School of Mathematics, Statistics and Actuarial Science
https://repository.maseno.ac.ke/handle/123456789/1316
Mon, 06 Jul 2020 05:19:09 GMT2020-07-06T05:19:09ZStochastic Modeling of Bamboo Population Growth and Optimal Harvesting
https://repository.maseno.ac.ke/handle/123456789/1455
Stochastic Modeling of Bamboo Population Growth and Optimal Harvesting
OMWANSA, Arori Wilfred
Population growth and harvest modeling is an active area of current research.
There has been an effort to move from deterministic Ordinary Differential Equations
(ODE) to Stochastic Differential Equations (SDE) modeling. Moreover,
the latter is most realistic in describing life systems that are often perturbed by
unpredictable environmental activity. Bamboo growth and harvest modeling was
motivated by the “Tobacco to Bamboo” (TTB) Project where farmers in selected
sections of Homabay and Migori Counties in Kenya were persuaded to plant bamboo
instead of tobacco. This was met with pessimism due to the lengthy wait,
at least three years, before harvesting. They also needed to know the expected
income compared to the tobacco income they used to earn. This study therefore
sought to explore suitable models that could be used to determine optimal
expected sustainable bamboo yield. In view of this, data from the TTB project
was analyzed to determine parameters including population growth rate r, carrying
capacity K and population size at time t,Nt. ODEs and SDEs were used
in modeling equilibrium populations and maximum sustainable yield. SDEs were
solved using Itˆo calculus and associated Fokker–Planck equations. The Monte-
Carlo simulation procedure was used to construct population trajectories under
various model parameter values. A stochastic model with both growth rate and
harvest parameters coupled with white noise and a three year delayed continuous
harvest proportional to population size was developed. This was found to be
most suitable since it ensures maximum mean sustainable yield without the risk
of extinction as long as noise was kept at low levels. The model may not only be
applied in bamboo harvesting strategies but also other renewable resources that
have similar population dynamics.
Tue, 01 Jan 2019 00:00:00 GMThttps://repository.maseno.ac.ke/handle/123456789/14552019-01-01T00:00:00ZUnsteady MHD heat and mass transfer over an infinite Porous flat plate with convective surface boundary Conditions
https://repository.maseno.ac.ke/handle/123456789/1175
Unsteady MHD heat and mass transfer over an infinite Porous flat plate with convective surface boundary Conditions
ODERO, Isaiah Otieno
Unsteady MHD heat and mass transfer over an infinite flat plate with convective surface boundary condition problems have received little attention yet they are of great importance in many scientific and engineering fields. Past studies by various researchers in the field of MHD fluid flows seems to have ignored the effects of ion-slip and Hall currents on velocity, temperature and concentration profiles of fluid flow. In this research, unsteady MHD heat and mass transfer of an electrically conducting fluid over an infinite flat porous plate with convective surface boundary conditions is studied and more specifically to investigate the contribution of the combined effects of ion-slip and Hall currents on the velocity, temperature and concentration of the fluid subject to cooling and heating of the plate by free convectional currents and constant heat flux. The objective of this study was to formulate and solve the coupled partial differential equations of momentum, energy and concentration of species describing the flow. The flow equations were non-dimensionalized, transformed then programmed into a mathematica code and results generated in graphs. The effects of physical parameters on velocity, temperature and concentration fields are analyzed from graphs. Our analysis of the graphical results obtained shows that velocity and thermal boundary layer thickness increase with increase in ion-slip and Hall parameters for the cooling of the plate by free convection in the presence of constant heat flux. The concentration of the fluid increases with increase in time or decrease in mass diffusion parameter or withdrawal of suction velocity. The results can serve as prototype for practical propulsion type of problems, for example, generation of propulsion force in moving ship.
Phd Thesis
Mon, 01 Jan 2018 00:00:00 GMThttps://repository.maseno.ac.ke/handle/123456789/11752018-01-01T00:00:00ZComputation of efficient nash equilibria for experimental economic games
https://repository.maseno.ac.ke/handle/123456789/1058
Computation of efficient nash equilibria for experimental economic games
ESILABA, Rhodah Ong'awa
Game theory has been used to study a wide variety of human and animal behaviors. It looks for states of equilibrium, sometimes called solutions. Nash equilibrium is the central solution concept with diverse applications for most games in game theory. However some games have no Nash equilibrium, others have only one Nash equilibrium and the rest have multiple Nash equilibria. For games with multiple equilibria, different equilibria can have different rewards for the players thus causing a challenge on their choice of strategies. In this study, to solve the problems associated with existence of multiple equilibria in games, we identified and computed the most efficient Nash equilibrium in such experimental economic games. To achieve this we described and carried out an experiment on a game that was modeled as a three-player experimental economic game. The results were recorded and by the best response sets method we identified all the Pure Nash equilibria and computed the most efficient Nash equilibrium for our experimental economic game. Using the Brauwer's fixed point theorem we verified the existence of mixed Nash equilibrium in the experimental economic game. The findings were that the most efficient equilibrium varied from one player to the other. An individual whose aim was to minimize risks played the risk dominant strategies whereas for those aiming to maximize their profits, the payoff dominant strategies were played in cooperation to achieve the most efficient Nash Equilibrium for the experimental economic game. The computation of most efficient Nash Equilibrium in games can be applied to most situations in competitive Economic environment that are faced with multiple choices on which strategy is optimal.
PHD Thesis
Wed, 01 Jan 2014 00:00:00 GMThttps://repository.maseno.ac.ke/handle/123456789/10582014-01-01T00:00:00ZAbsolutely Continuous Spectrum of fourth Order Di_erence Operators With unbounded Coe_cients on the Hilbert space `2(N)
https://repository.maseno.ac.ke/handle/123456789/1057
Absolutely Continuous Spectrum of fourth Order Di_erence Operators With unbounded Coe_cients on the Hilbert space `2(N)
MOGOI, Evans N.
Sturm-Liouville operators and Jacobi matrices have so far been developed in parallel for many years. A result in one _eld usually leads to a result in the other. However not much in terms of spectral theory has been done in the discrete setting compared to the continuous version especially in higher order operators. Thus, we have investigated the de_ciency indices of fourth order di_erence operator generated by a fourth order di_erence equation and located the absolutely continuous spectrum of its self-adjoint extension as well as the spectral multiplicity
using the M-matrix. The results are useful to mathematicians and can be applied in quantum mechanics to calculate time dilation and length contraction as used in Lorentz-Fotzgeralds transformations. The study has been carried out through asymptotic summation as outlined in Levinson Benzaid Lutz-theorem. This involved: reduction of a fourth order di_erence equation into _rst order, computation of the eigenvalues, proof of uniform dichotomy condition, calculating the de_ciency indices and locating absolutely continuous spectrum. In this case we have found the absolutely continuous spectrum to be the whole set of real numbers of spectral multiplicity one.
PHD Thesis
Thu, 01 Jan 2015 00:00:00 GMThttps://repository.maseno.ac.ke/handle/123456789/10572015-01-01T00:00:00Z