$$k_1=\phi(s),\quad k_2=\psi(s),$$
...pace, with [[Curvature|curvature]] $\phi(s)$ and [[Torsion|torsion]] $\psi(s)$. A necessary and sufficient condition for a curve to be in a plane is tha
2 KB (304 words) - 19:04, 26 January 2024
The number $s$ equal to the square root of the [[Arithmetic mean|arithmetic mean]] of the
$$s=\sqrt\frac{a_1^2+\dots+a_n^2}n.$$
259 bytes (45 words) - 13:55, 30 December 2018
...or]] of any element is a principal left ideal on an idempotent element of $S$.
Examples include the monoid of [[binary relation]]s on a set $A$ under composition of relations, with the empty relation as zer
714 bytes (106 words) - 16:43, 23 November 2023
...ntinuously on $t \in \mathbf{R}$. For $s \in \mathbf{R}$, denote by $C _ { S } : \mathbf{R} \rightarrow \mathcal{L} ( V )$ the solution of the initial v
\begin{equation*} X ( s ) = 0 , X ^ { \prime } ( s ) = I. \end{equation*}
2 KB (315 words) - 16:46, 1 July 2020
is called the remainder (in Peano's form). Given the asymptotic expansion
\Gamma ( s + 1 ) = \sqrt {2 \pi s } \left (
2 KB (344 words) - 09:03, 6 January 2024
...There are various generalizations of a self-perimeter for the unit sphere $S$ in a normed space of dimension greater than two (see [[#References|[5]]],
...69) pp. 431–443</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> S. Gołab, "Sur la longuer d'indicatrice dans la géometrie plane de Minkow
2 KB (271 words) - 14:01, 1 October 2014
A locally trivial [[Fibration|fibration]] $ f: S ^ {2n - 1 } \rightarrow S ^ {n} $
Here, for example, $ X \star S ^ {0} = SX $,
3 KB (436 words) - 22:11, 5 June 2020
...ecisely, a homomorphism of an automaton $ \mathfrak A _ {1} = (A _ {1} , S _ {1} , B _ {1} , \phi _ {1} , \psi _ {1} ) $
into an automaton $ \mathfrak A _ {2} = (A _ {2} , S _ {2} , B _ {2} , \phi _ {2} , \psi _ {2} ) $(
3 KB (366 words) - 18:49, 5 April 2020
...onvergence of a sequence. What is needed is convergence of nets. A net $ S : D \rightarrow X $
converges to a point $ s \in X $
1 KB (190 words) - 08:02, 6 June 2020
...taining $R$. If $\bar R = R$, then $R$ is said to be integrally closed in $S$ (cf. also [[Integral ring]]).
...ty $R$ is called normal if it is reduced (i.e. has no [[nilpotent element]]s $\neq 0$) and is integrally closed in its complete ring of fractions (cf. [
2 KB (305 words) - 16:09, 11 September 2016
A \prod _ {S} B &\ \mathop \rightarrow \limits ^ { {p _ A}} \ & A \\
B &\ \mathop \rightarrow \limits _ \beta \ &S . \\
2 KB (209 words) - 11:42, 8 February 2020
An element of an algebraic structure $S$, often denoted $1$, $I$ or $e$, with a specific property with respect to a
\forall x \in S \ \ 1 * x = x * 1 = x\ .
375 bytes (55 words) - 18:27, 13 December 2014
\omega \wedge ( d \omega ) ^ {s} ( x) \neq 0 ,\ \
( d \omega ) ^ {s+1} ( x) = 0 ;
2 KB (331 words) - 07:53, 9 January 2024
...s the [[evolute]] of $\bar\gamma$. If $\mathbf{r} = \mathbf{r}(s)$ (where $s$ is the arc length parameter of $\gamma$) is the equation of $\gamma$, then
\bar{\mathbf{r}} = \mathbf{r}(s) + (c-s)\tau(s) \,,
2 KB (317 words) - 21:09, 17 December 2017
...ernel of an integral operator|Kernel of an integral operator]]) $ K ( x, s) $,
$ a \leq x, s \leq b $,
1 KB (223 words) - 22:10, 5 June 2020
...s therefore a consequence of the Riemann conjecture on the zeros of $\zeta(s)$ (cf. [[Riemann hypotheses|Riemann hypotheses]]). It is known (1982) that
...r la croissance de la fonction zêta(s)", Bull. des sciences mathématiques, série 2, vol. 32, 1908. Claude Henri Picard
2 KB (299 words) - 18:59, 7 December 2014
$$ \int \limits_0^1 \dots \int \limits_0^1 |S|^{2k} d \alpha_1 \dots d \alpha_n, $$
$$ S = \sum_{1 \leq x \leq P} e^{2 \pi i (\alpha_1 x + \dots + \alpha_n x^n)}, $
580 bytes (91 words) - 21:35, 14 January 2017
A mapping $s : Y \rightarrow X$ for which $p \circ s = \mathrm{id}_Y$. In a wider sense, a section of any morphism in an arbitra
...a section over $U$ of $p$ is a mapping $s : U \rightarrow X$ such that $p(s(u)) = u$ for all $u \in U$.
769 bytes (149 words) - 18:13, 15 November 2014
A formula expressing the surface area $S$ of a triangle in terms of its sides $a$, $b$ and $c$:
$$S=\sqrt{p(p-a)(p-b)(p-c)},$$
527 bytes (83 words) - 18:02, 17 April 2023
''least upper bound, on a set $ S $''
which is the finest of all topologies on $ S $
3 KB (490 words) - 08:27, 6 June 2020