Related papers: The $k$-Compound of a Difference-Algebraic System
Sequential dynamical systems (SDS) are used to model a wide range of processes occurring on graphs or networks. The dynamics of such discrete dynamical systems is completely encoded by their phase space, a directed graph whose vertices and…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
In this article, we prove that Dirac brackets for Hamiltonian and non-Hamiltonian constrained systems can be derived recursively. We then study the applicability of that formulation in analysis of some interesting physical models.…
The use of quadratic residues to construct matrices with specific determinant values is a familiar problem with connections to many areas of mathematics and statistics. Our research has focused on using cubic residues to construct matrices…
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…
Understanding the relationship between microscopic structure and macroscopic thermodynamic properties is a central challenge in the study of complex fluids. The Kirkwood-Buff (KB) theory offers an elegant and powerful framework for bridging…
The paper develops the method for construction of the families of particular solutions to the nonlinear Partial Differential Equations (PDE) without relation to the complete integrability. Method is based on the specific link between…
A regular way to define an additive coproduct (or ``coaddition'') on the q-deformed differential complexes is proposed for quantum groups and quantum spaces related to the Hecke-type R-matrices. Several examples of braided coadditive…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form,…
We prove some properties of analytic multiplicative and sub-multiplicative cocycles. The results allow to construct natural invariant analytic sets associated to complex dynamical systems.
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial…
A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in…
In this paper, we discuss some problems of elementary plane differential geometry and kinematics. Although the results are not new, the consistent use of complex-valued functions (plane curves) of a real variable (parameter) allows to…
In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.
Differential graded (DG) commutative algebra provides powerful techniques for proving theorems about modules over commutative rings. These notes are a somewhat colloquial introduction to these techniques. In order to provide some motivation…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…