我们研究了P[subscript g]=0 的复曲面x 上的ADE 向量丛和仿射ADE 向量丛。 / 首先，我们假设x 上有一个ADE 奇异点。这个奇异点在极小分解Y 中的例外轨迹是一条相应形式的ADE 曲线。利用这条ADE 曲线和向量丛的扩张，我们构造了Y 上的一个ADE 向量丛，而且这个向量丛可以下降到x上。此外，我们利用Y 上( -1)- 曲线的组合，描述了他们的极小表示向量丛。 / 其次，我们假设x 是一个椭圆曲面，而且x 上有一个仿射ADE 形式的奇异纤维。类似于以前，我们构造了X 上的一个仿射ADE 向量丛，而且这个向量丛在这条仿射ADE 曲线上的每一个不可约成分上都是平凡的。 / 然后，当X 是P²上突起n ≤9 个点时, x 上有一个典型的En 向量丛。我们详细的研究了x 的几何和这个E[subscript n] 向量丛的可变形性之间的关系。 / We study ADE and affine ADE bundles over complex surfaces X with P[subscript g] = 0. / First, we suppose X admits an ADE singularity. The exceptional locus of this singularity in the minimal resolution Y is an ADE curve of corresponding type. Using this ADE curve and bundle extensions, we construct an ADE bundle over Y which can descend to X. Furthermore, we describe their minuscule representation bundles in terms of configuration of (reducible) (-1)-curves. / Second, we assume X is an elliptic surface with a singular fiber of affine ADE type. Similar to above studies, we construct the affine ADE bundle over X which is trivial on each irreducible component of the affine ADE curve. / Third, when X is the blowup of P² at n ≤9 points, there is a canonical E[subscript n] bundle over it. We give a detailed study of the relationship between the geometry of X and the deformability of this bundle. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chen, Yunxia. / On t.p. "g" is subscript. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 84-87). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Chapter I --- ADE bundles --- p.9 / Chapter 1 --- ADE Lie algebra bundles --- p.10 / Chapter 1.1 --- ADE singularities --- p.10 / Chapter 1.2 --- ADE bundles --- p.12 / Chapter 2 --- Minuscule representations and ( -1)-curves --- p.16 / Chapter 2.1 --- Standard representations --- p.16 / Chapter 2.2 --- Minuscule representations --- p.17 / Chapter 2.3 --- Configurations of ( -1)-curves --- p.17 / Chapter 2.4 --- Minuscule representations from ( -1)-curves --- p.19 / Chapter 2.5 --- Bundles from ( -1)-curves --- p.21 / Chapter 2.6 --- Outline of Proofs for g ≠E₈ --- p.22 / Chapter 3 --- A[subscript n] case --- p.24 / Chapter 3.1 --- A[subscript n] standard representation bundle Lη^(An,Cn+1) --- p.24 / Chapter 3.2 --- An Lie algebra bundle Sη^(An) --- p.28 / Chapter 3.3 --- An minuscule representation bundle Lη^(An,^kCn+1) --- p.28 / Chapter 4 --- Dn case --- p.30 / Chapter 4.1 --- Dn standard representation bundle Lη^(Dn;C2n) --- p.30 / Chapter 4.2 --- Dn Lie algebra bundle Sη^(Dn) --- p.34 / Chapter 4.3 --- Dn spinor representation bundles Lη^(Dn;S±06) --- p.34 / Chapter 5 --- En case --- p.39 / Chapter 5.1 --- E₆ case --- p.39 / Chapter 5.2 --- E₇ case --- p.42 / Chapter 5.3 --- E₈ case --- p.44 / Chapter 6 --- Proof of Theorem 1.2.1 --- p.45 / Chapter II --- Affine ADE bundles --- p.50 / Chapter 7 --- Affine ADE Lie algebra bundles --- p.51 / Chapter 7.1 --- Affine ADE curves --- p.51 / Chapter 7.2 --- Affine ADE bundles --- p.53 / Chapter 8 --- Trivialization of E₀ gover Ci's after deformations --- p.57 / Chapter 8.1 --- Trivializations in loop ADE cases --- p.58 / Chapter 8.2 --- Trivializations in affine ADE cases --- p.60 / Chapter 8.3 --- Proof (except the loop E₈ case) --- p.60 / Chapter 8.4 --- Proof for the loop E₈ case --- p.62 / Chapter III --- Deformability --- p.65 / Chapter 9 --- En-bundle over Xn with n≤9 --- p.66 / Chapter 9.1 --- En-bundle over Xn with n ≤ 9 --- p.66 / Chapter 9.2 --- Deformability of such E₀E₈ --- p.68 / Chapter 9.3 --- Negative curves in X9 --- p.70 / Chapter 9.4 --- Proof of Theorems 9.2.1 and 9.2.2 --- p.75 / Chapter A --- Minuscule configurations --- p.78 / Chapter B --- A ffine Lie algebras --- p.80

