Related papers: On Difference Equations Motivated by Modelling the…

By analogy with work of Hitchin on integrable systems, we construct natural relaxations of several kinds of moduli spaces of difference equations, with special attention to a particular class of difference equations on an elliptic curve…

We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our description is local, which offers the potential to speed up…

This book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple theoretical tool that enables an exact treatment of diverse more complex lattice-statistical models.…

This paper has a double goal, the first one is to make a slight survey of some theoretical results about the existence of positively invariant curves that allow to describe important properties of the set of bounded orbits and its boundary…

Over the last few years lattice techniques have been used to investigate candidate theories of new physics beyond the Standard Model. This review gives a survey of results from these studies. Most of these investigations have been of…

Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of…

Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with…

We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…

We develop a general stability analysis for objective structures, which constitute a far reaching generalization of crystal lattice systems. We show that these particle systems, although in general neither periodic nor space filling, allow…

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

Let L^1(G) and M(G) be group algebra and measure algebra of a locally compact group G, respectively and D:L^1(G)-->M(G) be a continuous linear map. We consider D behaving like derivation or anti-derivation at orthogonal elements for several…

Patient-specific computational models of the heart are powerful tools for cardiovascular research and medicine, with demonstrated applications in treatment planning, device evaluation, and surgical decision-making. Yet constructing such…

A behavior of one class of mappings with finite distortion at a neighborhood of the origin is investigated. There is proved a lower estimate of distortion of a distance under mappings mentioned above.

Here we analyze the behavior of dynamically coupled maps, based on those introduced in a series of papers by Ito and Kaneko (Phys. Rev. Lett. 88:028701, 2002 and Phys. Rev. E 67:046226, 2003). We show how the microscopic coupling mechanism…

In a recent paper, Diaz-Guilera et al. [Phys. Rev. E 57, 3820 (1998)] analyze the mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators. In essence, their analysis consists in the study of the…

Basic issues of the general model-building framework of the mechanics of complex bodies are discussed. Attention is focused on the representation of the material elements, the conditions for the existence of ground states in conservative…

The Weyl relations, the harmonic oscillator, the hydrogen atom, the Dirac equation on the lattice are presented with the help of the difference equations and the orthogonal polynomials of discrete variable. This area of research is…

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we…

Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…

This paper is about the hearts arising from torsion pairs of finite type in the category of modules over the Kronecker algebra. After a characterization of the simple objects in these hearts, we describe their atom spectrum and compute…