We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain Ω ⊂ R , N 1, with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a rate r−τ , τ > 1, towards the identity. As a canonical application we show that the correspon...

we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

Time-decaying harmonic oscillators yield dispersive estimates with weak decay, and change the threshold power of nonlinearity between short long range. In non-critical case for time-decaying oscillator, this can be characterized by polynomial nonlinearities. However, in critical case, it is difficult to characterize using only terms, thus we use logarithmic nonlinear terms.

By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the qoscillator are obtained. They satisfy a q-oscillator algebra as a consequence of the shape-invariance of the Hamiltonian. A second set of q-oscillator is derived from the exact Heisenberg operator solution. Now the q-oscillator stands on th...

Abstract. Assume that f is Dunkl polyharmonic in R (i.e. (∆h) f = 0 for some integer p, where ∆h is the Dunkl Laplacian associated to a root system R and to a multiplicity function κ, defined on R and invariant with respect to the finite Coxeter group). Necessary and successful condition that f is a polynomial of degree ≤ s for s ≥ 2p− 2 is proved. As a direct corollary, a Dunkl harmonic functi...

where GK is the pluricomplex Green’s function of K with pole at infinity, d = ∂ + ∂̄, and d = (i/2π)(∂̄ − ∂). The support of μK is contained in the Shilov boundary of K. When n = 1, the measure μK is simply harmonic measure for the domain C − K evaluated at infinity. See Section 2. Let F : C → C be a regular polynomial endomorphism; that is, one which extends holomorphically to CP. The filled Jul...

Any planar shape P can be embedded isometrically as part of a convex surface S ⊂ R such that ∂P supports the positive curvature of S. Of particular interest is the case when P is a filled polynomial Julia set and the curvature is proportional to the measure of maximal entropy. The (flat) surface Q = S \P is the associated cap. In this article, we study the cap construction when the curvature is...

The information entropy of Gegenbauer polynomials is relevant since this is related to the angular part of the information entropies of certain quantum mechanical systems such as the harmonic oscillator and the hydrogen atom in D dimensions. We give an effective method to compute the entropy for Gegenbauer polynomials with an integer parameter and obtain the first few terms in the asymptotic ex...

Any planar shape P ⊂ C can be embedded isometrically as part of the boundary surface S of a convex subset of R such that ∂P supports the positive curvature of S. The complement Q = S \P is the associated cap. We study the cap construction when the curvature is harmonic measure on the boundary of (Ĉ\P,∞). Of particular interest is the case when P is a filled polynomial Julia set and the curvatur...

It is proved that the Laurent expansion of the following Gauss hypergeometric functions, are an arbitrary integer nonnegative numbers, a, b, c are an arbitrary numbers and ε is an arbitrary small parameters, are expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with polynomial coefficients. An efficient algorithm for the calculation of the higher-order coefficients o...