { log } m } = \frac { \operatorname { log } a _ { R } } { \operatorname { log } n } \text { for all } m , n \geq 2$ ; confidence 0.063
+
185. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a01021052.png ; $f ( z )$ ; confidence 1.000
  
−
186. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f13024029.png ; $[ \left( \begin{array} { l } { a } \\ { b } \end{array} \right) \left( \begin{array} { l } { c } \\ { d } \end{array} \right) \left( \begin{array} { l } { e } \\ { f } \end{array} \right) ] : =$ ; confidence 0.645
+
186. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120040/a1200409.png ; $( 0 , \infty )$ ; confidence 1.000
  
−
187. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230124.png ; $= \frac { 1 } { k ! ! ! } \sum _ { \sigma } \operatorname { sign } \sigma \times \times L ( K _ { \sigma 1 } , \ldots , X _ { \sigma k } ) ) ( \omega ( X _ { \sigma ( k + 1 ) } , \ldots , X _ { \sigma ( k + 1 ) } ) ) +$ ; confidence 0.142
+
187. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040202.png ; $( 1 < p < \infty )$ ; confidence 1.000
  
−
188. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120050/l12005018.png ; $f ( x ) = \operatorname { lim } _ { N \rightarrow \infty } \frac { 4 } { \pi ^ { 2 } } \int _ { 0 } ^ { N } \operatorname { cosh } ( \pi \tau ) \operatorname { Im } K _ { 1 / 2 + i \tau } ( x ) F ( \tau ) d \tau$ ; confidence 0.580
+
188. https://www.encyclopediaofmath.org/legacyimages/k/k130/k130050/k13005020.png ; $10 ^ { 19 }$ ; confidence 1.000
  
−
189. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021024.png ; $\ldots \rightarrow D _ { 2 } \stackrel { \delta _ { 2 } } { \rightarrow } D _ { 1 } \stackrel { \delta _ { 1 } } { \rightarrow } D _ { 0 } \stackrel { \delta _ { 0 } } { \rightarrow } M \rightarrow 0$ ; confidence 0.319
+
189. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016420/b01642029.png ; $[ y ]$ ; confidence 1.000
  
−
190. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120040/c12004070.png ; $\times [ CF ( \zeta - z , w ) - \frac { ( n - 1 ) ! ( | \zeta | ^ { 2 m } - \langle \overline { \zeta } , z | ^ { m } ) ^ { n } } { [ 2 \pi i | \zeta | ^ { 2 m } \{ \overline { \zeta } , \zeta - z \} ] ^ { N } } \sigma _ { 0 } ]$ ; confidence 0.191
+
190. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120100/f12010056.png ; $[ 0 , \pi ]$ ; confidence 1.000
  
−
191. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230132.png ; $+ \frac { - 1 } { k ! ( 1 - 1 ) ! } \sum _ { \sigma } \operatorname { sign } \sigma \times \times L ( [ K ( X _ { \sigma 1 } , \ldots , X _ { \sigma k } ) , X _ { \sigma ( k + 1 ) } ] , X _ { \sigma ( k + 2 ) } , \ldots )$ ; confidence 0.291
+
191. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007014.png ; $21$ ; confidence 1.000
  
−
192. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120050/l12005017.png ; $f ( x ) = \operatorname { lim } _ { N \rightarrow \infty } \frac { 4 } { \pi ^ { 2 } } \int _ { 0 } ^ { N } \operatorname { cosh } ( \pi \tau ) \operatorname { Re } K _ { 1 / 2 + i \tau } ( x ) F ( \tau ) d \tau$ ; confidence 0.737
+
192. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110100/b110100184.png ; $\sqrt { n }$ ; confidence 1.000
  
−
193. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120270/s12027032.png ; $A _ { s } ^ { + } = \left\{ \begin{array} { l l } { f : } & { f \in A _ { s } } \\ { f : } & { f ^ { ( s ) } \text { has no change of } \operatorname { sign } \operatorname { in } ( a , b ) } \end{array} \right\}$ ; confidence 0.358
+
193. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120110/h1201104.png ; $\int _ { \Gamma } f ( z ) d z = 0$ ; confidence 1.000
  
−
194. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s13062056.png ; $\left\{ \begin{array} { l l } { \phi ( 0 , \lambda ) = 1 , } & { \theta ( 0 , \lambda ) = 0 } \\ { \phi ^ { \prime } ( 0 , \lambda ) = 0 , } & { \theta ^ { \prime } ( 0 , \lambda ) = 1 } \end{array} \right.$ ; confidence 0.412
+
194. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110170/a1101703.png ; $t = 0$ ; confidence 1.000
  
−
195. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011058.png ; $R _ { n } \stackrel { \omega } { \rightarrow } R \text { and } \operatorname { lim } _ { \varepsilon \rightarrow 0 } \operatorname { sup } _ { n } \int _ { 0 } ^ { \varepsilon } z R _ { n } ( d z ) = 0$ ; confidence 0.236
+
195. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016720/b01672015.png ; $( n , n - 1 )$ ; confidence 1.000
  
−
196. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b120430116.png ; $\varepsilon \left( \begin{array} { l l } { \alpha } & { \beta } \\ { \gamma } & { \delta } \end{array} \right) = \left( \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right)$ ; confidence 0.819
+
196. https://www.encyclopediaofmath.org/legacyimages/b/b130/b130090/b13009036.png ; $m ( \xi ) ^ { - 1 }$ ; confidence 1.000
  
−
197. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c120080100.png ; $T _ { 10 } = \left[ \begin{array} { c c } { A _ { 1 } } & { A _ { 2 } } \\ { 0 } & { 0 } \end{array} \right] , T _ { 01 } = \left[ \begin{array} { c c } { 0 } & { 0 } \\ { A _ { 3 } } & { A _ { 4 } } \end{array} \right]$ ; confidence 0.564
+
197. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120060/a12006039.png ; $f ( t )$ ; confidence 1.000
  
−
198. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120020/d1200201.png ; $( P ) v ^ { * } = \left\{ \begin{array} { c c } { \operatorname { min } } & { c ^ { T } x } \\ { \text { s.t. } } & { A _ { 1 } x \leq b _ { 1 } } \\ { } & { A _ { 2 } x \leq b _ { 2 } } \\ { x \geq 0 } \end{array} \right.$ ; confidence 0.129
+
198. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120110/p1201104.png ; $19$ ; confidence 1.000
  
−
199. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120090/e12009026.png ; $\frac { \partial F _ { \mu \nu } } { \partial x ^ { \sigma } } + \frac { \partial F _ { \nu \sigma } \sigma } { \partial x ^ { \mu } } + \frac { \partial F _ { \sigma \mu } } { \partial x ^ { \nu } } = 0$ ; confidence 0.769
+
199. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130040/c13004030.png ; $= 4 \operatorname { log } 2 + 2 - \frac { 4 } { \pi } ( 2 G + 1 ),$ ; confidence 1.000
  
−
200. https://www.encyclopediaofmath.org/legacyimages/g/g120/g120040/g120040164.png ; $= D _ { t } ^ { m } u + \sum _ { j = 1 } ^ { m } \sum _ { | \alpha | \leq m - j } p _ { j , \alpha } ( t , x ) D _ { t } ^ { j } D _ { x } ^ { \alpha } u = f ( t , x ) , D _ { t } ^ { j } u ( 0 , x ) = u _ { j } ^ { 0 } ( x ) , \quad j = 0 , \ldots , m - 1$ ; confidence 0.410
+
200. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120140/e12014017.png ; $\rho ( f ) > 0$ ; confidence 1.000
  
−
201. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010011.png ; $\left\{ \begin{array} { l l } { \gamma \geq \frac { 1 } { 2 } } & { \text { forn } = 1 } \\ { \gamma > 0 } & { \text { forn } = 2 } \\ { \gamma \geq 0 } & { \text { forn } \geq 3 } \end{array} \right.$ ; confidence 0.191
+
201. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023030/c0230302.png ; $T ( g )$ ; confidence 1.000
  
−
202. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m130140112.png ; $= \{ z : \sum _ { l = 1 } ^ { n } b _ { j } ^ { l } | c _ { l } ^ { p } ( z _ { 1 } - a _ { 1 } ) + \ldots + c _ { l n } ^ { p } ( z _ { n } - a _ { n } ) | ^ { 2 } < r _ { j , k } ^ { 2 } \} , b _ { j } ^ { l } > 0 ; j = 1 , \ldots , n ; k = 1,2 ; p = 1 , \ldots , n$ ; confidence 0.067
+
202. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005071.png ; $- A ( t )$ ; confidence 1.000
  
−
203. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130080/w13008025.png ; $d \omega _ { 3 } ( \lambda ) = \frac { \lambda ^ { g + 1 } - \frac { 1 } { 2 } \sigma _ { 1 } \lambda ^ { g } + \beta _ { 1 } \lambda ^ { g - 1 } + \ldots + \beta _ { g } } { \sqrt { R _ { g } ( \lambda ) } } d \lambda$ ; confidence 0.731
+
203. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012043.png ; $\{ ( 21 ) \}$ ; confidence 1.000
  
−
204. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040538.png ; $\varphi _ { 0 } ^ { 0 } , \ldots , \varphi _ { n _ { 0 } } ^ { 0 } - 1 \supset \psi ^ { 0 } ; \ldots ; \varphi _ { 0 } ^ { m - 1 } , \ldots , \varphi _ { n _ { m - 1 } } ^ { m - 1 } - 1 \supset \psi ^ { m - 1 } \vdash _ { G }$ ; confidence 0.092
+
204. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120180/b12018014.png ; $\alpha = \sqrt { 2 }$ ; confidence 1.000
  
−
205. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b1200106.png ; $\{ x _ { 1 } ^ { \prime } , x _ { 2 } ^ { \prime } , u ^ { \prime } , \frac { \partial u ^ { \prime } } { \partial x _ { 1 } ^ { \prime } } , \frac { \partial u ^ { \prime } } { \partial x _ { 2 } ^ { \prime } } \}$ ; confidence 0.970
+
205. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120160/e12016013.png ; $i = \sqrt { - 1 }$ ; confidence 1.000
  