Wen, Chengfeng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 77-83). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

自從 Onnes 于1911 年發現超導現象以來，超導就一直是凝聚態領域非常熱門的一個課題。隨之而來的一個問題是超導在量子尺寸效應的影響下將如何變化。在1959 年，Anderson 提出了一個超導受尺寸影響而消失的判據：當超導體的尺寸足够小以至於超導體費米面附近電子的平均能隙大於超導能隙或與其相當時，超導便被尺寸效應破壞。基於這個判據，超導和費米面附近的電子態密度密切相關。Si(111)表面上生長的鉛島在調製費米面附近的態密度上是一個很好的系統，因為它既可以在垂直方向上通過量子阱態調節，也可以通過水平方向的尺寸限制來調節。另外，相對於其他系綜或者粉末超導體，在Si(111)表面上生長的單個鉛島系統上研究超導排除了諸如尺寸分佈，顆粒間相互耦合以及相位漲落等因素對於超導的影響。 / 在這篇論文的緒論中，我首先簡單介紹了基本的超導知識，如 BCS 理論，Eliashberg 理論以及超導在超導體-絶緣體-正常金屬形成的隧道結上的表現形式。跟著，我重點回顧了之前在系綜超導體以及金屬納米結構中進行的超導尺寸效應研究。對於目前廣泛研究的鉛島系統，我將重點談及最近發現的贗能隙，這對研究鉛島的超導至關重要。 / 在第二章，我簡單介紹了樣品的生長和掃描隧道譜的相關知識。爲了分析鉛島的超導譜，我們用了兩種方法去分析他們。一種是零電壓下電導的方法，另一種是超導譜分析方法。在這章的最後，我詳細介紹了Dynes 方程及去捲積的方法。 / 在第三章，我將介紹我博士學習期間一個非常重要的工作，提高儀器的能量分辨率。通過改造儀器結構，合理的接地，屏蔽射頻噪聲，以及清除電壓源的噪聲，我成功地將能量分辨率從0.9 meV 提高到0.2 meV。在最後我會將儀器改進后的結果與之前的結果儀器與其他組的結果進行比較。 / 在儀器改進之前，我們發現那時的測量結果非常差，由此得出的結論也是不正確的。爲了比較儀器改造的重要性，在第四章，我將簡單介紹儀器改進前的結果。在當時差的條件下，我們探測出對於9ML 厚的鉛島，3.2 K 以上不超導的鉛島尺寸，大約為30 nm²。並且鉛島經歷了一個從強電子聲子耦合到弱電子聲子耦合的轉變。 / 在儀器改進之後，我們不僅糾正了之前在九層鉛島上進行超導研究時的一些結論。此外，也觀察到了由於尺寸變化或者費米面上態密度變化導致超導的細微區別。由於尺寸效應，我們發現在一些小的鉛島上存在一個過渡區。另外，由於八層鉛島費米面上的態密度比九層的高，超導轉變溫度也因此有一個系統性的提高。對於這兩個層數的鉛島，他們的超導轉變溫度都隨尺寸減小受到一個緩慢的抑制。對於非常小的鉛島，我們發現其仍然超導。這和Anderson 判據的預期以及其他實驗結果不一致，激發我們進一步探索是否非晶化的潤濕層參與了這種非常小的鉛島的超導。 / 這些工作，對於全面理解超導的尺寸效應以及態密度影響是非常基本和關鍵的，這也將進一步激發人們在這個領域進行更多的探索。 / Superconductivity has always been a hot topic in the field of condensed matter physics since its discovery by Onnes in 1911. How the superconductivity was affected by size attracted much attention especially after P. W. Anderson proposed a criterion of the breakdown of superconductivity in 1959, where the superconductors will lose their superconductivity when the energy level spacing at Fermi level (E[subscript F]) is comparable to or larger than the superconducting energy gap. As stated in the criterion, the superconductivity correlates greatly with the density of states (DOS) at E[subscript F] within the superconducting gap. The system of individual Pb islands grown on Si(111) provides an ideal platform to modulate the DOS at EF through both the quantum size confinement and the quantum well states (QWS) effects. Moreover, this system excludes the problems of size distribution, couplings among particles and phase fluctuation of the previously studied ensembles of particles. / In my thesis, I first introduce briefly the basic knowledge of superconductivity, such as BCS theory and Eliashberg theory, as well as its behaviors in a normal metal-insulator-superconductor tunneling junction. Then the study of superconductivity by quantum size effect on ensemble superconductors and metallic nanostructures is reviewed. For the widely studied system of Pb islands, I discuss in more detail the recently discovered pseudogap which was important and critical for analyzing the superconductivity. / In chapter 2, the knowledge of sample growth is given and a simple introduction to scanning tunneling spectroscopy is presented. To study the superconductivity spectra of Pb islands, we use two methods to analyze them, one the zero bias conductance (ZBC) method and the other the superconductivity spectrum analysis. In the end of this chapter, Dynes function and deconvolution procedure are introduced in detail. / In chapter 3, I introduce one of my important works in my Phd study, to improve the instrumental energy resolution. By reconstructing the instrumental structure, grounding