Image compression is a means to perform transmission or storage of visual data in the most economical way. Though many algorithms have been reported, research is still needed to cope with the continuous demand for more efficient transmission or storage. This research work explores and implements polynomial fitting techniques as means to perform block-based lossy image compression. In an attempt to investigate nonpolynomial models, a region-based scheme is implemented to fit the whole image using bell-shaped functions. The idea is simply to view an image as a 3D geographical map consisting of hills and valleys. However, the scheme suffers from high computational demands and inferiority to many available image compression schemes. Hence, only polynomial models get further considerations. A first order polynomial (plane) model is designed to work in a multiplication- and division-free (MDF) environment. The intensity values of each image block are fitted to a plane and the parameters are then quantized and coded. Blocking artefacts, a common drawback of block-based image compression techniques, are reduced using an MDF line-fitting scheme at blocks’ boundaries. It is shown that a compression ratio of 62:1 at 28.8dB is attainable for the standard image PEPPER, outperforming JPEG, both objectively and subjectively for this part of the rate-distortion characteristics. Inter-block prediction can substantially improve the compression performance of the plane model to reach a compression ratio of 112:1 at 27.9dB. This improvement, however, slightly increases computational complexity and reduces pipelining capability. Although JPEG2000 is not a block-based scheme, it is encouraging that the proposed prediction scheme performs better in comparison to JPEG 2000, computationally and qualitatively. However, more experiments are needed to have a more concrete comparison. To reduce blocking artefacts, a new postprocessing scheme, based on Weber’s law, is employed. It is reported that images postprocessed using this scheme are subjectively more pleasing with a marginal increase in PSNR (<0.3 dB). The Weber’s law is modified to perform edge detection and quality assessment tasks. These results motivate the exploration of higher order polynomials, using three parameters to maintain comparable compression performance. To investigate the impact of higher order polynomials, through an approximate asymptotic behaviour, a novel linear mapping scheme is designed. Though computationally demanding, the performances of higher order polynomial approximation schemes are comparable to that of the plane model. This clearly demonstrates the powerful approximation capability of the plane model. As such, the proposed linear mapping scheme constitutes a new approach in image modeling, and hence worth future consideration.

In this thesis we take a specialized approach to edge-colouring by focusing exclusively on multigraphs with high chromatic index. The bulk of our results can be classified into three categories. First, we prove results which aim to characterize those multigraphs achieving known upper bounds. For example, Goldberg's Theorem says that χ'≤ Δ+1+(Δ-2}/(g₀+1) (where χ' denotes chromatic index, Δ denotes maximum degree, and g₀ denotes odd girth). We characterize this bound by proving that for a connected multigraph G, χ'= Δ+1+(Δ-2}/(g₀+1) if and only if G=μC_g₀ and (g₀+1)|2(μ-1) (where μ denotes maximum edge-multiplicity). Our second category of results are new upper bounds for chromatic index in multigraphs, and accompanying polynomial-time edge-colouring algorithms. Our bounds are all approximations to the famous Seymour-Goldberg Conjecture, which asserts that χ'≤ max{⌈ρ⌉, Δ+1} (where ρ=max{(2|E[S]|)/(|S|-1): S⊆V, |S|≥3 and odd}). For example, we refine Goldberg's classical Theorem by proving that χ'≤ max{⌈ρ⌉, Δ+1+(Δ-3)/(g₀+3)}. Our third category of results are characterizations of high chromatic index in general, with particular focus on our approximation results. For example, we completely characterize those multigraphs with χ'> Δ+1+(Δ-3)/(g₀+3). The primary method we use to prove results in this thesis is the method of Tashkinov trees. We first solidify the theory behind this method, and then provide general edge-colouring results depending on Tashkinov trees. We also explore the limits of this method, including the possibility of vertex-colouring graphs which are not line graphs of multigraphs, and the importance of Tashkinov trees with regard to the Seymour-Goldberg Conjecture.

The purpose of this study was to create a proof-of-concept piezoelectric actuator system capable of meeting the performance requirements necessary for actuation of a trailing edge flap for a helicopter main rotor blade. Due to extremely small displacements produced by piezoelectric actuators, their output is amplified several times in order to produce the required displacement for this device. The amplification is accomplished in two stages. The first stage, mechanical amplification, uses differential length lever arms to increase the piezoelectric actuator output. The second stage, hydraulic amplification, is coupled to the first stage and uses differential area pistons to further amplify the output of the mechanical amplifier. The actuation systems force and displacement output is characterized based on frequency.

