Like other learning paradigms, the performance of the genetic algorithms (GAs) is dependent on the parameter choice, on the problem representation, and on the fitness landscape. Accordingly, a GA can show good or weak results even when applied on the same problem. Following this idea, the crossover operator plays an important role, and its study is the object of the present paper. A mathematica...

This paper proposes a fault detection method for an actuator fault of an aluminum plate thermal process with input constraints. Operator-based robust right coprime factorization approach is utilized in this method. In details, after creating a mathematical model, a robust tracking operator system is designed. Following this, design of the fault detection system is given. Finally, experiment is ...

My research is in Functional Analysis (AMS classification 46), Operator Theory (47), Global Analysis (58), Probability Theory (60), and Combinatorics (05). Most of what I do relates to functional inequalities, often arising in mathematical physics, in many different contexts. Much of my recent work is in and around free probability theory, an important and relatively new field at the confluence...

Starting from a mathematical reinterpretation of the classical crossover operator, a new type of crossover is introduced. The proposed new crossover operator gives better performances than the classical 1 point, 2 point or uniform crossover operators. In the paper a theorical investigation of the behaviour of the new crossover is presented. In comparison to the classical crossover operator, it ...

We present a general theory for regularization models of the Navier-Stokes equations based on the Leray deconvolution model with a general deconvolution operator designed to fit a few important key properties. We provide examples of this type of operator, such as the modified TikhonovLavrentiev and modified Iterated Tikhonov-Lavrentiev operators, and study their mathematical properties. An exis...

Starting from a mathematical reinterpretation of the classical crossover operator, a new type of crossover is introduced. The proposed new crossover operator gives better performances than the classical 1 point, 2 point or uniform crossover operators. In the paper a theorical investigation of the behaviour of the new crossover is presented. In comparison to the classical crossover operator, it ...

In this paper, we introduce a multiscale operator which, together with some morphological tools, can be used to reconnect broken components of an image. This operator extracts the orientation field from the image components and can be applied to both binary and grayscale pictures. Although we illustrate its application in the fingerprint domain, the approach described here can be easily extende...

The paper addresses existence, uniqueness and approximation methods for a certain class of nonlinear parabolic quasi-variational inequality (QVI) problems with special gradient-type constraints. Problems of this nature are common in the mathematical modeling of superconductors and ionization in electrostatics. The results are developed based on monotone operator theory , C 0 semigroup methods a...

Ultimate Opening (UO) is a powerful operator based on numerical residues. In a multi-scale framework, it analyzes an image under a series of increasing openings. Contrasted objects are detected when they are filtered out by an opening, generating an important residue. Gradual transitions make this operator underestimate the contrast of blurred objects. In this paper we propose a solution to thi...

We provide the mathematical foundation for the Xm-Jacobi spectral theory. Namely, we present a self-adjoint operator associated to the differential expression with the exceptional Xm-Jacobi orthogonal polynomials as eigenfunctions. This proves that those polynomials are indeed eigenfunctions of the self-adjoint operator (rather than just formal eigenfunctions). Further, we prove the completenes...