In this paper, we study the right regular representation RΓ of a finite group G on the vector space consisting of vector valued functions on Γ\G with a subgroup Γ of G and give a trace formula using the work of M.-F. Vignéras.

The parabolic scalar curvature equation is a reaction-diffusion type equation on an (n − 1)-manifold Σ, the time variable of which shall be denoted by r. Given a function R on [r0, r1)×Σ and a family of metrics γ(r) on Σ, when the coefficients of this equation are appropriately defined in terms of γ and R, positive solutions give metrics of prescribed scalar curvature R on [r0, r1)× Σ in the fo...

We consider commutative string rewriting systems (Vector Addition Systems, Petri nets), i.e., string rewriting systems in which all pairs of letters commute. We are interested in reachability: given a rewriting system R and words v and w, can v be rewritten to w by applying rules from R? A famous result states that reachability is decidable for commutative string rewriting systems. We show that...

This paper uses the theory of dual equivalence graphs to give explicit Schur expansions for several families of symmetric functions. We begin by giving a combinatorial definition of the modified Macdonald polynomials and modified HallLittlewood polynomials indexed by any diagram δ ⊂ Z × Z, written as H̃δ(X; q, t) and H̃δ(X; 0, t), respectively. We then give an explicit Schur expansion of H̃δ(X; 0,...

I review the effects of flavor conversion of neutrinos from stellar collapse due to masses and mixing, and discuss the motivations for their study. I consider in detail the sensitivity of certain observables (characteristics of the energy spectra of νe and ν̄e events) to the 13-mixing (sin 2 θ13) and to the type of mass hierarchy/ordering (sign[∆m213]). These observables are: the ratio of averag...

The Jucys-Murphy elements for wreath products Γn associated to any finite group Γ are introduced and they play an important role in our study on the connections between class algebras of Γn for all n and vertex algebras. We construct an action of (a variant of) the W1+∞ algebra acting irreducibly on the direct sum RΓ of the class algebras of Γn for all n in a group theoretic manner. We establis...

A surprisingly short geometric proof of the existence of sampling spaces with the interpolation property on the Heisenberg Lie group is given. This result was originally proved by of B. Currey and A. Mayeli [3]. In the loving memory of my father Dr. Germain Oussa. Let N be a locally compact group, and let Γ be a discrete subset of N. Let H be a leftinvariant closed subspace of L (N) consisting ...

We describe a general method for modeling gamma-ray burst prompt emission, and determine the range of magnetic field strength, electron energy, Lorentz factor of the source, and the distance of the source from the central explosion that is needed to account for the prompt γ-ray emission of a typical long duration burst. We find that for the burst to be produced via the synchrotron process unphy...

In this paper, all graphs are simple, i.e., without self-loops or parallel edges, unless otherwise stated. A weighted graph G is a triple (V (G), E(G), costG), where V (G) is the vertex set of G, E(G) is the edge set of G, and costG is a function from E(G) to nonnegative reals, called the cost function of G. For each edge e of G, we call costG(e) the cost of e. Let G be a (weighted) graph. For ...