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The purpose of this thesis is to study in depth the relationship between the curvature of space-time and the other geometrical objects which naturally arise in general relativity. Most of the results obtained apply to the generic case. Chapter 1 contains a discussion of certain aspects of fibre bundle theory required in later chapters which may be unfamiliar to many relativists, while chapter 2 contains preliminary material on curvature in relativity and proves a continuity property of the algebraic classification of the Weyl and energy-momentum tensors. Chapter 3 describes the generic behaviour of the Riemann, Weyl and energy-momentum tensors, and chapter 5 goes on to use this description to investigate the relationship of the Riemann tensor to the metric, conformal class and connection of space-time in the generic case. In particular it is proved that the Riemann tensor uniquely and continuously determines the connections. The information obtained in chapter 3 on the algebraic type of curvature in the general case is related in chapter 4 to the topology of the underlying manifold. In chapter 6 a topology is defined on the set of sectional curvatures of all Lorentz metrics on a given manifold. The remainder of the chapter attempts to do for the sectional curvature what was done for the Riemann tensor in chapter 5 but, because sectional curvature is more difficult to handle, the results obtained are necessarily more modest.

The limit of bandwidth efficiency is well known in wireless radio communication. Therefore, making use of bandwidth efficiently is very important. Among various technologies which can increase the bandwidth efficiency, space-time coding system is very popular technology recently. In this article, we¡¦ll discuss three common schemes in ST system¡GSpace-Time Trellis Coding (STTC), Space-Time Block Coding (STBC) and Differential Space-Time Block Coding (DSTBC). First, we¡¦ll introduce the basic model of ST systems in chapter 2. And in chapter 3, the error probability, which is a close form, of STBC and DSTBC systems in slow fading channel will be derived, according to the derivation of error probability in multi-channel communication systems¡i10¡j. Then, the channel model will be defined as a fast fading channel and the error probability of STBC system in this channel model will be derived in chapter 4. Furthermore, we¡¦ll derive the error probability of STBC system in multi-path slow fading channel. Finally, we¡¦ll make a conclusion to the works we did in this article. The contribution of this article are¡G1. We derive a bit error probably which is a close form of STBC and DSTBC systems in slow fading channel. 2. We analyze the performace of STBC system in fast fading channel and derive a bit error probability in this case. 3. We analyze the performance of STBC system in multi-path slow fading channel and get a result that the diversity gain will increase when use the RAKE receiver mentioned in this article.

In order to support large-scale integration of wind power into current electric energy system, accurate wind speed forecasting is essential, because the high variation and limited predictability of wind pose profound challenges to the power system operation in terms of the efficiency of the system. The goal of this dissertation is to develop advanced statistical wind speed predictive models to reduce the uncertainties in wind, especially the short-term future wind speed. Moreover, a criterion is proposed to evaluate the performance of models. Cost reduction in power system operation, as proposed, is more realistic than prevalent criteria, such as, root mean square error (RMSE) and absolute mean error (MAE). Two advanced space-time statistical models are introduced for short-term wind speed forecasting. One is a modified regime-switching, space-time wind speed fore- casting model, which allows the forecast regimes to vary according to the dominant wind direction and seasons. Thus, it avoids a subjective choice of regimes. The other one is a novel model that incorporates a new variable, geostrophic wind, which has strong influence on the surface wind, into one of the advanced space-time statistical forecasting models. This model is motivated by the lack of improvement in forecast accuracy when using air pressure and temperature directly. Using geostrophic wind in the model is not only critical, it also has a meaningful geophysical interpretation. The importance of model evaluation is emphasized in the dissertation as well. Rather than using RMSE or MAE, the performance of both wind forecasting models mentioned above are assessed by economic benefits with real wind farm data from Pacific Northwest of the U.S and West Texas. Wind forecasts are incorporated into power system economic dispatch models, and the power system operation cost is used as a loss measure for the performance of the forecasting models. From another perspective, the new criterion leads to cost-effective scheduling of system-wide wind generation with potential economic benefits arising from the system-wide generation of cost savings and ancillary services cost savings. As an illustration, the integrated forecasts and economic dispatch framework are applied to the Electric Reliability Council of Texas (ERCOT) equivalent 24- bus system. Compared with persistence and autoregressive models, the first model suggests that cost savings from integration of wind power could be on the scale of tens of millions of dollars. For the second model, numerical simulations suggest that the overall generation cost can be reduced by up to 6.6% using look-ahead dispatch coupled with spatio-temporal wind forecast as compared with dispatch with persistent wind forecast model.

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Thesis (Ph.D.) -- University of Texas at Dallas, 2006 / Includes vita. Includes bibliographical references (leaves 102-110)

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The purpose of this thesis is to study methods by which conformal vector fields on pseudo-Riemannian manifolds can be simplified. A vector field on a manifold M with metric g is conformal if its local flows preserve the metric g up to a scaling and unlike Killing vector fields, which preserve g exactly, it cannot in general be linearised in a neighbourhood of any given point. The difference is that a Killing vector field is affine, that is it preserves a connection on the manifold. In this case the connection is the canonical (Levi-Civita) connection associated with g, but affine vector fields with respect to any connection are linearisable. The task is to find new connections with respect to which the set of conformal vector fields, or some subset of them, are affine. Suppose that we have a manifold M with a pseudo-Riemannian conformal structure and an orthogonal splitting of the tangent bundle. We construct, for a natural choice of torsion, a unique connection in the principal bundle of frames adapted to the splitting. Moreover this connection is preserved by any transformations which preserve the splitting of the tangent bundle. Thus any conformal vector field which preserves the splitting is affine. The splitting can be chosen to reflect the tangent to the orbits of a subalgebra of conformal vector fields, the principal null directions of the Weyl tensor or the flow of a perfect fluid. We also give a study of conformal vector fields in three-dimensional Lorentzian manifolds. An equivalent of the Cotton-York tensor is used to investigate the behaviour of these vector fields at their fixed points in the same spirit as the Weyl tensor is used in four dimensions.