We give a very general isoperimetric comparison theorem which, as an important special case, gives hypotheses under which the spherically symmetric (n− 1)-spheres of a spherically symmetric n-manifold are isoperimetric hypersurfaces, meaning that they minimize (n − 1)-dimensional area among hypersurfaces enclosing the same n-volume. This result greatly generalizes the result of Bray (Ph.D. thes...

We consider a class of nonlinear Schrödinger / Gross-Pitaveskii (NLS-GP) equations, i.e. NLS with a linear potential. We obtain conditions for a symmetry breaking bifurcation in a symmetric family of states asN , the squared L2 norm (particle number, optical power), is increased. In the special case where the linear potential is a doublewell with well separation L, we estimate Ncr(L), the symme...

We revisit a geometric lower bound for Waring rank of polynomials (symmetric rank of symmetric tensors) of [LT10] and generalize it to a lower bound for rank with respect to arbitrary varieties, improving the bound given by the “non-Abelian” catalecticants recently introduced by Landsberg and Ottaviani. This is applied to give lower bounds for ranks of multihomogeneous polynomials (partially sy...

In symmetric tensor decomposition one expresses a given symmetric tensor T a sum of tensor powers of a number of vectors: T = v⊗d 1 + · · · + v ⊗d k . Orthogonal decomposition is a special type of symmetric tensor decomposition in which in addition the vectors v1, ..., vk are required to be pairwise orthogonal. We study the properties of orthogonally decomposable tensors. In particular, we give...

The stochastic Petri net (SPN) model is well suited to formal representation of concurrency, synchronization, and communication. In this paper we focus on discrete event simulation methods for SPN models with special structure and define a symmetric SPN. Exploiting properties of a symmetric SPN and underlying regenerative process structure, we establish steady state estimation procedures based ...

Abstract. We introduce two pairs of nondifferentiable multiobjective second order symmetric dual problems with cone constraints over arbitrary closed convex cones, which is different from the one proposed by Mishra and Lai [12]. Under suitable second order pseudo-invexity assumptions we establish weak, strong and converse duality theorems as well as self-duality relations. Our symmetric duality...