Bartlett corrections in Birnbaum-Saunders nonlinear regression models

Lemonte and Cordeiro [Birnbaum-Saunders nonlinear regression models, Comput. Stat. Data Anal. 53 (2009), pp. 4441-4452] introduced a class of Birnbaum-Saunders (BS) nonlinear regression models potentially useful in lifetime data analysis. We give a general matrix Bartlett correction formula to improve the likelihood ratio (LR) tests in these models. The formula is simple enough to be used analytically to obtain several closed-form expressions in special cases. Our results generalize those in Lemonte et al. [Improved likelihood inference in Birnbaum-Saunders regressions, Comput. Stat. DataAnal. 54 (2010), pp. 1307-1316], which hold only for the BS linear regression models. We consider Monte Carlo simulations to show that the corrected tests work better than the usual LR tests.

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.

The negative binomial-beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial-beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.

The McDonald extended distribution: properties and applications

We study a five-parameter lifetime distribution called the McDonald extended exponential model to generalize the exponential, generalized exponential, Kumaraswamy exponential and beta exponential distributions, among others. We obtain explicit expressions for the moments and incomplete moments, quantile and generating functions, mean deviations, Bonferroni and Lorenz curves and Gini concentration index. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. The applicability of the new model is illustrated by means of a real data set.

On Wald Residuals in Generalized Linear Models

A rigorous asymptotic theory for Wald residuals in generalized linear models is not yet available. The authors provide matrix formulae of order O(n(-1)), where n is the sample size, for the first two moments of these residuals. The formulae can be applied to many regression models widely used in practice. The authors suggest adjusted Wald residuals to these models with approximately zero mean and unit variance. The expressions were used to analyze a real dataset. Some simulation results indicate that the adjusted Wald residuals are better approximated by the standard normal distribution than the Wald residuals.

A log-linear regression model for the beta-Birnbaum-Saunders distribution with censored data

The beta-Birnbaum-Saunders (Cordeiro and Lemonte, 2011) and Birnbaum-Saunders (Birnbaum and Saunders, 1969a) distributions have been used quite effectively to model failure times for materials subject to fatigue and lifetime data. We define the log-beta-Birnbaum-Saunders distribution by the logarithm of the beta-Birnbaum-Saunders distribution. Explicit expressions for its generating function and moments are derived. We propose a new log-beta-Birnbaum-Saunders regression model that can be applied to censored data and be used more effectively in survival analysis. We obtain the maximum likelihood estimates of the model parameters for censored data and investigate influence diagnostics. The new location-scale regression model is modified for the possibility that long-term survivors may be presented in the data. Its usefulness is illustrated by means of two real data sets. (C) 2011 Elsevier B.V. All rights reserved.

BEM modeling of saturated porous media susceptible to damage

This paper deals with the numerical analysis of saturated porous media, taking into account the damage phenomena on the solid skeleton. The porous media is taken into poro-elastic framework, in full-saturated condition, based on Biot's Theory. A scalar damage model is assumed for this analysis. An implicit boundary element method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and two-dimensional elastostatic problems. The integration over boundary elements is evaluated using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear problem is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficacy. (C) 2011 Elsevier Ltd. All rights reserved.

IDM - A New Parallel Methodology to Calculate the Determinant of Matrices of the Order n, with Computational Complexity O(n)

This paper presents a new parallel methodology for calculating the determinant of matrices of the order n, with computational complexity O(n), using the Gauss-Jordan Elimination Method and Chio's Rule as references. We intend to present our step-by-step methodology using clear mathematical language, where we will demonstrate how to calculate the determinant of a matrix of the order n in an analytical format. We will also present a computational model with one sequential algorithm and one parallel algorithm using a pseudo-code.

