Related papers: Sine and cosine equations on commutative hypergrou…
In this paper we study properties of hyperholomorphic functions on commutative finite algebras. It is investigated the Cauchy-Riemann type conditions for hyperholomorphic functions. We prove that a hyperholomorphic function on a commutative…
The aim of this note is to show that any algebraic relation over $\overline{\mathbb{Q}}$ between the values of the trigonometric functions sine and cosine at algebraic points can be derived from the Pythagorean identity and the angle…
In this note we prove a selection of commutativity theorems for various classes of semigroups. For instance, if in a separative or completely regular semigroup $S$ we have $x^p y^p = y^p x^p$ and $x^q y^q = y^q x^q$ for all $x,y\in S$ where…
The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on…
An open problem about finite geometric progressions in syndetic sets leads to a family of diophantine equations related to the commutativity of translation and multiplication by squares.
Commutation formulae with respect to a non-symmetric affine connection are obtained in this paper. The components of commutation formulae in this paper are covariant derivatives of tensors with respect to symmetric and non-symmetric affine…
By using some tools of analysis, we establish some analytical properties such as monotonicity and inequalities involving the hyperbolic sine integral function. As applications of some of the established properties, we obtain some rational…
The Funk, cosine, and sine transforms on the unit sphere are indispensable tools in integral geometry. They are also known to be interesting objects in harmonic analysis. The aim of the paper is to extend basic facts about these transforms…
Systems of nonlinear ordinary differential equations are constructed, for which the general solution is algebraically expressed in terms of a finite number of particular solutions. Expressions of that type are called the nonlinear…
Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.
We consider integrable open chain models formulated in terms of generators of affine Hecke algebras. The hierarchy of commutative elements (which are analogs of the commutative transfer-matrices) are constructed by using the fusion…
In this article we study the structure of highest weight modules for quantum groups defined over a commutative ring with particular emphasis on the structure theory for invariant bilinear forms on these modules.
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
We establish an eigenfunctional theorem for positive operators, evocative of the Krein--Rutman theorem. A more general version gives a joint eigenfunctional for commuting operators.
The classical integral representation formulas for holomorphic functions defined on pseudoconvex domains in Stein manifolds play an important role in the constructive theory of functions of several complex variables. In this paper we…
We review the series solutions of the general and single-confluent Heun equations in terms of powers, ordinary-hypergeometric and confluent-hypergeometric functions. The conditions under which the expansions reduce to finite sums as well as…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
Superconformal blocks and crossing symmetry equations are among central ingredients in any superconformal field theory. We review the approach to these objects rooted in harmonic analysis on the superconformal group that was put forward in…
We prove recursive formulas for sums of squares and sums of triangular numbers in terms of sums of divisors functions and we give a variety of consequences of these formulas. Intermediate applications include statements about positivity of…
In this note we obtain the solutions of four $q$-functional equations and express the solutions in $q$-operator forms. These equations give sufficient conditions for $q$-operator methods.