Dissertations / Theses on the topic 'Local curvature'
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Friday, Brian Matthew. "VANISHING LOCAL SCALAR INVARIANTS ON GENERALIZED PLANE WAVE MANIFOLDS." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/884.
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Characterizing a manifold up to isometry is a challenging task. A manifold is a topological space. One may equip a manifold with a metric, and generally speaking, this metric determines how the manifold “looks". An example of this would be the unit sphere in R3. While we typically envision the standard metric on this sphere to give it its familiar shape, one could define a different metric on this set of points, distorting distances within this set to make it seem perhaps more ellipsoidal, something not isometric to the standard round sphere. In an effort to distinguish manifolds up to isometry, we wish to compute meaningful invariants. For example, the Riemann curvature tensor and its surrogates are examples of invariants one could construct. Since these objects are generally too complicated to compare and are not real valued, we construct scalar invariants from these objects instead. This thesis will explore these invariants and exhibit a special family of manifolds that are not flat on which all of these invariants vanish.
We will go on to properly define, and gives examples of, manifolds, metrics, tangent vector fields, and connections. We will show how to compute the Christoffel symbols that define the Levi-Civita connection, how to compute curvature, and how to raise and lower indices so that we can produce scalar invariants. In order to construct the curvature operator and curvature tensor, we use the miracle of pseudo-Riemannian geometry, i.e., the Levi-Civita connection, the unique torsion free and metric compatible connection on a manifold. Finally, we examine Generalized Plane Wave Manifolds, and show that all scalar invariants of Weyl type on these manifolds vanish, despite the fact that many of these manifolds are not flat.
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Scholtes, Sebastian [Verfasser]. "Geometric curvature energies : from local to global ; from discrete to smooth / Sebastian Scholtes." Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2014. http://d-nb.info/1066812713/34.
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Razive, Mohammad Nahid Islam. "Evaluation of linear segment length and local curvature radius along airfoil leading and trailing edges." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/42027.
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Airfoil is the basic profile geometry of impeller and turbine blades. The operational efficiency of these blades is governed by stringent tolerance specifications on the airfoils. The specified tolerances are commonly evaluated from discrete coordinate data collected in sections by a touch-probe coordinate measuring machine (CMM). These measurement data are subject to inspection inaccuracies associated with CMM measurement operation. Apart from well-known inspection parameters like profile tolerance, profile thickness and edge radius, the leading edge (LE) and trailing edge (TE) are specified with a unique set of geometric parameters like the maximum linear segment length restriction and the minimum curvature radius restriction. This thesis focuses on evaluating these two localized geometric restrictions along the leading edge and trailing edge of an airfoil.
This thesis first presents a robust algorithm to identify the longest linear segment. The main feature of the proposed algorithm is the explicit consideration of measurement uncertainty. The algorithm starts by detecting relatively small linear segments and then merges these segments to determine the longest feasible linear segment under given measurement uncertainty. The effect of measurement uncertainty and data point resolution on the performance of the presented algorithm is demonstrated through case studies.
Once the linear segments are identified and excluded, the remaining data points only belong to the non-linear segments. As minimum radius can occur at any location, curvature radius at each point along the non-linear segments is evaluated. Curvature radius at a specific point can only be estimated from its neighborhood. The chosen neighborhood size needs to be balanced between capturing local curvature attribute and effectively considering the effect of measurement uncertainty. An algorithm is thus proposed to evaluate radius via a rolling scheme of five consecutive data points in order to retrieve the local curvature information of the mid-point. A statistical approach is employed where all feasible radii are considered in order to reliably estimate the desired radius. Biarc construction is used as a tool to calculate radius. Compared with existing radius estimation methods, the proposed method has demonstrated to yield better accuracy with varying measurement uncertainty and data point resolution.
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Xu, Xun [Verfasser]. "Stem Cell Instruction via Appropriate Geometry and Local Curvature of Microstructured Polymeric Substrates / Xun Xu." Berlin : Freie Universität Berlin, 2019. http://d-nb.info/1182314481/34.