properly, shielding RF noise, and cleaning the voltage gap source, the instrumental energy resolution has been improved greatly from ~0.9 meV to ~0.2 meV. I compare our current results both with previous results and results from other groups. / Before the instrumental improvement, we find that the measurements were very poor and the conclusion thus obtained were incorrect. To show the importance of the instrumental improvement, I introduce briefly the previous work in chapter 4. Under the poor instrumental condition, we found that the limiting size of superconductivity above 3.2 K was determined to be ~30 nm² for 9 ML thick Pb islands and that Pb island superconductors undergo a change from strong to weak electron-phonon coupling. / After the instrumental improvement, we not only correct some conclusions of the previous studies on superconductivity of 9 ML Pb islands, but also observed the more non-trivial variation of superconductivity from the change of island size or density of state (DOS) at Fermi level (E[subscript F]) by the quantum well states (QWS). A critical regime is observed for small Pb islands. As the DOS of 8 ML Pb islands at E[subscript F] is larger than that of 9 ML Pb islands, the transition temperatures (T[subscript C]) of 8 ML Pb islands hold a systematic difference larger than those of 9 ML Pb islands. The T[subscript C] results for both 8 ML and 9 ML Pb islands follow the same gradual suppression and the ratio 2△(0)/k[subscript B]T[subscript C] remains unchanged by the size effect. Further study indicates that for very small 8 ML and 9 ML Pb islands they are still superconducting, inconsistent with the Anderson criteria and other experimental results. This observation suggests a possible role of wetting layer on superconductivity of these small Pb islands. / This work, I believe, is fundamentally interesting and beneficial to understand deeply the phenomena of superconductivity modulated by size effect and DOS change at E[subscript F] and will inspire more future studies in this field. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Liu, Jiepeng = 掃描隧道譜研究Si(111)表面上單個鉛島的超導尺寸效應及態密度影響 / 羅杰鵬. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 136-144). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Liu, Jiepeng = Sao miao sui dao pu yan jiu Si(111) biao mian shang dan ge qian dao de chao dao chi cun xiao ying ji tai mi du ying xiang / Luo Jiepeng. / Chapter 1 --- Superconductivity affected by quantum size effect --- p.2 / Chapter 1.1 --- Overview --- p.3 / Chapter 1.2 --- Basic theories to superconductivity --- p.4 / Chapter 1.2.1 --- BeS theory --- p.5 / Chapter 1.2.2 --- Eliashberg equation --- p.8 / Chapter 1.2.3 --- Superconductivity of S-I-N tunneling junction --- p.10 / Chapter 1.3 --- Size effect of superconductivity for ensemble or powder superconductors --- p.12 / Chapter 1.3.1 --- Anderson criteria --- p.13 / Chapter 1.3.2 --- Size-dependent T[subscript C] for different superconductors --- p.13 / Chapter 1.4 --- Size effect of superconductivity for metallic nanostructures --- p.17 / Chapter 1.4.1 --- Metallic nanostructures --- p.17 / Chapter 1.4.2 --- Quantum well states of metallic nanostructures --- p.18 / Chapter 1.4.3 --- Pb nanostructures on Si(111)-7 x 7 --- p.20 / Chapter 1.5 --- summary --- p.25 / Chapter 2 --- Experimental introductions and data analysis methods --- p.26 / Chapter 2.1 --- Experimental introduction --- p.27 / Chapter 2.1.1 --- Growth of Pb islands --- p.28 / Chapter 2.1.2 --- Substrates effects --- p.32 / Chapter 2.2 --- STS studies of Pb islands --- p.36 / Chapter 2.2.1 --- Basic knowledge of STS --- p.36 / Chapter 2.2.2 --- STS results of Pb islands --- p.40 / Chapter 2.3 --- Data analysis methods --- p.41 / Chapter 2.3.1 --- Zero bias conductance analysis --- p.41 / Chapter 2.3.2 --- Superconductivity spectrum analysis --- p.43 / Chapter 2.4 --- Dynes function fitting --- p.44 / Chapter 2.4.1 --- Dynes function --- p.44 / Chapter 2.4.2 --- Deconvolution --- p.47 / Chapter 2.4.3 --- BCS-like analysis --- p.49 / Chapter 2.5 --- Summary --- p.50 / Chapter 3 --- Instrument improvements --- p.51 / Chapter 3.1 --- Previously existed problems --- p.52 / Chapter 3.2 --- Problem analysis and solutions --- p.54 / Chapter 3.2.1 --- Structure and Preamplifier --- p.54 / Chapter 3.2.2 --- Grounding --- p.56 / Chapter 3.2.3 --- Bias voltage source cleaning --- p.57 / Chapter 3.2.4 --- RF noise shielding --- p.60 / Chapter 3.3 --- Tip drift in perpendicular direction when taking STS --- p.65 / Chapter 3.4 --- Improved results --- p.68 / Chapter 3.4.1 --- Comparisons with previous results --- p.68 / Chapter 3.4.2 --- Comparisons with other groups --- p.69 / Chapter 3.5 --- Summary --- p.72 / Chapter 4 --- Superconductivity of 9 ML thick Pb islands with poor energy resolution --- p.75 / Chapter 4.1 --- STS results --- p.76 / Chapter 4.1.1 --- STS results at large energy scale --- p.76 / Chapter 4.1.2 --- STS results at small energy scale Zero bias conductance analysis --- p.79 / Chapter 4.2.1 --- ZBC results --- p.79 / Chapter 4.2.2 --- Comparisons with theoretical calculations --- p.83 / Chapter 4.3 --- Superconductivity spectrum analysis --- p.85 / Chapter 4.3.1 --- Method to obtain superconductivity spectra --- p.86 / Chapter 4.3.2 --- BCS-like analysis --- p.93 / Chapter 4.4 --- Explanation and possible mechanism --- p.97 / Chapter 4.5 --- Summary --- p.99 / Chapter 5 --- DOS modulated superconductivity with improved energy resolution --- p.101 / Chapter 5.1 --- Introduction --- p.102 / Chapter 5.2 --- Experiments --- p.103 / Chapter 5.3 --- Behaviors of zero bias conductance results --- p.104 / Chapter 5.3.1 --- Power law behavior --- p.104 / Chapter 5.3.2 --- Critical regime and To determination --- p.106 / Chapter 5.4 --- Recheck previous results --- p.112 / Chapter 5.4.1 --- Pseudogap --- p.112 / Chapter 5.4.2 --- Transition temperature --- p.115 / Chapter 5.5 --- DOS modulated superconductivity --- p.121 / Chapter 5.5.1 --- Quantum well states of 8 ML and 9 ML Pb islands --- p.121 / Chapter 5.5.2 --- T[subscript C] behavior on a 8 ML and 9 ML Pb island --- p.123 / Chapter 5.5.3 --- Superconductivity behaviors for a set of 8 ML and 9 ML Pb islands --- p.124 / Chapter 5.5.4 --- Superconductivity of very small Pb islands --- p.129 / Chapter 5.6 --- Summary --- p.130 / Chapter 6 --- Conclusions and outlook --- p.132 / Chapter 6.1 --- Conclusions --- p.133 / Chapter 6.2 --- Outlook --- p.134 / Bibliography --- p.136

Resumo: O objetivo deste trabalho foi avaliar o efeito de diferentes tratamentos de superfície da cerâmica Y-TZP na resistência de união, durabilidade e discrepância marginal. Para os testes de resistência adesiva, foram obtidos 144 corpos de prova (cp) da cerâmica VITA In-Ceram YZ for InLab (5,25 x 3,75 x 4,5 mm), que foram divididos em 6 grupos (G) (n=24), conforme o tratamento de superfície: G1: sem tratamento (controle); G2: jateamento com partículas de alumínio revestidas por sílica (CoJet®-Sand, 3M ESPE AG) (silicatização); G3: vitrificação 1 (Glaze Spray VITA AKZENT), condicionamento com ácido fluorídrico (HF) (1 min); G4: vitrificação 