Let G = Aut(T ) be the group of automorphisms of a homogeneous tree T , and let Γ be a lattice subgroup of G. Let π be the tensor product of two spherical irreducible unitary representations of G. We give an explicit decomposition of the restriction of π to Γ. We also describe the spherical component of π explicitly, and this decomposition is interpreted as a multiplication formula for associat...

In this short note we propose a new method for construction new nice arrangement on the sphere Sd using the spaces of spherical harmonic.

Consider a sequence of point sets on S, where each set X is a spherical ndesign with m points, where m = O(n), and where the spherical distance between points of X is at least λ/ √ m, for some λ common to all sets of the sequence. For each X of such a sequence, the Coulomb energy E(X) is bounded by E(X) 6 1 2 m2 + O(m). The first term and the order of the second term are the same as for the bou...

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...

Introduction: To date, gold nanoparticles (GNPs) have been demonstrated to have great potential as contrast agent for CT imaging and therapeutics. This study was designed to evaluate any effect on X-ray attenuation that might result from using GNPs with a variety of size, surface chemistries and shapes.   Materials and Methods: Spherical GNPs and gold nanorod...

a green low-cost and reproducible yeast mediated synthesis of silver nanoparticles is reported. the synthesis is performed at room temperature. x-ray and transmission electron microscopy analyses are performed to ascertain the formation of ag nanoparticles. nanoparticles almost spherical in shape having a size of 6-20 nm are found.

An L-spherical code is a set of Euclidean unit vectors whose pairwise inner products belong to the set L. We show, for a fixed α, β > 0, that the size of any [−1,−β] ∪ {α}-spherical code is at most linear in the dimension. In particular, this bound applies to sets of lines such that every two are at a fixed angle to each another.

In the context of the p-spin spherical model we show how saddle points of the

We present the results of an empirical study, which investigated the effects of the amount of information and the type of information refuted in refutation texts. The study compared the effects of three refutation texts on elementary school children’s understanding of the scientific concept of the Earth. One text refuted only the belief that the Earth is flat, the second refuted in addition the...

Received ; accepted – 2 – ABSTRACT Numerical simulations of galaxy clusters including two species – baryonic gas and dark matter particles – are presented. Cold Dark Matter spectrum, Gaussian statistics and flat universe are assumed. The dark matter component is evolved numerically by means of a standard particle mesh method. The evolution of the baryonic component has been studied numerically ...