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Bustamante, Juan Pablo Mamani. "Influência local com procura \"forward\" em modelos de regressão linear." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/104/104131/tde-19012017-112532/.
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A identificação de observações influentes e/ou aberrantes de um conjunto de dados é conhecida como uma parte das análises de diagnóstico. Esta técnica de diagnóstico têm como uma das finalidades verificar a robustez de um modelo estatístico, pois a não identificação dos dados influentes pode afetar a análise ou obter resultados incorretos. As metodologias comumente utilizadas para o diagnóstico de observações influentes em modelos de regressão são métodos de influência global (Belsey et al., 1980). Cook (1986) introduziu um método geral para avaliar a influência local de pequenas perturbações no modelo estatístico ou nos dados, usando diferentes tipos de perturbações. Como complemento às técnicas de detecção de observações discrepantes, é proposto o método procura \\forward\", por Atkinson e Riani (2000), que é uma metodologia para detectar observações atípicas mascaradas. Neste trabalho, propomos o uso da influência local com procura \"forward\" na obtenção de observações mascaradas influentes considerando modelos de regressão linear.The identification of influential and/or atypical observations in a data set is known as a part of the diagnostic analysis. One of the purposes of the diagnostic analysis is to verify the robustness of a statistical model, as the non-identification of influential observations can affect the analysis or may cause the obtainment of incorrect results. The most commonly used methodology for the diagnostic of influential observations in regression models are the global influence (Belsey et al., 1980). Cook (1986) introduced a general method to evaluate the local influence of small perturbations in the statistical model or in the data set using different perturbation schemes. As a complement to the techniques of detection atypical observations, it is proposed the forward search procedure by Atkinson e Riani (2000), which is a methodology to detect the masked atypical observations in a data set. In this work we propose the use of the local influence approach together with the forward search to obtain the masked influential observations in linear regression models.
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Wells-Day, Benjamin Michael. "Structure of singular sets local to cylindrical singularities for stationary harmonic maps and mean curvature flows." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/290409.
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In this paper we prove structure results for the singular sets of stationary harmonic maps and mean curvature flows local to particular singularities. The original work is contained in Chapter 5 and Chapter 8. Chapters 1-5 are concerned with energy minimising maps and stationary harmonic maps. Chapters 6-8 are concerned with mean curvature flows and Brakke flows. In the case of stationary harmonic maps we consider a singularity at which the spine dimension is maximal, and such that the weak tangent map is homotopically non-trivial, and has minimal density amongst singularities of maximal spine dimen- sion. Local to such a singularity we show the singular set is a bi-Hölder continuous homeomorphism of the unit disk of dimension equal to the maximal spine dimension. A weak tangent map is translation invariant along a subspace, and invariant under dilations, so it completely defined by its values on a sphere. Such a map is said to be homotopically non-trivial if the mapping of a sphere into some target manifold cannot be deformed by a homotopy to a constant map. For an n-dimensional mean curvature flow we consider a singularity at which we can find a shrinking cylinder as a tangent flow, that collapses on an (n−1)-dimensional plane. Local to such a singularity we show that all singularities have such a cylindrical tangent, or else have lower Gaussian density than that of the shrinking cylinder. The subset of cylindrical singularities can be shown to be contained in a finite union of parabolic (n − 1)-dimensional Lipschitz submanifolds. In the case that the mean curvature flow arises from elliptic regularisation we can show that all singularities local to a cylindrical singularity with (n − 1)-dimensional spine are either cylindrical singularities with (n − 1)-dimensional spine, or contained in a parabolic Hausdorff (n − 2)-dimensional set.
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Zhang, Zichen. "Local gradient estimate for porous medium and fast diffusion equations by Martingale method." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:551f79f8-b309-4a1f-8afa-c7dc433dad82.
