$x =~
s/\n*\<table .*?\<\/table\>\n*\
s*/\n\$\$•\$\$\n/sg;
$x =~
s/<img align[^>]*>/\$•\$/sg;
804 bytes (123 words) - 13:38, 20 June 2014
''of a semi-group $S$''
...x of a semi-group $S$ if and only if $N$ is a class of some congruence on $S$ (cf. [[Congruence (in algebra)|Congruence (in algebra)]]).
683 bytes (121 words) - 20:27, 14 April 2014
...armonic function|harmonic function]] in a bounded simply-connected domain $S^+$ which, on the boundary $L$ of the domain, satisfies the condition
$$A(s)\frac{du}{dn}+B(s)\frac{du}{ds}+c(s)u=f(s),$$
734 bytes (129 words) - 19:41, 14 August 2014
...properties 1) $U(s,s) = I$; 2) $U(t,x)U(x,s) = U(t,s)$; and 3) $U(t,s) = U(s,t)^{-1}$.
...satisfied automatically. Under some circumstances, the restriction $t \ge s$ is a natural one, and the inverse need not exist at all.
740 bytes (119 words) - 18:43, 16 October 2017
...They are situated in the tangent plane to $S$ and have the same radius as $S$.
953 bytes (148 words) - 17:28, 1 August 2014
$$\prod_p\left(1-\frac{1}{p^s}\right)^{-1},$$
...erges absolutely for all $s>1$. The analogous product for complex numbers $s=\sigma+it$ converges absolutely for $\sigma>1$ and defines in this domain t
557 bytes (85 words) - 18:50, 18 October 2014
...[S]$ consists precisely of those rows of $I$ corresponding to vertices in $S$.
330 bytes (65 words) - 14:49, 10 January 2016
\def\S{\mathcal S} % subfamily
(in analogy to [[Helly's theorem]]) the smallest natural number $k$
549 bytes (88 words) - 12:15, 12 December 2013
[[Algebra|algebra]] $\Phi(S)$ over a field $\Phi$ with a basis $S$ that is at the same time a multiplicative
[[Semi-group|semi-group]]. In particular, if $S$ is a group, one obtains a
2 KB (344 words) - 19:41, 8 December 2015
...either $K(s,t)\equiv0$ if $a\leq s<t\leq b$ or $K(s,t)\equiv0$ if $a\leq t<s\leq b$. If such a function is the kernel of a linear integral operator, act
520 bytes (95 words) - 19:03, 27 April 2014
...[#References|[1]]], and if $S$ is a normal scheme, $A$ is projective over $S$, [[#References|[2]]].
1 KB (194 words) - 11:29, 27 January 2024
...which may be used to exhibit properties of various [[Dirichlet L-function]]s.
The Hurwitz zeta function $\zeta(\alpha,s)$ is defined for real $\alpha$, $0 < \alpha \le 1$ as
722 bytes (101 words) - 09:28, 19 March 2023
''of a semi-group $S$''
...complete inverse image of the [[unit element]] under some homomorphism of $S$ onto a [[Monoid|semi-group with unit element]].
644 bytes (108 words) - 18:31, 13 December 2014
..., method of]]). In Bateman's method, the degenerate kernel $ K _ {N} (x, s) $
K _ {N} (x, s) =
2 KB (269 words) - 10:33, 29 May 2020
\int\limits _ { a } ^ { b } \int\limits _ { a } ^ { b } K(x, s)
\phi (x) \overline{ {\psi (s) }}\; dx ds ,
839 bytes (120 words) - 10:59, 29 May 2020
See [[S-duality|$S$-duality]].
