RP-Department of Statistics and Actuarial Sciencehttp://ir-library.ku.ac.ke/handle/123456789/132792022-12-02T15:53:15Z2022-12-02T15:53:15ZHierarchical Penalized Mixed ModelNdung’u, A. W.Mwalili, S.Odongo, L.http://ir-library.ku.ac.ke/handle/123456789/225002021-09-18T00:04:24Z2019-01-01T00:00:00ZHierarchical Penalized Mixed Model
Ndung’u, A. W.; Mwalili, S.; Odongo, L.
Penalized spline has been a popular method for estimating an unknown function in the non-parametric regression due to their use of low-rank spline
bases, which make computations tractable. However its performance is poor
when estimating functions that are rapidly varying in some regions and are
smooth in other regions. This is contributed by the use of a global smoothing
parameter that provides a constant amount of smoothing across the function.
In order to make this spline spatially adaptive we have introduced hierarchical penalized splines which are obtained by modelling the global smoothing
parameter as another spline.
A research article published in Open Journal of Statistics
2019-01-01T00:00:00ZSignificance of Coriolis F Significance of Coriolis Force on E ce on Eyring-P yring-Powell Flow Ov owell Flow Over A Rotating Non-uniform SurfaceOke, Abayomi SamuelMutuku, Winifred Ndukuhttp://ir-library.ku.ac.ke/handle/123456789/223572021-06-28T06:31:18Z2021-01-01T00:00:00ZSignificance of Coriolis F Significance of Coriolis Force on E ce on Eyring-P yring-Powell Flow Ov owell Flow Over A Rotating Non-uniform Surface
Oke, Abayomi Samuel; Mutuku, Winifred Nduku
Coriolis force plays significant roles in natural phenomena such as atmospheric dynamics, weather
patterns, etc. Meanwhile, to circumvent the unreliability of Newtonian law for flows involving
varying speed, Eyring-Powell fluid equations are used in computational fluid dynamics. This paper
unravels the significance of Coriolis force on Eyring-Powell fluid over the rotating upper horizontal surface of a paraboloid of revolution. Relevant body forces are included in the Navier-Stokes
equations to model the flow of non-Newtonian Eyring-Powell fluid under the influence of Coriolis
force. Using similarity transformation, the governing equations are nondimensionalized, thereby
transforming the nonlinear partial differential equations to a system of boundary value nonlinear
ordinary differential equations. The shooting technique is adopted to convert the boundary value
problem to an initial value problem, which is in turn solved using the Runge-Kutta-Gill Scheme. At
low Coriolis force, temperature profiles increase as Eyring-Powell parameter increases, whereas at
high Coriolis force, temperature profiles decrease with increasing Eyring-Powell parameter.
An Article Published in Applications and Applied Mathematics: An International Journal
2021-01-01T00:00:00ZNewtonian Heating on MHD Stagnation-Point Flow over a Flat PlateOyem, Anselm O.Mutuku, WinifredEdogbanya, Helen O.Oke, SamuelGarbas, Babangida B.http://ir-library.ku.ac.ke/handle/123456789/221502021-06-28T06:31:14Z2021-01-01T00:00:00ZNewtonian Heating on MHD Stagnation-Point Flow over a Flat Plate
Oyem, Anselm O.; Mutuku, Winifred; Edogbanya, Helen O.; Oke, Samuel; Garbas, Babangida B.
A study on incompressible, steady magnetohydrodynamic (MHD) stagnation point flow of an electrically
conducting fluid over a flat plate with variable thermal diffusivity and Newtonian heating has been considered. The
governing partial differential equations were transformed using suitable similarity variables to couple nonlinear
differential equations. The transformed equations are solved using the Runge-Kutta fourth order scheme with the
shooting technique method. The effects of the various dimensionless flow parameters are presented in tables and
graphs in terms of velocity and temperature profiles. Numerical computations for skin friction coefficient and
Nusselt number are done. It was observed that thermal radiation parameter decreases the rate of heat transfer on the
surface but increases in skin-friction coefficient while, increase in the viscosity and thermal diffusivity variation
parameter increases both the skin-friction coefficient and rate of heat transfer. The results are in conformity with
existing results
An Article Published in FUW Trends in Science & Technology Journal
2021-01-01T00:00:00ZModeling the Effect of Inpatient Rehabilitation of Tobacco Smokers on Smoking DynamicsNyamai, Amos MwendwaMutuku, Winifred N.http://ir-library.ku.ac.ke/handle/123456789/221172021-06-28T06:31:18Z2021-01-01T00:00:00ZModeling the Effect of Inpatient Rehabilitation of Tobacco Smokers on Smoking Dynamics
Nyamai, Amos Mwendwa; Mutuku, Winifred N.
Aims:
1. Develop and analyze a mathematical model of the effect of inpatient rehabilitation of tobacco smokers
on tobacco smoking using Kenya as a case study.
2. Perform stability analysis on the smoking free equilibrium point and endemic equilibrium point of the
model.
3. Use numerical simulation to investigate the impact of inpatient rehabilitation of tobacco smokers on
smoking.
Place and Duration of Study: Department of Mathematics and Actuarial Science, School of Pure and
Applied Sciences (SPAS), Kenyatta University, Kenya, between May 2019 and September 2020.
Tobacco smoking is a serious burden in Kenya and the world at large. Smoking harms nearly every organ of
the body and affects the overall health of a person. Despite the overwhelming facts about the consequences of
tobacco smoking, it remains a bad wont which is socially accepted and widely spread. In this research we
numerically analyze the dynamics of smoking incorporating the impact of inpatient rehabilitation to curb the
smoking habit. We first present a three-compartment model incorporating inpatient rehabilitation, then
develop the system of ordinary differential equations governing the smoking dynamics. The basic
reproduction number is determined using next generation matrix method. The model equilibria were computed and the stability analysis carried out. The results of stability analysis indicate that the disease-free
equilibrium (DFE) is both locally and globally asymptotically stable for RS < 1 while the endemic equilibrium
is both locally and globally asymptotically stable for RS > 1. Numerical simulations of model carried out with
the help of MATLAB shows that, when rehabilitation is implemented effectively, it helps in minimization of
smoking in the community
An Article Published in Journal of Advances in Mathematics and Computer Science
2021-01-01T00:00:00Z