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We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
This is the first part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. We prove two main results concerning systems that are regular singular at…
In this paper, we consider Caputo type fractional stochastic time-delay system with permutable matrices. We derive stochastic analogue of variation of constants formula via a newly defined delayed Mittag-Leffer type matrix function. Thus,…
We consider solutions of the Cauchy problem for semilinear equations with (possibly) different L\'evy operators. We provide various results on their convergence under the assumption that symbols of the involved operators converge to the…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
Given two systems $P=(P_j(D))_{j=1}^N$ and $Q=(Q_j(D))_{j=1}^M$ of linear partial differential operators with constant coefficients, we consider the spaces ${\mathcal E}_\omega^P$ and ${\mathcal E}_\omega^Q$ of $\omega$-ultradifferentiable…
In the given paper we consider finite difference approximations to systems of polynomially-nonlinear partial differential equations whose coefficients are rational functions over rationals in the independent variables. The notion of strong…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II…
We study the stability and stabilizability of a continuous-time switched control system that consists of the time-invariant $n$-dimensional subsystems \dot{x}=A_ix+B_i(x)u\quad (x\in\mathbb{R}^n, t\in\mathbb{R}_+ \textrm{and}…
After a brief survey of the definition and the properties of Lambda-symmetries in the general context of dynamical systems, the notion of "Lambda-constant of motion'' for Hamiltonian equations is introduced. If the Hamiltonian problem is…
We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous…
In this paper implicit and explicit exact difference schemes (EDS) for system $\textbf{x}' = A\textbf{x}$ of three linear differential equations with constant coefficients are constructed. Numerical simulations for stiff problem and for…
This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…
The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…