Spin-2 Fields and Helicity

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

A statistical law for multiplicities of SU(3) irreps (lambda, mu) in the plethysm {eta} circle times(3) {m} -> (lambda, mu)

A statistical law for the multiplicities of the SU(3) irreps (lambda, mu) in the reduction of totally symmetric irreducible representations {m} of U(N), N = (eta + 1) (eta + 2)/2 with eta being the three-dimensional oscillator major shell quantum number, is derived in terms of the quadratic and cubic invariants of SU(3), by determining the first three terms of an asymptotic expansion for the multiplicities. To this end, the bivariate Edgeworth expansion known in statistics is used. Simple formulae, in terms of m and eta, for all the parameters in the expansion are derived. Numerical tests with large m and eta = 4, 5 and 6 show good agreement with the statistical formula for the SU(3) multiplicities.

Metodologia para determinar parâmetros petrofísicos de corte em um campo de petróleo: o caso Socororo, bacia do Oriente, Venezuela

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Coexisting spatio-temporal scales in neuroscience

In this study I propose an epistemological discussion of multiple spatio-temporal scales in neuroscience. Are such scales merely convenient levels of description of structure and function, or do they correspond to irreducible levels of brain organization? What criteria should we employ in order to reduce one level to another, or to identify levels that are not reducible to others? Should we think of these criteria as based on empirical and/or theoretical reasons? Beginning with an empirical criterion - the necessity of different experimental methodologies for the measurement of different phenomena in the same system - I summarize spatial and temporal scales currently used in neuroscience and discuss the possibility of a more general theoretical criterion. I conclude that multiscaling should be recognized as a central concept in the epistemology of neuroscience.

Spectroscopic studies of the Eu3+ and Er3+ ions in the fluorozirconate LaZr2F11 matrix

An investigation by optical spectroscopy of the Eu3 + and Er3 + active ions in the crystallized fluorozirconate matrix LaZr2F11 is presented. The D-5(1) --> F-7(0-5) emission lines of Eu3 + are used to extract the F-7(0-5) energy scheme and the observed extinctions permit the deduction of irreducible representations (IRREPS) associated with corresponding sub-levels in the D-2 symmetry. The crystal field analysis was carried out on a 387 x 387 basis set, comprising the F-7, D-5(1,2,3) F-5(1,2), (5)G(1,2,3) and P-3(1,2,3,4,5,6) terms of the Eu-3 (+) 4f(6) configuration. The deviation and rms are 6.8 and 7.9 cm (-1), respectively for 38 levels and ten parameters. The experimental crystal field parameters are in good agreement with the ab-initio ones. Moreover, the relative intensities of the D-5(0) --> F-7(2,3,4) emissions are well reproduced by an 'ab-initio' calculation, except for three lines. The Er3 + ions introduced in LaZr2F11, microcrystals also lie in an unique crystallographic site. A total of 31 energy levels were recorded and the crystal field analysis led to 6.6 and 7.8 cm (-1) for the deviation and rms, respectively, for nine variable parameters taken into account. The experimental CF parameters for Er3 + and Eu3 + are very similar, which seems to show that the host lattice contracts around the smaller Er3 + ion. The informations given by both Eu3 + and Eu3 + optical probes in LaZr2F11 are very consistent with the structure previously determined for the isotypic PrZr2F11 fluoride. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Projective Fourier duality and Weyl quantization

The Weyl-Wigner correspondence prescription, which makes great use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. Both an Abelian and a symmetric projective Kac algebra are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras.

Absorption and fluorescence of Er3+-doped LiYF4: Measurements and simulation

Er3+:LiYF4 single crystal has been studied by absorption and fluorescence spectroscopy in the IR-visible-UV (0-44000 cm-1) region from 4.2 K to room temperature. Polarized spectra were recorded in order to assign numerous Stark levels of electronic transitions mentioned but not attributed before in the related literature and to discuss the irreducible representations (irreps) of the 4I15/2 sublevels. A parametric hamiltonian, including free ion (Eν, α, β, γ, Tλ, ζ, Mk and Pi) and crystal field parameters (B2 0, B4 0, B4 4, B6 0 and B6 4) in an approximate D2d symmetry for the rare earth site in this scheelite type structure, was used to simulate 109 energy positions of the Er ion with a r.m.s. standard deviation of 14.6 cm-1. A comparison with previously published results for Nd3+ in the same matrix is done. © 1998 Elsevier Science S.A.