−
206. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m13014078.png ; $d \overline { \zeta } [ k ] = d \overline { \zeta } _ { 1 } \wedge \ldots \wedge d \overline { \zeta } _ { k - 1 } \wedge d \overline { \zeta } k + 1 \wedge \ldots \wedge d \overline { \zeta }$ ; confidence 0.263
+
206. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012027.png ; $( 3,1 )$ ; confidence 1.000
  
−
207. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006042.png ; $A _ { k } = \left( \begin{array} { c c } { A _ { k } ^ { \prime } } & { 0 } \\ { i \Phi ^ { \prime \prime } \sigma _ { k } \Phi ^ { \prime } } & { A _ { k } ^ { \prime \prime } } \end{array} \right) ( k = 1,2 )$ ; confidence 0.865
+
207. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016430/b0164307.png ; $m + 1$ ; confidence 1.000
  
−
208. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120210/b12021041.png ; $0 \rightarrow D _ { n } \stackrel { \delta _ { n } } { \rightarrow } \ldots \stackrel { \delta _ { 1 } } { \rightarrow } D _ { 0 } \stackrel { \delta _ { 0 } } { \rightarrow } C \rightarrow 0$ ; confidence 0.378
+
208. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120170/c1201703.png ; $\gamma_{00}> 0$ ; confidence 1.000
  
−
209. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120230/f120230131.png ; $= \frac { 1 } { k ! ! ! } \sum _ { \sigma } \operatorname { sign } \sigma \times \times [ K ( X _ { \sigma 1 } , \ldots , X _ { \sigma k } ) , L ( X _ { \sigma ( k + 1 ) } , \ldots , X _ { \sigma ( k + 1 ) } ) ] +$ ; confidence 0.218
+
209. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f1302405.png ; $ \epsilon = \pm 1$ ; confidence 1.000
  
−
210. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140104.png ; $q R ( x ) = \sum _ { j \in Q _ { 0 } } x _ { j } ^ { 2 } - \sum _ { \langle \beta : i \rightarrow j ) \in Q _ { 1 } } x _ { i } x _ { j } + \sum _ { \langle \beta : i \rightarrow j ) \in Q _ { 1 } } x _ { , j } x _ { i } x _ { j }$ ; confidence 0.112
+
210. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120170/b12017014.png ; $( 1 + | \xi | ^ { 2 } ) ^ { \alpha / 2 }$ ; confidence 1.000
  
−
211. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120120/a12012032.png ; $\left. \begin{array} { l } { x \sum _ { j = i } ^ { N } \beta _ { j } v _ { j } } \\ { \text { ject to } \sum _ { j = 1 } ^ { n } \alpha _ { j } v _ { j } \leq \mu _ { i } } \\ { v _ { j } \geq 0 } \end{array} \right.$ ; confidence 0.116
+
211. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018092.png ; $t = 2$ ; confidence 1.000
  
−
212. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130320/a13032058.png ; $( N ) = \frac { \alpha \operatorname { log } ( \frac { 1 - \beta } { \alpha } ) + ( 1 - \alpha ) \operatorname { log } ( \frac { \beta } { 1 - \alpha } ) } { ( p - q ) \operatorname { log } ( q / p ) }$ ; confidence 0.993
+
212. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008059.png ; $H ^ { 1 } ( \Omega )$ ; confidence 1.000
  
−
213. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120080/c12008026.png ; $A _ { 1 } = \left[ \begin{array} { c c c } { A _ { 11 } } & { \dots } & { A _ { 1 m } } \\ { \dots } & { \dots } & { \dots } \\ { A _ { m 1 } } & { \dots } & { A _ { m m } } \end{array} \right] \in C ^ { m n \times m n }$ ; confidence 0.187
+
213. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120150/p12015048.png ; $\partial \Omega$ ; confidence 1.000
  
−
214. https://www.encyclopediaofmath.org/legacyimages/d/d030/d030270/d03027032.png ; $= \frac { 1 } { ( p + 1 ) \pi } \int _ { - \pi } ^ { \pi } [ f ( x + t ) \operatorname { sin } \frac { 2 n + 1 - p } { 2 } t \frac { \operatorname { sin } ( p + 1 ) t / 2 } { 2 \operatorname { sin } ^ { 2 } t / 2 } ] d t$ ; confidence 0.993
+
214. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130070/v13007067.png ; $\alpha = ( 2 \lambda - 1 ) / ( 1 - \lambda ) ^ { 2 }$ ; confidence 1.000
  
−
215. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068170/o06817012.png ; $= 1 - \frac { 2 } { \pi } \sum _ { k = 1 } ^ { \infty } ( - 1 ) ^ { k - 1 } \int _ { ( 2 k - 1 ) \pi } ^ { 2 k \pi } \frac { e ^ { - t ^ { 2 } \lambda / 2 } } { \sqrt { - t \operatorname { sin } t } } d t , \quad \lambda > 0$ ; confidence 0.429
+
215. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120040/b120040140.png ; $\theta \in ( 0,1 )$ ; confidence 1.000
  
−
216. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o13006036.png ; $\mathfrak { V } ^ { \prime } = ( A _ { 1 } ^ { \prime } , A _ { 2 } ^ { \prime } , H ^ { \prime } , \Phi ^ { \prime } , E , \sigma _ { 1 } , \sigma _ { 2 } , \gamma ^ { \prime } , \tilde { \gamma } ^ { \prime } )$ ; confidence 0.556
+
216. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011490/a01149073.png ; $f ^ { \prime } ( x )$ ; confidence 1.000
  
−
217. https://www.encyclopediaofmath.org/legacyimages/q/q120/q120080/q12008039.png ; $\frac { 1 } { 2 ( 1 - \sigma _ { p - 1 } ) ( 1 - \sigma _ { p } ) } [ \sum _ { k = 1 } ^ { q - 1 } \lambda _ { k } b _ { k } ^ { ( 2 ) } + ( 1 - \sigma _ { p - 1 } ) \frac { b _ { q } ^ { ( 2 ) } } { b _ { \gamma } } ] , 1 \leq p \leq q - 1$ ; confidence 0.354
+
217. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120070/k12007016.png ; $f ( \pi - t ) = f ( t )$ ; confidence 1.000
  
−
218. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120230/a12023058.png ; $\times \int _ { \Gamma } f ( \zeta ) ( \frac { \operatorname { grad } \psi } { \langle \operatorname { grad } \psi , \zeta \rangle } ) ^ { q } CF ( \zeta , \operatorname { grad } \psi )$ ; confidence 0.323
+
218. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120130/l12013098.png ; $17$ ; confidence 1.000
  
−
219. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130060/g130060128.png ; $\sigma ( \Omega ( A ) ) = \left\{ \begin{array} { c c } { \text { boundary of } K _ { 1,2 } ( A ) } & { n = 2 } \\ { \cup _ { i , j = 1 , i \neq j } ^ { n } K _ { i , j } ( A ) } & { n \geq 3 } \end{array} \right.$ ; confidence 0.149
+
219. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130050/e13005011.png ; $\Gamma ( \lambda )$ ; confidence 1.000
  
−
220. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120020/i1200202.png ; $f ( x ) = \frac { 1 } { ( \pi x ) ^ { 2 } } \int _ { 0 } ^ { \infty } \tau \operatorname { sinh } ( 2 \pi \tau ) \times x | \Gamma ( \frac { 1 } { 2 } - \mu - i \tau ) | ^ { 2 } W _ { \mu , i \tau } ( x ) F ( \tau ) d$ ; confidence 0.818
+
220. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130100/t13010052.png ; $\operatorname{Hom}_H( T , - )$ ; confidence 1.000
  
−
221. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120050/i12005057.png ; $\operatorname { lim } _ { n \rightarrow \infty } H ( \theta _ { n } , \Theta _ { 0 } ) = 0 , \operatorname { lim } _ { n \rightarrow \infty } n H ^ { 2 } ( \theta _ { n } , \Theta _ { 0 } ) = \infty$ ; confidence 0.856
+
221. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010220/a01022098.png ; $( p + 1 )$ ; confidence 1.000
  
−
222. https://www.encyclopediaofmath.org/legacyimages/j/j120/j120020/j120020170.png ; $c E [ | U _ { \tau } ^ { * } | ^ { N } ] \leq \operatorname { sup } _ { 0 < r < 1 } \int _ { \partial D } | f ( r e ^ { i \vartheta } ) | ^ { p } \frac { d \vartheta } { 2 \pi } \leq C E [ | U _ { \tau } ^ { * } | ^ { p } ]$ ; confidence 0.092
+
222. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120140/t120140102.png ; $\sigma ( T _ { \phi } )$ ; confidence 1.000
  
−
223. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m1201509.png ; $\left( \begin{array} { c c c } { x _ { 11 } ( . ) } & { \dots } & { x _ { 1 n } ( . ) } \\ { \vdots } & { \square } & { \vdots } \\ { x _ { p 1 } ( . ) } & { \dots } & { x _ { p n ( \lambda } ) } \end{array} \right)$ ; confidence 0.161
+
223. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012040.png ; $\{ 111 \}$ ; confidence 1.000
  
−
224. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130070/w13007046.png ; $\operatorname { ch } V ( \lambda ) = \frac { \sum _ { w \in W } ( - 1 ) ^ { l ( w ) } e ^ { w ( \lambda + \rho ) - \rho } } { \prod _ { \alpha \in \Delta ^ { - } ( 1 - e ^ { \alpha } ) ^ { d i m g _ { \alpha } } } }$ ; confidence 0.113
+
224. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120030/b12003011.png ; $A , B > 0$ ; confidence 1.000
  
−
225. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130110/w13011045.png ; $\operatorname { lim } _ { N \rightarrow \infty } \operatorname { sup } _ { \varepsilon } \| \frac { 1 } { N } \sum _ { n = 1 } ^ { N } f ( T ^ { n } x ) g ( S ^ { n } y ) e ^ { 2 \pi i n \varepsilon } \| = 0$ ; confidence 0.914
+
225. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120190/w12019035.png ; $f ( x , p )$ ; confidence 1.000
  
