Research Papers/Topics in Mathematics

Christoffel symbols

An overview of Christoffel symbols and covariant derivative 

Covariant derivative & Christoffel symbols

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

Pagano's theorem. A generalized form of the Dirichlet integral involving Laplace Transforms techniques

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 -...

Laplace Transform application in Control System

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...

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 whole 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 ...

GROUP 3 RIEMANN NTEGRATION ON R^n

1 Riemann Integration 21.1 Partitions and Riemann sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.1 Definition  (Partition P of size  > 0) . . . . . . . . . . . . . . . . . . . . 21.1.2 Definition (Selection of evaluations points zi) . . . . . . . . . . . . . . . . 21.1.3 De finition (Riemann sum for the function f(x)) . . . . . . . . . . . . . . 21.1.4 Defi nition (Integrability of the function f(x)) . . . . . . . . . . . . . . . 21.1.5 De finition (Notation for integrab...

Arithmetic of Analysis (Supremum and Infimum)

I can still remember my expression and feeling when we were asked to show that sup(A + B) = sup(A) + sup(B). It was an herculean task because the concept was too difficult to grasp with the use of approximation property until I discovered an easy route. In a bid to restrict my papers to just few pages, I will focus more on examples than theorems.

Properties of Operations on Soft Ideals and Idealistic Soft Ring

Abstract: Soft set theory initiated by Molodtsov is an important mathematical tool that deals with uncertainties about imprecision and vagueness. Research on soft ideals of ring has been carried out by other researchers. In this paper, we discuss on some properties of soft ring ideals and idealistic soft ring. We state and prove some important theorems and propositions on soft ring ideals and idealistic of soft ring that has not been studied by other researchers.

Differential Forms: A Tool for Linearizing Second Order Ordinary Differential Equations

Abstract: In this paper, we presented the differential forms method which is used in the linearization of second order non-linear differential equations. The differential forms used here is limited to 2-forms with their respective operations. After presentation of the method, an example is used to illustrate the procedure of the linearization problem. Keywords Linearization, Differential forms, Differential Equations, Second Order

Numerical Treatment of General Third Order Ordinary Differential Equations Using Taylor Series as Predictor

This work considers the direct solution of general third order ordinary differential equation. Themethod is derived by collocating and interpolating the approximate solution in power series. Asingle hybrid three-step method is developed. Taylor series is used to generate the independentsolution at selected grid and off grid points. The order, zero stability and convergence of themethod were established. The developed method is then applied to solve some initial valueproblems of third order OD...

Effect of Computer-Instructional Package on the Performances of Senior Secondary Students in Quadratic Equations in Bida Educational Zone of Niger state, Nigeria.

AbstractThis study investigates the Effect of Computer- Instructional Package (COMPUTER INSTRUCTIONAL PACKAGE) on the Performance of Senior Secondary Students in Quadratic Equation in Bida Educational Zone of Niger State, Nigeria. The study examined the significant of performances of students thought using computer instructional package andLecture method. The sample consisted of 120 senior secondary school students drawn from four secondary schools. Stratified random sampling was used toselec...

On the Stability of Endemic Equilibrium State of HIV/AIDS Model with Irresponsible Infective Immigrants

ABSTRACTIn this paper, a non–linear mathematical model is proposed to study the effects of irresponsible infected immigrants on the spread of HIV/AIDS in a heterogeneous population with a constant recruitment of susceptible receptors. Theequilibrium points, stability analysis, and numerical solution on the model are presented. The Routh–Hurwitz stability condition was employed to examine the stability of the disease– free equilibrium and Next Gene...

MODELING CHOLERA DYNAMICS WITH CONTROLS

ABSTRACT. In this paper, we present and analyze a choleraepidemiological model with control measures incorporated. Thismodel is extended from the one proposed in [16] by includingthe effects of vaccination, therapeutic treatment, and water san-itation. Equilibrium analysis is conducted in the case with con-stant controls for both epidemic and endemic dynamics. Opti-mal control theory is applied to seek cost-effective solution ofmultiple time-dependent intervention strategies against chol...

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