Departamento de Matemática Aplicada
http://hdl.handle.net/10481/31361
20181115T17:55:50Z

Numerical Approximation using Evolution PDE Variational Splines
http://hdl.handle.net/10481/50935
Numerical Approximation using Evolution PDE Variational Splines
Kouibia Krichi, Abdelouahed; Pasadas Fernández, Miguel; Belhaj, Zakaria
This article deals with a numerical approximation method using an evolutionary partial differential equation
(PDE) by discrete variational splines in a finite element space. To formulate the problem, we need an evolutionary
PDE equation with respect to the time and the position, certain boundary conditions and a set of
approximating points. We show the existence and uniqueness of the solution and we study a computational
method to compute such a solution. Moreover, we established a convergence result with respect to the time
and the position. We provided several numerical and graphic examples of approximation in order to show
the validity and effectiveness of the presented method.

The genus, the Frobenius number, and the pseudoFrobenius numbers of numerical semigroups of type two
http://hdl.handle.net/10481/49818
The genus, the Frobenius number, and the pseudoFrobenius numbers of numerical semigroups of type two
RoblesPérez, Aureliano M.; Rosales González, José Carlos
In this paper we study some questions on numerical semigroups of type two. On the one hand, we investigate the relation between the genus and the Frobenius number. On the other hand, for two fixed positive integers
g1, g2, we give necessary and sufficient conditions in order to have a numerical semigroup S such that {g1, g2} is the set of its pseudoFrobenius numbers and, moreover, we build explicitly families of such numerical semigroups.
This article has been published in a revised form in "Proceedings of the Royal Society of Edinburgh. Section A: Mathematics" https://doi.org/10.1017S0308210515000840. This version is free to view and download for private research and study only. Not for redistribution, resale or use in derivative works. © copyright Cambridge University Press.

The Frobenius number in the set of numerical semigroups with fixed multiplicity and genus
http://hdl.handle.net/10481/49814
The Frobenius number in the set of numerical semigroups with fixed multiplicity and genus
RoblesPérez, Aureliano M.; Rosales González, José Carlos
We compute all possible numbers that are the Frobenius number of a numerical semigroup when multiplicity and genus are fixed. Moreover, we construct explicitly numerical semigroups in each case.
Electronic version of an article published as International Journal of Number Theory, 2017, Vol. 13, No. 04 : pp. 10031011 https://doi.org/10.1142/S1793042117500531 © copyright World Scientific Publishing Company http://www.worldscientific.com/

Frobenius pseudovarieties in numerical semigroups
http://hdl.handle.net/10481/49813
Frobenius pseudovarieties in numerical semigroups
RoblesPérez, Aureliano M.; Rosales González, José Carlos
The common behavior of several families of numerical semigroups led up to defining the Frobenius varieties. However, some interesting families were out of this definition. In order to overcome this situation, in this paper we introduce the concept of (Frobenius) pseudovarieties. Moreover, we will show that most
of the results for varieties can be generalized to pseudovarieties.
This is a postpeerreview, precopyedit version of an article published in Annali di Matematica Pura ed Applicata. The final authenticated version is available online at: https://doi.org/10.1007/s1023101303751.

Numerical semigroups in a problem about costeffective transport
http://hdl.handle.net/10481/49801
Numerical semigroups in a problem about costeffective transport
RoblesPérez, Aureliano M.; Rosales González, José Carlos
Let N be the set of nonnegative integers. A problem about how to transport profitably an organized group of persons leads us to study the set T formed by the integers n such that the system of inequalities, with nonnegative integer coefficients, a_1x_1+⋯+a_px_p<n<b_1x_1+⋯+b_px_p
has at least one solution in N^p. We will see that T∪{0} is a numerical semigroup. Moreover, we will show that a numerical semigroup S can be obtained in this way if and only if {a+b−1,a+b+1}⊆S, for all a,b∈S∖{0}. In addition, we will demonstrate that such numerical semigroups form a Frobenius variety and we will study this variety. Finally, we show an algorithmic process in order to compute T.