64 bytes (8 words) - 17:07, 3 November 2014
An integral equation in which the unknown function $\phi(s)$ occurs in a linear fashion:
$$A(x)\phi(x)+\int\limits_DK(x,s)\phi(s)ds=f(x),\quad x\in D.$$
378 bytes (72 words) - 16:46, 7 July 2014
A [[Symmetric operator|symmetric operator]] $S$ on a Hilbert space $H$ for which there exists a number $c$ such that
...n $A$ with the same lower bound $c$ (Friedrichs' theorem). In particular, $S$ and its extension have the same deficiency indices (cf. [[Defective value|
652 bytes (99 words) - 17:01, 2 July 2014
'' $ S $ with kernel $ A $''
with an epimorphism $ \phi : G \rightarrow S $
3 KB (416 words) - 12:53, 19 March 2023
Let $ S = \{ p _ {1} \dots p _ {n} \} $
...ight-line dual of the [[Voronoi diagram|Voronoi diagram]] generated by $ S $
2 KB (247 words) - 17:32, 5 June 2020
$$x=\Delta s-\frac{k_1^2\Delta s^3}{6}+o(\Delta s^3),$$
$$y=\frac{k_1\Delta s^2}{2}+\frac{k_1'\Delta s^3}{6}+o(\Delta s^3),$$
1 KB (245 words) - 16:53, 30 July 2014
algebra of Borel sets of an $ s $-
dimensional Euclidean space $ \mathbf R ^ {s} $.
6 KB (799 words) - 08:01, 6 June 2020
The direct product of automata $ \mathfrak A _ {i} = ( A _ {i} , S _ {i} , B _ {i} , \phi _ {i} , \psi _ {i} ) $,
is the automaton $ \mathfrak A = (A, S, B, \phi , \psi ) $
4 KB (613 words) - 18:49, 5 April 2020
...\setminus G(S)$ is a sub-semi-group (being, clearly, the largest ideal in $S$); such a semi-group is called a semi-group with isolated group part. The f
.... Soc. (1961)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> E.S. Lyapin, "Semigroups" , Amer. Math. Soc. (1974) (Translated from Russia
2 KB (266 words) - 15:55, 22 July 2014
An algebra $ S $
in which there are distinguished subspaces $ S _ \alpha $,
3 KB (378 words) - 19:39, 5 June 2020
\zeta(s)=\sum_{n=1}^\infty\frac{1}{n^s},\quad s=\sigma+it,
...f the zeta-function $\zeta(s)$ lie on the straight line $\operatorname{Re} s = 1/2$.
1 KB (160 words) - 20:17, 18 October 2014
''of valency $ s \geq 1 $''
A tensor of type $ ( 0, s) $,
3 KB (408 words) - 17:31, 5 June 2020
...gnals. Suppose that functions $ q ( y, s ^ \prime ; \widetilde{y} , s ^ {\prime\prime} ) $,
$ s ^ \prime , s ^ {\prime\prime} \in S $,
4 KB (540 words) - 16:43, 4 June 2020
...[[Clifford semi-group]]. The set $S^*$ of all characters of a semi-group $S$ forms a commutative semi-group with identity (the character semi-group) un
(\chi*\psi)(a) = \chi(a)\cdot\psi(a)\,,\ \ a\in S\,,\ \ \chi,\psi\in S^* \ .
3 KB (459 words) - 19:54, 1 January 2018
\int\limits _ { a } ^ { b } K ( x , s ) \phi ( s) d s ,
\int\limits _ { a } ^ { b } K ( x , s ) \phi ( s) d s = f ( s)
2 KB (335 words) - 16:32, 13 July 2021
...the power is in the interval $1\le p < \infty$, then the $L^p$ space $L^p(S, F, \mu)$ contains the equivalence classes of complex measurable functions
\int_S |f(s)|^p \; d\mu(s) < \infty
1 KB (217 words) - 14:53, 11 November 2023
...generating series for $\Lambda(n)$ is the logarithmic derivative of $\zeta(s)$:
-\frac{\zeta'(s)}{\zeta(s)} = \sum_n \Lambda(n) n^{-s}\ \ \ (\Re s > 1)
1 KB (164 words) - 18:33, 18 October 2014
...
s mapping $f : X \to Q^n$, $n = 1, 2, \dots ,$ is inessential (Aleksandrov'
s theorem).
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> P.
