The primary purpose of this study was to investigate experimentally the following questions: (1) What is the relative effectiveness of the vector approach and the traditional approach to teaching certain topics in plane analytic geometry to high school students in terms of achievement and understanding? (2) Does teaching these topics in plane analytic geometry via vectors produce more transfer to other topics in analytic geometry (mainly solid analytic geometry) than teaching these topics via the traditional approach? / Typescript. / "December, 1968." / "Submitted to the Department of Mathematics Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: E. D. Nichols, Professor Directing Dissertation. / Includes bibliographical references.

by Yuen Wai Ching. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 54-55). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Group Analysis --- p.9 / Chapter 2.1 --- Groups and Differential Equations --- p.9 / Chapter 2.2 --- Prolongation --- p.11 / Chapter 2.3 --- The Prolongation Formula --- p.14 / Chapter 3 --- Symmetry Group For the Eikonal Equation --- p.17 / Chapter 4 --- An Optimal System For the Eikonal Equation --- p.25 / Chapter 5 --- Group Invariant Solutions --- p.33 / Chapter 5.1 --- Straight Lines --- p.33 / Chapter 5.2 --- Stationary Solutions --- p.33 / Chapter 5.3 --- Traveling Waves --- p.34 / Chapter 5.4 --- Circles --- p.37 / Chapter 5.5 --- Spirals --- p.38 / Chapter 6 --- Appendix --- p.50 / A Group Analysis for some Geometric Evolution Equations --- p.4 / Bibliography

A Tutte trail T of a graph G is a trail such that every component of GnV (T) has at most three edges connecting it to T. In 1992, Bill Jackson conjectured that every 2-edge-connected graph G has a Tutte closed trail. In this thesis, we show that Jackson's conjecture is true when G is embedded on the plane and the projective plane. We also give some partial results when G is embedded on the torus.

Typescript (Photocopy). / Digitized by Kansas Correctional Industries

This thesis presents the nonlinear in-plane behaviour of circular fixed arches subjected to thermal loading only. Due to the nonlinear prebuckling behaviour of arches and its effects, classical buckling theory which is founded on geometric prebuckling linearity can not predict the in-plane buckling of arches accurately. Based on a nonlinear formulation of the strain and displacement relationship and considering constant thermal distributions only, virtual work formulations are used to establish the differential equations of in-plane equilibrium and the statical boundary conditions, from which the nonlinear equilibrium equations are derived in closed form and which are suitable to use in design. By considering the adjacent buckled configurations, the differential buckling equilibrium equations are formulated from the principle of virtual work as well, and the analytical solutions for the nonlinear buckling of fixed arches are obtained. It is shown that nonlinear elastic buckling of a fixed in the plane of it curvature can not occur when it is subjected to thermal loading only, except if the arch is as a straight column. By using the algebraic representation of nonlinear in-plane equilibrium derived in this thesis, the elastic response of fixed arches at elevated temperatures and the attainment of first yield are examined in detail. The arch deflects transversely without bound in the elastic range at elevated temperatures, whereas it will yield first at the top extreme fibre of the cross section at the supports when a critical temperature is reached. The influence of several parameters such as the included angle is also considered. Based on the models of stress distributions at cross sections, the spread of yield both through the cross section and along the length of the arch is studied. It is indicated that the progress of yielding causes the first two hinges to form at the supports of the fixed arches, and then moment redistribution leads to the generation of the third hinge at the crown with an increase of temperature. Thus nonlinear plastic hinge analysis can be applied to the arch analysis under thermal loading.

A novel method of predicting the multiaxial high-cycle fatigue strength of metallic components is proposed and verified for various steel, aluminium and cast iron alloys. The proposed Fatigue Damage Function shows superior multiaxial fatigue strength prediction compared to the established methods of Gough and Pollard, McDiarmid and Carpinteri and Spagnoli. A new material property, the Normal Stress Sensitivity Factor, is also introduced and its applicability is verified according to published test results of sixteen different structural alloys. To highlight the effectiveness of the proposed criterion, for industrial applications, a case study has been conducted on heat-treated and not heat-treated automatic transmission output shafts.

