In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a symmetric critical operator P1, such that a nonzero subsolution of a symmetric nonnegative operator P0 is a ground state. Particularly, if Pj := −∆ + Vj , for j = 0, 1, are two nonnegative Schrödinger operators defined on Ω ⊆ R such that P1 is critical in Ω with a ground state φ, the function ψ 0 is a...

In this paper, the nonlinear free vibrations of thin symmetric and non-symmetric cross-ply composite plates subjected to biaxial initial stresses are investigated. Because of their excellent properties such as specific strength and specific stiffness, composite plates have wide applications in aerospace and mechanical structures. Based on Von-Karman's strain-displacement relations and using Gal...

When joined to a stipulated neighborhood digraph, an objective function deÞned on the solution space of a real combinatorial optimization problem forms a landscape. Grover shows that landscapes satisfying a certain difference equation have properties favorable to local search. Studying only symmetric and regular neighborhood digraphs, Stadler deÞnes elementary landscapes as those which can be r...

For every symmetric (“palindromic”) word S(A,B) in two positive definite letters and for each fixed n-by-n positive definite B and P , it is shown that the symmetric word equation S(A,B) = P has an n-by-n positive definite solution A. Moreover, if B and P are real, there is a real solution A. The notion of symmetric word is generalized to allow non-integer exponents, with certain limitations. I...

We study the stability of the replica-symmetric solution of a two-sublattice infinite-range spin-glass model, which can describe the transition from an antiferromagnetic to a spin-glass state. The eigenvalues associated with replica-symmetric perturbations are in general complex. The natural generalization of the usual stability condition is to require the real part of these eigenvalues to be p...

We introduce a notion of left-symmetric bialgebra which is an analogue of the notion of Lie bialgebra. We prove that a left-symmetric bialgebra is equivalent to a symplectic Lie algebra with a decomposition into a direct sum of the underlying vector spaces of two Lagrangian subalgebras. The latter is called a parakähler Lie algebra or a phase space of a Lie algebra in mathematical physics. We i...

Effective dielectric constants of diphase composite dielectrics are simulated by Monte Carlo-finite element method on three-dimensional lattice. Effective dielectric constants with coefficients of variation less than 5.5% are obtained for different ratios of dielectric constants of the two phases, ranging from 10 to 700. Various mixing rules and equations are fitted to these data and the accura...

This paper discusses Skyrmions on the 3-sphere coupled to fermions. The resulting Dirac equation commutes with a generalized angular momentum G. For G = 0 the Dirac equation can be solved explicitly for a constant Skyrme configuration and also for a SO(4) symmetric hedgehog configuration. We discuss how the spectrum changes due to the presence of a non-trivial winding number, and also consider ...