−
226. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c120010158.png ; $f ( z ) = \frac { 1 } { ( 2 \pi i ) ^ { N } } \int _ { \partial \Omega } \frac { f ( \zeta ) \sigma \wedge ( \overline { \partial } \sigma ) ^ { n - 1 } } { ( 1 + \langle z , \sigma \} ) ^ { N } } , z \in E$ ; confidence 0.319
+
226. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120020/c12002020.png ; $\int _ { 0 } ^ { \infty }$ ; confidence 1.000
  
−
227. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120050/i12005058.png ; $0 < \operatorname { liminf } _ { x \rightarrow \infty } \beta ( n , \alpha , \theta ; T ) \leq \operatorname { limsup } _ { n \rightarrow \infty } \beta ( n , \alpha , \theta ; T ) < 1$ ; confidence 0.693
+
227. https://www.encyclopediaofmath.org/legacyimages/s/s120/s120330/s12033013.png ; $( 111,11,1 )$ ; confidence 1.000
  
−
228. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066960/n0669604.png ; $\frac { e ^ { - ( x + \lambda ) / 2 } x ^ { ( n - 2 ) / 2 } } { 2 ^ { x / 2 } \Gamma ( 1 / 2 ) } \sum _ { r = 0 } ^ { \infty } \frac { \lambda ^ { r } x ^ { r } } { ( 2 r ) ! } \frac { \Gamma ( r + 1 / 2 ) } { \Gamma ( r + n / 2 ) }$ ; confidence 0.200
+
228. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120050/d12005014.png ; $f ( x ) = g ( x )$ ; confidence 1.000
  
−
229. 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
+
229. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025830/c02583036.png ; $u ( T ) = 0$ ; confidence 1.000
  
−
230. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120010/b12001026.png ; $= \frac { \partial u } { \partial \xi } - 2 \lambda \operatorname { sin } ( \frac { u ( \xi , \eta ) + u ^ { \prime } ( \xi ^ { \prime } ( \xi , \eta ) , \eta ^ { \prime } ( \xi , \eta ) ) } { 2 } )$ ; confidence 0.990
+
230. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120150/d12015056.png ; $4 p ^ { 2 }$ ; confidence 1.000
  
−
231. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130010/i13001052.png ; $\overline { d } _ { ( 1 ^ { n } ) } \preceq \overline { d } _ { ( 2,1 ^ { n - 2 } ) } \preceq \ldots \preceq \overline { d } _ { ( k , 1 ^ { n - k } ) } \preceq \ldots \preceq \overline { d } _ { ( n ) }$ ; confidence 0.240
+
231. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120120/d12012011.png ; $A G$ ; confidence 1.000
  
−
232. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130130/p13013010.png ; $M ( A _ { n } ) \cong \left\{ \begin{array} { l l } { Z _ { 2 } } & { \text { if } n \geq 4 , n \neq 6,7 } \\ { Z _ { 6 } } & { \text { if } n = 6,7 } \\ { \{ e \} } & { \text { if } n < 4 } \end{array} \right.$ ; confidence 0.588
+
232. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a13004027.png ; $\Gamma ^ { \prime } \subseteq \Gamma$ ; confidence 1.000
  
−
233. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130450/s1304507.png ; $r s = \frac { \sum _ { i = 1 } ^ { n } ( R _ { i } - \overline { R } ) ( S _ { i } - S ) } { \sqrt { \sum _ { i = 1 } ^ { n } ( R _ { i } - \overline { R } ) ^ { 2 } \sum _ { i = 1 } ^ { n } ( S _ { i } - \overline { S } ) ^ { 2 } } } =$ ; confidence 0.316
+
233. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130620/s13062022.png ; $y ( 0 , \lambda ) = 0$ ; confidence 1.000
  
−
234. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120070/w1200705.png ; $\{ f , g \} = \sum ( \frac { \partial f } { \partial p _ { j } } \frac { \partial g } { \partial q _ { j } } - \frac { \partial f } { \partial q _ { j } } \frac { \partial g } { \partial p _ { j } } )$ ; confidence 0.901
+
234. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020016.png ; $p ( T ) = 0$ ; confidence 1.000
  
−
235. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120010/c120010154.png ; $f ( z ) = \frac { 1 } { ( 2 \pi i ) ^ { n } } \int _ { \partial \Omega } \frac { f ( \zeta ) s \wedge ( \overline { \partial } s ) ^ { n - 1 } } { \langle \zeta - z , s \rangle ^ { \lambda } } , z \in E$ ; confidence 0.246
+
235. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120100/b12010032.png ; $G ( t )$ ; confidence 1.000
  
−
236. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130040/i13004036.png ; $\operatorname { sup } _ { 0 < | y | < \pi } | \int _ { - \infty } ^ { \infty } \varphi ( x ) e ^ { - i y x } d x - \sum _ { - \infty } ^ { \infty } \varphi ( k ) e ^ { - i k x } | \leq C \| \varphi \| _ { B V }$ ; confidence 0.347
+
236. https://www.encyclopediaofmath.org/legacyimages/c/c025/c025140/c025140158.png ; $\Gamma ( E )$ ; confidence 1.000
  
−
237. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120190/m1201908.png ; $\times \operatorname { lim } _ { N \rightarrow \infty } \int _ { 1 / N } ^ { N } \tau \operatorname { tanh } ( \frac { \pi \tau } { 2 } ) P _ { ( i \tau - 1 ) / 2 } ( 2 x ^ { 2 } + 1 ) F ( \tau ) d \tau$ ; confidence 0.852
+
237. https://www.encyclopediaofmath.org/legacyimages/l/l057/l057000/l057000101.png ; $f ( 0 , x ) = 0$ ; confidence 1.000
  
−
238. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520446.png ; $| f ( V ) | \leq \mathfrak { c } _ { 1 } | V | ^ { \gamma } \quad \text { and } \quad | \sum _ { j = 1 } ^ { n } \frac { \partial f } { \partial v _ { j } } \tilde { \phi } ; | > c _ { 2 } | V | ^ { \gamma + m }$ ; confidence 0.105
+
238. https://www.encyclopediaofmath.org/legacyimages/b/b015/b015540/b01554032.png ; $( 0,0 )$ ; confidence 1.000
  
−
239. https://www.encyclopediaofmath.org/legacyimages/s/s090/s090670/s09067011.png ; $\left. \begin{array} { l l l } { \square } & { C } & { \square } \\ { \square _ { f } } & { \swarrow } & { \square } & { \searrow _ { g } } \\ { A } & { } & { \square } & { B } \end{array} \right.$ ; confidence 0.169
+
239. https://www.encyclopediaofmath.org/legacyimages/l/l110/l110030/l11003090.png ; $P ( A ) = 0$ ; confidence 1.000
  
−
240. https://www.encyclopediaofmath.org/legacyimages/v/v110/v110060/v1100608.png ; $\Delta ^ { 2 } u \equiv \frac { \partial ^ { 4 } u } { \partial x ^ { 4 } } + 2 \frac { \partial ^ { 4 } u } { \partial x ^ { 2 } \partial y ^ { 2 } } + \frac { \partial ^ { 4 } u } { \partial y ^ { 4 } }$ ; confidence 0.993
+
240. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t12006015.png ; $\gamma = ( 3 \pi ^ { 2 } ) ^ { 2 / 3 }$ ; confidence 1.000
  
−
241. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120020/b12002016.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { n ^ { 1 / 4 } } { ( \operatorname { log } n ) ^ { 1 / 2 } } \frac { \| \alpha _ { n } + \beta _ { n } \| } { \| \alpha _ { n } \| ^ { 1 / 2 } } = 1$ ; confidence 0.827
+
241. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s130540101.png ; $G = E ( R )$ ; confidence 1.000
  
−
242. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120060/m1200603.png ; $\frac { \partial \vec { B } } { \partial t } = \operatorname { rot } [ \vec { v } \times \vec { B } ] , \frac { \partial \rho } { \partial t } + \operatorname { div } \rho \vec { v } = 0$ ; confidence 0.955
+
242. https://www.encyclopediaofmath.org/legacyimages/b/b016/b016420/b01642049.png ; $0 < p < 1$ ; confidence 1.000
  
−
243. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120260/c1202601.png ; $\left\{ \begin{array} { l } { u _ { t } - u _ { k x } = 0 , \quad 0 < x < 1,0 < t } \\ { u ( 0 , t ) = u ( 1 , t ) = 0 , \quad 0 < t } \\ { u ( x , 0 ) = u ^ { 0 } ( x ) , \quad 0 \leq x \leq 1 } \end{array} \right.$ ; confidence 0.527
+
243. https://www.encyclopediaofmath.org/legacyimages/n/n067/n067520/n067520326.png ; $A =$ ; confidence 1.000
  
−
244. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008093.png ; $m = \frac { \operatorname { sinh } ( \frac { H } { k _ { B } T } ) } { [ \operatorname { sinh } ^ { 2 } ( \frac { H } { k _ { B } T } ) + \operatorname { exp } ( - \frac { 4 J } { k _ { B } T } ) ] ^ { 1 / 2 } }$ ; confidence 0.975
+
244. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130650/s13065039.png ; $\mu ^ { \prime } > 0$ ; confidence 1.000
  
−
245. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120130/m12013092.png ; $\left. \begin{array} { l } { \frac { d N } { d t } = N ( - 2 \alpha N - \delta F + \lambda ) } \\ { \frac { d F } { d t } = F ( 2 \beta N + \gamma F ^ { p } - \varepsilon ) } \end{array} \right.$ ; confidence 0.974
+
245. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018086.png ; $10 ^ { - 16 }$ ; confidence 1.000
  
−
246. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130140/p13014053.png ; $\psi ( \gamma ) : = \frac { 2 } { \pi ^ { 2 } } \int _ { 0 } ^ { \operatorname { min } ( 1,1 / \gamma ) } \frac { \operatorname { arccos } ( \gamma t ) } { \sqrt { 1 - t ^ { 2 } } } d t , \gamma > 0$ ; confidence 0.680
+
246. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130140/s13014036.png ; $\lambda = ( 4,2,1 )$ ; confidence 1.000
  
