A class of singular first order differential equations with applications in reaction-diffusion

Agências Financiadoras: FCT e MIUR

Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

A 5GHz/1.8V CMOS Active Balun Integrated with LNA

The development of high performance monolithic RF front-ends requires innovative RF circuit design to make the best of a good technology. A fully differential approach is usually preferred, due to its well-known properties. Although the differential approach must be preserved inside the chip, there are cases where the input signal is single-ended such as RF image filters and IF filters in a RF receiver. In these situations, a stage able to convert single-ended into differential signals (balun) is needed. The most cited topology, which is capable of providing high gain, consists on a differential stage with one of the two inputs grounded. Unfortunately, this solution has some drawbacks when implemented monolithically. This work presents the design and simulated results of an innovative high-performance monolithic single to differential converter, which overcomes the limitations of the circuits.The integration of the monolithic active balun circuit with an LNA on a 0.18μm CMOS process is also reported. The circuits presented here are aimed at 802.11a. Section 2 describes the balun circuit and section 3 presents its performance when it is connected to a conventional single-ended LNA. Section 4 shows the simulated performance results focused at phase/amplitude balance and noise figure. Finally, the last section draws conclusions and future work.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

Lesões da substância branca por ressonância magnética: uma avaliação entre as ponderações DWI e T2 FLAIR

RESUMO: Objetivos – Determinar a sensibilidade e especificidade das ponderações Difusão (DWI) e T2 Fluid-Attenuated Inversion Recovery (FLAIR) na avaliação de lesões da substância branca (SB) e verificar em que medida se complementam, por forma a criar um conjunto de boas práticas na RM cranioencefálica de rotina. Metodologia – Recorrendo-se a uma metodologia quantitativa, efetuou-se uma análise retrospetiva da qual foram selecionados 30 pacientes, 10 sem patologia e 20 com patologia (2 com EM, 7 com Leucoencefalopatia, 6 com doença microangiopática e 5 com patologia da substância branca indefinida). Obteve-se uma amostra de 60 imagens, nomeadamente: 30 imagens ponderadas em DWI e 30 em T2 FLAIR. Recorrendo ao programa Viewdex®, três observadores avaliaram um conjunto de imagens segundo sete critérios: visibilidade, deteção, homogeneidade, localização, margens e dimensões da lesão e capacidade de diagnóstico. Com os resultados obtidos recorreu-se ao cálculo de sensibilidade e especificidade pelas Curvas ROC, bem como à análise estatística, nomeadamente, Teste-T, Índice de Concordância Kappa e coeficiente de correlação de Pearson entre as variáveis em estudo. Resultados – Os resultados de sensibilidade e de especificidade obtidos para a ponderação T2 FLAIR foram superiores (0,915 e 0,038, respetivamente) aos da ponderação DWI (0,08 e 0,100, respetivamente). Não se verificaram variâncias populacionais significativas. Obteve-se uma elevada correlação linear entre as variáveis com um valor r situado entre 0,8 e 0,99. Verificou-se também uma variabilidade considerável entre os observadores. Conclusões – Dados os baixos valores de sensibilidade e especificidade obtidos para a DWI, sugere-se que esta deva ser incluída no protocolo de rotina de crânio como auxiliar no diagnóstico diferencial com outras patologias.

Capillary bridging and long-range attractive forces in a mean-field approach

When a mixture is confined, one of the phases can condense out. This condensate, which is otherwise metastable in the bulk, is stabilized by the presence of surfaces. In a sphere-plane geometry, routinely used in atomic force microscope and surface force apparatus, it, can form a bridge connecting the surfaces. The pressure drop in the bridge gives rise to additional long-range attractive forces between them. By minimizing the free energy of a binary mixture we obtain the force-distance curves as well as the structural phase diagram of the configuration with the bridge. Numerical results predict a discontinuous transition between the states with and without the bridge and linear force-distance curves with hysteresis. We also show that similar phenomenon can be observed in a number of different systems, e.g., liquid crystals and polymer mixtures. (C). 2004 American Institute of Physics.

