On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.

Representation type of Jordan algebras

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved.

Galois orders in skew monoid rings

We introduce a new class of noncommutative rings - Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Calms orders generalizes classical orders in noncommutative rings and contains many important examples, such as the Generalized Weyl algebras, the universal enveloping algebra of the general linear Lie algebra, associated Yangians and finite W-algebras (C) 2010 Elsevier Inc All rights reserved

On Polar Foliations and the Fundamental Group

In this work we investigate the relation between the fundamental group of a complete Riemannian manifold M and the quotient between the Weyl group and reflection group of a polar action on M, as well as the relation between the fundamental group of M and the quotient between the lifted Weyl group and lifted reflection group. As applications we give alternative proofs of two results. The first one, due to the author and Toben, implies that a polar action does not admit exceptional orbits, if M is simply connected. The second result, due to Lytchak, implies that the orbits are closed and embedded if M is simply connected. All results are proved in the more general case of polar foliations.

Hamiltonian constraint analysis of vector field theories with spontaneous Lorentz symmetry breaking

Recent investigations of various quantum-gravity theories have revealed a variety of possible mechanisms that lead to Lorentz violation. One of the more elegant of these mechanisms is known as Spontaneous Lorentz Symmetry Breaking (SLSB), where a vector or tensor field acquires a nonzero vacuum expectation value. As a consequence of this symmetry breaking, massless Nambu-Goldstone modes appear with properties similar to the photon in Electromagnetism. This thesis considers the most general class of vector field theories that exhibit spontaneous Lorentz violation-known as bumblebee models-and examines their candidacy as potential alternative explanations of E&M, offering the possibility that Einstein-Maxwell theory could emerge as a result of SLSB rather than of local U(1) gauge invariance. With this aim we employ Dirac's Hamiltonian Constraint Analysis procedure to examine the constraint structures and degrees of freedom inherent in three candidate bumblebee models, each with a different potential function, and compare these results to those of Electromagnetism. We find that none of these models share similar constraint structures to that of E&M, and that the number of degrees of freedom for each model exceeds that of Electromagnetism by at least two, pointing to the potential existence of massive modes or propagating ghost modes in the bumblebee theories.

Vector Theory of Spontaneous Lorentz Violation

Classical electromagnetism predicts two massless propagating modes, which are known as the two polarizations of the photon. On the other hand, if the Lorentz symmetry of classical electromagnetism is spontaneously broken, the new theory will still have two massless Nambu-Goldstone modes resembling the photon. If the Lorentz symmetry is broken by a bumblebee potential that allows for excitations out of the minimum, then massive modes arise. Furthermore, in curved spacetime, such massive modes will be created through a process other than the usual Higgs mechanism because of the dependence of the bumblebee potential on both the vector field and the metric tensor. Also, it is found that these massive modes do not propagate due to the extra constraints.

Uma implementação geral de elementos de contorno e sua aplicação a problemas de flexão de placas

o presente trabalho aborda a aplicação do método dos elementos de contorno (MEC) para solução de problemas de flexão linear e geometricamente não-linear de placas semiespessas. Os modelos de placa empregados consideraram a influência do cisalhamento através de teorias de primeira ordem, especificamente as de Mindlin e Reissner. Uma formulação integral unificada dos modelos de placa utilizados é desenvolvida para o operador de Navier do problema, onde foram mantidos alguns termos de ordem superior no tensor deformação de Green. A formulação integral do problema de membrana acoplado ao de flexão é igualment desenvolvida, levando a um sistema de equações integrais não-lineares que descreve completamente problemas de placas que envolvem grandes deslocamentos. Estas equações podem ser particularizadas para problemas de flexão linear e estabilidade elástica. Tendo em vista a necessidade de se considerar derivadas dos deslocamentos translacionais, as equações integrais correspondentes ao gradiente dos deslocamentos também foram deduzidas, caracterizando uma formulação hipersingular. o método empregado para solução numérica do sistema de equações integrais foi o método direto dos elementos de contorno. Um tratamento das integrais fortemente singulares presentes nas equações foi realizado, baseado em expansões assint6ticas dos núcleos. Deste procedimento resulta uma abordagem regularizada que emprega apenas quadraturas padrão de Gauss-Legendre.

