Related papers: Variational Sequences, Representation Sequences an…
Variational and divergence symmetries are studied in this paper for linear equations of maximal symmetry in canonical form, and the associated first integrals are given in explicit form. All the main results obtained are formulated as…
A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are…
We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications…
In this talk we summarize some recent developments in perturbative QCD and their application to particle physics phenomenology.
We present a method to obtain symmetries for second-order systems of ordinary difference equations and how to use them to reduce the order. We also introduce a technique of finding conservation laws for such systems.
In this paper we discuss the unitary inequivalentness in quantum physics. Then based on some of the current outstanding problems in theoretical physics, we will show the important role of this concept to better understand the physical…
This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
The possibilities that, in the realm of the detection of the so--called deformed dispersion relation, a light source with a continuous distribution of frequencies offers is discussed. It will be proved that the presence of finite coherence…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
After a quick review of the representation theory of the symmetric group, we give an exposition of the tools brought about by the so-called half-infinite wedge representation of the infinite symmetric group. We show how these can be applied…
Morphic sequences form a natural class of infinite sequences, typically defined as the coding of a fixed point of a morphism. Different morphisms and codings may yield the same morphic sequence. This paper investigates how to prove that two…
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…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…
A speculative discussion on the role of various symmetries in physics.