A(x) = \int_{a}^{b} K(t,s) ~ x(s) ~ \mathrm{d}{s};
A(x) = \int_{a}^{b} K(t,s) ~ g(s,x(s)) ~ \mathrm{d}{s};
2 KB (399 words) - 05:44, 7 December 2016
...[[Dirichlet series]]. It is used in the study of [[arithmetic function]]s and yields a proof of the [[Prime number theorem]]. It was proved by [[No
...function|analytic]] for $\Re s \ge 1$, except for a simple [[pole]] at $s=1$ with residue 1. Then the [[Limit of a function|limit]] as $x$ goes to i
2 KB (298 words) - 20:23, 15 November 2023
...) it can be represented as the union of non-intersecting components (Luzin's criterion).
356 bytes (55 words) - 21:57, 19 December 2014
...p $S$ is separable if and only if its characters separate the elements of $S$.
947 bytes (144 words) - 17:58, 22 December 2023
...age of the particle was zero, then the generating function $F(t,s)={\rm E}s^{\mu(t)}$ of the number of particles $\mu(t)$ satisfies the non-linear inte
$$F(t,s) = \int_0^th(F(t-u,s))dG(u) + s(1-G(t)).$$
1 KB (204 words) - 19:33, 28 October 2014
''constructed from an automorphism $S$ of a [[Measure space|measure space]] $(X,\nu)$ and a measurable function $
...re. The motion takes place in such a way that the second coordinate of $(x,s)$ increases with unit speed until it reaches the value $f(x)$, and then the
2 KB (367 words) - 14:04, 30 August 2014
...the property that no element of $S$ is equal to a sum of two elements of $S$. It is known that in general a subset of $M$ of size $n$ contains a sum-f
The [[Cameron–Erdős conjecture]], proved by Ben Green in 2003, asserts that the set $\{1,\ldots
660 bytes (110 words) - 16:47, 23 November 2023
associating to each [[Semi-group|semi-group]] $ S $
a congruence $ \rho ( S) $(
5 KB (767 words) - 14:54, 7 June 2020
...dius function for a one-parameter family of spheres with centres in $\zeta(s)$, then the canal surface enveloping this family is characterized by the fo
\langle r - \zeta(s), r - \zeta(s) \rangle = R^2(s) \,,
3 KB (414 words) - 09:10, 26 March 2023
f ( s ) = \int\limits _ { 0 } ^ \infty {e ^ {- st } } {dG ( t ) } = {\lim\lim
If the integral converges for some complex number $ s _ {0} $,
2 KB (240 words) - 22:15, 5 June 2020
...dimensional sphere $S^2$; also, every cactoid is a monotone open image of $S^2$.
460 bytes (78 words) - 22:20, 1 November 2014
...o describe the conversion of a substrate in an enzymatic reaction. Let $ S ( t ) $
The reaction rate is proportional to $ S ( t ) $
4 KB (605 words) - 08:00, 6 June 2020
\sum_{\mathfrak{p}\in A} N(\mathfrak{p})^{-s} = a \log\frac{1}{1-s} + g(s)
holds, where $g(s)$ is regular in the closed half-plane $\mathrm{Re}(s) \ge 1$, then $A$ is a regular set of prime ideals and $a$ is called its Di
2 KB (310 words) - 09:04, 26 November 2023
f ( s) \sim \sum _ { n } A _ {n} e ^ {\Lambda _ {n} \tau }
\sum _ { n } A _ {n} e ^ {\Lambda _ {n} s } ,\ \alpha < \tau < \beta ,
3 KB (422 words) - 19:35, 5 June 2020
...this means that with each integer (or natural number) a transformation $ S _ {n} : W \rightarrow W $
S _ {n+m} (w) = \
3 KB (418 words) - 05:47, 18 May 2022
$ {\mathcal F} _ {s} \subseteq {\mathcal F} _ {t} \subseteq {\mathcal F} $,
$ s \leq t $,
1 KB (210 words) - 19:42, 5 June 2020
\frac{y ^ {s + 2k } ds }{s ( s + 1) \dots ( s + 2k) }
1 KB (147 words) - 19:35, 5 June 2020
...Lyapunov's first method for investigating stability is based) and Lyapunov's second method (see [[Lyapunov function|Lyapunov function]]). The results an
936 bytes (124 words) - 17:08, 7 February 2011
* H. S. M. Coxeter, S. L. Greitzer, "Geometry Revisited", Mathematical Association of America (19
513 bytes (74 words) - 16:32, 14 August 2023
...ional manifold which is homotopy equivalent to the $n$-dimensional sphere $S^n$ is homeomorphic to it; at present (1991) it has been proved for all $n\g
...align="top">[a1]</TD> <TD valign="top"> S. Smale, "Generalized Poincaré's conjecture in dimensions greater than four" ''Ann. of Math. (2)'' , '''74'
1 KB (197 words) - 17:53, 10 April 2023