Many empirical studies show that both equity volatility and its trading volume have long range dependence and can be modeled as fractional integrated processes. The objective of this study is to investigate relationship between volatility and volume.We adopt four estimators of volatility, which includes the squared log returns, historical volatility, iterative t estimators and $GARCH$ estimators. The results show that among the four estimators squared log returns usually have the largest integration orders and produce hightest ratios of fractional cointegration. The fractional integrated orders are estimated separately and jointly, and the cointegration parameters are estimated by ordinary least squares, a narrow band frequency domain least squares method and a semiparametric estimator of Whittle likelihood. Models are also established when volatility and volume are not fractional cointegrated.

Laser based underwater triangulation ranging is sensitive to the environmental conditions and laser beam profile. Also, its ranging quality is greatly affected by the algorithm choices for peak detection and for image processing. By utilizing the merging least-squares approximation for laser image processing, it indeed succeeds in increasing quality of triangulation ranging in water; however, this result was obtained on the use of a laser beam with nearly circular cross-section. Therefore, by using an ellipse-like laser beam cross-section for range finding, we are really interested in understanding the quality of range finding with different peak detection algorithms. Besides, the ellipse orientation of the laser spot projected on the image plane would be various. We are also interested in learning about the relationship between the ellipse orientation and the quality of range finding. In this study, peak detection algorithms are investigated by considering four different laser beam cross-sections which are ircle, horizontal ellipse, oblique ellipse, and vertical ellipse. First, we employ polynomial regression for processing laser image to study the effect of polynomial degree on quality of triangulation ranging. It was found that the linear regression achieves the best ranging quality than others. Then, according to this result, the ranging quality associated with peak detection is evaluated by employing three different algorithms which are the illumination center, twice illumination center and the illumination center with principal component analysis. We found that the ranging quality by using the illumination center with principal component analysis is the best, next is twice illumination center, and last the illumination center. This result indicates that the orientation of elliptical laser beam has an influential effect on the quality of range finding. In addition, the ranging quality difference among peak detection algorithms is significantly reduced by implementing the merging least-squares approximation rlaser image processing. This result illustrates that the merging least-squares approximation does reduce the effect of peak detection algorithm on the quality of range finding.

Spatial processing that exploits the diversity provided by smart antenna arrays, in which the adaptive beamformer is employed, is another alternative to increase the efficiency of wireless system capacity and performance without allocating additional frequency spectrum. An array beamformer is a processor used in conjunction with an array of sensors to provide a versatile form of spatial filtering; it can be designed to form main lobe in direction corresponding to the desired source and nulling the interferences from others direction. They are two types of adaptive array beamformer structures, viz., broadband and narrowband array structures. To deal with the wideband desired signal or interferences the broadband array beamformer is preferred. For broadband interferences suppression, many adaptive array beamforming algorithms, based on the linearly constrained have been extensively used. In this thesis, the beamspace approach for designing the broadband antenna array beamformer, with frequency invariant character, is devised and implemented with the sliding window linearly constrained RLS (SW-LC-RLS) algorithm, to deal with the broadband moving jammers (or interferences) suppression. Also, to combat the pointing error effect of desired user¡¦s look direction, the derivative constraint is adopted for devising the derivative SW-LC-RLS beamforming algorithm for broadband moving jammers suppression. Computer simulation results confirmed that the proposed scheme is more robust against the moving jammers over the conventional algorithms. It can be applied to the existing wideband wireless communications systems to achieve desired performance for supporting high data rate communication services.

There exist many methods for facial recognition, such as eigenface, templates, artificial neural networks, etc., based on the given facial sample data (patterns). When an input facial image (target) involve simple geometrical transformations and illumination, the performance of these methods are not very satisfactory. In this thesis, following Li et al., we propose a new face recognition system, which can eliminate translation, rotation, scaling, and prospective transformations of facial images automatically, and can also eliminate illumination. According to facial features, we use this method to find the best transformation and the closet illumination, and then to eliminate them for identification by the best matching between a target and the patterns. Finally, we use the least squares method to recognize the target. This method is validated by numerical examples.

