In this paper we present a mathematical programming formulation for the ω invariant of a numerical semigroup for each of its minimal generators. The model consists of solving a problem of optimizing a linear function over the efficient set of a multiobjective linear integer program. We offer a methodology to solve this problem and we provide some computational experiments to show the applicabil...

The purpose of this paper is to introduce a new spline approximation scheme for retarded functional differential equations. The special feature of this approximation scheme is that it preserves the product space structure of retarded systems and approximates the adjoint semigroup in a strong sense. These facts guarantee the convergence of the solution operators for the differential Riccati equa...

We introduce the notion of diagonal ranks of semigroups, which are numerical characteristics of semigroups. Some base properties of diagonal ranks are obtained. A new criterion for a monoid being a group is obtained using diagonal ranks. For some semigroup classes we investigate whether their diagonal acts are finitely generated or not. For the semigroups of full transformations, partial transf...

Analysis of the Berlekamp-Massey-Sakata algorithm for decoding onepoint codes leads to two methods for improving code rate. One method, due to Feng and Rao, removes parity checks that may be recovered by their majority voting algorithm. The second method is to design the code to correct only those error vectors of a given weight that are also geometrically generic. In this work, formulae are gi...

The resolvent Krylov subspace method builds approximations to operator functions f(A) times a vector v. For the semigroup and related operator functions, this method is proved to possess the favorable property that the convergence is automatically faster when the vector v is smoother. The user of the method does not need to know the presented theory and alterations of the method are not necessa...

Let Q be a parameter ideal of a Noetherian local ring (R, m). The Goto number g(Q) of Q is the largest integer g such that Q : m is integral over Q. We examine the values of g(Q) as Q varies over the parameter ideals of R. We concentrate mainly on the case where dimR = 1, and many of our results concern parameter ideals of a numerical semigroup ring.

Let us consider a 3-numerical semigroup S = 〈a, b,N 〉. Given m ∈ S, the triple (x, y, z) ∈ N3 is a factorization of m in S if xa+ yb+ zN = m. This work is focused on finding the full set of factorizations of any m ∈ S and as an application we compute the catenary degree of S. To this end, we relate a 2D tessellation to S and we use it as a main tool.

We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free...

Inspired by the results of [APR], we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the symmetric inverse semigroup, the dual symmetric inverse semigroup, the maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and the factor power of the symmetric group. Furthermore we extend the Gelfand model for the semigroup algebr...

A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the as...