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.

This thesis is concerned with the solution of large systems of linear algebraic equations in which the matrix of coefficients is sparse. Such systems occur in the numerical solution of elliptic partial differential equations by finite-difference methods. By applying some well-known iterative methods, usually used to solve linear PDE systems, the thesis investigates their applicability to solve a set of four mildly nonlinear test problems. In Chapter 4 we study the basic iterative methods and semiiterative methods for linear systems. In particular, we derive and apply the CS, SOR, SSOR methods and the SSOR method extrapolated by the Chebyshev acceleration strategy. In Chapter 5, three ways of accelerating the SOR method are described together with the applications to the test problems. Also the Newton-SOR method and the SOR-Newton method are derived and applied to the same problems. In Chapter 6, the Alternating Directions Implicit methods are described. Two versions are studied in detail, namely, the Peaceman-Rachford and the Douglas-Rachford methods. They have been applied to the test problems for cycles of 1, 2 and 3 parameters. In Chapter 7, the conjugate gradients method and the conjugate gradient acceleration procedure are described together with some preconditioning techniques. Also an approximate LU-decomposition algorithm (ALUBOT algorithm) is given and then applied in conjunction with the Picard and Newton methods. Chapter 8 contains the final conclusions.

No description available.

Glycosaminoglycans (GAGs) are linear polysaccharides expressed ubiquitously on animal cell surfaces and within extracellular matrices. GAGs usually occur as parts of proteoglycans and often accomplish their biological functions through their interactions with proteins. GAG oligosaccharides for this work were produced via enzymatic digest of heparin, followed by gel filtration and ion exchange chromatography. Two tetrasaccharide species obtained from this digest were characterised using 1H and 13C NMR spectroscopy. Complement factor H (fH) is a regulatory protein of the alternative pathway of the complement system, a major component of human innate immunity. Acting as a cofactor to factor I, fH inhibits C3b-initiated complement activation on host cells, protecting cells from auto immune attack. This study focused on the interaction of factor H with GAGs, which are thought to be among the markers allowing factor H to distinguish between self and non self surfaces. Binding studies of two heparin-binding sites in fH are presented. These include the C-terminal modules 19 and 20 (fH~19-20) and fH~7-8. FH~7, fH~7-8 and fH~19-20 were produced recombinantly in various isotope forms. The techniques used to study the protein-GAG interactions in this work encompass NMR spectroscopy, mass spectrometry, gel mobility shift assays (GMSA) and chemical cross linking. Several genetic studies suggest that a common polymorphism in the heparin-binding module fH~7, Y402H, plays a role in the development of age-related macular degeneration (AMD). The work presented here included preparation and backbone resonance assignment of a 13C, 15N- labelled sample of fH~ 7-8 via triple resonance NMR experiments. Further NMR experiments were employed to investigate the role of the lysine and arginine sidechains of fH~7 in GAG binding. These studies were combined with the preparation and characterisation of a covalently cross linked GAG-protein complex using NMR and mass spectrometry. A range of fH~19-20 mutations that are linked to a severe kidney disease, atypical haemolytic uraemic syndrome (aHUS), were characterised using GMSA. No correlation between the disease and the heparin binding properties of the aHUS mutants was observed. The mutant proteins were also characterised with respect to their ability to compete with full-length fH in a physiological complement assay. Simultaneous binding of WT fH~19-20 to GAGs and C3d, the relevant fragment of C3b, was assessed using NMR. NMR experiments were also conducted with NK1, which comprises the two N-terminal heparin-binding modules of hepatocyte growth factor/scatter factor (HGF/SF), and heparin as well as dermatan sulfate-derived GAGs. Relaxation studies on a human defensin, HBD2, were performed to assess the role of GAGs in HBD2 self-association.

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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.

This paper is primarily concerned with the fundamental properties of a linear algebra of finite order over a field. A discussion of linear sets of finite order over a field is used as an introduction to these properties.

This paper is a study of linear operators defined on normed linear spaces. A basic knowledge of set theory and vector spaces is assumed, and all spaces considered have real vector spaces. The first chapter is a general introduction that contains assumed definitions and theorems. Included in this chapter is material concerning linear functionals, continuity, and boundedness. The second chapter contains the proofs of three fundamental theorems of linear analysis: the Open Mapping Theorem, the Hahn-Banach Theorem, and the Uniform Boundedness Principle. The third chapter is concerned with applying some of the results established in earlier chapters. In particular, the concepts of compact operators and Schauder bases are introduced, and a proof that an operator is compact if and only if its adjoint is compact is included. This chapter concludes with a proof of an important application of the Open Mapping Theorem, namely, the Closed Graph Theorem.

Many of the phenomena studied in the natural and social sciences are governed by processes which are discrete and nonlinear in nature, while the most highly developed and commonly used mathematical models are linear and continuous. There are significant differences between the discrete and the continuous, the nonlinear and the linear cases, and the development of mathematical models which exhibit the discrete, nonlinear properties occurring in nature and society is critical to future scientific progress. This thesis presents the basic theory of discrete dynamical systems and stability analysis and explores several applications of this theory to nonlinear systems which model interactions involving economic agents and biological populations. In particular we will explore the stability properties of equilibria associated with inter-species and intergenerational population dynamics in biology and market price and agent composition dynamics in economics.

No description available.