...closed if it is bounded by the two plane domains interior to the curves of intersection of planes $\pi_1$ and $\pi_2$ with it.
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$#C+1 = 17 : ~/encyclopedia/old_files/data/I052/I.0502010 Intersection index (in algebraic geometry)
The number of points in the intersection of $ n $
2 KB (289 words) - 06:42, 29 December 2021
...ll these sets (the set of elements common to all $A_\alpha$) is called the intersection of these sets.
The intersection of these sets is denoted by $\bigcap A_\alpha$.
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- the [[centroid]] (''i.e.'' the centre of mass), the common intersection point of the three medians (see [[Median (of a triangle)]]);
- the incentre, the common intersection point of the three bisectrices (see [[Bisectrix|Bisectrix]]) and hence the
2 KB (333 words) - 08:29, 23 November 2023
...$A_i = \{ n \in \mathbf{Z} : n > i \}$ is centred; any family in which the intersection of all members is not empty is centred. Every finite centred family of sets
...s compact if and only if every centred family of closed sets has non-empty intersection. Centred families of closed sets in a topological space are used for the co
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in the same plane defined as follows: 1) the intersection of $ G ^ {*} $
is either empty or is the entire circle, depending on whether the intersection of $ G $
2 KB (241 words) - 16:44, 4 June 2020
...point $H$ of intersection of the altitudes of a triangle, the point $S$ of intersection of its [[Median (of a triangle)|median]]s (the [[centroid]]), and the centr
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In a topological space $X$ a subset which is the countable intersection of open sets. See [[Borel set]] and also [[F-sigma]].
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...ion of all modular maximal right ideals (cf. [[Modular ideal]]); it is the intersection of all modular maximal left ideals; it contains all quasi-regular one-sided
...adical $J(A)$ is the intersection of all right maximal ideals and also the intersection of all left maximal ideals. Nakayama's lemma says that if $M$ is a finitely
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...$ denote the operations of [[union of sets|union]], [[intersection of sets|intersection]], [[Difference of two sets|difference]], and [[complementation]] of sets,
...{P}(X)$ of a set $X$ (the set of subsets of $X$), in contrast to union and intersection. This ring is the same as the ring of $\mathbb{Z}/2\mathbb{Z}$-valued funct
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The ellipse of least surface area obtained as the intersection of a one-sheet [[Hyperboloid|hyperboloid]] with a plane perpendicular to it
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An ideal $I$ of a ring $R$ which cannot be expressed as the intersection of a right [[fractional ideal]] $r(I,A)$ and an ideal $B$, each strictly la
...or left and right fractional ideals, and that every ideal decomposes as an intersection of finitely many indecomposable ideals. Then for every ideal $Q$ there exis
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...rsection of the bisectrix of the angle $C$ with $AB$, and the point $L$ of intersection of the bisectrix of the external angle $C$ with $AB$ forms a [[harmonic qua
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The intersection $M$ of all subspaces containing $A$. The set $M$ is also called the subspac
...l of a set $A$ is called the ''[[linear closure]]'' of $A$; it is also the intersection of all closed subspaces containing $A$.
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...all maximal modular right ideals of an associative ring coincides with the intersection of all maximal left modular ideals and is the [[Jacobson radical]] of the r
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...of these is the point of intersection of $l$ and $l'$, then the points of intersection of $AB'$ and $A'B$, $BC'$ and $B'C$, $AC'$ and $A'C$ are collinear.
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...posite to this vertex at a point on the line passing through the points of intersection of the remaining pairs of non-adjacent sides of the pentagon (see Fig. b).
...t $C$ and $D$ with the sides $AD$ and $BC$, respectively, and the point of intersection of $AB$ and $CD$ are collinear (see Fig. c).
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...d $L^{i+1} = L L^i$, $i \ge 0$, with $\lambda$ denoting the empty string), intersection with [[regular language]]s, morphisms (non-erasing in the context-sensitive
1) union, Kleene ${+}$, non-erasing morphisms, inverse morphisms, and intersection with regular languages is closed under concatenation;
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The point of intersection of the lines joining the vertices of a triangle to the points where the sid
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$#C+1 = 57 : ~/encyclopedia/old_files/data/I052/I.0502020 Intersection index (in homology)
...erizing the algebraic (i.e. including orientation) number of points in the intersection of two subsets of complementary dimensions (in [[General position|general p
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...f a given ring is a [[lattice]], $S(R)$, with respect to the operations of intersection and join of subrings. The set of ideals (cf. [[Ideal]]) of this ring forms
2 KB (297 words) - 17:54, 3 January 2016
...und the circles $c$ and $c'$ while preserving the distance $TT'$, i.e. the intersection line will be an ellipse ($MF'+MF=TT'$, $MF'=MT'$ and $MF=MT$). In the case
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...sets in $X$ with empty intersection contains a finite subfamily with empty intersection; 2) every [[Ultrafilter|ultrafilter]] in $X$ is convergent; and 3) every op
1 KB (185 words) - 20:48, 16 October 2014
...dges that have no common vertex are called opposite; the points $P,Q,R$ of intersection of the opposite edges are called diagonal points.
If $S$ and $T$ are the points of intersection of the line $PQ$ with the lines $AD$ and $BC$, then the four points $P,Q,S,
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An ideal $I$ in a ring which cannot be expressed as the intersection of two strictly larger ideals: that is, $I = J \cap K \Rightarrow I=J \ \te
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The [[Closure of a set|closure]] of the [[linear hull]] of $A$; the intersection of all closed linear subspaces of $T$ containing $A$.
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...ction, respectively union, of a finite number, and the union, respectively intersection, of any number of elements of $\mathfrak G$, respectively $\mathfrak F$, is
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...n $R$ is the smallest transitive relation containing $R$: equivalently the intersection of all transitive relations containing $R$ (there exists at least one such,
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The point of intersection of the straight lines joining the vertices of a triangle to the points at w
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...with as simplices the finite non-empty subsets of $\alpha$ with non-empty intersection. In particular, the vertices of $K(\alpha)$ are the non-empty elements of $
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A point $x$ such that every neighbourhood of it has non-empty intersection with $A$. The set of all proximate points forms the closure $[A]$, or $\bar
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...ions containing the zero and identity operations and which is closed under intersection of projections (i.e., taking the greatest lower bound) and union of project
1 KB (219 words) - 14:33, 24 September 2014
...nvex polygon is the [[convex hull]] of a finite set of points and also the intersection of a finite number of closed half-spaces.