In mesoscale manufacturing desired dimensional and surface characteristics are defined, but edge conditions are not specified in design. The final edge conditions that exist in mesoscale objects are created not only by the manufacturing process but, because of their size, also by part handling procedures. In these parts, the concern is not only with burrs, which can be formed by some mesoscale manufacturing processes, but also with the shape and size of the edge. These properties are critically important as the edge can constitute a large percentage of the smallest features of mesoscale objects. Undefined edge geometry can result in measurement, assembly, and operational difficulties. Due to the potential problems caused by edge conditions, it is desirable to have the ability to measure and characterize the edge conditions of parts. This thesis considers mesoscale measurement tools to provide an edge measurement tool recommendation based on edge size and properties. A set of analysis techniques is developed to determine the size and shape of the measured edge, locate any local inconsistencies such as burrs or dents, and track trends in calculated parameters as a function of edge position. Additionally, a standard method for communicating design requirements is suggested in order to differentiate between acceptable and unacceptable edges.

Due to wireless communication technologies, positioning technologies, and mobile computing develop quickly, mobile services are becoming practical and important on big spatiotemporal databases management. Mobile service users move only inside a spatial network, e.g. a road network. They often issue the K Nearest Neighbor (KNN) query to obtain data objects reachable through the road network. The challenge problem of mobile services is how to efficiently answer the data objects which user interest to the corresponding mobile users. Therefore, how to effectively modeling road networks, effectively indexing, and querying on the road networks have become a popular topic. Lu et. al. have proposed a road network model that captures the real-life road networks better than previous models. Then, based on their model, they have proposed a RNG (Road Network Grid) index for speeding up the KNN query on real-life road networks. The RNG index structure is a quad-tree structure and a point-based structure. However, in their model, they divide the double track road which U-turn is allowed at some parts. This modeling does not capture the real-life road networks accurately. Since they divide the road, this makes the number of points of the graph increase. The number of times of partitioning the graph increases. It increases the execution time of constructing the index structure. The format of the leaf node of the RNG index makes the search time increase. Moreover, the query processing on the RNG index structure has to visit the root repeatedly. This condition makes the search time increase. Therefore, in this thesis, we propose a network model that captures the real-life road networks. We do not have to divide the real-life roads when we map the real-life roads into graph. We map the real-life road networks into graph directly. Then, based on our network model, we propose an EBNA (Edge-Based Nine-Area tree) index structure to make the search time of obtaining the interest edge information quickly. The EBNA index structure is an edge-based index structure. We store all of the edge information on the leaf node. We can obtain the edge information directly. Each edge information entry has a pointer point to link edges. Links of each edge entry consist a graph. This graph makes the KNN query processing visit the root only one time. From our simulation result, we show that the performance of constructing the EBNA index is better than constructing the RNG index and the performance of the KNN query processing by using EBNA index is better than the KNN query processing by using RNG index.

We call a finite simple graph G = (V (G),E(G)) to be Z-semimagic if it admits an edge labeling l : E(G) ¡÷ Z {0} such that the induced vertex sum labeling l+(v) = uv∈E(G) l(uv) is constant. The constant is called a semimagic index, or an index for short, of G under the labeling l. We consider the set of all possible semimagic indices r such that G is Z-semimagic with a semimagic index r, and denote it by IZ(G). We call IZ(G) the index set of G with respect to Z. In this thesis, we decide the index set IZ(G) for G being regular graphs, complete bipartite graphs, wheel graphs and fan graphs. Also, we determine whether 0 ∈ IZ(G) for G being complete multi-partite graphs.

Along with the advancement of technology, image display devices such as mobile phones, computers and televisions are ubiquitous everywhere in our lives. Due to the different sizes of display devices, digital image scaling technology is often used on the devices while presenting images. For example, when large-size photos are viewed on mobile phones, they tend to present as scaled-down images of the entire pictures, making the main subjects quite small and thus causing inconvenience for viewers. On this account, this study has offered an efficient and high-quality intelligent content-aware image resizing system to solve this problem. This system will first analyze the main area of the image, and then applies an intelligent compression process on the entire image. By doing this, images can still have a complete main subject even after being compressed, not only achieving an excellent visual effect while making the main subject more prominent and obvious, but also reducing the data volume of images. Except for various sizes of display devices, this technology can also be applied on video transmission (H.264/AVC) to effectively reduce the data volume of images, making a substantial contribution to both the image scaling and video coding.

