in the present paper the linear oscillator in r3 with z =constanthas been considered. the aim is to determine the necessary conditions forthe persistence of periodic solutions under discontinuous perturbations. a newapproach based on a computational method has been used. at the end weapply our method on an example.

Work of both authors was partially supported by the NSF Grant DMS-9610444 and by a DEPSCoR Grant administered through the ARO. The rst author was also partially supported by an NSF EPSCoR Grant. The content of this article does not necessarily re ect the position or the policy of the federal government. The theory of classical waves in periodic high contrast photonic and acoustic media leads to...

We address the existence and stability of two-dimensional solitons in optical or matter-wave media, which are supported by purely nonlinear lattices in the form of a periodic array of cylinders with self-focusing nonlinearity, embedded into a linear material. We show that such lattices can stabilize two-dimensional solitons against collapse. We also found that stable multipoles and vortex solit...

In the present paper we introduce analogs of almost periodic functions on the unit circle. We study certain uniform algebras generated by such functions, prove corona theorems for them and describe their maximal ideal spaces. 1. Formulation of Main Results 1.1. The classical almost periodic functions on the real line first introduced by H. Bohr in the 1920s play an important role in various are...

The article is devoted to the following question. Consider a periodic self-adjoint difference (differential) operator on a graph (quantum graph) G with a co-compact free action of the integer lattice Z. It is known that a local perturbation of the operator might embed an eigenvalue into the continuous spectrum (a feature uncommon for periodic elliptic operators of second order). In all known co...

Rosetting and non-rosetting lymphocytes collected from normal individuals were stained for the presence of beta-glucuronidase, periodic-acid Schiff activity, gamma glutamyl transpeptidase, acid phosphatase, and alpha-naphthyl butyrate esterase. Lymphocytes which formed rosettes with sheep erythrocytes and non-rosette forming lymphocytes contained cytochemical reaction products for all five stai...

Given any compact connected manifold M , we describe Copen sets of iterated functions systems (IFS’s) admitting fully-supported ergodic measures whose Lyapunov exponents alongM are all zero. Moreover, these measures are approximated by measures supported on periodic orbits. We also describe C-open sets of IFS’s admitting ergodic measures of positive entropy whose Lyapunov exponents along M are ...

In this paper, we discuss a direct measure for the proportion of periodic and aperiodic components in speech signals. Further, in the periodic regions, we estimate the pitch period. This method is particularly useful in situations where the speech signal contains simultaneous periodic and aperiodic energy, as in the case of breathy vowels and some voiced obstruents. The performance of this algo...