SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Involutions and free pairs of bicyclic units in integral group rings

If * : G -> G is an involution on the finite group G, then * extends to an involution on the integral group ring Z[G] . In this paper, we consider whether bicyclic units u is an element of Z[G] exist with the property that the group < u, u*> generated by u and u* is free on the two generators. If this occurs, we say that (u, u*)is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, Z[G] contains a free bicyclic pair.

Cantor-Bernstein Sextuples for Banach Spaces

Let X and Y be Banach spaces isomorphic to complemented subspaces of each other with supplements A and B. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain a necessary and sufficient condition on the sextuples (p, q, r, s, u, v) in N with p + q >= 1, r + s >= 1 and u, v is an element of N*, to provide that X is isomorphic to Y, whenever these spaces satisfy the following decomposition scheme A(u) similar to X(P) circle plus Y(q) B(v) similar to X(r) circle plus Y(s). Namely, Phi = (p - u)(s - v) - (q + u)(r + v) is different from zero and Phi divides p + q and r + s. These sextuples are called Cantor-Bernstein sextuples for Banach spaces. The simplest case (1, 0, 0, 1, 1, 1) indicates the well-known Pelczynski`s decomposition method in Banach space. On the other hand, by interchanging some Banach spaces in the above decomposition scheme, refinements of the Schroeder-Bernstein problem become evident.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Group identities on symmetric units

Let F be an infinite field of characteristic different from 2, G a group and * an involution of G extended by linearity to an involution of the group algebra FG. Here we completely characterize the torsion groups G for which the *-symmetric units of FG satisfy a group identity. When * is the classical involution induced from g -> g(-1), g is an element of G, this result was obtained in [ A. Giambruno, S. K. Sehgal, A. Valenti, Symmetric units and group identities, Manuscripta Math. 96 (1998) 443-461]. (C) 2009 Elsevier Inc. All rights reserved.

Equivariant Nielsen root theory for G-maps

Let X be a compact Hausdorff space, Y be a connected topological manifold, f : X -> Y be a map between closed manifolds and a is an element of Y. The vanishing of the Nielsen root number N(f; a) implies that f is homotopic to a root free map h, i.e., h similar to f and h(-1) (a) = empty set. In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group. (C) 2010 Elsevier B.V. All rights reserved.

Stress distribution in the cervical region of an upper central incisor in a 3D finite element model

The aim of this study was to evaluate the stress distribution in the cervical region of a sound upper central incisor in two clinical situations, standard and maximum masticatory forces, by means of a 3D model with the highest possible level of fidelity to the anatomic dimensions. Two models with 331,887 linear tetrahedral elements that represent a sound upper central incisor with periodontal ligament, cortical and trabecular bones were loaded at 45º in relation to the tooth's long axis. All structures were considered to be homogeneous and isotropic, with the exception of the enamel (anisotropic). A standard masticatory force (100 N) was simulated on one of the models, while on the other one a maximum masticatory force was simulated (235.9 N). The software used were: PATRAN for pre- and post-processing and Nastran for processing. In the cementoenamel junction area, tensile forces reached 14.7 MPa in the 100 N model, and 40.2 MPa in the 235.9 N model, exceeding the enamel's tensile strength (16.7 MPa). The fact that the stress concentration in the amelodentinal junction exceeded the enamel's tensile strength under simulated conditions of maximum masticatory force suggests the possibility of the occurrence of non-carious cervical lesions such as abfractions.

Inverse analysis FOR two-dimensional structures using the boundary element method

Inverse analysis is currently an important subject of study in several fields of science and engineering. The identification of physical and geometric parameters using experimental measurements is required in many applications. In this work a boundary element formulation to identify boundary and interface values as well as material properties is proposed. In particular the proposed formulation is dedicated to identifying material parameters when a cohesive crack model is assumed for 2D problems. A computer code is developed and implemented using the BEM multi-region technique and regularisation methods to perform the inverse analysis. Several examples are shown to demonstrate the efficiency of the proposed model. (C) 2010 Elsevier Ltd. All rights reserved,

An electromechanical finite element model for piezoelectric energy harvester plates

Vibration-based energy harvesting has been investigated by several researchers over the last decade. The goal in this research field is to power small electronic components by converting the waste vibration energy available in their environment into electrical energy. Recent literature shows that piezoelectric transduction has received the most attention for vibration-to-electricity conversion. In practice, cantilevered beams and plates with piezoceramic layers are employed as piezoelectric energy harvesters. The existing piezoelectric energy harvester models are beam-type lumped parameter, approximate distributed parameter and analytical distributed parameter solutions. However, aspect ratios of piezoelectric energy harvesters in several cases are plate-like and predicting the power output to general (symmetric and asymmetric) excitations requires a plate-type formulation which has not been covered in the energy harvesting literature. In this paper. an electromechanically coupled finite element (FE) plate model is presented for predicting the electrical power output of piezoelectric energy harvester plates. Generalized Hamilton`s principle for electroelastic bodies is reviewed and the FE model is derived based on the Kirchhoff plate assumptions as typical piezoelectric energy harvesters are thin structures. Presence of conductive electrodes is taken into account in the FE model. The predictions of the FE model are verified against the analytical solution for a unimorph cantilever and then against the experimental and analytical results of a bimorph cantilever with a tip mass reported in the literature. Finally, an optimization problem is solved where the aluminum wing spar of an unmanned air vehicle (UAV) is modified to obtain a generator spar by embedding piezoceramics for the maximum electrical power without exceeding a prescribed mass addition limit. (C) 2009 Elsevier Ltd. All rights reserved.

