ABSTRACT Mathematical models describing the variations in the plasma glucose and insulin levels over time in an insulin - dependent diabetic person (IDD patient) were formulated. We showed that these models can correctly describe these variations when we solved them sirnuttaneously by andytical approach rather than the normal numerical approach employed for solving non-linear differential equations. The effect of the various parameters involved in the model were tested and it was shown ...
Abstract In this research we studied Fourier transform and Fourier Analysis. We first introduced an analytical formulation using Hilbert space. We utilized the principle of uniform boundedness and the open mapping theorem to establish the convergence of Fourier series and the existence of Fourier transform. Here the geometry of Hilbert space has been involved. Then we applied Fourier transform to Engineering problems, these include Motion group, Robotics, Statistical mechanics, Mass de...
Abstract The description of the spectra tiling properties and Gabor orthonormal bases generated by the unit cubes and of the exponential for the 𝑛-cube are characterized. In addition the uniformity of non-uniform Gabor bases, atomic characterizations of modulation spaces through Gabor representations with Weyl-Heisenberg frames on Hilbert space, slanted matrices and Banach frames are clearly improved. We obtain the density, stability, generated characteristic function and Hamiltonian defo...
Abstract This study is an applied analytical one that helps in solving problems of the limit cycle and critical points for Planar systems. We introduced the classification of stable and unstable critical points of linear and nonlinear systems. The study found that the linear systems do not have a limit cycle. The study dealt with isolated limit cycle with its different patterns in an analytical and applied manner in the differential Planar systems of the second degree. The study investigated...
Abstract Complex Analysis And Conformal Mapping Play A Central Role In Mathematical Sciences And Theoretical Physics. The Traditional Applications Include Differential Equations, Harmonic Analysis, Potential Theory And Fluid Mechanics. Of Particular Interest To This Study Is The Complexfied Minkowski Space And Its Corresponding Spin Space Model Which Is Appropriate For The Description Of Quantum Field Theory. Moreover, For An Ambitious Scheme To Incorporate Gravitational Field In A Quantized...
ABSTRACT Manifolds are generalization of curves and surfaces to arbitrary higher dimensions. They are of many kinds, one of them being topological manifolds. The main feature common to manifolds is that every point of the space is in one to one correspondence with a point in another space. Hausdorff manifolds have been developed on infinite dimensional spaces such as Banach spaces and Fréchet spaces. Topological properties of non-Hausdorff manifolds have been studied and the notion of compa...
ABSTRACT A category is defined as an algebraic structure that has objects that are linked by morphisms. Categories were created as a foundation of mathematics and as a way of relating algebraic structures and systems of topological spaces. Any foundation of mathematics must include algebra, topology, and analysis. Algebra and topology have been studied extensively in category theory but not the analysis. This is partly due to the algebraic nature of category theory and the fact that the axio...
Abstract This thesis consists of two chapters, of which the first presents a categorial study of the concept of initiality (also known as projective generation) and the second gives applications in the.theory of uniform and quasi-uniform spaces, The' first three sections of chapter 1 expound basic aspects of initiality, such as its relation to categorial limits and to embeddings, the· latter being defined with respect to a faithful functor to a bicategory. The notion of a separated object wi...
Abstract Due to the 2008 financial crisis, investors have become more risk averse in investing in equities and have increased their holdings in bonds as they are believed to be less risky. However, South African interest rates have been volatile over the past decade due to changes in the inflation rate. This has caused the returns of bond portfolios to be uncertain since bond prices are inversely related to interest rates. It is thus imperative to manage the interest rate risk inherent in bo...
ABSTRACT In this theses, we investigate certain key aspects of mathematical modelling to explain the epidemiology of HIV/AIDS, Tuberculosis, Hepatitis B, Tumour,diabetes and stroke at the workplace and assess the potential benefits of proposed control strategies. The compartmental epidemiological modelling approach was used in the formulation of the models on HIV/AIDS, tuberculosis (TB), Hepatitis B (HBv), Tumour and Diabetes pandemic. In each of the cases, the dynamics of the disease was st...
We study the operator commuting and essential commutant of analytic Toeplitz operators module the compact operators and Toeplitz operators in several complex variables and on the Bergman space of the until ball. We show the ordered groups and some exact sequences and the commutator ideal of the Toeplitz algebras of spherical isometries and on the Bergman spaces of the unit ball in the unitary space. We give the lower bounds in the matrix, new estimate for the vector-valued and matrix-va...
In this work we discuss the scope of Lagrangian mechanics and constrained systems. We discuss the problem of central force two–bodies and its formal solution. Also we study the rotations and rigid bodies by using Euler’s equations, Lagrangian description and Legender transformations with some examples and applications.
ABSTRACT This thesis, Design-Reality Gaps in Open Source Information Systems Development: An Action Research Study of Education and Healthcare Systems in Tanzania, presents a theoretical and empirical informed analysis of Free Open Source Software (FOSS) development in the domain of health and education information systems in Tanzania. Historically, FOSS development has been driven by user-developer communities who are also the users of FOSS applications. The use of Foss applications in ...
This study introduces the mechanical elements that are the main components in the dynamic modeling of mechanical systems. It discusses the electrical elements of voltage and current source, resistor, capacitor, inductor, and operational amplifier. We derive mathematical models for electrical systems. The transfer function, enables connecting the input to the output of a dynamic system into the Laplace domain for single-input, single output, multiple-input and multiple output systems. It ...
Twistor theory has been invented by R. Penrose in order to generalize gravity. He introduced a geometrical model for Minkowski space. This geometrical setup has been generalized in solving particle differential equations. In particular zero-rest-mass field equation have been treated this way as a Contour integral of complex twistor function. In our study we consider geometrical interpretations and solutions of conformal field equations. We also studied Twistors in curved space-time and ...