Pusat Pengajian Sains Matematik - Tesis

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Improving Forecasting Accuracy For Time Series Data Using Fuzzy Techniques And Wavelet Transform
(2025-07)
Hobaykan A., Alenezy Abdullah
This study focuses on improving the accuracy of stock market forecasting for the Saudi Arabia stock exchange (Tadawul) by employing advanced modeling techniques and adaptive learning approaches. The study utilizes the maximum overlapping discrete wavelet transform (MODWT) in conjunction with various mathematical functions to analyze daily stock price indices data from October 2011 to December 2019.
Wh Factorizationanditsapplication In Graphenergies
(2025-01)
Mohamed, Bashir Dlal Juma
Hourglass matrix is a square matrix obtained from quadrant interlocking factorization, known as WH factorization, which can be represented in mixed graph. Recent establishment of hourglass matrix and its factorization technique does not show the all the properties of the matrix. In this thesis, properties of WH factorization were put forward which include its existence for every strict dominant diagonal matrix, that its HSYSTEM forms a lower triangular invertible matrix and its counterpart W-matrix forms an upper triangular invertible matrix. To optimize WH factorization, a variant cramer’s rule is used to show that it has an advantage over the traditional cramer’s rule. It can be concluded that the block WH factorization technique is able to partition the matrix for effective factorization. The matrix obtained from WH factorization is known to be well represented as mixed graph, but not as topological index graph. There are over 50 types of graph energies obtained from degree based topological indices, only eight types are considered for the mixed hourglass graph: first and second zagreb energy, first and second hyper-zagreb energy, first and second guorava energy, and first and second hyper-guorava energy. Furthermore, all considered energies are compared to conclude that the energies give value of even numbers while the graph energy ratio (ratio between laplacian energy and the mixed energy of mixed hourglass graph) is odd.
Isolated Signalised Intersection Optimisation Under Mixed Traffic Flow
(2024-11)
Zhu, Hongtao
Traffic congestion has become a severe problem. Numerous studies have focused on optimising intersection performance under homogeneous traffic flow, which refers to a situation on a road where vehicle dimensions do not vary much from each other and vehicles behave similarly in terms of speed and following distance. However, few studies have considered mixed traffic flow. Mixed traffic flow is exceedingly stochastic and non-linear, with numerous traffic compositions which limit the largescale application of previously proposed methods. Hence, the intersection performance under mixed traffic flow is optimised from two aspects: intersection layout and signal timing. For intersection layout, this study considers an existing one-lane left-turn bypass intersection. To improve the intersection performance, an alternative two-lane left-turn bypass intersection layout is proposed. A simulation study to compare the proposed intersection with the two other intersection layouts under mixed traffic flow is conducted. The results show that the proposed intersection outperforms the two other layouts. For signal timing, this study considers the multi-objective signal timing optimisation problem for isolated intersection under mixed traffic flow. The findings demonstrate that traffic signal plans yielded by the proposed method have more advantages in reducing traffic congestion compared to the existing traffic signal plans. A main contribution of this study is the consideration of mixed traffic flow by including two-wheeled vehicles in the model.
Pengautomasian Penganalisisan Nota-Nota Kaki Penyata Kewangan Berasaskan Pengetahuan
(1991-07)
Wan Abdul Razak, Rohaya Amal
Matlamat utama di sini adalah untuk memperolehi suatu rekabentuk model yang bersifat pedagogi bagi transformasil penjelmaan nota kaki penyata kewangan (dalam bentuk teks) ke dalam bentuk perwakilan pengetahuan berasaskan kerangka. Perwakilan implementasi yang dipilih untuk tugas ini ialah perwakilan Framelog [Zahran 87, 89, 90], yang pada dasarnya merupakan gabungan dua formalisma pengetahuan, iaitu struktur kerangka dan formalisma logik.
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.

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