On the Baker-Akhiezer function in the AKNS scheme

Expressions for the Baker-Akhiezer function and their logarithmic space and time derivatives are derived in terms of the matrix elements of U - V matrices and 'squared basis functions'. These expressions generalize the well known formulas for the KdV equation case and establish links between different forms of the Whitham averaging procedure.

Topological signatures in CMB temperature anisotropy maps

We propose an alternative formalism to simulate cosmic microwave background (CMB) temperature maps in Lambda CDM universes with nontrivial spatial topologies. This formalism avoids the need to explicitly compute the eigenmodes of the Laplacian operator in the spatial sections. Instead, the covariance matrix of the coefficients of the spherical harmonic decomposition of the temperature anisotropies is expressed in terms of the elements of the covering group of the space. We obtain a decomposition of the correlation matrix that isolates the topological contribution to the CMB temperature anisotropies out of the simply connected contribution. A further decomposition of the topological signature of the correlation matrix for an arbitrary topology allows us to compute it in terms of correlation matrices corresponding to simpler topologies, for which closed quadrature formulas might be derived. We also use this decomposition to show that CMB temperature maps of (not too large) multiply connected universes must show patterns of alignment, and propose a method to look for these patterns, thus opening the door to the development of new methods for detecting the topology of our Universe even when the injectivity radius of space is slightly larger than the radius of the last scattering surface. We illustrate all these features with the simplest examples, those of flat homogeneous manifolds, i.e., tori, with special attention given to the cylinder, i.e., T-1 topology.

First quantized approaches to neutrino oscillations and second quantization

Neutrino oscillations are treated from the point of view of relativistic first quantized theories and compared to second quantized treatments. Within first quantized theories, general oscillation probabilities can be found for Dirac fermions and charged spin 0 bosons. A clear modification in the oscillation formulas can be obtained and its origin is elucidated and confirmed to be inevitable from completeness and causality requirements. The left-handed nature of created and detected neutrinos can also be implemented in the first quantized Dirac theory in the presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. Concerning second quantized approaches, it is shown in a calculation using virtual neutrino propagation that both neutrinos and antineutrinos may also contribute as intermediate particles. The sign of the contributing neutrino energy may have to be chosen explicitly without being automatic in the formalism. At last, a simple second quantized description of the flavor oscillation phenomenon is devised. In this description there is no interference terms between positive and negative components, but it still gives simple normalized oscillation probabilities. A new effect appearing in this context is an inevitable but tiny violation of the initial flavor of neutrinos. The probability loss due to the conversion of left-handed neutrinos to right-handed neutrinos is also presented.

Duffin-Kemmer-Petiau and Klein-Cordon-Fock equations for electromagnetic, Yang-Mills and external gravitational field interactions: proof of equivalence

Starting from the Generating functional for the Green Function (GF), constructed from the Lagrangian action in the Duffin-Kemmer-Petiau (DKP) theory (L-approach) we strictly prove that the physical matrix elements of the S-matrix in DKP and Klein-Gordon-Fock (KGF) theories coincide in cases of interacting spin O particles with external and quantized Maxwell and Yang-Mills fields and in case of external gravitational field (without or with torsion), For the proof we use the reduction formulas of Lehmann, Symanzik and Zimmermann (LSZ). We prove that many photons and Yang-Mills particles GF coincide in both theories too. (C) 2000 Elsevier B.V. B.V. All rights reserved.

