Bifurcation theory of nonlinear boundary value problems

The theory of bifurcation of solutions to two-point boundary value problems is developed for a system of nonlinear first order ordinary differential equations in which the bifurcation parameter is allowed to appear nonlinearly. An iteration method is used to establish necessary and sufficient conditions for bifurcation and to construct a unique bifurcated branch in a neighborhood of a bifurcation point which is a simple eigenvalue of the linearized problem. The problem of bifurcation at a degenerate eigenvalue of the linearized problem is reduced to that of solving a system of algebraic equations. Cases with no bifurcation and with multiple bifurcation at a degenerate eigenvalue are considered.

The iteration method employed is shown to generate approximate solutions which contain those obtained by formal perturbation theory. Thus the formal perturbation solutions are rigorously justified. A theory of continuation of a solution branch out of the neighborhood of its bifurcation point is presented. Several generalizations and extensions of the theory to other types of problems, such as systems of partial differential equations, are described.

The theory is applied to the problem of the axisymmetric buckling of thin spherical shells. Results are obtained which confirm recent numerical computations.

An investigation into the value of yam (Dioscorea rotundata) peels as energy source in the diet of Oreochromis niloticus fry fed in indoor glass aquaria

The study was designed to investigate the value of the peels of yam (Dioscorea rotundata) as energy source in the diet of Oreochromis niloticus fry and to investigate the level of inclusion of this peels that will give optimum growth performance. Four diets, three levels of yam peels and a control, was prepared and tested on O. niloticus fry (mean weight of 0.27g) for ten weeks. Fifteen (15) O. niloticus fry were grouped in each of the glass aquaria, measuring 60x30x3Ocm and with a maximum capacity of 52 liters of water. The fry were fed twice daily at 10% biomass. The fry were weighed weekly to determine weight increment or otherwise and the quality of feed was adjusted accordingly. DTl (70% yam peels and 30% yellow maize) in the carbohydrate mixture gave the best performance. The fry fed this diet, gained a mean weight of 1.20g for the period of the experiment. The poorest performance in terms of growth was from fry fed the control diet (100% yellow maize in the carbohydrate mixture). Fry fed this diet gained mean weight of 0.80g for the duration of the experiment. Analysis of the various growth indices like SGR, PER, FCR and NPU shows that DTl was the overall best diet with an SGR value of I. 92 and FCR of 54.10. The difference in weight gain by fry fed the three levels of yam peels diet and the control diet (100% yellow maize) was not statistically significant (P>0.05)

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).

Flood risk management: What are the main drivers of prevention?

4 p.

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.

Modeling the Links between Biodiversity, Ecosystem Services and Human Wellbeing in the Context of Climate Change: Results from an Econometric Analysis on the European Forest Ecosystems

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.

The role of specially designated wildlife sites in freshwater conservation - an English perspective

The value of specially designated sites in conserving biodiversity has been a hotly debated issue for many years. The debate has recently been given fresh impetus by the creation of Natural England, the new Government Agency responsible for the protection and enhancement of the natural environment in England, and the challenges facing the management of designated sites resulting from the increasingly tangible effects of climate change. In the freshwater environment, the role of designated sites is very much under the spotlight because of the implementation of the European 'Water Framework' Directive, which aspires to holistic, ecologically-based management of aquatic habitats.This paper explores the underlying premises of, and rationale for, special site designations for wildlife, and provides a frank account of the inevitable clash of management philosophies that designated sites create in the freshwater environment, drawing on experiences of managing designated freshwater sites in England over the past decade. A positive role is outlined for designated sites in freshwater conservation, which addresses these management conflicts in a way that not only meets Government obligations towards these sites but also paves the way for enlightened, progressive management of the wider freshwater resource. As part of this account, attempts are made to clarify the relationship between key biodiversity-related policy drivers in the freshwater environment, and to explain how the spectre of climate change can be addressed within designated site management. The importance of strategic freshwater science, collaboratively designed and funded, in maximising the value of the designated freshwater site network to the wider freshwater habitat resource, is stressed.

Hypoxic and low pH water in the nearshore marine environments of Monterey Bay, California: characterizing a decade of oxygen and pH, and drivers of variability.

A decade-long time series recorded in southern Monterey Bay, California demonstrates that the shallow, near-shore environment (17 m depth) is regularly inundated with pulses of cold, hypoxic and low pH water. During these episodes, oxygen can drop to biologically threatening levels, and pH levels were lower than expected. Weekly water chemistry monitoring revealed that the saturation state of aragonite (the more soluble form of calcium carbonate) was often below saturation and had a moderate positive relationship with pH, however, analytical and human error could be high. Pulses of hypoxia and low pH water with the greatest intensity arise at the onset of the spring upwelling season, and fluctuations are strongly semidurnal (tidal) and diurnal. Arrival of cold, hypoxic water on the inner shelf typically occurs 3 days after the arrival of a strong upwelling event and appears to be driven by upwelling modulated by internal tidal fluctuations. I found no relationship between the timing of low-oxygen events and the diel solar cycle nor with terrestrial nutrient input. These observations are consistent with advection of hypoxic water from the deep, offshore environment where water masses experience a general decline of temperature, oxygen and pH with depth, and inconsistent with biochemical forcing. Comparisons with concurrent temperature and oxygen time series taken ~20 km away at the head of the Monterey Canyon show similar patterns but even more intense hypoxic events due to stronger semidiurnal forcing there. Analysis of the durations of exposure to low oxygen levels establishes a framework for assessing the ecological relevance of these events. Increasing oceanic hypoxia and acidification of both surface and deep waters may increase the number, intensity, duration and spatial extent of future intrusions along the Pacific coast. Evaluation of the resiliency of nearshore ecosystems such as kelp forests, rocky reefs and sandy habitats, will require consideration of these events.

Diseño de una tarjeta de drivers para un inversor de potencia.

[EN]The purpose of this project is to design a system which improves the e ciency of power inverters. The project is focused in the analysis of the di erent power semiconductors (based on silicon, silicon carbide and gallium nitride) and driver applications. This system can be implemented in di erent future versions of power inverters and in many kind of applications like electrical vehicles. Other than that, it can be also implemented on any machinery requiring an inverter obtaining more energy and reduce manufacturing costs.

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.