On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

Stability and convergence analysis of a neural model applied in nonlinear systems optimization

A neural model for solving nonlinear optimization problems is presented in this paper. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The network is shown to be completely stable and globally convergent to the solutions of nonlinear optimization problems. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are presented to validate the developed methodology.

Stability and convergence of general multistep and multivalue methods with variable step size.

Thesis--University of Illinois.

Stability and convergence of variable order multistep methods,

Includes bibliographical references.

Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models.

The evolution of a quantitative phenotype is often envisioned as a trait substitution sequence where mutant alleles repeatedly replace resident ones. In infinite populations, the invasion fitness of a mutant in this two-allele representation of the evolutionary process is used to characterize features about long-term phenotypic evolution, such as singular points, convergence stability (established from first-order effects of selection), branching points, and evolutionary stability (established from second-order effects of selection). Here, we try to characterize long-term phenotypic evolution in finite populations from this two-allele representation of the evolutionary process. We construct a stochastic model describing evolutionary dynamics at non-rare mutant allele frequency. We then derive stability conditions based on stationary average mutant frequencies in the presence of vanishing mutation rates. We find that the second-order stability condition obtained from second-order effects of selection is identical to convergence stability. Thus, in two-allele systems in finite populations, convergence stability is enough to characterize long-term evolution under the trait substitution sequence assumption. We perform individual-based simulations to confirm our analytic results.

Human capital distribution, growth and convergence

This paper studies the dynamic relationship between distribution and endogenous growth in an overlapping generations model with accumulation of human and physical capital. It is shown how human capital can determine a relationship between per capita growth rates and inequality in the distribution of income. Family background effects and spillovers in the transmission of human capital generate a dynamics in which aggregate variables depend not only on the stock, but also on the distribution of human capital. The evolution of this distribution over time is then characterized under different assumptions on private returns and the form of the externality in the technology for humancapital. Conditions for existence, uniqueness and stability of a constant growth equilibrium with a stationary distribution are derived. Increasing returns, idiosyncratic abilities and the possibility of poverty traps are explicitely characterized in a closed form solution of the equilibrium dynamics, showing the role played by technology and preferences parameters.

Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

Chitosan Nanoparticles Loaded The Herbicide Paraquat: The Influence Of The Aquatic Humic Substances On The Colloidal Stability And Toxicity.

Polymeric nanoparticles have been developed for several applications, among them as carrier system of pesticides. However, few studies have investigated the fate of these materials in the environment in relation to colloidal stability and toxicity. In nature, humic substances are the main agents responsible for complexation with metals and organic compounds, as well as responsible for the dynamics of these nanoparticles in aquatic and terrestrial environments. In this context, the evaluation of the influence of aquatic humic substances (AHS) on the colloidal stability and toxicity of polymeric nanoparticles of chitosan/tripolyphosphate with or without paraquat was performed. In this study, the nanoparticles were prepared by the ionic gelation method and characterized by size distribution measurements (DLS and NTA), zeta potential, infrared and fluorescence spectroscopy. Allium cepa genotoxicity studies and ecotoxicity assays with the alga Pseudokirchneriella subcapitata were used to investigate the effect of aquatic humic substances (AHS) on the toxicity of this delivery system. No changes were observed in the physical-chemical stability of the nanoparticles due to the presence of AHS using DLS and NTA techniques. However some evidence of interaction between the nanoparticles and AHS was observed by infrared and fluorescence spectroscopies. The ecotoxicity and genotoxicity assays showed that humic substances can decrease the toxic effects of nanoparticles containing paraquat. These results are interesting because they are important for understanding the interaction of these nanostructured carrier systems with species present in aquatic ecosystems such as humic substances, and in this way, opening new perspectives for studies on the dynamics of these carrier systems in the ecosystem.

Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

Stability and in vitro penetration study of rutin incorporated in a cosmetic emulsion through an alternative model biomembrane

