# User:Ulf Rehmann/Test5

## Algebraic curve

Nr. Image of png File $\TeX$, 1st version $\TeX$, 2nd version Confidence, F?

name of png

Algebraic curve
1.(23.) $g \leq \left\{ \begin{array} { l l } { \frac { ( n - 2 ) ^ { 2 } } { 4 } } & { \text { for even } n } \\ { \frac { ( n - 1 ) ( n - 3 ) } { 4 } } & { \text { for odd } n } \end{array} \right.$ $$g \leq \left\{ \begin{array} { l l } { \frac { ( n - 2 ) ^ { 2 } } { 4 } } & { \text { for even } n, } \\ { \frac { ( n - 1 ) ( n - 3 ) } { 4 } } & { \text { for odd } n, } \end{array} \right.$$ conf 0.698

png = a01145065.png (65)

## Algebraic geometry

Nr. Image of png File $\TeX$, 1st version $\TeX$, 2nd version Confidence, F?

name of png

Algebraic geometry
2.(116.) $\theta = \int _ { 0 } ^ { \lambda } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ $$\empty$$ conf 0.997

png = a01150014.png(14)

3.(133.) $\omega = 2 \int _ { 0 } ^ { 1 / c } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ $$\empty$$ conf 0.973

png = a01150021.png(21)

4.(67.) $\overline { w } = 2 \int _ { 0 } ^ { 1 / \varepsilon } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ $$\widetilde{ w } = 2 \int _ { 0 } ^ { 1 / \varepsilon } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } },$$ conf 0.107

png = a01150022.png(22)

5.(105.) $\theta ( v + \pi i r ) = \theta ( r ) , \quad \theta ( v + \alpha _ { j } ) = e ^ { L _ { j } ( v ) } \theta ( v )$ $$\empty$$ conf 0.775

png = a01150044.png(44)

6.(17.) $\left( \begin{array} { l l } { \alpha } & { b } \\ { c } & { d } \end{array} \right) \equiv \left( \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) ( \operatorname { mod } 7 )$ $$\empty$$ conf 0.440

png = a01150078.png(78)

## Algebraic surface

!colspan="5" | Algebraic surface

Nr. Image of png File $\TeX$, 1st version $\TeX$, 2nd version Confidence, F?

name of png

7.(144.) $0 \rightarrow O _ { V } \rightarrow E _ { \alpha } \rightarrow T _ { V } \rightarrow 0$ $$0 \rightarrow {\cal O} _ { V } \rightarrow E _ { \alpha } \rightarrow T _ { V } \rightarrow 0$$ conf 0.981

png = a011640132.png(132)

8.(73.) $M = \operatorname { dim } \operatorname { Im } ( H ^ { 1 } ( V , E _ { \alpha } ) \rightarrow H ^ { 1 } ( V , T _ { V } ) )$ $$\empty$$ conf 0.997

png = a011640137.png(137)

9.(88.) $\operatorname { dim } _ { k } H ^ { 2 } ( V , E _ { \alpha } ) + \operatorname { dim } _ { k } H ^ { 2 } ( V , T _ { V } )$ $$\empty$$ conf 0.996

png = a011640139.png(139)

10.(117.) $N _ { m } = \left( \begin{array} { c } { m + 3 } \\ { 3 } \end{array} \right) - d m + 2 t + \tau + p - 1$ $$\empty$$ conf 0.369

png = a01164027.png(27)

11.(72.) $p _ { \alpha } ( V ) = \left( \begin{array} { c } { n - 1 } \\ { 3 } \end{array} \right) - d ( n - 1 ) + 2 t + \tau + p - 1$ $$\empty$$ conf 0.396

png = a01164029.png(29)

12.(68.)* $p _ { x } ( V ) = - \operatorname { dim } _ { k } H _ { 1 } ( V , O _ { V } ) + \operatorname { dim } _ { k } H ^ { 2 } ( V , O _ { V } ) =$ $$p _ { \alpha } ( V ) = - \operatorname { dim } _ { k } H _ { 1 } ( V , {\cal O} _ { V } ) + \operatorname { dim } _ { k } H ^ { 2 } ( V , {\cal O} _ { V } ) =$$ conf 0.756 F

png = a01164047.png(47)

13.(93.)* $1 + p _ { x } ( V ) = \frac { \operatorname { deg } ( c _ { 1 } ^ { 2 } ) + \operatorname { deg } ( c _ { 2 } ) } { 12 }$ $$1 + p _ { \alpha } ( V ) = \frac { \operatorname { deg } ( c _ { 1 } ^ { 2 } ) + \operatorname { deg } ( c _ { 2 } ) } { 12 },$$ conf 0.752 F

png = a01164053.png(53)

## Cartan subalgebra

Nr. Image of png File $\TeX$, 1st version $\TeX$, 2nd version Confidence, F?

name of png

14.(33.)* $\mathfrak { g } 0 = \{ X \in \mathfrak { g } : \forall H \in \mathfrak { t } \exists \mathfrak { n } X , H \in Z ( ( \text { ad } H ) ^ { n } X , H ( X ) = 0 ) \}$ $$\mathfrak { g }_0 = \big\{ X \in \mathfrak { g } : \forall H \in \mathfrak { t } \exists { n }_{X,H} \in {\mathbb Z} ( ( \text { ad } H ) ^ { n_{X , H} } ( X ) = 0 ) \big\}$$ conf 0.110 F

png = c0205509.png(9)

How to Cite This Entry:
Ulf Rehmann/Test5. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ulf_Rehmann/Test5&oldid=44165