The shape of soap films and Plateau borders

We have calculated the shapes of flat liquid films, and of the transition region to the associated Plateau borders (PBs), by integrating the Laplace equation with a position-dependent surface tension γ(x), where 2x is the local film thickness. We discuss films in either zero or non-zero gravity, using standard γ(x) potentials for the interaction between the two bounding surfaces. We have investigated the effects of the film flatness, liquid underpressure, and gravity on the shape of films and their PBs. Films may exhibit 'humps' and/or 'dips' associated with inflection points and minima of the film thickness. Finally, we propose an asymptotic analytical solution for the film width profile.

Tris(2-Ethylhexyl) trimellitate (TOTM) a potential reference fluid for high viscosity. Part II: density measurements at temperatures from (293 to 373)K and pressures up to 85MPa

In Part I of the present work we describe the viscosity measurements performed on tris(2-ethylhexyl) trimellitate or 1,2,4-benzenetricarboxylic acid, tris(2-ethylhexyl) ester (TOTM) up to 65 MPa and at six temperatures from (303 to 373)K, using a new vibrating-wire instrument. The main aim is to contribute to the proposal of that liquid as a potential reference fluid for high viscosity, high pressure and high temperature. The present Part II is dedicated to report the density measurements of TOTM necessary, not only to compute the viscosity data presented in Part I, but also as complementary data for the mentioned proposal. The present density measurements were obtained using a vibrating U-tube densimeter, model DMA HP, using model DMA5000 as a reading unit, both instruments from Anton Paar GmbH. The measurements were performed along five isotherms from (293 to 373)K and at eleven different pressures up to 68 MPa. As far as the authors are aware, the viscosity and density results are the first, above atmospheric pressure, to be published for TOTM. Due to TOTM's high viscosity, its density data were corrected for the viscosity effect on the U-tube density measurements. This effect was estimated using two Newtonian viscosity standard liquids, 20 AW and 200 GW. The density data were correlated with temperature and pressure using a modified Tait equation. The expanded uncertainty of the present density results is estimated as +/- 0.2% at a 95% confidence level. Those results were correlated with temperature and pressure by a modified Tait equation, with deviations within +/- 0.25%. Furthermore, the isothermal compressibility, K-T, and the isobaric thermal expansivity, alpha(p), were obtained by derivation of the modified Tait equation used for correlating the density data. The corresponding uncertainties, at a 95% confidence level, are estimated to be less than +/- 1.5% and +/- 1.2%, respectively. No isobaric thermal expansivity and isothermal compressibility for TOTM were found in the literature. (C) 2014 Elsevier B.V. All rights reserved.

Experimental apparatus for finger ECG biometrics

Current Electrocardiographic (ECG) signal acquisition methods are generally highly intrusive, as they involve the use of pre-gelled electrodes and cabled sensors placed directly on the person, at the chest or limbs level. Moreover, systems that make use of alternative conductive materials to overcome this issue, only provide heart rate information and not the detailed signal itself. We present a comparison and evaluation of two types of dry electrodes as interface with the skin, targeting wearable and low intrusiveness applications, which enable ECG measurement without the need for any apparatus permanently fitted to the individual. In particular, our approach is targeted at ECG biometrics using signals collected at the hand or finger level. A custom differential circuit with virtual ground was also developed for enhanced usability. Our work builds upon the current stateof-the-art in sensoring devices and processing tools, and enables novel data acquisition settings through the use of dry electrodes. Experimental evaluation was performed for Ag/AgCl and Electrolycra materials, and results show that both materials exhibit adequate performance for the intended application.

An application of structural equation modeling of test dispositional optimism as mediator or moderator in quality of life in patients with chronic disease

The aim of the present study was to test a hypothetical model to examine if dispositional optimism exerts a moderating or a mediating effect between personality traits and quality of life, in Portuguese patients with chronic diseases. A sample of 540 patients was recruited from central hospitals in various districts of Portugal. All patients completed self-reported questionnaires assessing socio-demographic and clinical variables, personality, dispositional optimism, and quality of life. Structural equation modeling (SEM) was used to analyze the moderating and mediating effects. Results suggest that dispositional optimism exerts a mediator rather than a moderator role between personality traits and quality of life, suggesting that “the expectation that good things will happen” contributes to a better general well-being and better mental functioning.