Wave equations with mass and dissipation

In this paper we consider a wave model with non-effective mass and dissipation terms and provide asymptotic descriptions of its representation of solutions. In particular we conclude sharp estimates for a corresponding energy and estimates of dispersive type.Comment: 28 pages; some minor corrections of typo

Semilinear wave equation with time-dependent exponential speed of propagation, mass and dissipation

In order to prove global existence (in time) of small data energy solutions to the semilinear Cauchy problem for the wave equation with time-dependent exponential speed of propagation mass and dissipation we will derive sharp linear estimates for the solution and its derivatives

Klein-Gordon models with non-effective time-dependent potential

In this thesis we study the asymptotic properties for the solution of the Cauchy problem for the Klein-Gordon equation with non-effective time-dependent potential. The main goal was define a suitable energy related to the Cauchy problem and derive decay estimates for such energy. Strichartz’ estimates and results of scattering and modified scattering was established. The C m theory and the stabilization condition was applied to treat the case where the coefficient of the potential term has very fast oscillations. Moreover, we consider a semi-linear wave model scale-invariant time- dependent with mass and dissipation, in this step we used linear estimates related with the semi-linear model to prove global existence (in time) of energy solutions for small data and we show a blow-up result for a suitable choice of the coefficients.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Nesta tese estudamos as propriedades assintóticas para a solução do problema de Cauchy para a equação de Klein-Gordon com potencial não efetivo dependente do tempo. O principal objetivo foi definir uma energia adequada relacionada ao problema de Cauchy e derivar estimativas para tal energia. Estimativas de Strichartz e resultados de scatering e scatering modificados também foram estabelecidos. A teoria C m e a condição de estabilização foram aplicados para tratar o caso em que o coeficiente da massa oscila muito rápido. Além disso, consideramos um mod- elo de onda semi-linear scale-invariante com massa e dissipação dependentes do tempo, nesta etapa usamos as estimativas lineares de tal modelo para provar ex- istência global (no tempo) de solução de energia para dados iniciais suficientemente pequenos e demonstramos um resultado de blow-up para uma escolha adequada dos coeficientes

Equação da onda com dissipação não efetiva dependente do tempo

The objective of this dissertation is to construct structural representations of the solutions to Cauchy problems for weakly dissipative wave equations below scaling and to deduce Strichartz type estimate Lp − Lq, q ≥ 2, for the solutions and its energy. Furthermore, we show that there is a asymptotic equivalence between the solutions for free waves equation and the solutions for the weakly dissipative wave equation.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)O objetivo desta dissertação é a construção de uma representação estrutural das soluções do problema de Cauchy, para equação da onda com dissipação fraca abaixo de escala e deduzir estimativas do tipo Strichartz Lp − Lq, q ≥ 2 para as soluções e sua energia. Além disso, mostraremos que existe uma certa equivalência assintótica entre as soluções para equação da onda livre e as soluções para a equação da onda com dissipação fraca

The MTHFR promoter hypermethylation pattern associated with the A1298C polymorphism influences lipid parameters and glycemic control in diabetic patients

Abstract Background Polymorphisms in the gene encoding methylenetetrahydrofolate reductase (MTHFR) have been investigated as risk factors for microvascular complications of diabetes; however, simultaneous analysis of these polymorphisms and the methylation pattern of the gene has never been conducted. The objective of the present study was to evaluate the simultaneous relationship between MTHFR methylation and MTHFR C6TT7 and A1298C polymorphisms with metabolic, inflammatory and oxidative stress parameters related to microvascular complications, diabetic retinopathy (DR) and diabetic nephropathy (DN) in diabetic patients. Methods A total of 107 patients who were diagnosed in the previous 5 to 10 years were recruited and divided into groups with complications (DR and/or DN) or without complications. Methylation analysis of the gene promoter was conducted using the MSP technique, and analysis of the A1298C and C677T polymorphisms was conducted using the restriction fragment length polymorphism (RFLP) assay. Microalbuminuria was determined using urine samples, and other analytes of interest were determined in blood samples using commercial kits. The Mann–Whitney and Chi square statistical tests were used with significance considered at p < 0.05. Results Subjects with a hypermethylated profile and the 1298AA genotype showed the highest levels of blood glucose (p = 0.03), total cholesterol (p = 0.0001) and LDL cholesterol (p = 0.0006). The same profile was associated with higher levels of HbA1c (p = 0.025), glycemia (p = 0.04) and total cholesterol (0.004) in the control group and total cholesterol (p = 0.005) and LDL cholesterol (p = 0.002) in the complications group. Serum creatinine was higher in subjects in the hypermethylated group with the genotype 677CC only in the control group (p = 0.0020). The methylated profile in presence of 677CC + 1298AA and the 677CT/TT +1298AA haplotypes showed higher levels of total cholesterol (p = 0.0024; 0.0031) and LDL cholesterol (p = 0.0060; 0.0125) than 1298AC/CC carriers. The fasting glycemia was higher in hypermethylated profile in the presence of 677CC/1298AA haplotype (p = 0.0077). Conclusion The hypermethylated methylation profile associated with the 1298AA genotype appeared to be connected to higher values of glycemia, total cholesterol and LDL cholesterol