A description of ligand field effects in the Di-μ-Azido-Bis [{Azido(N,N-diethylethylenediamine)}Copper(II)] compound by the simple overlap model

We present a theoretical description of ligand field effects in the di-μ-azido- bis[{azido(N,N-diethylethylenediamine)} copper(II)] compound by the Simple Overlap Model. The ligand field Hamiltonian is expressed in terms of irreducible tensor operators for an assumed D3h site symmetry occupied by the copper ion. The ligand field parameters, calculated from the available structural data, indicate that the copper ion is under the influence of a very strong ligand field. The energy of the d-d absorption band is well reproduced phenomenologically by the model.

Galilean covariance and non-relativistic Bhabha equations

We apply a five-dimensional formulation of Galilean covariance to construct non-relativistic Bhabha first-order wave equations which, depending on the representation, correspond either to the well known Dirac equation (for particles with spin 1/2) or the Duffin-Kemmer-Petiau equation (for spinless and spin 1 particles). Here the irreducible representations belong to the Lie algebra of the 'de Sitter group' in 4 + 1 dimensions, SO(5, 1). Using this approach, the non-relativistic limits of the corresponding equations are obtained directly, without taking any low-velocity approximation. As a simple illustration, we discuss the harmonic oscillator.

Energy and angular momentum of the gravitational field in the teleparallel geometry

The Hamiltonian formulation of the teleparallel equivalent of general relativity is considered. Definitions of energy, momentum and angular momentum of the gravitational field arise from the integral form of the constraint equations of the theory. In particular, the gravitational energy-momentum is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. The definition for the gravitational energy is investigated in the context of the Kerr black hole. In the evaluation of the energy contained within the external event horizon of the Kerr black hole, we obtain a value strikingly close to the irreducible mass of the latter. The gravitational angular momentum is evaluated for the gravitational field of a thin, slowly rotating mass shell. © 2002 The American Physical Society.

A dimension formula for reduced plethysms

The boson calculus formalism is used to construct realizations of basis states of irreducible representations of unitary groups taking as a paradigm the interacting boson models of atomic nuclei. These realizations, together with a theorem on plethysms for obtaining branching rules, allowed us to obtain a dimension formula for reduced plethysms. © 2005 IOP Publishing Ltd.

Aspectos dinâmicos e ergódicos dos intercâmbios de intervalos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Campos de vetores lineares reversíveis equivariantes

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

Psicanálise, antropologia e alteridade: apontamentos para um debate

Este trabalho trata da temática da alteridade, tomando-a como mote para um diálogo entre a psicanálise e a antropologia. Neste sentido, a partir de uma incursão pela noção de estrangeiro na obra de Freud, enfatiza a ideia de que a diferença imposta pelo inconsciente é dona de uma narrativa e de uma temporalidade particulares que se recusam a obedecer aos ditames do pensamento representacional. Em decorrência disto, a estranheza e a negatividade do encontro analítico aparecem como lugares do possível, ampliando o conceito de alteridade e as capacidades da interpretação, agora um meio-termo entre a produção de sentido e a experiência do vazio. Eis a lição da não lição proposta por este inquietante outro do inconsciente à antropologia e, em maior escala, às ciências sociais: admitir a possibilidade do sentido, mas não necessariamente o seu encerramento, fornecendo assim uma expressão menos comprometida a um estrangeiro agora irredutível a códigos preestabelecidos.

Polinômios irredutíveis: critérios e aplicações

Pós-graduação em Matemática em Rede Nacional - IBILCE