Existence and multiplicity of solutions for a prescribed mean-curvature problem with critical growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Co-existence of t(6;13)(p21;q14.1) and trisomy 12 in chronic lymphocytic leukemia

We report a case of a 57-year-old man diagnosed with chronic lymphocytic leukemia (CLL) and presence of a rare t(6;13)(p21;q14.1) in association with an extra copy of chromosome 12. Classical cytogenetic analysis using the immunostimulatory combination of DSP30 and IL-2 showed the karyotype 47,XY,t(6;13)(p21;q14.1), +12 in 75% of the metaphase cells. Spectral karyotype analysis (SKY) confirmed the abnormality previously seen by G-banding. Additionally, interphase fluorescence in situ hybridization using an LSI CEP 12 probe performed on peripheral blood cells without any stimulant agent showed trisomy of chromosome 12 in 67% of analyzed cells (134/200). To the best of our knowledge, the association of t(6;13)(p21;q14.1) and +12 in CLL has never been described. The prognostic significance of these new findings in CLL remains to be elucidated. However, the patient has been followed up since 2009 without any therapeutic intervention and has so far remained stable.

On the existence of G-equivariant maps

Let G be a compact Lie group. Let X, Y be free G-spaces. In this paper, by using the numerical index i (X; R), under cohomological conditions on the spaces X and Y, we consider the question of the existence of G-equivariant maps f: X -> Y.

Existence and concentration of solutions for a class of biharmonic equations

Some superlinear fourth order elliptic equations are considered. A family of solutions is proved to exist and to concentrate at a point in the limit. The proof relies on variational methods and makes use of a weak version of the Ambrosetti-Rabinowitz condition. The existence and concentration of solutions are related to a suitable truncated equation. (C) 2012 Elsevier Inc. All rights reserved.

Existence of Solutions for Abstract Non-Autonomous Neutral Differential Equations

In this paper we discuss the existence of mild and classical solutions for a class of abstract non-autonomous neutral functional differential equations. An application to partial neutral differential equations is considered.

EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.

SUFFICIENT CONDITIONS ON DIFFUSIVITY FOR THE EXISTENCE AND NONEXISTENCE OF STABLE EQUILIBRIA WITH NONLINEAR FLUX ON THE BOUNDARY

A reaction-diffusion equation with variable diffusivity and non-linear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.

Amplification of the flgE gene provides evidence for the existence of a Brazilian borreliosis

INTRODUCTION: The symptoms of Brazilian borreliosis resemble the clinical manifestations of Lyme disease (LD). However, there are differences between the two in terms of epidemiological and laboratory findings. Primers usually employed to diagnose LD have failed to detect Borrelia strains in Brazil. OBJECTIVE: We aimed to identify the Brazilian Borrelia using a conserved gene that synthesizes the flagellar hook (flgE) of Borrelia burgdorferi sensu lato. METHOD: Three patients presenting with erythema migrans and positive epidemiological histories were recruited for the study. Blood samples were collected, and the DNA was extracted by commercial kits. RESULTS: The gene flgE was amplified from DNA of all selected patients. Upon sequencing, these positive samples revealed 99% homology to B. burgdorferi flgE. CONCLUSION: These results support the existence of borreliosis in Brazil. However, it is unclear whether this borreliosis is caused by a genetically modified B. burgdorferi sensu stricto or by a new species of Borrelia spp.

On existence and uniqueness of positive solutions to a class of fractional boundary value problems

[EN] The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ′ ( 0 ) = 0 , where 2 < α ≤ 3 and D 0 + α is the Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem in partially ordered metric spaces. The autonomous case of this problem was studied in the paper [Zhao et al., Abs. Appl. Anal., to appear], but in Zhao et al. (to appear), the question of uniqueness of the solution is not treated. We also present some examples where we compare our results with the ones obtained in Zhao et al. (to appear). 2010 Mathematics Subject Classification: 34B15

Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems

[EN] We establish the existence and uniqueness of a positive and nondecreasing solution to a singular boundary value problem of a class of nonlinear fractional differential equation. Our analysis relies on a fixed point theorem in partially ordered sets.

Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

A multi-regional view on aging societies accounting for the existence of non-tradable goods

This thesis assesses the question, whether accounting for non-tradable goods sectors in a calibrated Auerbach-Kotlikoff multi-regional overlapping-generations-model significantly affects this model’s results when simulating the economic impact of demographic change. Non-tradable goods constitute a major part of up to 80 percent of GDP of modern economies. At the same time, multi-regional overlapping-generations-models presented by literature on demographic change so far ignored their existence and counterfactually assumed perfect tradability between model regions. Moreover, this thesis introduces the assumption of an increasing preference share for non-tradable goods of old generations. This fact-based as-sumption is also not part of models in relevant literature. rnThese obvious simplifications of common models vis-à-vis reality notwithstanding, this thesis concludes that differences in results between a model featuring non-tradable goods and a common model with perfect tradability are very small. In other words, the common simplifi-cation of ignoring non-tradable goods is unlikely to lead to significant distortions in model results. rnIn order to ensure that differences in results between the ‘new’ model, featuring both non-tradable and tradable goods, and the common model solely reflect deviations due to the more realistic structure of the ‘new’ model, both models are calibrated to match exactly the same benchmark data and thus do not show deviations in their respective baseline steady states.rnA variation analysis performed in this thesis suggests that differences between the common model and a model with non-tradable goods can theoretically be large, but only if the bench-mark tradable goods sector is assumed to be unrealistically small.rnFinally, this thesis analyzes potential real exchange rate effects of demographic change, which could occur due to regional price differences of non-tradable goods. However, results show that shifts in real exchange rate based on these price differences are negligible.rn

Distinct eosinophil cytokine expression patterns in skin diseases - the possible existence of functionally different eosinophil subpopulations

The function of eosinophils has been attributed to host defense, immunomodulation, and fibrosis. Although eosinophils are found among infiltrating cells in a broad spectrum of skin diseases, their pathogenic role remains uncertain. This study aimed to analyze the cytokine expression by eosinophils in different skin diseases.