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This thesis focuses on a certain type of nonlinear parabolic partial differential equations, i.e. PME and FDE. Chapter 1 consists of a survey on results related to PME and FDE, and a short review on some works about deriving gradient estimates in probabilistic ways. In Chapter 2 we estimate gradient on space variables of solutions to the heat equation on Euclidean space. The main idea is to construct two semimartingales by letting the solution and its gradient running backward on the path space of a diffusion process. Estimates derived from decompositions of those two semimartingales are then combined to give rise to an upper bound on gradient that only involves the maximum of the initial data and time variable. In particular, it is independent of the dimension. In Chapter 3 we carry the idea in Chapter 2 onto the study of positive solutions to PME or FDE, and obtained a similar type of bound on |∇u| for local solutions to PME or FDE on Euclidean space. In existing literature there have always been constraints on m. By considering a more general form of transformation on u and introducing a family of equivalent measures on path space, we add more flexibility to our method. Thus our result is valid for a larger range of m. For global solutions, when m violates our constraint, we need two-sided bound on u to control |∇u|. In Chapter 4 we utilize maximum principle to derive Li-Yau type gradient estimate for PME on a compact Riemannian manifold with Ricci curvature bounded from below. Our result is able to yield a Harnack inequality possessing the right order in time variable when the lower bound of Ricci curvature is negative.
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Shiping, Liu. "Synthetic notions of curvature and applications in graph theory." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-102197.
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The interaction between the study of geometric and analytic aspects of Riemannian manifolds and that of graphs is a very amazing subject. The study of synthetic curvature notions on graphs adds new contributions to this topic. In this thesis, we mainly study two kinds of synthetic curvature notions: the Ollivier-Ricci cuvature on locally finite graphs and the combinatorial curvature on infinite semiplanar graphs.
In the first part, we study the Ollivier-Ricci curvature. As known in Riemannian geometry, a lower Ricci curvature bound prevents geodesics from diverging too fast on average. We translate this Riemannian idea into a combinatorial setting using the Olliver-Ricci curvature notion. Note that on a graph, the analogue of geodesics starting in different directions, but eventually approaching each other again, would be a triangle. We derive lower and upper Ollivier-Ricci curvature bounds on graphs in terms of number of triangles, which is sharp for instance for complete graphs. We then describe the relation between Ollivier-Ricci curvature and the local clustering coefficient, which is an important concept in network analysis introduced by Watts-Strogatz.
Furthermore, positive lower boundedness of Ollivier-Ricci curvature for neighboring vertices imply the existence of at least one triangle. It turns out that the existence of triangles can also improve Lin-Yau\'s curvature dimension inequality on graphs and then produce an implication from Ollivier-Ricci curvature lower boundedness to the curvature dimension inequality.
The existence of triangles prevents a graph from being bipartite. A finite graph is bipartite if and only if its largest eigenvalue equals 2. Therefore it is natural that Ollivier-Ricci curvature is closely related to the largest eigenvalue estimates. We combine Ollivier-Ricci curvature notion with the neighborhood graph method developed by Bauer-Jost to study the spectrum estimates of a finite graph. We can always obtain nontrivial estimates on a non-bipartite graph even if its curvature is nonpositive. This answers one of Ollivier\'s open problem in the finite graph setting.
In the second part of this thesis, we study systematically infinite semiplanar graphs with nonnegative combinatorial curvature. Unlike the previous Gauss-Bonnet formula approach, we explore an Alexandrov approach based on the observation that the nonnegative combinatorial curvature on a semiplanar graph is equivalent to nonnegative Alexandrov curvature on the surface obtained by replacing each face by a regular polygon of side length one with the same facial degree and gluing the polygons along common edges.
Applying Cheeger-Gromoll splitting theorem on the surface, we give a metric classification of infinite semiplanar graphs with nonnegative curvature. We also construct the graphs embedded into the projective plane minus one point. Those constructions answer a question proposed by Chen.
We further prove the volume doubling property and Poincare inequality which make the running of Nash-Moser iteration possible. We in particular explore the volume growth behavior on Archimedean tilings on a plane and prove that they satisfy a weak version of relative volume comparison with constant 1.
With the above two basic inequalities in hand, we study the geometric function theory of infinite semiplanar graphs with nonnegative curvature. We obtain the Liouville type theorem for positive harmonic functions, the parabolicity. We also prove a dimension estimate for polynomial growth harmonic functions, which is an extension of the solution of Colding-Minicozzi of a conjecture of Yau in Riemannian geometry.
