by Chun-pong Cheung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 48-51). / Chapter Chapter 1 --- INTRODUCTION --- p.1 / Chapter §.1.1 --- Toeplitz and Circulant Matrix --- p.1 / Chapter §1.2 --- Conjugate Gradient Method --- p.5 / Chapter §1.3 --- Outline of the Thesis --- p.9 / Chapter Chapter 2 --- INVERSE PROBLEM --- p.11 / Chapter §2.1 --- Inverse Problem --- p.11 / Chapter §2.2 --- Tikhonov Regularization --- p.12 / Chapter Chapter 3 --- FAST ALGORITHM ON THERMAL TOMOGRAPHY --- p.14 / Chapter §3.1 --- Introduction --- p.15 / Chapter §3.2 --- Linearization --- p.15 / Chapter §3.3 --- Regularization by the Identity Operator --- p.17 / Chapter §3.4 --- Regularization by the Laplacian Operator --- p.18 / Chapter §3.5 --- Preconditioning with the Laplacian --- p.21 / Chapter Chapter 4 --- COMPUTERIZED TOMOGRAPHY SCAN --- p.27 / Chapter §4.1 --- Projection Problem --- p.27 / Chapter §4.2 --- Radon Transform --- p.29 / Chapter §4.3 --- Reformulation of Projection Problem --- p.31 / Chapter §4.4 --- Numerical Experiments --- p.35 / Chapter §4.5 --- Sirhplification of Formula --- p.41 / References --- p.48

Wu, Lijiang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 102-105). / Abstracts in English and Chinese. / Chapter 0 --- Introduction --- p.6 / Chapter 1 --- Background knowledge --- p.9 / Chapter 1.1 --- Comparison theorems --- p.9 / Chapter 1.2 --- Bochner techniques --- p.13 / Chapter 1.3 --- Eigenvalue estimates for Laplacian operator --- p.14 / Chapter 1.4 --- Spectral theory for Schrodinger operator on Rieman- nian manifolds --- p.16 / Chapter 2 --- Vanishing theorems --- p.20 / Chapter 2.1 --- Liouville type theorem for Lp subharmonic functions --- p.20 / Chapter 2.2 --- Generalized type of vanishing theorem --- p.21 / Chapter 3 --- Finite dimensionality results --- p.28 / Chapter 3.1 --- Three types of integral inequalities --- p.28 / Chapter 3.2 --- Weak Harnack inequality --- p.34 / Chapter 3.3 --- Li's abstract finite dimensionality theorem --- p.37 / Chapter 3.4 --- Applications of the finite dimensionality theorem --- p.42 / Chapter 4 --- Ends of Riemannian manifolds --- p.48 / Chapter 4.1 --- Green's function --- p.48 / Chapter 4.2 --- Ends and harmonic functions --- p.53 / Chapter 4.3 --- Some topological applications --- p.72 / Chapter 5 --- Splitting theorems --- p.79 / Chapter 5.1 --- Splitting theorems for manifolds with non-negative Ricci curvature --- p.79 / Chapter 5.2 --- Splitting theorems for manifolds of Ricci curvature with a negative lower bound --- p.83 / Chapter 5.3 --- Manifolds with the maximal possible eigenvalue --- p.93 / Bibliography --- p.102

Dehn surgery and the notion of reducible manifolds are both important tools in the study of 3-manifolds. The Cabling Conjecture of Francisco González-Acuña and Hamish Short describes the purported circumstances under which Dehn surgery can produce a reducible manifold. This thesis extends the work of James Allen Hoffman, who proved the Cabling Conjecture for knots of bridge number up to four. Hoffman built upon the combinatorial machinery used by Cameron Gordon and John Luecke in their solution to the knot complement problem. The combinatorial approach starts with the graphs of intersection of a thin level sphere of the knot and the reducing sphere in the surgered manifold. Gordon and Luecke's proof then proceeds by induction on certain cycles. Hoffman provides more insight into the structure of the base case of the induction (i.e. in an innermost cycle or a graph containing no such cycles). Hoffman uses this structure in a case-by-case proof of the Cabling Conjecture for knots of bridge number up to four. We find trees with specific properties in the graph of intersection, and use them to provethe existence of structure which provides lower bounds on the number of the aforementioned innermost cycles. Our results combined with a recent lower bound on the number of vertices inside the innermost cycles succinctly prove the conjecture for bridge number up to five and suggests an approach to the conjecture for knots of higher bridge number.

I do not know what inspires me to use geometric shapes in my artwork. It may have started when I took my first jewelry and metalworking class in college. For one assignment, I had to find an artist and make an artwork that was inspired by his artworks. I choose is Sol Lewitt because I simply liked his opened cubes. Since I started studying in Jewelry and Metalwork and Sculpture at the University of Iowa, I my artworks are still based on geometric shapes. I enjoy them because they are shapes that I see around me everyday; such as textbooks, chairs, doors etc. In my thesis, I will explain my artworks and the techniques that I used, why I made them, what inspired me. My first semester, I just made containers which were based on geometric shapes. After that my ideas and concepts evolved to a simple object based on geometric shapes with no function. A simple geometric object without a function is better for exploring beautiful geometric. Firstly, I find a subject that I can use my ideas and concepts on. It can be something that I see everyday such as myself, faucet, jewelry etc. Sometimes, I find an interesting thing in textbooks, magazines and catalogs. Other times, I find them when I buy materials for my artworks; just shopping at the hardware. There are many things around me that I could use to create my artworks. I just choose some of them to make art and finish assignments.

