Abstract This project work examines the use of Lagrange multipliers to calculus of variation (isoperimetric problem). Basic definition of terms were given, necessary and sufficient condition for a function to be maxima or minima, how to identify Lagrange multipliers .in any given problem and general useage of largange multipliers, Lagrange multiplier in unconstraint and constraint problems, theorems and proof related to Lagrange multipliers. Literature review, Euler's Multiplier rule anisoper...
Abstract We Show the uniqueness of the norm on the Lebesgue space of the compact group. We give some applications of the property of Kazhdan to the method of automatic continuity. We determine the similarity of quasinilpotent operators. The symmetric Meixner- Pollaczek polynomials and a system of orthogonal polynomials with Hardy spaces for the strip are considered. We investigate the behaviour of the Lebesgue space of the integral means of the analytic functions and the vector- valued BMOA ...
Abstract In this research we consider discontinuous dynamical systems. We discuss the uniqueness of solutions and the stability analysis. We also report a number of sufficient conditions for uniqueness. We also present specific results to piecewise continuous vector fields and differential inclusions, with some examples and applications
Abstract In this research we consider discontinuous dynamical systems. We discuss the uniqueness of solutions and the stability analysis. We also report a number of sufficient conditions for uniqueness. We also present specific results to piecewise continuous vector fields and differential inclusions, with some examples and applications
Among other atmospheric region, ionosphere, which is the ionized region of the atmosphere, is considered to impose serious limitation on radio wave transmission while the effect of other layers, more especially, the troposphere is often treated as negligible. At higher frequency, radio waves pass through the ionosphere and are attenuated due to the free electrons present in it. However, recent studies have shown that while the ionospheric disturbances can be predicted on a global scale, trop...
Abstract We give characterizations of isometric shift operators and Backward shifts on Banach spaces with linear isometries between subspaces of continuous functions. We show the inverse spectral theory for the Ward equation and for the 2+1. Chiral model, we also consider the isometric shifts and metric spaces. We also study the Cauchy problem of the Ward equation. We discuss the relative Position of four subspaces in of Hilbert space, with an indecomposable representations ofQuivers on infi...
In this research, we deal with three forms of Stokes’ theorem. The version known to Stokes’ appears in the last chapter, along with its inseparable companions, Green’s theorem and the Divergence theorem. We discuss how these three theorems can be derived from the modern Stokes theorem, which appears in chapter (4), with some applications on oriented manifolds with boundary. In addition to applications of Maxwell’s field equations.
ABSTRACT This study was put in place in order to review simple model problems in continuum mechanics with internal body forces. The main objective of this study is to analyze simple model problems in continuum mechanics with internal body forces, which include the steady flow between parallel plates with internal body forces, which include review of internal body forces with its applications, internal body forces and moments, string with internal body forces, membrane with internal body forc...
Abstract This work takes a look at different computational algorithms used in solving initial value problems and how these algorithms arc derived from Taylor's series. It also made use of the Euler and Runge-Kutta method to solve initial value problems in order to compare the performance of the two methods.
Abstract This project report deals with the class of asymptotically demicontractive mappings in Hilbert spaces. We noted some historical aspects concerning the concept of asymptotically demicontractivity and studied a regularized variant of the Krasnoselskii-Mann iteration scheme, which ensured the strong convergence of the generated sequence towards the least norm element of the set of _xed points of asymptotically demicontractive mapping.
ABSTRACT The study of WEIGHTS AND RANKS OF CAUSES OF ROAD ACCIDENTS USING ANALYTIC HIERARCHY PROCESS (AHP) IN DODOMA REGION has been conducted in order to provide a broad understanding to the seriousness of problem of Road Accidents in Tanzania. Since the problem of road accidents in Tanzania is highly increasing year after year, various preventive measures have been taken to reduce the rate of road accidents. Thus it is important to understand the actual causes which have high contribution ...
ABSTRACT This dissertation centers on comparing two methods based on consistence and ranking preservation of alternatives in analytic hierarchy process(AHP) by using the best job example. These two methods logarithmic least square method (LLSM) and eigenvalue method (EM) are used to develop approximations of ratio scales from a positive reciprocal matrix. The measurement of consistency and rank preservation are the main criteria for comparison of these two methods. The priorities obtained f...
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 . We obtain new regular exact solutions to the field equations for uncharged relativistic stellar objects with vanishing pressure anisotropy. We assume a quadratic equation of state and a choice of measure of anisotropy and a metric function defining one of the gravitational potentials. In our exact models, we regain anisotropic and isotropic results generated by other researchers as a special case. It is interesting that our results are in agreement with Minkowski space-time and ear...
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...