−
247. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130050/v130050120.png ; $( u _ { m } ( v ) ) _ { n } ( w ) = \sum _ { i \geq 0 } ( - 1 ) ^ { i } \left( \begin{array} { c } { m } \\ { i } \end{array} \right) ( u _ { m } - i ( v _ { n } + i ( w ) ) - ( - 1 ) ^ { m } v _ { m + n } - i ( u _ { i } ( w ) ) )$ ; confidence 0.155
+
247. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120210/c120210120.png ; $\Gamma ( \theta )$ ; confidence 1.000
  
−
248. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130080/z13008038.png ; $= \frac { ( \alpha + 1 ) _ { k + l } } { ( \alpha + 1 ) _ { k } ( \alpha + 1 ) _ { l } } \sum _ { j = 0 } ^ { \operatorname { min } ( k , l ) } \frac { ( - k ) _ { j } ( - l ) } { ( - k - l - \alpha ) j ! } r ^ { k + l - 2 j }$ ; confidence 0.187
+
248. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120110/a12011023.png ; $n + 3$ ; confidence 1.000
  
−
249. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130130/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
+
249. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120510/b12051024.png ; $10 ^ { - 4 }$ ; confidence 1.000
  
−
250. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120020/b12002022.png ; $\operatorname { limsup } _ { n \rightarrow \infty } \pm \frac { n ^ { 1 / 4 } } { ( \operatorname { log } \operatorname { log } n ) ^ { 3 / 4 } } ( \alpha _ { n } ( t ) + \beta _ { n } ( t ) ) =$ ; confidence 0.985
+
250. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130070/m13007016.png ; $p ^ { 0 } > 0$ ; confidence 1.000
  
−
251. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020079.png ; $\operatorname { max } _ { r = 1 , \ldots , c n } \frac { | z _ { 1 } ^ { \prime } + \ldots + z _ { n } ^ { \prime } | } { \operatorname { min } _ { k = 1 , \ldots , n } | z _ { k } ^ { \prime } | } \geq m$ ; confidence 0.067
+
251. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007025.png ; $b = 3$ ; confidence 1.000
  
−
252. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110155.png ; $= 2 ^ { 2 n k } \int _ { \Phi ^ { 2 k } } ^ { \alpha _ { 1 } ( Y _ { 1 } ) \ldots \alpha _ { 2 k } ( Y _ { 2 k } ) \cdot \alpha _ { 2 k + 1 } } ( X + \sum _ { 1 \leq j < l \leq 2 k } ( - 1 ) ^ { j + l } ( Y _ { j } - Y _ { l } ) )$ ; confidence 0.131
+
252. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016092.png ; $\alpha + \beta$ ; confidence 1.000
  
−
253. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130080/z13008045.png ; $= \frac { ( - 1 ) ^ { k + l } } { ( \alpha + 1 ) _ { k + l } } ( 1 - z z ) ^ { - \alpha } ( \frac { \partial } { \partial z } ) ^ { l } ( \frac { \partial } { \partial z } ) ^ { k } ( 1 - z z ) ^ { k + l + \alpha }$ ; confidence 0.924
+
253. https://www.encyclopediaofmath.org/legacyimages/h/h046/h046320/h04632074.png ; $B ( z )$ ; confidence 1.000
  
−
254. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120150/b120150168.png ; $f _ { i } ( \vartheta ) = \frac { \operatorname { exp } ( g ( \vartheta ) + h ( i ) ) } { 1 + \operatorname { exp } ( g ( \vartheta ) + h ( i ) ) } , \vartheta \in \Theta , i = 1 , \ldots , n$ ; confidence 0.726
+
254. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130070/c13007018.png ; $\left( \frac { 1 - t ^ { 2 } } { 1 + t ^ { 2 } } , \frac { 2 t } { 1 + t ^ { 2 } } \right).$ ; confidence 1.000
  
−
255. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120560/b1205605.png ; $h = h ( M ) = \operatorname { inf } _ { \Gamma } \frac { \operatorname { Vol } ( \Gamma ) } { \operatorname { min } \{ \operatorname { Vol } ( M _ { 1 } ) , \text { Vol } ( M _ { 2 } ) \} }$ ; confidence 0.188
+
255. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120100/n12010043.png ; $\varphi ( 0 ) = 1$ ; confidence 1.000
  
−
256. https://www.encyclopediaofmath.org/legacyimages/l/l130/l130080/l13008015.png ; $\operatorname { log } \operatorname { max } \{ | P _ { i } ( \omega ) | \} \geq - d ^ { \mu } ( c _ { 1 } d + c _ { 2 } h ) + c _ { 3 } d ^ { \nu } \operatorname { log } \frac { \rho } { | \omega | }$ ; confidence 0.531
+
256. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007067.png ; $- ( 1 / \sqrt { 12 } - \varepsilon )$ ; confidence 1.000
  
−
257. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120190/m1201906.png ; $\int _ { 0 } ^ { \infty } | f ( x ) | ^ { 2 } \frac { d x } { x } = \frac { 4 } { \pi ^ { 2 } } \int _ { 0 } ^ { \infty } \tau \operatorname { tanh } ( \frac { \pi \tau } { 2 } ) | F ( \tau ) | ^ { 2 } d \tau$ ; confidence 0.972
+
257. https://www.encyclopediaofmath.org/legacyimages/h/h120/h120040/h12004023.png ; $\xi < \eta < \lambda$ ; confidence 1.000
  
−
258. https://www.encyclopediaofmath.org/legacyimages/n/n120/n120020/n12002097.png ; $\operatorname { lim } _ { n \rightarrow \infty } \frac { 1 } { n } \operatorname { log } P [ X _ { 1 } + \ldots + X _ { n } \geq n m ] = \int _ { m _ { 0 } } ^ { m } \frac { x - m } { V _ { F } ( x ) } d x$ ; confidence 0.193
+
258. https://www.encyclopediaofmath.org/legacyimages/d/d034/d034260/d03426074.png ; $[ n ]$ ; confidence 1.000
  
−
259. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130500/s13050021.png ; $\frac { | \nabla ( A ) | } { \left( \begin{array} { c } { n } \\ { l + 1 } \end{array} \right) } \geq \frac { | A | } { \left( \begin{array} { l } { n } \\ { l } \end{array} \right) }$ ; confidence 0.226
+
259. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120020/c12002069.png ; $1 \leq k \leq n - 1$ ; confidence 1.000
  
−
260. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/t12020057.png ; $\operatorname { inf } _ { z _ { j } , w _ { j } } \operatorname { max } _ { k \in S _ { 1 } , \atop m \in S _ { 2 } } \frac { | h ( m , k ) | } { M _ { d } ^ { \prime } ( k ) M _ { d } ^ { \prime \prime } ( m ) }$ ; confidence 0.056
+
260. https://www.encyclopediaofmath.org/legacyimages/l/l120/l120100/l12010089.png ; $\sqrt { - \Delta }$ ; confidence 1.000
  
−
261. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023086.png ; $( \frac { \partial } { \partial x } ) ^ { \alpha } = ( \frac { \partial } { \partial x _ { 1 } } ) ^ { \alpha _ { 1 } } \dots ( \frac { \partial } { \partial x _ { x } } ) ^ { \alpha _ { N } }$ ; confidence 0.072
+
261. https://www.encyclopediaofmath.org/legacyimages/p/p120/p120120/p12012044.png ; $\{ 3 \}$ ; confidence 1.000
  
−
262. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120140/f12014037.png ; $\operatorname { log } \frac { z ( \zeta ) - z ( \zeta ^ { \prime } ) } { \zeta - \zeta ^ { \prime } } = - \sum _ { k , l = 1 } ^ { \infty } \alpha _ { k l } \zeta ^ { - k } \zeta ^ { \prime - l }$ ; confidence 0.556
+
262. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120120/m1201209.png ; $( A ^ { \prime } , f ^ { \prime } )$ ; confidence 1.000
  
−
263. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f120210103.png ; $= [ \sum _ { l = 0 } ^ { \infty } \sum _ { n = 0 } ^ { N } a _ { l } ^ { n } z ^ { n + i } ( \frac { \partial } { \partial z } ) ^ { n } ] [ \sum _ { k = 0 } ^ { \infty } c _ { k } ( \lambda ) z ^ { \lambda + k } ] =$ ; confidence 0.352
+
263. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120170/a12017036.png ; $= 1$ ; confidence 1.000
  
−
264. https://www.encyclopediaofmath.org/legacyimages/n/n066/n066630/n06663076.png ; $\Omega ^ { k } ( f ^ { ( s ) } , \delta ) = \operatorname { sup } _ { | k | = 10 \leq t \leq \delta } \| \Delta _ { t h } ^ { k } f ^ { ( s ) } \| _ { L _ { p } ( \Omega _ { k t } ) } \leq M \delta ^ { * - s }$ ; confidence 0.088
+
264. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a01021011.png ; $z = x + i y$ ; confidence 1.000
  
−
265. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130170/w13017059.png ; $\operatorname { det } \Sigma = \operatorname { exp } \{ ( 2 \pi ) ^ { - 1 } \int _ { - \pi } ^ { \pi } \operatorname { log } \operatorname { det } 2 \pi f ( \lambda ) d \lambda \}$ ; confidence 0.984
+
265. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016083.png ; $16,000$ ; confidence 1.000
  
−
266. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120010/z12001038.png ; $( e _ { i } ) _ { t } x ^ { ( j ) } = ( \left( \begin{array} { c } { i + j } \\ { i + 1 } \end{array} \right) + t \left( \begin{array} { c } { i + j } \\ { i } \end{array} \right) x ^ { ( i + j ) }$ ; confidence 0.551
+
266. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120050/o12005010.png ; $\int _ { 0 } ^ { \infty } w ( s ) d s = \infty,$ ; confidence 1.000
  
−
267. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120250/c1202506.png ; $C = \frac { \operatorname { det } \mu } { \operatorname { trace } ^ { 2 } \mu } \text { or } C ^ { \prime } = \frac { \operatorname { det } \mu } { \operatorname { trace } \mu }$ ; confidence 0.973
+
267. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022700/c02270028.png ; $( f , g )$ ; confidence 1.000
  
