Related papers: On the lattice point covering problem in dimension…
A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this…
In this paper we deduce the Lebesgue and the Knaster--Kuratowski--Mazurkiewicz theorems on the covering dimension, as well as their certain generalizations, from some simple facts of toric geometry. This provides a new point of view on this…
Predicting protein secondary structure using lattice model is one of the most studied computational problem in bioinformatics. Here secondary structure or three dimensional structure of protein is predicted from its amino acid sequence.…
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
Random packing of unoriented regular polygons and star polygons on a two-dimensional flat, continuous surface is studied numerically using random sequential adsorption algorithm. Obtained results are analyzed to determine saturated random…
Spherical coverings on the S2 sphere and their algebraic numbers are given for the putatively optimal global solutions for some n-congruent spherical caps with minimal radius to completely cover the S2 sphere. A few locally optimal…
We present a dual representation of the partition function of the charged scalar field in which the complex action problem at non-zero chemical potential is absent. In this dual representation Monte Carlo simulations are possible and we…
This article introduces and studies Minkowski Bisectors, Minkowski Cells, and Lattice Coverings.
In this paper, we investigate topological modes of different physical systems defined on arbitrary two-dimensional curved surfaces. We consider the shallow water equations, inhomogeneous Maxwell's equations, Jackiw-Rebbi model and show how…
We present a complex matrix gauge model defined on an arbitrary two-dimensional orientable lattice. We rewrite the model's partition function in terms of a sum over representations of the group U(N). The model solves the general…
The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We…
The double-layer potential plays an important role in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known, and only for the first one…
In this note we classify all triples (a,b,i) such that there is a convex lattice polygon P with area a, and b respectively i lattice points on the boundary respectively in the interior. The crucial lemma for the classification is the…
Two-dimensional atomic arrays exhibit a number of intriguing quantum optical phenomena, including subradiance, nearly perfect reflection of radiation and long-lived topological edge states. Studies of emission and scattering of photons in…
For a partial lattice L the so-called two-point extension is defined in order to extend L to a lattice. We are motivated by the fact that the one-point extension broadly used for partial algebras does not work in this case, i.e. the…
The Dedekind-Birkhoff theorem for finite-height modular lattices has previously been generalized to complete modular lattices using the theory of regular coverings. In this paper, we investigate regular coverings in lattices of filters and…
We introduce reflexive polytopes of index l as a natural generalisation of the notion of a reflexive polytope of index 1. These l-reflexive polytopes also appear as dual pairs. In dimension two we show that they arise from reflexive…
Some aspects of the multidimensional soliton geometry are considered.
In this paper we study the structure of complex points of codimension 2 real submanifolds in complex $n$ dimensional manifolds. We show that the local structure of a complex point up to isotopy only depends on their type (either elliptic or…
We present a general analysis of two-dimensional optical lattice models that give rise to topologically non-trivial insulating states. We identify the main ingredients of the lattice models that are responsible for the non-trivial…