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Publication On solvable septics(2005-01-07) LAU JING FENG; MATHEMATICS; LANG MONG LUNGThe problem of solving the general irreducible polynomial in one variable and expressing its roots in radicals has been proposed ages ago. Since then the case of solving general quadratics, cubics and quartics has been solved and it took a few centuries before Abel and Galois demonstrated the impossibility to solve general equations of degree higher than 4. In two recent papers [D] and [H], Dummit and respectively Hagedorn provide methodologies to solve the general solvable quintic and sextic. In this thesis, we shall adopt the techniques in [D] to give a qualitative description of solving solvable irreducible polynomials of arbitrary prime degree and apply these results to solve for two of the roots of x^7+x^6-12x^5-7x^4+28x^3+14x^2-9x+1=0 which can be used to express cos 2 pi/29 in radicals.References[D] D. S. Dummit, Solving Solvable Quintics, Mathematics of Computation, Volume 57, Issue 195, 387-401, 1991.[H] T. R. Hagedorn, General Formulas for Solving Solvable Sextic Equations, Journal of Algebra, Volume 233, Issue 2, 704-757, 2000.Publication VALUATION OF CAPPED STOCK LOANS WITH REGIME SWITCHING(2011) SHI WEI; MATHEMATICS; XIA JIANMINGPublication INDEPENDENT SETS OF MAXIMAL SIZE IN REGULAR GRAPHS(2009) LOO CHEE WEE; MATHEMATICS; KU CHENG YEAWPublication LATTICE METHODS FOR MULTIDIMENSIONAL NUMERICAL INTEGRATION(2007) ZHAO YA; MATHEMATICS; HARALD NIEDERREITERPublication LAGRANGE MECHANICS AND THE BUBBLE WORLD(2014) VALERIE CHAN CHU TING; MATHEMATICS; BRETT MCINNESPublication SOLVING NEAREST COVARIANCE MATRIX PROBLEM WITH EQUALITY AND INEQUALITY CONSTRAINTS(2011) ZHAO YANG; MATHEMATICS; TOH KIM CHUANPublication On the Fractional Metric Dimension of Convex Polytopes(Hindawi Limited, 2021-09-23) Aslam, M. K.; Javaid, Muhammad; Zhu, Q.; Raheem, Abdul; MATHEMATICSIn order to identify the basic structural properties of a network such as connectedness, centrality, modularity, accessibility, clustering, vulnerability, and robustness, we need distance-based parameters. A number of tools like these help computer and chemical scientists to resolve the issues of informational and chemical structures. In this way, the related branches of aforementioned sciences are also benefited with these tools as well. In this paper, we are going to study a symmetric class of networks called convex polytopes for the upper and lower bounds of fractional metric dimension (FMD), where FMD is a latest developed mathematical technique depending on the graph-theoretic parameter of distance. Apart from that, we also have improved the lower bound of FMD from unity for all the arbitrary connected networks in its general form. © 2021 M. K. Aslam et al.Publication PORTFOLIO OPTIMISATION(2020) CHEN ZHILIANG; MATHEMATICS; VINCENT TANPublication CONTINUOUS-TIME MEAN-VARIANCE PORTFOLIO SELECTION(2007) LU JUN; MATHEMATICS; LOU JIANN HUAPublication DEFAULT CORRELATION AND DEFAULTABLE BONDS(2005) LI YA NAN; MATHEMATICS; JIN XING