Pusat Pengajian Sains Matematik - Tesis
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- PublicationMagmas And The Twelve Local Moufang Identities(2025-05)Lee, Han ZhouQuasigroup is a binary system in which the specification of any two of x,y and z in the equation x · y = z determines the third element uniquely. A loop is a quasigroup with a (two-sided) identity element. A magma is a generalization of loops that does not satisfy the quasigroup condition. The (four) moufang identities are identities which are equivalent to each other in the variety of loops, for which a direct and comprehensive proof is provided. Each moufang identity involves three variables. By transforming a variable into a constant in each identity, the four moufang identities can be localized into twelve local identities. However, these local moufang identities are not generally equivalent to each other in the variety of magmas. Hence, this thesis aims to introduce not-too-restrictive conditions to magmas such that relationships can be found between these local identities. The automated reasoning tool prover9 and the finite model builder mace4 are used to obtain some of the important results in this thesis.
- PublicationDevelopment Of Non-Standard Finite Difference Methods For Systems Of Fractional Differential Equations With Application To Mathematical Biology Problems(2025-08)Masoud, Al Kathiri Said SalimNon-standard finite difference schemes (NSFDSs) have been proven highly effective in solving non-fractional differential equations. However, the applications of these schemes to physical phenomena, e.g., biological disease models, remain largely unexplored. Therefore, in this thesis, a mechanism has been developed to implement these schemes beyond the existing limitations of solving smaller fractional models.
- PublicationEnhanced Optimal Homotopy Asymptotic Multiple Parameters Method For Solving Fuzzy Fractional Differential Equations(2025-09)Alshbeel, Abdallah Eshbeel AbdallahThis thesis addresses these challenges by applying and extending the Optimal Homotopy Asymptotic Method (OHAM) to solve both linear and nonlinear FFDEs. The main contribution is the development of a generalized OHAM framework that incorporates advanced forms of fractional derivatives, specifically the Caputo-Katugampola (CK) derivative with two parameters and theAtangana–Baleanu–Caputo (ABC) derivative with Mittag–Leffler (ML) kernels involving three parameters.
- PublicationExploring The Relationships Between China'S Crude Oil Futures Market And Other Related Markets: New Findings(2025-04)Wu, YiminThis study examines the shanghai crude oil futures (scof) market, assessing its interactions with china’s new energy sectors—such as photovoltaic, energy storage, and wind power industries—and its connections with financial stock markets across asia (china, korea, japan, singapore, and india), as well as key macroeconomic indicators like inflation, money supply, and exchange rates. Using data spanning from 2000 to the most recent available, and employing econometric models including the spillover index, dcc-garch, nardl, and svar models, the analysis reveals substantial links between scof and financial markets in major oil-importing asian countries. Although scof is still influenced by international oil futures, its launch has helped moderate the relationship between global oil prices and china's industrial growth. However, spillover effects to other markets are limited, and the impact on china's macroeconomic variables remains minor. This research provides insights into scof's role in mitigating global oil price shocks and its connections within the broader financial and energy market landscape, aiding stakeholders in navigating the evolving scof market
- PublicationStudy Of Irr-Topological Groups And Isocompactness For Locally Semi-Compact Spaces(2025-04)Wang, ZhongliOver the years, generalized open sets have been a focal point of research for mathematicians. Many of the topological properties of locally semi-compact spaces remain unknown, and their connections with other topological spaces are still unclear. This work will focus on these problems and mainly consists of two parts. The first part focuses on the generalizations and applications of locally semi-compact spaces, while the second part primarily deals with the applications of isocompact spaces in locally compact topological groups. In the first part, we primarily accomplished three works. First, we obtain some new topological properties of locally semi-compact spaces, and introduce the new definition of semi-k spaces, which generalizes the concept of locally semi-compact. Second, the relations between separation axioms and locally semi-compact spaces, between semi-countably compact spaces and semi-k spaces, and between locally semi-compact spaces and s-paracompact spaces are established. Third, and most importantly, we obtain some applications of locally semi-compact spaces in s-topological groups and irr-topological groups. Additionally, we prove when locally