We show that the long-range Ewald operator can be resolved as erf(ωr12)/r12 = ∑k ϕk*(r1) ϕk(r2), where ϕk is proportional to the product of a spherical Bessel function and a spherical harmonic. We demonstrate the use of this new resolution by calculating the long-range Coulomb energy of the nanodiamond crystallite C84H64 and the long-range exchange energy of the graphene C96H24. The resolution ...

A general theoretical procedure is presented to remove known probe-position errors in spherical near-field data to obtain highly accurate far fields. We represent the measured data as a Taylor series in terms of the displacement errors and the ideal spectrum of the antenna. This representation is then assumed to be an actual near field on a regularly spaced error-free spherical grid. The ideal ...

We solve for spectrum, obtain explicitly and study group properties of eigenfunc-tions of Dirac operator on the Riemann sphere S 2. The eigenvalues λ are nonzero integers. The eigenfunctions are two-component spinors that belong to representations of SU (2)-group with half-integer angular momenta l = |λ| − 1 2. They form on the sphere a complete orthonormal functional set alternative to convent...

It is an open conjecture that generalized Bessel functions associated with root systems have a positive product formula for non-negative multiplicity parameters of the associated Dunkl operators. In this paper, a partial result towards this conjecture is proven, namely a positive radial product formula for the non-symmetric counterpart of the generalized Bessel function, the Dunkl kernel. Radia...

This lecture addresses the concept of form factor in magnetic scattering of thermal neutrons, analyzing its meaning, discussing its measurement by polarized neutrons and detailing its computation for the ions by the spherical tensor operator formalism.

by using generalized salagean differential operator a newclass of univalent holomorphic functions with fixed finitely manycoefficients is defined. coefficient estimates, extreme points,arithmetic mean, and weighted mean properties are investigated.