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...r contact with $S$ at $x$ one can select the quadrics in which the line of intersection with $S$ has a singular point $x$ with three coincident tangents. On the su
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...h (possibly empty), and a subset $F\subset X$ is closed if and only if its intersection with every simplex is closed. Every simplicial space is a [[Cellular space|
2 KB (252 words) - 16:30, 9 April 2014
is a vector group if and only if its partial order is an intersection of total orders on $ G $.
where this intersection is taken over all combinations of signs $ \epsilon _ {i} = \pm 1 $,
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...solutely convex if and only if for any elements $g\not\in H$, $a\in H$ the intersection $S(g)\cap S(ga)$ is non-empty, where $S(x)$ is the minimal invariant sub-se
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The minimal [[Convex set|convex set]] containing $M$; it is the intersection of all convex sets containing $M$. The convex hull of a set $M$ is denoted
The closure of the convex hull is called the closed convex hull. It is the intersection of all closed half-spaces containing $M$ or is identical with $E^n$. The pa
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...of a set $M$ in a topological space $X$ is a point $x\in X$ such that the intersection of $M$ with any neighbourhood of $x$ has the same cardinality as the entire
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...the intersection points of the opposite sides, and let $C$ and $D$ be the intersection points of the diagonals $SQ$ and $PR$ of $PQRS$ with the straight line $AB$
2 KB (278 words) - 13:42, 29 April 2014
...mension theory and the theory of multiplicities (and [[Intersection theory|intersection theory]]), cf. [[#References|[a1]]], [[#References|[a2]]], [[#References|[a
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A point $a\in A$ such that the intersection of some [[Neighbourhood|neighbourhood]] of $a$ with $A$ consists of the poi
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...utions is, by definition, the [[Intersection index (in algebraic geometry)|intersection index (in algebraic geometry)]] of the hypersurfaces \eqref{*} at the respe
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...[[injective hull]] $E$ of the module $M/N$ (cf. [[Injective module]]) the intersection of the kernels of the homomorphisms from $E$ into $E_1$ is trivial. Another
3 KB (455 words) - 19:51, 5 October 2017
...the complex [[projective plane]] is an asymmetric variety, since the self-intersection of the complex straight line is $+1$ or $-1$, depending on the orientation.
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A subset of $X$ that is the intersection of an [[open set]] and a [[closed set]] in $X$: equivalently, a subset that
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Two closed curves obtained as the intersection of two cylinders the axes of which intersect at right angles. The parametri
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...mension $k\times l$, where $1<k<m$, $1<l<n$, formed by the elements at the intersection of $k$ specified rows and $l$ specified columns of $A$ with retention of th
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A submodule $E$ of $M$ is essential it has a non-trival intersection with every non-trivial submodule of $M$: that is, $E \cap L = 0$ implies $L
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...each point $M$ in $\pi$ is put into correspondence with the point $M_1$ of intersection of the straight line $SM$ with $\pi_1$ (if $SM$ is not parallel to $\pi_1$,
...subspace of minimal dimension containing $U$ and $T$ and let $U_1$ be the intersection of $W$ and $V_1$.
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$#C+1 = 58 : ~/encyclopedia/old_files/data/I052/I.0502000 Intersection homology
...pecial stress on [[Poincaré duality|Poincaré duality]] in its homological (intersection) form: Let $ M $
7 KB (1,043 words) - 22:13, 5 June 2020
...ity on two straight lines $a$ and $b$ and let $G$ and $K$ be the points of intersection of these lines with the absolute of the space. Then the angle $\phi$ betwee
...the direction vectors of the isotropic lines passing through the point of intersection of the lines $a$ and $b$.
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...ential submodule. The sum of all inessential submodules coincides with the intersection of all maximal submodules. A left ideal $I$ belongs to the Jacobson radical
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Thus, one of the tangents at the node has intersection multiplicity at least $4$ with the curve at that point.
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The intersection of all flats (translates of subspaces) of $V$ containing $M$.
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...]]) consisting of cosets with respect to closed submodules has a non-empty intersection. Every linearly-compact module is a complete topological group.
...every finite intersection of elements of $\{V_\alpha\}$ is non-empty, the intersection $\bigcap V_\alpha$ is non-empty. Such a linear subvariety is closed.
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...to be ''essential'' if whenever $H$ is a non-trivial subgroup of $G$, the intersection of $S$ and $H$ is non-trivial: here "non-trivial" means "containing an ele
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A plane curve obtained as the intersection of a circular cone with a plane not passing through the vertex of the cone
...rix is called the parameter. A parabola is a symmetric curve; the point of intersection of a parabola with its axis of symmetry is called the vertex of the parabol
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...which there exists a family of cardinality $\tau$ of sets open in $X$ with intersection $A$. It is usually denoted by $\psi(A,X)$. The pseudo-character $\psi(A,X)$
...s the smallest infinite cardinal number $\tau$ such that each point is the intersection of a family of cardinality $\leq\tau$ of sets which are open in $X$. Spaces
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The curve of intersection of the surfaces of a sphere of radius $R$ and a certain circular cylinder o
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...perations of [[Union of sets|union]] $R_1\cup R_2$, [[Intersection of sets|intersection]] $R_1\cap R_2$, and negation or [[Relative complement|complementation]] $R
...the Cartesian product $A \times B$. As before we may speak of the union, intersection or negation of $R$ as a relation on $A \times B$. The transpose $R^t$ is n
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such that the following (compactness-type) intersection property holds:
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The foci of a second-order curve can be defined as the points of intersection of the tangents to that curve from the [[circular points]] of the plane. Th
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...e ring]] with unit element in which any [[Prime ideal|prime ideal]] is the intersection of the [[maximal ideal]]s containing it, i.e. a ring any integral quotient
...a (non-commutative) ring $A$ is a Jacobson ring if every prime ideal is an intersection of [[primitive ideal]]s or, equivalently, if every prime factor ring $A/\ma
3 KB (415 words) - 20:32, 19 January 2016
The intersection of two nets of circles is a pencil of circles. An elliptic net contains onl
...e of which is parabolic can only be an elliptic or a parabolic pencil. The intersection of two nets one of which is non-degenerate can only be a non-degenerate pen
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...d by the spherical [[Polygon|polygon]] (see Fig.) which is obtained by the intersection of the faces of the polyhedral angle with a sphere of unit radius with cent
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with non-empty intersection, i.e. $ \cap \{ {U } : {U \in \mathfrak B ^ \prime } \} \neq \emptyset
has the finite intersection property (i.e. the intersection of any finite number of $ U _ \alpha $
4 KB (580 words) - 09:08, 26 March 2023
set, but their intersection need not be. A set which is a finite intersection of $ \kappa a $-
2 KB (408 words) - 06:29, 30 May 2020
are coprime, then the intersection of $ V $
are not coprime, this intersection also lies on an unknotted torus $ T ^ {2} \subset S ^ {3} $,
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intersection and union. The ideal of the intersection $X\cap Y$ is identical
identical with the intersection of their ideals ${\mathfrak A}_X \cap {\mathfrak A}_Y$. Any set ${\bar k}^n
4 KB (616 words) - 21:49, 30 March 2012
The point of intersection of the three altitudes of a triangle, one of the classical [[triangle centr
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...any two (or any set of) subgroups of a group $G$ is a subgroup of $G$. The intersection of all subgroups of $G$ containing all elements of a certain non-empty set
3 KB (467 words) - 14:22, 30 August 2014
...pole $O$ intersects the cochleoid; the tangents to the cochleoid at these intersection points pass through the same point.