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Santos, Makson Sales. "Métricas com Q-curvatura constante via um fluxo não local e um princípio do máximo para o operador de Paneitz." Universidade Federal de Sergipe, 2015. https://ri.ufs.br/handle/riufs/5804.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESNão consta
O objetivo desta dissertação é expor com detalhes o resultado de Gursky-Malchiodi. Dada uma variedade Riemanniana (M,g) de dimensão n>4 com curvatura escalar não negativa e Q-curvatura semipositiva, existe uma métrica conforme a g com Q-curvatura constante positiva. Com estas hipóteses mostra-se um princípio do máximo forte para o operador de Paneitz, que é um operador diferencial parcial não linear de quarta ordem. A partir daí define-se um fluxo não local e, utilizando funções testes, modificamos conformemente a métrica inicial tal que o fluxo converge sequencialmente para uma métrica conforme de Q-curvatura constante positiva e curvatura escalar positiva.
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Ferrari, Antonio Luiz. "Variabilidade e tendência da temperatura e pluviosidade nos municípios de Pirassununga, Rio Claro, São Carlos e São Simão (SP): estudo sobre mudança climática de curto prazo em escala local." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/18/18139/tde-23112012-133929/.
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O objetivo desta pesquisa é estudar a variabilidade e tendência dos elementos climáticos pluviosidade e temperatura, em quatro localidades do estado de São Paulo - Pirassununga, Rio Claro, São Carlos e São Simão -, que constituem parte da área de treinamento de voo da Academia da Força Aérea, para confirmar a hipótese de que essas alterações indicam indícios de mudanças climáticas de curto prazo, em escala local e que essas mudanças poderão afetar, no futuro, o planejamento das missões de treinamento de voo na AFA. Para isso foram utilizados, primeiramente, os dados mensais e anuais de temperatura e pluviosidade de uma série temporal de 34 anos (1976 a 2009) e, depois, de uma série mais curta, de 16 anos (1994 a 2009). Para a análise das condições climáticas de São Carlos, Rio Claro e São Simão foram utilizados os dados mensais e anuais de temperatura e pluviosidade de uma série temporal de 16 anos (1994 a 2009). Para efeito da análise estatística da variabilidade climática da temperatura e pluviosidade dentro da série temporal escolhida, foram aplicados os cálculos da média aritmética, do desvio padrão, do coeficiente de variação e da amplitude térmica. Para a análise da tendência, aplicou-se a técnica da regressão linear e os testes estatísticos não-paramétricos, conhecidos como testes de Mann-Kendall e Curvatura de Sen. Os resultados da pesquisa mostraram que a variabilidade mensal e anual da pluviosidade para as quatro localidade é semelhante e bem acentuada e que não existem tendências significativas para essa variável nas quatro localidades. Para as temperaturas em Pirassununga, a temperatura média apresentou grande variabilidade mensal. Para Rio Claro, São Carlos e São Simão a variabilidade anual das temperaturas foi baixa, próxima da estabilidade, com exceção da temperatura mínima, que apresentou grande variabilidade para as três localidades. Quanto à tendência para Pirassununga, apenas a temperatura média apresentou tendência decrescente e significativa. Os resultados obtidos para as temperaturas de Rio Claro, São Carlos e São Simão indicam tendências crescentes e/ou decrescentes, mas todas insignificantes.The aim of this research is to study the variability and tendency in climatic elements, rainfall and temperature in four cities in the state of São Paulo: Pirassununga, Rio Claro, São Carlos and São Simão which are part of the flight training area of the Air Force Academy, in order to confirm the hypothesis that those alterations indicate signs of climatic variations in the short term, according to the local parameters and that those variations may change the schedule of the flight training missions at AFA. Monthly and annual data regarding to temperature and rainfall, recorded during a period of 34 years (1976-2009) were firstly considered during the study, followed by a shorter period of 16 years (1994-2009). In order to analyze the climatic conditions in São Carlos, Rio Claro and São Simão, monthly and annual data about temperature and rainfall collected during a period of 16 years (1994-2009) were considered. For purposes of statistical analysis of the climatic variability of temperature and rainfall within the chosen period of time, calculation of the arithmetic mean, standard deviation, coefficient of variation and temperature range were applied. In order to analyze such tendency, the linear regression model and non-parametric statistical tests, known as Mann-Kendall and Sen Curvature were applied. The results of the research showed that the monthly and annual variability of the rainfall in the four cities is similar and well marked and that there are not significant tendencies in that variable in the four cities. Relating to temperature in Pirassununga, the average temperature showed large monthly variability. In Rio Claro, São Carlos and São Simão, the annual temperature variability was low, tending to be stable, except for the minimum temperature which showed a large variability. Concerning to Pirassununga, just the average temperature tended to be decreasing and significant. The results obtained for the temperatures in Rio Claro, São Carlos and São Simão tended to be increasing and/or decreasing, but such tendencies were irrelevant.
