A comment on a nonideal centrifugal vibrator machine behavior with soft and hard springs

This paper concerns a type of rotating machine (centrifugal vibrator), which is supported on a nonlinear spring. This is a nonideal kind of mechanical system. The goal of the present work is to show the striking differences between the cases where we take into account soft and hard spring types. For soft spring, we prove the existence of homoclinic chaos. By using the Melnikov's Method, we show the existence of an interval with the following property: if a certain parameter belongs to this interval, then we have chaotic behavior; otherwise, this does not happen. Furthermore, if we use an appropriate damping coefficient, the chaotic behavior can be avoided. For hard spring, we prove the existence of Hopf's Bifurcation, by using reduction to Center Manifolds and the Bezout Theorem (a classical result about algebraic plane curves).

Zero sets of bivariate Hermite polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Número de Milnor associado a curvas reduzidas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Resonances and subharmonic bifurcations of large amplitude periodic orbits of planar polynomial vector fields

In this work are studied periodic perturbations, depending on two parameters, of planar polynomial vector fields having an annulus of large amplitude periodic orbits, which accumulate on a symmetric infinite heteroclinic cycle. Such periodic orbits and the heteroclinic trajectory can be seen only by the global consideration of the polynomial vector fields on the whole plane, and not by their restriction to any compact set. The global study involving infinity is performed via the Poincare Compactification. It is shown that, for certain types of periodic perturbations, one can seek, in a neighborhood of the origin in the parameter plane, curves C-(m) of subharmonic bifurcations, for which the periodically perturbed system has subharmonics of order m, for any integer m.

O problema isoperimétrico e aplicações para o ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

A Parameterization Technique for the Continuation Power Flow Developed from the Analysis of Power Flow Curves

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

GREEN-FUNCTION FOR A SPIN-1/2 PARTICLE IN AN EXTERNAL PLANE-WAVE ELECTROMAGNETIC-FIELD

The Green function for a spin-1/2 charged particle in the presence of an external plane wave electromagnetic field is calculated by algebraic techniques in terms of the free-particle Green function.

Anomalous metamagnetic-like transition in a FeRh/Fe3Pt interface occurring at T approximate to 120 K in the field-cooled-cooling curves for low magnetic fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The rolling ball problem on the plane revisited

By a sequence of rollings without slipping or twisting along segments of a straight line of the plane, a spherical ball of unit radius has to be transferred from an initial state to an arbitrary final state taking into account the orientation of the ball. We provide a new proof that with at most 3 moves, we can go from a given initial state to an arbitrary final state. The first proof of this result is due to Hammersley ( 1983). His proof is more algebraic than ours which is more geometric. We also showed that generically no one of the three moves, in any elimination of the spin discrepancy, may have length equal to an integral multiple of 2 pi.

Direct Observation of Tetragonal Distortion in Epitaxial Structures through Secondary Peak Split in a Synchrotron Radiation Renninger Scan

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mathematical analysis of maximum power generated by photovoltaic systems and fitting curves for standard test conditions

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I- 100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

Maturation and growth curves of Macrobrachium Carcinus (Linnaeus) (Crustacea, Decapoda, Palaemonidae) from Ribeira de Iguape River, southern Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Models for the analysis of growth curves for rearing tinamous (Rhynchotus rufescens) in captivity

Growth curves models provide a visual assessment of growth as a function of time, and prediction body weight at a specific age. This study aimed at estimating tinamous growth curve using different models, and at verifying their goodness of fit. A total number 11,639 weight records from 411 birds, being 6,671 from females and 3,095 from males, was analyzed. The highest estimates of a parameter were obtained using Brody (BD), von Bertalanffy (VB), Gompertz (GP,) and Logistic function (LG). Adult females were 5.7% heavier than males. The highest estimates of b parameter were obtained in the LG, GP, BID, and VB models. The estimated k parameter values in decreasing order were obtained in LG, GP, VB, and BID models. The correlation between the parameters a and k showed heavier birds are less precocious than the lighter. The estimates of intercept, linear regression coefficient, quadratic regression coefficient, and differences between quadratic coefficient of functions and estimated ties of quadratic-quadratic-quadratic segmented polynomials (QQQSP) were: 31.1732 +/- 2.41339; 3.07898 +/- 0.13287; 0.02689 +/- 0.00152; -0.05566 +/- 0.00193; 0.02349 +/- 0.00107, and 57 and 145 days, respectively. The estimated predicted mean error values (PME) of VB, GP, BID, LG, and QQQSP models were, respectively, 0.8353; 0.01715; -0.6939; -2.2453; and -0.7544%. The coefficient of determination (RI) and least square error values (MS) showed similar results. In conclusion, the VB and the QQQSP models adequately described tinamous growth. The best model to describe tinamous growth was the Gompertz model, because it presented the highest R-2 values, easiness of convergence, lower PME, and the easiness of parameter biological interpretation.

Avaliação da coluna vertebral: relação entre gibosidade e curvas sagitais por método não-invasivo

Os objetivos do estudo foram avaliar o alinhamento, no plano sagital, da coluna de indivíduos com alterações na medida da gibosidade, comparando com um grupo sem alterações; testar a confiabilidade do instrumento utilizado e verificar se existem correlações entre as medidas da gibosidade e os valores das curvaturas vertebrais. Foram avaliados 40 jovens, divididos em grupo controle - ausência ou presença de gibosidades inferiores a 0,5 cm na curvatura torácica e 0,7 cm na lombar (n=20) e, grupo experimental - gibosidades superiores às descritas (n=20). A gibosidade e as curvaturas no plano sagital foram mensuradas com um instrumento adaptado a um nível d'água e o teste de Adams. As coletas foram realizadas em duas datas distintas, nos dois grupos. Após aplicação do teste Mann-Whitney não foi encontrada diferença entre as ocasiões de coletas e, emparelhando-se os grupos, foi encontrada diferença apenas na medida cervical. Na verificação de existência de relação entre as medidas coletadas, foi encontrada correlação linear (Spearmann) no grupo controle - curvatura torácica e gibosidade torácica; em ambos os grupos - curvaturas torácica e lombar; e no grupo experimental - gibosidade torácica e as curvaturas lombar e sacral e, curvatura sacral e curvaturas torácica e lombar. Pôde-se concluir que a medida da gibosidade tem relações com as curvaturas no plano sagital. Por ser um método confiável, simples e acessível, pode ser reproduzido sem altos custos financeiros e sem causar prejuízo à saúde do paciente.