Two-body Dirac equation approach to the deuteron

The two-body Dirac(Breit) equation with potentials associated to one-boson-exchanges with cutoff masses is solved for the deuteron and its observables calculated. The 16-component wave-function for the Jπ = 1+ state contains four independent radial functions which satisfy a system of four coupled differential equations of first order. This system is numerically integrated, from infinity towards the origin, by fixing the value of the deuteron binding energy and imposing appropriate boundary conditions at infinity. For the exchange potential of the pion, a mixture of direct plus derivative couplings to the nucleon is considered. We varied the pion-nucleon coupling constant, and the best results of our calculations agree with the lower values recently determined for this constant.

On the integrable perturbations of the Camassa-Holm equation

We present an investigation of the nonlinear partial differential equations (PDE) which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose we use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure. © 2000 American Institute of Physics.

The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

Darboux-Bäcklund transformations and rational solutions of the painlevé IV equation

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian representations for rational solutions are obtained by successive actions of the Darboux-Bäcklund transformations. ©2010 American Institute of Physics.

On stability of differential equations with piecewise constant argument using dichotomic maps

This paper deals with the study of the basic theory of existence, uniqueness and continuation of solutions of di®erential equations with piecewise constant argument. Results about asymptotic stability of the equation x(t) =-bx(t) + f(x([t])) with argu- ment [t], where [t] designates the greatest integer function, are established by means of dichotomic maps. Other example is given to illustrate the application of the method. Copyright © 2011 Watam Press.

Necessary conditions of optimality for state constrained infinite horizon differential inclusions

This article presents and discusses necessary conditions of optimality for infinite horizon dynamic optimization problems with inequality state constraints and set inclusion constraints at both endpoints of the trajectory. The cost functional depends on the state variable at the final time, and the dynamics are given by a differential inclusion. Moreover, the optimization is carried out over asymptotically convergent state trajectories. The novelty of the proposed optimality conditions for this class of problems is that the boundary condition of the adjoint variable is given as a weak directional inclusion at infinity. This improves on the currently available necessary conditions of optimality for infinite horizon problems. © 2011 IEEE.

Differential phosphorylation, desensitization, and internalization of α1A-adrenoceptors activated by norepinephrine and oxymetazoline

Loss of response on repetitive drug exposure (i.e., tachyphylaxis) is a particular problem for the vasoconstrictor effects of medications containing oxymetazoline (OXY), an α1-adrenoceptor (AR) agonist of the imidazoline class. One cause of tachyphylaxis is receptor desensitization, usually accompanied by phosphorylation and internalization. It is well established that a1A-ARs are less phosphorylated, desensitized, and internalized on exposure to the phenethylamines norepinephrine (NE), epinephrine, or phenylephrine (PE) than are the a1B and a1D subtypes. However, here we show in human embryonic kidney-293 cells that the low-efficacy agonist OXY induces G protein-coupled receptor kinase 2-dependent a1A-AR phosphorylation, followed by rapid desensitization and internalization (∼40% internalization after 5 minutes of stimulation), whereas phosphorylation of α1A-ARs exposed to NE depends to a large extent on protein kinase C activity and is not followed by desensitization, and the receptors undergo delayed internalization (∼35% after 60 minutes of stimulation). Native α1A-ARs from rat tail artery and vas deferens are also desensitized by OXY, but not by NE or PE, indicating that thisproperty of OXY is not limited to recombinant receptors expressed in cell systems. The results of the present study are clearly indicative of agonist-directed a1A-AR regulation. OXY shows functional selectivity relative to NE and PE at a1A-ARs, leading to significant receptor desensitization and internalization, which is important in view of the therapeutic vasoconstrictor effects of this drug and the varied biologic process regulated by α1A-ARs. Copyright © 2013 by The American Society for Pharmacology and Experimental Therapeutics.

Semigrupos de operadores lineares e equações diferenciais em espaços de Banach

Pós-graduação em Matemática Universitária - IGCE

Semigrupos de operadores lineares e aplicações

Pós-graduação em Matemática Universitária - IGCE

Estudo clássico completo do formalismo de Hamilton-Jacobi

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Avaliação das condições de secagem no rendimento e na qualidade do óleo de linhaça (Linum usitatissimum L.)

