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 We find two new classes of exact solutions for the Einstein-Maxwell equations. The solutions are obtained by considering charged anisotropic matter with a linear equation of state consistent with quark stars. The field equations are integrated by specifying forms for the measure of anisotropy and a gravitational potential which are physically reasonable. The solutions found generalize the Mark-Harko model and the Komathiraj-Maharaj model. A graphical analysis indicates that the matt...
Abstract We find new exact solutions to the Einstein-Maxwell field equation for charged anisotropy stellar bodies. We are considering the stellar object that is anisotropic and charged with linear equation of state consistent with quark stars. We have new choice of measure of anisotropy and adopted Sunzu’s metric function. The solutions are obtained after considering the transformed Einstein-Maxwell field equations for charged anisotropic matter. In our models we regain previous anisotropi...
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 The dynamic buckling loads of some imperfection-sensitive elastic structures subjected to slowly varying time dependent loading are determined using perturbation procedures. First, we consider an elastically imperfect column resting on a softening nonlinear elastic foundation. The governing differential equation has two small parameters. We determine the dynamic buckling load of this column subjected to the stipulated loading for three different cases. The cases are when the small p...
ABSTRACT Let H be a real Hilbert space and K a nonempty, closed and convex subset of H. Let T : K ! K be an asymptotically nonexpansive map with a nonempty xed points set. Let fng1n =1 and ftng1 n=1 be real sequences in (0,1). Let fxng be a sequence generated from an arbitrary x0 2 K by yn = PK[(1 tn)xn]; n 0 xn+1 = (1 n)yn + nTnyn; n 0: where PK : H ! K is the metric projection. Under some appropriate mild conditions on fng1n =1 and ftng1 n=1, we prove that fxng converges strongly ...
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...
Abstract Mathematical study of human pulse wave was studied with the view to gaining an insight into physiological situations. Fluid –Structure interaction (FSI) in blood flow is associated with pressure pulse wave arising from ventricular ejection. Solution of the coupled system of nonlinear PDEs that arose from the FSI was sought in order to determine pressure. Further study on pressure pulse waves showed that the Korteweg-de Vries (KdV) equations hold well for the propagation of nonline...
Abstract In recent years, advance in technology have made it possible for the stock markets to trade in real time and also for large dataset to be available for statistical analysis. Thus, we examined the impact of macroeconomic variables on the stock returns of 114 companies listed on the Nigerian Stock Exchange Market. We have established the mathematical framework required to solve our model and perform various empir- ical analysis on the stock market data and macroeconomic variable. The f...