156 resultados para Weak Solution


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The effects of electron irradiation on NiO-containing solid solution systems are described. Partially hydrated NiO solid solutions, e. g. , NiO-MgO, undergo surface reduction to Ni metal after examination by TEM. This surface layer results in the formation of Moire interference patterns.

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This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

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Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

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A newly developed computational approach is proposed in the paper for the analysis of multiple crack problems based on the eigen crack opening displacement (COD) boundary integral equations. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix to determine all the unknown CODs step by step. To deal with the interactions among cracks for multiple crack problems, all cracks in the problem are divided into two groups, namely the adjacent group and the far-field group, according to the distance to the current crack in consideration. The adjacent group contains cracks with relatively small distances but strong effects to the current crack, while the others, the cracks of far-field group are composed of those with relatively large distances. Correspondingly, the eigen COD of the current crack is computed in two parts. The first part is computed by using the fictitious tractions of adjacent cracks via the local Eshelby matrix derived from the traction boundary integral equations in discretized form, while the second part is computed by using those of far-field cracks so that the high computational efficiency can be achieved in the proposed approach. The numerical results of the proposed approach are compared not only with those using the dual boundary integral equations (D-BIE) and the BIE with numerical Green's functions (NGF) but also with those of the analytical solutions in literature. The effectiveness and the efficiency of the proposed approach is verified. Numerical examples are provided for the stress intensity factors of cracks, up to several thousands in number, in both the finite and infinite plates.

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We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

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Corporate governance (CG) denotes the rules of business decision-making and directs the internal mechanism of companies to follow the output of the rules. It includes the customs, policies, laws and institutions as a set of processes that affects the way in which a corporation is directed, administered or controlled.

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Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

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The convergence of corporate social responsibility (CSR) and corporate governance (CG) has changed the corporate accountability mechanism. This has developed a socially responsible ‘corporate self-regulation’, a synthesis of governance and responsibility in the companies of strong economies. However, unlike in the strong economies, this convergence has not been visible in the companies of weak economies, where the civil society groups are unorganised, regulatory agencies are either ineffective or corrupt and the media and non-governmental organisations do not mirror the corporate conscience. Using the case of Bangladesh, this article investigates the convergence between CSR and CG in the self-regulation of companies in a less vigilant environment.

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A new optimal control model of the interactions between a growing tumour and the host immune system along with an immunotherapy treatment strategy is presented. The model is based on an ordinary differential equation model of interactions between the growing tu- mour and the natural killer, cytotoxic T lymphocyte and dendritic cells of the host immune system, extended through the addition of a control function representing the application of a dendritic cell treat- ment to the system. The numerical solution of this model, obtained from a multi species Runge–Kutta forward-backward sweep scheme, is described. We investigate the effects of varying the maximum al- lowed amount of dendritic cell vaccine administered to the system and find that control of the tumour cell population is best effected via a high initial vaccine level, followed by reduced treatment and finally cessation of treatment. We also found that increasing the strength of the dendritic cell vaccine causes an increase in the number of natural killer cells and lymphocytes, which in turn reduces the growth of the tumour.

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"Even though Corporate Social Responsibility (CSR) has become a widely accepted concept promoted by different stakeholders, business corporations' internal strategies, known as corporate self-regulation in most of the weak economies, respond poorly to this responsibility. Major laws relating to corporate regulation and responsibilities of these economies do not possess adequate ongoing influence to insist on corporate self-regulation to create a socially responsible corporate culture. This book describes how the laws relating to CSR could contribute to the inclusion of CSR principles at the core of the corporate self-regulation of these economies in general, without being intrusive in normal business practice. It formulates a meta-regulation approach to law, particularly by converging patterns of private ordering and state control in contemporary corporate law from the perspective of a weak economy. It proposes that this approach is suitable for alleviating regulators' limited access to information and expertise, inherent limitations of prescriptive rules, ensuring corporate commitment, and enhance the self-regulatory capacity of companies. This book describes various meta-regulation strategies for laws to link social values to economic incentives and disincentives, and to indirectly influence companies to incorporate CSR principles at the core of their self-regulation strategies. It investigates this phenomenon using Bangladesh as a case study."--publisher website

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The semantic of the terms “sustainable development” and “corporate social responsibility” have changed over time to a point where these concepts have become two interrelated processes for ensuring the far-reaching development of society. Their convergence has given dimension to the environmental and corporate regulation mechanisms in strong economies. This article deals with the question of how the ethos of this convergence could be incorporated into the self-regulation of businesses in weak economies where nonlegal drivers are either inadequate or inefficient. It proposes that the policies for this incorporation should be based on the precepts of meta-regulation that have the potential to hold force majeure, economic incentives, and assistance-related strategies to reach an objective from the perspective of weak economies.

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The microstructure of an artificial grain boundary in an YBa2Cu3O7-δ (YBCO) thin film grown on a (100)(110), [001]-tilt yttria-stabilized-zirconia (YSZ) bicrystal substrate has been studied using transmission electron microscopy (TEM). The orientation relationship between the YBCO film and the YSZ substrate was [001]YBCO∥[001]YSZ and [110]YBCO∥[100]YSZ for each half of the bicrystal film. However, the exact boundary geometry of the bicrystal substrate was not transferred to the film. The substrate boundary was straight while the film boundary was wavy. In several cases there was bending of the lattice confined within a distance of a few basal-plane lattice spacings from the boundary plane and microfaceting. No intergranular secondary phase was observed but about 25% of the boundary was covered by c-axis-tilted YBCO grains and a-axis-oriented grains, both of which were typically adjacent to CuO grains or surrounded by a thin Cu-rich amorphous layer.

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Weak links were fabricated by pulsed laser deposition of YBa 2Cu3Ox thin films on Y-ZrO2 bicrystal substrates. They were formed by transferring the bicrystal boundary into the epitaxial film during the film growth. Their properties were determined by the misorientation angle ( theta ) between the two halves of the bicrystal. The transport properties of the weak links were studied as a function of theta and an exponential dependence of the weak link critical current density was observed for angles up to 45 degrees . Clear Josephson effects with good microwave and magnetic field response were observed.

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We have studied weak links and dc-SQUIDs made from pulsed laser deposited YBa2Cu3O7-δ thin films on Y-ZrO 2 bicrystal substrates. The transport properties of the weak links were studied as a function of the misorientation angle (θ) between the two halves of the bicrystal and an exponential dependence of the weak link critical current density was observed for angles up to 40°at 77 K. Josephson effects with clear microwave and magnetic field responses were observed. An optimum dc-SQUID performance at 77 K was obtained for θ=32°. At this temperature, we achieved a periodic magnetic field response with a modulation depth of 12 μV.

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A5/1 is a shift register based stream cipher which provides privacy for the GSM system. In this paper, we analyse the loading of the secret key and IV during the initialisation process of A5/1. We demonstrate the existence of weak key-IV pairs in the A5/1 cipher due to this loading process; these weak key-IV pairs may generate one, two or three registers containing all-zero values, which may lead in turn to weak keystream sequences. In the case where two or three registers contain only zeros, we describe a distinguisher which leads to a complete decryption of the affected messages.