Shell curvature as an initial deformation: A geometrically exact finite element approach

An alternative approach for the analysis of arbitrarily curved shells is developed in this paper based on the idea of initial deformations. By `alternative` we mean that neither differential geometry nor the concept of degeneration is invoked here to describe the shell surface. We begin with a flat reference configuration for the shell mid-surface, after which the initial (curved) geometry is mapped as a stress-free deformation from the plane position. The actual motion of the shell takes place only after this initial mapping. In contrast to classical works in the literature, this strategy enables the use of only orthogonal frames within the theory and therefore objects such as Christoffel symbols, the second fundamental form or three-dimensional degenerated solids do not enter the formulation. Furthermore, the issue of physical components of tensors does not appear. Another important aspect (but not exclusive of our scheme) is the possibility to describe exactly the initial geometry. The model is kinematically exact, encompasses finite strains in a totally consistent manner and is here discretized under the light of the finite element method (although implementation via mesh-free techniques is also possible). Assessment is made by means of several numerical simulations. Copyright (C) 2009 John Wiley & Sons, Ltd.

QUADRANT-SEARCHING: A NEW TECHNIQUE TO REDUCE THE SEARCH SPACE OF THE INVERSE PROBLEM OF EIT USING BEM TO THE DIRECT PROBLEM

The image reconstruction using the EIT (Electrical Impedance Tomography) technique is a nonlinear and ill-posed inverse problem which demands a powerful direct or iterative method. A typical approach for solving the problem is to minimize an error functional using an iterative method. In this case, an initial solution close enough to the global minimum is mandatory to ensure the convergence to the correct minimum in an appropriate time interval. The aim of this paper is to present a new, simple and low cost technique (quadrant-searching) to reduce the search space and consequently to obtain an initial solution of the inverse problem of EIT. This technique calculates the error functional for four different contrast distributions placing a large prospective inclusion in the four quadrants of the domain. Comparing the four values of the error functional it is possible to get conclusions about the internal electric contrast. For this purpose, initially we performed tests to assess the accuracy of the BEM (Boundary Element Method) when applied to the direct problem of the EIT and to verify the behavior of error functional surface in the search space. Finally, numerical tests have been performed to verify the new technique.

Connexin36, an Essential Element in the Rod Pathway, Is Highly Expressed in the Essentially Rodless Retina of Gallus gallus

Electrical coupling provided by connexins (Cx) in gap junctions (GJ) plays important roles in both the developing and the mature retina. In mammalian nocturnal species, Cx36 is an essential component in the rod pathway, the retinal circuit specialized for night, scotopic vision. Here, we report the expression of Cx36 in a species (Gallus gallus) that phylogenetic development endows with an essentially rodless retina. Cx36 gene is very highly expressed in comparison with other Cxs previously described in the adult retina, such as Cx43, Cx45, and Cx50. Moreover, real-time PCR, Western blot, and immunofluorescence all revealed that Cx36 expression massively increased over time during development. We thoroughly examined Cx36 in the inner and outer plexiform layers, where this protein was particularly abundant. Cx36 was observed mainly in the off sublamina of the inner plexiform layer rather than in the on sublamina previously described in the mammalian retina. In addition, Cx36 colocalized with specific cell markers, revealing the expression of this protein in distinct amacrine cells. To investigate further the involvement of Cx36 in visual processing, we examined its functional regulation in retinas from dark-adapted animals. Light deprivation markedly up-regulates Cx36 gene expression in the retina, resulting in an increased accumulation of the protein within and between cone synaptic terminals. In summary, the developmental regulation of Cx36 expression results in particular circuitry-related roles in the chick retina. Moreover, this study demonstrated that Cx36 onto- and phylogenesis in the vertebrate retina simultaneously exhibit similarities and particularities. J. Comp. Neurol. 512:651-663, 2009. (C) 2008 Wiley-Liss, Inc.

An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

Keratoconus prediction using a finite element model of the cornea with local biomechanical properties

PURPOSE: The ability to predict and understand which biomechanical properties of the cornea are responsible for the stability or progression of keratoconus may be an important clinical and surgical tool for the eye-care professional. We have developed a finite element model of the cornea, that tries to predicts keratoconus-like behavior and its evolution based on material properties of the corneal tissue. METHODS: Corneal material properties were modeled using bibliographic data and corneal topography was based on literature values from a schematic eye model. Commercial software was used to simulate mechanical and surface properties when the cornea was subject to different local parameters, such as elasticity. RESULTS: The simulation has shown that, depending on the corneal initial surface shape, changes in local material properties and also different intraocular pressures values induce a localized protuberance and increase in curvature when compared to the remaining portion of the cornea. CONCLUSIONS: This technique provides a quantitative and accurate approach to the problem of understanding the biomechanical nature of keratoconus. The implemented model has shown that changes in local material properties of the cornea and intraocular pressure are intrinsically related to keratoconus pathology and its shape/curvature.

Promoção da saúde: elemento instituinte?

O artigo inclui na discussão sobre os resultados da promoção da saúde um argumento de natureza epistemológica, levando em consideração o contexto contemporâneo de mudanças econômicas, políticas e culturais do qual ela é parte e expressão. Destacam-se, por um lado, as suspeitas que recaem sobre o projeto da Modernidade, sejam elas decorrentes do crescimento das incertezas ou da irrealização de promessas e, por outro lado, as tentativas de equacionamento do binômio determinação/autonomia, como questões sensíveis a uma ruptura dos modos de conhecer na contemporaneidade. Propõe-se considerar a dinâmica social e abordá-la como a união e a tensão da história feita e da história se fazendo, para melhor compreender o alcance e os resultados da promoção da saúde. A conclusão é que a promoção da saúde deve continuar buscando o desenvolvimento de ações cada vez mais efetivas, mas deve fazê-lo sem abdicar da possibilidade de manter-se próxima da energia social livre e em ebulição, que caracteriza o elemento instituinte de uma produção histórica.