ON THREE-PARAMETER FAMILIES of FILIPPOV SYSTEMS - THE FOLD-SADDLE SINGULARITY

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

Three-parameter soil-water transient equations in horizontal water-transport analysis

For data obtained from horizontal soil column experiments, the determination of soil-water transport characteristics and functions would be aided by a single-form equation capable of objectively describing water content theta vs. time t at given position x(f). Our study was conducted to evaluate two such possible equations, one having the form of the Weibull frequency distribution, and the other being called a bipower form. Each equation contained three parameters, and was fitted by nonlinear least squares to the experimental data from three separate columns of a single soil. Across the theta range containing the measured data points obtained by gamma-ray attenuation, the two equations were in close agreement. The resulting family of theta(x(f),t) transients, as obtained from either equation, enabled the evaluation of exponent n in the t(n) dependence of the positional advance of a given theta. Not only was n found to be <0.5 at low theta values, but it also increased with theta and tended toward 0.5 as theta approached its sated (near-saturated) value. Some quantitative uncertainty in n(theta) does arise due to the reduced number of data points available at the higher water contents. Without claiming non-Boltzmann behavior (n < 0.5) as necessarily representative of all soils, we nonetheless consider n(theta) to be worthy of further study for evaluating its significance and implications.

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].

Hopf-zero bifurcations of reversible vector fields

We study the dynamics of a class of reversible vector fields having eigenvalues (0, alphai, -alphai) around their symmetric equilibria. We give a complete list of all normal forms for such vector fields, their versal unfoldings, and the corresponding bifurcation diagrams of the codimensional-one case. We also obtain some important conclusions on the existence of homoclinic and heteroclinic orbits, invariant tori and symmetric periodic orbits.

Double-blind comparison of venlafaxine and amitriptyline in outpatients with major depression with or without melancholia

The purpose of this study was to compare the efficacy and tolerability of venlafaxine and amitriptyline in outpatients with major depression with or without melancholia. This was an 8-week, multicentre, randomized, double-blind, parallel-group comparison of venlafaxine and amitriptyline. Outpatients with DSM-IV major depression, a minimum score of 20 on the 21-item Hamilton Depression Rating Scale (HAM-D), and depressive symptoms for at least 1 month were eligible. Patients were randomly assigned to venlafaxine or amitriptyline, both drugs titrated to a maximum of 150 mg/day until study day 15. The primary efficacy variables were the final on-therapy scores on the HAM-D, Montgomery-Asberg Depression Rating Scale and Clinical Global Impression severity scales. Data were evaluated on an intent-to-treat basis using the LOCF method. One hundred and 16 patients were randomized, and 115 were evaluated for efficacy. Both drugs showed efficacy in the treatment of depression with or without melancholia. No significant differences were noted between treatments for any efficacy parameter. However, significantly (p < 0.05) more patients in the amitriptyline group had at least one adverse event. These results should support the efficacy and tolerability of venlafaxine in comparison with amitriptyline for treating major depression with or without melancholia.

Neutrinoless double beta decay with and without Majoron-like boson emission in a 3-3-1 model

We consider the contributions to the neutrinoless double beta decays in a SU(3)L⊗U(1)N electroweak model. We show that for a range of parameters in the model there are diagrams involving vector-vector-scalar and trilinear scalar couplings which can be potentially as contributing as the light massive Majorana neutrino exchange one. We use these contributions to obtain constraints upon some mass scales of the model, such as the masses of the new charged vector and scalar bosons. We also consider briefly the decay in which, in addition to the two electrons, a Majoron-like boson is emitted. ©2001 The American Physical Society.

A note on non-degenerate umbilics and the path formulation for bifurcation problems

Path formulation can be used to classify and structure efficiently multiparameter bifurcation problems around fundamental singularities: the cores. The non-degenerate umbilic singularities are the generic cores for four situations in corank 2: the general or gradient problems and the ℤ 2-equivariant (general or gradient) problems. Those categories determine an interesting 'Russian doll' type of structure in the universal unfoldings of the umbilic singularities. One advantage of our approach is that we can handle one, two or more parameters using the same framework (even considering some special parameter structure, for instance, some internal hierarchy). We classify the generic bifurcations that occur in those cases with one or two parameters.

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.

Generic bifurcation of refracted systems

In this article we discuss some qualitative and geometric aspects of non-smooth dynamical systems theory. Our goal is to study the diagram bifurcation of typical singularities that occur generically in one parameter families of certain piecewise smooth vector fields named Refracted Systems. Such systems has a codimension-one submanifold as its discontinuity set. © 2012 Elsevier Ltd.