S. Aleksandrov, "Topologie" , '''1''' , Springer (1974)</TD></TR><TR><TD v
1 KB (230 words) - 06:26, 14 January 2017
...imes$ denotes the tensor product over the ring of integers, and $(r\otimes s)b = rbs$. For every left $R$-module $M$ one has the situation ${}_R M_E$, w
...}_R C_S$ that is left $R$-linear and right $S$-linear. The category of $(R,S)$-bimodules with bimodule morphisms is a [[Grothendieck category]].
2 KB (277 words) - 17:01, 23 November 2023
$$\frac h6(S+S'+4S''),$$
...e $h$ is the distance between the bases, $S$ and $S'$ are their areas and $S''$ is the area of the intersection that has equal distance to both bases.
967 bytes (161 words) - 16:41, 8 May 2024
P_n(F) = \{ s \in \mathrm{GL}_n(F) : \text{last row}\,(s) = (0,0,\ldots,1) \} \ .
...ean (cf. also [[Archimedean axiom]]), both conjectures are true (Bernstein's theorems).
1,010 bytes (146 words) - 08:10, 23 March 2018
...ng $A$ with an identity, then the symmetric algebra of $M$ is the algebra $S(M) = T(M)/I$, where $T(M)$ is the [[tensor algebra]] of $M$ and $I$ is the
S(M) = \bigoplus_{p \ge 0} S^p(M)
3 KB (487 words) - 18:21, 11 April 2017
''Ore's condition''
...]]s intersect is ''left reversible'': $\forall a,b, \in S\ \exists x,y \in S \ :\ ax = by$. A commutative semi-group is reversible, as $ab=ba$. A semi
588 bytes (88 words) - 11:41, 2 October 2016
For each $ s> 0 $,
let $ \tau _ {s} $
2 KB (273 words) - 16:15, 13 January 2021
$$\phi(x)+\int\limits_a^bK(x,s)f[s,\phi(s)]ds=0,\quad a\leq x\leq b,$$
...i.e. all its eigen values are positive. If, in addition, the function $f(x,s)$ is continuous and satisfies the condition
2 KB (338 words) - 11:07, 24 August 2014
Let $ S $
be a symbol with $ \omega \notin S $.
3 KB (455 words) - 08:11, 6 June 2020
...ays regular (cf. [[Maximal torus|Maximal torus]]). In general, a torus $ S \subset G $
is regular if and only if its centralizer $ C _{G} (S) $
2 KB (286 words) - 15:07, 17 December 2019
...s the same as the [[Voronoi diagram|Voronoi diagram]] of that set $S$. If $S$ is a [[Lattice|lattice]], it is also called the Dirichlet–Voronoi tiling
509 bytes (70 words) - 19:53, 29 April 2014
...special conditions: a right translation of a [[Semi-group|semi-group]] $ S $
for any $ x, y \in S $;
4 KB (612 words) - 08:26, 6 June 2020
''of a non-cooperative game $ \Gamma = \langle J , \{ S _ {i} \} _ {i \in J } , \{ H _ {i} \} _ {i \in J } \rangle $''
...on-cooperative game]] $ \widetilde \Gamma = \langle J , \{ \widetilde{S} {} _ {i} \} _ {i \in J } , \{ \widetilde{H} {} _ {i} \} _ {i \in J } \
4 KB (563 words) - 08:09, 6 June 2020
...$ there exist antipodes with a common image; 2) Any mapping of the sphere $
S^n$ into itself in which the images of antipodes are antipodes is an [[essen
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> K. Borsuk, "Drei
Sätze über die $n$-dimensionale euklidische Sphäre" ''Fund. Math.'' , '''
1 KB (163 words) - 06:23, 28 October 2017
...om mappings are those for which $\mathsf{P}\{\sigma=s\} = n^{-n}$ for all $s \in\Sigma_n$. A realization of such a random mapping is the result of a sim
782 bytes (121 words) - 17:57, 22 November 2016
In order that a surface $ S $
with metric $ d s ^ {2} $
1 KB (165 words) - 08:11, 6 June 2020
A measurable, in general complex-valued, function $ K (x, s) $
satisfying the conditions: 1) $ \overline{ {K (x, s) }}\; = K (s, x) $
873 bytes (124 words) - 11:32, 30 May 2020
$#C+1 = 15 : ~/encyclopedia/old_files/data/S083/S.0803210 Sample variance,
S _ {n} ( x) = \
2 KB (247 words) - 08:12, 6 June 2020
be independent random variables, let $ S _ {k} = \sum_{i=1}^ {k} X _ {i} $
{\mathsf P} \left \{ \max _ {1\leq k \leq n } ( S _ {k} - m ( S _ {k} -
2 KB (317 words) - 10:43, 20 January 2024
...ow \mathcal{P}S$ is a ''closure operation'' if for all $A,B \in \mathcal{P}S$:
A pair $(S,\mathrm{Cl})$ is a ''closure space'' if and only if $\mathrm{Cl}$ satisfies
2 KB (285 words) - 17:42, 13 October 2023
\sum_{n=1}^\infty \frac{1}{n^s} = \prod_p \left({1 - \frac{1}{p^s} }\right)^{-1}
...prime numbers $p$. The Euler identity also holds for all complex numbers $s = \sigma + it$ with $\sigma > 1$.