−
268. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130240/f1302409.png ; $\langle a b | c d e \rangle \rangle = \langle \langle a b c \rangle \rangle + \varepsilon \langle c | b a d \rangle e \rangle + \langle c d \langle a b e \rangle \rangle$ ; confidence 0.506
+
268. https://www.encyclopediaofmath.org/legacyimages/i/i130/i130010/i13001061.png ; $( 5,4,3 ^ { 2 } )$ ; confidence 1.000
  
−
269. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120210/f120210104.png ; $= \sum _ { i = 0 } ^ { \infty } \sum _ { k = 0 } ^ { \infty } c _ { k } ( \lambda ) z ^ { i } \sum _ { n = 0 } ^ { N } a _ { i } ^ { n } z ^ { n } ( \frac { \partial } { \partial z } ) ^ { n } z ^ { \lambda + k } =$ ; confidence 0.479
+
269. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120050/a12005080.png ; $\{ A ( t ) \}$ ; confidence 1.000
  
−
270. https://www.encyclopediaofmath.org/legacyimages/o/o130/o130060/o130060120.png ; $\Phi ^ { * } ( \xi _ { 1 } \sigma _ { 1 } + \xi _ { 2 } \sigma _ { 2 } ) | _ { \mathfrak { E } ( \lambda ) } : \mathfrak { E } ( \lambda ) \rightarrow \tilde { \mathfrak { C } } ( \lambda )$ ; confidence 0.228
+
270. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040227.png ; $16$ ; confidence 1.000
  
−
271. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t13005072.png ; $D _ { A } = \left( \begin{array} { c c c c } { 0 } & { 0 } & { 0 } & { 0 } \\ { A _ { 1 } } & { 0 } & { 0 } & { 0 } \\ { A _ { 2 } } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - A _ { 2 } } & { A _ { 1 } } & { 0 } \end{array} \right)$ ; confidence 0.935
+
271. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145094.png ; $2 g - 2$ ; confidence 1.000
  
−
272. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120190/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
+
272. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130240/a130240109.png ; $( \alpha , \beta , \gamma ) ^ { \prime } = \beta$ ; confidence 1.000
  
−
273. https://www.encyclopediaofmath.org/legacyimages/w/w120/w120110/w120110253.png ; $\tilde { h } ( X ) ^ { - 1 } = 1 + \operatorname { sup } _ { \alpha } | q _ { \alpha } ( X ) | + H ( X ) \operatorname { sup } _ { \alpha } \| q _ { \alpha } ^ { \prime } ( X ) \| _ { G _ { X } } ^ { 2 }$ ; confidence 0.695
+
273. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130040/a130040225.png ; $\varphi \approx \psi$ ; confidence 1.000
  
−
274. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120080/a12008023.png ; $\alpha ( u , v ) = \int _ { \Omega } [ \sum _ { i , j = 1 } ^ { m } \alpha _ { i , j } \frac { \partial u } { \partial x _ { i } } \frac { \partial \sigma } { \partial x _ { j } } + c ( x ) u v ] d x$ ; confidence 0.237
+
274. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130080/m13008024.png ; $[ 0 , \sigma ]$ ; confidence 1.000
  
−
275. https://www.encyclopediaofmath.org/legacyimages/c/c130/c130250/c13025014.png ; $C ( \beta ) = \prod _ { j = 1 } ^ { n } \frac { \operatorname { exp } ( z _ { j } ^ { T } ( T _ { j } ) \beta ) } { \sum _ { k \in R _ { j } } \operatorname { exp } ( z _ { k } ^ { T } ( T _ { j } ) \beta ) }$ ; confidence 0.916
+
275. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120180/a12018075.png ; $\lambda = 1$ ; confidence 1.000
  
−
276. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120190/m12019012.png ; $\times \Gamma ( \frac { 1 } { 2 } - k - i \tau ) \int _ { 1 } ^ { \infty } P _ { i \tau } ^ { ( k ) } ( x ) f ( x ) d x , f ( x ) = \int _ { 0 } ^ { \infty } P _ { i \tau } ^ { ( k ) } - 1 / 2 ( x ) F ( \tau ) d \tau$ ; confidence 0.705
+
276. https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a011450155.png ; $3 g - 3$ ; confidence 1.000
  
−
277. https://www.encyclopediaofmath.org/legacyimages/o/o068/o068080/o0680806.png ; $\dot { q } _ { i } = A _ { i \alpha } q _ { \alpha } + B _ { i \alpha \beta } q _ { \alpha } q _ { \beta } + \frac { \partial } { \partial z } K ( z ) \frac { \partial q _ { i } } { \partial z }$ ; confidence 0.704
+
277. https://www.encyclopediaofmath.org/legacyimages/h/h110/h110260/h11026061.png ; $B ( x , y )$ ; confidence 1.000
  
−
278. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120020/o12002013.png ; $\omega ( \tau ) = \frac { \tau } { \operatorname { sinh } ( \pi \tau ) } | \frac { \Gamma ( c - \alpha + \frac { i \tau } { 2 } ) } { \Gamma ( \alpha + \frac { i \tau } { 2 } ) } | ^ { 2 }$ ; confidence 0.855
+
278. https://www.encyclopediaofmath.org/legacyimages/c/c023/c023720/c02372094.png ; $\mu \geq 0$ ; confidence 1.000
  
−
279. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130370/s13037016.png ; $d ( x , y ) = \operatorname { inf } _ { \lambda \in \Lambda } \operatorname { max } \{ \| \lambda \| , \operatorname { sup } _ { 0 \leq t \leq 1 } | x ( t ) - y ( \lambda ( t ) ) | \}$ ; confidence 0.864
+
279. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130100/f13010071.png ; $g ( x ) = f ( x )$ ; confidence 1.000
  
−
280. https://www.encyclopediaofmath.org/legacyimages/b/b120/b120430/b12043045.png ; $\Delta x ^ { n } = \sum _ { m = 0 } ^ { n } \left[ \begin{array} { c } { n } \\ { m } \end{array} \right] _ { q } x ^ { n } \otimes x ^ { n - m } , S x ^ { n } = ( - 1 ) ^ { n } q ^ { n ( n - 1 ) / 2 } x ^ { n }$ ; confidence 0.173
+
280. https://www.encyclopediaofmath.org/legacyimages/a/a110/a110040/a110040180.png ; $12$ ; confidence 1.000
  
−
281. https://www.encyclopediaofmath.org/legacyimages/e/e035/e035000/e035000133.png ; $H _ { \epsilon } ^ { \prime } ( \xi ) = \frac { 1 } { 2 } \sum _ { i = 1 } ^ { \infty } \operatorname { log } \operatorname { max } \{ \frac { \lambda _ { i } } { f ( \epsilon ) } , 1 \}$ ; confidence 0.990
+
281. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130030/m13003028.png ; $f ( z ) = ( 1 - z ) f ( z ^ { 2 } )$ ; confidence 1.000
  
−
282. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023054.png ; $= \int _ { a } ^ { b } [ \frac { \partial L } { \partial y } ( \sigma ^ { 1 } ( x ) ) - \frac { d } { d x } ( \frac { \partial L } { \partial y ^ { \prime } } ( \sigma ^ { 1 } ( x ) ) ) ] z ( x ) d x =$ ; confidence 0.831
+
282. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120180/c120180351.png ; $B ( g ) =$ ; confidence 1.000
  
−
283. https://www.encyclopediaofmath.org/legacyimages/h/h130/h130070/h13007031.png ; $\Delta : = \left( \begin{array} { c c c } { a _ { 11 } } & { \dots } & { a _ { 1 r } } \\ { \vdots } & { \square } & { \vdots } \\ { a _ { r 1 } } & { \dots } & { a _ { m } } \end{array} \right)$ ; confidence 0.732
+
283. https://www.encyclopediaofmath.org/legacyimages/z/z130/z130110/z13011094.png ; $\mu ( i , m + 1 ) - \mu ( i , m ) =$ ; confidence 1.000
  
−
284. https://www.encyclopediaofmath.org/legacyimages/p/p130/p130130/p13013073.png ; $\zeta _ { \lambda } ^ { + \lambda } = \zeta _ { \lambda } ^ { - \lambda } = i ^ { ( n - \gamma ( \lambda ) ) / 2 } \sqrt { ( \lambda _ { 1 } \ldots \lambda _ { \gamma } ( \lambda ) ) }$ ; confidence 0.071
+
284. https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g1300209.png ; $\beta = - i$ ; confidence 1.000
  
−
285. https://www.encyclopediaofmath.org/legacyimages/s/s130/s130580/s1305809.png ; $\xi _ { l } = \xi _ { l } ^ { 0 } \operatorname { sin } ( \omega t - \varepsilon _ { l } ) , \quad \xi _ { r } = \xi _ { r } ^ { 0 } \operatorname { sin } ( \omega t - \varepsilon _ { r } )$ ; confidence 0.980
+
285. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120160/a12016038.png ; $f ( u ) ( 1 - A )$ ; confidence 1.000
  
−
286. https://www.encyclopediaofmath.org/legacyimages/v/v130/v130060/v1300605.png ; $\operatorname { exp } ( \sum _ { n \in N + 1 / 2 } \frac { y _ { n } } { n } x ^ { n } ) \operatorname { exp } ( - 2 \sum _ { n \in N + 1 / 2 } \frac { \partial } { \partial y _ { n } } x ^ { - n } )$ ; confidence 0.321
+
286. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120190/f1201904.png ; $\{ 1 \} < H < G$ ; confidence 1.000
  
−
287. https://www.encyclopediaofmath.org/legacyimages/w/w130/w130110/w13011019.png ; $\operatorname { lim } _ { N \rightarrow \infty } \operatorname { sup } _ { \varepsilon } | \frac { 1 } { N } \sum _ { n = 1 } ^ { N } f ( T ^ { n } x ) e ^ { 2 \pi i n \varepsilon } | = 0$ ; confidence 0.507
+
287. https://www.encyclopediaofmath.org/legacyimages/v/v120/v120030/v12003013.png ; $\lambda ( E ) < \delta$ ; confidence 1.000
  
−
288. 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
+
288. https://www.encyclopediaofmath.org/legacyimages/o/o120/o120050/o1200503.png ; $\varphi ( 0 ) = 0$ ; confidence 1.000
  
