منابع مشابه
Planar Harmonic Polynomials of Type B
The hyperoctahedral group acting on R is the Weyl group of type B and is associated with a two-parameter family of differential-difference operators {Ti : 1 ≤ i ≤ N}. These operators are analogous to partial derivative operators. This paper finds all the polynomials h on R which are harmonic, ∆Bh = 0 and annihilated by Ti for i > 2, where the Laplacian ∆B = ∑ N i=1 T 2 i . They are given explic...
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In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...
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Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on RN . The Dunkl operators are denoted by Tj for 1 ≤ j ≤ N, and the Laplacian ∆κ = ∑j=1 T2 j . This paper finds the homogeneous harmonic polynomials annihilated by all Tj for j > 2. The structure constants with respect to the Gaussian and sphere inner...
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We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a similarity transformation. Both algorithms are based on the fact, well-known in Harmonic Analysis, that the Laplacian operator commutes with orthogonal transformatio...
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In this work we studied the approximation of the fundamental solution of the Laplace operator in two-dimensional space u = log(|x|) by harmonic polynomials. We analyzed the best approximation in the semi-ring with fixed outer radius and inner radius ? tending to zero. We observed exponential convergence in the degree of polynomials used for approximation. However, with inner radius tending to z...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1999
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/32/46/308