We investigate the iterated Kronecker product of a square matrix with itself and prove an invariance property for symmetric subspaces. This motivates the definition of an iterated symmetric Kronecker product and the derivation of an explicit formula for its action on vectors. We apply our result for describing a linear change in the matrix parametrization of semiclassical wave packets.

We show that in a symmetric m-convex algebra without algebraic zero divisors, any self-adjoint and invertible element is either positive or negative. As a consequence we obtain that a symmetric m-convex algebra containing no algebraic zero divisors and for which every positive element has a positive square root is isomorphic to C + Rad(A).

correlation of heat transfer coefficients for air flow through the regenerator constructed from randomly paked spheres is reported for the symmetric-balanced mode of operation. the experimental results have been correlated by the least square regression has been obtained.the present correlation has been compared with the heat transfer coefficient correlations in the literature.

We show that in a symmetric m-convex algebra without algebraic zero divisors, any self-adjoint and invertible element is either positive or negative. As a consequence we obtain that a symmetric m-convex algebra containing no algebraic zero divisors and for which every positive element has a positive square root is isomorphic to C + Rad(A).

Abstract. We consider the equation −∆u = wu on a square domain in R, with Dirichlet boundary conditions, where w is a given positive function that is invariant under all (Euclidean) symmetries of the square. This equation is shown to have a solution u, with Morse index 2, that is neither symmetric nor antisymmetric with respect to any nontrivial symmetry of the square. Part of our proof is comp...

 In this paper, we investigate the evolution of supercontinuum and femtosecond optical pulses generation through square lattice elliptical-core photonic crystal fiber (PCF) at 1550 nm by using both full-vector multipole method (M.P.M) and novel concrete algorithms: symmetric  split-step Fourier (SSF) and  fourth order Runge Kutta (RK4) which is an accurate method to solve the general  nonlinear...

In this paper discrete time-varying systems are considered. The study of spectral properties in a time-varying framework is performed by defining a suitable operator on the Hilbert space of square summable sequences. This setting gives a parameterization of square summable symmetric solutions for time-varying Riccati equations.