This paper discusses a multispecies discrete Gilpin-Ayala mutualism system with feedback controls. We firstly obtain the permanence of the system. Assuming that the coefficients in the system are almost periodic positive sequences, we obtain the sufficient conditions for the existence of a unique almost periodic positive solution which is globally attractive.

In this paper, we consider the almost periodic solutions of a discrete cooperation system with feedback controls. Assuming that the coefficients in the system are almost periodic sequences, we obtain the existence and uniqueness of the almost periodic solution which is uniformly asymptotically stable. Keywords—Discrete cooperation model; Almost periodic solution; Feedback control; Lyapunov func...

We define, for a locally compact quantum group G in the sense of Kustermans– Vaes, the space of LUC (G) of left uniformly continuous elements in L∞(G). This definition covers both the usual left uniformly continuous functions on a locally compact group and Granirer’s uniformly continuous functionals on the Fourier algebra. We show that LUC (G) is an operator system containing the C∗-algebra C0(...

Consider the operator T = − d dx2 + x2 + q(x) in L2(R), where real functions q, q′ and ∫ x 0 q(s) ds are bounded. In particular, q is periodic or almost periodic. The spectrum of T is purely discrete and consists of the simple eigenvalues {μn}n=0, μn < μn+1. We determine their asymptotics μn = (2n+1)+(2π) −1 ∫ π −π q( √ 2n + 1 sin θ) dθ+O(n−1/3).

In this paper, we study a class of nonlinear Duffing equations with a deviating argument and establish some sufficient conditions for the existence of positive almost periodic solutions of the equation. These conditions are new and complement to previously known results.

We study connections between operator theoretic properties of Toeplitz operators acting on suitable Besikovitch spaces and factorizations of their symbols which are matrix valued almost periodic functions of several real variables. Among other things, we establish the existence of a twisted canonical factorization for locally sectorial symbols, and characterize one-sided invertibility of Toepli...

A class of translation bounded complex measures, which have the form of weighted Dirac combs, on locally compact Abelian groups is investigated. Given such a Dirac comb, we are interested in its diffraction spectrum which emerges as the Fourier transform of the autocorrelation measure. We present a sufficient set of conditions to ensure that the diffraction measure is a pure point measure. Simu...