−
289. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003022.png ; $H ^ { \bullet } ( \Gamma \backslash X , \overline { M \otimes C } ) \rightleftarrows H ^ { \bullet } ( \Gamma \backslash X , \Omega ^ { \bullet } ( \tilde { M } _ { C } ) )$ ; confidence 0.176
+
289. https://www.encyclopediaofmath.org/legacyimages/z/z120/z120020/z12002046.png ; $55 + 21 + 5 = 81\text{kilometres}$ ; confidence 1.000
  
−
290. https://www.encyclopediaofmath.org/legacyimages/e/e130/e130030/e13003043.png ; $\rightarrow H ^ { \bullet - 1 } ( \partial ( \Gamma \backslash X ) , \tilde { M } ) \rightarrow H _ { C } ^ { \bullet } ( \Gamma \backslash X , \tilde { M } ) \rightarrow$ ; confidence 0.459
+
290. https://www.encyclopediaofmath.org/legacyimages/t/t130/t130050/t130050163.png ; $\operatorname{index}( A - \lambda ) = 1$ ; confidence 1.000
  
−
291. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e12023053.png ; $= \int _ { a } ^ { b } [ \frac { \partial L } { \partial y } ( \sigma ^ { 1 } ( x ) ) z ( x ) + \frac { \partial L } { \partial y ^ { \prime } } ( \sigma ^ { 1 } ( x ) ) z ^ { \prime } ( x ) ] d x =$ ; confidence 0.826
+
291. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007064.png ; $- ( \sqrt { 2 } + \varepsilon )$ ; confidence 1.000
  
−
292. https://www.encyclopediaofmath.org/legacyimages/e/e120/e120230/e120230123.png ; $E ^ { \mathscr { A } } ( L ) = \sum _ { | \alpha | = 0 } ^ { k } ( - 1 ) ^ { | \alpha | } \gamma ^ { - 1 } D ^ { \alpha } ( \gamma \frac { \partial L } { \partial y _ { \alpha } ^ { \alpha } } )$ ; confidence 0.101
+
292. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120060/t120060136.png ; $\operatorname{curl}A = B$ ; confidence 1.000
  
−
293. https://www.encyclopediaofmath.org/legacyimages/i/i120/i120080/i12008088.png ; $\pm [ \operatorname { exp } ( \frac { 2 J } { k _ { B } T } ) \operatorname { cosh } ^ { 2 } ( \frac { H } { k _ { B } T } ) - 2 \operatorname { sinh } ( \frac { 2 J } { k _ { B } T } ) ] ^ { 1 / 2 }$ ; confidence 0.916
+
293. https://www.encyclopediaofmath.org/legacyimages/c/c120/c120190/c12019048.png ; $\sigma ( D )$ ; confidence 1.000
  
−
294. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120150/m12015058.png ; $\times \operatorname { etr } \{ - \frac { 1 } { 2 } \Sigma ^ { - 1 } ( X - M ) \Psi ^ { - 1 } ( X - M ) ^ { \prime } \} , X \in R ^ { p \times n } , M \in R ^ { p \times n } , \Sigma > 0 , \Psi > 0$ ; confidence 0.851
+
294. https://www.encyclopediaofmath.org/legacyimages/d/d120/d120290/d12029065.png ; $f ( q )$ ; confidence 1.000
  
−
295. https://www.encyclopediaofmath.org/legacyimages/m/m130/m130140/m13014077.png ; $\nu ( \zeta - a ) = \frac { 1 } { ( 2 \pi i ) ^ { n } } \sum _ { k = 1 } ^ { n } ( - 1 ) ^ { k - 1 } ( \overline { \zeta } _ { k } - \overline { a } _ { k } ) d \overline { \zeta } [ k ] \wedge d \zeta$ ; confidence 0.831
+
295. https://www.encyclopediaofmath.org/legacyimages/a/a130/a130070/a13007066.png ; $- ( 1 - \varepsilon )$ ; confidence 1.000
  
−
296. https://www.encyclopediaofmath.org/legacyimages/t/t120/t120200/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
+
296. https://www.encyclopediaofmath.org/legacyimages/k/k120/k120120/k1201209.png ; $x ^ { 2 }$ ; confidence 1.000
  
−
297. https://www.encyclopediaofmath.org/legacyimages/a/a120/a120200/a12020056.png ; $P _ { j } P _ { k } = \left\{ \left. \begin{array} { l l } { P _ { k } } & { \text { for } j = k } \\ { 0 } & { \text { for } j \neq k } \end{array} \right. ( j , k = 1 , \dots , n ) \right.$ ; confidence 0.545
+
297. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120140/f12014059.png ; $| \zeta | = 1$ ; confidence 1.000
  
−
298. https://www.encyclopediaofmath.org/legacyimages/b/b110/b110220/b110220170.png ; $( r _ { D } \oplus z _ { D } ) \otimes R : ( H _ { M } ^ { i + 1 } ( X , Q ( m + 1 ) ) z ^ { \otimes R } ) \oplus ( B ^ { m } ( X ) \otimes R ) \rightleftarrows H _ { D } ^ { i + 1 } ( X _ { / R } , R ( m + 1 ) )$ ; confidence 0.151
+
298. https://www.encyclopediaofmath.org/legacyimages/f/f120/f120150/f120150125.png ; $\Phi ( X , Y )$ ; confidence 1.000
  
−
299. https://www.encyclopediaofmath.org/legacyimages/c/c022/c022110/c0221105.png ; $X ^ { 2 } = \sum _ { i = 1 } ^ { k } \frac { ( \nu _ { i } - n p _ { i } ) ^ { 2 } } { n p _ { i } } = \frac { 1 } { n } \sum \frac { \nu _ { i } ^ { 2 } } { p _ { i } } - n , \quad n = \nu _ { 1 } + \ldots + \nu _ { k }$ ; confidence 0.495
+
299. https://www.encyclopediaofmath.org/legacyimages/a/a010/a010210/a01021014.png ; $p ( z )$ ; confidence 1.000
  
−
300. https://www.encyclopediaofmath.org/legacyimages/f/f130/f130090/f13009025.png ; $\left. \begin{array}{l}{ U _ { 0 } ( x , y ) = 0 }\\{ U _ { 1 } ( x , y ) = 1 }\\{ U _ { n } ( x , y ) = x U _ { n - 1 } ( x , y ) + y U _ { n - 2 } ( x , y ) }\\{ n = 2 , 3 , \ldots }\end{array} \right.$ ; confidence 0.223
+
300. https://www.encyclopediaofmath.org/legacyimages/m/m120/m120070/m12007041.png ; $50$ ; confidence 1.000

