Bibliography: leaves 108-113. / ii, 113 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1998?

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 17 October 2016. / The role of mathematical inequalities in the growth of different branches of mathematics as well as in other areas of science is well recognized in the past several years. The uses of contributions of Newton and Euler in mathematical analysis have resulted in a numerous applications of modern mathematics in physical sciences, engineering and other areas sciences and hence have employed a dominat effect on mathematical inequalities. Mathematical inequalities play a dynamic role in numerical analysis for approximation of errors in some quadrature rules. Speaking more specifically, the error approximation in quadrature rules such as the mid-point rule, trapezoidal rule and Simpson rule etc. have been investigated extensively and hence, a number of bounds for these quadrature rules in terms of at most second derivative are proven by a number of researchers during the past few years. The theorey of mathematical inequalities heavily based on theory of convex functions. Actually, the theory of convex functions is very old and its commencement is found to be the end of the nineteenth century. The fundamental contributions of the theory of convex functions can be found in the in the works of O. Hölder [50], O. Stolz [151] and J. Hadamard [48]. At the beginning of the last century J. L. W. V. Jensen [72] first realized the importance convex functions and commenced the symmetric study of the convex functions. In years thereafter this research resulted in the appearance of the theory of convex functions as an independent domain of mathematical analysis. Although, there are a number of results based on convex function but the most celebrated results about convex functions is the Hermite-Hadamard inequality, due to its rich geometrical significance and many applications in the theory of means and in numerical analysis. A huge number of research articles have been written during the last decade by a number of mathematicians which give new proofs, generalizations, extensions and refitments of the Hermite-Hadamard inequality. Applications of the results for these classes of functions are given. The research upshots of this thesis make significant contributions in the theory of means and the theory of inequalities. / MT 2017

by Chu Chiu Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Bibliography: leaves 31-32. / Introduction / Chapter Section 1. --- A Minimization Problem / Chapter Section 2. --- Radial Symmetry of The Solution / Chapter Section 3. --- Proof of The Main Theorem / References

by Chan Ho Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 128-[131]). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Information Theory --- p.1 / Chapter 1.2 --- Approaches for characterizing Γ*n --- p.4 / Chapter 1.3 --- Outline of the thesis --- p.7 / Chapter 2 --- Quasi-Uniformity --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- Box Assignment --- p.9 / Chapter 2.2.1 --- Box Assignment --- p.9 / Chapter 2.2.2 --- Conditional Box Assignment --- p.17 / Chapter 2.3 --- Quasi-Uniform Random Variables --- p.18 / Chapter 2.4 --- Main Theorems --- p.20 / Chapter 2.4.1 --- Preliminaries --- p.20 / Chapter 2.4.2 --- Main Theorems --- p.25 / Chapter 2.5 --- Quasi-Uniformity and Inequality --- p.32 / Chapter 2.5.1 --- Quasi-Uniformity and Inequality --- p.32 / Chapter 2.6 --- A New Perspective of Information Inequality --- p.34 / Chapter 2.6.1 --- Combinatorial Inequality --- p.34 / Chapter 2.6.2 --- Relations between combinatorial inequalities and informa- tion inequalities --- p.36 / Chapter 2.7 --- Summary --- p.40 / Chapter 3 --- Groups and Quasi Uniformity --- p.41 / Chapter 3.1 --- Introduction --- p.41 / Chapter 3.2 --- Group --- p.42 / Chapter 3.3 --- Group Represent ability --- p.47 / Chapter 3.4 --- Tightness of Group Represent ability --- p.54 / Chapter 3.4.1 --- Tightness of γn --- p.54 / Chapter 3.5 --- Abelian group represent able --- p.58 / Chapter 3.5.1 --- Δ operator and sub cone con(γαb) --- p.63 / Chapter 3.5.2 --- Decomposition of con(γαb) --- p.67 / Chapter 3.6 --- Summary --- p.73 / Chapter 4 --- Linear Representability --- p.74 / Chapter 4.1 --- Introduction --- p.74 / Chapter 4.2 --- Preliminaries of Vector Space --- p.75 / Chapter 4.3 --- Linear Representability --- p.80 / Chapter 4.3.1 --- Orthogonal Space --- p.80 / Chapter 4.3.2 --- Linear Representability --- p.81 / Chapter 4.3.3 --- Direct Sum --- p.90 / Chapter 4.3.4 --- Conditional Entropy --- p.93 / Chapter 4.4 --- Tightness of γαb --- p.95 / Chapter 4.5 --- Reverse Representation --- p.98 / Chapter 4.6 --- Summary --- p.106 / Chapter A --- AEP and BOX ASSIGNMENT --- p.107 / Chapter B --- Proof of Chapter 4's lemma --- p.110 / Chapter C --- Tightness of and Ψαb --- p.118

A Dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the Degree of Master of Science. Johannesburg 2015. / This Dissertation focuses on the Jacobi polynomial. Specifically, it discusses certain aspects of the zeros of the Jacobi polynomial such as the interlacing property and quasiorthogonality. Also found in the Dissertation is a chapter on the inequalities of the zeros of the Jacobi polynomial, mainly those developed by Walter Gautschi.

University of Macau / Faculty of Science and Technology / Department of Mathematics

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

No description available.

This thesis concerns the solution of variational inequalities (VIs) with analytic center cutting plane methods (ACCPMs). A convex feasibility problem reformulation of the variational inequality is used; this reformulation applies to VIs defined with pseudo-monotone, single-valued mappings or with maximal monotone, multi-valued mappings. / Two cutting plane methods are presented: the first is based on linear cuts while the second uses quadratic cuts. The first method, ACCPM-VI (linear cuts), requires mapping evaluations but no Jacobian evaluations; in fact, no differentiability assumption is needed. The cuts are placed at approximate analytic centers that are tracked with infeasible primal-dual Newton steps. Linear equality constraints may be present in the definition of the VI's set of reference, and are treated explicitly. The set of reference is assumed to be polyhedral, or is convex and iteratively approximated by polyhedra. Alongside of the sequence of analytic centers, another sequence of points is generated, based on convex combinations of the analytic centers. This latter sequence is observed to converge to a solution much faster than the former sequence. / The second method, ACCPM-VI (quadratic cuts), has cuts based on both mapping evaluations and Jacobian evaluations. The use of such a richer information set allows cuts that guide more accurately the sequence of analytic centers towards a solution. Mappings are assumed to be strongly monotone. However, Jacobian approximations, relying only on mapping evaluations, are observed to work very well in practice, so that differentiability of the mappings may not be required. There are two versions of the ACCPM-VI (quadratic cuts), that differ in the way a new analytic center is reached after the introduction of a cut. One version uses a curvilinear search followed by dual Newton centering steps. The search entails a full eigenvector-eigenvalue decomposition of a dense matrix of the order of the number of variables. The other version uses two line searches, primal-dual Newton steps, but no eigenvector-eigenvalue decomposition. / The algorithms described in this thesis were implemented in the M ATLAB environment. Numerical tests were performed on a variety of problems, some new and some traditional applications of variational inequalities.