NPR (Non-Photo-Realistic Rendering) is a new and quick-developed research topic in Image Processing. The main purpose of NPR is to generate pencil sketching¡Bwatercolor and oil painting, something different from photos, automatically by computer algorithms. On the other hand, there is another technique called PR (Photo-Realistic Rendering). The goal of PR is to generate real objects by computer algorithms, such as Matting or Inpainting. Furthermore, NPR includes two modes¡Gone is with physical model, researchers could write programs to simulate NPR by the properties of physical model. Without physical model, researchers could write programs to simulate NPR by their observation and deliberation. This thesis to the latter, there is no physical model in NPR. In the viewpoint of artists, drawing is performance of light and shadow. Then, in scientific, drawing depends on the degree of luminance. Luminance supports artists block and direction when drawing. Moreover, This thesis is mainly simulating oil painting with impressionist.

The cutter is a fundamental machine tool used extensively throughout manufacturing industries. The performance and quality of the cutter have a direct influence upon the cutting precision, product quality and production rate. Invigorating the domestic cutter industry and establishing a characteristic syscxtem of cutter technology requires that new technology be imported, the constraints of previous experience be overcome, a fundamental research and development capability be developed and new machine tool materials be adopted Two basic approaches exist when considering geometrical models of the cutter. In the first approach, developing new cutters and establishing an optimal set of cutter design parameters is performed in accordance with general cutting theory and the operational functions of the machine tool. Meanwhile, in the second approach, the structural requirements and design parameters of an ideal cutter are used to establish a geometrical cutter model which describes the various contours of the cutter. Developing an accurate geometrical model is an essential prerequisite to realizing the com-puter-aided design of a cutter, and is necessary in order to apply the theory of cutter design and manufacturing theory to the practical manufacturing proc-ess. Moreover, the geometrical model provides the basis for interference checking and manufacturing error analysis. Modern cutter design and manufacturing technologies integrate the results from a diverse range of previous studies, including those performed within the fields of fundamental mathematical theory, computer-aided ap-plication technology, modern design technology, material science and manufacturing technology. In each field, technological progress is reliant upon the development of mathematical theory. In the present study, differen-tial geometry, conjugate theory, engagement relationship theory, coordinate transfer and numerical methods are used to develop a systematic method for the design, simulation, manufacturing and compensation of special revolving cutters. Using the proposed mathematical models, this paper presents real-izable and effective manufacturing models for these revolving cutters. Fur-thermore, the Taguchi method and power signal analysis techniques are em-ployed to investigate the effects of different cutting-edge curves on the cut-ting characteristics of Inconel tool material. The basic research activities performed within the present study can be summarized as follows: 1.The study develops geometrical models for the cutting-edge curves and flute designs of ball-end cutters, truncated-cone ball-end cutters and toroid-cone shape cutters. Applying the inverse-envelope theory, a geometrical model for the cross-section of the grinding wheel used to grind the required helical groove on the cutter is developed. Further-more, the relative positions and velocities of the grinding wheel and workpiece during the NC manufacturing of the cutter are developed and investigated via a process of computer simulation. Finally, a compensation method is developed which resolves the problems of residual revolution surface and localized non-existence of the cutting-edge. The theoretical models and results provide a valuable source of reference for the NC manufacturing of revolving cutters. 2.A series of experiments are performed to investigate the effects of the cutting-edge geometry on the machining performance when machining Inconel 718. The Taguchi method is adopted to determine the set of optimal machining parameters for a variety of cutting-edge types, in-cluding those of the truncated-cone ball-end cutter, the plane type, the S type and the traditional type. The results of these experiments serve as a valuable reference for the automated machining of aero-materials. 3.Study the design and manufacture of the cutting-edge curve, flute sur-face and the coning angle of the grinding wheel for both the rotating burr and the revolving cutter, and discuss the difference of the related geometrical models. Also, the practical cutting-edge curve and the feeding rate of the relative movement for the cutter of the two and half axes processes of the NC machine have been discussed.

In this study, we establish a car body PEC model by using a NEC-2-based numerical software. Based on this model, we then carry out a series of simulations and analysis in the FM band concerning the effects of various car structures on antenna patterns. The results have been compared with those available in open literature in order to verify our model. The simulation results show that the roof support pillars significantly affect the antenna patterns. We investigate the ripples caused by the finite ground plane in the antenna patterns, and propose a new edge treatment technique. Our results indicate that a significant reduction of these unwanted ripples can be obtained, if the proposed technique is applied. The effect of car glasses and human body is also taken into consideration. At last, the issue of studying the effects at higher frequencies is addressed. Two approaches are used, including UTD, and PO. Satisfactory results are obtained.