Results 251 to 260 of about 418,034 (290)

Contact Vectors of Point Lattices

Mathematical Notes, 2023
The contact vectors of a lattice \(L\) are vectors \(l\) which are minimal in the \(l^{2}\)-norm in their parity class. In this paper, the author shows that, in the space of all symmetric matrices, the set of all contact vectors of the lattice \(L\) defines the subspace \(M(L)\) containing the Gram matrix \(A\) of the lattice \(L\).
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Vector Lattices Associated with Ordered Vector Spaces

Mediterranean Journal of Mathematics, 2010
The vector lattice generated by a real Archimedean vector space \(V\) is considered. It is proved that the cone \(C\) of all positive linear forms on \(V\) separates elements of \(V\). Then the positive linear forms are determined in terms of conical measures on the cone \(C\).
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Prime Ideals in Vector Lattices

Canadian Journal of Mathematics, 1962
Projectors, spectral functions, carriers, and collections of these objects are some of the tools which have been used to study vector lattices. One of our objectives in this paper is to show that these various approaches are not essentially different. We do this by proving that each of the above-mentioned objects can be identified with a collection of ...
Johnson, D. G., Kist, J. E.
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Successive refinement lattice vector quantization

IEEE Transactions on Image Processing, 2002
Lattice Vector quantization (LVQ) solves the complexity problem of LBG based vector quantizers, yielding very general codebooks. However, a single stage LVQ, when applied to high resolution quantization of a vector, may result in very large and unwieldy indices, making it unsuitable for applications requiring successive refinement.
Debargha, Mukherjee, Sanjit K, Mitra
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Girsanov’s theorem in vector lattices

Positivity, 2019
The authors formulate and prove Girsanov's theorem in vector lattices. The methodology involves the theory of cross-variation processes, specifically the Kunita-Watanabe inequality, exponential processes, Itô's rule for multi-dimensional processes, and the integration by parts formula for martingales.
Grobler, Jacobus J., Labuschagne, Coenraad C. A.   +1 more
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Sampling short lattice vectors and the closest lattice vector problem

Proceedings 17th IEEE Annual Conference on Computational Complexity, 2003
We present a 2/sup O(n)/ time Turing reduction from the closest lattice vector problem to the shortest lattice vector problem. Our reduction assumes access to a subroutine that solves SVP exactly and a subroutine to sample short vectors from a lattice, and computes a (1+/spl epsi/)-approximation to CVP As a consequence, using the SVP algorithm from ...
M. Ajtai, R. Kumar, D. Sivakumar
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Extension of Vector Lattice Homomorphisms

Journal of the London Mathematical Society, 1986
Suppose B is a complete Boolean algebra, D a distributive lattice and \(\phi\) a lattice homomorphism from a sublattice, \(D_ 0\), of D, into B, then \(\phi\) can be extended to a lattice homomorphism of D into B. This generalizes Sikorski's extension theorem for Boolean algebras. It also leads to a new proof that if N is a complete vector lattice, L a
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On Vector Lattice-Valued Measures

Canadian Mathematical Bulletin, 1965
E. Hewitt [1] used the Daniell approach to define a real-valued measure function on a σ-algebra of the real line. He began by defining an arbitrary non-negative linear functional I on L∞ ∞(R), (the space of all complex-valued continuous functions on the real line R which vanish off some compact subset of R).
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PRIME VECTORS IN DEGENERATE LATTICES

Mathematics of the USSR-Sbornik, 1986
Translation from Mat. Sb., Nov. Ser. 126 (168), No.3, 291-306 (Russian) (1985; Zbl 0578.10044).
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4.1.1.3.1 Lattice vectors, reciprocal lattice vectors

2005
R. F. Wallis, S. Y. Tong
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