A singularly perturbed linear two-point boundary-value problem

We consider the following singularly perturbed linear two-point boundary-value problem:

Ly(x) ≡ Ω(ε)D_xy(x) - A(x,ε)y(x) = f(x,ε) 0≤x≤1 (1a)

By ≡ L(ε)y(0) + R(ε)y(1) = g(ε) ε → 0^+ (1b)

Here Ω(ε) is a diagonal matrix whose first m diagonal elements are 1 and last m elements are ε. Aside from reasonable continuity conditions placed on A, L, R, f, g, we assume the lower right mxm principle submatrix of A has no eigenvalues whose real part is zero. Under these assumptions a constructive technique is used to derive sufficient conditions for the existence of a unique solution of (1). These sufficient conditions are used to define when (1) is a regular problem. It is then shown that as ε → 0^+ the solution of a regular problem exists and converges on every closed subinterval of (0,1) to a solution of the reduced problem. The reduced problem consists of the differential equation obtained by formally setting ε equal to zero in (1a) and initial conditions obtained from the boundary conditions (1b). Several examples of regular problems are also considered.

A similar technique is used to derive the properties of the solution of a particular difference scheme used to approximate (1). Under restrictions on the boundary conditions (1b) it is shown that for the stepsize much larger than ε the solution of the difference scheme, when applied to a regular problem, accurately represents the solution of the reduced problem.

Furthermore, the existence of a similarity transformation which block diagonalizes a matrix is presented as well as exponential bounds on certain fundamental solution matrices associated with the problem (1).

Discounting the value of natural resources in costbenefit analysis: a case study for policy making

4 p.

The Equivalency Principle for Discounting the Value of Natural Assets: An Application to an Investment Project in the Basque Coast

25 p.

Value chain analysis for sea cucumber in the Philippines

This study examined the sea cucumber industry in the Philippines through the value chain lens. The intent was to identify effective pathways for the successful introduction of sandfish culture as livelihood support for coastal communities. Value chain analysis is a high-resolution analytical tool that enables industry examination at a detailed level. Previous industry assessments have provided a general picture of the sea cucumber industry in the country. The present study builds on the earlier work and supplies additional details for a better understanding of the industry's status and problems, especially their implications for the Australian Center for International Agricultural Research (ACIAR) funded sandfish project "Culture of sandfish (Holothuria scabra) in Asia- Pacific" (FIS/2003/059). (PDF contains 54 pages)

Value Estimation and Comparison in Multi-Attribute Choice

The following work explores the processes individuals utilize when making multi-attribute choices. With the exception of extremely simple or familiar choices, most decisions we face can be classified as multi-attribute choices. In order to evaluate and make choices in such an environment, we must be able to estimate and weight the particular attributes of an option. Hence, better understanding the mechanisms involved in this process is an important step for economists and psychologists. For example, when choosing between two meals that differ in taste and nutrition, what are the mechanisms that allow us to estimate and then weight attributes when constructing value? Furthermore, how can these mechanisms be influenced by variables such as attention or common physiological states, like hunger?

In order to investigate these and similar questions, we use a combination of choice and attentional data, where the attentional data was collected by recording eye movements as individuals made decisions. Chapter 1 designs and tests a neuroeconomic model of multi-attribute choice that makes predictions about choices, response time, and how these variables are correlated with attention. Chapter 2 applies the ideas in this model to intertemporal decision-making, and finds that attention causally affects discount rates. Chapter 3 explores how hunger, a common physiological state, alters the mechanisms we utilize as we make simple decisions about foods.

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

On the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamics

This investigation deals with certain generalizations of the classical uniqueness theorem for the second boundary-initial value problem in the linearized dynamical theory of not necessarily homogeneous nor isotropic elastic solids. First, the regularity assumptions underlying the foregoing theorem are relaxed by admitting stress fields with suitably restricted finite jump discontinuities. Such singularities are familiar from known solutions to dynamical elasticity problems involving discontinuous surface tractions or non-matching boundary and initial conditions. The proof of the appropriate uniqueness theorem given here rests on a generalization of the usual energy identity to the class of singular elastodynamic fields under consideration.

Following this extension of the conventional uniqueness theorem, we turn to a further relaxation of the customary smoothness hypotheses and allow the displacement field to be differentiable merely in a generalized sense, thereby admitting stress fields with square-integrable unbounded local singularities, such as those encountered in the presence of focusing of elastic waves. A statement of the traction problem applicable in these pathological circumstances necessitates the introduction of "weak solutions'' to the field equations that are accompanied by correspondingly weakened boundary and initial conditions. A uniqueness theorem pertaining to this weak formulation is then proved through an adaptation of an argument used by O. Ladyzhenskaya in connection with the first boundary-initial value problem for a second-order hyperbolic equation in a single dependent variable. Moreover, the second uniqueness theorem thus obtained contains, as a special case, a slight modification of the previously established uniqueness theorem covering solutions that exhibit only finite stress-discontinuities.