1 (Glaze Spray VITA AKZENT), silicatização; G5: vitrificação 2 (Glaze VITA AKZENT), condicionamento com HF (1 min); G6: vitrificação 2 (Glaze VITA AKZENT), silicatização. Após todos os tratamentos, as superfícies foram silanizadas por 5 min (ESPE-SIL) e a cimentação com Panavia F (Kuraray) foi realizada. Metade dos espécimes de cada tratamento foi ensaiada 24h após cimentação (SECO), a outra metade foi submetida à armazenagem (150 dias) e termociclagem (12.000x) (TC), e então realizado o ensaio de cisalhamento (1 mm/min). G7: G1+TC; G8: G2+TC; G9: G3+TC; G10: G4+TC; G11: G5+TC; G12: G6+TC. Superfícies tratadas foram analisadas por perfilometria óptica 3D para obtenção dos dados de rugosidade (Ra) e microscopia eletrônica de varredura (MEV) (1000x). Análise por energia dispersiva de raio-X (EDS) foi realizada para determinar os elementos químicos presentes na superfície de cada grupo. Para a análise de adaptação marginal foram confeccionadas 60 infraestruturas (adaptadas em um troquel metálico) nas quais foram realizados os mesmos tratamentos de superfície / Abstract: The aim of this study was to evaluate the effect of different surface treatments of Y-TZP ceramic on bond durability and marginal fit. 144 specimens of VITA In-Ceram YZ for InLab ceramic (5.25 x 3.75 x 4.5 mm) were obtained and divided into 6 groups (n=24) according to the surface treatment: G1: no treatment (control); G2: chairside tribochemical silica coating system (CoJet®-Sand, 3M ESPE AG) (Cojet); G3: vitrification 1 (Glaze Spray VITA AKZENT), conditioning with hydrofluoric acid (HF) (1 minute); G4: vitrification 1 (Glaze Spray VITA AKZENT), Cojet; G5: vitrification 2 (Glaze VITA AKZENT), conditioning with HF (1 minute); G6: vitification 2 (Glaze VITA AKZENT), Cojet. Then, the ceramic surfaces were silanized and the cementPanavia F (Kuraray) was applied. Half of the specimens from each treatment was tested 24 hours after cementation (DRY), the remaining specimens were stored in distilled water for150 days,thermocycled(12,000x) (AGING) and then the shear test was performed (1mm/minute). Conditioned surfaces were evaluated by 3D optical profilometry in order to obtain roughness data (Ra) and analysed by scan electronic microscopy (SEM) (1000x). Analysis by energy x-ray dispersive (EDS) was performed to determine the chemical elements present in each surface group. For analysis of marginal adaptation 60 crowns were produced (adapted into a metal die) and the same surface treatments were carried out on the internal surface of the crowns. The data were analysed using. The results suggest the vitrification 1 and vitrification 2 groups showed the highest bond strength compared to the control group. The highest marginal discrepancies were observed in the vitrification groups (117.36±29.61 to 105.78±12.23) comparing with the other groups (55.29±8.71 and 55.04±8.55). / Orientador: Luiz Felipe Valandro / Coorientador: Fernando Eidi Takahashi / Banca: Marco Antonio Bottino / Banca: Renata Marques Melo / Banca: Paulo Francisco Cesar / Banca: Marcelo Giannini / Doutor

