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 theor...

An overview of Christoffel symbols and covariant derivative

An overview of different forms of christoffel symbols in the covariant derivative expansion of the product between (1,1) tensors

The problem of integration technique over integrands of the form f(t)/t^n, can be solved by differentiation(n times) by using Leibniz's rule to get rid of t^n, that leads to integrate back (n times) to end the game which it's harder than the original problem.This work focuses on the derivation of the formula (Pagano's Theorem) which is a perfect tool to avoid that hard task. It allows to change the difficult n iterated integrals into a more outstanding easier problem which consists of n -...

Abstract: An introduction to Laplace Transform is the topic of this paper. It deals with what Laplace Transform is, and what is it actually used for. The definition of Laplace Transform and most of its important properties have been mentioned with detailed proofs. This paper also includes a brief overview of Inverse Laplace Transform as&nb...

LINEAR ALGEBRA IN MATHEMATICS

The mathematical equations and concepts we learned in schools can actually be summed up to be relevant in the prediction, estimation and understanding of certain real world situations or problems that surrounds us. Some examples could be, How can we predict the break of a new infectious disease affecting the country Nigeria? How can reduction in the import of items into the country Nigeria affect the long term economy of the country Nigeria? How can we apply certain mathematical concept in ...

ABSTRACT: Infectious disease has become a source of fear and superstition since the first ages of human civilization. In this study, we consider the Discrete SIR model for disease transmission to explain the use of this model and also show significant explanation as regard the model. We discuss the mathematics behind the model and various tools for judging effectiveness of policies ...

Mathematical models here serve as tools for understanding the epidemiology of Human Immunodeficiency Virus (HIV) and Acquired Immunodeficiency Syndrome (AIDS) if they are carefully constructed. The research emphasis is on the epidemiological impacts of AIDS and the rate of spread of HIV/AIDS in any given population through the numericalization of the Basic reproductive rate of infection (R0). Applicable Deterministic models, Classic Endemic Model (SIR), Commercial Sex Workers (CSW) model,...

The analysis of the dynamic buckling of a clamped finite imperfect viscously damped column lying on a quadratic-cubic elastic foundation using the methods of asymptotic and perturbation technique is presented. The proposed governing equation contains two small independent parameters (δ and ϵ) which are used in asymptotic expansions of the relevant variables. The results of the analysis show that the dynamic buckling load of column decreases with its imperfections as well as with the inc...

ABSTRACTIn this project work, we studied the Adams-Bashforth scheme for solving initial value problems. We gave an indebt explanation on the Adam-Bashforth scheme, its consistency, stability, and convergence, the two and three step methods were also derived. Numerical solutions were obtained using four (4) examples.TABLE OF CONTENTS Cover page i &nbs...

research work presents an important Banach Space in functional analysis which is known and called Hilbert space. We verified the crucial operations in this space and their applications in physics particularly in quantum mechanics. The operations are restricted to the unbounded linear operators densely defined in Hilbert space which is the case of prime interest in physics, precisely in quantum machines. Precisely, we discuss the role of unbounded linear operators in quantum mechanics partic...

Let K be a nonempty closed convex subset of a Banach space E and T : K → K be a nonexpansive mapping. Using a viscosity approximation method, we study the implicit midpoint rule of a nonexpansive mapping T. We establish a strong convergence theorem for an iterative algorithm in the framework of uniformly smooth Banach spaces and apply our result to obtain the solutions of an accretive mapping and a variational inequality problem. The numerical example which compares the rates of convergence...

The problem of fraction decomposition it's easy to solve by using the cover up method, when there are no repeated linear factors in the denominator . Nevertheless it could turn into a hard work if these factors are raised to a high power, where the cover up method doesn't work. This technique shows how to calculate these coefficients without solving large systems of equations with a clever rearrangement of the numerator.

shortly from the Espil's theorem, we can derive the generalized Dirichlet integral for any natural value when the whole integrand is raised to the n-th power.