Stellar Models in General Relativity

Neutron stars are some of the most fascinating objects in Nature. Essentially all aspects of physics seems to be represented inside them. Their cores are likely to contain deconfined quarks, hyperons and other exotic phases of matter in which the strong interaction is the dominant force. The inner region of their solid crust is penetrated by superfluid neutrons and their magnetic fields may reach well over 1012 Gauss. Moreover, their extreme mean densities, well above the densities of nuclei, and their rapid rotation rates makes them truly relativistic both in the special as well as in the general sense. This thesis deals with a small subset of these phenomena. In particular the exciting possibility of trapping of gravita-tional waves is examined from a theoretical point of view. It is shown that the standard condition R < 3M is not essential to the trapping mechanism. This point is illustrated using the elegant tool provided by the optical geometry. It is also shown that a realistic equation of state proposed in the literature allows stable neutron star models with closed circular null orbits, something which is closely related to trapped gravitational waves. Furthermore, the general relativistic theory of elasticity is reviewed and applied to stellar models. Both static equilibrium as well as radially oscillating configurations with elasticsources are examined. Finally, Killing tensors are considered and their applicability to modeling of stars is discussed

A spectroscopic and photometric study of MSP companions in Galactic Globular Clusters

This Thesis is devoted to the study of the optical companions of Millisecond Pulsars in Galactic Globular Clusters (GCs) as a part of a large project started at the Department of Astronomy of the Bologna University, in collaboration with other institutions (Astronomical Observatory of Cagliari and Bologna, University of Virginia), specifically dedicated to the study of the environmental effects on passive stellar evolution in galactic GCs. Globular Clusters are very efficient “Kilns” for generating exotic object, such as Millisecond Pulsars (MSP), low mass X-ray binaries(LMXB) or Blue Straggler Stars (BSS). In particular MSPs are formed in binary systems containing a Neutron Star which is spun up through mass accretion from the evolving companion (e.g. Bhattacharia & van den Heuvel 1991). The final stage of this recycling process is either the core of a peeled star (generally an Helium white dwarf) or a very light almos exhausted star, orbiting a very fast rotating Neutron Star (a MSP). Despite the large difference in total mass between the disk of the Galaxy and the Galactic GC system (up a factor 103), the percentage of fast rotating pulsar in binary systems found in the latter is very higher. MSPs in GCs show spin periods in the range 1.3 ÷ 30ms, slowdown rates ˙P 1019 s/s and a lower magnetic field, respect to ”normal” radio pulsars, B 108 gauss . The high probability of disruption of a binary systems after a supernova explosion, explain why we expect only a low percentage of recycled millisecond pulsars respect to the whole pulsar population. In fact only the 10% of the known 1800 radio pulsars are radio MSPs. Is not surprising, that MSP are overabundant in GCs respect to Galactic field, since in the Galactic Disk, MSPs can only form through the evolution of primordial binaries, and only if the binary survives to the supernova explosion which lead to the neutron star formation. On the other hand, the extremely high stellar density in the core of GCs, relative to most of the rest of the Galaxy, favors the formation of several different binary systems, suitable for the recycling of NSs (Davies at al. 1998). In this thesis we will present the properties two millisecond pulsars companions discovered in two globular clusters, the Helium white dwarf orbiting the MSP PSR 1911-5958A in NGC 6752 and the second case of a tidally deformed star orbiting an eclipsing millisecond pulsar, PSR J1701-3006B in NGC6266