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MARINELLI, GIUSEPPE. "Road geometry identification with mobile mapping techniques." Doctoral thesis, Politecnico di Torino, 2015. http://hdl.handle.net/11583/2606568.
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Durante il mio dottorato mi sono occupato di Tecniche e Tecnologie innovative per la ricostruzione della geometria dei tracciati stradali esistenti, quali ad esempio Mobile Mapping, analisi immagini e dati GIS; a fronte degli elevatissimi costi oggi richiesti per l’utilizzo di veicoli strumentati già reperibili in commercio per il raggiungimento di tali scopi, il valore aggiunto del lavoro di dottorato riguarda l’uso di strumenti a basso costo che comportano un rilevante lavoro di analisi, trattamento e correzione del dato che risente in maniera decisiva della medio/bassa qualità della strumentazione in uso.
L’obiettivo della ricerca è consistito nella realizzazione di un algoritmo di riconoscimento (in ambiente MATLAB) che sia in grado di restituire la geometria as-built di una strada esistente. Parte del lavoro è stata svolta nell’analisi e nell’estrazione delle curvature locali con approcci differenti (successive circonferenze locali, funzioni polinomiali di fitting locale di vario grado e con ampiezza di analisi variabile), nonché sullo studio degli angoli di deviazione locali.
Usando questi parametri, nel resto del lavoro, si è prima ricercata una metodologia d’identificazione dei diversi elementi che compongono la geometria stradale, e poi si è lavorato su procedure di fitting con svariate tecniche (minimi quadrati, metodi robusti e altri algoritmi) cercando di estrarre informazioni di carattere geometrico, quali raggi di curvatura e relativi centri, lunghezza e orientamento dei rettifili, fattori di scala delle curve di transizione.
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Huang, Conglin. "3D RECONSTRUCTION USING MULTI-VIEW IMAGING SYSTEM." UKnowledge, 2009. http://uknowledge.uky.edu/gradschool_theses/600.
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This thesis presents a new system that reconstructs the 3D representation of dental casts. To maintain the integrity of the 3D representation, a standard model is built to cover the blind spots that the camera cannot reach. The standard model is obtained by scanning a real human mouth model with a laser scanner. Then the model is simplified by an algorithm which is based on iterative contraction of vertex pairs. The simplified standard model uses a local parametrization method to obtain the curvature information. The system uses a digital camera and a square tube mirror in front of the camera to capture multi-view images. The mirror is made of stainless steel in order to avoid double reflections. The reflected areas of the image are considered as images taken by the virtual cameras. Only one camera calibration is needed since the virtual cameras have the same intrinsic parameters as the real camera. Depth is computed by a simple and accurate geometry based method once the corresponding points are identified. Correspondences are selected using a feature point based stereo matching process, including fast normalized cross-correlation and simulated annealing.
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Russo, Cibele Maria. ""Análise de um modelo de regressão com erros nas variáveis multivariado com intercepto nulo"." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-01082006-214556/.