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...gated. It is a complete chain, i.e., it is closed with respect to join and
intersection. The system <img align="absmiddle" border="0" src="https://www.encyclopedia
...ncyclopediaofmath.org/legacyimages/c/c110/c110400/c11040090.png" /> is the
intersection of a suitable set of prime subgroups. If <img align="absmiddle" border="0"
15 KB (2,061 words) - 17:13, 7 February 2011
...space|Hausdorff]] [[topological space]] in which a subset is closed if its intersection with any compact subset is closed. Every [[locally compact space|locally c
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If the partial order of $R$ is an intersection of total orders, then $R$ is a vector ring, and $R$ itself, provided with v
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...following axioms: $X$ itself and the empty set $\emptyset$ are closed; the intersection of any number of closed sets is closed; the union of finitely many closed s
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...numbers $2,3,5$. The icosahedral space can be defined analytically as the intersection of the surface
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...and is closed under the set-theoretic operations of finite union, finite intersection and taking complements, i.e. such that
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...he case $b=(1-a)^{-1}a(a+1)$, $c=-(1-a)^{-1}(a+1)^2$ the projection of the intersection is a [[Cardioid|cardioid]].
3 KB (479 words) - 11:37, 26 March 2023
...simultaneously left-, right- and middle-associative (or, equivalently, the intersection of the left, right and middle kernels of the loop). An element $a$ of a loo
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...tween the bases, $S$ and $S'$ are their areas and $S''$ is the area of the intersection that has equal distance to both bases.
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...int $x$ a condensation point (of a set $M$) in a topological space if (the intersection of $M$ with) every neighbourhood of $x$ is an uncountable set. (See also [[
861 bytes (136 words) - 09:56, 26 March 2023
...wo Borel subgroups of a group $G$ contains a maximal torus of $G$; if this intersection is a maximal torus, such Borel subgroups are said to be opposite. Opposite
3 KB (423 words) - 17:51, 27 April 2012
$#C+1 = 130 : ~/encyclopedia/old_files/data/I052/I.0502040 Intersection theory
...ent in some sense but that are in general position, and one then takes the intersection of $ Y ^ \prime $
12 KB (1,730 words) - 22:13, 5 June 2020
...here $f$ is the surface area of the triangle $MNP$ and $P$ is the point of intersection of the straight lines $m$ and $n$. The affine distance for two elements tan
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...sent any [[Ideal|ideal]] of a ring (or of another algebraic system) as the intersection of a finite number of ideals of special type (primary, tertiary, primal, un
is satisfied. The intersection theorem is valid for primary ideals: The intersection of two primary ideals having the same primary radical $ P $
7 KB (1,035 words) - 20:23, 4 April 2020
...decomposition|primary decomposition]], that is, can be represented as the intersection of finitely-many primary ideals. Similarly, an $A$-module is called a Laske
1 KB (157 words) - 11:43, 29 June 2014
...ins all solvable groups (cf. [[Solvable group|Solvable group]]) and if its intersection with the class of finite groups is the class of all finite solvable groups.
1 KB (163 words) - 17:20, 7 February 2011
...y small in relation to the coverings from the given uniform structure, the intersection of the elements of this system is not empty. On a topological group there a
...n Hausdorff compactification. All such spaces have the Baire property: The intersection of a countable family of non-empty open everywhere-dense sets is always non
5 KB (764 words) - 17:23, 9 December 2013
Helly's theorem on the intersection of convex sets with a common point: Let $ K $
...-empty intersection, then all the elements of this family have a non-empty intersection.
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...of symmetry of an elliptic paraboloid is called its axis and the point of intersection of the axis with the elliptic paraboloid is its vertex.
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such that the intersection of these congruences is the identity congruence and $ B/ \rho _ {i} \sime
is not representable as an intersection of strictly larger congruences). The theorem that every algebra is represen
3 KB (495 words) - 08:24, 6 June 2020
The [[characteristic subgroup]] $\Phi(G)$ of a group $G$ defined as the intersection of all [[maximal subgroup]]s of $G$, if there are any; otherwise $G$ is its
1 KB (169 words) - 20:06, 18 October 2017
...called a cone if it is closed under homomorphism, inverse homomorphism and intersection with regular languages. A cone that is closed under union, catenation and c
free homomorphism, inverse homomorphism, intersection with regular languages, union, catenation, and $ \lambda $-
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A cusp can also be defined via the so-called intersection number of two plane curves at a point, cf. [[#References|[a1]]], pp. 74-82.
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with the finite intersection property: for every finite subset $ \{ C _ {1} \dots C _ {n} \} \subset
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if and only if its intersection with each $ Y _ \alpha $
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An intersection of the set with an interval in the case of a set on a line, and with an ope
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...y them, if $ab=ba$ for any two elements $a \in A$ and $b \in B$ and if the intersection $A \cap B$ lies in the [[Centre of a group|centre]] $\mathcal{Z}(G)$. In pa
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the so-called nil radical of the ring; it coincides with the intersection of all prime ideals of $ A $.
i.e. the intersection of all prime ideals, consists of precisely the strongly-nilpotent elements.
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The
intersection of all (proper) maximal subgroups of <img align="absmiddle" border="0" src=
...iaofmath.org/legacyimages/f/f120/f120130/f12013071.png" /> is equal to the
intersection of all normal subgroups <img align="absmiddle" border="0" src="https://www.
16 KB (2,143 words) - 17:10, 7 February 2011
...in [[#References|[a2]]] H. Whitney also shows that the degree and the self-intersection number have different parity.