Latest revision as of 10:34, 31 March 2020

List

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

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

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

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

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

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

7. t12001091.png ; $\mathcal Z$ ; confidence 1.000

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

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

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

11. a130240348.png ; $( r - q ) \times p$ ; confidence 1.000

12. a130240424.png ; $( 1 \times p )$ ; confidence 1.000

13. a130240423.png ; $q \times 1$ ; confidence 1.000

14. a130240375.png ; $( n - r ) F$ ; confidence 1.000

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

16. a13004067.png ; $\psi \in \Gamma$ ; confidence 1.000

17. a12018084.png ; $10 ^ { 16 }$ ; confidence 1.000

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

19. a13032031.png ; $p < .5$ ; confidence 1.000

20. b12021067.png ; $\Theta( L ( \lambda ) )$ ; confidence 1.000

21. b01540048.png ; $s ( z )$ ; confidence 1.000

22. b1301906.png ; $F ( x ) = f ( M x )$ ; confidence 1.000

23. c120180506.png ; $N = N \times \{ 1 \} \times \{ 0 \}$ ; confidence 1.000

24. c12030069.png ; $n = \infty$ ; confidence 1.000

25. a110220101.png ; $R ( f )$ ; confidence 1.000

26. d13005022.png ; $m - 2 r$ ; confidence 1.000

27. a01225011.png ; $R > 0$ ; confidence 1.000

28. d12018084.png ; $C ( G )$ ; confidence 1.000

29. d12029018.png ; $f ( q ) = 1 / ( \sqrt { 5 } q ^ { 2 } )$ ; confidence 1.000

30. e12015070.png ; $\lambda _ { 1 } = \lambda _ { 2 }$ ; confidence 1.000

31. f12010041.png ; $( 8 \times 8 )$ ; confidence 1.000

32. f12015010.png ; $R ( A )$ ; confidence 1.000

33. g12003011.png ; $3 n + 2$ ; confidence 1.000

34. c026010588.png ; $J ( \alpha )$ ; confidence 1.000

35. i130090151.png ; $p < 12000000$ ; confidence 1.000

36. k13001019.png ; $T ( s )$ ; confidence 1.000

37. l0610509.png ; $f ^ { \prime } ( x ) = 0$ ; confidence 1.000

38. n13007025.png ; $m ( B ) = 0$ ; confidence 1.000

39. n067520368.png ; $\phi _ { i } ( 0 ) = 0$ ; confidence 1.000

40. p1201308.png ; $\theta$ ; confidence 1.000

41. c020280124.png ; $E ( \lambda )$ ; confidence 1.000

42. w120090131.png ; $\Delta ( \lambda ) ^ { \mu }$ ; confidence 1.000

43. w13009083.png ; $\iota( g ) = g ^ { \prime }$ ; confidence 1.000

44. p12011022.png ; $3$ ; confidence 1.000

45. a11001057.png ; $10$ ; confidence 1.000

46. a01160016.png ; $- 1$ ; confidence 1.000

47. c02544045.png ; $3 \times 3$ ; confidence 1.000

48. p1201103.png ; $15$ ; confidence 1.000

49. a130070132.png ; $10 ^ { 4 }$ ; confidence 1.000

50. a13007016.png ; $100$ ; confidence 1.000

51. a01148042.png ; $x ^ { 2 } + 1$ ; confidence 1.000

52. e12012092.png ; $( t + 1 )$ ; confidence 1.000

53. a110040163.png ; $24$ ; confidence 1.000

54. a011380171.png ; $1 + 1$ ; confidence 1.000

55. a13014045.png ; $\sqrt { 2 }$ ; confidence 1.000

56. s13062082.png ; $f ( \lambda )$ ; confidence 1.000

57. f0411402.png ; $( - \infty , + \infty )$ ; confidence 1.000

58. b12034062.png ; $f ( 0 ) > 0$ ; confidence 1.000

59. o130060186.png ; $f ( 0,0 )$ ; confidence 1.000

60. b11025029.png ; $g ( t )$ ; confidence 1.000

61. a13014041.png ; $\sqrt { 3 }$ ; confidence 1.000

62. a0111801.png ; $( 1,1 )$ ; confidence 1.000

63. a110040145.png ; $18$ ; confidence 1.000

64. o13002021.png ; $180$ ; confidence 1.000

65. c02322014.png ; $( - 1,1 )$ ; confidence 1.000

66. o13002022.png ; $41$ ; confidence 1.000

67. p12012031.png ; $( 1,4 )$ ; confidence 1.000

68. a12018091.png ; $23$ ; confidence 1.000

69. c13007017.png ; $( - 1,0 )$ ; confidence 1.000

70. b1200904.png ; $f ( 0 ) = 0$ ; confidence 1.000

71. a13007061.png ; $- 8$ ; confidence 1.000

72. a01183015.png ; $\{ 0,1 \}$ ; confidence 1.000

73. q13003028.png ; $( 4 \times 4 )$ ; confidence 1.000

74. v09603022.png ; $164$ ; confidence 1.000

75. f04147017.png ; $\bar{\lambda}$ ; confidence 1.000

76. d1200507.png ; $f ( y )$ ; confidence 1.000

77. w120090217.png ; $\nabla ( \lambda )$ ; confidence 1.000

78. a12003018.png ; $[ 0 , \infty )$ ; confidence 1.000

79. l12001041.png ; $( 2 \times 4 )$ ; confidence 1.000

80. k13007034.png ; $256$ ; confidence 1.000

81. b12036043.png ; $( 1 + 1 )$ ; confidence 1.000

82. c1300908.png ; $[ - 1,1 ]$ ; confidence 1.000

83. c02054039.png ; $( p - 1 )$ ; confidence 1.000

84. c1200405.png ; $( 2 n - 1 )$ ; confidence 1.000

85. h04704018.png ; $( 0,2 )$ ; confidence 1.000

86. a12020026.png ; $p ( t )$ ; confidence 1.000

87. a12018062.png ; $\lambda \neq 0$ ; confidence 1.000

88. s13051013.png ; $g ( u ) =$ ; confidence 1.000

89. d0334002.png ; $f ( t ) = 0$ ; confidence 1.000

90. s13058044.png ; $4 \times 4$ ; confidence 1.000

91. b13002048.png ; $( 3 \times 3 )$ ; confidence 1.000

92. d12006031.png ; $2 + 1$ ; confidence 1.000

93. m130140128.png ; $2 n ^ { 2 }$ ; confidence 1.000

94. p12012039.png ; $( 3 \times 3 )$ ; confidence 1.000

95. g1200309.png ; $3 n + 1$ ; confidence 1.000

96. d0321106.png ; $\mu > 0$ ; confidence 1.000

97. s13041061.png ; $\sqrt { z ^ { 2 } - 1 } > 0$ ; confidence 1.000

98. a1200604.png ; $\partial \Omega$ ; confidence 1.000

99. p12012029.png ; $( 1,2 )$ ; confidence 1.000

100. t1300708.png ; $g ( 0 ) = 0$ ; confidence 1.000

101. s12021022.png ; $\mu ( \lambda ) = \lambda$ ; confidence 1.000

102. a12018063.png ; $\lambda = 0$ ; confidence 1.000

103. g1101706.png ; $\sqrt { t }$ ; confidence 1.000

104. w12021036.png ; $( - 1 , + 1 )$ ; confidence 1.000

105. b1201407.png ; $2 t + 1$ ; confidence 1.000

106. p130100122.png ; $( 2 p + 1 )$ ; confidence 1.000

107. b12016041.png ; $f ^ { \prime } = f$ ; confidence 1.000

108. p12012033.png ; $( 2,4 )$ ; confidence 1.000

109. b11067055.png ; $( 2 n + 1 )$ ; confidence 1.000

110. n13005037.png ; $\mu > 1$ ; confidence 1.000

111. l05778081.png ; $30$ ; confidence 1.000

112. l120170246.png ; $\operatorname{max}( 3 , n )$ ; confidence 1.000

113. d032240214.png ; $( 1,0 )$ ; confidence 1.000

114. c0258308.png ; $\{ 0 \}$ ; confidence 1.000

115. a120160137.png ; $13$ ; confidence 1.000

116. a01180083.png ; $( i + 1 )$ ; confidence 1.000

117. p12012025.png ; $( 2,3 )$ ; confidence 1.000

118. a13012041.png ; $4 \mu$ ; confidence 1.000

119. a01160062.png ; $\pm 1$ ; confidence 1.000

120. s12033023.png ; $( 4 n - 1,2 n - 1 , n - 1 )$ ; confidence 1.000

121. a120160175.png ; $\alpha \in ( 0,1 )$ ; confidence 1.000

122. b1200905.png ; $f ^ { \prime } ( 0 ) = 1$ ; confidence 1.000

123. w120070123.png ; $( 2 + 1 )$ ; confidence 1.000

124. a1200308.png ; $f ( - x )$ ; confidence 1.000

125. a12024025.png ; $( p - 1 , p - 1 )$ ; confidence 1.000

126. a11006014.png ; $\Omega \times \Omega$ ; confidence 1.000

127. l13010047.png ; $| \xi | > R$ ; confidence 1.000

128. m13022024.png ; $194$ ; confidence 1.000

129. c02242033.png ; $( - \infty , \infty )$ ; confidence 1.000

130. s09067014.png ; $( f ^ { \prime } , g ^ { \prime } )$ ; confidence 1.000

131. a12018085.png ; $\operatorname { ln } 2$ ; confidence 1.000

132. d1203007.png ; $Y ( 0 ) = 0$ ; confidence 1.000

133. c02499012.png ; $[ - \pi , \pi ]$ ; confidence 1.000

134. s09106032.png ; $\{ f , g \}$ ; confidence 1.000

135. b12009027.png ; $| f | < 1$ ; confidence 1.000

136. f12010077.png ; $27$ ; confidence 1.000

137. i13001059.png ; $( 4 ^ { 2 } , 3 ^ { 2 } )$ ; confidence 1.000

138. s130540120.png ; $\{ - 1 , - 1 \}$ ; confidence 1.000

139. k12002011.png ; $( - 2 )$ ; confidence 1.000

140. p12012035.png ; $( 3,4 )$ ; confidence 1.000

141. a12016084.png ; $5$ ; confidence 1.000

142. m120030111.png ; $\rho ( 0 ) = 0$ ; confidence 1.000

143. l12001056.png ; $m + 2$ ; confidence 1.000

144. m06459013.png ; $[ 0 , + \infty )$ ; confidence 1.000

145. a01145010.png ; $f ( x , y )$ ; confidence 1.000

146. a13027066.png ; $\phi ( t ) > 0$ ; confidence 1.000

147. p12012042.png ; $\{ 21 \}$ ; confidence 1.000

148. p1201105.png ; $10$ ; confidence 1.000

149. a12005086.png ; $\lambda > \beta$ ; confidence 1.000

150. m13022022.png ; $171$ ; confidence 1.000

151. k12012023.png ; $[ - 1 , + \infty ]$ ; confidence 1.000

152. h04691024.png ; $2 ( n + 1 )$ ; confidence 1.000

153. o0680802.png ; $10 ^ { 28 }$ ; confidence 1.000

154. c13007020.png ; $( t ^ { 2 } , t ^ { 3 } )$ ; confidence 1.000

155. b120040158.png ; $f = x y$ ; confidence 1.000

156. g130040157.png ; $G ( n , m )$ ; confidence 1.000

157. a12025022.png ; $( q + 1 )$ ; confidence 1.000

158. b0160505.png ; $f ( \theta )$ ; confidence 1.000

159. s13002048.png ; $f ( u ) = 1$ ; confidence 1.000

160. d120230156.png ; $( n - i ) \times ( n - i )$ ; confidence 1.000

161. d13011027.png ; $2 ^ { 4 }$ ; confidence 1.000

162. a12012057.png ; $\lambda ( x , y )$ ; confidence 1.000

163. l05778080.png ; $20$ ; confidence 1.000

164. c130070117.png ; $\delta ( P ) = 0$ ; confidence 1.000

165. h13003034.png ; $q ( 0 ) = 1$ ; confidence 1.000

166. a12018055.png ; $\lambda \neq 1$ ; confidence 1.000

167. a130060105.png ; $( 0,1 )$ ; confidence 1.000

168. n13007023.png ; $[ - \infty , \infty ]$ ; confidence 1.000

169. t120200245.png ; $3 ( 4 )$ ; confidence 1.000

170. s12021024.png ; $\lambda \leq \mu$ ; confidence 1.000

171. a12012047.png ; $y = 0$ ; confidence 1.000

172. m130180120.png ; $\mu ( 0,1 ) + 1$ ; confidence 1.000

173. p12011020.png ; $4$ ; confidence 1.000

174. b13030064.png ; $n\geq 4381$ ; confidence 1.000

175. w120090206.png ; $\mu - \lambda$ ; confidence 1.000

176. w12013020.png ; $( A + i ) ^ { - 1 } - ( B + i ) ^ { - 1 }$ ; confidence 1.000

