Mathematics Research Papers/Topics

REGULARIZATION OF ILL-CONDITIONED LINEAR SYSTEMS

ABSTRACT The numerical solution of the linear system Ax = b, arises in many branches of applied mathematics, sciences, engineering and statistics. The most common source of these problems is in the numerical solutions of ordinary and partial differential equations, as well as integral equations. The process of discretization by means of finite differences often leads to the solution of linear systems, whose solution is an approximation to the solution of the original differential equation. If...

MELLIN TRANSFORM METHOD FOR THE VALUATION OF AMERICAN POWER PUT OPTION

Abstract American Power Put Option (APPO) is a financial contract with a nonlinear payoff that can be applied at any time on or before its expiration date and offers flexibility to investors. Analytical approximations and numerical techniques have been proposed for the valuation of Plain American Put Option (PAPO) but there is no known closed-form solution for the price of APPO. Mellin transform is a useful method for dealing with unstable mathematical systems. This study was designed to der...

COMPUTATIONAL METHODS FOR DENOISING HIGH-THROUGHPUT DATA

ABSTRACT T-cell diversity has a great influence on the ability of the immune system to recognise and fight the wide variety of potential pathogens in our environment. The current state of art approach to profiling T-cell diversity involves high-throughput sequencing and analysis of T-cell receptors (TCR). Although this approach produces huge amounts of data, the data has noise which might obscure the underlying biological picture. To correct these errors, two computational methods have been d...

A MATHEMATICAL MODEL FOR LENDING IN MICROFINANCE AND APPLICATIONS

ABSTRACT Loan default is one of the major problems facing most financial institutions. The solution to this problem has been the use of a mathematical model to determine the probability of default of clients of these financial institutions. This study proposes a mathematical model for predicting the probability of default of clients from a microfinance institution. The logistic and survival analysis methods were used in building the model. The results from the logistic regression model showed...

MATHEMATICAL MODEL FOR THE CONTROL OF MALARIA

ABSTRACT Many infectious diseases including malaria are preventable, yet they remain endemic in many communities due to lack of proper, adequate and timely control policies. Strategies for controlling the spread of any infectious disease include a rapid reduction in both the infected and susceptible populations. (if a cure is available) as well as a rapid reduction in the susceptible class if a vaccine is available. For diseases like malaria where there is no vaccine, it is still possible to ...

USING BEAM BALANCE TO ASSIST DBE STUDENTS TO IMPROVE ON THEIR CONCEPTUAL KNOWLEDGE OF LINEAR INEQUALITIES IN ONE VARIABLE

ABSTRACT This study was undertaken to assist DBE ONE „A‟ students of St. Francis College of Education, Hohoe to improve on their conceptual knowledge of linear inequalities in one variable using the beam balance model. The entire DBE ONE „A‟ students represented the population of the study. Data was gathered through instruments such as test in the form of pre-test and post-test. Due to the large size of the population a total of 40 students which represented 20% of the 200 DBE ONE �...

IN-SERVICE TEACHERS’ USE OF ICT IN TEACHING MATHEMATICS IN GHANA. A CASE STUDY IN THE CAPE COAST METROPOLIS

ABSTRACT This study was set out to examine the barriers to ICT integration into Mathematics teaching and learning in selected Senior High Schools in the Central Region of Ghana. Specifically, the study aimed to examine the effects of internal barriers (constructive teaching beliefs, teaching experience, attitudes toward computer and technology competence) and external barriers (access to technology use, level of training in the use of technology, time adequacy, as well as, the culture of the ...

LEAST SQUARES OPTIMIZATION WITH L 1-NORM REGULARIZATION

ABSTRACT The non-differentiable L1-norm penalty in the L1-norm regularized least squares problem poses a major challenge to obtaining an analytic solution. The study thus explores smoothing and non-smoothing approximations that yields differentiable loss functional that ensures a close-form solution in over-determined systems. Three smoothing approximations to the L1-norm penalty have been examined. These include the Quadratic, Sigmoid and Cubic Hermite. Tikhonov regularization is then a...

USING GEOMETER’S SKETCHPAD TO ENHANCE THE ABILITY TO LOCATE THE COORDINATES OF THE IMAGE OF A GEOMETRICAL OBJECT UNDER RIGID MOTION IN A CARTESIAN PLANE OF SENIOR HIGH SCHOOL 4 STUDENTS OF

ABSTRACT This research work was set out to see, if Geometer’s Sketchpad could be used to enhance the ability level of SHS 4 students of Osei Tutu II College in the location of the coordinate of the image of a point or geometrical object under Rigid Motion in a Cartesian plane. A non-probability sampling technique known as purposive sampling was employed to select the sample for the study. In all, 45 SHS 4 students comprising 34 girls and 11 boys were involved in the study. The main resear...

Controllability Results for Non-Linear Neutral Functional Differential Equations

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 theorem is used to forge a new and far- reaching result for the...

Christoffel symbols

An overview of Christoffel symbols and covariant derivative 

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  well  as  a  brief  overview  of application  in  control  system.  A  few  practical  life�...

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  ...


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