...are equal (see [[#References|[a1]]]). In this case the degree and the self-intersection number have different parity as well.
3 KB (505 words) - 16:52, 1 July 2020
...axis of two intersecting circles is the line passing through the points of intersection, and the radical axis of two touching circles is their common tangent. For
1 KB (221 words) - 06:14, 16 April 2023
...en (closed) relative to $E$, it is necessary and sufficient that it is the intersection of $E$ and a certain open (closed) set.
1 KB (176 words) - 13:57, 9 November 2014
...sects all the elements of some subsystem $\lambda'$ of $\lambda$, then the intersection of the elements of the system is not empty. Any finite system of closed sub
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...bgroup corresponds to that of a [[pure subgroup]] of an Abelian group. The intersection of isolated subgroups in an $R$-group is an isolated subgroup. A normal sub
1 KB (209 words) - 05:49, 20 June 2023
A congruence on an algebra $\mathbf{A}$ which is expressible as the intersection of all congruences on $\mathbf{A}$ whose factor algebras belong to some fix
1 KB (167 words) - 19:23, 12 December 2015
...al system of surfaces|triorthogonal system of surfaces]], then the line of intersection of any two surfaces of different families will be a curvature line for each
2 KB (232 words) - 17:13, 7 February 2011
...m one another by translation over $k\pi$ along the $x$-axis. The points of intersection with the $x$-axis are $(k\pi,0)$. These are also the points of inflection,
1 KB (213 words) - 18:15, 18 September 2014
...of all (equivalence classes of) representations whose kernels contain the intersection of the kernels of all the representations of this subset. For a commutative
1 KB (204 words) - 16:35, 15 May 2014
is the real line of their intersection, while the quadric $ Q _ {1} $
plane of intersection does not intersect the $ ( n - m - 1 ) $-
6 KB (872 words) - 08:09, 6 June 2020
...ne half-cone. 3) The intersecting plane meets both half-cones (Fig.c); the intersection is a [[Hyperbola|hyperbola]] — it consists of two congruent non-closed pa
...is an ellipse, a parabola or a hyperbola, respectively, if and only if its intersection with the line at infinity (cf. [[Projective plane|Projective plane]]) consi
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...closed intervals: Every family of nested closed intervals has a non-empty intersection ([[Cantor axiom|Cantor's axiom]]); in terms of upper or lower bounds of set
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...M$, with smooth image $f(L)\subset E^3$, such that for any $p\in f(L)$ the intersection of $M$ with the plane $\pi$ through $p$ and perpendicular to $f(L)$ is a [[
1 KB (168 words) - 16:30, 15 April 2014
of intersection of the conic with secants through $ P $(
is the intersection of the polars of these sets. The polar of the intersection of weakly-closed convex balanced sets $ A _ \alpha $
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...finite number of closed half-spaces. An infinite convex polyhedron is the intersection of a finite number of closed half-spaces containing at least one ray; the s
...nvex polyhedron is a special case of a [[Convex set|convex set]]. Being an intersection of half-spaces, a convex polyhedron is described by a system of linear ineq
11 KB (1,564 words) - 17:11, 7 February 2011
A plane algebraic curve of order four that is the line of intersection between the surface of a torus and a plane parallel to its axis (see Figure
1 KB (204 words) - 08:45, 12 November 2023
If a family of connected subsets has a non-empty intersection, then the union of the sets of this family is a connected set. For every po
The quasi-component of a point is the intersection of all open-closed subsets that contain this point. The component of a poin
8 KB (1,209 words) - 06:00, 22 April 2023
that are the poles of the $ ( n - 2 ) $-plane of their intersection with respect to the quadrics cut out on these planes by the absolute cone.
...int of intersection of the given lines, harmonically divided the points of intersection of the lines with the absolute lines.
7 KB (998 words) - 09:31, 21 March 2022
...ying in $O(a,\epsilon)$ and containing this pair of points has a non-empty intersection with $\Phi$. K. Menger and P.S. Urysohn proved that a closed set $\Phi$ lyi
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...et forms a [[Boolean algebra]] with the operations of [[union of sets]], [[intersection of sets]] and [[relative complement]].
1 KB (194 words) - 16:56, 25 November 2023
...of cosets is finite, $H$ is called a subgroup of finite index in $G$. The intersection of a finite number of subgroups of finite index itself has finite index (Po
1 KB (186 words) - 11:18, 20 April 2012
the union and intersection are defined: $ \Gamma = \cup _ {\alpha \in A } \Gamma _ \alpha $
...act valued) mappings is upper semi-continuous (convex-compact valued). The intersection and Cartesian product of any family of convex-compact valued mappings is co
7 KB (994 words) - 08:01, 6 June 2020
...bseteq\mathfrak P$ is closed if $C$ contains every ideal that contains the intersection of all ideals from $C$ (see [[Zariski topology]]). The structure space of a
1 KB (215 words) - 20:41, 1 October 2016
...The linking coefficient is equal to the [[Intersection index (in homology)|intersection index (in homology)]] of any $k$-chain $C^k$ such that $\partial C^k=\alpha
3 KB (548 words) - 20:58, 1 January 2019
The intersection of any family of linear varieties is again a linear variety.
1 KB (197 words) - 09:03, 26 November 2023
...first and the second pair of opposite angles is equal; or 4) the point of intersection of the diagonals bisects each of them. Various types of parallelograms are:
2 KB (265 words) - 17:11, 7 February 2011
i.e. to an intersection point of $ \overline{ {W ^ {n} }}\; $
1 KB (204 words) - 06:28, 30 May 2020
is the index of self-intersection for the class of divisors corresponding to $ D $ (see [[Riemann–Roch th
The intersection index defines an integer-valued bilinear form on $ N( X) $
10 KB (1,443 words) - 15:43, 1 March 2022
...rules with an empty right-hand side, also with respect to iteration). The intersection of a context-free language with a regular language is again a context-free
4 KB (627 words) - 19:42, 5 June 2020
...\pm5a,\ldots,$ with asymptotes $x=\pm2a,\pm4a,\pm6a,\ldots$. The points of intersection with the straight line $y=2a/\pi$ are points of inflection.