Superhydrophobic surfaces are able to entrap gas pockets in-between surface roughness elements when submerged in water. These entrapped gas pockets give these surfaces the potential to reduce drag due to the overlying flow being able to locally slip over the gas pockets, resulting in a mean slip at the surface. This thesis investigates the different effects that slip and the texturing of the surface have on turbulence over superhydrophobic surfaces. It is shown that, after filtering out the texture-induced flow, the background, overlying turbulence experiences the surface as a homogeneous slip boundary condition. For texture sizes, expressed in wall units, up to $L^+ \lesssim 20$ the only effect of the surface texture on the overlying flow is through this surface slip. The direct effect of slip does not modify the dynamics of the overlying turbulence, which remains canonical and smooth-wall-like. In these cases the flow is governed by the difference between two virtual origins, the virtual origin of the mean flow and the virtual origin experienced by the overlying turbulence. Streamwise slip deepens the virtual origin of the mean flow, while spanwise slip acts to deepen the virtual origin perceived by the overlying turbulence. The drag reduction is then proportional to the difference between the two virtual origins, reminiscent of drag reduction using riblets. The validity of slip-length models to represent textured superhydrophobic surfaces can resultantly be extended up to $L^+ \lesssim 20$. However, for $L^+ \gtrsim 25$ a non-linear interaction with the texture-coherent flow alters the dynamics of the background turbulence, with a reduction in coherence of large streamwise lengthscales. This non-linear interaction causes an increase in Reynolds stress up to $y^+ \lesssim 25$, and decreases the obtained drag reduction compared to that predicted from homogeneous slip-length models.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Mechanical Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Vita. / Includes bibliographical references. / Ph.D.

by Ka Wai Wong. / "June 1999." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / by Ka Wai Wong.

Ku Wah Kwan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 61-64). / Abstracts in English and Chinese. / Chapter 1 --- Basic 3-Dimensional Contact Geometry --- p.5 / Chapter 1.1 --- Introduction --- p.5 / Chapter 1.2 --- Contact Structure --- p.7 / Chapter 1.3 --- Darboux's Theorem --- p.11 / Chapter 1.4 --- Characteristic Foliation --- p.13 / Chapter 1.5 --- More About S3 with The Standard Contact Structure --- p.16 / Chapter 2 --- Legendrian Knots --- p.18 / Chapter 2.1 --- Basic Definition --- p.18 / Chapter 2.2 --- Front Projection --- p.19 / Chapter 2.3 --- Classical Legendrian Knot Invariants --- p.22 / Chapter 2.3.1 --- Thurston-Bennequin Invariant --- p.22 / Chapter 2.3.2 --- Rotation Number --- p.23 / Chapter 2.4 --- Stabilization --- p.24 / Chapter 3 --- Convex Surface Theory --- p.26 / Chapter 3.1 --- Contact Vector Field --- p.26 / Chapter 3.2 --- Convex Surfaces --- p.29 / Chapter 3.3 --- Flexibility of Characteristic Foliation --- p.34 / Chapter 3.4 --- Bennequin Inequality --- p.36 / Chapter 3.5 --- Bypass --- p.38 / Chapter 3.5.1 --- Modification of Dividing Curves through Bypass --- p.39 / Chapter 3.5.2 --- Relation of Bypass and Stabilizing Disk --- p.40 / Chapter 3.5.3 --- Finding Bypass --- p.40 / Chapter 3.6 --- Tight Contact Structures on Solid Tori --- p.41 / Chapter 4 --- Classification Results --- p.42 / Chapter 4.1 --- Unknot --- p.43 / Chapter 4.2 --- Positive Torus Knot --- p.45 / Chapter 5 --- Transverse Knots --- p.50 / Chapter 5.1 --- Basic Definition --- p.50 / Chapter 5.2 --- Self-linking Number --- p.54 / Chapter 5.3 --- Relation between Transverse Knot and Legendrian Knot --- p.55 / Chapter 5.4 --- Classification of Unknot and Torus Knot --- p.57 / Chapter 6 --- Recent Development --- p.60 / Bibliography --- p.61

