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We consider a new model for shunting inhibitory cellular neural networks, retarded functional differential equations with piecewise constant argument. The existence and exponential stability of almost periodic solutions are investigated. An…
We consider the problem of reconstructing a function given its values on a set of points with finite density. We prove that with probability one, the values of an almost periodic function on a random array of points (with finite density)…
There are many significant applied contexts that require the solution of discontinuous optimization problems in finite dimensions. Yet these problems are very difficult, both computationally and analytically. With the functions being…
We consider certain finite sets of circle-valued functions defined on intervals of real numbers and estimate how large the intervals must be for the values of these functions to be uniformly distributed in an approximate way. This is used…
Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…
Slice regular functions are a generalization of holomorphic functions to the setting of quaternions (and more generally, Clifford algebras). In this paper, we first establish the Bohr inequality for slice starlike functions and slice…
In this paper, we introduce several various classes of $c$-almost periodic type functions and their Stepanov generalizations, where $c\in {\mathbb C}$ and $|c|=1.$ We also consider the corresponding classes of $c$-almost periodic type…
In this paper, we use the variational approach to investigate recurrent properties of solutions for stochastic partial differential equations, which is in contrast to the previous semigroup framework. Consider stochastic differential…
A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…
An almost periodic function in finite-dimensional space extends to a holomorphic bounded function in a tube domain with a cone in the base if and only if the spectrum belongs to the conjugate cone. Also, an almost periodic function in…
In the present paper, we study the limit sets of the almost periodic functions $f(x)$. It is interesting that the values $r=\inf|f(x)|$ and $R=\sup|f(x)|$ may be expressed in the exact form. We show that the ring $r\leq |z|\leq R$ is the…
Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…
In this paper, we discuss the relationships between stability and almost periodicity for solutions of stochastic differential equations. Our essential idea is to get stability of solutions or systems by some inherited properties of Lyapunov…
In the paper under review, we analyze asymptotically almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. As auxiliary tools, we use subordination principles,…
The goal of this expository article is a fairly self-contained account of some averaging processes of functions along sequences of the form $(\alpha^n x)^{}_{n\in\mathbb{N}}$, where $\alpha$ is a fixed real number with $| \alpha | > 1$ and…
Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…
In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of…
Periodic Schur process is a generalization of the Schur process introduced in math.CO/0107056. We compute its correlation functions and their bulk scaling limits, and discuss several applications including asymptotic analysis of uniform…
In the paper under review, we introduce the notions of various types of generalized (asymptotical) almost periodicity with variable exponents. We define and thoroughly analyze an important subclass of (asymptotically) Stepanov almost…
We study the Banach algebras of bounded holomorphic functions on the unit disk whose boundary values, having, in a sense, the weakest possible discontinuities, belong to the algebra of semi-almost periodic functions on the unit circle. The…