1 KB (230 words) - 05:54, 15 April 2023
...is defined in terms of intersections of cycles (cf. [[Intersection theory|Intersection theory]]).
|valign="top"|{{Ref|Fu2}}||valign="top"| W. Fulton, "Intersection theory", Springer (1984) {{MR|0735435}} {{MR|0732620}} {{ZBL|0541.14005}}
4 KB (714 words) - 21:54, 24 April 2012
...all nilpotent groups (cf. [[Nilpotent group|Nilpotent group]]) and if its intersection with the class of finite groups is the class of all finite nilpotent groups
2 KB (245 words) - 17:21, 7 February 2011
...X$ such that a sequence $\{F_i\}$ of closed subsets of $X$ has a non-empty intersection whenever $F_i\supset F_{i+1}$ for all $i$ and each $F_i$ is a subset of som
1 KB (208 words) - 20:11, 12 July 2014
The intersection of all [[closed set]]s of $X$ containing the set $A$.
1 KB (198 words) - 16:57, 9 November 2014
to the point of intersection of the altitudes of the triangle. The Simson line is named after R. Simson,
2 KB (236 words) - 08:14, 6 June 2020
is the notation for the intersection of all subcomplexes of $ X $
the intersection $ F \cap \overline{t}\; $
7 KB (1,077 words) - 06:29, 30 May 2020
that is, the intersection of the truth domains of the predicates $R(x)$ and $P(x)$ is non-empty.
1 KB (212 words) - 07:30, 23 August 2014
...th remainder of dimension $\leq k$, then $X$ has an open base in which the intersection of the boundaries of any $k+1$ disjoint sets is compact; etc. If every conn
1 KB (228 words) - 14:25, 10 April 2014
...ideal is a finite irredundant intersection of [[primary ideal]]s. Here an intersection of primary ideals $ \mathfrak a = \cap \mathfrak a _ {i} $
contains an intersection of the others and if the $ \mathfrak a _ {i} $
5 KB (786 words) - 22:15, 5 June 2020
...Zariski topology]]) subsets. A locally closed subset is, by definition, an intersection of an open and a closed subset. The constructible subsets form a Boolean al
1 KB (202 words) - 17:38, 14 April 2018
...that a cocyclic group has a non-trivial minimal subgroup $M$, or that the intersection $M$ of all non-trivial subgroups of $G$ is non-trivial. Each element of $M
1 KB (202 words) - 14:02, 12 November 2023
is the intersection of all subspaces containing $ s $.
In a projective space the operations of addition and intersection of spaces are defined. The sum $ P _ {m} + P _ {k} $
10 KB (1,510 words) - 18:38, 13 January 2024
...ory of a set|Category of a set]]). A space $X$ is Baire if and only if the intersection of each countable family of dense open sets in $X$ is dense (cf. also [[Den
...is finer than $\rho$. A topology $\tau$ has the Slobodnik property if the intersection of each countable family of $\tau$-open $\rho$-dense sets in $X$ is $\rho$-
4 KB (610 words) - 08:48, 18 February 2024
* a $k\times k$ [[Matrix|matrix]] $B$ whose entries are located at the intersection of $k$ distinct columns and $k$ distinct rows of $A$; however a more common
1 KB (233 words) - 10:05, 20 December 2015
...s. The signature of this form is called the signature of the manifold. The intersection form is the most important invariant of a four-dimensional manifold. Two cl
...d every even, integer-valued, symmetric unimodular form is realized as the intersection form of a simply-connected four-dimensional topological manifold. In partic
6 KB (831 words) - 19:39, 5 June 2020
...has a feathering in every Hausdorff compactification. If a set $X$ is the intersection of a sequence $U_1,U_2,\ldots$ of sets open in a space $Y$, then the system
...eans that the set $\Delta = \{(x,x) : x \in X\}$ can be represented as the intersection of a countable family of open sets in $X \times X$. These results and other
6 KB (962 words) - 20:32, 23 September 2017
i.e. the intersection of all prime ideals of $ R $.
1 KB (240 words) - 08:02, 6 June 2020
These six operations are: union, concatenation, Kleene closure ${+}$, intersection with regular languages, morphisms, and inverse morphisms.
...ages]]) if it is closed under non-erasing morphisms, inverse morphisms and intersection with regular languages. A trio closed under union is called a semi-AFL. A s
4 KB (661 words) - 09:20, 2 April 2018
...folds in terms of the intersection pairing (cf. also [[Intersection theory|Intersection theory]]).
...e (with the base point representing $T_1$) and each edge represents a self-intersection. It is not presently known whether different signed trees can correspond to
7 KB (1,047 words) - 15:29, 4 October 2014
...of [[complementation]] in [[set theory]] on [[union of sets|union]] and [[intersection of sets]]; the analogous relationship between [[negation]] in [[proposition
1 KB (199 words) - 14:15, 12 November 2023
...l space $X$ is nowhere dense if, for every nonempty open $U\subset X$, the intersection $U\cap A$ is ''not'' dense in $U$. Common equivalent definitions are:
1 KB (187 words) - 19:07, 7 December 2023
...mbus, then the added term is equal to the product of the difference at the intersection of the path and the column by the coefficient associated with the side of t
...mbus, then the added term is equal to the product of the difference at the intersection of the path and the column by the half-sum of the coefficients associated w
7 KB (939 words) - 19:39, 5 June 2020
...hese hyperplanes which are the poles of their $ ( n - 2) $-hyperplane of intersection relative to the quadrics cut out by the absolute cone on the hyperplanes. I
...er with their point of intersection, harmonically separate their points of intersection with the absolute lines.