Lai Yuen-hoo. / Thesis submitted in: November 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 100-102). / Abstracts in English and Chinese. / Abstract --- p.i / 摘要 --- p.ii / Acknowledgment --- p.iii / List of Figures --- p.iv / Table of Content --- p.vii / Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Problem Definition --- p.1 / Chapter 1.2. --- Proposed Solution --- p.2 / Chapter 1.3. --- Thesis Contributions --- p.2 / Chapter 2. --- Modeling Approaches --- p.4 / Chapter 2.1. --- Polygon Modeling --- p.4 / Chapter 2.2. --- Patch Modeling --- p.6 / Chapter 2.3. --- Freehand Sketch-based Modeling --- p.7 / Chapter 2.4. --- Template Based Modeling --- p.8 / Chapter 2.5. --- Curve Interpolation Method --- p.9 / Chapter 3. --- Surface Operations --- p.11 / Chapter 3.1. --- Surface Blending --- p.11 / Chapter 3.2. --- Surface Trimming --- p.13 / Chapter 3.3. --- Boolean Operations --- p.14 / Chapter 4. --- Subdivision Surface --- p.16 / Chapter 4.1. --- Basic Principle --- p.16 / Chapter 4.2. --- Catmull-Clark Surface --- p.17 / Chapter 5. --- Modeling Algorithm Overview --- p.21 / Chapter 6. --- Subdivision Surface Generation --- p.23 / Chapter 6.1. --- Input Curves --- p.23 / Chapter 6.2. --- Surface Sweeping --- p.24 / Chapter 6.3. --- Subdivision Surface Fitting --- p.29 / Chapter 7. --- Surface Blending --- p.32 / Chapter 7.1. --- Introduction --- p.32 / Chapter 7.2. --- Problem Definition --- p.32 / Chapter 7.3. --- Algorithm Overview --- p.36 / Chapter 7.4. --- Blend Region Detection --- p.39 / Chapter 7.4.1. --- Collision Detection --- p.40 / Chapter 7.4.2. --- Result and Analysis --- p.42 / Chapter 7.5. --- "Mesh Refinement, Surface Fitting and Region Removal" --- p.46 / Chapter 7.5.1. --- Mesh Refinement --- p.46 / Chapter 7.5.1.1. --- Adaptive Subdivision --- p.46 / Chapter 7.5.1.2. --- Additional Subdivision Constraint --- p.47 / Chapter 7.5.2. --- Surface Fitting --- p.49 / Chapter 7.5.2.1. --- General Approach --- p.49 / Chapter 7.5.2.2. --- Surface Point Correspondence --- p.50 / Chapter 7.5.2.3. --- Numerical Fitting Method --- p.51 / Chapter 7.5.3. --- Unwanted Region Removal --- p.55 / Chapter 7.5.4. --- Result and Analysis --- p.56 / Chapter 7.6. --- Boundary Smoothing --- p.58 / Chapter 7.6.1. --- General Approach --- p.59 / Chapter 7.6.2. --- Constraint on Deformation Direction of Vertex --- p.61 / Chapter 7.6.3. --- Result and Analysis --- p.63 / Chapter 7.7. --- Blend Curves --- p.65 / Chapter 7.7.1. --- Problem Definition --- p.65 / Chapter 7.7.2. --- Proposed Solution Overview --- p.66 / Chapter 7.7.3. --- Maintenance of Regular Vertex Valence along Blend Curve --- p.67 / Chapter 7.7.3.1. --- Pairing Up Blend Boundary Vertices --- p.70 / Chapter 7.7.4. --- Minimization of Distortion Caused by Extraordinary Vertices --- p.72 / Chapter 7.7.5. --- Blend Vertex Position Optimization Function --- p.74 / Chapter 7.7.5.1. --- Face Normal Expression --- p.74 / Chapter 7.7.5.2. --- Face Normal Difference Energy Function --- p.77 / Chapter 7.7.5.3. --- Midpoint Distance Energy Function --- p.78 / Chapter 7.7.5.4. --- Weighted Least Square Energy Minimization --- p.78 / Chapter 8. --- Implementation --- p.81 / Chapter 8.1. --- Data Structure --- p.81 / Chapter 8.2. --- User Interface --- p.82 / Chapter 9. --- Results --- p.83 / Chapter 9.1. --- Surface Generation --- p.83 / Chapter 9.2. --- Surface Blending --- p.86 / Chapter 9.2.1. --- Ideal Case --- p.86 / Chapter 9.2.2. --- Angle of Insertion --- p.87 / Chapter 9.2.3. --- Surface Feature Near Intersection --- p.88 / Chapter 9.2.4. --- Comparison --- p.89 / Chapter 9.2.5. --- Other Examples --- p.92 / Chapter 9.3. --- Overall Performance --- p.94 / Chapter 9.4. --- Limitations --- p.97 / Chapter 9.4.1. --- Limitation on Generated Shape --- p.97 / Chapter 9.4.2. --- Limitation on Input Surfaces --- p.98 / Chapter 10. --- Conclusion and Future Work --- p.99 / References --- p.100