177. p12012041.png ; $\{ 1 ( 11 ) \}$ ; confidence 1.000

178. a12025014.png ; $( q + 2 )$ ; confidence 1.000

179. c02085023.png ; $\mu = 0$ ; confidence 1.000

180. p12013050.png ; $[ 1 , \infty )$ ; confidence 1.000

181. s13051015.png ; $g ( u ) = 0$ ; confidence 1.000

182. c022920100.png ; $| \zeta | > 1$ ; confidence 1.000

183. s130620135.png ; $\lambda,$ ; confidence 1.000

184. p12011012.png ; $120$ ; confidence 1.000

185. a01021052.png ; $f ( z )$ ; confidence 1.000

186. a1200409.png ; $( 0 , \infty )$ ; confidence 1.000

187. b120040202.png ; $( 1 < p < \infty )$ ; confidence 1.000

188. k13005020.png ; $10 ^ { 19 }$ ; confidence 1.000

189. b01642029.png ; $[ y ]$ ; confidence 1.000

190. f12010056.png ; $[ 0 , \pi ]$ ; confidence 1.000

191. a13007014.png ; $21$ ; confidence 1.000

192. b110100184.png ; $\sqrt { n }$ ; confidence 1.000

193. h1201104.png ; $\int _ { \Gamma } f ( z ) d z = 0$ ; confidence 1.000

194. a1101703.png ; $t = 0$ ; confidence 1.000

195. b01672015.png ; $( n , n - 1 )$ ; confidence 1.000

196. b13009036.png ; $m ( \xi ) ^ { - 1 }$ ; confidence 1.000

197. a12006039.png ; $f ( t )$ ; confidence 1.000

198. p1201104.png ; $19$ ; confidence 1.000

199. c13004030.png ; $= 4 \operatorname { log } 2 + 2 - \frac { 4 } { \pi } ( 2 G + 1 ),$ ; confidence 1.000

200. e12014017.png ; $\rho ( f ) > 0$ ; confidence 1.000

201. c0230302.png ; $T ( g )$ ; confidence 1.000

202. a12005071.png ; $- A ( t )$ ; confidence 1.000

203. p12012043.png ; $\{ ( 21 ) \}$ ; confidence 1.000

204. b12018014.png ; $\alpha = \sqrt { 2 }$ ; confidence 1.000

205. e12016013.png ; $i = \sqrt { - 1 }$ ; confidence 1.000

206. p12012027.png ; $( 3,1 )$ ; confidence 1.000

207. b0164307.png ; $m + 1$ ; confidence 1.000

208. c1201703.png ; $\gamma_{00}> 0$ ; confidence 1.000

209. f1302405.png ; $ \epsilon = \pm 1$ ; confidence 1.000

210. b12017014.png ; $( 1 + | \xi | ^ { 2 } ) ^ { \alpha / 2 }$ ; confidence 1.000

211. a12018092.png ; $t = 2$ ; confidence 1.000

212. a12008059.png ; $H ^ { 1 } ( \Omega )$ ; confidence 1.000

213. p12015048.png ; $\partial \Omega$ ; confidence 1.000

214. v13007067.png ; $\alpha = ( 2 \lambda - 1 ) / ( 1 - \lambda ) ^ { 2 }$ ; confidence 1.000

215. b120040140.png ; $\theta \in ( 0,1 )$ ; confidence 1.000

216. a01149073.png ; $f ^ { \prime } ( x )$ ; confidence 1.000

217. k12007016.png ; $f ( \pi - t ) = f ( t )$ ; confidence 1.000

218. l12013098.png ; $17$ ; confidence 1.000

219. e13005011.png ; $\Gamma ( \lambda )$ ; confidence 1.000

220. t13010052.png ; $\operatorname{Hom}_H( T , - )$ ; confidence 1.000

221. a01022098.png ; $( p + 1 )$ ; confidence 1.000

222. t120140102.png ; $\sigma ( T _ { \phi } )$ ; confidence 1.000

223. p12012040.png ; $\{ 111 \}$ ; confidence 1.000

224. b12003011.png ; $A , B > 0$ ; confidence 1.000

225. w12019035.png ; $f ( x , p )$ ; confidence 1.000

226. c12002020.png ; $\int _ { 0 } ^ { \infty }$ ; confidence 1.000

227. s12033013.png ; $( 111,11,1 )$ ; confidence 1.000

228. d12005014.png ; $f ( x ) = g ( x )$ ; confidence 1.000

229. c02583036.png ; $u ( T ) = 0$ ; confidence 1.000

230. d12015056.png ; $4 p ^ { 2 }$ ; confidence 1.000

231. d12012011.png ; $A G$ ; confidence 1.000

232. a13004027.png ; $\Gamma ^ { \prime } \subseteq \Gamma$ ; confidence 1.000

233. s13062022.png ; $y ( 0 , \lambda ) = 0$ ; confidence 1.000

234. a12020016.png ; $p ( T ) = 0$ ; confidence 1.000

235. b12010032.png ; $G ( t )$ ; confidence 1.000

236. c025140158.png ; $\Gamma ( E )$ ; confidence 1.000

237. l057000101.png ; $f ( 0 , x ) = 0$ ; confidence 1.000

238. b01554032.png ; $( 0,0 )$ ; confidence 1.000

239. l11003090.png ; $P ( A ) = 0$ ; confidence 1.000

240. t12006015.png ; $\gamma = ( 3 \pi ^ { 2 } ) ^ { 2 / 3 }$ ; confidence 1.000

241. s130540101.png ; $G = E ( R )$ ; confidence 1.000

242. b01642049.png ; $0 < p < 1$ ; confidence 1.000

243. n067520326.png ; $A =$ ; confidence 1.000

244. s13065039.png ; $\mu ^ { \prime } > 0$ ; confidence 1.000

245. a12018086.png ; $10 ^ { - 16 }$ ; confidence 1.000

246. s13014036.png ; $\lambda = ( 4,2,1 )$ ; confidence 1.000

247. c120210120.png ; $\Gamma ( \theta )$ ; confidence 1.000

248. a12011023.png ; $n + 3$ ; confidence 1.000

249. b12051024.png ; $10 ^ { - 4 }$ ; confidence 1.000

250. m13007016.png ; $p ^ { 0 } > 0$ ; confidence 1.000

251. a13007025.png ; $b = 3$ ; confidence 1.000

252. a12016092.png ; $\alpha + \beta$ ; confidence 1.000

253. h04632074.png ; $B ( z )$ ; confidence 1.000

254. c13007018.png ; $\left( \frac { 1 - t ^ { 2 } } { 1 + t ^ { 2 } } , \frac { 2 t } { 1 + t ^ { 2 } } \right).$ ; confidence 1.000

255. n12010043.png ; $\varphi ( 0 ) = 1$ ; confidence 1.000

256. a13007067.png ; $- ( 1 / \sqrt { 12 } - \varepsilon )$ ; confidence 1.000

257. h12004023.png ; $\xi < \eta < \lambda$ ; confidence 1.000

258. d03426074.png ; $[ n ]$ ; confidence 1.000

259. c12002069.png ; $1 \leq k \leq n - 1$ ; confidence 1.000

260. l12010089.png ; $\sqrt { - \Delta }$ ; confidence 1.000

261. p12012044.png ; $\{ 3 \}$ ; confidence 1.000

262. m1201209.png ; $( A ^ { \prime } , f ^ { \prime } )$ ; confidence 1.000

263. a12017036.png ; $= 1$ ; confidence 1.000

264. a01021011.png ; $z = x + i y$ ; confidence 1.000

265. a12016083.png ; $16,000$ ; confidence 1.000

266. o12005010.png ; $\int _ { 0 } ^ { \infty } w ( s ) d s = \infty,$ ; confidence 1.000

267. c02270028.png ; $( f , g )$ ; confidence 1.000

268. i13001061.png ; $( 5,4,3 ^ { 2 } )$ ; confidence 1.000

269. a12005080.png ; $\{ A ( t ) \}$ ; confidence 1.000

270. a110040227.png ; $16$ ; confidence 1.000

271. a01145094.png ; $2 g - 2$ ; confidence 1.000

272. a130240109.png ; $( \alpha , \beta , \gamma ) ^ { \prime } = \beta$ ; confidence 1.000

273. a130040225.png ; $\varphi \approx \psi$ ; confidence 1.000

274. m13008024.png ; $[ 0 , \sigma ]$ ; confidence 1.000

275. a12018075.png ; $\lambda = 1$ ; confidence 1.000

276. a011450155.png ; $3 g - 3$ ; confidence 1.000

277. h11026061.png ; $B ( x , y )$ ; confidence 1.000

278. c02372094.png ; $\mu \geq 0$ ; confidence 1.000

279. f13010071.png ; $g ( x ) = f ( x )$ ; confidence 1.000

280. a110040180.png ; $12$ ; confidence 1.000

281. m13003028.png ; $f ( z ) = ( 1 - z ) f ( z ^ { 2 } )$ ; confidence 1.000

282. c120180351.png ; $B ( g ) =$ ; confidence 1.000

283. z13011094.png ; $\mu ( i , m + 1 ) - \mu ( i , m ) =$ ; confidence 1.000

284. g1300209.png ; $\beta = - i$ ; confidence 1.000

285. a12016038.png ; $f ( u ) ( 1 - A )$ ; confidence 1.000

286. f1201904.png ; $\{ 1 \} < H < G$ ; confidence 1.000

287. v12003013.png ; $\lambda ( E ) < \delta$ ; confidence 1.000

288. o1200503.png ; $\varphi ( 0 ) = 0$ ; confidence 1.000

289. z12002046.png ; $55 + 21 + 5 = 81\text{kilometres}$ ; confidence 1.000

290. t130050163.png ; $\operatorname{index}( A - \lambda ) = 1$ ; confidence 1.000

291. a13007064.png ; $- ( \sqrt { 2 } + \varepsilon )$ ; confidence 1.000

292. t120060136.png ; $\operatorname{curl}A = B$ ; confidence 1.000

293. c12019048.png ; $\sigma ( D )$ ; confidence 1.000

294. d12029065.png ; $f ( q )$ ; confidence 1.000

295. a13007066.png ; $- ( 1 - \varepsilon )$ ; confidence 1.000

296. k1201209.png ; $x ^ { 2 }$ ; confidence 1.000

297. f12014059.png ; $| \zeta | = 1$ ; confidence 1.000

298. f120150125.png ; $\Phi ( X , Y )$ ; confidence 1.000

299. a01021014.png ; $p ( z )$ ; confidence 1.000

300. m12007041.png ; $50$ ; confidence 1.000

How to Cite This Entry:
Maximilian Janisch/latexlist/latex/NoNroff/1. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximilian_Janisch/latexlist/latex/NoNroff/1&oldid=44411
Retrieved from "https://encyclopediaofmath.org/index.php?title=User:Maximilian_Janisch/latexlist/latex/NoNroff/1&oldid=44936"