7 KB (1,046 words) - 09:03, 13 May 2022
the intersection index $ D ^ {r} \cdot Y $
cf. [[Intersection index (in algebraic geometry)|Intersection index (in algebraic geometry)]]). For other criteria of ampleness see [[#Re
6 KB (950 words) - 12:37, 29 December 2021
a planar curve obtained by the intersection of a circular cone with a plane not passing through the vertex of the cone
...cond axis. The axes of the ellipse are its axes of symmetry. The points of intersection of the ellipse with the axes of symmetry are called its vertices. The major
4 KB (640 words) - 21:38, 24 April 2012
...be an open cone in a real [[topological vector space]] $k$, let $V$ be the intersection of $K$ with a bounded open ball with centre at $0\in k$, and let $U\neq\emp
1 KB (235 words) - 10:40, 26 May 2016
In terms of normal sheaves one can express the self-intersection $ Y \cdot Y $
that is locally a complete intersection, then $ {\mathcal N} _ {Y/X} ^ {*} $
5 KB (799 words) - 08:03, 6 June 2020
sphere if and only if the determinant of the matrix of the integral bilinear intersection $ ( - 1 ) ^ {n} $-
is parallelizable, the diagonal of the intersection matrix of $ 2k $-
9 KB (1,361 words) - 12:24, 10 April 2023
...d surface $M^n$ lying in $N^{n+1}$, the [[Intersection index (in homology)|intersection index (in homology)]] in $N^{n+1}$ of any closed curve $\alpha$ in $M^n$ sa
4 KB (714 words) - 16:10, 5 August 2014
...ed over species in analogy to operations defined over sets, such as union, intersection and others, but since they are to be understood in the specific intuitionis
2 KB (295 words) - 16:47, 19 January 2024
...ytic and algebraic tools. Thus, for instance, the problem of the number of intersection points between a straight line and a circle is reduced to the analytic prob
...[Hyperbola|hyperbola]] and a [[Parabola|parabola]], which are the lines of intersection between a circular cone and planes which do not pass through its vertex (cf
8 KB (1,255 words) - 18:47, 5 April 2020
...e to $K$. If $L_1$ and $L_2$ are normal extensions of $K$, then so are the intersection $L_1 \cap L_2$ and the composite $L_1 \cdot L_2$. However, when $L/K'$ and
2 KB (288 words) - 18:30, 11 April 2016
A family of sets open in $X$ and such that each point of $X$ is the intersection of all elements in the family containing it. A pseudo-basis exists only in
2 KB (280 words) - 07:51, 23 August 2014
is a point in the intersection of the hyperplanes $ \pi _ {1} \dots \pi _ {n + 1 } $
is the maximum number of points of intersection of $ X $
7 KB (1,079 words) - 16:43, 4 June 2020
...A normal space is called perfectly normal if every closed set in it is the intersection of countably many open sets. Every perfectly-normal space is a hereditarily
.../n0676609.png" />-normal spaces in which every closed canonical set is the intersection of countably many open canonical sets are called perfectly $\kappa$-normal.
5 KB (733 words) - 20:41, 19 December 2014
...kew lines have a unique common perpendicular. The equation (as the line of intersection of two planes) of this common perpendicular to the lines $ \mathbf r = \m
2 KB (283 words) - 08:56, 8 April 2023
[[Intersection theory|intersection theory]] provides a satisfactory modern framework. Enumerative geometry dea
{{Cite|Fu2}} for a complete reference on intersection theory; for historical surveys and a discussion of enumerative geometry, se
8 KB (1,263 words) - 08:49, 30 March 2012
...metry axis of a hyperbolic paraboloid is said to be its axis; the point of intersection of a hyperbolic paraboloid with the axis is known as the apex. If $p=q$, th
2 KB (252 words) - 11:12, 25 May 2016
of closed sets has a non-empty intersection; and 3) every open covering of cardinality $ m \in [ a , b ] $
4 KB (577 words) - 08:32, 16 June 2022
...)$, which has good functoriality properties and is equipped with a graded intersection product, at least after tensoring it by $\mathbf{Q}$.
$p \geq 0$, give rise to arithmetic intersection numbers, which are real numbers when their geometric counterparts are integ
8 KB (1,219 words) - 21:00, 13 July 2020
...ch together with each polytope contains all its faces and is such that the intersection between the polytopes is either empty or is a face of each of them. An exam
2 KB (301 words) - 17:51, 11 April 2014
...c notions: $X$ is a submultiset of $Y$ if $\epsilon_X \le \epsilon_Y$, the intersection of $X$ and $Y$ corresponds to $\min(\epsilon_X, \epsilon_Y)$, the union to
2 KB (265 words) - 19:01, 9 November 2023
is equal to the intersection of all maximal modular right (left) ideals of $ R $;
is also equal to the intersection of the kernels of all irreducible right (left) representations of $ R $(
5 KB (764 words) - 08:09, 6 June 2020
be the point of intersection of $ u $
be the point of intersection of $ u $
7 KB (1,026 words) - 08:08, 6 June 2020
The intersection of a family of congruences $\pi_i$, $i \in I$, in the lattice of relations
2 KB (277 words) - 22:08, 12 November 2016
that have a non-empty intersection. There is an obvious simplicial mapping $ \omega _ { {\mathcal A} ^ \pr
set is a finite intersection of closures of open sets. A $ T _ \lambda $-
6 KB (823 words) - 08:09, 6 June 2020
space corresponding to these points according to (a2) have a common point of intersection, say $ ( \theta _ {s} , \rho _ {s} ) $.
...r subsets of picture points can be found by searching coincident points of intersection in the parameter space. In practice this is done by quantizing both paramet
5 KB (768 words) - 22:11, 5 June 2020
...been chosen and a segment of unit length has been specified. The point of intersection ($0$) of the coordinate axes is said to be the coordinate origin. One of th
2 KB (278 words) - 22:36, 16 March 2014
...it is further required that some finite subfamily of the $C_i$ have empty intersection, one obtains the concept of an $S$-weakly infinite-dimensional space.
2 KB (275 words) - 17:01, 5 October 2017
...e set of points $M$ for which $OM=CB$, where $B$ and $C$ are the points of intersection of the line $OM$ with a circle and the tangent $AB$ to the circle at the po
2 KB (300 words) - 09:39, 26 March 2023
...nt conics belonging to one plane. The two other focal points are points of intersection of a conic with a characteristic of its plane.
and the four points of intersection of the conic with an adjacent conic in the same plane. The geometric proper
8 KB (1,191 words) - 06:39, 9 April 2023
...$M_2$, $M_3$, $M_4$ and $M_1'$, $M_2'$, $M_3'$, $M_4'$ are obtained by the intersection of the same quadruple of straight lines $m_1$, $m_2$, $m_3$, $m_4$, then
2 KB (296 words) - 09:34, 13 April 2014
Let $u$ be the axis coinciding with the line of intersection of the planes $0xy$ and $0x'y'$, oriented so that the three lines $0z$, $0z
2 KB (331 words) - 14:12, 13 November 2014
The intersection of connected subgroups of an exponential Lie group is connected. The centra
2 KB (253 words) - 22:20, 14 November 2014
then the entry at the intersection of the $ i $-
2 KB (300 words) - 16:43, 4 June 2020
...s \cup \tilde U_k$, where $\tilde U_i$ is the largest open set in $bX$ the intersection of which with $X$ is the set $U_i$ ($X$ is assumed to be [[Completely-regul
2 KB (294 words) - 16:43, 24 September 2017
...of $\nu$-primitive $A$-modules. The radical $J_{1/2}(A)$ is defined as the intersection of the maximal right module ideals. All four radicals are different, and
5 KB (767 words) - 11:23, 27 October 2014
The set-theoretical intersection of this family, that is, $ \cap F $.
