Positive solutions for the p-Laplacian involving critical and supercritical nonlinearities with zeros

In this paper we show the existence of multiple solutions to a class of quasilinear elliptic equations when the continuous non-linearity has a positive zero and it satisfies a p-linear condition only at zero. In particular, our approach allows us to consider superlinear, critical and supercritical nonlinearities. (C) 2009 Elsevier Masson SAS. All rights reserved.

Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zeros

Using a combination of several methods, such as variational methods. the sub and supersolutions method, comparison principles and a priori estimates. we study existence, multiplicity, and the behavior with respect to lambda of positive solutions of p-Laplace equations of the form -Delta(p)u = lambda h(x, u), where the nonlinear term has p-superlinear growth at infinity, is nonnegative, and satisfies h(x, a(x)) = 0 for a suitable positive function a. In order to manage the asymptotic behavior of the solutions we extend a result due to Redheffer and we establish a new Liouville-type theorem for the p-Laplacian operator, where the nonlinearity involved is superlinear, nonnegative, and has positive zeros. (C) 2009 Elsevier Inc. All rights reserved.

Monotone positive solutions for a fourth order equation with nonlinear boundary conditions

This work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions. The results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions. Numerical simulations are also presented. (C) 2009 Elsevier Ltd. All rights reserved.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Bayesian Estimation of the Logistic Positive Exponent IRT Model

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric ICC treats both correct and incorrect answers symmetrically, which results in a logical contradiction in ordering examinees on the ability scale. A data set corresponding to a mathematical test applied in Peruvian public schools is analyzed, where comparisons with other parametric IRT models also are conducted. Several model comparison criteria are discussed and implemented. The main conclusion is that the LPE and RLPE IRT models are easy to implement and seem to provide the best fit to the data set considered.

False-positive results of a rapid K39-based strip test and Chagas disease

Background: The definitive diagnosis of visceral. leishmaniasis (VL) requires invasive procedures with demonstration of amastigotes in tissue or promastigotes in culture. Unfortunately, these approaches require laboratory materials not available in poor countries where the disease is endemic. The correct diagnosis of VL is important, and made more difficult by the fact that several common tropical diseases such as malaria, disseminated tuberculosis, and enteric fever share the same clinical presentation. Serological tests have been developed to replace parasitological diagnosis in the field. A commercially available K39-based strip test for VL has been developed for this purpose. The endemic area of leishmaniasis in Brazil overlaps the endemic area of Chagas disease, a disease that can cause false-positive serological test results. The aim of this study was to evaluate the incidence of false-positive exams using a rapid test for VL in patients with Chagas disease. Methods: A rapid test based on the recombinant K39 antigen of Leishmania was used in: (1) 30 patients with confirmed Chagas disease, (2) 30 patients with a serological diagnosis of Chagas disease by ELISA, indirect immunofluorescence, indirect hemagglutination, and chemiluminescence, (3) 30 healthy patients from a non-endemic area as the control group, (4) 30 patients with confirmed VL, and (5) 20 patients with proved cutaneous leishmaniasis. Results: The sensitivity and specificity of the rapid strip test were 100% when compared with healthy volunteers and those with confirmed Chagas disease. One false-positive result occurred in the group with Chagas disease diagnosed by serological tests (specificity of 96%). Conclusion: The rapid test based on recombinant K39 is a useful diagnostic assay, and a false-positive result rarely occurs in patients with a serological diagnosis of Chagas disease. (C) 2008 International Society for Infectious Diseases. Published by Elsevier Ltd. All rights reserved.

Description of costandard modules for Schur superalgebra S(2 vertical bar 1) in positive characteristic

We describe the characters of simple modules and composition factors of costandard modules for S(2 vertical bar 1) in positive characteristics and verify a conjecture of La Scala-Zubkov regarding polynomial superinvariants for GL(2 vertical bar 1).