Rutin is employed as antioxidant and to prevent the capillary fragility and, when incorporated in cosmetic emulsions, it must target the action site. In vitro cutaneous penetration studies through human skin is the ideal situation, however, there are difficulties to obtain and to maintain this tissue viability. Among the membrane models, shed snake skin presents itself as pure stratum corneum, providing barrier function similar to human and it is obtained without the animal sacrifice. The objectives of this research were the development and stability evaluation of a cosmetic emulsion containing rutin and propylene glycol (penetration enhancer) and the evaluation or rutin in vitro cutaneous penetration and retention from the emulsion, employing an alternative model biomembrane. Emulsion was developed with rutin and propylene glycol, both at 5.0% w/w. Active substance presented on the formulation was quantified by a validated spectrophotometric method at 361.0 nm. Rutin Rutin cutaneous penetration and retention was performed in vertical diffusion cells with shed snake skin of Crotalus durissus, as alternative model biomembrane, and distilled water and ethanol 99.5% (1:1), as receptor fluid. The experiment was conducted for six hours, at 37.0 +/- 0.5 degrees C with constant stirring of 300 rpm. Spectrophotometry at 410.0 nm, previously validated, determined the active substance after cutaneous penetration/ retention. Emulsion did not promote rutin cutaneous penetration through C. durissus skin, retaining 0.931 +/- 0.0391 mu g rutin/mg shed snake skin. The referred formulation was chemically stable for 30 days after stored at 25.0 +/- 2.0 degrees C, 5.0 +/- 0.5 degrees C and 45.0 +/- 0.5 degrees C. In conclusion, it has not been verified the active cutaneous penetration through the model biomembrane, but only its retention on the Crotalus durissus stratum corneum, condition considered stable for 30 days.

Development of nitrosyl ruthenium complex-loaded lipid carriers for topical administration: improvement in skin stability and in nitric oxide release by visible light irradiation

The prominent nitric oxide (NO) donor [Ru(terpy)(bdqi)NO](PF(6))(3) has been synthesized and evaluated with respect to noteworthy biological effects due to its NO photorelease, including vascular relaxation and melanoma cell culture toxicity. The potential for delivering NO in therapeutic quantities is tenable since the nitrosyl ruthenium complex (NRC) must first reach the ""target tissue"" and then release the NO upon stimulus. In this context. NRC-loaded lipid carriers were developed and characterized to further explore its topical administration for applications such as skin cancer treatment. NRC-loaded solid lipid nanoparticles (SLN) and nanostructured lipid carriers were prepared via the microemulsification method, with average diameters of 275 +/- 15 nm and 211 +/- 31 nm and zeta potentials of -40.7 +/- 10.4 mV and -50.0 +/- 7.5 mV, respectively. In vitro kinetic studies of NRC release from nanoparticles showed sustained release of NRC from the lipid carriers and illustrated the influence of the release medium and the lyophilization process. Stability studies showed that NO is released from NRC as a function of temperature and time and due to skin contact. The encapsulation of NRC in SLN followed by its lyophilization, significantly improved the complex stability. Furthermore, of particular interest was the fact that in the NO photorelease study, the NO release from the NRC-loaded SLN was approximately twice that of just NRC in solution. NRC-loaded SLN performs well enough at releasing and protecting NO degradation in vitro that it is a promising carrier for topical delivery of NO. (C) 2010 Elsevier B.V. All rights reserved.

The effects of dietary supplementation of methionine on genomic stability and p53 gene promoter methylation in rats

Methionine is a component of one-carbon metabolism and a precursor of S-adenosylmethionine (SAM), the methyl donor for DNA methylation. When methionine intake is high, an increase of S-adenosylmethionine (SAM) is expected. DNA methyltransferases convert SAM to S-adenosylhomocysteine (SAH). A high intracellular SAH concentration could inhibit the activity of DNA methyltransferases. Therefore, high methionine ingestion could induce DNA damage and change the methylation pattern of tumor suppressor genes. This study investigated the genotoxicity of a methionine-supplemented diet. It also investigated the diet`s effects on glutathione levels, SAM and SAH concentrations and the gene methylation pattern of p53. Wistar rats received either a methionine-supplemented diet (2% methionine) or a control diet (0.3% methionine) for six weeks. The methionine-supplemented diet was neither genotoxic nor antigenotoxic to kidney cells, as assessed by the comet assay. However, the methionine-supplemented diet restored the renal glutathione depletion induced by doxorubicin. This fact may be explained by the transsulfuration pathway, which converts methionine to glutathione in the kidney. Methionine supplementation increased the renal concentration of SAH without changing the SAM/SAH ratio. This unchanged profile was also observed for DNA methylation at the promoter region of the p53 gene. Further studies are necessary to elucidate this diet`s effects on genomic stability and DNA methylation. (C) 2011 Elsevier ay. All rights reserved.

Accelerated Stability and Moisturizing Capacity of Emulsions Presenting Lamellar Gel Phase Obtained from Brazilian Natural Raw Material

Oil-in-water (O/W) emulsions containing gel phase were developed with cupuassu and/or cocoa butter from Brazilian ecosystem. They were subjected to storage advanced stability tests (SAST) and to in vivo corneometry evaluation. The evaluated emulsions showed great performance in the evaluated conditions considering that no significant variation was observed. The moisturizing potential was advantageous even without the moisturizing active. The formulation was considered a good cosmetic moisturizing cream and a promise as a drug carrier.