We consider the two-player game chomp on posets associated to numerical semigroups and show that the analysis of strategies for chomp is strongly related to classical properties of semigroups. We characterize which player has a winning-strategy for symmetric semigroups, semigroups of maximal embedding dimension and several families of numerical semigroups generated by arithmetic sequences. Furt...

We give an algorithm to compute the set of primitive elements for an embedding dimension three numerical semigroups. We show how we use this procedure in the study of the construction of L-shapes and the tame degree of the semigroup.

We present an abstract framework for semilinear parabolic problems based on analytic semigroup theory. The same framework is used for numerical discretization based on the finite element method. We prove local existence of solutions and local error estimates. These are applied in the context of dynamical systems. The framework is also used to analyze the finite element method for a stochastic p...

We extend results on Weierstrass semigroups at ramified points of double covering of curves to any numerical semigroup whose genus is large enough. As an application we strengthen the properties concerning Weierstrass weights stated in [To]. 0. Introduction Let H be a numerical semigroup, that is, a subsemigroup of (N,+) whose complement is finite. Examples of such semigroups are the Weierstras...

Semidiscrete finite element approximation of the linear stochastic wave equation with additive noise is studied in a semigroup framework. Optimal error estimates for the deterministic problem are obtained under minimal regularity assumptions. These are used to prove strong convergence estimates for the stochastic problem. The theory presented here applies to multi-dimensional domains and spatia...

We show that transition to longitudinal instability of strong detonation solutions of reactive compressible Navier–Stokes equations is generically associated with Hopf bifurcation to nearby time-periodic “galloping”, or “pulsating”, solutions, in agreement with physical and numerical observation. The analysis is by pointwise semigroup techniques introduced by the authors and collaborators in pr...

In this paper we study the numerical solution for an p−Laplacian type of evolution system Ht + ∇ × [|∇ × H|p−2∇ × H] = F(x, t), p > 2 in two space dimensions. For large p this system is an approximation of Bean’s critical-state model for type-II superconductors. By introducing suitable transformation, the system is equivalent to a nonlinear parabolic equation. For the nonlinear parabolic proble...

This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.

We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the generated semigroup is shown to be bounded by the upper real part of the numerical range of the underlying quadratic operator pencil.

Consider an interval I ⊆ Q . Set S(I) = {m ∈ N : ∃ n ∈ N , mn ∈ I}. This turns out to be a numerical semigroup, and has been the subject of considerable recent investigation (see Chapter 4 of [2] for an introduction). Special cases include modular numerical semigroups (see [4]) where I = [mn , m n−1 ] (m,n ∈ N ), proportionally modular numerical semigroups (see [3]) where I = [mn , m n−s ] (m,n...