Übersetzung für 'taking values in' von Englisch nach Deutsch

taking values in {adv}

mit Wertebereichmath.

• More narrowly still, one may generalize the DFT by either changing the target (taking values in a field other than the complex numbers), or the domain (a group other than a finite cyclic group), as detailed in the sequel.
• So the Massey product can be regarded as a function defined on triples of classes such that the product of the first or last two is zero, taking values in the above quotient group.
• We have a 4-dimensional differentiable manifold M, a gauge group G, which has as "dynamical" fields a 2-form B taking values in the adjoint representation of G, and a connection form A for G.
• It is concerned with generalizations of the concept of holomorphic function to functions defined and taking values in complex Banach spaces (or Fréchet spaces more generally), typically of infinite dimension.
• In mathematics, the Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing "n" of an elliptic curve "E", taking values in "n"th roots of unity.

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• Numerous further characterizations of such manifolds exist, in particular capturing the property of their having "many" holomorphic functions taking values in the complex numbers.
• In algebraic geometry one can also define analogous Stiefel–Whitney classes for vector bundles with a non-degenerate quadratic form, taking values in etale cohomology groups or in Milnor K-theory.
• It has the advantage of working also for complex-valued random variables or for random variables taking values in any measurable space (which includes topological spaces endowed by appropriate σ-algebras).
• In theoretical physics, a non-abelian gauge transformation means a gauge transformation taking values in some group "G", the elements of which do not obey the commutative law when they are multiplied.
• The notion of invariant given above generalizes naturally to tori over arbitrary base schemes, with functions taking values in more general rings.

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• Numerous further characterizations of such manifolds exist, in particular capturing the property of their having "many" holomorphic functions taking values in the complex numbers.
• The following is a typical existence and uniqueness theorem for Itô SDEs taking values in "n"-dimensional Euclidean space R"n" and driven by an "m"-dimensional Brownian motion "B"; the proof may be found in Øksendal (2003, §5.2).
• (taking values in "H") is continuous in T. The equivalence of these two definitions can be seen by observing that a subbase for both topologies is given by the sets [...] (where "T0" is any bounded operator on "H", "x" is any vector and ε is any positive real number).
• The notion of support also extends in a natural way to functions taking values in more general sets than [...] and to other objects, such as measures or distributions.
• This finite-dimensional version generalizes to functions [...] and [...] taking values in a normed space which could be for example a sequence space or an inner product space.

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• ] taking values in a complex vector space described concretely as [...] , defined on flat spacetime (Minkowski space) [...].