*Correspondence: [email protected] 1School of Mathematical Science, University of Science and Technology of China, Hefei, 230036, China 2School of Mathematics and Statistics, Hefei Normal University, Hefei, 230601, China Full list of author information is available at the end of the article Abstract This paper is concerned with a class of neutral Nicholson blowflies models with leakage delays...

It is shown in this paper that if BG is the Stone-ech compactification of a group G, and G satisfying a certain condition, then there is a weakly recurrent point in BG which is not almost periodic, and if another condition will be added, then there is a recurrent point in 8G which is not almost periodic point.

In the context of Free Probability Theory, we study two different constructions that provide new examples of factors of type II1 with prescribed fundamental group. First we investigate state-preserving group actions on the almost periodic free Araki-Woods factors satisfying both a condition of mixing and a condition of free malleability in the sense of Popa. Typical examples are given by the fr...

We consider abstract differential equations of the form u′(t) = Au(t)+f(t) or u′′(t)=Au(t)+f(t) in Banach spaces X, where f(·), R→X is almost-periodic, while A is a linear operator, (A)⊂X →X. If the solution u(·) is likewise almost-periodic, R→X, we establish connections between their Bohr-transforms, û(λ) and f̂ (λ). 2000 Mathematics Subject Classification. 34C27, 34G10.

This paper considers the existence of positive almost-periodic solutions for almost-periodic LotkaVolterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.

In this work, we study the existence of almost periodic solutions for some partial neutral functional differential equations. Using the variation of constants formula and the spectral decomposition of the phase space developed in [6], we prove that the existence of an almost periodic solution is equivalent to the existence of a bounded solution on R+.

In order to obtain the conditions for the existence of periodic and almost periodic solutions of Volterra difference equations, x(n+1) = f(n, x(n))+ ∑n s=−∞ F (n, s, x(n+ s), x(n)), we consider certain stability properties, which are referred to as (K, ρ)-weakly uniformly-asymptotic stability and (K, ρ)-uniformly asymptotic stability. Moreover, we discuss the relationship between the ρ-separati...

A group is called D-quasirandom if all of its nontrivial representations over the complex numbers have dimensions at least D. In this paper, we investigate the extent to which quasirandomness is a local property; more precisely, we study the question of whether a non-principal ultraproduct of a given sequence of quasirandom groups remains quasirandom, and whether the ultraproduct of a sequence ...

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 ...

By using some new analytical techniques, modified inequalities and Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions for the existence of at least one positive almost periodic solution of a kind of two-species model of facultative mutualism with time delays are obtained. Further, the global asymptotic stability of the positive almost periodic solution of thi...