Відмінності між версіями «Формули MS Word MathType»
(Нова сторінка: <math> \operatorname{erfc}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt = \frac{e^{-x^2}}{x\sqrt{\pi}}\sum_{n=0}^\infty (-1)^n \frac{(2n)!}{n!(2x)^{2n}} </...) |
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| Рядок 4: | Рядок 4: | ||
\frac{e^{-x^2}}{x\sqrt{\pi}}\sum_{n=0}^\infty (-1)^n \frac{(2n)!}{n!(2x)^{2n}} | \frac{e^{-x^2}}{x\sqrt{\pi}}\sum_{n=0}^\infty (-1)^n \frac{(2n)!}{n!(2x)^{2n}} | ||
</math> | </math> | ||
| + | |||
| + | <wikitex> | ||
| + | Let $Q$ be any finite set, and $\mathcal B=2^Q$ be the collection of the subsets of | ||
| + | $Q$. Let $f:\mathcal B\rightarrow \mathbb R$ be a function assigning real numbers to | ||
| + | the subsets of $Q$ and suppose $f$ satisfies the following conditions: | ||
| + | :(i) $f(A)\ge 0$ for all $A\subseteq Q$, $f(\emptyset)=0$, | ||
| + | :(ii) $f$ is monotone, i.e. if $A\subseteq B\subseteq Q$ then $f(A)\le f(B)$, | ||
| + | :(iii) $f$ is submodular, i.e. if $A$ and $B$ are different subsets of $Q$ then | ||
| + | $$ \eqno{(2)} | ||
| + | f(A)+f(B)\ge f(A\cap B) + f(A\cup B). | ||
| + | $$ | ||
| + | </wikitex> | ||
Версія за 15:12, 25 грудня 2009
[math]\operatorname{erfc}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt = \frac{e^{-x^2}}{x\sqrt{\pi}}\sum_{n=0}^\infty (-1)^n \frac{(2n)!}{n!(2x)^{2n}}[/math]
<wikitex> Let $Q$ be any finite set, and $\mathcal B=2^Q$ be the collection of the subsets of $Q$. Let $f:\mathcal B\rightarrow \mathbb R$ be a function assigning real numbers to the subsets of $Q$ and suppose $f$ satisfies the following conditions:
- (i) $f(A)\ge 0$ for all $A\subseteq Q$, $f(\emptyset)=0$,
- (ii) $f$ is monotone, i.e. if $A\subseteq B\subseteq Q$ then $f(A)\le f(B)$,
- (iii) $f$ is submodular, i.e. if $A$ and $B$ are different subsets of $Q$ then
$$ \eqno{(2)}
f(A)+f(B)\ge f(A\cap B) + f(A\cup B).
$$ </wikitex>
