Related papers: Algebraic relations between moments of plane polyg…
We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…
Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be…
We prove that the number of dissections of a given polygon into triangles with fixed areas of faces is finite and that an equidissection is algebraic as long as the vertices of the original polygon have algebraic coordinates.
A class of associative (super) algebras is presented, which naturally generalize both the symmetric algebra $Sym(V)$ and the wedge algebra $\wedge (V)$, where $V$ is a vector-space. These algebras are in a bijection with those subsets of…
Using the algebraic approach Lie symmetries of time dependent Schroedinger equations for charged particles interacting with superpositions of scalar and vector potentials are classified. Namely, all the inequivalent equations admitting…
We present some methods for constructing connected spatial geometric configurations $(p_{q}, n_{k})$ of points and lines, preserved by the same rotations (and reflections) of Euclidean space $E^{3}$ as the chosen Platonic solid. In this…
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.
In this paper we give a toric representation of the associated ring of a polyomino which is obtained by removing a convex polyomino from its ambient rectangle.
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…
This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…
In this paper we review some connections between harmonic analysis and the modern theory of automorphic forms. We indicate in some examples how the study of problems of harmonic analysis brings us to the important objects of the theory of…
Symplectic vector spaces are the phase spaces of linear mechanical systems. The symplectic form describes, for example, the relation between position and momentum as well as current and voltage. The category of linear Lagrangian relations…
In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…
We explicitly describe the defining relations for simple Lie algebra of vector fields with polynomial coefficients and its subalgebras of divergence free, hamiltonian and contact vector fields, and for the Poisson algebra (realized on…
This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…
We present structures comprised of identical convex polyhedra which are interlocked geometrically. These sets cannot be disassembled by removing individual polyhedra by translations and/or rotations. The shapes that permit interlocking…
We prove that for some potentials (including the Newtonian one, and the potential of Helmholtz vortices in the plane) relative equilibria consisting of two homothetic regular polygons of arbitrary size can only occur if the masses at each…
We investigate the maximum number of intersections between two polygons with p and q vertices, respectively, in the plane. The cases where p or q is even or the polygons do not have to be simple are quite easy and already known, but when p…
We give an overview of some recent developments concerning harmonic and other moments of plane domains, their relationship to the Cauchy and exponential transforms, and to the meromorphic resultant and elimination function. The paper also…
In two nearby atoms, the dipole-dipole interaction can couple transitions with orthogonal dipole moments. This orthogonal coupling accounts for a number of interesting effects, but strongly depends on the geometry of the setup. Here, we…