Coupled-Cluster-Berechnungen von Parametern der Kernspin-Resonanz-Spektroskopie

Coupled-Cluster-Berechnungen von Parametern derKernspin-Resonanz-Spektroskopie Dissertationsschrift von Alexander A.Auer, Mainz 2002 Im Rahmen einer Studie der Berechnung von 13C-Verschiebungenwerdendie Einfluesse von Elektronenkorrelation, Basissatz,Gleichgewichtsgeometrie sowie Schwingungs- und Rotationseffekten separat betrachtet.Dabei zeigt sich, dass dieCoupled-Cluster-Singles-Doubles-Methode mitstoerungstheoretischer Behandlung der Dreifachanregungen(CCSD(T)) mit entsprechend grossen Basissaetzen bei Beruecksichtigung derNullpunktsschwingungseffekte Ergebnisse mit ca. 1 ppm Abweichung zum Experiment liefert. Eine Analyse der Elektronenkorrelationseffekte beiCoupled-Cluster- (CC-) Berechnungen von indirekten Spin-Spin-Kopplungskonstanten zeigt, dassCC-Methoden mit Hartree-Fock-Orbitalrelaxation zur Berechnung derKopplungskonstanten ungeeignet sind. Eine Loesung ist die Verwendung unrelaxierter CC-Methoden,in denendie HF-Orbitalrelaxation aus der Berechnung der gestoertenWellenfunktion ausgeschlossen wird. Full-Configuration-Interaction-Berechnungen fuer Borhydridzeigen,dass auf CC-Singles-Doubles-Niveau (CCSD) 94% und aufCC-Singles-Doubles-Triples-Niveau (CCSDT) 99% der Korrelationseffekte beschrieben werden. Weiterhin istdie Beruecksichtigung der Nullpunktsschwingung sowie die Wahl eines ausreichend grossen Basissatzes wichtig. Auf Grundlage der vorangegangenen Studien werden im letztenTeil zwei Beispiele zur Anwendung hochgenauer Berechnungen vonNMR-Parametern vorgestellt.Im Rahmen einer Studie der Spin-Spin-Kopplungskonstanten vonCyclopentan wird eine Karplus-Beziehungzwischen den Kopplungskonstanten und der Konformation desMolekuels aufgestellt, desweiteren werden die NMR-Parameter von Methylidinphosphanuntersucht.

Spin-Restricted Coupled-Cluster-Theorie fuer offenschalige Zustaende

Spin-Restricted Coupled-Cluster-Theorie fuer offenschaligeZustaende Die Berechnung von Energien und Eigenschaften offenschaligerAtome undMolekuele mit Hilfe der hochgenauenCoupled-Cluster-(CC)-Theoriewar bisher mit einem - im Vergleich zur BerechnunggeschlossenschaligerZustaende - erhoehten Rechenaufwand und der sogenannten'Spinkontamination' behaftet. Um diesen Problemenentgegenzuwirken,stellten P.G.Szalay und J.Gauss die 'Spin-RestrictedCoupled-Cluster-Theorie' vor. Im Rahmen dieser Arbeit wird die urspruenglich aufDublett-Zustaendebeschraenkte Theorie so verallgemeinert, dass jederbeliebige Spinzustandmit einem einheitlichen Satz von Gleichungen beschriebenwerden kann. Dadie Moller-Plesset-(MP)-Stoerungstheorie bei der BerechnungoffenschaligerZustaende mit aehnlichen Problemen behaftet ist, wirddarueberhinaus dieSpin-Restricted-(SR)-MP-Stoerungstheorie zweiter und dritterOrdnungeingefuehrt. Um Molekueleigenschaften berechnen zu koennen,werdenanalytische Ableitungen der Energie sowohl fuer den SR-CC-als auch denSR-MP-Ansatz hergeleitet. Bei den folgenden Testrechnungenstellt sichheraus, dass sowohl SR-CC- als auch SR-MP-Ansaetze diegleiche Genauigkeitbieten wie konventionelle CC- und MP-Ansaetze. Dabei sinddieSpinerwartungswerte der SR-CC-Wellenfunktionen identisch mitdem exaktenWert. Im Rahmen der Testrechnungen stellt sich heraus, dassder SR-CC-Ansatz nicht 'size-konsistent', der numerische Fehler abervernachlaessigbar klein ist. Abschliessend werden dieHintergruende derfehlenden 'Size-Konsistenz' diskutiert.

Funzioni zeta e fattorizzazione unica in anelli quadratici di curve su campi finiti

In questa tesi si esaminano alcune questioni riguardanti le curve definite su campi finiti. Nella prima parte si affronta il problema della determinazione del numero di punti per curve regolari. Nella seconda parte si studia il numero di classi di ideali dell’anello delle coordinate di curve piane definite da polinomi assolutamente irriducibili, per ottenere, nel caso delle curve ellittiche, risultati analoghi alla classica formula di Dirichlet per il numero di classi dei campi quadratici e delle congetture di Gauss.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.