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 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 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...

ABSTRACT In this work, necessary and sufficient conditions are investigated and proved for the controllability of nonlinear functional neutral differential equations. The existence, form, and uniqueness of the optimal control of the linear systems are also derived. Global uniform asymptotic stability for nonlinear infinite neutral differential systems are investigated and proved and ultimately, the Shaefers’ fixed point theorem is used to forge a new and farreaching result for the existenc...

Abstract We present in this thesis the numerical solution to the partial differential equations of parabolic type using the finite-difference methods, namely explicit and Crank-Nicolson methods. We account the local truncation error of the two schemes by using Taylor series and discuss the consistency or compatibility, convergence and stability of these schemes for the parabolic equations. We present vector and matrix norms, also a necessary and sufficient condition for stability. Finally s...

Abstract We show that if a pair of weights (u, ) satisfies a sharp Ap - bump condition in the scale of all log bumps certain loglog bumps , then Haar shifts map ( ) into (u) with a constant quadratic in the complexity of the shift . This in turn implies the two weight boundedness for all Calderón – Zygmund operators. We obtain a generalized version of the former theorem valid for a larger family of Calderón – Zygmund operators in any ambient space . We present a bilinear Tb theorem for...

Abstract Dynamical Systems is the study of the long-term behavior of evolving systems. In this research we studied Lagrangian and Hamiltonian Dynamical systems using Clifford manifolds. The Clifford analogue of Lagrangian and Hamilton Dynamical systems is introduced. In fact a new dynamics on Clifford manifold has been constructed via some local canonical basis. This construction provides wide applications to Physical equations and their geometrical interpretation.

Abstract We find the approximate solution for hyperbolic equation in one space dimension using two finite different schemes: Lax- Wendroff and upwind schemes Then, we study Fourier analysis of these two schemes. we also approximate the numerical solution of system of hyperbolic equations by using finite volume scheme and leap-frog schemes. As well, we study the Fourier analysis of these two schemes. Finally, we study the consistency, convergence and stability for hyperbolic equation in one s...

ABSTRACT The study of magnetohydrodynamics (MHD) flow has received much attention in the past years owing to its applications in MHD generators, plasma studies, nuclear reactor, geothermal energy extractions, purifications of metal from non-metal enclosures, polymer technology and metallurgy. In view of the above, theoretical analysis of the effects of buoyancy force, velocity slip, temperature jump and thermal radiation on entropy generation rate were investigated on electrically conducting...

ABSTRACT There are several real life data sets that do not follow the Normal distribution; these category of data sets are either negatively or positively skewed. However, some could be slightly skewed while others could be heavily skewed. Meanwhile, most of the existing standard theoretical distributions are deficient in terms of performance when applied to data sets that are heavily skewed. To this end, the aim of this study is to extend the Inverse Exponential distribution by inducing it ...

Abstract The role of generalized ordinary differential equation (Kurzweil equation) in applying the technique of topological dynamics to the study of classical ordinary differential equation as outlined in [3, 4, 47, 51-58, 88-90] is a major motivation for studying this class of equations associated with the weak forms of the Lipschitzian quantum stochastic differential equations. In this work, existence and uniqueness of solution of quantum stochastic differential equations associated with ...

Abstract The numerical solutions of initial value problems of general second order ordinary differential equations have been studied in this work. A new class of continuous implicit hybrid one step methods capable of solving initial value problems of general second order ordinary differential equations has been developed using the collocation and interpolation technique on the power series approximate solution. The one step method was augmented by the introduction of offstep points in order ...