Comportamento caótico em modelos matemáticos de câncer

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Toroidal solitons in 3+1 dimensional integrable theories

We analyze the integrability properties of models defined on the symmetric space SU(2)/U(1) in 3 + 1 dimensions, using a recently proposed approach for integrable theories in any dimension. We point out the key ingredients for a theory to possess an infinite number of local conservation laws, and discuss classes of models with such property, We propose a 3 + 1-dimensional, relativistic invariant field theory possessing a toroidal soliton solution carrying a unit of topological charge given by the Hopf map. Construction of the action is guided by the requirement that the energy of static configuration should be scale invariant. The solution is constructed exactly. The model possesses an infinite number of local conserved currents. The method is also applied to the Skyrme-Faddeev model, and integrable submodels are proposed. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Sobre os grupos de Gottlieb

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Class Notes for Math 918: Cohen Macaulay Modules, Instructor Roger Wiegand

Topics covered are: Cohen Macaulay modules, zero-dimensional rings, one-dimensional rings, hypersurfaces of finite Cohen-Macaulay type, complete and henselian rings, Krull-Remak-Schmidt, Canonical modules and duality, AR sequences and quivers, two-dimensional rings, ascent and descent of finite Cohen Macaulay type, bounded Cohen Macaulay type.

Generalizations of Lie Algebras

The generalizations of Lie algebras appeared in the modern mathematics and mathematical physics. In this paper we consider recent developments and remaining open problems on the subject. Some of that developments have been influenced by lectures given by Professor Jaime Keller in his research seminar. The survey includes Lie superalgebras, color Lie algebras, Lie algebras in symmetric categories, free Lie tau-algebras, and some generalizations with non-associative enveloping algebras: tangent algebras to analytic loops, bialgebras and primitive elements, non-associative Hopf algebras.

Modeling the emergence of HIV-1 drug resistance resulting from antiretroviral therapy: Insights from theoretical and numerical studies

The use of antiretroviral therapy has proven to be remarkably effective in controlling the progression of human immunodeficiency virus (HIV) infection and prolonging patient's survival. Therapy however may fail and therefore these benefits can be compromised by the emergence of HIV strains that are resistant to the therapy. In view of these facts, the question of finding the reason for which drug-resistant strains emerge during therapy has become a worldwide problem of great interest. This paper presents a deterministic HIV-1 model to examine the mechanisms underlying the emergence of drug-resistance during therapy. The aim of this study is to determine whether, and how fast, antiretroviral therapy may determine the emergence of drug resistance by calculating the basic reproductive numbers. The existence, feasibility and local stability of the equilibriums are also analyzed. By performing numerical simulations we show that Hopf bifurcation may occur. The model suggests that the individuals with drug-resistant infection may play an important role in the epidemic of HIV. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

New characterizations for hyperbolic cylinders in anti-de Sitter spaces

In this paper we study complete maximal spacelike hypersurfaces in anti-de Sitter space H-1(n+1) with either constant scalar curvature or constant non-zero Gauss-Kronecker curvature. We characterize the hyperbolic cylinders H-m(c(1)) x Hn-m(c(2)), 1 <= m <= n - 1, as the only such hypersurfaces with (n - 1) principal curvatures with the same sign everywhere. In particular we prove that a complete maximal spacelike hypersurface in H-1(5) with negative constant Gauss-Kronecker curvature is isometric to H-1(c(1)) x H-3(c(2)). (C) 2012 Elsevier Inc. All rights reserved.

ENERGY AND VOLUME OF VECTOR FIELDS ON SPHERICAL DOMAINS

We present a "boundary version" for theorems about minimality of volume and energy functionals on a spherical domain of an odd-dimensional Euclidean sphere.

Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.