In the thesis, epitaxial ZnO films were grown by chemical vapor deposition method (CVD) on LiGaO2 (001) substrate. Zinc 2,4-pentanedionate monohydrate [Zn (C5H7O2) 2. H2O] , used as the zinc precursor, was vaporized at the temperature between 130 to 140¢J. Then the vapor was carried by a mixture of N2/O2 gas flow into the furnace where the (001) LGO substrate located. The parameters of growth temperature, growth pressure and growth time were adjusted to found the best ZnO films growth conditions. After CVD growth, the crystal structure, crystal quality, surface morphology, optical properties, surface roughness and micro-structure properties of the specimens were analyzed by X-ray diffraction (XRD), scanning electron microscopy (SEM), photoluminescence (PL), atomic force microscopy (AFM) and transmission electron microscopy (TEM). This study was divided into three parts. In the first parts, the dependence of growth characteristics on the different growth temperatures was investigated. The best surface morphology and crystal quality of ZnO films were grown under the growth temperature of 550 ¢J. In the second parts, the growth of ZnO films under various pressures was investigated. High orientation (0002)ZnO films were grown at lower growth pressure of 50 torr. In the third parts, the dependence of growth time on the ZnO films quality was investigated under growth temperature of 550 ¢Jand growth pressure of 50 torr.

In This Thesis , We primarily introduce some results with suppression of ground bounce noise in high-speed PCB by the formal researchers and summarize their advantages and weaknesses .In the next section .we explain why the EBG (Electromagnetic Band Gap ) design structure is from PBG (Photonic Band Gap ) concept in optical research field and that its principle can suppress GBN . We also summarize their advantages and weaknesses .In the following part, we define five parameters of EBG design structure to find the optimal solution by HFSS simulation method .The optimal solution can enlarge the bandwidth of suppression of GBN to 5.40GHz.We prove the accuracy of HFSS simulation method by actual measurement . When the EBG basic cell gradually compact from n=9.their characteristics are according to 1.central frequency towards high frequency 2.bandwidth of suppression of GBN is more broadband 3. forbiddance band depth becomes wider. Finally we oppose some new EBG design structures to solve some problems of old EBG design structure .These new EBG design structures can enhance signal integrity (SI) and law frequency response. Include three items 1.Meander design structure 2. Buddha design structure 3. Budder design structure .We also prove the accuracy of HFSS simulation method by actual measurement.

The researches of this thesis are divided into two parts. One is to investigate the applicability of ANSI C63.5 in high frequencies of 1 GHz to 6 GHz. In general, the Standard Site Method (SSM) of C63.5 is usually used to calculate the antenna factors for the calibration of broadband antennas. Through the theoretical calculations, the numerical simulations and measurements, we found that the discrepancies between the calibrated results of horizontal and vertical polarization related to the un-dipole-like pattern in higher frequencies. Furthermore, we analyzed the relations of the antenna factors, the heights of receive antennas and the radiation patterns. We also found that the predicted calibration results can be close to the practical ones by including the effects of radiation patterns. The other research is to study the issue about the ground plane size of a test site. The ground plane size of a qualified test site must be larger than the minimum size defined by C63.7. For this reason, we provide a method which combines the tilted antennas measurement with a trapezoid shape ground. By using this method in the smaller ground size, we can obtain the measured results close to those obtained in the larger ground size. This method can effectively reduce the required ground size and then decrease the installation cost of a test site. Meanwhile, this method can be applied for both of the horizontal and vertical polarizations.

Due to the advances of image system, most researches are developed on high-resolution system. However, the low-resolution system have an advantage over the high-resolution system on processing speed, saving space and power consumption. From the research of hexagonal grid, we know that from the view of microcosmic, the angle resolution and connection of hexagonal grid are better than rectangular grid, so images on hexagonal grid also have the better quality. Almost input and output systems of image device are on rectangular grid, so its technology and theory are developed on rectangular grid system. For a displaying system, fonts and images are the main elements. If we want to substitute hexagonal grid system for rectangular grid system, they will be primary factories that we consider. In this research based on rectangular grid system, we will apply the plane parametric curves and fill algorithm on hexagonal grid system, and probe into the displaying method of fonts and images on hexagonal grid system.