Today's home network usually involves connecting multiple PCs and peripheral devices, such as printers and scanners, together in a network. This provides the benefit of allowing the PCs in the network to share Internet access and other resources. However, it is expected in the future, the home area network (HAN) will grow and extend to other home devices such as home entertainment systems (including digital TV, hi-fi stereo, etc.), appliances, webcam, security alarm system, etc. Connecting other home devices to a HAN provides users with many benefits not available in today's home networks. For example, home devices capable of connecting to the future HAN are able to share the content downloaded from broadband access anywhere in the home. Users can also have remote access and control of their home devices. To extend the home area network to all these different home devices, however, means that the traffic between the ISP and future HAN will be very different from the traffic generated by today’s home network. In today's home network, which consists mainly of multiple PCs, a best-effort approach is able to satisfy the need, since most of the traffic generated by PCs is not real-time in nature. However, in future HANs, it is anticipated that traffic generated from home devices requiring real-time applications such as multimedia entertainment systems, teleconferencing, etc. will occupy a large proportion of the traffic between the ISP and future HANs. In addition, given the variety of home devices that could potentially be added to future HANs, the amount and variety of traffic between the ISP and a future HAN will certainly be very different from today's home network that is dominated by Internet/data traffic. To allow HAN users of these real-time applications and various types of home devices to continue enjoying seamless experiences in using their home devices without noticing significant delays or unnecessary interruptions, it is important for the ISP to be able to effectively manage the channel to the home so that it can provide sufficient bandwidth to ensure high QoS for home applications. The aim of this thesis is to understand the types of traffic that will be expected and to develop an analytical model that will represent the traffic behaviour between the ISP and future HANs to understand how to manage the channel to provide high QoS. In this thesis, we use the continuous-time PH/M/n/m preemptive priority queue to model the traffic behaviour between the ISP and a future HAN. Three classes of traffic are defined in this model: real-time, interactive, and unclassified. Each of these three traffic classes receives a unique priority level. From the model one can approximate the amount of bandwidth required to be allocated for each traffic class for each household so that the total bandwidth required is minimized while the QoS requirements (delay and blocking probability) of the traffic generated by the home devices are met. Thus this model could potentially be used as a network planning tool for ISPs to estimate how much bandwidth they need to provide per household for homes that use home area network. Alternatively, it could also be used to estimate what quality of service (e.g. what is the mean delay and blocking probability expected) given a certain amount of bandwidth per household. / October 2006

Developing a robust method of image watermarking that resists rotation, scaling and/or translation (RST) transformations is widely considered to be a more challenging task than developing a method resistant to other attacks. Altering the orientation or size of the image, even only slightly, reduces the receiver¡¦s ability to retrieve the watermark. Protecting against both geometric distortion and signal processing with blind detection is even more problematic. This investigation proposes a novel approach, based on the properties of histograms to measure the numerous global features of all pixels in a cover image and to construct the three-dimensional feature space. The feature space is dynamically partitioned to identify several blocks used to embed the watermark. One feature of the pixels is modified to form a specially distributed histogram for embedding the watermark in a blind digital watermarking method that can be applied to color images. Experimental results demonstrate the robustness of the proposed method against common geometric attacks and signal processing.

I describe an exact method for computing roots of a system of multivariate polynomials with rational coefficients, called the rational univariate reduction. This method enables performance of exact algebraic computation of coordinates of the roots of polynomials. In computational geometry, curves, surfaces and points are described as polynomials and their intersections. Thus, exact computation of the roots of polynomials allows the development and implementation of robust geometric algorithms. I describe applications in robust geometric modeling. In particular, I show a new method, called numerical perturbation scheme, that can be used successfully to detect and handle degenerate configurations appearing in boundary evaluation problems. I develop a derandomized version of the algorithm for computing the rational univariate reduction for a square system of multivariate polynomials and a new algorithm for a non-square system. I show how to perform exact computation over algebraic points obtained by the rational univariate reduction. I give a formal description of numerical perturbation scheme and its implementation.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 199-201). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 199-201). Also available on the Internet.

For control systems that evolve on Euclidean spaces, Jacobian linearization is a common technique in many control applications, analysis, and controller design methodologies. However, the standard linearization method along a non-trivial reference trajectory does not directly apply in a geometric theory where the state space is a differentiable manifold. Indeed, the standard constructions involving the Jacobian are dependent on a choice of coordinates. The procedure of linearizing a control affine system along a non-trivial reference trajectory is studied from a differential geometric perspective. A coordinate-invariant setting for linearization is presented. With the linearization in hand, the controllability of the geometric linearization is characterized using an alternative version of the usual controllability test for time-varying linear systems. The various types of stability are defined using a metric on the fibers along the reference trajectory and Lyapunov's second method is recast for linear vector fields on tangent bundles. With the necessary background stated in a geometric framework, Kalman's theory of quadratic optimal control is understood from the perspective of the Maximum Principle. Finally, following Kalman, the resulting feedback from solving the infinite time optimal control problem is shown to uniformly asymptotically stabilize the linearization using Lyapunov's second method. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2007-12-19 16:59:47.76