MST-Department of Mathematics
http://ir-library.ku.ac.ke/handle/123456789/210
2021-03-06T01:04:46ZGraphs Whose Automorphism Groups Contain or Represent the Alternating Groups, An and Symmetric Groups, Sn
http://ir-library.ku.ac.ke/handle/123456789/21770
Graphs Whose Automorphism Groups Contain or Represent the Alternating Groups, An and Symmetric Groups, Sn
Otieno, Hosea Odhiambo
There have been many investigations on the combinatorial structures and invariants over the group actions on the subsets of its elements. Studies on Group Theory have yielded varied and important results in the advancement of Algebra. Several studies have also been made on Graph Theory. Some Mathematicians have studied the concept of automorphisms on graphs thereby yielding important results. Automorphism groups from graphs containing the cyclic and dihedral groups, Cn and Dn respectively have been constructed using Schur’s Algorithm. In this project, we have extended the work to graphs whose Automorphism groups contain the Alternating Group An as well as those representing Symmetric group Sn. The graphs whose Automorphism groups contain or represent the Alternating Group An and Symmetric group Sn respectively have been constructed. Schur’s algorithm has been employed to construct these graphs. The actions of the Alternating Group An and the Symmetric group Sn have been shown to be transitive using the Cauchy- Frobenius Lemma and the Orbit-Stabilizer Theorem. The Automorphism graphs for the groups An and Sn have been constructed for 𝓃=3,4,𝐴𝑛𝑑 5.. The number of graphs whose groups of Automorphism contain An is 2 being the null and the complete graphs. The number of graphs whose groups of Automorphism represent Sn is 2 being the null and the complete graphs. We have presented the results of our findings from our workings as theorems and constructed the applicable graphs.
A Project Submitted in Partial Fulfillment of the Requirements for the Award of the Degree of Master of Science (Pure Mathematics) in the School of Pure and Applied Sciences of Kenyatta University. November, 2020
2020-11-01T00:00:00ZFlow of Contaminants in Urban Ground Water
http://ir-library.ku.ac.ke/handle/123456789/21769
Flow of Contaminants in Urban Ground Water
Mukabwa, Musavi Sammy
Groundwater contamination occurs when man-made products such as gasoline, oil, road salts and chemicals get into the groundwater and cause it to become unsafe and unfit for human use. Drinking contaminated groundwater can have serious health effects. Diseases such as hepatitis and dysentery may be caused by contamination from septic tank waste. Poisoning may be caused by toxins that have leached into well water supplies. Wildlife can also be harmed by contaminated groundwater. Other long-term effects such as certain types of cancer may also result from exposure to polluted water. In this study the flow of contaminants in urban ground water is investigated. An analytical model for predicting groundwater contamination in isotropic and homogeneous porous formations was derived. The impact of dispersion and diffusion coefficients was included in the solution of the advection-dispersion equation (ADE), subjected to transient (time-dependent) boundary conditions at the origin. A retardation factor and zero-order production terms are included in the ADE. Analytical solutions were obtained using the Laplace Integral Transform Technique (LITT) and the concept of linear isotherm. Analytical solutions for linearly space- and time-dependent hydrodynamic dispersion coefficients along with molecular diffusion coefficients are presented. Analytical solutions are explored for the Peclet number. Numerical solutions are obtained by explicit finite difference methods and are compared with analytical solutions. Numerical results are analysed for different types of geological porous formations i.e., aquifer and aquitard. The accuracy of results is evaluated by the root mean square error (RMSE). The results of this study reveal that there is a very good agreement between the analytical solution and the numerical solution. It’s also clear from the results that the concentration values are less in aquifer than in aquitard. The Peclet number is found to be significant at very large values.
A Project Submitted in Partial Fulfillment of the Requirements for the Award of the Degree of Master of Science in Applied Mathematics in the School of Pure and Applied Sciences of Kenyatta University. June, 2020
2020-07-01T00:00:00ZBioconvection of a Newtonian Nanofluid Over a Vertical Plate in Presence of Gyrotactic Microorganisms
http://ir-library.ku.ac.ke/handle/123456789/21747
Bioconvection of a Newtonian Nanofluid Over a Vertical Plate in Presence of Gyrotactic Microorganisms
Kibe, John Ngugi
Bioconvection induced by gyrotactic microorganisms in a Newtonian nanofluid past a
permeable vertical plate is studied. Addition of motile microorganisms to a suspension of
nanoparticles in a basefluid enhances mass transfer and mixing in most microsystems in
addition to the enhancement of the convectional properties of the nanofluid. This concept has
solved many heating problems in various areas including civil engineering, chemical
engineering and mechanical engineering. The present study looks into the movement of
motile microorganisms present in a nanofluid over a vertical plate for purposes of saving
energy through the enhancement of heat transfer. The objectives are to formulate and solve
the mathematical equations governing bioconvection of a Newtonian Nanofluid flow along a
vertical plate, investigate the effects of gyrotactic microorganisms on the temperature and
velocity and temperature profiles of the nanofluid and to analyse the effects of nanoparticles
on microorganisms concentration, temperature and velocity profile. Ordinary differential
equations are obtained from the governing partial differential equations by use of similarity
variables. To numerically solve the ODE’s, the Runge-Kutta Ferhlberg method is used with
the shooting technique. Further, an investigation on the effects of controlling parameters on
several numbers and dimensionless quantities of our interest. It is found that the Nusselt
Number, the Sherwood Number and Skin Friction are strongly affected by nanofluid and
bioconvection parameters
A research project submitted in partial fulfilment of the requirements for the degree of Master of Science in applied mathematics in the school of pure and applied sciences of Kenyatta University. December, 2019
2019-12-01T00:00:00ZAnalysis of Magnetohydrodynamic Stagnation Point Flow Due to a Fluid towards a Convectively Heated Permeable Stretching Sheet
http://ir-library.ku.ac.ke/handle/123456789/21746
Analysis of Magnetohydrodynamic Stagnation Point Flow Due to a Fluid towards a Convectively Heated Permeable Stretching Sheet
Mwangi, Njoroge Kelvin
Stagnation-point flow of an electrically conducting fluid over a continuously stretching surface in presence of magnetic fields is significant in many industrial processes such as the metallurgy, polymer processing, glass blowing, filaments drawn through quiescent electrically conducting fluid subject to magnetic fields, cooling of metallic plate, hot rolling, wire drawing, aerodynamic extrusion of plastic sheets, crystal growing. In these applications of stagnation point flow, the desired output depends largely on the rate of heating and the velocity of the fluid on the surface. The required rate will be achieved by variation of various thermophysical parameters such as suction parameter, Grashoff number, Hartmann number and buoyancy parameter. The resulting nonlinear partial differential equations governing this flow were reduced to nonlinear ordinary differential equations using similarity transformations and the resulting equations solved numerically using the fourth order Runge-Kutta scheme with a shooting technique. Graphical results were presented and discussed quantatively with respect to the effects of thermophysical parameters on both velocity and temperature profiles of the fluid. From the study we note that an increase in Grashoff number (Gr), Hartmann number (Ha) and suction parameter resulted to a corresponding increase in fluid velocity. The fluid temperature also increased with increase in Gr and Ha but decreased with increase in suction parameter and buoyancy parameter.
A Research Project Submitted in Partial Fulfillment of the Requirement for the Award of the Degree of Masters of Science in Applied Mathematics in the School of Pure and Applied Sciences of Kenyatta University. October, 2020
2020-10-01T00:00:00Z