2 KB (279 words) - 19:13, 14 December 2015
...sitive integers with greatest common divisor $1$. The Frobenius number of $S$ is the largest natural number that cannot be written as a linear integer c
314 bytes (50 words) - 15:24, 10 August 2014
...Hilb}_{X/S}(S^*)=\Hom_S(S^*,\operatorname{Hilb}(X/S))$. In particular, if $S$ is the spectrum of a field $k$ (cf. [[Spectrum of a ring|Spectrum of a rin
...$. For any connected ground scheme $S$ the scheme $\operatorname{Hilb}^P(X/S)$ is also connected [[#References|[2]]].
3 KB (484 words) - 05:48, 17 April 2024
...ng to $S$. The Aitken $\Delta ^ { 2 }$ process consists of transforming $( S _ { n } )$ into the new sequence $( T _ { n } )$ defined, for $n = 0,1 , \d
...} + S _ { n } } = S _ { n } - \frac { \Delta S _ { n } } { \Delta ^ { 2 } S _ { n } }, \end{equation*}
9 KB (1,390 words) - 20:20, 25 January 2024
...ut its mean surface by a [[Conjugate net|conjugate net]] of lines. Let $ S $
...aucour congruence. Then there is a family of surfaces corresponding to $ S $
2 KB (305 words) - 08:11, 6 June 2020
...rity) $\phi_i(v+u)=\phi_i(v)+\phi_i(u)$. These axioms were introduced by L.S. Shapley [[#References|[1]]] for an axiomatic definition of the expected pa
$$\phi_i(v)=\sum_{i\in S}\frac{(|S|-1)!(n-|S|)!}{n!}[v(S)-v(S\setminus\{i\})].$$
2 KB (304 words) - 12:43, 19 August 2014
..., is an extension of the Darboux pencil. A (non-developable) hypersurface $S$ degenerates into a hyper-quadric if and only if its generalized [[Darboux
<TR><TD valign="top">[1]</TD> <TD valign="top"> S.P. Finikov, "Projective-differential geometry" , Moscow-Leningrad (1937)
2 KB (240 words) - 08:52, 8 April 2023
...eory of canonical correlations the random variables $ X _ {1} \dots X _ {s} $
and $ X _ {s+1} \dots X _ {s + t } $,
2 KB (363 words) - 06:29, 30 May 2020
$#C+1 = 50 : ~/encyclopedia/old_files/data/S087/S.0807200 Star body
An open set $ \mathfrak S $
3 KB (521 words) - 20:42, 16 January 2024
Two functions $ K ( x, s) $
and $ K _ {1} ( x, s) $
3 KB (440 words) - 17:48, 13 January 2024
...p in the ring of all endomorphisms of this group is a division ring (Schur's lemma).
