Research Papers/Topics in Mathematics

THE MATHEMATICAL MODELLING CONCEPT pt1

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 ...

Discrete time mathematical SIR model for disease transmission

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  ...

On Application of Mathematical Modeling in the Spread of HIV/AIDS Epidemic

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,...

Dynamic Buckling of a Clamped Finite Column Resting on a Non – linear Elastic Foundation

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...

THE ADAMS-BASHFORTH ITERATIVE SCHEME FOR INITIAL VALUE PROBLEMS

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...

Application of Unbounded Hilbert Linear Operations in Quantum Mechanics

 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...

The Implicit Midpoint Rule of Non-expansive Mappings and Applications in Uniformly Smooth Banach Space

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...

Espil's high power partial fraction decomposition theorem.

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.

Espil's theorem corollary

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

Integration technique using Laplace Transforms. A generalized form of the Dirichlet integral.

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 (Espil'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-1 ...

It is Time to Move Research Expenditures to the Denominator in University Metrics

An unintended consequence of using “research expenditures” as a figure of merit for universities is to reduce the research output per dollar invested by discouraging the diffusion of superior, lower-cost, open-source scientific equipment.

Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure"[1]) is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.[2]The 3rd-century astronomers first noted that the lengths of the sides of a right-angle triangle and the angles between those sides have fixed relationships: that is, if at least the...

SPECTRAL METHOD SOLUTION OF VOLTERRA INTEGRAL EQUATIONS VIA THIRD KIND CHEBYSHEV

Contents1 General Introduction 11.1 Background of Study . . . . . . . . . .11.2 Integral Equation . . . . . . . . . .......21.2.1 Fredholm integral equation . . .31.2.2 Volterra integral equation . . . . 41.3 Polynomials . . . . . . . . . . . . . . . . . 41.4 Orthogonal Polynomials . . . . . . .51.5 Chebyshev Polynomials . . . . . . . 61.5.1 Chebyshev polynomial of the first kind Tr(x) . . . . . 61.5.2 Chebyshev polynomial of second kind Ur(x) . . . . . 61.5.3 Chebyshev polynomials of third-k...

Systematic study of z transform and its analysis on Discrete Time Systems

                    ABSTRACTIn this project work, we have established a systematic study of z transform and its analysis on Discrete Time (DT) systems. The researcher also deal with Linear Time Invariant (LTI) system and Difference Equation as examples of DT systems. The right and left shift was use as a method of solution of the z transform to linear difference equation.CHAPTER 1          &nb...

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