Modeling and identification of freeplay nonlinearity

A nonlinear analysis is performed for the purpose of identification of the pitch freeplay nonlinearity and its effect on the type of bifurcation of a two degree-of-freedom aeroelastic system. The databases for the identification are generated from experimental investigations of a pitch-plunge rigid airfoil supported by a nonlinear torsional spring. Experimental data and linear analysis are performed to validate the parameters of the linearized equations. Based on the periodic responses of the experimental data which included the flutter frequency and its third harmonics, the freeplay nonlinearity is approximated by a polynomial expansion up to the third order. This representation allows us to use the normal form of the Hopf bifurcation to characterize the type of instability. Based on numerical integrations, the coefficients of the polynomial expansion representing the freeplay nonlinearity are identified. Published by Elsevier Ltd.

Rationale, study design, and analysis plan of the Alveolar Recruitment for ARDS Trial (ART): Study protocol for a randomized controlled trial

Background: Acute respiratory distress syndrome (ARDS) is associated with high in-hospital mortality. Alveolar recruitment followed by ventilation at optimal titrated PEEP may reduce ventilator-induced lung injury and improve oxygenation in patients with ARDS, but the effects on mortality and other clinical outcomes remain unknown. This article reports the rationale, study design, and analysis plan of the Alveolar Recruitment for ARDS Trial (ART). Methods/Design: ART is a pragmatic, multicenter, randomized (concealed), controlled trial, which aims to determine if maximum stepwise alveolar recruitment associated with PEEP titration is able to increase 28-day survival in patients with ARDS compared to conventional treatment (ARDSNet strategy). We will enroll adult patients with ARDS of less than 72 h duration. The intervention group will receive an alveolar recruitment maneuver, with stepwise increases of PEEP achieving 45 cmH(2)O and peak pressure of 60 cmH2O, followed by ventilation with optimal PEEP titrated according to the static compliance of the respiratory system. In the control group, mechanical ventilation will follow a conventional protocol (ARDSNet). In both groups, we will use controlled volume mode with low tidal volumes (4 to 6 mL/kg of predicted body weight) and targeting plateau pressure <= 30 cmH2O. The primary outcome is 28-day survival, and the secondary outcomes are: length of ICU stay; length of hospital stay; pneumothorax requiring chest tube during first 7 days; barotrauma during first 7 days; mechanical ventilation-free days from days 1 to 28; ICU, in-hospital, and 6-month survival. ART is an event-guided trial planned to last until 520 events (deaths within 28 days) are observed. These events allow detection of a hazard ratio of 0.75, with 90% power and two-tailed type I error of 5%. All analysis will follow the intention-to-treat principle. Discussion: If the ART strategy with maximum recruitment and PEEP titration improves 28-day survival, this will represent a notable advance to the care of ARDS patients. Conversely, if the ART strategy is similar or inferior to the current evidence-based strategy (ARDSNet), this should also change current practice as many institutions routinely employ recruitment maneuvers and set PEEP levels according to some titration method.

Bifurcation analysis of an aeroelastic system with concentrated nonlinearities

Analytical and numerical analyses of the nonlinear response of a three-degree-of-freedom nonlinear aeroelastic system are performed. Particularly, the effects of concentrated structural nonlinearities on the different motions are determined. The concentrated nonlinearities are introduced in the pitch, plunge, and flap springs by adding cubic stiffness in each of them. Quasi-steady approximation and the Duhamel formulation are used to model the aerodynamic loads. Using the quasi-steady approach, we derive the normal form of the Hopf bifurcation associated with the system's instability. Using the nonlinear form, three configurations including supercritical and subcritical aeroelastic systems are defined and analyzed numerically. The characteristics of these different configurations in terms of stability and motions are evaluated. The usefulness of the two aerodynamic formulations in the prediction of the different motions beyond the bifurcation is discussed.