587 bytes (95 words) - 19:54, 11 April 2014
\int\limits _ \Omega K ( x , s , \phi ( s) ) d s + f ( x) ,\ \
...bounded closed set in a finite-dimensional Euclidean space and $ K ( x , s , t ) $
3 KB (455 words) - 08:27, 6 June 2020
...tioned into left ideals which are (necessarily isomorphic) groups; and d) $S$ is the direct product of a group and a right zero semi-group (cf. [[Idempo
1 KB (167 words) - 17:09, 8 January 2021
...{a_s\}$ and $\{b_s\}$ be certain sets of complex numbers, $s\in S$, where $S$ is a finite or an infinite set of indices. The following inequality of Hö
...q \Bigl(\sum\limits_{s\in S}|a_s|^p\Bigr)^{\frac1p}\Bigl(\sum\limits_{s\in S}|b_s|^q\Bigr)^{\frac1q},
4 KB (729 words) - 16:13, 29 November 2012
If $ \mathbf r = \mathbf r ( s) $(
where $ s $
3 KB (450 words) - 19:38, 5 June 2020
L(a,s) = \sum_{n=1}^\infty a(n) n^{-s}
L(a,s) + L(b,s) = \sum_{n=1}^\infty (a+b)(n) n^{-s}
2 KB (358 words) - 17:25, 11 November 2023
A function $(x,s)\mapsto K_n(x,s)$ that is formed from the given kernel $K$ of an [[Integral operator|integr
$$K_1(x,s)=K(x,s),\quad K_n(x,s)=\int\limits_a^bK_{n-1}(x,t)K(t,s)dt.$$
2 KB (292 words) - 19:24, 9 October 2014
...phere]]. This group is presented by generators $R$, $S$ and relations $R^3=S^3=(RS)^2$.
* {{Ref|a1}} H.S.M. Coxeter, "Regular complex polytopes", Cambridge Univ. Press (1991) pp. 7
365 bytes (50 words) - 13:54, 8 April 2023
...ally assumed that the effect of the noise on the signal is additive: $x(t)=s(t)+n(t)$. In such a situation the problems of signal extraction are as outl
...More involved varieties of the initial hypothesis are also studied: $x(t)=s(t)+n(t)$ starting from some moment, possibly random, of time $\tau$, which
2 KB (383 words) - 14:54, 13 August 2014
...ring of fractions (cf. [[Fractions, ring of|Fractions, ring of]]) $ A [ S ^ {-1} ] $,
where $ S $
4 KB (713 words) - 21:35, 4 January 2021
''of a convex surface $S$''
...ting from some point $O\in S$ and belonging to the convex body bounded by $S$. The limit cone is defined uniquely, up to a parallel displacement dependi
1 KB (161 words) - 05:57, 18 October 2014
defined by G.W. Whitehead. In $ S ^ {k} $
Then the product of spheres $ S ^ {m} \times S ^ {n} $
4 KB (505 words) - 15:48, 29 March 2021
...$ is introduced on the bicharacteristic strip, then its equations $x_i=x_i(s)$, $i=1,\dots,n$, are defined by solving a system of $2n$ ordinary differen
\begin{equation}\dot x_i(s)=Q_{\xi_i},\quad\dot\xi_i=-Q_{x_i},\quad i=1,\dots,n.\label{*}\end{equation
3 KB (419 words) - 22:32, 10 December 2018
with at most a countable set of states $ S $:
i, j \in S.
2 KB (239 words) - 09:50, 29 October 2023
A morphism of schemes $ f: X \rightarrow S $
such that the pre-image of any open affine subscheme in $ S $
3 KB (464 words) - 05:59, 19 March 2022
U = \alpha _ {1} X _ {1} + \dots + \alpha _ {s} X _ {s} ,\ \
V = \beta _ {1} X _ {s+1} + \dots + \beta _ {t} X _ {s+t} $$
3 KB (346 words) - 08:00, 25 April 2022
A model of the manifold of lines in a three-dimensional elliptic space $ S _ {3} $
on a pair of two-dimensional elliptic planes $ S _ {2} $.
3 KB (461 words) - 19:40, 5 June 2020
...$. The shortest-path problem is to find a least cost (shortest) path from $s$ to every other vertex (node) $i$.
...eeds by constructing, one node at a time, a subtree $T$ rooted at $s$ (an $s$-[[arborescence]]). If $\Gamma$ is connected, $T$ will be a spanning subtre
2 KB (405 words) - 19:42, 6 September 2017
$$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