Ondas e instabilidades em plasmas com inomogeneidades suaves na densidade e no campo magnético de equilíbrio

No presente trabalho, estudamos a absorção e amplificação de ondas eletromagnéticas que se propagam em plasmas com densidade e temperatura fracamente inomogêneas, imersos em um campo magnético também inomogêneo, tendo como base a teoria cinética, dentro do contexto da aproximação local. Esse estudo se dá efetivamente a partir da obtenção do tensor dielétrico do plasma, que deve ser empregado na relação de dispersão. Iniciamos com uma revisão dos conceitos básicos sobre plasmas homogêneos e inomogêneos. Os fundamentos da teoria cinética também foram abordados. Apresentamos uma revisão de trabalhos anteriores que enfocam o mesmo tema, embora descrevendo separadamente os dois tipos de inomogeneidades. A partir desses trabalhos, obtivemos um tensor dielétrico geral, que descreve de forma simultânea as inomogeneidades do campo magnético de equilíbrio e da função distribuição de equilíbrio.Tal tensor foi obtido a partir de um sólido desenvolvimento teórico, que garante a correta descrição da troca de energia entre as ondas e as partículas do plasma. Abordamos os aspectos gerais das instabilidades de deriva, direcionando o estudo à faixa de frequência das ondas híbridas inferiores, e às instabilidades LHDI e MTSI (IWI). Utilizamos perfis lineares de inomogeneidades de campo magnêtico ambiente e densidade para modelar a região da magnetosfera conhecida como neutral sheet. Particularizamos o tensor dielétrico para o estudo específico das instabilidades LHDI e MTSI (IWI), para o tipo de perfil citado acima. Apresentamos uma nova rela»c~ao de dispers~ao para plasmas inomogêneos, que incorpora explicitamente as derivadas espaciais do tensor dielétrico do plasma. Usamos o tensor que unifica os tratamentos das inomogeneidades do campo e densidade nessa relação de dispersão, e obtivemos uma descrição unificada das instabilidades LHDI e MTSI (IWI).

Remoção de ruídos sísmicos utilizando transformada de wavelet 1D e 2D com software em desenvolvimento

In the Hydrocarbon exploration activities, the great enigma is the location of the deposits. Great efforts are undertaken in an attempt to better identify them, locate them and at the same time, enhance cost-effectiveness relationship of extraction of oil. Seismic methods are the most widely used because they are indirect, i.e., probing the subsurface layers without invading them. Seismogram is the representation of the Earth s interior and its structures through a conveniently disposed arrangement of the data obtained by seismic reflection. A major problem in this representation is the intensity and variety of present noise in the seismogram, as the surface bearing noise that contaminates the relevant signals, and may mask the desired information, brought by waves scattered in deeper regions of the geological layers. It was developed a tool to suppress these noises based on wavelet transform 1D and 2D. The Java language program makes the separation of seismic images considering the directions (horizontal, vertical, mixed or local) and bands of wavelengths that form these images, using the Daubechies Wavelets, Auto-resolution and Tensor Product of wavelet bases. Besides, it was developed the option in a single image, using the tensor product of two-dimensional wavelets or one-wavelet tensor product by identities. In the latter case, we have the wavelet decomposition in a two dimensional signal in a single direction. This decomposition has allowed to lengthen a certain direction the two-dimensional Wavelets, correcting the effects of scales by applying Auto-resolutions. In other words, it has been improved the treatment of a seismic image using 1D wavelet and 2D wavelet at different stages of Auto-resolution. It was also implemented improvements in the display of images associated with breakdowns in each Auto-resolution, facilitating the choices of images with the signals of interest for image reconstruction without noise. The program was tested with real data and the results were good

Avaliação mesoscópica da origem, distribuição e ramificação do nervo radial no braço do gato doméstico (Felis catus domesticus, Linnaeus, 1758)

The present study evaluated the origin, distribution and ramification of the radial nerves were studied in 30 adult domestic cats. The sample included 15 females and 15 males of unknown breed. The specimens were fixed in 10% formaldehyde solution. The radial nerve showed many fascicles from the origin also your ramification in superficial and deep branches. Radial nerves were observed to originate, in 16 cases (26.7%), from the ventral branch of the sixth cervical spinal nerve; in 60 cases (100%), from the ventral branch of the seventh cervical spinal nerve; in 60 cases (100%), from the ventral branch of the eight cervical nerve and in 60 cases (100%), from the ventral branch of the first thoracic nerve. The radial nerves branched out, in all of the animals studied (100.0%), to the tensor fasciae antebrachii, long, accessory, medial and lateral heads of the triceps branchii and anconeus muscles. The radial nerve emits of 14 to 25 nervous branches in this region. However, the branch of the sixth cervical spinal nerve and the nervous fascicles reveal significant differences (p <= 0.05), respectively, in or with relation to sex of the animals and the studied region.

