52 research outputs found

    On the lowest eigenvalue of Laplace operators with mixed boundary conditions

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    In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions

    Two isoperimetric inequalities for the Sobolev constant

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    In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalises an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.Comment: 11 page

    Littoral sensitivity index (LSI) to oil spills along the Santa Catarina island and adjacent areas

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    This paper describes the Environmental Sensitivity Index (ESI) for oil-spill accidents for the Santa Catarina Island and surrounded areas. The shoreline classification was obtained according to the Guidelines for ESI elaboration, established by the Environmental Quality Secretariat of the Environmental Ministry (SQA/MMA, 2002). Field works and literature review were conduced in order to fulfill all the required information for the classification. All information was processed by a geographic information software system, Arc Map 8.3. The study area was divided into 291 segments, resulting in 447,5 km of shoreline classification. Index 10 is the most frequent in the study area, representing about 36% (mangroves, salt marshes and vegetated river-margins). The index 7 was not determined in the study area. The resulting ESI maps are articulated in 7 Operational Maps at 1:50.000 scales

    Population analysis of the GLB1 gene in South Brazil

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    Infantile GM1 gangliosidosis is caused by the absence or reduction of lysosomal beta-galactosidase activity. Studies conducted in Brazil have indicated that it is one of the most frequent lysosomal storage disorders in the southern part of the country. To assess the incidence of this disorder, 390 blood donors were tested for the presence of two common mutations (1622–1627insG and R59H) in the GLB1 gene. Another group, consisting of 26 GM1 patients, and the blood donors were tested for the presence of two polymorphisms (R521C and S532G), in an attempt to elucidate whether there is a founder effect. The frequencies of the R59H and 1622–1627insG mutations among the GM1 patients studied were 19.2% and 38.5%, respectively. The frequency of polymorphism S532G was 16.7%, whereas R521C was not found in the patients. The overall frequency of either R59H or 1622–1627insG was 57.7% of the disease-causing alleles. This epidemiological study suggested a carrier frequency of 1:58. Seven different haplotypes were found. The 1622–1627insG mutation was not found to be linked to any polymorphism, whereas linkage disequilibrium was found for haplotype 2 (R59H, S532G) (p < 0.001). These data confirm the high incidence of GM1 gangliosidosis and the high frequency of two common mutations in southern Brazil

    Unified Homogenization Theory for Magnetoinductive and Electromagnetic Waves in Split Ring Metamaterials

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    A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the metamaterial as a cubic arrangement of coupled LC circuits, giving the relation between currents and local magnetic field. The second equation comes from macroscopic Maxwell equations, and gives the relation between the macroscopic magnetic field and the average magnetization of the metamaterial. It is shown that electromagnetic and magnetoinductive waves propagating in the metamaterial are obtained from this analysis. Therefore, the proposed time and spatially dispersive permeability accounts for the characterization of the complete spectrum of waves of the metamaterial. Finally, it is shown that the proposed theory is in good quantitative and qualitative agreement with full wave simulations.Comment: 4 pages, 3 figure

    New approaches to the treatment of orphan genetic disorders: Mitigating molecular pathologies using chemicals

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    With the advance and popularization of molecular techniques, the identification of genetic mutations that cause diseases has increased dramatically. Thus, the number of laboratories available to investigate a given disorder and the number of subsequent diagnosis have increased over time. Although it is necessary to identify mutations and provide diagnosis, it is also critical to develop specific therapeutic approaches based on this information. This review aims to highlight recent advances in mutation-targeted therapies with chemicals that mitigate mutational pathology at the molecular level, for disorders that, for the most part, have no effective treatment. Currently, there are several strategies being used to correct different types of mutations, including the following: the identification and characterization of translational readthrough compounds; antisense oligonucleotide-mediated splicing redirection; mismatch repair; and exon skipping. These therapies and other approaches are reviewed in this paper
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