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Metric topologies can be viewed as one-dimensional measures. This dissertation is a topological study of two-dimensional measures. Attention is focused on locally convex vector topologies on infinite dimensional real spaces. A nabla (referred to in the literature as a 2-norm) is the analogue of a norm which assigns areas to the parallelograms. Nablas are defined for the classical normed spaces and techniques are developed for defining nablas on arbitrary spaces. The work here brings out a strong connection with tensor and wedge products. Aside from the normable theory, it is shown that nabla topologies need not be metrizable or Mackey. A class of concretely given non-Mackey nablas on the ℓp and Lp spaces is introduced and extensively analyzed. Among other results it is found that the topological dual of ℓ₁ with respect to these nabla topologies is C₀, one of the spaces infamous for having no normed predual. Also, a connection is made with the theory of two-norm convergence (not to be confused with 2-norms). In addition to the hard analysis on the classical spaces, a duality framework from which to study the softer aspects is introduced. This theory is developed in analogy with polar duality. The ideas corresponding to barrelledness, quasi-barrelledness, equicontinuity and so on are developed. This dissertation concludes with a discussion of angles in arbitrary normed spaces and a list of open questions.

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Virus infection of mammalian cells induces several stress mechanisms, including autophagy and type-I interferon (IFN). Autophagy, a cellular homeostatic mechanism in which intracellular materials are sequestered into double-membrane vesicles and targeted to lysosomes for degradation, is also activated in response to virus infection. Most positive single-stranded RNA viruses studied to date utilise autophagy to increase virus replication. IFN is a potent anti-viral mechanism, which can be divided into two parts: (i) induction and secretion of IFN and (ii) IFN signalling and priming of uninfected cells for a rapid response upon infection and induction of an anti-viral state in infected cells. Alphaviruses are medically important RNA viruses. Semliki Forest virus (SFV) provides a well-characterised model for studying alphavirus infection. A number of strains have been identified, which differ in virulence in adult mice. In this thesis three hypotheses were investigated: (i) that SFV infection induces autophagy in cell culture and utilises this response to enhance virus replication, (ii) that the quality, quantity and/or protective efficacy of the IFN response differ between virus strains and between human and murine cells and (iii) that non-structural protein (nsP)-2 and/or nsP3 antagonise the IFN response. SFV4, SFV L10 and SFV A7(74) infection induced autophagy in Huh7 cells as early as one hour post-infection. Pharmacological induction or inhibition of autophagy had no affect on SFV4 replication, except at a very low multiplicity of infection. NsP3, capsid and dsRNA rarely colocalised with the autophagosome marker LC3. Taken together these results indicate that SFV does not use autophagosomes for replication and autophagy is not important in controlling SFV4 infection at a high MOI, at least in Huh7 cells. However, autophagy may be important in controlling SFV4 spread at a low MOI. An IFN bioassay was established. In fibroblasts, SFV4, SFV L10 and SFV A7(74) induced relatively little IFN in comparison to that induced by Sendai virus. In human fibroblasts, similar levels of IFN were induced by all three virus strains. In mouse fibroblasts, SFV4 induced more IFN than SFV L10. Treatment of fibroblasts with IFN prior to infection greatly reduced, but did not abolish, the replication and spread of all three strains. Therefore, SFV is sensitive to IFN. Analysis of IFN signalling demonstrated that all three strains of SFV inhibited STAT1 phosphorylation during infection of fibroblasts. The growth and viability of SFV infected cells varied between human and mouse cells. The complete genetic sequences of SFV L10 and SFV A7(74) were determined using Solexa (Illumina) sequencing and compared to the sequence of SFV4. The sequences of SFV L10 and SFV4 were extremely similar; only seven differences were identified. Multiple amino acid substitutions were identified in SFV A7(74) compared to SFV4, these mostly mapped to nsP3. To investigate the hypothesis that nsP2 and or nsP3 antagonise the IFN response, two virus mutants were studied: SFV4nsP2RDR and SFV4nsP3Δ50. SFV4nsP2RDR encodes a point mutation in the nuclear localisation signal of nsP2, which largely restricts nsP2 to the cell cytoplasm. SFV4nsP3Δ50 contains a deletion of 50 amino acids in the C-terminus hyperphosphorylated region of nsP3. Neither mutant inhibited STAT1 phosphorylation as efficiently as WT SFV4; SFV4nsP2RDR was particularly poor at inhibiting STAT1 phosphorylation. Both mutants induced more IFN in fibroblasts than SFV4. In summary, autophagy had a limited affect on SFV replication. In contrast, strains of SFV were highly sensitive to IFN, but antagonised this response through the nsP2 protein inhibiting STAT1 phosphorylation.

The purpose of this thesis is the study of the Lie algebras of affine vector fields and curvature collineations of space-time, the aim being, in the first case, to obtain upper bounds on the dimension of the Lie algebra of affine vector fields (under the assumption that the space-time is non-flat) as well as to obtain a characterization of such vector fields in terms of other types of symmetries. In the case of curvature collineations the aim was that of characterizing space-times which may admit an infinite-dimensional Lie algebra of curvature collineations as well as to find local characterizations of such vector fields. Chapters 1 and 2 consist of introductory material, in Differential Geometry (Ch.l) and General Relativity (Ch.2). In Chapter 3 we study homothetic vector fields which admit fixed points. The general results of Alekseevsky (a) and Hall (b) are presented, some being deduced by different methods. Some further details and results are also given. Chapter 4 is concerned with space-times that can admit proper affine vector fields. Using the holonomy classification obtained by Hall (c) it is shown that there are essentially two classes to consider. These classes are analysed in detail and upper bounds on the dimension of the Lie algebra of affine vector fields of such space-times are obtained. In both cases local characterizations of affine vector fields are obtained. Chapter 5 is concerned with space-times which may admit proper curvature collineations. Using the results of Halford and McIntosh (d) , Hall and McIntosh (e) and Hall (f) we were able to divide our study into several classes The last two of these classes are formed by those space-times which admit a (1 or 2-dimensional) non-null distribution spanned by vector fields which contract the Riemann tensor to zero. A complete analysis of each class is made and some general results concerning the infinite-dimensionality problem are proved. The chapter ends with some comments in the cases when the distribution mentioned above is null.

International Telemetering Conference Proceedings / October 17-20, 1994 / Town & Country Hotel and Conference Center, San Diego, California / Testing of airborne weapons systems often requires that a scoring system be placed on the target drone to obtain critical miss distance data. Advanced weapons utilizing directional warheads often require a scoring system which yields vector, miss distance and miss direction, information. Scalar scoring systems currently in use are relatively simple and inexpensive. Vector scoring systems are typically complex and the cost of systems which are currently available or are being developed can be prohibitively expensive. Due to the current military budget decline, development of a low cost vector scoring system is desirable This paper introduces a low cost vector scoring system developed for airborne target drones and based on an inexpensive scalar scoring system currently in use. To meet the low cost criteria, vector operation is achieved via minimal modifications to the existing scalar system.