2 KB (275 words) - 04:11, 6 June 2020
...set coincides with itself. This is equivalent to the requirement that the intersection of all neighbourhoods of a point $ x \in X $
2 KB (275 words) - 08:25, 6 June 2020
with index of self-intersection $ ( C ^ {2} ) _ {X} > 0 $.
which is a smooth rational curve with index of self-intersection $ ( S _ {n} ^ {2} ) _ {F} = - n $.
5 KB (707 words) - 16:26, 2 March 2022
...es the other. For example, each of the operations [[union of sets]] and [[intersection of sets]] distributes over the other.
2 KB (301 words) - 19:27, 24 January 2016
...mical systems) for a set $E$ in a topological space $X$ which contains the intersection of a countable number of open dense subsets in $X$. The terminology is in g
It is more common to call (a set containing) an intersection of countably many dense open sets [[Residual set|residual]] or comeager, fo
4 KB (704 words) - 11:07, 6 September 2013
...e. Think of the Boolean algebra of all subsets of a given set under union, intersection and complement to interpret these formulas.
2 KB (335 words) - 15:09, 13 August 2014
...roblem of additive type may also be regarded as the problem of finding the intersection of arithmetical sums of sets. For instance, the set $ M $
2 KB (277 words) - 19:35, 5 June 2020
...sic set has the structure of a closed subscheme $B$ in $X$, defined as the intersection of all divisors of the movable part of the linear system. The removal of th
2 KB (288 words) - 04:27, 15 February 2024
The polygon resulting from the intersection of the pyramid by the plane is called the upper base, while the base of the
2 KB (400 words) - 21:32, 11 April 2014
<TR><TD valign="top">[2]</TD> <TD valign="top"> C. Chevalley, "Intersection of algebraic and algebroid varieties" ''Trans. Amer. Math. Soc.'' , '''57'
2 KB (317 words) - 17:54, 10 January 2016
...ation is the intersection of their images and, conversely, the image of an intersection is the sum of the images. In particular, the image of a point is a hyperpla
6 KB (878 words) - 14:59, 2 May 2023
* A singular (non-smooth) point of an algebraic curve which is a transversal intersection of smooth branches;
...e node (or ''nodal point'', also ''nodal singularity'') is a point of self-intersection of smooth branches of the curve.
5 KB (753 words) - 09:03, 12 December 2013
...centre $O$ of the sphere, then a so-called great circle is obtained as the intersection. A unique great circle can be drawn through any two points $A$ and $B$ on t
...gle $A'BC'$ between the tangents of the corresponding arcs at the point of intersection $B$ or by the dihedral angle formed by the planes $OBA$ and $OBC$.
8 KB (1,389 words) - 15:53, 19 April 2014
...1}$ and $\overrightarrow{M_0M_2}$, where $M_1$ and $M_2$ are the points of intersection of the circle and an arbitrary straight line passing through $M_0$. In part
2 KB (298 words) - 06:25, 12 October 2023
...andt subgroup $\omega ( G )$ of a [[Group|group]] $G$ is defined to be the intersection of the normalizers of all the subnormal subgroups of $G$ (cf. also [[Subnor
...nilpotent (cf. [[Nilpotent group|Nilpotent group]]), $\omega ( G )$ is the intersection of the normalizers of all the subgroups of $G$. The latter is called the no
11 KB (1,625 words) - 07:40, 10 February 2024
one takes the intersection with $ D $
2 KB (293 words) - 18:47, 5 April 2020
Any union and any intersection of subcomplexes of $ X $
2 KB (333 words) - 16:43, 4 June 2020
intersection and a countable union of ${\mathcal A}$-sets is an ${\mathcal A}$-set. Any
2 KB (327 words) - 14:21, 15 August 2023
...three points $A,B,C$ and $A_1,B_1,C_1$ are given, other than the point of intersection of the lines; if $CB_1$ is parallel to $BC_1$ and $CA_1$ is parallel to $AC
2 KB (344 words) - 17:16, 31 March 2018
...fmath.org/legacyimages/n/n066/n066970/n066970132.png" /> is defined as the
intersection of all elements of the form <img align="absmiddle" border="0" src="https://
21 KB (2,970 words) - 17:28, 7 February 2011
be two domains in the plane with non-empty intersection and such that the solution to the Dirichlet problem for the Laplace equatio
...2]]]) can be applied to finding a solution to the Dirichlet problem in the intersection of two domains $ A $
6 KB (852 words) - 08:12, 6 June 2020
...ssociative rings and algebras|Non-associative rings and algebras]]) is the intersection of its maximal subalgebras. Unlike the group case, where the Frattini subgr
2 KB (323 words) - 13:52, 25 April 2014
...d lying in different faces, or, in other words, by the angle formed by the intersection of the dihedral angle and a plane normal to the edge.
2 KB (324 words) - 09:48, 26 May 2016
...int operators on a separable Hilbert space such that $A+B$, defined on the intersection of the domains of $A$ and $B$, is essentially self-adjoint. And in the form
2 KB (344 words) - 21:49, 3 December 2017
...wo arbitrary points all points of the segment connecting these points. The intersection of any family of convex sets is itself a convex set.
