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 the symmetric group S5 on the cosets of its non-maximal subgroups is an aspect that seems to have received less attention for sometime. Most studies have infact looked on the action of symmetric group S5 on the cosets of its maximal subgroups leaving many properties about its action on non-maximal subgroups unknown. This project has therefore looked at the action of the symmetric group S5, on the cosets of some of its non-maximal subgroups. Namely; the cyclic grou...
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...
ABSTRACT A triple system is an absolutely fascinating concept in projective geometry. This project is an extension of previously done work on triple systems, specifically the triples that fit into a Fano plane and the (i, j, k) triples of the quaternion group. Here, we have explored and determined the existence of triple systems in Z ∗ n for n = p, n = pq, n = 2mp and n = pqr with m ∈ N, p, q, r ∈ P, and p > q > r. A triple system in Z ∗ n has been denoted by (k1, k2, k3) where there...
ABSTRACT In this project we compare the performance of two different estimators of the population total. One estimator is model-based and the other one is model assisted. We look at model-based properties of the two estimators. We observe that under the general model, the biases of the two estimators are different
ABSTRACT Many authors have studied the suborbital graphs of various group actions and their corresponding properties. This thesis investigates the actions of the cyclic group and the dihedral group on the diagonals of a regular -gon and the properties of their corresponding suborbital graphs. In addition, it focuses on the action of the multiplicative group of units on , the set of non zero elements in . The properties of the corresponding suborbital graphs to this action are also investigat...
ABSTRACT Tuberculosis, an air-borne infectious disease, remains a major threat to public health in Kenya. In this study we derived a system of non-linear ordinary differential equations from SLICR mathematical model of TB to study the effects of hygiene consciousness as a control strategy against TB in Kenya. The effective basic reproduction number (R0) of the model was determined by the next generation matrix approach. We established and analysed the equilibrium points. Using the Routh-Hurw...
ABSTRACT In malaria endemic areas, fever is commonly caused by malaria infection but it may be a manifestation of several childhood diseases for example bacterial and viral illnesses. Malaria microscopy is the gold standard for diagnosis of malaria although other diagnostic platforms do exist for example rapid diagnostic tests. The World Health Organization recommends parasitological diagnosis by microscopy or rapid diagnostic test for all children under the age of 5 years. However, in malar...
ABSTRACT For a period spanning 50 years, research on the ranks, subdegrees and properties of suborbital graphs of various groups e.g. Sn , PSL(2, ), PSL(2,q) and PGL(2,q) has drawn the attention of several mathematicians. In this study, we find the ranks and subdegrees of the actions of the cyclic group, the dihedral group and the affine group on some given sets. In addition, the properties of suborbital graphs corresponding to these actions are examined. To do these, we adopt a method that r...
ABSTRACT The action of Projective Special Linear group PSL(2; q) on the cosets of its subgroups is studied. Primitive permutation representations of PSL(2; q) have been previously studied by Tchuda (1986), Bon and Cohen (1989) and Kamuti (1992). In particular, the permutation representations on the cosets of Cq1 k ; Cq+1 k ; Pq; A4 and D2(q1) k are studied. In the case where it was previously done, we employ a dierent method or otherwise quote the results for completeness purpose. Thu...
ABSTRACT 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 presen...