Value of information in product recovery decisions: A Bayesian approach

There is a widespread recognition of the need for better information sharing and provision to improve the viability of end-of-life (EOL) product recovery operations. The emergence of automated data capture and sharing technologies such as RFID, sensors and networked databases has enhanced the ability to make product information; available to recoverers, which will help them make better decisions regarding the choice of recovery option for EOL products. However, these technologies come with a cost attached to it, and hence the question 'what is its value?' is critical. This paper presents a probabilistic approach to model product recovery decisions and extends the concept of Bayes' factor for quantifying the impact of product information on the effectiveness of these decisions. Further, we provide a quantitative examination of the factors that influence the value of product information, this value depends on three factors: (i) penalties for Type I and Type II errors of judgement regarding product quality; (ii) prevalent uncertainty regarding product quality and (iii) the strength of the information to support/contradict the belief. Furthermore, we show that information is not valuable under all circumstances and derive conditions for achieving a positive value of information. © 2010 Taylor & Francis.

Smoked marine fish from Western Region, Ghana: a value chain assessment

The value chain analysis of ths report focused on smoked marine fish- overwhelmingly the most important fish product originating in Western Region, Ghana. Smoked fish from Western Region is mainly destined for the domestic market where demand is very strong. Small quantities of smoked fish are destined for markets in Togo, Benin and Nigeria. The underlying objective of the fisheries value chain analysis is to identify opportunities for growth in the fisheries value chain, with an emphasis on those opportunities that have the potential to generate significant additional livelihoods, particularly at the level of the fishing communities and for low-income groups. The results from the value chain analysis will be used to identify pilot interventions to promote those livelihood outcomes. The main focus for the study is smoked fish (major species/product forms) destined for domestic markets. However, work will also be undertaken on the fresh fish trade and frozen fish to find out more about the significance of these value chains.

Financial Value Added FVA: uma nova ferramenta para a medição do desempenho financeiro das empresas

O objetivo dessa pesquisa é apresentar uma ferramenta alternativa ao valor econômico adicionado na mensuração da performance empresarial correlacionada com o valor de mercado. Na revisão da literatura apresenta-se o conceito de estrutura e custo de capital, utilizando a metodologia do CAPM e do APT. São igualmente apresentadas as principais medidas financeiras de desempenho tais como: retorno operacional sobre o investimento, retorno sobre o patrimônio liquido, retorno sobre os ativos, além de outras formas para cálculo do retorno. Na sequência introduzimos o conceito de lucro residual e o valor econômico adicionado, discutindo suas vantagens, desvantagens, dificuldades e limitações dessa ferramenta. Através do EVA podemos calcular o valor de mercado adicionado, fundamental para o cálculo do valor patrimonial ajustado. Também é apresentado nessa obra a interpretação do EVA pela ótica do modelo Fleuriet de planejamento financeiro. Após essa explanação teórica é apresentado o Financial Value Added proposto por esse trabalho, como alternativa ao Valor Econômico Adicionado na mensuração do desempenho empresarial. Essa ferramenta exclui da base de cálculo as receitas e despesas econômicas, uma vez que as mesmas em alguns casos distorcem o resultado como é constatado no teste com as empresas: Sadia S.A. e Perdigão S.A. onde os resultados foram 54% na Sadia e 13% na Perdigão superiores ao EVA. Em nenhum momento argumenta-se a substituição do EVA, apenas a introdução do FVA como alternativa nos casos em que o EVA não funcione adequadamente.

Impacts of climate change and variability on fish value chains in Uganda

This study examines the vulnerability of fish pr oduction in Uganda, particularly as it r elates to the predicted impacts from climate change, using the concept of the value chain. The value chain approach has been recommended as a useful tool to study specific challenges facing a sector resulting from various drivers of change, including climate. Critically, such analyses can reveal context-specific response strategies to enhance a sector (Jacinto and Pomer oy 2010). The specific purpose of the study was to identify curr ent and potential impacts of climate change and corresponding adaptation strategies in fish value chains. The study builds upon information fr om earlier value chain analyses on fisheries and aquaculture production in Uganda to provide a more in-depth understanding of issues facing the fish industry, in particular, those to be incorporated in the CGIAR Resear ch Program Livestock and Fish.