Path formulation for Z(2) circle plus Z(2)-equivariant bifurcation problems

M. Manoel and I. Stewart 0101) classify Z(2) circle plus Z(2)-equivariant bifurcation problems up to codimension 3 and 1 modal parameter, using the classical techniques of singularity theory of Golubistky and Schaeffer [8]. In this paper we classify these same problems using an alternative form: the path formulation (Theorem 6.1). One of the advantages of this method is that the calculates to obtain the normal forms are easier. Furthermore, in our classification we observe the presence of only one modal parameter in the generic core. It differs from the classical classification where the core has 2 modal parameters. We finish this work comparing our classification to the one obtained in [10].

Reversible equivariant Hopf bifurcation

In this paper we study codimension-one Hopf bifurcation from symmetric equilibrium points in reversible equivariant vector fields. Such bifurcations are characterized by a doubly degenerate pair of purely imaginary eigenvalues of the linearization of the vector field at the equilibrium point. The eigenvalue movements near such a degeneracy typically follow one of three scenarios: splitting (from two pairs of imaginary eigenvalues to a quadruplet on the complex plane), passing (on the imaginary axis), or crossing (a quadruplet crossing the imaginary axis). We give a complete description of the behaviour of reversible periodic orbits in the vicinity of such a bifurcation point. For non-reversible periodic solutions. in the case of Hopf bifurcation with crossing eigenvalues. we obtain a generalization of the equivariant Hopf Theorem.

Finite group actions on products of spheres

In this work we make some contributions to the theory of actions of finite groups on products of spheres. Suppose that the group Z(q)(tau) acts freely on the product of k copies of spheres. Question: Is r less than or equal to k? We solve this question for several values of r and k.

D-n-forced symmetry breaking of O(2)-equivariant problems

We use singularity theory to classify forced symmetry-breaking bifurcation problemsf(z, lambda, mu) = f(1)(z, lambda) + muf(2)(z, lambda, mu) = 0,where f(1) is O(2)-equivariant and f(2) is D-n-equivariant with the orthogonal group actions on z is an element of R-2. Forced symmetry breaking occurs when the symmetry of the equation changes when parameters are varied. We explicitly apply our results to the branching of subharmonic solutions in a model periodic perturbation of an autonomous equation and sketch further applications.

Effects of self-assembly process of latex spheres on the final topology of macroporous silica

This paper surveys the topology of macroporous silica prepared using latex templates covering the submicrometric range (0.1-0.7 mu m). The behavior of latex spheres in aqueous dispersion has been analyzed by dynamic light scattering (DLS) measurement indicating the most appropriate conditions to form well-defined cubic arrays. The optical behavior of latex spheres has been analyzed by transmittance and reflectance measurements in order to determine their diameter and filling factor when they were assembled in bidimensional arrays. Macroscopic templates have been obtained by a centrifugation process and their crystalline ordering has been confirmed by porosimetry and scanning electron microscopy. These self-assembled structures have been used to produce macroporous silica, whose final topology depends on the pore size distribution of the original template. It has been seen that latex spheres are ordered in a predominant fcc arrangement with slipping of tetragonal pores due to the action of attractive electrostatic interactions. The main effect is to change the spherical shape of voids in macroporous silica into a hexagonal configuration with possible applications to fabricate photonic devices with novel optical properties. (c) 2005 Elsevier B.V. All rights reserved.

double-struck D signn-forced symmetry breaking of double-struck O sign (2)-equivariant problems

We use singularity theory to classify forced symmetry-breaking bifurcation problems f(z, λ, μ) = f1 (z, λ) + μf2(z, λ, μ) = 0, where f1 is double-struck O sign (2)-equivariant and f2 is double-struck D sign n-equivariant with the orthogonal group actions on z ∈ ℝ2. Forced symmetry breaking occurs when the symmetry of the equation changes when parameters are varied. We explicitly apply our results to the branching of subharmonic solutions in a model periodic perturbation of an autonomous equation and sketch further applications.

Path formulation for multiparameter D3-equivariant bifurcation problems

We implement a singularity theory approach, the path formulation, to classify D3-equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a Ba-miniversal unfolding f0 of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of F0 onto its unfolding parameter space. We apply our results to degenerate bifurcation of period-3 subharmonics in reversible systems, in particular in the 1:1-resonance.

Magnetic properties of synthetic eumelanin - Preliminary results

We report an experimental and theoretical study of magnetic properties of synthetic eumelanin. The magnetization curves are determined by using both a vibrating sample magnetometer and a superconducting quantum interferometer device in an extended range of magnetic fields ranging from -10 kOe to 10 kOe at different temperatures. We find that the eumelanin magnetization can be qualitatively explained in terms of a simple model of dipolar spheres with an intrinsic magnetic moment. The latter one is experimentally measured by using X-band electron paramagnetic resonance. Our findings indicate that synthetic melanins are superparamagnetic.

Esquizofrenia: intervenção em Instituição Pública de Saúde

Les premiers concepts de schizophrénie comprenaient des définitions non-spécifiques sur le trouble schizophrénique. Ce n est qu en 1980 que Crow a proposé la classification la plus connue pour ce trouble: la distinction en soustypes I et II, de symptomatologie positive ou négative, les symptômes du syndrome positif correspondant aux hallucinations et aux délires et ceux du syndrome négatif au repli affectif et à la pauvreté du discours. Bien que la thérapie médicamenteuse présente des avancées dans le traitement de la maladie, la psychothérapie est la plus indiquée pour remédier aux préjudices sociaux et interpersonnels que celle-ci provoque. L objectif de cette étude est de relater une intervention comportementale, dans un Centre de Soins Psychosocial, auprès d une patiente de 19 ans, en utilisant des Exercices de Réadaptation Psychosociale (SAT) en tant que la possibilité de traitement de la schizophrénie. Ce processus a contribué à une réduction du stéréotype de la maladie chez la jeune patiente, considérant qu elle a élargi son répertoire social et a rendu possible des avancées dans les sphères psychologique, sociale et professionnelle.

Electrochemical study of o-toluidine blue impregnated in mesoporous silica channels

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bacterial cellulose-silica organic-inorganic hybrids

Bacterial cellulose (BC) hydrated membranes present nanometric reticulated structure that can be used as a template in the preparation of new organic-inorganic hybrids. BC-silica hybrids were prepared from BC membranes and tetraethoxysilane, (TEOS) at neutral pH conditions at room temperature. Macroscopically homogeneous membranes were obtained containing up to 66 wt.% of silica spheres, 20-30 nm diameter. Scanning electron micrographs clearly show the silica spheres attached to cellulose microfibrils. By removing the cellulose, the silica spheres can be easily recovered. The new hybrids are stable up to 300 degrees C and display a broad emission band under UV excitation assigned to oxygen-related defects at the silica particles surface. Emission color can be tuned by changing the excitation wavelength.

Carbon-coated SnO2 nanobelts and nanoparticles by single catalytic step

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)