Related papers: Almost periodic functions on the quantum time scal…
In this work the existence of periodic solutions is studied for the Hamiltonian functions (Formula presented.) where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
The paper studies the structure of high-order adiabatic approximation of a wave function for slowly changing Hamiltonians. A constructive technique for explicit separation of fast and slow components of the wave function is developed. The…
We construct time quasi-periodic solutions to nonlinear wave equations on the torus in arbitrary dimensions. All previously known results (in the case of zero or a multiplicative potential) seem to be limited to the circle. This generalizes…
We show that a problem on minimal periods of solutions of Lipschitz functional differential equations is closely related to the unique solvability of the periodic problem for linear functional differential equations. Sharp bounds for…
The aim of this paper is studying the problem of almost periodicity of almost periodic lattice dynamical systems of the form $u_{i}'=\nu (u_{i-1}-2u_i+u_{i+1})-\lambda u_{i}+F(u_i)+f_{i}(t)\ (i\in \mathbb Z,\ \lambda >0)$. We prove the…
All the almost periodic solutions for non integrable PDEs found in the literature are very regular (at least $C^\infty$) and, hence, very close to quasi periodic ones. This fact is deeply exploited in the existing proofs. Proving the…
We are concerned with some extensions of the classical Liouville theorem for bounded harmonic functions to solutions of more general equations. We deal with entire solutions of periodic and almost periodic parabolic equations including the…
Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classical functional equations involving shifts by the…
We present an effective Hamiltonian theory available for some quasi-periodically driven quantum systems which does not need the knowledge of the Fourier frequencies of the control signal. It could also be available for some chaotically…
We extend topological string methods in order to perform WKB approximations for quantum mechanical problems with higher order potentials efficiently. This requires techniques for the evaluation of the relevant quantum periods for Riemann…
In this paper, we first use the Bohr property to give a definition of Besicovitch almost periodic functions, and study some basic properties of Besicovitch almost periodic functions, including the equivalence of the Bohr property and the…
In this paper, we analyze multi-dimensional Bohr $({\mathcal B},c)$-almost periodic type functions. The main structural characterizations for the introduced classes of Bohr $({\mathcal B},c)$-almost periodic type functions are established.…
For a class of $\mathbb{R}^d$-ations and $\mathbb{Z}^d$-actions on the $n$-dimensional torus $\mathbb{T}^n$, we characterize their unique ergodicity and establish a theorem of Weyl type. This result allows us to establish an isomorphism…
In this paper, we analyze multi-dimensional Weyl almost periodic type functions in Lebesgue spaces with variable exponents. The introduced classes seem to be new and not considered elsewhere even in the constant coefficient case. We provide…
This paper presents a new generalized Mackey-Glass model with a non-linear harvesting term and mixed delays. The main purpose of this work is to study the existence and the exponential stability of the pseudo almost periodic solution for…
Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the…
We design a physical wave-pulse neural network (WPNN) for both wave and pulse propagation, which gives more degrees of freedom for neural coding than spike neural networks (SNN). We define the rules and the information entropy of this kind…
We study signal processing tasks in which the signal is mapped via some generalized time-frequency transform to a higher dimensional time-frequency space, processed there, and synthesized to an output signal. We show how to approximate such…
The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand sides are small. In the case that all…