Conceptual problem for noncommutative inflation and the new approach for nonrelativistic inflationary equation of state

In a previous paper, we connected the phenomenological noncommutative inflation of Alexander, Brandenberger and Magueijo [ Phys. Rev. D 67 081301 (2003)] and Koh and Brandenberger [ J. Cosmol. Astropart Phys. 2007 21 ()] with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group-like procedure in which even Hopf algebras (roughly the symmetries of noncommutative spaces) could lead to the equation of state of inflationary radiation. Nevertheless, in this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons being bounded from above) and the Fock-space structure of the representation which leads to the fundamental inflationary equations of state. We show that the Fock structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like leading to a problematic scattering theory, for example. We suggest replacing the Fock space by one of two possible structures that we propose. One of them relates to the general theory of Hopf algebras (here explained at an elementary level) while the other is based on a representation theorem of von Neumann algebras (a generalization of the Clebsch-Gordan coefficients), a proposal already suggested by us to take into account interactions in the inflationary equation of state.

Verzweigung periodischer Lösungen bei rein nichtlinearen Differentialgleichungssystemen in der Ebene

Zusammenfassung:In dieser Arbeit werden die Abzweigung stationärer Punkte und periodischer Lösungen von isolierten stationären Punkten rein nichtlinearer Differentialgleichungen in der reellenEbene betrachtet.Das erste Kapitel enthält einige technische Hilfsmittel, während im zweiten ausführlich das Verhalten von Differentialgleichungen in der Ebene mit zwei homogenen Polynomen gleichen Grades als rechter Seite diskutiert wird.Im dritten Kapitel beginnt der Hauptteil der Arbeit. Hier wird eine Verallgemeinerung des Hopf'schen Verzweigungssatzes bewiesen, der den klassischen Satz als Spezialfall enthält.Im vierten Kapitel untersuchen wir die Abzweigung stationärer Punkte und im letzten Kapitel die Abzweigung periodischer Lösungen unter Störungen, deren Ordnung echt kleiner ist, als die erste nichtverschwindende Näherung der ungestörten Gleichung.Alle Voraussetzungen in dieser Arbeit sind leicht nachzurechnen und es werden zahlreiche Beispiele ausführlich diskutiert.

Die Rolle von Hopfkategorien und Operaden in störungstheoretischen Quantenfeldtheorien

Die Vorhersagen störungstheoretischer Quantenfeldtheorienzeigen eine gute Übereinstimmung mit experimentellgemessenen Werten. Bei diesen störungstheoretischenBerechnungen treten allerdings Ultraviolettdivergenzen auf,die keine physikalische Interpretation der Ergebnisseermöglichen. Durch Renormierung dieser Theorien erhält manjedoch berechnbare Ergebnisse mit hoher experimentellerVorhersagekraft. Der Renormierungsvorgang kann durch eineHopfalgebra, die sogenannte 'Hopfalgebra der Wurzelbäume',beschrieben werden.Die vorliegende Arbeit leistet einen Beitrag für weitereUntersuchungen dieser Hopfalgebrenstruktur und Bestimmungneuer mathematischer Methoden zur Beschreibung desRenormierungsvorgangs. Dazu wird die algebraische Strukturvon Renormierung aus der Sicht der Kategorientheorie und derTheorie von Operaden untersucht.Aus Sicht der Kategorientheorie lassen sich die den Renormierungsprozess beschreibenden mathematischen Größen ineiner Kategorie zusammenfassen. Eine additive Strukturermöglicht dabei die Berücksichtigung beliebigerRenormierungsschemata. Auf dieser Kategorie kann einassoziativitätsverletzendes Produkt definiert werden, wobeidie Verletzung durch einen sogenannten 'Assoziator'kontrolliert werden kann. Die Struktur wird auf die einerHopfkategorie erweitert, so daß eine kategorientheoretischeUntersuchung des Renormierungsprozesses ermöglicht wird.Diese Hopfkategorie wird aus Sicht von Renormierunginterpretiert, wobei Beispielrechnungen die definierteStruktur verdeutlichen.Aus algebraischer Sicht kann aufgrund der graphischenDarstellung des Operadenproduktes eine Bijektivität zwischenWurzelbäumen und Operaden gezeigt werden. Auf diesenOperaden kann wiederum eine Hopfalgebrenstruktur definiertwerden. Beispiele verdeutlichen diese Bijektivität.