Related papers: Sine and cosine equations on commutative hypergrou…
A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.
In the present paper we introduce a commutative hypergroup associated with a hyperfield of a compact commutative hypergroup based on a discrete commutative hypergroup. Moreover we investigate the dual hyperfield and show the dual relation.…
In this paper, we establish the theory of $\sigma$-solvable hypergroups, study some properties of $\sigma$-solvable hypergroups and give similar results of Hall's Theorem in $\sigma$-solvable hypergroups.
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of…
Computations in the cohomology of finite groups.
A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of…
For a broad class of Frechet-Lie supergroups we prove that there exists a correspondence between positive definite smooth superfunctions and matrix coefficients of unitary representations. We also give a characterization of linear…
The sine-Gordon equation has hyperelliptic al function solutions over a hyperelliptic Jacobian for $y^2 = f(x)$ of arbitrary genus $g$. This article gives an extension of the sine-Gordon equation to that over subvarieties of the…
In this paper we study multilinear morphisms between commutative group schemes and the associated tensor constructions. We will also do some explicit calculations and give examples that show that this theory behaves in a way that one would…
We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…
In the former part of this paper, we summarize our previous results on infinite series involving the hyperbolic sine function, especially, with a focus on the hyperbolic sine analogue of Eisenstein series. Those are based on the classical…
New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of…
In this paper, we first construct generalized $q^2$-cosine, $q^2$-sine and $q^2$-exponential functions. We then use $q^2$-exponential function in order to define and investigate a $q^2$-Fourier transform. We establish $q$-analogues of…
These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…
A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to…
We solve connection problem between fundamental solutions at singular points $0$ and $1$ for the generalized hypergeometric function, using analytic continuation of the integral representation. All connection coefficients are products of…
In this paper we study the coefficients of the powers of an ordinary generating function and their properties. A new class of functions based on compositions of an integer $n$ is introduced and is termed composita. We present theorems about…
Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the present authors considered primarily sine sums associated…
The current status of the application of covariant density functional theory to the description of fission barriers in actinides and superheavy nuclei is reviewed. The achievements and open problems are discussed.