Abstract In this work, we try to set up a geometric setting for Lagrangian systems that allows to appreciate both theorems of Emmy Noether. We consistently use differential form and a geometric approach, in this research, we also discuss electrodynamics with gauge potentials as an instance of differential co-homology. Also we emphasize the role of observables with some examples and applications.

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 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 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 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...