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We consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition. We introduce a nonlinear projection on subsemimodules: the projection of a point is the maximal approximation from below of the point…
In the framework of quantum group theory we obtain a noncommutative analog for the algebra of functions in a bounded symmetric domain, endowed with a whole symmetry. Also we provide a construction for its faithfull irreducible…
In this article we discuss some applications of the construction of the Ap\'ery set of a good semigroup in $\mathbb{N}^d$ given in the previous paper [Partition of the complement of good semigroup ideals and Ap\'ery sets, Communications in…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
We construct representations of the enveloping algebra $U_q osp(2,2)$ in terms of finite difference operators and we discuss this result in the framework of quasi-exactly-solvable equations.
We generalize the notion of symmetric semigroups, pseudo symmetric semigroups, and row factorization matrices for pseudo Frobenius elements of numerical semigroups to the case of semigroups with maximal projective dimension (MPD…
We consider conjugation action of symmetric group on the semigroup of all partial functions and develop a machinery to investigate character formulas and multiplicities. In particular, we determine nilpotent matrices whose orbit under…
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
In previous work of the authors and their collaborators (see Progress in Math, vol. 114, Birk\"auser, 1993) it was shown how the equivalence of several constructions of residue currents associated to complete intersection families of (germs…
For a set of nonnegative integers $A$, denote by $R_{A}(n)$ the number of unordered representations of the integer $n$ as the sum of two different terms from $A$. In this paper we partially describe the structure of the sets, which have…
In this paper we establish a new equivalence relation on the spaces of almost periodic functions which allows us to prove a result like Bohr's equivalence theorem extended to the case of all these functions.
We discuss representations of monogenic functions over very regular groups.
In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
The article is devoted to holomorphic and meromorphic functions of quaternion and octonion variables. New classes of quasi-conformal and quasi-meromorphic mappings are defined and investigated. Properties of such functions such as their…
The paper discusses relations between the structure of the complex Fermi surface below the spectrum of a second order periodic elliptic equation and integral representations of certain classes of its solutions. These integral…
This survey aims to highlight some of the consequences that representable (and continuous) functionals have in the framework of Banach quasi *-algebras. In particular, we look at the link between the notions of *-semisimplicity and full…
This paper examines various kinds of subspaces of the non-commutative spaces that are modelled on quasi-projective commutative schemes. It is shown how intersections and unions of weakly closed subspaces, closed subspaces, their weakly open…
We analyze Fourier hyperfunction and hyperfunction semigroups with non-densely defined generators and their connections with local convoluted $C$-semigroups. Structural theorems and spectral characterizations give necessary and sufficient…
Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…