Addition theorems for vector spherical harmonics require the determination of the Gaunt coefficients that appear in a linearization expansion of the product of two associated Legendre functions. This paper presents an algorithm for the efficient calculation of these coefficients through solving the most appropriate (lower triangular) linear system and derives all relevant recurrence relations n...

We present a supersymmetric model of fermion masses with SU(4)×SU(2)2×U(1)X gauge group with matter in fundamental and antisymmetric tensor representations only. The up, down, charged lepton and neutrino Yukawa matrices are distinguished by different Clebsch-Gordan coefficients due to contracting over SU(4) and SU(2)R indices. We obtain a hierarchical light neutrino mass spectrum with bi-large ...

Velleda Baldoni, Nicole Berline, Michèle Vergne. Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope. Matthias Beck, Christian Haase, Bruce Reznick, Michèle Vergne, Volkmar Welker and Ruriko Yoshida. Integer Points in Polyhedra-Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics, American Mathematical Society, pp.1...

We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kähler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex potentials and rederive the existence of an infinite set of conserved currents. We perform a canonical analysis to find the explicit form of the algebra of conser...

A summary of the properties of the Wigner Clebsch-Gordan coefficients and isoscalar factors for the group SU3 in the SU2⊗U1 decomposition is presented. The outer degeneracy problem is discussed in detail with a proof of a conjecture (Braunschweig's) which has been the basis of previous work on the SU3 coupling coefficients. Recursion relations obeyed by the SU3 isoscalar factors are produced, a...

If R, S, T are irreducible SL3(C)-representations, we give an easy and explicit description of a basis of the space of equivariant maps R⊗S → T (Theorem 3.1). We apply this method to the rationality problem for invariant function fields. In particular, we prove the rationality of the moduli space of plane curves of degree 34. This uses a criterion which ensures the stable rationality of some qu...

This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D = 2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D = 3. These interbasis expansion coefficients are found to be analytic continuat...

In this article we investigate the structure of a twisted cohomology group of the first homology of a trivalent graph with a coefficient associated with its quantum Clebsch-Gordan condition. By using this investigation we shall show the existence of the external edge cocycles defined in [3] and a finite algorithm to construct such cocycles. Such cocycles are used for a combinatorial realization...

BACKGROUND AND PURPOSE Stroke scales are intended to measure stroke severity for the purpose of clinical trials. Scores have been used to determine trial entry, to compare patient groups within or between trials, or as a secondary end point. The use of scores as an end point in meta-analysis has not been validated, but such analyses have nevertheless been performed when equivocal results have b...

Objective measures of environmental attributes have been used to understand how neighborhood environments relate to physical activity. However, this method relies on detailed spatial data, which are often not easily available. Walk Score® is a free, publicly available web-based tool that shows how walkable a given location is based on objectively-derived proximity to several types of local dest...