Dispositivos planares integrados utilizando método dinâmico com metamateriais e PBG

This work presents a theoretical, numerical and computation analysis of parameters of a rectangular microstrip antenna with metamaterial substrate, fin line as a coupler and also integrated devices like integrated filter antenna. It is applied theory to full-wave of Transverse Transmission Line - TTL method, to characterize the magnitude of the substrate and obtain the general equations of the electromagnetic fields. About the metamaterial, they are characterized by permittivity and permeability tensor, reaching to the general equations for the electromagnetic fields of the antenna. It is presented a study about main representation of PBG(Photonic Band Gap) material and its applied for a specific configuration. A few parameters are simulated some structures in order to reduce the physical dimensions and increase the bandwidth. The results are presented through graphs. The theoretical and computational analysis of this work have shown accurate and relatively concise. Conclusions are drawn and suggestions for future work

Confinamento de fónons ópticos em estruturas piezoelétricas periódicas e quasiperiódicas

We study the optical-phonon spectra in periodic and quasiperiodic (Fibonacci type) superlattices made up from III-V nitride materials (GaN and AlN) intercalated by a dielectric material (silica - SiO2). Due to the misalignments between the silica and the GaN, AlN layers that can lead to threading dislocation of densities as high as 1010 cm−1, and a significant lattice mismatch (_ 14%), the phonon dynamics is described by a coupled elastic and electromagnetic equations beyond the continuum dielectric model, stressing the importance of the piezoelectric polarization field in a strained condition. We use a transfer-matrix treatment to simplify the algebra, which would be otherwise quite complicated, allowing a neat analytical expressions for the phonon dispersion relation. Furthermore, a quantitative analysis of the localization and magnitude of the allowed band widths in the optical phonon s spectra, as well as their scale law are presented and discussed

Condições de energia de hawking e ellis e a equação de raychaudhuri

In the Einstein s theory of General Relativity the field equations relate the geometry of space-time with the content of matter and energy, sources of the gravitational field. This content is described by a second order tensor, known as energy-momentum tensor. On the other hand, the energy-momentum tensors that have physical meaning are not specified by this theory. In the 700s, Hawking and Ellis set a couple of conditions, considered feasible from a physical point of view, in order to limit the arbitrariness of these tensors. These conditions, which became known as Hawking-Ellis energy conditions, play important roles in the gravitation scenario. They are widely used as powerful tools for analysis; from the demonstration of important theorems concerning to the behavior of gravitational fields and geometries associated, the gravity quantum behavior, to the analysis of cosmological models. In this dissertation we present a rigorous deduction of the several energy conditions currently in vogue in the scientific literature, such as: the Null Energy Condition (NEC), Weak Energy Condition (WEC), the Strong Energy Condition (SEC), the Dominant Energy Condition (DEC) and Null Dominant Energy Condition (NDEC). Bearing in mind the most trivial applications in Cosmology and Gravitation, the deductions were initially made for an energy-momentum tensor of a generalized perfect fluid and then extended to scalar fields with minimal and non-minimal coupling to the gravitational field. We also present a study about the possible violations of some of these energy conditions. Aiming the study of the single nature of some exact solutions of Einstein s General Relativity, in 1955 the Indian physicist Raychaudhuri derived an equation that is today considered fundamental to the study of the gravitational attraction of matter, which became known as the Raychaudhuri equation. This famous equation is fundamental for to understanding of gravitational attraction in Astrophysics and Cosmology and for the comprehension of the singularity theorems, such as, the Hawking and Penrose theorem about the singularity of the gravitational collapse. In this dissertation we derive the Raychaudhuri equation, the Frobenius theorem and the Focusing theorem for congruences time-like and null congruences of a pseudo-riemannian manifold. We discuss the geometric and physical meaning of this equation, its connections with the energy conditions, and some of its several aplications.

Teoria cinética não extensiva: efeitos físicos em gases e plasmas

The standard kinetic theory for a nonrelativistic diluted gas is generalized in the spirit of the nonextensive statistic distribution introduced by Tsallis. The new formalism depends on an arbitrary q parameter measuring the degree of nonextensivity. In the limit q = 1, the extensive Maxwell-Boltzmann theory is recovered. Starting from a purely kinetic deduction of the velocity q-distribution function, the Boltzmann H-teorem is generalized for including the possibility of nonextensive out of equilibrium effects. Based on this investigation, it is proved that Tsallis' distribution is the necessary and sufficient condition defining a thermodynamic equilibrium state in the nonextensive context. This result follows naturally from the generalized transport equation and also from the extended H-theorem. Two physical applications of the nonextensive effects have been considered. Closed analytic expressions were obtained for the Doppler broadening of spectral lines from an excited gas, as well as, for the dispersion relations describing the eletrostatic oscillations in a diluted electronic plasma. In the later case, a comparison with the experimental results strongly suggests a Tsallis distribution with the q parameter smaller than unity. A complementary study is related to the thermodynamic behavior of a relativistic imperfect simple fluid. Using nonequilibrium thermodynamics, we show how the basic primary variables, namely: the energy momentum tensor, the particle and entropy fluxes depend on the several dissipative processes present in the fluid. The temperature variation law for this moving imperfect fluid is also obtained, and the Eckart and Landau-Lifshitz formulations are recovered as particular cases

Influência das propriedades estruturais e magnetostrictivas na dinâmica da magnetização de multicamadas magnéticas amorfas

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