On equivalence of Duffin-Kemmer-Petiau and Klein-Gordon equations

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

Leitura e Interpretação de Dados Prontos em um Ambiente de Modelagem e Tecnologias Digitais: o mosaico em movimento

Neste artigo, analisamos a leitura e a interpretação de dados prontos coletados por alunos para desenvolverem projetos de modelagem. Consideramos dados prontos as informações coletadas na Internet, como um gráfico ou uma fórmula, sem maiores explicações de como foram geradas. Com isso, repensamos o mosaico de pesquisas do GPIMEM, grupo de pesquisa ao qual pertencemos e que desenvolve pesquisas sobre modelagem e informática há cerca de vinte anos. Na análise, privilegiamos a apresentação oral e o relatório escrito de um grupo de alunas do Curso de Ciências Biológicas da Universidade Estadual Paulista (UNESP). Os dados prontos sugerem uma nova faceta na relação entre tecnologias digitais e modelagem: eles parecem ser tratados de maneira idêntica a dados empíricos usualmente coletados em outros trabalhos de modelagem encontrados na literatura. Assim, o mosaico de pesquisas sobre o tema ganha novas dimensões na medida em que a Internet parece modificar a própria noção do que são dados.

Avaliação do estado nutricional precedente ao uso de nutrição enteral

CONTEXTO: O adequado diagnóstico do estado nutricional é de vital importância para a prescrição da terapia nutricional enteral no ambiente hospitalar. OBJETIVO: Avaliar indicadores do estado nutricional em pacientes ingressantes na terapia nutricional enteral em uma unidade hospitalar. MÉTODOS: Estudo transversal com 100 pacientes adultos, sendo analisado o estado nutricional de ingresso à terapia nutricional enteral, por meio do índice de massa corporal obtido do peso e estatura estimados a partir de fórmulas de predição, e de indicadores laboratoriais do estado metabólico e nutricional. RESULTADOS: do total, 29% dos pacientes foram classificados como desnutridos pelo índice de massa corporal, enquanto 80% dos mesmos apresentaram albumina abaixo do valor de referência (<3,2 g/dL). Não houve diferença na distribuição das causas de base da internação entre os grupos classificados quanto ao estado nutricional pelo índice de massa corporal, prevalecendo as doenças cardiovasculares e pulmonares entre as principais causas. As concentrações abaixo dos valores de referência de albumina não foram diferentes entre os grupos classificados pelo índice de massa corporal e pelo diagnóstico de internação. CONCLUSÃO: O índice de massa corporal estimado foi indicador específico do estado nutricional, porém pouco sensível, enquanto a albumina mostrou-se mais sensível, o que reafirma a necessidade da combinação de vários indicadores para obtenção de um adequado diagnóstico nutricional.

Construção e uso do pulverizador-logarítmico manual

Descreve-se a construção do pulverizador-logarítmico, seu funcionamento e gama de aplicações. Deduzem-se as fórmulas matemáticas em que o mesmo se baseia. Apresentam-se ábacos que permitem determinar a concentração de calda em qualquer ponto da área pulverizada.

Orbital perturbations using geopotential coefficients up to high degree and order: Highly eccentric orbits

Several methods have been proposed for calculations of the eccentricity function for a high value of the eccentricity, however they cannot be used when the high degree and order coefficients of gravity fields are taken into account. The method proposed by Wnuk(1) is numerically stable in this case, but when is used. a large number of terms occurs in formulas for geopotential perturbations. In this paper we propose an application of expansions of some functions of the eccentric anomaly E as well as Hansen coefficients in power series of (e - e*), where e* is a fixed value of the eccentricity derived by da Silva Fernandes(2,3,4). These series are convergent for all e < 1.

Morse basis expansion applied to diatomic molecules

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

Air-sea interaction studies at the station occupied by R/V Sirius

The transfer formulas are used to compute hourly values of sensible and latent heat exchanges for the period July 29 to July 31, 1974. Also, values of eddy shearing stress at the sea surface, Bowen's ratio and dissipation of kinetic energy are computed. The data used cover part of the GATE period for station 20 occupied by the Brazilian Naval Ship R/V Sirius in the Equatorial Atlantic (0730 N 4000 W). The variations in the computed values are studied in relation to rainfall and the synoptic situation. © 1980 D. Reidel Publishing Co.

