The key of presented diploma thesis is to find a way to take shape of roads into account when performing network analysis. Methods of mathematical representation of shape of lines are discussed; the curvature is chose for later use. Then the relation between road's curvature and speed is discussed - the model for setting the speed is suggested. Important part of the thesis is focused on implementation in GIS. Designed model is implemented by Python in the ArcGIS for Desktop. Due to testing on specific examples, it was confirmed, that the taking the shape characteristics into account provides high précising of network analysis.

We adress an obstacle problem for (graphical) mean curvature flow with Dirichlet boundary conditions. Using (an adapted form of) the standard implicit time-discretization scheme we derive the existence of distributional solutions satisfying an appropriate variational inequality. Uniqueness of this flow and asymptotic convergence towards the stationary solution is proven.

A teoria das transforma»ções de superfícies de curvatura constante começou, no fim do século XIX, com o trabalho [3] de A.V. Bäcklund e, em seguida, recebeu importantes contribuições por parte de diversos geômetras, entre eles, L. Bianchi e C. Guichard (veja, por exemplo, [5, 6, 7, 17]). Nessa dissertação apresentamos alguns dos mais importantes resultados desse tópico da geometria diferencial que estão relacionados às superfícies de curvatura média (ou gaussiana não nula) constante. Tais superfícies estão associadas a soluções de equações diferenciais parciais de segunda ordem e não lineares. A interpretação analítica da teoria das transformações de superfícies de curvatura constante nos capacita obter soluções dessas equações diferenciais parciais a partir de uma outra dada, mediante integração de um sistema de equações diferenciais, chamado transformação de Bäcklund. Então, os teoremas de permutabilidade fornecem uma \"fórmula de superposição\" para a construção algébrica de novas soluções / The theory on transformations of surfaces with constant curvature begins, in the late nineteen century, with the article [3] of A.V. Bäcklund and, after, received important contributions from various geometricians, among others, L. Bianchi and C. Guichard (see, for example, [5, 6, 7, 17]). In this dissertation we outline some of the most important results on the theory of surfaces of constant mean (or gaussian) curvature. Such surfaces are associated to the solutions of nonlinear partial differential equations of second order. The analytic interpretation of the theory on transformations of constant curvature surfaces provides a method of obtaining, from a given solution of these partial differential equations, a new solution of the same equation, by integrating a system of differential equations, called Bäcklund transformation. Then, the permutability theorems give a \"superposition formula\" to construct, algebraically, new solutions

O objetivo deste trabalho e desenvolver um instrumento computadorizado para análise da superfície anterior da córnea humana, gerando para isto, um mapa topográfico bidimensional em código de cores. Utilizando a córnea como um espelho esférico convexo, projeta-se anéis luminosos sobre sua superfície e aquisiciona-se com uma câmera a imagem por ela refletida. Esta imagem e digitalizada e armazenada em um microcomputador para posterior processamento. Através de técnicas de computação gráfica e processamento de imagens digitais, extrai-se da imagem as informações necessárias para construção da topografia desejada. Por fim, a topografia e apresentada em forma de mapas coloridos, sendo cada cor associada a uma determinada dioptria, transmitindo ao médico oftalmologista uma noção exata da superfície da córnea do paciente em análise. / The main goal of this work is to develop a computerized instrument for the analysis of the anterior portion of the human cornea, which displays its result in topographic color maps. Approximating the cornea to a spherical convex mirror, and by projecting a known pattern over it, the reflected image is captured and stored. By means of computer graphics technology and image processing, the necessary information for mathematical calculations is extracted. The resulting maps are color-coded in accordance to the degree of power of each corneal region, that is, to the diopter value. The ophthalmologist can then make important diagnostics and surgery tactics from the analysis of these topographic maps.

Wo, Weifeng. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 99-102). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

by Fan Xuqian. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 99-100). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- The Theorem of Efimov --- p.7 / Chapter 2.1 --- The Idea of the Proof of the Efimov's Theorem --- p.8 / Chapter 2.2 --- Proof of the Efimov's Main Lemma --- p.12 / Chapter 2.3 --- Proof of Lemma 2.3 --- p.48 / Chapter 2.4 --- Proof of Lemma 2.4 --- p.52 / Chapter 3 --- Isometric Immersion into R3 of Complete Surfaces with Negative Curvature --- p.62 / Chapter 3.1 --- The Sketch of the Proof of Theorem 3.1 --- p.66 / Chapter 3.2 --- Proof of Lemma 3.4 --- p.75 / Chapter 3.3 --- Proof of Lemma 3.5 --- p.76 / Chapter 3.4 --- Proof of Lemma 3.6 --- p.86 / Chapter 3.5 --- Proof of Lemma 3.7 --- p.89 / Chapter 3.6 --- The Geometric Properties of the Immersion --- p.95

