Related papers: On Difference Equations Motivated by Modelling the…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
A few subjects which strongly intertwine our field are discussed: K --> Pi Pi decay, chiral symmetry on the lattice and a few other selected topics. Open questions are touched also on perturbation theory, locality, Gribov copies, CP…
We study a second order ordinary differential equation corresponding to rotationally symmetric $p$-harmonic maps. We show unique continuation and Liouville's type theorems for positive solutions. We discuss the existence of bounded positive…
We consider the lattice of coarse structures on a set $X$ and study metrizable, locally finite and cellular coarse structures on $X$ from the lattice point of view.
A relationship between the tetrahedron equation for maps and the consistency property of integrable discrete equations on $\mathbb{Z}^3$ is investigated. Our approach is a generalization of a method developed in the context of Yang-Baxter…
The physical consistency of the match of piecewise-$C^0$ metrics is discussed. The mathematical theory of gravitational discontinuity hypersurfaces is generalized to cover the match of regularly discontinuous metrics. The mean-value…
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…
Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for…
We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we…
A general structure is developed from which a system of integrable partial difference equations is derived generalising the lattice KdV equation. The construction is based on an infinite matrix scheme with as key ingredient a (formal)…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
In this paper we develop a theory of linear differential systems analogous to the classical one for ODEs, including the obtaining of fundamental matrices, the development of a variation of parameters formula and the expression of the…
We construct a dynamical lattice model based on a crossed module of possibly non-abelian finite groups. Its degrees of freedom are defined on links and plaquettes, while gauge transformations are based on vertices and links of the…
In 1986, Oliver Pretzel studied the set of orientations of a connected finite graph $G$ and showed that any two such orientations having the same flow-difference around all closed loops can be obtained from one another by a succession of…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map…
A generalized gauge invariant Ising model on random surfaces with non-trivial topology is proposed and investigated with the dual transformation. It is proved that the model is self-dual in case of a self-dual lattice. In special cases the…
We identify limit stable pairs and stable framed sheaves as epimorphisms and monomorphisms, respectively, in tilts of the standard heart, under suitable conditions. We then identify the moduli spaces with the corresponding Quot spaces,…
Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results…
The paper studies the harmonic maps on a direction between a Riemannian space and a generalized Lagrange space. Also, it is proved there that the solutions of C^2 class of certain ODEs or PDEs are harmonic maps, in the sense of this paper.