Abstract This project is concerned with the review of some boundary value problems for nonlinear ordinary differential equations using topological and variational methods. A more classical boundary value problems for ordinary differential equations (like the boundary value problems on a ball, initial value problems, problems on annular domains and positone problems) which represent the main interest of a wide number of researchers in the world is studied. Contents Certification ii Dedication ...

ABSTRACT Mathematical Models describing the variations in the volume of the system, concentration of reactant (s) yet to react, temperature of the system, and the temperature of the cooling jacket over time in a non-isothermal CSTR that handles a simple, irreversible, first order or second order exothermic reaction in liquid phase were formulated. This work is with a particular reference to the synthesis of propylene from cyclopropane and that of cumene (isopropyl benzene) from benzene and pr...

ABSTRACT We comparatively studied gas phase concentration and gas temperature of three way catalytic converter models. We considered channel level models and provided concise solutions for them. Solutions to the models were graphically represented and we found that gas phase temperature increases with time and gas phase concentration of gaseous species attain light-off at temperature above 600K. TABLEOFCONTENTS Title page………………………………………………………………...

Abstract A single server Markovian queuing system called the M/M/1 queuing system with two distinct customer types namely; the constraint customer type and the un-constraint customer type is studied. This model is that of a production system with heterogeneous customer structures devoid of a single customer in the intersection category group wise. Initially, relevant literature covering methodologies, analysis and results derived for single server production systems are reviewed and a gap ide...

Abstract Let Xn = { } 1,2,…,n be a finite n -element set and let Sn An and Dn , be the Symmetric, Alternating and Dihedral groups of Xn , respectively. In this thesis we obtained and discussed formulae for the number of even and odd permutations (of an n − element set) having exactly k fixed points in the alternating group and the generating functions for the fixed points. Further, we give two different proofs of the number of even and odd permutations (of an n − element set) having ex...

ABSTRACT GeoGebra is a free computer application software that provides an algebra view, geometry view, spreadsheet view and an input bar. This study looked at if and how this resource can be used to enhance the teaching of Geometry in secondary schools in Kajiado County in Kenya. The objectives of this study were to assess the applicability of GeoGebra in the teaching of mathematics in secondary schools in Kenya. The relationship in performance of students taught with the help of this innov...

ABSTRACT This study assesses the performance of three numerical turbulence models; k -e , k -w and k -w - SST in predicting heat transfer due to natural convection inside an air filled cavity. The heat transfer due to natural convection inside a rectangular closed cavity should be modeled to include the effect of turbulence for Rayleigh number greater than or equal to 9 10 .The non-linear terms i j u u and qi u in the averaged momentum and energy equations respectively were modeled using...

ABSTRACT The purpose of this study was to explore the various challenges and opportunities influencing integration of ICT in teaching and learning Mathematics in secondary schools in Nairobi County. The study sought to: Determine the levels of ICT integration in teaching and learning Mathematics; identify the challenges and opportunities of ICT use in teaching and learning Mathematics; and identify best pedagogical practices used in teaching Mathematics using ICT. The study adopted Rogers’s...

ABSTRACT The action of the symmetric group Sn on ordered subsets from the set X 1, 2, , n is an aspect that seems to have received little attention for a long time. Most studies have focused on the action of n S on unordered subsets leaving many properties about its action on ordered subsets unknown. This research is set to determine the rank and subdegrees of n S acting on r X , the set of all ordered r-element subsets from X. Particular cases when r 2, 3 and 4 have b...

ABSTRACT The Galois group of a certain type of field extension is a specific group associated with the field extension. The study of field extensions and their relationship to the polynomials that give rise to them via the Galois groups came to be called Galois Theory in honor of Everiste Galois who first discovered them in 1830. In this project we find the extensions of whose Galois group is isomorphic to, , and the quaternion group . In each case we identify the extension, then work ou...

Abstract The concept of the cycle index formulas of a permutation group was discovered in the year 1937. Since then cycle index formulas of several groups have been studied by di_erent scholars. For instance the cycle index of the dihedral group Dn acting on the set of vertices of a regular ngon is known and has been applied in enumeration of di_erent mathematical structures. In this study the relationship between the cycle index formula of a semidirect product group and the cycle index f...

ABSTRACT Trigonometry topics are very important in mathematics education as trigonometric functions have many applications in fields such as adverse physics, mechanical and electrical engineering, music, astronomy and biology. Any challenges encountered by students in learning affect overall performance in the subject. The purpose of the study was to determine the pedagogical factors affecting learning of the topic in secondary schools and recommendation made. The objectives of the study were...

Abstract Platonic solids are 3-dimensional regular, convex polyhedrons. Each of the faces are equidistant and equiangular to each other in any of the solids. They derive their name from the ancient Greek philosopher, Plato who wrote about them in his dialogue, the Timaeus as reported by Cornford (2014). The solids features have fascinated mathematicians for decades including the renown geometer, Euclid: In his Book XIII of the Elements, as rewrote by Heath et al. (1956), he successfully�...

ABSTRACT The action of and on the cosets of their subgroups is a very active area in enumerative combinatorics. Most researchers have concentrated on the action of these groups on the cosets of their maximal subgroups. For instance Tchuda computed the subdegrees of the primitive permutation representations of . Kamuti determined the subdegrees of primitive permutation representations of . He also constructed suborbital graphs corresponding to the action of on the cosets of However many prope...

ABSTRACT In this study the effects of applying variable pressure gradient to a MHD fluid flowing between two plates in an inclined magnetic field was carried out. It involved an unsteady hydromagnetic fluid flowing through two plates where the upper plate was porous and moving with a constant velocity in a direction that is contrary to fluid flow direction. The lower plate was non-porous and stationary. In the past years, research studies relating to MHD fluid flow through plates have been do...