Примеры использования Subspaces на Английском языке и их переводы на Русский язык
{-}
-
Colloquial
-
Official
The Gaussian coefficients count subspaces of a finite vector space.
Every compact operator on a complex Banach space has a nest of closed invariant subspaces.
The plane and line are linear subspaces in R3, which always go through zero.
More generally, any one-dimensional representation is irreducible by virtue of having no proper nontrivial subspaces.
So for example, the(1/2, 1/2) representation has spin 1 andspin 0 subspaces of dimension 3 and 1 respectively.
He solved Banach's problem of norming subspaces in conjugate Banach spaces as well as a problem posted by Calderón and Lions concerning interpolation in factor spaces.
Thus, one can regard a finite vector space as a q-generalization of a set, and the subspaces as the q-generalization of the subsets of the set.
For example, all subspaces of a Noetherian space, are Noetherian themselves; all subgroups and quotient groups of a Noetherian group are likewise, Noetherian; and, mutatis mutandis, the same holds for submodules and quotient modules of a Noetherian module.
It says that every sufficiently high-dimensional normed vector space will have low-dimensional subspaces that are approximately Euclidean.
Note that, according to the above paragraph, there are subspaces with spin both 3/2 and 1/2 in the last two cases, so these representations cannot likely represent a single physical particle which must be well-behaved under SO3.
Let V be the three dimensional vector space defined over the field F. The projective plane P(V) PG(2, F)consists of the one dimensional vector subspaces of V called points and the two dimensional vector subspaces of V called lines.
The propositions of incidence are derived from the following basic result on vector spaces:given subspaces U and W of a(finite dimensional) vector space V, the dimension of their intersection is dim U+ dim W- dim U+ W.
For example, the vertices of a complex polygon are points in the complex plane C 2{\displaystyle\mathbb{C}^{2}}, and the edges are complex lines C 1{\displaystyle\mathbb{C}^{1}}existing as(affine) subspaces of the plane and intersecting at the vertices.
A Clebsch-Gordan decomposition can be applied showing that an(m, n)representation have SO(3)-invariant subspaces of highest weight(spin) m+ n, m+ n- 1,…,| m- n|, where each possible highest weight(spin) occurs exactly once.
At the junction of singularity theory and differential topology, Cerf theory is the study of families of smooth real-valued functions f: M→ R{\displaystyle f\colon M\to\mathbb{R}} on a smooth manifold M{\displaystyle M},their generic singularities and the topology of the subspaces these singularities define, as subspaces of the function space.
Bearing in mind that the geometric dimension of the projective space P(V) associated to V is dim V- 1 andthat the geometric dimension of any subspace is positive, the basic proposition of incidence in this setting can take the form: linear subspaces L and M of projective space P meet provided dim L+ dim M≥ dim P. The following sections are limited to projective planes defined over fields, often denoted by PG(2, F), where F is a field.
The power of capital shown when well managed agile in its political and social circumstances, flows from a globalization context characterized by low density technique andcapitalist rationality inherent miniature peripherals provide vertical solidarity subspaces front the dynamics of engineering systems that direct the functioning of technical objects useful to the production.
The finance and structured by the technical services and information, under"tv action" allow a global action and a social and economic modernization,tend to perform their activities in a limited way in subspaces in a globalization context, where the elements of infrastructure, technology, skilled personnel and capital available is incipient.
In contrast to the classical reflexive spaces the class Ste of stereotype spaces is very wide(it contains, in particular, all Fréchet spaces and thus, all Banach spaces), it forms a closed monoidal category, and it admits standard operations(defined inside of Ste) of constructing new spaces,like taking closed subspaces, quotient spaces, projective and injective limits, the space of operators, tensor products, etc. The category Ste have applications in duality theory for non-commutative groups.
Subspace scanners active.
Subspace, trans-dimensional, you name it.
Subspace field fragmentation is beginning.
There were subspace ruptures extending out several light- years.
Scanners are reading major subspace disruption at their last co-ordinates.
These functions form a subspace which we"quotient out", making them equivalent to the zero function.
A subspace disruption.
A weight subspace of highest weight(spin) j is(2j+ 1)-dimensional.
Calibrating sensors for subspace.
The harmonic polynomials form a vector subspace of the vector space of polynomials over the field.
Sensors picking up subspace oscillations again.