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.

The efficiency of urine dipsticks for the diagnosis of urinary tract infection

Urinary tract infection (UTI) is one of the most prevalent pathologies in developed countries, particularly in women, characterized by the presence of bacterial growth in any part of the urinary system. Currently, urine culture is considered the gold standard method for the diagnosis of UTI. However, this method has several disadvantages including the time necessary for obtaining the results and the associated high costs. Therefore, it is important to evaluate new efficient and valuable methods for the diagnosis of these infections. Objectives: Presently, dipsticks are considered a possible valuable alternative to urine culture. This method has very low costs associated and the results can be obtained in few minutes. Here we aim to compare the sensibility, specificity, predictive value of a positive test and a negative test of both methods in order to determine the efficiency of the test strips method and also to characterize the microorganism more frequently isolated.

Perimetria de hiperacuidade preferencial no estudo do edema macular diabético

Introdução – A diabetes é uma das maiores epidemias do último século. Mais de 250 milhões de pessoas, em todo o mundo, sofrem de diabetes. Das complicações derivadas da diabetes são as principais causas de cegueira, de insuficiência renal e de amputação de membros inferiores, derivando estes, predominantemente, da disfunção vascular. Quando surge perda de pericitos na parede vascular ocorrem uma série de alterações da microcirculação que levam ao aparecimento de microaneurismas e outras alterações vasculares que possibilitam a passagem de componentes sanguíneos para o tecido retiniano adjacente que, em situação de normalidade, não ocorreriam, sendo esta uma das causas do edema macular exsudativo diabético. A perimetria de hiperacuidade preferencial (PHP) é um teste psicofísico que pretende detetar metamorfopsias na Degenerescência Macular ligada à Idade (DMI). Uma vez que o edema macular diabético (EMD) se destaca como uma das principais causas de deficiência visual e baixa visão, pretende-se verificar a eficácia do PHP no estudo do edema macular diabético, respondendo à seguinte questão: “Qual a capacidade do perímetro de hiperacuidade preferencial em detetar metamorfopsias em pacientes com edema macular diabético?“ Metodologia – Estudo quantitativo, do tipo descritivo e correlacional. Selecionou-se uma amostra de 33 pacientes, onde se analisou um total de 60 olhos. Resultados – A sensibilidade do PHP na deteção de metamorfopsias associadas ao EMD na tomografia de coerência ótica (OCT) foi de 70,6%, a especificidade foi de 11,5% e a eficiência global do teste de 45%. Comparando os resultados encontrados no PHP e no OCT, constatou-se a existência de uma correlação inversa fraca (Phi = -0,215). Conclusões – Este novo método de diagnóstico revela-se sensível, contudo pouco específico e eficaz na deteção de metamorfopsias consequentes da existência de EMD. - ABSTRACT - Introduction – Preferential hyperacuity perimeter (PHP) is a new psychophysical test, which principle is based on the detection of metamorphopsia in age-related macular degeneration (AMD). It is intended to verify its effectiveness in the study of diabetic macular edema (DME). When there is loss of pericytes in the vascular wall occur a number of microcirculatory changes that lead to the appearance of microaneurysms and other vascular changes that allow the passage of blood components to the surrounding retinal tissue than in normal situation does not occur, this being one of the causes exudative diabetic macular edema. Methodology – It was performed a quantitative study, using descriptive and correlational analysis. A sample of 33 patients was selected, and 60 eyes were analyzed. Results – The sensitivity of PHP on the detection of metamorphopsia associated to EMD was 70.6%, the specificity was 11.5% and the global efficiency of the test was 45%. It was found a weak negative correlation (Phi= -0.215) between the PHP and optical coherence tomography (OCT). Conclusions – This new method of diagnosis was sensitive, but not very specific and effective on the detection of metamorphopsia, due to the DME.

A importância das tarefas realizadas em sala de aula no desenvolvimento da resolução criativa de problemas

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e do 2.º Ciclo do Ensino Básico

The problem of estimating the volatility of zero coupon bond interest rate

Financial literature and financial industry use often zero coupon yield curves as input for testing hypotheses, pricing assets or managing risk. They assume this provided data as accurate. We analyse implications of the methodology and of the sample selection criteria used to estimate the zero coupon bond yield term structure on the resulting volatility of spot rates with different maturities. We obtain the volatility term structure using historical volatilities and Egarch volatilities. As input for these volatilities we consider our own spot rates estimation from GovPX bond data and three popular interest rates data sets: from the Federal Reserve Board, from the US Department of the Treasury (H15), and from Bloomberg. We find strong evidence that the resulting zero coupon bond yield volatility estimates as well as the correlation coefficients among spot and forward rates depend significantly on the data set. We observe relevant differences in economic terms when volatilities are used to price derivatives.

