Synonymer & Information om | Engelska ordet POINTWISE

Exempel på hur man kan använda POINTWISE i en mening

• In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence.
• Addition of endomorphisms arises naturally in a pointwise manner and multiplication via endomorphism composition.
• Topological rings occur in mathematical analysis, for example as rings of continuous real-valued functions on some topological space (where the topology is given by pointwise convergence), or as rings of continuous linear operators on some normed vector space; all Banach algebras are topological rings.
• On this underlying set one defines addition and scalar multiplication pointwise, and "multiplication" in the incidence algebra is a convolution defined by.
• Define the linear map T : V → V pointwise by Tx = Mx, where on the right-hand side x is interpreted as a column vector and M acts on x by matrix multiplication.
• In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm.
• Since this subsequence also converges in measure to f, there exists a further subsequence, which converges pointwise to f almost everywhere, hence the previous variation of Fatou's lemma is applicable to this subsubsequence.
• More generally, any bundles of Lie algebras is Lie algebroid with zero anchor and Lie bracket defined pointwise.
• As more sinusoids are used, this approximation error approaches a limit of about 9% of the jump, though the infinite Fourier series sum does eventually converge almost everywhere (pointwise convergence on continuous points) except points of discontinuity.
• Equicontinuity appears in the formulation of Ascoli's theorem, which states that a subset of C(X), the space of continuous functions on a compact Hausdorff space X, is compact if and only if it is closed, pointwise bounded and equicontinuous.
• A closed proper convex function f is the pointwise supremum of the collection of all affine functions h such that h ≤ f (called the affine minorants of f).
• Isotopy classes of tangles form a tensor category, where for the category structure, one can compose two tangles if the bottom end of one equals the top end of the other (so the boundaries can be stitched together), by stacking them – they do not literally form a category (pointwise) because there is no identity, since even a trivial tangle takes up vertical space, but up to isotopy they do.
• The name reflects the fact that the drastic t-norm is the pointwise smallest t-norm (see the properties of t-norms below).
• In differential geometry and theoretical physics, the classification of electromagnetic fields is a pointwise classification of bivectors at each point of a Lorentzian manifold.
• In mathematics, Baire functions are functions obtained from continuous functions by transfinite iteration of the operation of forming pointwise limits of sequences of functions.
• Moreover, the proof of Brendle and Schoen only uses the weaker assumption of pointwise rather than global pinching.
• More generally, the category of elements plays a key role in the proof that every weighted colimit can be expressed as an ordinary colimit, which is in turn necessary for the basic results in theory of pointwise left Kan extensions, and the characterization of the presheaf category as the free cocompletion of a category.
• The justification of this view is that no subluminal Hubble volume will exist and pointwise superluminal expansion (the generalization of the Big Bang theory) will prevail everywhere or at least in a vast region of the universe.
• Uniform Cauchy convergence and pointwise convergence of a subsequence imply uniform convergence of the sequence, and if the codomain is complete, then uniform Cauchy convergence implies uniform convergence.
• The pointwise stabilizer O of an octad is an abelian group of order 16, exponent 2, each of whose involutions moves all 16 points outside the octad.

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