...A closed convex set is the intersection of its supporting half-spaces. The intersection of a finite number of closed half-spaces is a convex polyhedron. The [[face
9 KB (1,558 words) - 17:30, 23 October 2017
...erically has a certain property if the property holds outside (a countable intersection of) open dense set(s). For instance, a polynomial has generically no double
2 KB (324 words) - 12:46, 4 September 2014
should have non-empty intersection with $ E _ {f} $
2 KB (311 words) - 19:43, 5 June 2020
...a triangle is F. Morley's theorem (1899), stating that the three points of intersection of the adjacent trisectors of the angles of an arbitrary triangle form an e
2 KB (321 words) - 13:05, 7 December 2014
A theorem on the product of the simple ratios in which the points of intersection of an algebraic curve with the sides of a triangle divide these sides. Supp
2 KB (347 words) - 10:08, 4 June 2020
where the right-hand side is the [[Intersection index (in homology)|intersection index]] of the classes $ z _ {1} $
5 KB (839 words) - 06:50, 28 April 2024
...is called the complement of the set $A$ (in $X$). The operations of union, intersection and taking the complement are connected by the so-called [[de Morgan laws]]
8 KB (1,307 words) - 19:50, 30 November 2014
...f polynomial ideals. In particular, he developed the [[Intersection theory|intersection theory]] on a non-singular projective algebraic variety. The results of the
...ly projective) over an arbitrary ground field, the theory of divisors, the intersection theory for such varieties, and the general theory of Abelian varieties, whi
8 KB (1,165 words) - 16:08, 1 April 2020
...r $k$. Two parabolic subgroups of a group $G$ are called opposite if their intersection is a Levi subgroup of each of them. A closed subgroup of a group $G$ is a p
...containing $B$. Each parabolic subgroup coincides with its normalizer. The intersection of any two parabolic subgroups contains a subgroup of $G$ that is conjugate
5 KB (932 words) - 11:43, 17 December 2019
...omain|integral domain]]. In this case every maximal ideal is prime and the intersection of all prime ideals is the radical of the null ideal (i.e. is the set of ni
2 KB (393 words) - 08:07, 6 June 2020
...is a continuum, the components of a Hausdorff compactum are continua, the intersection of a decreasing sequence of continua is a continuum. No continuum can be d
2 KB (336 words) - 15:31, 23 July 2012
...\Delta<0$, the double point is said to be a nodal point or a point of self-intersection; e.g. for the curve
2 KB (417 words) - 11:59, 26 March 2023
are called the faces of the analytic polyhedron. The intersection of any $ k $
2 KB (335 words) - 18:47, 5 April 2020
The property of a subgroup to be subnormal is transitive. An intersection of subnormal subgroups is again a subnormal subgroup. The subgroup generate
3 KB (420 words) - 10:03, 3 January 2021
...he second by the angular coordinates $\alpha$ and $\beta$ of the points of intersection of the chord with the circumference of the disc; in the third case by the C
2 KB (374 words) - 10:24, 16 March 2023
...Hamilton group contains a subgroup isomorphic to the quaternion group. The intersection of all non-trivial subgroups of the quaternion group (and also of any gener
2 KB (350 words) - 14:38, 2 August 2014
be a contravariant functor of global [[Intersection theory|intersection theory]] from $ V ( k) $
does not, in some sense, depend on the intersection theory of $ C $,
8 KB (1,244 words) - 10:52, 16 March 2023
...f it coincides with its socle. The socle of $M$ can also be defined as the intersection of all the essential submodules of $M$. The socle is the largest semi-simpl
2 KB (371 words) - 15:04, 19 November 2023
..., $S(g)$ does not contain the unit of $G$ and if for any $x,y\in S(g)$ the intersection $S(x)\cap S(y)$ is non-empty.
2 KB (365 words) - 20:04, 12 July 2014
...the ideals in a regular commutative Banach algebra: A closed ideal is the intersection of maximal ones ( "it admits spectral synthesis" ) if and only if its annih
as cospectrum, namely the intersection of all closed maximal ideals corresponding to the points of $ E $.
9 KB (1,382 words) - 08:22, 6 June 2020
...(see [[#References|[1]]]). One of them reduces to the requirement that an intersection of $ \widetilde{X} $
2 KB (374 words) - 16:44, 4 June 2020
is a normal complete intersection of $ X $(
...ld in étale cohomology [[#References|[a4]]] and in [[Intersection homology|intersection homology]] [[#References|[a5]]], [[#References|[a6]]]. For the proof of the
11 KB (1,584 words) - 11:51, 8 April 2023
which may be traversed such that the points of self-intersection are visited only twice. For a curve to be unicursal it is necessary and suf
2 KB (342 words) - 13:37, 7 June 2020
The converse is true for free groups, but not in general: The intersection of two verbal subgroups may not be a verbal subgroup.
2 KB (363 words) - 11:34, 12 January 2021
the self-intersection index of the anti-canonical divisor $ (- K _ {X} ^ {3} ) \leq 64 $.
then the self-intersection index $ d = H ^ {3} $
6 KB (869 words) - 13:13, 26 March 2023
...tification]] $\overline{\mathbf R^n}$); and 2) the images of any non-empty intersection $V_x\cap V_y$ (under the two homeomorphisms to $\mathbf R^n$ or $\overline{
2 KB (357 words) - 11:31, 27 October 2014
...int $A$ distinct from the centre of a given pencil of circles the point of intersection $A'$ of the circles of the pencil passing through $A$.
3 KB (469 words) - 18:16, 17 December 2017
...]] $I$ of a [[ring]] $R$ (or of a submodule $N$ of a [[module]] $M$) as an intersection of primary ideals (primary submodules, cf. [[Primary ideal]]). The primary
2 KB (386 words) - 20:06, 5 October 2017
for the wave equation is determined only by the initial data at the intersection of the initial manifold with the characteristic cone of $ ( M, t) $
depends only on the initial data at the intersection of the initial manifold with the characteristic conoid if and only if the [
6 KB (856 words) - 12:26, 24 March 2024
...gebraic variety $V\subset P^g$ of dimension $n$ is the number of points of intersection with a generic hyperplane of dimension $g-n$ in $P^g$. Thus, the degree of
3 KB (391 words) - 13:15, 7 April 2023
...family of non-empty closed sets of a topological space $X$ has a non-empty intersection, is one of the definitions of compactness of $X$ (see [[#References|[1]]],
8 KB (1,230 words) - 20:30, 21 January 2021
can be uniquely represented as the intersection of homogeneous prime ideals:
3 KB (364 words) - 08:09, 13 July 2022
...ational boundary component $F_{i}$ of $X ^ { * }$, and $\Gamma_{i}$ is the intersection of $\Gamma$ with the stabilizer of $F_{i}$. In addition, $V$ and each $V _
...rsection cohomology [[#References|[a4]]] (cf. also [[Intersection homology|Intersection homology]]) of the Baily–Borel compactification coincides with its $L^{2}
13 KB (1,983 words) - 17:00, 1 July 2020
...mined by the class of all primary rings; the least special radical; or the intersection of the prime ideals of the ring;
...mitive rings; the intersection of all primitive ideals of the ring; or the intersection of all modular maximal right (left) ideals. It is a quasi-regular ideal con
16 KB (2,540 words) - 08:09, 6 June 2020
The intersection of any set of normal subgroups is normal, and the subgroup generated by any
2 KB (406 words) - 22:11, 5 March 2012
so that its image is the intersection (generally incomplete) of the quadrics containing it [[#References|[1]]].
...></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> A.N. Tyurin, "On the intersection of quadrics" ''Russian Math. Surveys'' , '''30''' : 6 (1975) pp. 51–106 '
11 KB (1,607 words) - 08:08, 6 June 2020
...s greatest element, that is, the identity with respect to the operation of intersection.
2 KB (403 words) - 19:25, 3 April 2016