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.

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.

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.

Compression Efficiency Analysis of Wyner-Ziv Video Coding with Motion Compensated Side Information Interpolation

The Wyner-Ziv video coding (WZVC) rate distortion performance is highly dependent on the quality of the side information, an estimation of the original frame, created at the decoder. This paper, characterizes the WZVC efficiency when motion compensated frame interpolation (MCFI) techniques are used to generate the side information, a difficult problem in WZVC especially because the decoder only has available some reference decoded frames. The proposed WZVC compression efficiency rate model relates the power spectral of the estimation error to the accuracy of the MCFI motion field. Then, some interesting conclusions may be derived related to the impact of the motion field smoothness and the correlation to the true motion trajectories on the compression performance.

Reward-risk efficiency in proportional reinsurance with different risk measures

We have studied, in particular under normality of the implied random variables, the connections between different measures of risk such as the standard deviation, the W-ruin probability and the p-V@R. We discuss conditions granting the equivalence of these measures with respect to risk preference relations and the equivalence of dominance and efficiency of risk-reward criteria involving these measures. Then more specifically we applied these concepts to rigorously face the problem of finding the efficient set of de Finetti’s variable quota share proportional reinsurance.

From efficiency to optimality in proportional reinsurance under group correlation

Based on our recent discovery of closed form formulae of efficient Mean Variance retentions in variable quota-share proportional reinsurance under group correlation, we analyzed the influence of different combination of correlation and safety loading levels on the efficient frontier, both in a single period stylized problem and in a multiperiod one.

Direct multisearch for multiobjective optimization

In practical applications of optimization it is common to have several conflicting objective functions to optimize. Frequently, these functions are subject to noise or can be of black-box type, preventing the use of derivative-based techniques. We propose a novel multiobjective derivative-free methodology, calling it direct multisearch (DMS), which does not aggregate any of the objective functions. Our framework is inspired by the search/poll paradigm of direct-search methods of directional type and uses the concept of Pareto dominance to maintain a list of nondominated points (from which the new iterates or poll centers are chosen). The aim of our method is to generate as many points in the Pareto front as possible from the polling procedure itself, while keeping the whole framework general enough to accommodate other disseminating strategies, in particular, when using the (here also) optional search step. DMS generalizes to multiobjective optimization (MOO) all direct-search methods of directional type. We prove under the common assumptions used in direct search for single objective optimization that at least one limit point of the sequence of iterates generated by DMS lies in (a stationary form of) the Pareto front. However, extensive computational experience has shown that our methodology has an impressive capability of generating the whole Pareto front, even without using a search step. Two by-products of this paper are (i) the development of a collection of test problems for MOO and (ii) the extension of performance and data profiles to MOO, allowing a comparison of several solvers on a large set of test problems, in terms of their efficiency and robustness to determine Pareto fronts.

Predicted VO2 on 6 minutes walk test for FAP liver transplanted patients

Physical function is limited post-liver transplantation and exercise training can improve exercise capacity following transplantation but previously assessment of functional capacity is necessary. The 6 minute walk test (6MWT) is routinely used for studying patient’s exercise capacity and is less expensive and time consuming than a Cardiopulmonary Exercise Test (CPXT). There have been some studies looking at the relationship between 6MWT and peak VO2 in patients but few presented an adequate equation for predicted peak VO2 from 6MWT to transplanted patients and none for Familial Amyloidotic Polyneuropathy (FAP) liver transplanted patients (FAPTx). The aim of this study was to compare the validity of 6 equations as predictors of VO2 from the 6MWT and compare it with directly measured VO2 in patients FAPTx.

PV system modeling by five parameters and in situ test

This paper focuses on a novel formalization for assessing the five parameter modeling of a photovoltaic cell. An optimization procedure is used as a feasibility problem to find the parameters tuned at the open circuit, maximum power, and short circuit points in order to assess the data needed for plotting the I-V curve. A comparison with experimental results is presented for two monocrystalline PV modules.

A one-dimensional prescribed curvature equation modeling the corneal shape

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.