The selection and learning of kernel functions is a very important but rarely studied problem in the field of support vector learning. However, the kernel function of a support vector regression has great influence on its performance. The kernel function projects the dataset from the original data space into the feature space, and therefore the problems which can not be done in low dimensions could be done in a higher dimension through the transform of the kernel function. In this paper, there are two main contributions. Firstly, we introduce the gradient descent method to the learning of kernel functions. Using the gradient descent method, we can conduct learning rules of the parameters which indicate the shape and distribution of the kernel functions. Therefore, we can obtain better kernel functions by training their parameters with respect to the risk minimization principle. Secondly, In order to reduce the number of support vectors, we use the orthogonal least squares method. By choosing the representative support vectors, we may remove the less important support vectors in the support vector regression model. The experimental results have shown that our approach can derive better kernel functions than others and has better generalization ability. Also, the number of support vectors can be effectively reduced.

This article emphasizes on fitting GARCH option pricing model with Taiwan stock market. Duan¡¦s(1995) NGARCH option pricing model is adopted. Duan solved the European option by simulation, this article follow the method and extents to pricing American option. In general, simulation approach is not convenient to solve American options as well as European options. However, the least-squares method proposed by Longstaff and Schwartz is a simple and powerful tool, so this article tests the method. The NGARCH model has parameters, and base on loglikelihood function, we fit the model with empirical observations to obtain parameters. Then we can simulate the stock prices, once stock prices are simulated, the option value can be priced. Since the article simulates the option, there should be the antithetic approaches instead of simulation. In practice, the Black-Schoels model is the benchmark for pricing European option, so this article compares the simulated European options with Black-Scholes. For American option, this article compares the simulated American options which are priced by least-squares method with trinomial tree (finite difference method).

Self-assembly has big importance in synthesizing supramolecular structures. Highly fluorescent molecular squares with boradiazaindacene (BODIPY) building blocks were obtained via usage of metal driven self-asembly. The boradiazaindacene units were connected with the Pd(II) complex unit enforcing a near-90 degree angle between the building blocks. Thus, we believe we have the first example of BODIPY carrying fluorescent squares. With collective experience in BODIPY chemistry in our group, we may have the first example of functionalizable molecular square. Self-assembled light harvesting systems will be ultimate biomimetic example of photosynthetic reaction center.

This study aims to simulate a vapor compression refrigeration cycle, working with either butane (R-600) or isobutane (R-600a). For this purpose a computer program is written to design a household refrigerator, by modeling a steady-state, vapor compression cycle, with user defined input data. Each refrigerator component can be designed separately, as well as parts of a single refrigeration system in the program. In order to determine the refrigerant thermophysical properties at different states, least squares polynomial equations for different properties of R-600 and R-600a have been developed. Computer program is used for refrigeration cycle analysis, variable speed compressor design and calculating coefficient of performance (COP) and irreversibility of the cycle. Sample-preliminary designs have been carried out for different refrigeration loads, room and cold space temperatures with the program, to compare the performance characteristics of the refrigerants. Designs have been performed at different refrigeration loads, room and cold space temperatures. It is observed that for the same conditions R-600 has slightly better performance characteristics than those of R-600a.

A net is a special configuration of lines and points in the projective plane. There are certain restrictions on the number of its lines and points. We proved that there cannot be any (4,4) nets in CP^2. In order to show this, we use tropical algebraic geometry. We tropicalize the hypothetical net and show that there cannot be such a configuration in CP^2.

The aim of this thesis is to develop a flow solver that has the ability to obtain an accurate numerical solution fast and efficiently with minimum user intervention. In this study, a two-dimensional viscous, laminar, incompressible flow solver based on Least-Squares Spectral Element Method (LSSEM) is developed. The LSSEM flow solver can work on hp-type nonconforming grids and can perform p-type adaptive refinement. Several benchmark problems are solved in order to validate the solver and successful results are obtained. In particular, it is demonstrated that p-type adaptive refinement on hp-type non-conforming grids can be used to improve the quality of the solution. Moreover, it is found that mass conservation performance of LSSEM can be enhanced by using p-type adaptive refinement strategies while keeping computational costs reasonable.