Related papers: Orthogonal relational systems
An integrable system is often formulated as a flat connection, satisfying a Lax equation. It is given in terms of compatible systems having a common solution called the ``wave function" $\Psi$ living in a Lie group $G$, which satisfies some…
In this paper, we start by giving the definitions and basic facts about hyperoctahedral number system. There is a natural correspondence between the integers expressed in the latter and the elements of the hyperoctahedral group when we use…
Given an irreducible well-generated complex reflection group W with Coxeter number h, we call a Coxeter element any regular element (in the sense of Springer) of order h in W; this is a slight extension of the most common notion of Coxeter…
Many systems exhibit complex interactions between their components: some features or actions amplify each other's effects, others provide redundant information, and some contribute independently. We present a simple geometric method for…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
We perform a classification of third order integrable systems of evolution equations with respect to higher symmetries. Applying it, we consider polynomial systems that are 0-homogeneous under a suitable weighting of variables with main…
A relational structure R is ultrahomogeneous if every isomorphism of finite induced substructures of R extends to an automorphism of R. We classify the ultrahomogeneous finite binary relational structures with one asymmetric binary relation…
A relation algebra is called measurable when its identity is the sum of measurable atoms, and an atom is called measurable if its square is the sum of functional elements. In this paper we show that atomic measurable relation algebras have…
The system whose Hamiltonian is a linear combination of the generators of SU(1,1) group with time-dependent coefficients is studied. It is shown that there is a unitary relation between the system and a system whose Hamiltonian is simply…
Let ${\mathcal P}\subset{\mathbb Z}^2$ be a convex polygon with each vertex in it labeled by an element from a finite set and such that the labeling of each vertex $v\in {\mathcal P}$ is uniquely determined by the labeling of all other…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Let $G$ be a real compact Lie group, such that $G=G^0\rtimes C_2$, with $G^0$ simple. Here $G^0$ is the connected component of $G$ containing the identity and $C_2$ is the cyclic group of order $2$. We give a criterion for whether an…
The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be…
We consider relations with no order on their attributes as in Database Theory. An independent partition of the set of attributes S of a finite relation R is any partition X of S such that the join of the projections of R over the elements…
We study one-parameter expanding evolution families of simply connected domains in the complex plane described by infinite systems of evolution parameters. These evolution parameters in some cases admit Hamiltonian formulation and lead to…
As we said in our previous work [4], the main idea of our research is to introduce a class of Lie groupoids by means of co-adjoint representation of a Lie groupoid on its isotropy Lie algebroid, which we called coadjoint Lie groupoids. In…
Relativistic and nonrelativistic anyons are described in a unified formalism by means of the coadjoint orbits of the symmetry groups in the free case as well as when there is an interaction with a constant electromagnetic field. To deal…
The concept of a Sheffer operation known for Boolean algebras and orthomodular lattices is extended to arbitrary directed relational systems with involution. It is proved that to every such relational system there can be assigned a Sheffer…
An orthogonal involution on a central simple algebra becoming isotropic over any splitting field of the algebra, becomes isotropic over a finite odd degree extension of the base field (provided that the characteristic of the base field is…
The problem of "what is 'system'?" is in the very foundations of modern quantum mechanics. Here, we point out the interest in this topic in the information-theoretic context. E.g., we point out the possibility to manipulate a pair of…