Sobre polinomios de Laurent ortogonales y fórmulas de cuadratura en la circunferencia unidad

El objetivo de esta tesis es el de unificar la Teoría de Sistemas Bi-ortogonales de Polinomios Trigonométricos (eje real), introducida por Szegö en 1963 como herramienta fundamental en el estudio de fórmulas de cuadratura con máximo grado de precisión trigonométrico y el de manifestar que las sucesiones de polinomios de Laurent ortogonales (circunferencia unidad) son la clave para el diseño de tales fórmulas.

Constitución y democracia: la cuadratura del círculo

Sin lugar a dudas, uno de los debates teóricos y empíricos determinantes de la filosofía política del siglo XXI es el de la democracia. Se encuentran diferentes concepciones de la democracia dependiendo de la filosofía pública subyacente en la teoría que respalda el sistema político. Una es la conservadora, de tinte elitista, que desconfía de la intervención ciudadana en los asuntos públicos, debido a los rasgos de irracionalidad y las tendencias plebiscitarias que caracterizan el accionar de las mayorías; otra visión opuesta es la populista, que tiene como punto de partida una actitud de confianza en las capacidades cívicas de las mayorías que actúan colectivamente y de su tendencia a actuar siempre de manera racional y, encontramos, además, la concepción deliberativa de la democracia que parte también de una actitud de confianza en torno a las capacidades de la ciudadanía, pero sin la necesidad de presuponer una conexión ontológica, necesaria, entre la voluntad mayoritaria y la razón. A su vez, la teoría nos ofrece dos grandes corrientes de pensamientos en lo que al control judicial de las leyes se refiere. De un lado, están los teóricos que aceptan la revisión judicial de las leyes y, con ello, que frente a los aspectos fundamentales que regulan la vida colectiva los jueces tengan la “última palabra”, pese a su carácter contramayoritario; de otro lado, están los teóricos críticos del control judicial de las leyes y del hecho de que los jueces tengan la última palabra en los aspectos fundamentales de la organización de la vida social. Esta última corriente de pensamiento, apela al carácter contramayoritorio del poder judicial para cuestionar el hecho de que en una democracia los jueces tengan la posibilidad de declarar la inconstitucionalidad de una norma jurídica derivada de los órganos políticos que eligen las mayorías y, por tanto, anular sus efectos. Estas temáticas, cuya actualidad es indiscutible, reclaman de la academia un análisis desde el punto de vista jurídico y político del papel del poder judicial en los sistemas democráticos contemporáneos. En este quehacer se abre paso el VI Seminario Internacional de Teoría General del Derecho y el libro que el lector hoy tiene en sus manos, que parte de las experiencias investigativas de sus autores, convirtiéndose en una obra que aporta al debate contemporáneo en torno a la cuadratura del círculo: Constitución y democracia. Son, pues, doce trabajos de autores nacionales e internacionales que se dejan en manos del lector y de su juicio.

A geometrical approach of 3-D FEA for educational purposes applied to electrostatic fields

A geometrical approach of the finite-element analysis applied to electrostatic fields is presented. This approach is particularly well adapted to teaching Finite Elements in Electrical Engineering courses at undergraduate level. The procedure leads to the same system of algebraic equations as that derived by classical approaches, such as variational principle or weighted residuals for nodal elements with plane symmetry. It is shown that the extension of the original procedure to three dimensions is straightforward, provided the domain be meshed in first-order tetrahedral elements. The element matrices are derived by applying Maxwell`s equations in integral form to suitably chosen surfaces in the finite-element mesh.

The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

The Kumaraswamy Weibull distribution with application to failure data

For the first time, we introduce and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Renyi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

The beta modified Weibull distribution

A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

A log-extended Weibull regression model

A bathtub-shaped failure rate function is very useful in survival analysis and reliability studies. The well-known lifetime distributions do not have this property. For the first time, we propose a location-scale regression model based on the logarithm of an extended Weibull distribution which has the ability to deal with bathtub-shaped failure rate functions. We use the method of maximum likelihood to estimate the model parameters and some inferential procedures are presented. We reanalyze a real data set under the new model and the log-modified Weibull regression model. We perform a model check based on martingale-type residuals and generated envelopes and the statistics AIC and BIC to select appropriate models. (C) 2009 Elsevier B.V. All rights reserved.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

General results for the beta-modified Weibull distribution

We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

On super-RS algebra and Drinfeld realization of quantum affine superalgebras

We describe the realization of the super-Reshetikhin-Semenov-Tian-Shansky (RS) algebra in quantum affine superalgebras, thus generalizing the approach of Frenkel and Reshetikhin to the supersymmetric (and twisted) case. The algebraic homomorphism between the super-RS algebra and the Drinfeld current realization of quantum affine superalgebras is established by using the Gauss decomposition technique of Ding and Frenkel. As an application, we obtain Drinfeld realization of quantum affine superalgebra U-q [osp(1/2)((1))] and its degeneration - central extended super-Yangian double DY(h over bar) [osp(1/2)((1))].

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Factorization of elliptic boundary value problems by invariant embedding and application to overdetermined problems

Dissertação para obtenção do Grau de Doutor em Matemática

Life cycle of Trypanosoma cruzi (y strain) in mice

Since 1958, we have studied experimental Chagas' disease (CD) by subcutaneous inoculation of 1,000 blood forms of Trypanosoma cruzi (Y strain) in Balb/C. mice. Evolution of parasitemia remained constant, beginning on the 5th and 6th day of the disease, increasing progressively, achieving a maximum on about the 30th day. After another month, only a few forms were present, and they disappeared from the circulation after the third month, as determined from direct examination of slides and the use of a Neubauer Counting Chamber. These events coincided with the appearance of amastigote nests in the tissues (especially the cardiac ones), starting the first week, and following the Gauss parasitemia curve, but they were not in parallel until the chronic stage. In 1997, we began to note the following changes: Parasites appeared in the circulation during the first week and disappeared starting on the 7th day, and there was a coincident absence of the amastigote nests in the tissues. A careful study verified that young forms in the evolutionary cycle of T. cruzi (epi + amastigotes) began to appear alongside the trypomastigotes in the circulation on the 5th and 7th post-inoculation day. At the same time, rounded, oval, and spindle shapes were seen circulating through the capillaries and sinusoids of the tissues, principally of the hematopoietic organs. Stasis occurs because the diameter of the circulating parasites is greater than the vessels, and this makes them more visible. Examination of the sternal bone marrow revealed young cells with elongated forms and others truncated in the shape of a "C" occupying the internal surface of the blood cells that had empty central portions (erythrocytes?). We hypothesize that there could be a loss of virulence or mutation of the Y strain of Trypanosoma cruzi.