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ADJ | zero-dimensional | - | - |

мат. нульмерный {adj} | zero-dimensional |

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- The empty sum convention allows the
**zero**-**dimensional**vector space "V"={0} to have a basis, namely the empty set. - Integration is a kind of "summation" over a continuum, or more precisely and generally, over a differentiable manifold. Integration over a
**zero**-**dimensional**manifold reduces to summation. - A
**zero**-**dimensional**space with respect to the small inductive dimension has a base consisting of clopen sets. **Zero**-**dimensional**models are also commonly referred to as Energy Balance Models (or EBM's).- Since the trace of a commutator is zero, and the trace of the identity is the dimension of the representation, the representation must be
**zero dimensional**. - A discrete group is the same thing as a
**zero**-**dimensional**Lie group (uncountable discrete groups are not second-countable, so authors who require Lie groups to satisfy this axiom do not regard these groups as Lie groups). - In string theory, particles are modeled not as
**zero**-**dimensional**points but as one-dimensional extended objects called strings. - As a special case, a non-empty topological space is
**zero**-**dimensional**with respect to the covering dimension if every open cover of the space has a refinement consisting of disjoint open sets so that any point in the space is contained in exactly one open set of this refinement. - FGLM algorithm is such a basis conversion algorithm that works only in the
**zero**-**dimensional**case (where the polynomials have a finite number of complex common zeros) and has a polynomial complexity in the number of common zeros. - He obtained his PhD in 1983 from Florida State University with thesis "Generalized Three-Manifolds with
**Zero**-**Dimensional**Singular Set" written under the direction of Robert Christopher Lacher. - "
**Zero**"-**dimensional**vowel systems, with one phonemic vowel only, have been postulated for Nuxálk, Kabardian and some Abkhaz dialects, as well as several Central Chadic languages such as Moloko. - If "V" has exactly two subrepresentations, namely the
**zero**-**dimensional**subspace and "V" itself, then the representation is said to be irreducible; if it has a proper subrepresentation of nonzero dimension, the representation is said to be reducible. - The analog of charge conjugation can be defined for higher-
**dimensional**gamma matrices, with an explicit construction for Weyl spinors given in the article on Weyl–Brauer matrices. - For a non-negative integer "n", an "n"-
**dimensional**local field is a complete discrete valuation field whose residue field is an ("n" − 1)-dimensional local field. - The starting point for string theory is the idea that the point-like particles of quantum field theory can also be modeled as one-
**dimensional**objects called strings. - For example, if "M" is a
**zero**-**dimensional**2-point manifold, the module [...] is finitely-generated and projective over [...] but is not free, and so cannot correspond to the sections of any (constant-rank) vector bundle over "M" (all of which are trivial).

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