相关论文: On Compatibility of Discrete Relations

This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition,…

We consider a linear algebra approach to establishing a discrete comparison principle for a nonmonotone class of quasilinear elliptic partial differential equations. In the absence of a lower order term, we require local conditions on the…

One of the main contributions which Volker Weispfenning made to mathematics is related to Groebner bases theory. In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational…

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law…

Cellular Automata are discrete-time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata (PCA), are…

A Comprehensive Grobner system for a parametric ideal I in K(A)[X] represents the collection of all Grobner bases of the ideals I' in K[X] obtained as the values of the parameters A vary in K. The recent algorithms for computing them…

The interaction within a hybrid system consisting of a spherical metal nanoparticle and a nearby organic dye molecule is formulated in a combined quantum-classical approach. Whereas the nanoparticle's polarization field is treated in…

The quantum systems with finite-dimensional Hilbert space have several applications and are intensively explored theoretically and experimentally. The mathematical description of these systems follows the analogy with the usual…

We analyze a dual mixed nonconforming discretization of a generalized Darcy-Forchheimer model. Compared to the analogous scheme proposed by Girault and Wheeler, we consider general, i.e., nonquadratic, Forchheimer nonlinearities; we admit…

This paper formulates and studies the concepts of approximate (alternating) bisimulation relations characterizing equivalence relations between interconnected systems and their abstractions. These equivalence relations guarantee that the…

In this paper we present a new approach to Grothendieck duality on schemes. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic geometry. We obtain…

The main focus of this paper is to explore how much similarity between two stochastic differential systems. Motivated by the conjugate theory of stochastic dynamic systems, we study the relationship between two systems by finding…

Numerous exact relations exist that relate the effective elastic properties of composites to the elastic properties of their components. These relations can not only be used to determine the properties of certain composites, but also…

We generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximating the low-energy excitations than charge-basis states, as…

This paper proposes a method for set-valued state estimation of nonlinear, discrete-time systems. This is achieved by combining graphs of functions representing system dynamics and measurements with the hybrid zonotope set representation…

A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open…

The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns…

Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…

We present a method which allows reduction of a size of a simulated system. The method can be applied to any system where one can define a finite set of possible states of the system and an elementary process which transforms one state of…

We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gr\"obner bases to clarify crucial notions concerning compatibility…