Simple components of the center of FG/J(FG)

Let G be a finite group, F a field, FG the group ring of G over F, and J(FG) the Jacobson radical of FG. Using a result of Berman and Witt, we give a method to determine the structure of the center of FG/J(FG), provided that F satisfies a field theoretical condition.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

New classes of spatial central configurations for the n+3-body problem

In this paper, we show the existence of new families of spatial central configurations for the n + 3-body problem, n >= 3. We study spatial central configurations where n bodies are at the vertices of a regular n-gon T and the other three bodies are symmetrically located on the straight line that is perpendicular to the plane that contains T and passes through the center of T. The results have simple and analytic proofs. (c) 2010 Elsevier Ltd. All rights reserved.

A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

Adaptação para a língua Portuguesa e aplicação de protocolo de avaliação das disartrias de origem central em pacientes com Doença de Parkinson

OBJETIVO: traduzir e adaptar protocolo desenvolvido por pesquisadores alemães, adequando-o às características fonéticas e linguísticas do português falado no Brasil. Caracterizar os componentes de fala mais alterados na população com doença de Parkinson, comparando-os com grupo de sujeitos normais na mesma faixa etária. MÉTODOS: realizou-se a tradução e adaptação do protocolo. Posteriormente foram avaliados 21 pacientes com diagnóstico neurológico de Doença de Parkinson nos estágios Hoehn &Yarh, entre 2 e 3, e 10 sujeitos normais. O protocolo incluía avaliação da respiração, fonação, ressonância, articulação, prosódia e a análise acústica dos parâmetros vocais. RESULTADOS: o protocolo mostrou-se de fácil aplicação clínica. Nos sujeitos com doença de Parkinson foram observadas alterações predominantes na fonação (85,9%) e articulação (42,9%). CONCLUSÃO: o estudo demonstrou ser o protocolo uma ferramenta eficiente para a avaliação da disartria em pacientes com doença de Parkinson.

Síndrome do incisivo central superior solitário: relato de caso

INTRODUÇÃO: a presença de um incisivo central superior solitário é um evento bastante incomum na população. A prevalência da chamada Síndrome do Incisivo Central Superior Solitário (SICSS) é verificada em 1:50.000 nascimentos, sendo registrado um maior acometimento no sexo feminino. Essa alteração no desenvolvimento da oclusão dentária é caracterizada por más formações estruturais, sobretudo na região de linha média do paciente. O diagnóstico precoce e o tratamento adequado dessa síndrome são de grande importância, pois essa condição talvez seja um indicativo de que o paciente pode apresentar outras más formações congênitas severas, não devendo ser a SICSS considerada uma simples anomalia dentária. Os procedimentos ortodônticos, nesses casos, variam dependendo do grau de comprometimento das estruturas ósseas da maxila, da oclusão em si, e principalmente da sutura palatina mediana. OBJETIVO: discutir, baseado em evidências científicas, aspectos importantes relacionados à SICSS, bem como apresentar um caso clínico de paciente do sexo feminino com SICSS, que foi submetida a tratamento ortodôntico na Clínica Odontológica Integrada Infantil da Universidade Federal de Santa Maria (UFSM) / RS. CONCLUSÃO: pela análise crítica da literatura, verifica-se ser muito importante o diagnóstico correto e precoce acerca dessa síndrome, visto que há possibilidade da mesma estar associada a outros problemas de desenvolvimento. Além disso, o paciente acometido pela SICSS deve ser assistido por uma equipe multidisciplinar de saúde, de forma a otimizar os resultados clínicos e devolver-lhe qualidade de vida.

Long-term treatment with alendronate increases the surgical difficulty during simple exodontias - an in vivo observation in Holtzman rats

Background: Atraumatic teeth extractions protocols are highly encouraged in patients taking bisphosphonates (Bps) to reduce surgical trauma and, consequently, the risk of jaws osteonecrosis development. In this way, this paper aims to report the findings of increased surgical difficulty during simple exodontias in animals treated with bisphosphonates.Methods: Sixty male Holtzman rats were randomly distributed into three groups of 20 animals and received daily subcutaneous administration of 1 mg/kg (AL1) or 3 mg/kg (AL3) of alendronate or saline solution (CTL). After 60 days of drug therapy all animals were submitted to first lower molars extractions under general anesthesia. Operatory surgical time and the frequency of teeth fractures were measured as principal outcomes and indicators of surgical difficulty degree.Results: Animals treated with alendronate (AL1 and AL3) were associated to higher operatory times and increased frequency of teeth fractures compared to match controls.Conclusions: The bisphosphonate therapy may be associated with an increased surgical difficulty and trauma following simple exodontias protocols, which is considered a critical issue when it comes to osteonecrosis development.

Some experiments with high order compact methods using a computer algebra software - Part I

We consider a procedure for obtaining a compact fourth order method to the steady 2D Navier-Stokes equations in the streamfunction formulation using the computer algebra system Maple. The resulting code is short and from it we obtain the Fortran program for the method. To test the procedure we have solved many cavity-type problems which include one with an analytical solution and the results are compared with results obtained by second order central differences to moderate Reynolds numbers. (c) 2005 Elsevier B.V. All rights reserved.

A simple graphical model of small mammal succession after fire in the Brazilian cerrado

We studied the succession of small mammal species after fire in the cerrado (Neotropical savanna) of Central Brazil. Populations of small mammals were sampled with live-trapping techniques in a series of nine sites of different successional age, ranging from 1 to 26 years after fire. Ten species of small mammals were captured through all the seral stages of succession. Species richness ranged from two to seven species by seral stage. The species were arranged in different groups with respect to abundance along the succession: the first was composed of early successional species that peaked <2 years after fire (Calomys callosus, C. tener, Thalpomys cerradensis, Mus musculus, Thylamys velutinus); the second occurred or peaked 2-3 years after fire (Necromys lasiurus, Gracilinanus sp., Oryzomys scoth). Gracilinanus agilis peaked in the last seral stage. Species richness of small mammals showed an abrupt decrease from an average of four species immediately after fire to two species 5-26 years after the last fire. We propose a simple graphical model to explain the pattern of species richness of small mammals after fire in the cerrado. This model assumes that the occurrence of species of small mammals is determined by habitat selection behavior by each species along a habitat gradient. The habitat gradient is defined as the ratio of cover of herbaceous to woody vegetation. The replacement of species results from a trade-off in habitat requirements for the two habitat variables.

Deformations of N=2 superconformal algebra and supersymmetric two-component Camassa-Holm equation

This paper is concerned with a link between central extensions of N = 2 superconformal algebra and a supersymmetric two-component generalization of the Camassa-Holm equation. Deformations of superconformal algebra give rise to two compatible bracket structures. One of the bracket structures is derived from the central extension and admits a momentum operator which agrees with the Sobolev norm of a co-adjoint orbit element. The momentum operator induces, via Lenard relations, a chain of conserved Hamiltonians of the resulting supersymmetric Camassa-Holm hierarchy.

A simple action for a free fractional spin particle

By studying classical realizations of the sl(2, R-fraktur sign) algebra in a two dimensional phase space (q,π), we have derived a continuous family of new actions for free fractional spin particles in 2 + 1 dimensions. For the case of light-like spin vector (SμSμ = 0), the action is remarkably simple. We show the appearence of the Zitterbewegung in the solutions of the equations of motion, and relate the actions to others in the literature at classical level. © 1997 Elsevier Science B.V.

Closed expressions for Lie algebra invariants and finite transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements requires the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.