De origem asiática, a semente de linhaça (Linum usitatissimum L.) pertence à família das Lináceas e é obtida a partir do linho. A semente da linhaça é ainda a maior fonte alimentar de lignanas, compostos fotoquímicos parecidos com o estrogênio, que podem desempenhar ação anticancerígena. Rica em fibras solúveis tem aproximadamente 40% do seu peso composto por óleos ricos em Ômega 3, entre os quais se destaca o α-linolênico. A secagem é a operação unitária segundo o qual ocorre eliminação da água por evaporação ou sublimação, presente em um material, mediante a aplicação de calor com condições controladas. Visando averiguar o comportamento das sementes de linhaça durante a operação de secagem, o presente trabalho teve como objetivo principal realizar o planejamento experimental e analisar estatísticamente os resultados empregados para quantificar a influência da temperatura do ar (T), tempo de secagem (t), velocidade do ar de fluidização (Uf) e carga de sólidos (Cs), sobre a razão de umidade (Xr), rendimento em óleo (Rend.) e os parâmetros oleoquimicos. A estimativa do ponto ótimo de operação foi determinada em função das variáveis de entrada aplicando o conceito de desejabilidade global. Dentre as condições estabelecidas neste trabalho, o valor ótimo da Função Desejabilidade é quando T é deslocada próximo ao nível alto (72 oC), t para o mínimo (3 h), Uf para o ponto próximo ao central (0,83 m/s) e a Cs para o nível alto (500g), obtendo-se assim: 0,126 para Xr; 36,92 % para Rend.; 4,51 mg KOH/g para IA; 22,52 meqO2/Kg IP e 0,31% para DC. Foram obtidas as isotermas de dessorção das sementes de linhaça nas temperaturas de 40, 60 e 80°C. Os dados experimentais foram avaliados usando seis modelos matemáticos. A entalpia e a entropia diferencial de dessorção foram estimadas por meio das relações de Clausius-Clapeyron e Gibbs-Helmholtz, respectivamente. Os modelos de GAB e Peleg ajustaram adequadamente os dados experimentais. A teoria da compensação entalpia-entropia foi aplicada com sucesso às isotermas de dessorção e indica que o mecanismo de dessorção de umidade das sementes de linhaça pode ser considerado como controlado pela entalpia. A secagem das sementes de linhaça previamente umidificadas foram avaliadas em um secador de leito fixo e fluidizado, as corridas experimentais foram realizadas nas temperaturas de 40, 60 e 80°C, dentre dos cinco modelos propostos, o modelo de Midilli et al, foi o melhor modelo que melhor ajustou aos dados experimentais. Foi observado que a difusividade efetiva para as sementes de linhaça aumentou com a elevação da temperatura do ar de secagem para a secagem em leito fixo e fluidizado. A dependência da difusividade em relação à temperatura foi descrita pela equação de Arrhenius, por meio da qual se estimou para ambos os processos de secagem.

Differential effects of variation in athletes training on myocardial morphophysiological adaptation in men: Focus on I-123-MIBG assessed myocardial sympathetic activity

High intensity systematic physical training leads to myocardial morphophysiological adaptations. The goal of this study was to investigate if differences in training were correlated with differences in cardiac sympathetic activity.58 males (19-47 years), were divided into three groups: strength group (SG), (20 bodybuilders), endurance group (EG), (20 endurance athletes), and a control group (CG) comprising 18 healthy non-athletes. Cardiac sympathetic innervation was assessed by planar myocardial I-123-metaiodobenzylguanidine scintigraphy using the early and late heart to mediastinal (H/M) ratio, and washout rate (WR).Left ventricular mass index was significantly higher both in SG (P < .001) and EG (P = .001) compared to CG without a statistical significant difference between SG and EG (P = .417). The relative wall thickness was significantly higher in SG compared to CG (P < .001). Both left ventricular ejection fraction and the peak filling rate showed no significant difference between the groups. Resting heart rate was significantly lower in EG compared to CG (P = .006) and SG (P = .002). The late H/M ratio in CG was significantly higher compared to the late H/M for SG (P = .003) and EG (P = .004). However, WR showed no difference between the groups. There was no significant correlation between the parameters of myocardial sympathetic innervation and parameters of left ventricular function.Strength training resulted in a significant increase in cardiac dimensions. Both strength and endurance training seem to cause a reduction in myocardial sympathetic drive. However, myocardial morphological and functional adaptations to training were not correlated with myocardial sympathetic activity.

Differential Evolutionary Constraints in the Evolution of Chemoreceptors: A Murine and Human Case Study

Chemoreception is among the most important sensory modalities in animals. Organisms use the ability to perceive chemical compounds in all major ecological activities. Recent studies have allowed the characterization of chemoreceptor gene families. These genes present strikingly high variability in copy numbers and pseudogenization degrees among different species, but the mechanisms underlying their evolution are not fully understood. We have analyzed the functional networks of these genes, their orthologs distribution, and performed phylogenetic analyses in order to investigate their evolutionary dynamics. We have modeled the chemosensory networks and compared the evolutionary constraints of their genes in Mus musculus, Homo sapiens, and Rattus norvegicus. We have observed significant differences regarding the constraints on the orthologous groups and network topologies of chemoreceptors and signal transduction machinery. Our findings suggest that chemosensory receptor genes are less constrained than their signal transducing machinery, resulting in greater receptor diversity and conservation of information processing pathways. More importantly, we have observed significant differences among the receptors themselves, suggesting that olfactory and bitter taste receptors are more conserved than vomeronasal receptors.

General method for reducing the two-body Dirac equation

A semirelativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schrödinger-type equations is also discussed. © 1992 American Institute of Physics.

Virasoro Action on Imaginary Verma Modules and the Operator Form of the KZ-Equation

We define the Virasoro algebra action on imaginary Verma modules for affine and construct an analogue of the Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a realization of imaginary Verma modules in terms of sums of partial differential operators.