Related papers: Sine and cosine equations on commutative hypergrou…

It is well known that many famous Burnside-type problems have positive solutions for PI-groups and PI-algebras. In the present article we also consider various Burnside-type problems for PI-groups and PI-representations of groups.

This is a brief survey of recent results by the authors devoted to one of the most important operators of integral geometry. Basic facts about the analytic family of cosine transforms on the unit sphere and the corresponding Funk transform…

Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…

Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…

The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree $n$ are…

We develop a Galois theory of commutative rings under actions of finite inverse semigroups. We present equivalences for the definition of Galois extension as well as a Galois correspondence theorem. We also show how the theory behaves in…

We obtain asymptotic and exact formulae of growth functions for some families of $n$-valued coset groups. We also describe connections between the theory of $n$-valued groups and Symbolic Dynamics.

In this paper, we obtain recursion formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function. We also give finite and infinite summation formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function.

In this paper, we establish the theory of nilpotent hypergroups and study some properties of nilpotent hypergroups and provided some structural characterizations of nilpotent hypergroups.

Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…

We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…

A generalization of Jacobi's elliptic functions is introduced as inversions of hyperelliptic integrals. We discuss the special properties of these functions, present addition theorems and give a list of indefinite integrals. As a physical…

In this paper, we establish some new inequalities for class of SX(h,I) convex functions which are supermultiplicative or superadditive and nonnegative. And we also give some applications for special means.

Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…

The maximum principle for holomirphic functions in the quantum ball is formulated. A proof can be found in [8] (see the bibliography).

In the paper, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the…

An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.

We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or…

We establish several summation formulae for hypergeometric and basic hypergeometric series involving noncommutative parameters and argument. These results were inspired by a recent paper of J. A. Tirao [Proc. Nat. Acad. Sci. 100 (14)…

Inspired by recent work by Closset, Kim and Willett, we derive a new formula for the superconformal (or supersymmetric) index of 4d N=1 theories. Such a formula is a finite sum, over the solution set of certain transcendental equations that…