Studies on the nutritional value of cassava (Manihot utillisima) peels as energy source in the diet of Oreochromis niloticus fry fed in indoor glass aquaria

This study, though, has as its core objective cost reduction in aquaculture nutrition was equally designed to investigate the value of the peels of cassava (Manihot utillisima) as energy source in the diet of Oreochromis niloticus fry. Three levels of cassava peels diet and a control (100% yellow maize in the carbohydrate mixture) was prepared and tested on O. niloticus fry for ten (10) weeks. The fry with mean weight of 0.32g were grouped fifteen (15) in each of the glass aquaria measuring 60x30x30cm with a maximum capacity of 52 litres of water. The fry were fed twice daily at 10% biomass. Weekly, the fry were weighed to determine the weight increment or otherwise and the quality of feed adjusted accordingly. Water quality parameters like temperature, pH and dissolved oxygen (D.0) were monitored and found to be at desirable level. DT 3 (97 % cassava peels and 3% yellow maize) in the carbohydrate mixture gave the best growth performance. The fry fed, this diet gained mean weight of 1.18g for the period of the experiment. However, 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 0.80 for the duration of the experiment. Analysis of the various growth indices like SGR, PER, FCR and NPU shows that DT3 was the overall best diet with an SGR value of2.40 and FCR of 43.83. However, DT 1 (70% cassava peels and 30% yellow maize) gave the poorest SGR of 1.61 and FCR of 67.58. The difference in weight gain among the fry fed the three levels of cassava peels diet and the control was not statically significant (P>0.05)

Boundary value problems for stochastic differential equations

A theory of two-point boundary value problems analogous to the theory of initial value problems for stochastic ordinary differential equations whose solutions form Markov processes is developed. The theory of initial value problems consists of three main parts: the proof that the solution process is markovian and diffusive; the construction of the Kolmogorov or Fokker-Planck equation of the process; and the proof that the transistion probability density of the process is a unique solution of the Fokker-Planck equation.

It is assumed here that the stochastic differential equation under consideration has, as an initial value problem, a diffusive markovian solution process. When a given boundary value problem for this stochastic equation almost surely has unique solutions, we show that the solution process of the boundary value problem is also a diffusive Markov process. Since a boundary value problem, unlike an initial value problem, has no preferred direction for the parameter set, we find that there are two Fokker-Planck equations, one for each direction. It is shown that the density of the solution process of the boundary value problem is the unique simultaneous solution of this pair of Fokker-Planck equations.

This theory is then applied to the problem of a vibrating string with stochastic density.

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).

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.