http://hdl.handle.net/123456789/1073 Tue, 07 Apr 2026 17:40:31 GMT 2026-04-07T17:40:31Z http://hdl.handle.net/123456789/12164 Global Stability of a Predator-Prey Fishery Model With Non-Selective Harvesting: A Study of Linear Optimal Control Suka, Cephas Tay A proposed two-dimensional modified Lotka-Volterra fishery model in terms of predator-prey aims to explore the effect of non-selective harvesting on the predator and the prey populations. The study delves into various essential aspects of the dynamical system, comprising positivity, uniform boundedness and persistence. Points of equilibrium are identified. The system’s local and global stability are thoroughly examined and discussed. Moreover, the research explores the concept of bionomic equilibrium, a scenario where economic rent is entirely dissipated. Extending the bioeconomic model, the study investigates a linear optimal control problem to determine the most effective harvesting strategy. Utilising Pontryagin’s maximum principle, the optimal control is characterised. The findings indicate that maximum allowable effort should be exerted whenever the net revenue per unit effort surpasses the total net marginal revenue of predator and prey stocks. Numerical simulations, with data on the marine artisanal fishery in Ghana, are conducted to validate the theoretical discoveries. The outcomes reveal that the fishery can support sustainable harvesting of both predator (tuna) and prey (sardinella) populations, so far as the optimal harvesting effort is set at 100,000 fishing trips annually. xii, 68p:, ill. Fri, 01 Mar 2024 00:00:00 GMT http://hdl.handle.net/123456789/12164 2024-03-01T00:00:00Z http://hdl.handle.net/123456789/12143 Solution of Inverse Eigenvalue Problem for Singular Symmetric and Hermitian Matrices of Ranks Five and Six Kumordzi, Michael In this work, the inverse eigenvalue problem is studied in the context of singular symmetric and Hermitian matrices, with a particular emphasis on ranks five and six. We looked into ways to solve singular symmetric and Hermitian matrices’ Inverse Eigenvalue Problem (IEP). We devised a method to reconstruct such matrices from their eigenvalues, based on a solvability lemma. Through innovative methodologies, we aim to provide effective solutions for determining the original matrices from their eigenvalues, shedding light on challenges posed by singularity and higher rank. In the case of n × n matrix, the number of independent matrix elements would reduced xi 75p:, ill Fri, 01 Dec 2023 00:00:00 GMT http://hdl.handle.net/123456789/12143 2023-12-01T00:00:00Z http://hdl.handle.net/123456789/11857 Flexible Bayesian Methods For Inflation Modelling In Ghana FREMPONG, MOHAMMED Inflation data may exhibit structural instability that might have been engineered by informative macroeconomic variables. Failure to include this relevant economic information in the statistical modelling procedure may produce disingenuous information leading to wrong conclusion. In view of this, this thesis proposed Bayesian-Gaussian process regression, GPR methods based on compound covariance function for modelling inflation in Ghana. The approach model inflation as a mean zero Gaussian process in terms of the observation time with a compound covariance function designed to account for the short-, medium-, and long-term structural characteristics of the inflation process. Macroeconomic variables that drive inflation are incorporated into the model via the covariance using moment-based statistics as alternative macroeconomic predictors. The moment-based macroeconomic predictors serve as transformed predictors and were built based on the existing interrelationships among the variables such that they allow automatic control of the interrelationships, autocorrelation and outliers. This allows Bayesian GPR to be applied to macroeconomic data in which there exist interrelationships. MCMC inference methods were built for the developed GPR models and experimented using real macroeconomic data from Bank of Ghana (BoG) website. Results show that Bayesian GPR models with moment-based macroeconomic predictors outperform their original data predictors in fitting inflation on food and non- food data. xiv,151p:, ill. Mon, 01 May 2023 00:00:00 GMT http://hdl.handle.net/123456789/11857 2023-05-01T00:00:00Z http://hdl.handle.net/123456789/11843 Stochastic Optimal Control Of Systems Driven By Stochastic Differential Equations Of Mean-Field Type With Irregular Drift Coefficients Tchoumegne, Sorelle Murielle Toukam The main objective of this work is to maximize a performance functional subjected to a controlled stochastic di erential equation of mean- eld type using the stochastic maximum principle approach. The controlled mean- eld stochastic di erential equation has a non smooth drift and is driven by a one dimensional Brownian motion. We started by rst showing that, considering a corresponding sequence of mean- eld stochastic di erential equations with a smooth drift coe cient, the corresponding sequence of solutions will converge to the solution of the mean- eld stochastic di erential equation. We study the representation of the stochastic (Sobolev) di erential ow, via a time-space local time integration argument. Lastly, we look at a control problem where the state process follows the dynamics of a mean- eld stochastic di erential equation. Since the drift coe cient is non smooth, we characterize the optimal control through an approximate performance functional which is derived using the Ekeland's variational principle. Afterwards, we pass to the limit and prove convergence of the stochastic maximum principle. ix, 138p; , ill. Wed, 01 Nov 2023 00:00:00 GMT http://hdl.handle.net/123456789/11843 2023-11-01T00:00:00Z