Aureliano M. Robles-Pérez

An Analysis of Edge Detection by Using the Jensen-Shannon Divergence

This work constitutes a theoretical study of the edge-detection method by means of the Jensen-Shannon divergence, as proposed by the authors. The overall aim is to establish formally the suitability of the procedure of edge detection in digital images, as a step prior to segmentation. In specific, an analysis is made not only of the properties of the divergence used, but also of the methods sensitivity to the spatial variation, as well as the detection-error risk associated with the operating conditions due to the randomness of the spatial configuration of the pixels. Although the paper deals with the procedure based on the Jensen-Shannon divergence, some problems are also related to other methods based on local detection with a sliding window, and part of the study is focused to noisy and textured images.

The Numerical Semigroup of Phrases' Lengths in a Simple Alphabet

Let 𝒜 be an alphabet with two elements. Considering a particular class of words (the phrases) over such an alphabet, we connect with the theory of numerical semigroups. We study the properties of the family of numerical semigroups which arise from this starting point.

A maximum principle for bounded solutions of the telegraph equation in space dimension three

A maximum principle is proved for the weak solutions u is an element of L-infinity(R x T-3) of the telegraph equation u(tt) - Delta(x)u + cu(t) + lambda(u) = f(t, x), in space dimension three, when c > 0, lambda is an element of (0, c(2)/4] and f is an element of L-infinity (R x T-3) (Theorem 1). The result is extended to a solution and a forcing belonging to a suitable space of bounded measures (Theorem 2). Those results provide a method of upper and lower solutions for the semilinear equation u(tt) - Delta(x)u + cut = F(t, x, it)

Numerical semigroups with a given set of pseudo-Frobenius numbers

The pseudo-Frobenius numbers of a numerical semigroup are those gaps of the numerical semigroup that are maximal for the partial order induced by the semigroup. We present a procedure to detect if a given set of integers is the set of pseudo-Frobenius numbers of a numerical semigroup and, if so, to compute the set of all numerical semigroups having this set as set of pseudo-Frobenius numbers.

The Frobenius problem for numerical semigroups with embedding dimension equal to three

If S is a numerical semigroup with embedding dimension equal to three whose minimal generators are pairwise relatively prime numbers, then S =ha;b;cb dai with a;b;c;d positive integers such that gcd(a;b) = gcd(a;c) = gcd(b;d) = 1, c2f2;:::;a 1g, anda < b < cb da. In this paper we give formulas, in terms ofa;b;c;d, for the genus, the Frobenius number, and the set of pseudo-Frobenius numbers ofha;b;cb dai in the case in which the interval a ; b d contains some integer.

Frobenius restricted varieties in numerical semigroups

The common behaviour of many families of numerical semigroups led to defining, firstly, the Frobenius varieties and, secondly, the (Frobenius) pseudo-varieties. However, some interesting families are still not covered by these definitions. To overcome this situation, here we introduce the concept of Frobenius restricted variety (or R-variety). We generalize most of the results for varieties and pseudo-varieties to R-varieties. In particular, we study the tree structure that arises within them.

On a transport problem and monoids of non-negative integers

A problem about how to transport profitably a group of cars leads us to studying the set T formed by the integers n such that the system of inequalities, with non-negative integer coefficients,

The Frobenius number in the set of numerical semigroups with fixed multiplicity and genus

\begin{aligned} a_1x_1 +\cdots + a_px_p + \alpha \le n \le b_1x_1 +\cdots + b_px_p - \beta \end{aligned}