Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

Quantum current algebra for the AdS(5) x S(5) superstring

The sigma model describing the dynamics of the superstring in the AdS(5) x S(5) background can be constructed using the coset PSU(2, 2 vertical bar 4)/SO(4, 1) x SO(5). A basic set of operators in this two dimensional conformal field theory is composed by the left invariant currents. Since these currents are not (anti) holomorphic, their OPE`s is not determined by symmetry principles and its computation should be performed perturbatively. Using the pure spinor sigma model for this background, we compute the one-loop correction to these OPE`s. We also compute the OPE`s of the left invariant currents with the energy momentum tensor at tree level and one loop.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

The Bullough-Dodd model coupled to matter fields

The Bullough-Dodd model is an important two-dimensional integrable field theory which finds applications in physics and geometry. We consider a conformally invariant extension of it, and study its integrability properties using a zero curvature condition based on the twisted Kac-Moody algebra A(2)((2)). The one- and two-soliton solutions as well as the breathers are constructed explicitly. We also consider integrable extensions of the Bullough-Dodd model by the introduction of spinor (matter) fields. The resulting theories are conformally invariant and present local internal symmetries. All the one-soliton solutions, for two examples of those models, are constructed using a hybrid of the dressing and Hirota methods. One model is of particular interest because it presents a confinement mechanism for a given conserved charge inside the solitons. (C) 2008 Elsevier B.V. All rights reserved.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

Lie algebra methods for the applications to the statistical theory of turbulence

Approximate Lie symmetries of the Navier-Stokes equations are used for the applications to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to involve the Reynolds number dependence into scaling laws. Moreover, the optimal systems of all finite-dimensional Lie subalgebras of the approximate symmetry transformations of the Navier-Stokes are constructed. We show how the scaling groups obtained can be used to introduce the Reynolds number dependence into scaling laws explicitly for stationary parallel turbulent shear flows. This is demonstrated in the framework of a new approach to derive scaling laws based on symmetry analysis [11]-[13].

POLYNOMIAL IDENTITIES OF FINITE DIMENSIONAL SIMPLE ALGEBRAS

Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities.

The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras

We address two problems with the structure and representation theory of finite W-algebras associated with general linear Lie algebras. Finite W-algebras can be defined using either Kostant`s Whittaker modules or a quantum Hamiltonian reduction. Our first main result is a proof of the Gelfand-Kirillov conjecture for the skew fields of fractions of finite W-algebras. The second main result is a parameterization of finite families of irreducible Gelfand-Tsetlin modules using Gelfand-Tsetlin subalgebra. As a corollary, we obtain a complete classification of generic irreducible Gelfand-Tsetlin modules for finite W-algebras. (C) 2009 Elsevier Inc. All rights reserved.

Contravariantly finite subcategories closed under predecessors

Let A be an Artin algebra and mod A be the category of finitely generated right A-modules. We prove that an additive full subcategory C of mod A closed under predecessors is contravariantly finite if and only if its right Ext-orthogonal is covariantly finite, or if and only if the Ext-injectives in C define a cotilting module (over the support algebra of C) or, equivalently, if and only if C is the support of the representable functors given by the Ext-injectives. (C) 2009 Elsevier Inc. All rights reserved.

On invariant Rings of Sylow subgroups of finite classical groups

In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained a minimal generating set which is also a SAGBI basis. Moreover, we computed the relations among the generators and showed that the invariant ring for these groups are a complete intersection. This shows that, even though the invariant rings of the Sylow p-subgroups of the general linear group are polynomial, the same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant elds for the Sylow p-subgroups of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n and q. This is an important step in order to obtain the generators and relations for the invariant rings of all these groups.

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Two-dimensional position-dependent massive particles in the presence of magnetic fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Cortical Bone Stress Distribution in Mandibles with Different Configurations Restored with Prefabricated Bar-Prosthesis Protocol: A Three-Dimensional Finite-Element Analysis

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

Finite Element Stress Analysis of Edentulous Mandibles with Different Bone Types Supporting Multiple-Implant Superstructures

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

Periodontal ligament influence on the stress distribution in a removable partial denture supported by implant: a finite element analysis

Objective: The non-homogenous aspect of periodontal ligament (PDL) has been examined using finite element analysis (FEA) to better simulate PDL behavior. The aim of this study was to assess, by 2-D FEA, the influence of non-homogenous PDL on the stress distribution when the free-end saddle removable partial denture (RPD) is partially supported by an osseointegrated implant. Material and Methods: Six finite element (FE) models of a partially edentulous mandible were created to represent two types of PDL (non-homogenous and homogenous) and two types of RPD (conventional RPD, supported by tooth and fibromucosa; and modified RPD, supported by tooth and implant [10.00x3.75 mm]). Two additional FE models without RPD were used as control models. The non-homogenous PDL was modeled using beam elements to simulate the crest, horizontal, oblique and apical fibers. The load (50 N) was applied in each cusp simultaneously. Regarding boundary conditions the border of alveolar ridge was fixed along the x axis. The FE software (Ansys 10.0) was used to compute the stress fields, and the von Mises stress criterion (sigma vM) was applied to analyze the results. Results: The peak of sigma vM in non-homogenous PDL was higher than that for the homogenous condition. The benefits of implants were enhanced for the non-homogenous PDL condition, with drastic sigma vM reduction on the posterior half of the alveolar ridge. The implant did not reduce the stress on the support tooth for both PDL conditions. Conclusion: The PDL modeled in the non-homogeneous form increased the benefits of the osseointegrated implant in comparison with the homogeneous condition. Using the non-homogenous PDL, the presence of osseointegrated implant did not reduce the stress on the supporting tooth.