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A range of siliceous, ferruginous and ferromanganiferous deposits are intercalated with, and overlie the lavas of the Late Cretaceous northern Oman ophiolite. Most of the deposits lie on the upper surface of the spreading event lavas; spreading event magmatism and later seamount-building events are coeval to relatively small metalliferous sediment deposits. The mineralogical and geochemical characteristics of these sediments are a function of the interaction between local hydrothermal systems, the marine depositional environment, and early diagenetic transformations. Various techniques are employed to objectively determine the actual end-member component compositions from which the metalliferous sediments formed. The sediments are a mixture of primary biosiliceous oozes and hydrothermal metallic components which were deposited at or near a marginal ocean-basin spreading axis during Cenomanian time. Factor analysis, selective acid leaching experiments and linear programming modelling identify six geologically reasonable end-members, which represent biosiliceous sediment, carbonate sediment, detrital sediment, hydrogenous sediment, and hydrothermal sediment. The techniques show that the sediments have a complicated hydrothermal history which is associated with the evolution of the Oman ophiolite. The hydrothermal component is sub-divided into high temperature and low temperature end-members which are characteristic of the proto-seamount and proto- rift event environments respectively. Vent proximal and vent-distal facies are described. The geochemistry of the deposits provides evidence for calcareous pelagic dissolution by hydrothermal fluids, which resulted in the relative concentration of a hyaloclastic component. The deposits which were not early-lithified are epidotized. Metamorphic transformation of the primary sediment occurred prior to eruption of the upper lava unit. The techniques which have been used to describe the range, composition and distribution of the end-member components provide a flexible framework for the characterisation of geological mixing in all marine metalliferous sediments.

A special case of the linear programming problem, the transportation problem, is the subject of this thesis. The development of a solution to the transportation problem is based on fundamental concepts from the theory of linear algebra and matrices.

Finally, as combinatorial applications of complex quadratic optimization; we consider Max 3-Cut with fixed nodes constraints, Max 3-Dicut with weight constraints, Max 3-XOR, and so on, and present corresponding bounds on the approximation ratios. / Quadratic optimization problems with complex-valued decision variables, in short called complex quadratic optimization problems, find many applications in engineering. In this dissertation, we study several instructive models of complex quadratic optimization, as well as its applications in combinatorial optimization. The tool that we use is a combination of semidefinite programming (SDP) relaxation and randomization technique, which has been well exploited in the last decade. Since most of the optimization models are NP-hard in nature, we shall design polynomial time approximation algorithms for a general model, or polynomial time exact algorithms for some restricted instances of a general model. / To enable the analysis, we first develop two basic theoretical results: one is the probability formula for a bivariate complex normal distribution vector to be in a prescribed angular region, and the other one is the rank-one decomposition theorem for complex positive semidefinite matrices. The probability formula enables us to compute the expected value of a randomized (with a specific rounding rule) solution based on an optimal solution of the SDP relaxation problem, while the rank-one decomposition theorem provides a new proof of the complex S -lemma and leads to novel deterministic rounding procedures. / With the above results in hand, we then investigate the models and applications of complex quadratic optimization via semidefinite programming in detail. We present an approximation algorithm for a convex quadratic maximization problem with discrete complex decision variables, where the approximation analysis is based on the probability formula. Besides, an approximation algorithm is proposed for a non-convex quadratic maximization problem with discrete complex decision variables. Then we study a limit of the model, i.e., a quadratic maximization problem with continuous unit module decision variables. The problem is shown to be strongly NP-hard. Approximation algorithms are described for the problem, including both convex case and non-convex case. Furthermore, if the objective matrix has a sign structure, then a stronger approximation result is shown to hold. In addition, we use the complex matrix decomposition theorem to solve complex quadratically constrained complex quadratic programming. We consider several interesting cases for which the corresponding SDP relaxation admits no gap with the true optimal value, and consequently, this yields polynomial time procedures for solving those special cases of complex quadratic optimization. / Huang Yongwei. / "August 2005." / Adviser: Shuzhong Zhang. / Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 4033. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 142-155). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

Thesis (M.S.)--Naval Postgraduate School, 2002. / Thesis advisor(s): David Olwell, Samuel E. Buttrey. Includes bibliographical references (p. 79). Also available online.