⇄Change DirectionTranslation for 'zero-dimensional' from English to Russian
 ADJ zero-dimensional | - | -
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## Translation for 'zero-dimensional' from English to Russian

zero-dimensional
Usage Examples English
• 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).