Comparação de métodos para determinar biomassa na região amazônica

The aboveground biomass content of a region can be estimated by either direct or indirect methods. Direct methods correspond to the biomass content determination with scales and extrapolation of results to larger areas. It is a destructive and very laborious procedure. Indirect methods utilize formulas whose entrance parameters are obtained from forest inventories. Forest inventories are made with the purpose to plan exploration and land use and the inventory data are frequently not suitable for biomass estimation. Problems with both methods increase in the Amazon region, where little information is available on forest biomass. The objective of this paper is to establish, by comparing the application of the indirect and direct methods in the determination of the biomass, the more appropriate indirect formulation to represent the characteristic vegetation of a region in the amazonian forest. A 0.2 hectare area was chosen, which was part of a major forest clearing experiment conducted in Tomé Açu, a town located 250 km south of Belém, the capital of the Brazilian state of Pará. The entire biomass in the area was weighted with scales during the three weeks that followed the cut of the forest in July 1994. A detailed inventory was carried out in the area and then the indirect method was applied in the data. Seven different formulas for determining biomass were used. Comparison of the data of real mass and the mass obtained through the application of the seven formulas indicated that the more suitable for the region is given by FW = α · φβ · Hγ, where FW is total fresh weight (kg), φ is the diameter at breast height (cm), H is the total height of the tree and α, β and γ are regression coefficients (equal to 0.026, 1.529 and 1.747, respectively).

Equivalence of the Duffin-Kemmer-Petiau and Klein-Gordon-Fock equations

A strict proof of the equivalence of the Duffin-Kemmer-Petiau and Klein-Gordon Fock theories is presented for physical S-matrix elements in the case of charged scalar particles minimally interacting with an external or quantized electromagnetic field. The Hamiltonian canonical approach to the Duffin - Kemmer Petiau theory is first developed in both the component and the matrix form. The theory is then quantized through the construction of the generating functional for the Green's functions, and the physical matrix elements of the S-matrix are proved to be relativistic invariants. The equivalence of the two theories is then proved for the matrix elements of the scattered scalar particles using the reduction formulas of Lehmann, Symanzik, and Zimmermann and for the many-photon Green's functions.

Prescriptionless light-cone integrals

Perturbative quantum gauge field theory as seen within the perspective of physical gauge choices such as the light-cone gauge entails the emergence of troublesome poles of the type (k · n)-α in the Feynman integrals. These come from the boson field propagator, where α = 1, 2, ⋯ and nμ is the external arbitrary four-vector that defines the gauge proper. This becomes an additional hurdle in the computation of Feynman diagrams, since any graph containing internal boson lines will inevitably produce integrands with denominators bearing the characteristic gauge-fixing factor. How one deals with them has been the subject of research over decades, and several prescriptions have been suggested and tried in the course of time, with failures and successes. However, a more recent development at this fronteer which applies the negative dimensional technique to compute light-cone Feynman integrals shows that we can altogether dispense with prescriptions to perform the calculations. An additional bonus comes to us attached to this new technique, in that not only it renders the light-cone prescriptionless but, by the very nature of it, it can also dispense with decomposition formulas or partial fractioning tricks used in the standard approach to separate pole products of the type (k · n)-α[(k - p) · n]-β (β = 1, 2, ⋯). In this work we demonstrate how all this can be done.

Higher-dimensional twistor transforms using pure spinors

Hughston has shown that projective pure spinors can be used to construct massless solutions in higher dimensions, generalizing the four-dimensional twistor transform of Penrose. In any even (euclidean) dimension d = 2n, projective pure spinors parameterize the coset space SO(2n)/U(n), which is the space of all complex structures on ℝ2n. For d = 4 and d = 6, these spaces are ℂℙ1 and ℂℙ3 and the appropriate twistor transforms can easily be constructed. In this paper, we show how to construct the twistor transform for d > 6 when the pure spinor satisfies nonlinear constraints, and present explicit formulas for solutions of the massless field equations. © SISSA/ISAS 2005.