This paper is a continuation of my previous paper in Mathematica Bohemica and solves the same problem but by means of another method. It deals with almost periodic solutions of a certain type of almost periodic systems of differential equations.

In this paper we study homogenization problem for strong Markov processes on Rd having infinitesimal generators Lf(x)=?Rd(f(x+z)?f(x)???f(x),z?1{|z|?1})k(x,z)?(dz)+?b(x),?f(x)?,f?Cb2(Rd) in periodic media, where ? is a nonnegative measure that does not charge the origin 0, satisfies ?Rd(1?|z|2)?(dz)<? and can be singular with respect to Lebesgue Rd. Under proper scaling show scaled converge wea...

We study the local optimality of periodic point sets in $\mathbb{R}^n$ for energy minimization Gaussian core model, that is, radial pair potential functions $f_c(r)=e^{-c r}$ with $c>0$. By considering suitable parameter spaces $m$-periodic sets, we can locally rigorously analyze within family having same density. derive a characterization being $f_c$-critical all $c$ terms weighted spherical $...

We consider the Schrödinger operator on the so-called zigzag periodic metric graph (a continuous version of zigzag nanotubes) with a periodic potential. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite number of eigenvalues with infinite multiplicity. We describe all compactly supported (localization) eigenfunctions with the ...

Abstract Let $\varphi $ be Euler’s function and fix an integer $k\ge 0$ . We show that for every initial value $x_1\ge 1$ , the sequence of positive integers $(x_n)_{n\ge 1}$ defined by $x_{n+1}=\varphi (x_n)+k$ all $n\ge is eventually periodic. Similarly, values $x_1,x_2\ge $x_{n+2}=\varphi (x_{n+1})+\varphi periodic, provided k even.

This paper discusses a discrete multispecies Gilpin-Ayala mutualism system. We first study the permanence and global attractivity of the system. Assume that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive and uniformly asymptotically stable by constructing a suit...

The paper is concerned with conditions for the existence of almost periodic solutions of the following abstract functional differential equation u̇(t) = Au(t)+[Bu](t)+f(t), where A is a closed operator in a Banach space X, B is a general bounded linear operator in the function space of all X-valued bounded and uniformly continuous functions that satisfies a so-called autonomous condition. The ob...

The paper studies different variants of almost periodicity notion. We introduce the class of eventually strongly almost periodic sequences where some suffix is strongly almost periodic (=uniformly recurrent). The class of almost periodic sequences includes the class of eventually strongly almost periodic sequences, and we prove this inclusion to be strict. We prove that the class of eventually ...

A procedure for designing exact reconstruction lter banks for tree-structured sub-band coders. where p(n) = jx(n)j 2 =kxk 2. Note that d = exp H(x) where H(x), deened in Equation 55 above, is the entropy of the sequence x. Beylkin in 1] observed earlier that computing the periodic discrete wavelet transform of all N circulant shifts of an N-point periodic signal requires computing only N log 2 ...