10 resultados para Polynomial vector field
em Bulgarian Digital Mathematics Library at IMI-BAS
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Toric coordinates and toric vector field have been introduced in [2]. Let A be an arbitrary vector field. We obtain formulae for the divA, rotA and the Laplace operator in toric coordinates.
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2000 Mathematics Subject Classification: 37J55, 53D10, 53D17, 53D35.
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The problem of efficient computing of the affine vector operations (addition of two vectors and multiplication of a vector by a scalar over GF (q)), and also the weight of a given vector, is important for many problems in coding theory, cryptography, VLSI technology etc. In this paper we propose a new way of representing vectors over GF (3) and GF (4) and we describe an efficient performance of these affine operations. Computing weights of binary vectors is also discussed.
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∗ Partially supported by INTAS grant 97-1644
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It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).
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Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90
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2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30
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2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.
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2000 Mathematics Subject Classification: 12D10.
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2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.