Francisco M. Fernández

Constituent quark model study of the meson spectra

The spectrum is studied in a generalized constituent quark model constrained in the study of the NN phenomenology and the baryon spectrum. An overall good fit to the available experimental data is obtained. A detailed analysis of all sectors from the light-pseudoscalar and vector mesons to bottomonium is performed paying special attention to the existence and nature of some non well-established states. These results should serve as a complementary tool in distinguishing conventional quark model mesons from glueballs, hybrids or multiquark states.

Large Order Perturbation Theory and Summation Methods in Quantum Mechanics

The problems usually found in Theoretical Chemistry and Physical Chemistry involve the use of quantum mechanical models which, as a general rule, do not have exact solutions. Due to this very compelling reason a formidable effort has been devoted to develop approximate methods to solve the Schrodinger equation from the very birth of the Quantum Mecha nics.

On an iteration method for eigenvalue problems

We discuss a recently proposed asymptotic iteration method for eigenvalue problems. We analyse its rate of convergence, the use of adjustable parameters to improve it and the relationship with an alternative method based on the same ideas.

A family of complex potentials with real spectrum

We consider a two-parameter non-Hermitian quantum mechanical Hamiltonian operator that is invariant under the combined effects of parity and time reversal transformations. Numerical investigation shows that for some values of the potential parameters the Hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other parity times time reversal symmetric models which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.

Replacement method and enhanced replacement method versus the genetic algorithm approach for the selection of molecular descriptors in QSPR/QSAR theories.

We compare three methods for the selection of optimal subsets of molecular descriptors from a much greater pool of such regression variables. On the one hand is our enhanced replacement method (ERM) and on the other is the simpler replacement method (RM) and the genetic algorithm (GA). These methods avoid the impracticable full search for optimal variables in large sets of molecular descriptors. Present results for 10 different experimental databases suggest that the ERM is clearly preferable to the GA that is slightly better than the RM. However, the latter approach requires the smallest amount of linear regressions and, consequently, the lowest computation time.

Quark-model study of few-baryon systems

We review the application of non-relativistic constituent quark models to study one, two and three non-strange baryon systems. We present results for the baryon spectra, potentials and observables of the nucleon?nucleon (NN), N?, ?? and NN*(1440) systems, and binding energies of three non-strange baryon systems. We emphasize the observable effects related to quark antisymmetry and its interplay with quark dynamics.

Strong-coupling expansions for the -symmetric oscillators

We study the traditional problem of convergence of perturbation expansions when the hermiticity of the Hamiltonian is relaxed to a weaker symmetry. An elementary and quite exceptional cubic anharmonic oscillator is chosen as an illustrative example of such models. We describe its perturbative features paying particular attention to the strong-coupling regime. Efficient numerical perturbation theory proves suitable for such a purpose.

The Nucleon-nucleon interaction in terms of quark degrees of freedom

A modified quark-quark interaction is applied to study the nucleon-nucleon interaction. The quark potential is suggested by instanton models and includes pion ( pi ) and sigma ( sigma ) exchanges as non-perturbative components and the one-gluon exchange as a perturbative one. The nucleon-nucleon potential derived from this model presents short-range repulsion and medium-range attraction besides the usual pion tail. Using this interaction the nucleon-nucleon phase shifts within the resonating group method have been calculated. They agree reasonably well with experimental values.

A comparative QSAR on 1,2,5-thiadiazolidin-3-one 1,1-dioxide compounds as selective inhibitors of human serine proteinases.

Selective inhibitors of target serine proteinases have a potential therapeutic role for the treatment of various inflammatory and related diseases. We develop a comparative quantitative structure-activity relationships based analysis on compounds embodying the 1,2,5-thiadiazolidin-3-one 1,1-dioxide scaffold. By means of classical Molecular Dynamics we obtain the conformation of each lowest-energy molecular structure from which we derive more than a thousand of structural descriptors necessary for building predictive QSAR models. We resort to two different modeling approaches with the purpose of testing the consistency of our results: (a) multivariable linear regressions based on the replacement method and forward stepwise regression, and (b) the calculation of flexible descriptors with the CORAL program. All the models are properly validated by means of standard procedures. The resulting QSAR models are supposed to be of great utility for the rational search and design (including synthesis and/or in vitro biochemical studies) of new effective non-peptidyl inhibitors of serine proteinases.

Advances in the replacement and enhanced replacement method in QSAR and QSPR theories.

The selection of an optimal set of molecular descriptors from a much greater pool of such regression variables is a crucial step in the development of QSAR and QSPR models. The aim of this work is to further improve this important selection process. For this reason three different alternatives for the initial steps of our recently developed enhanced replacement method (ERM) and replacement method (RM) are proposed. These approaches had previously proven to yield near optimal results with a much smaller number of linear regressions than the full search. The algorithms were tested on four different experimental data sets, formed by collections of 116, 200, 78, and 100 experimental records from different compounds and 1268, 1338, 1187, and 1306 molecular descriptors, respectively. The comparisons showed that one of the new alternatives further improves the ERM, which has shown to be superior to genetic algorithms for the selection of an optimal set of molecular descriptors from a much greater pool. The new proposed alternative also improves the simpler and the lower computational demand algorithm RM.