Comportamento dinâmico não-linear de um sistema mecânico com vibrações associadas a uma transição brusca na rigidez

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Avaliação do efeito de janela e descoloração nos filtros Wiener-Hopf

A presente dissertação consta de estudos sobre deconvolução sísmica, onde buscamos otimizar desempenhos na operação de suavização, na resolução da estimativa da distribuição dos coeficientes de reflexão e na recuperação do pulso-fonte. Os filtros estudados são monocanais, e as formulações consideram o sismograma como o resultado de um processo estocástico estacionário, e onde demonstramos os efeitos de janelas e de descoloração. O principio aplicado é o da minimização da variância dos desvios entre o valor obtido e o desejado, resultando no sistema de equações normais Wiener-Hopf cuja solução é o vetor dos coeficientes do filtro para ser aplicado numa convolução. O filtro de deconvolução ao impulso é desenhado considerando a distribuição dos coeficientes de reflexão como uma série branca. O operador comprime bem os eventos sísmicos a impulsos, e o seu inverso é uma boa aproximação do pulso-fonte. O janelamento e a descoloração melhoram o resultado deste filtro. O filtro de deconvolução aos impulsos é desenhado utilizando a distribuição dos coeficientes de reflexão. As propriedades estatísticas da distribuição dos coeficientes de reflexão tem efeito no operador e em seu desempenho. Janela na autocorrelação degrada a saída, e a melhora é obtida quando ela é aplicada no operador deconvolucional. A transformada de Hilbert não segue o princípio dos mínimos-quadrados, e produz bons resultados na recuperação do pulso-fonte sob a premissa de fase-mínima. O inverso do pulso-fonte recuperado comprime bem os eventos sísmicos a impulsos. Quando o traço contém ruído aditivo, os resultados obtidos com auxilio da transformada de Hilbert são melhores do que os obtidos com o filtro de deconvolução ao impulso. O filtro de suavização suprime ruído presente no traço sísmico em função da magnitude do parâmetro de descoloração utilizado. A utilização dos traços suavizados melhora o desempenho da deconvolução ao impulso. A descoloração dupla gera melhores resultados do que a descoloração simples. O filtro casado é obtido através da maximização de uma função sinal/ruído. Os resultados obtidos na estimativa da distribuição dos coeficientes de reflexão com o filtro casado possuem melhor resolução do que o filtro de suavização.

Estimativas inferiores para dimensão de Hausdorff de repulsores não-uniformemente expansores

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Linear parameter varying control design for rotating systems supported by journal bearings

Linear parameter varying (LPV) control is a model-based control technique that takes into account time-varying parameters of the plant. In the case of rotating systems supported by lubricated bearings, the dynamic characteristics of the bearings change in time as a function of the rotating speed. Hence, LPV control can tackle the problem of run-up and run-down operational conditions when dynamic characteristics of the rotating system change significantly in time due to the bearings and high vibration levels occur. In this work, the LPV control design for a flexible shaft supported by plain journal bearings is presented. The model used in the LPV control design is updated from unbalance response experimental results and dynamic coefficients for the entire range of rotating speeds are obtained by numerical optimization. Experimental implementation of the designed LPV control resulted in strong reduction of vibration amplitudes when crossing the critical speed, without affecting system behavior in sub- or supercritical speeds. (C) 2012 Elsevier Ltd. All rights reserved.

Buccal Bone Plate Remodeling After Immediate Implant Placement With and Without Synthetic Bone Grafting and Flapless Surgery: Radiographic Study in Dogs

Recent studies in animals have shown pronounced resorption of the buccal bone plate after immediate implantation. The use of flapless surgical procedures prior to the installation of immediate implants, as well as the use of synthetic bone graft in the gaps represent viable alternatives to minimize buccal bone resorption and to favor osseointegration. The aim of this study was to evaluate the healing of the buccal bone plate following immediate implantation using the flapless approach, and to compare this process with sites in which a synthetic bone graft was or was not inserted into the gap between the implant and the buccal bone plate. Lower bicuspids from 8 dogs were bilaterally extracted without the use of flaps, and 4 implants were installed in the alveoli in each side of the mandible and were positioned 2.0 mm from the buccal bone plate (gap). Four groups were devised: 2.0-mm subcrestal implants (3.3 x 8 mm) using bone grafts (SCTG), 2.0-mm subcrestal implants without bone grafts (SCCG), equicrestal implants (3.3 x 10 mm) with bone grafts (EGG), and equicrestal implants without bone grafts (ECCG). One week following the surgical procedures, metallic prostheses were installed, and within 12 weeks the dogs were sacrificed. The blocks containing the individual implants were turned sideways, and radiographic imaging was obtained to analyze the remodeling of the buccal bone plate. In the analysis of the resulting distance between the implant shoulder and the bone crest, statistically significant differences were found in the SCTG when compared to the ECTG (P = .02) and ECCG (P = .03). For mean value comparison of the resulting linear distance between the implant surface and the buccal plate, no statistically significant difference was found among all groups (P > .05). The same result was observed in the parameter for presence or absence of tissue formation between the implant surface and buccal plate. Equicrestally placed implants, in this methodology, presented little or no loss of the buccal bone. The subcrestally positioned implants presented loss of buccal bone, even though synthetic bone graft was used. The buccal bone, however, was always coronal to the implant shoulder.

Hero's journey in bifurcation diagram

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films. (C) 2011 Elsevier B.V. All rights reserved.