by Lei Ka Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 70-71). / Abstracts in English and Chinese. / Chapter 0 --- Introduction --- p.5 / Chapter 1 --- Dirichlet Problem at infinity --- p.9 / Chapter 1.1 --- The Geometric Boundary --- p.9 / Chapter 1.2 --- Dirichlet Problem --- p.15 / Chapter 2 --- The Martin Boundary --- p.29 / Chapter 2.1 --- The Martin Metric --- p.30 / Chapter 2.2 --- The Representation Formula --- p.31 / Chapter 2.3 --- Uniqueness of Representation --- p.36 / Chapter 3 --- The Geometric boundary and the Martin boundary --- p.42 / Chapter 3.1 --- Estimates for harmonic functions in cones --- p.42 / Chapter 3.2 --- A Harnack Inequality at Infinity --- p.49 / Chapter 3.3 --- The kernel function --- p.54 / Chapter 3.4 --- The Main Theorem --- p.55 / Chapter 4 --- Positive Harmonic Functions on Product of Manifolds --- p.61 / Chapter 4.1 --- Splitting Theorem --- p.61 / Chapter 4.2 --- Riemannian Halfspace and the parabolic Martin boundary --- p.62 / Chapter 4.3 --- Splitting of parabolic Martin kernels --- p.63 / Chapter 4.4 --- Proof of theorem 4.1 --- p.66 / Bibliography

by Ho Wing Kin. / Thesis submitted in: July 1997. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 89-92). / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- The Euler-Lagrange Equation for Capillary Surfaces --- p.6 / Chapter 1.2 --- The Capillary Tube --- p.12 / Chapter 2 --- Comparison Principles --- p.16 / Chapter 2.1 --- The General Comparison Principle --- p.16 / Chapter 2.2 --- Applications --- p.24 / Chapter 3 --- Existence Criteria --- p.30 / Chapter 3.1 --- Necessary Conditions --- p.31 / Chapter 3.2 --- Sufficient Conditions --- p.35 / Chapter 4 --- Uniqueness --- p.53 / Chapter 4.1 --- General Bounded Domains Case --- p.53 / Chapter 4.2 --- Infinite Strip Case --- p.56 / Chapter 5 --- Gradient Estimate of Surfaces of Constant Mean Curvature --- p.66 / Chapter 5.1 --- The Gradient Estimate --- p.67 / Chapter 5.2 --- Behavior as R→ 1 --- p.70 / Chapter 5.3 --- Existence of the Comparison Surfaces --- p.76 / Chapter 5.4 --- Ro is Best Possible --- p.82 / Appendix Mean Curvature --- p.85

O trabalho realizado consiste no desenvolvimento das equações pertinentes à teoria de cascas, implementação de programas de elementos finitos em Matlab e resolução de problemas de casca numéricos e analíticos. No desenvolvimento da teoria de cascas é evidenciada a aplicação da curvatura da estrutura no cálculo das forças e momentos resultantes para uma superfície de casca simplificada a uma estrutura localmente bidimensional. O problema de casca é resolvido analiticamente para um caso de curvatura simples e comparado com a resolução por elementos finitos em um programa desenvolvido pelo autor, em que a utilização da curvatura para o cálculo das forças e momentos resultantes é inserida na programação. A análise de elementos finitos é realizada para casos de casca com curvatura simples e dupla curvatura e de duas formas, sendo que a primeira utiliza elementos cujas normais médias são empregadas na montagem da matriz de rigidez, constituindo um elemento de casca e a segunda aplica normais a cada nó de cada elemento, tendo-se assim uma superfície facetada, com comportamento de placa em cada elemento. Os resultados obtidos mostram que o impacto da aplicação da curvatura em geral é pequeno nas regiões mais críticas para as forças e momentos resultantes, como na região de engaste. Porém, algumas regiões da casca apresentam grandes variações, e caso sejam de importância para o usuário, cabe uma análise mais detalhada em que o emprego da curvatura possa ser considerado. / This work presents the development of the shell theory equations, implementation of finite element programs in Matlab and the resolution of numerical and analytical shell problems. Along with the development of the shell theory, the application of the curvature of the structure in the calculation of stress and couple resultants for a shell structure simplified to a bidimensional problem become clear. The shell problem is solved analytically, by means of the application of the shell equations in a shell with simple curvature, and this solution is compared with the numerical solution using the finite element program implemented, considering the curvature of the structure for the stress and couple resultants. Finite element analysis is performed for the simple and double curvature cases of shells, and in two distinct ways, the first one considering averaged normals for neighbor elements, which produces shell elements, the second one using normals to each node of each element, which results in locally flat elements, behaving as plates. Results obtained show that the impact of the application of the curvature in the resultants is usually small in the most critical points, such as the crimp. However, some regions of the shell present huge variation, and further analysis is recommended, since the application of the curvature can be important.

by Guan-xin Li. / "January 1999." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (p. 223-225). / 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. / Abstracts in English and Chinese.