SZEGO and PARA-ORTHOGONAL POLYNOMIALS on THE REAL LINE: ZEROS and CANONICAL SPECTRAL TRANSFORMATIONS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Szego{double acute} and para-orthogonal polynomials on the real line: Zeros and canonical spectral transformations

We study polynomials which satisfy the same recurrence relation as the Szego{double acute} polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szego{double acute} polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szego{double acute} polynomials, para-orthogonal polynomials and associated quadrature rules are also studied. Finally, again with positive values for the reflection coefficients, interlacing properties of the Szego{double acute} polynomials and polynomials arising from canonical spectral transformations are obtained. © 2012 American Mathematical Society.

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and gamma(5) chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.

Evidence of distinct phase transformations in lithium phosphate glass Li2O-P2O5

The purpose of this work is to study the Li2O-P2O5 glass using the differential scanning calorimetry (DSC) and x-ray diffraction (XRD) techniques to understand the crystallization process in this glass matrix. To study the glass by DSC, screened samples with different particle sizes to resolve the crystallization peaks were used. Both crystallization peaks were attributed to Li6P6O18 and LiPO3 phases. This evidence was corroborated by XRD analysis on glasses annealed at different temperatures in order to crystallize these phases.

Type-II Backlund transformations via gauge transformations

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

Permutability of Backlund transformations for N=2 supersymmetric sine-Gordon

The permutability of two Backlund transformations is employed to construct a nonlinear superposition formula and to generate a class of solutions for the N=2 super sine-Gordon model. We present explicitly the one and two soliton solutions.

Structuralism and the Applicability of Mathematics

In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.

Influence of the Al content on the phase transformations in Cu-Al-Ag alloys

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

beta Phase transformations in the Cu-11mass%Al alloy with Ag additions

In the Cu-Al system, due to the sluggishness of the beta a dagger" (alpha + gamma(1)) eutectoid reaction, the beta phase can be retained metastably. During quenching, metastable beta alloys undergo a martensitic transformation to a beta' phase at Al low content. The ordering reaction beta a dagger" beta(1) precedes the martensitic transformation. The influence of Ag additions on the reactions containing the beta phase in the Cu-11mass%Al alloy was studied using differential scanning calorimetry and in situ X-ray diffractometry. The results indicated that, on cooling, two reactions are occurring in the same temperature range, the beta -> (alpha + gamma(1)) decomposition reaction and the beta -> beta(1) reaction, with different reaction mechanisms (diffusive for the former and ordering for the latter) and, consequently, with different reaction rates. For lower cooling rates, the dominant is the decomposition reaction and for higher cooling rates the ordering reaction prevails. on heating, the (alpha + gamma(1)) -> beta reverse eutectoid reaction occurs with a resulting beta phase saturated with alpha. The increase of Ag concentration retards the beta -> (alpha + gamma(1)) decomposition reaction and the beta -> beta(1) ordering reaction, which occurs in the same temperature range, becomes the predominant process.

Modelagem Matemática e Tecnologias de Informação e Comunicação: a realidade do mundo cibernético como um vetor de virtualização

Neste artigo construímos um entrelaçamento teórico-filosófico que tem como objetivo discutir a relação entre Modelagem Matemática e realidade do mundo cibernético. em particular, essa abrangência da realidade é evidenciada como um possível vetor de virtualização, isto é, como um aspecto que pode influenciar o modo como a problemática que envolve uma determinada situação ou entidade é compreendida. Para tanto, fazemos uma associação entre Modelagem Matemática e as transformações que envolvem os modos de ser denotados por real, possível, atual e virtual, tendo como base ilustrativa as quatro causas aristotélicas. Complementando essa associação, assumimos uma concepção de problema que permite uma consolidação entre as relações estabelecidas e, também, uma concepção de realidade que entende o mundo cibernético como uma de suas dimensões. Por fim, apresentamos um exemplo de Modelagem Matemática ocorrido em sala de aula, que visa caracterizar a realidade do mundo cibernético como um vetor de virtualização.

Photo-induced transformations in chalcogenide nanocomposite layers

Investigations of photo-induced structural transformations (PST) and related changes of optical parameters in amorphous chalcogenide layers were further developed towards the establishment of their dependence on the compositional modulation of the material at nanoscale-dimensions (similar to3-10 nm) and possible improvement of optical recording parameters as well. Besides the known amorphous-amorphous PST, photo-stimulated interdiffusion and crystallization in multilayer structures were found as a useful method for amplitude-phase optical relief formation. The last two types of PST were influenced by size restrictions and efficiently operated by the composition and by the modulation period of the layered nanocomposite. Experimental evidences were obtained in Se-, AsSe-, Se0.4Te0.6-containing layered or quasi zero-dimensional structures based on As2S3 or SiOx and MgF2 matrix. Comparison was made with As2S3- and GeS2-based multicomponent layers, containing Se, Te and Ga. (C) 2004 Elsevier B.V. All rights reserved.

Mathematics teaching life histories in the study of teachers' perceptions of change

The aim of this paper is to discuss teachers' perceptions of change in their thought and/or practice over time and their perceptions of what kind of experiences or challenges might have influenced those changes. Two mathematics teaching life histories of Brazilian teachers are examined, considering a context of curriculum development in the state of São Paulo, Brazil. Reflection on teachers' thought and practice and interest in their own development, including interest in their own learning of mathematics, seemed to be the most important internal aspects influencing change and development. Close support seemed to be the most important external aspect. The retrospective analysis put a good face on personal change and development. (C) 2000 Elsevier B.V. Ltd. All rights reserved.