Pusat Pengajian Sains Matematik - Tesis

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A Wavelet-Based Approach For The Analytical Solutions Of Fractional Differential Equations And The Numerical Solutions Of Fractional Integral Equations
(2024-11)
Loong, Marcus Ong Wei
Following the rise of fractional-order models and consequently, their fractional governing equations, new analytical and numerical methods have been developed and studied extensively. However, amidst the multitude of integral transform methods, there have been no research done on the application of the continuous wavelet transform to analytically solve fractional differential equations. To fill this gap, the present dissertation derives an analytical method based on this integral transform by applying it to the riemann-liouville integral and derivative, and the caputo derivative. With the help of theorems and techniques in calculus and fractional calculus, important results in functional analysis and properties of the continuous wavelet transform, it is found that poisson wavelet transform of order n = 1 is able to yield meaningful results, suitable for solving fractional-order equations. To demonstrate this, the scheme is applied to solve two fractional differential equations, defined based on each of the aforementioned fractional derivatives, wherein the exact solutions were successfully obtained. On the other hand, much of the numerical analysis of fractional equations have been focused on that of differential equations and thus, algorithms for fractional integral equations have been found wanting. Motivated by the prowess of the legendre wavelet in solving fractional differential equations numerically, this thesis strives to construct a numerical scheme based on this wavelet for fractional integral equations.
Bayes And Least-Squares Procedures In Sampling From Finite Populations
(1984-04)
Mehrotra, Pretta Latha
In this thesis, we shall consider estimation 1n finite populations under a model-based superpopulation approach using least-squares and Bayesian prediction procedures. Greater emphasis will be placed on the Bayesian inference. The first chapter covers a general preview of the 'classical' fixed population approach and the superpopulation model-based approach, the general survey design framework used and a literature review relevant to this study.
Modified Deterministic Modelling For Tuberculosis Infection
(2024-03)
Sulayman, Fatima
Tuberculosis (TB), caused by the Mycobacterium tuberculosis, is one of the contagious disease that mainly attacks human lungs and caused 10.6 million new infection globally, with an average of 1.6 million people dying. In general, mathematical modelling can serve to understand the transmission pattern and identify suitable controls in preventing the infections. Through mathematical modelling as well, the dynamics of an infection can be predicted more effectively. This in turn leads to the main purpose of this thesis where four compartmental deterministic models for tuberculosis infection is proposed. The developed models addressed the important factors related to the transmission of tuberculosis infection, such as public health education and hospital treatment, an imperfect vaccine, nonlinear saturated recovery (treatment) and optimal control.
Modelling The Nexus Between Energy-Economic Growth Using The Long Panel Data Estimations
(2024-01)
Sim, Khang Yi
This thesis examines a two-way causal relationship between energy consumption and economic growth for two panel groups, i.e., low and lower-middle-income economies (Group 1) and high-income economies (Group 2), over 1990–2019 with quarterly datasets. Apart from the first objective, this thesis aims to address various estimation issues related to long panel data that conventional panel models frequently overlook, covering nonstationary or cointegration, slope heterogeneity, cross-sectional dependence and dynamic effect.
Improvement Of Curve Construction Using Bi-Qt Bezier Curves And Approximation To Two Types Of Bezier Curves
(2024-02)
Nordin, Mohamad Ekram
A new approach, namely an optimized bi-QT-Bezier, for fitting curves to given 2D, is proposed. The conventional approach includes additional constraints to uniquely determine the biarc. The proposed method integrates the formulation of a single biarc based on the Quadratic Trigonometric (QT)-Bezier curve with Particle Swarm Optimization (PSO). The proposed bi-QT-Bezier curve is advantageous in curve fitting as it provides an optimized value of α from the PSO method.

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