Wu Yiu-Bun. / Thesis submitted in: September 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 122-123). / Abstracts in English and Chinese. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Previous Works --- p.2 / Chapter 2.1. --- Surface Patch Approach / Chapter 2.2. --- Triangular Facet Approach / Chapter Chapter 3. --- The Decomposition Algorithm --- p.7 / Chapter 3.1. --- Input to the Algorithm / Chapter 3.2. --- Overview of the Algorithm / Chapter 3.2.1. --- Voronoi Diagram Development / Chapter 3.2.2. --- Feature Point Determination / Chapter 3.2.3. --- Correspondence Establishment / Chapter 3.2.4. --- Surface Approximation / Chapter 3.3. --- Output of the Algorithm / Chapter Chapter 4. --- Voronoi Diagram Development --- p.16 / Chapter 4.1. --- Triangulation of the Parametric Space / Chapter 4.1.1. --- Degree of Triangulation / Chapter 4.2. --- Locating Bisectors / Chapter 4.2.1. --- Bisector Centroids / Chapter 4.2.2. --- Sub-triangulation / Chapter 4.3. --- Finalizing Bisectors / Chapter Chapter 5. --- Feature Point Determination --- p.31 / Chapter 5.1. --- Definition of Feature Points / Chapter 5.1.1. --- Continuous Sharp Turns / Chapter 5.1.2. --- Discrete Sharp Turns / Chapter 5.2. --- Parametric Coordinates of Feature Points / Chapter Chapter 6. --- Vertices Correspondence Attachment --- p.42 / Chapter 6.1. --- Validity of Correspondences / Chapter 6.2. --- Shape Normalization / Chapter 6.2.1. --- Normalization with Relative Position / Chapter 6.3. --- Ranking Process / Chapter 6.3.1. --- Forward and Backward Attachment / Chapter 6.3.2. --- Singly Linked Bisector Vertices / Chapter Chapter 7. --- Surface Fitting --- p.58 / Chapter 7.1. --- Parametric Patches / Chapter 7.1.1. --- Definition of Parametric Patch Region / Chapter 7.1.2. --- Local Parametric Coordinate System / Chapter 7.2. --- Parametric Grids / Chapter 7.2.1. --- Sample Points on the Patch Boundary / Chapter 7.2.2. --- Grid Generation / Chapter 7.3. --- Surface Patches Construction / Chapter 7.3.1. --- Knot Vectors / Chapter 7.3.2. --- Control Vertices / Chapter Chapter 8. --- Worked Example --- p.71 / Chapter 8.1. --- Example 1: Deformed Plane 1 / Chapter 8.2. --- Example 2: Deformed Plane 2 / Chapter 8.3. --- Example 3: Sphere / Chapter 8.4. --- Example 4: Hemisphere 1 / Chapter 8.5. --- Example 5: Hemisphere 2 / Chapter 8.6. --- Example 6: Shoe / Chapter 8.7. --- Example 7: Shark Main Body / Chapter 8.8. --- Example 8: Mask 1 / Chapter 8.9. --- Example 9: Mask 2 / Chapter 8.10. --- Example 10: Toy Car / Chapter Chapter 9. --- Result and Analysis --- p.101 / Chapter 9.1. --- Continuity between Patches / Chapter 9.2. --- Special Cases --- p.102 / Chapter 9.2.1. --- Degenerated Patch / Chapter 9.2.2. --- S-Shaped Feature / Chapter 9.3. --- Comparison --- p.105 / Chapter 9.3.1. --- Example 1: Deformed Plane 1 / Chapter 9.3.2. --- Example 2: Deformed Plane 2 / Chapter 9.3.3. --- Example 3: Sphere / Chapter 9.3.4. --- Example 4: Hemisphere 1 / Chapter 9.3.5. --- Example 5: Hemisphere 2 / Chapter 9.3.6. --- Example 6: Shoe / Chapter 9.3.7. --- Example 7: Shark Main Body / Chapter 9.3.8. --- Example 8: Mask 1 / Chapter 9.3.9. --- Example 9: Mask 2 / Chapter 9.3.10. --- Example 10: Toy Car / Chapter Chapter 10. --- Conclusion --- p.119 / References --- p.122