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Para analisar características de interesse a respeito de um conjunto de dados reais da área de Odontologia apresentado em Hadgu & Koch (1999), ajustaremos um modelo de regressão linear multivariado com erros nas variáveis com intercepto nulo. Este conjunto de dados é caracterizado por medições de placa bacteriana em três grupos de voluntários, antes e após utilizar dois líquidos de bochecho experimentais e um líquido de bochecho controle, com medições (sujeitas a erros de medição) no início do estudo, após três e seis meses de utilização dos líquidos. Neste caso, uma possível estrutura de dependência entre as medições feitas em um mesmo indivíduo deve ser incorporada ao modelo e, além disto, temos duas variáveis resposta para cada indivíduo. Após a apresentação do modelo estatístico, iremos obter estimativas de máxima verossimilhança dos parâmetros utilizando o algoritmo iterativo EM e testaremos as hipóteses de interesse utilizando testes assintóticos de Wald, razão de verossimilhanças e score. Como neste caso não existe um teste ótimo, faremos um estudo de simulação para verificar o comportamento das três estatísticas de teste em relação a diferentes tamanhos amostrais e diferentes valores de parâmetros. Finalmente, faremos um estudo de diagnóstico buscando identificar possíveis pontos influentes no modelo, considerando o enfoque de influência local proposto por Cook (1986) e a medida de curvatura normal conformal desenvolvida por Poon & Poon (1999).To analyze some characteristics of interest in a real odontological data set presented in Hadgu & Koch (1999), we propose the use of a multivariate null intercept errors-in-variables regression model. This data set is composed by measurements of dental plaque index (with measurement errors), which were measured in volunteers who were randomized to two experimental mouth rinses (A and B) or a control mouth rinse. The measurements were taken in each individual, before and after the use of the respective mouth rinses, in the beginning of the study, after three months from the baseline and after six months from the baseline. In this case, a possible structure of dependency between the measurements taken within the same individual must be incorporated in the model. After presenting the statistical model, we obtain the maximum likelihood estimates of the parameters using the numerical algorithm EM, and we test the hypotheses of interest considering asymptotic tests (Wald, likelihood ratio and score). Also, a simulation study to verify the behavior of these three test statistics is presented, considering diferent sample sizes and diferent values for the parameters. Finally, we make a diagnostic study to identify possible influential observations in the model, considering the local influence approach proposed by Cook (1986) and the conformal normal curvature proposed by Poon & Poon (1999).
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Hu, Min. "Local variation in bending stiffness in structural timber of Norway spruce : for the purpose of strength grading." Licentiate thesis, Linnéuniversitetet, Institutionen för byggteknik (BY), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-38119.
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Most strength grading machines on the European market use an averagemodulus of elasticity (MOE), estimated on a relatively large distance along awood member, as the indicating property (IP) to bending strength. Theaccuracy of such grading machines in terms of coefficient of determination israther low at R2 ≈ 0.5. This research is motivated by a desire to increase theaccuracy of the strength grading in the industry today. The aim of the presentstudy is to contribute knowledge of local variation in bending stiffness/MOEwith high resolution and thus locate weak sections due to stiffness reducingfeatures (the most important is knots) for structural timber.The present study introduces three methods that involve structural dynamics,classical beam theory and optical measurement to assess local wood stiffness.Specifically: The dynamic method, in which a wood member is treated as an ordinaryphysical structure and the local stiffness is studied by exploring itsdynamic properties. In Method II, a bending MOE profile is established based on local fibre angle information. The local fibre orientation is detected through highresolution laser scanning based on the tracheid effect. For Method III, a bending MOE profile is established using surfacestrain information under four-point bending. A high resolution strainfield is obtained using the digital image correlation (DIC) technique. From the present study, the two latter methods are more favourable inevaluating the local stiffness within a piece of structural timber. Moreover, thestudy reveals that the established bending MOE profiles using the two lattermethods, i.e. based on information of the local fibre angle and surface strain,agree reasonably well. However, for some patterns of knot clusters, the localbending MOE, calculated on the basis of fibre angles, is significantly higherthan the local bending MOE estimated on the basis of surface strain.De flesta av de utrustningar för hållfasthetssortering som utnyttjas på deneuropeiska marknaden använder ett medelvärde på elasticitetsmodulen(MOE), beräknat på en relativt stor längd av en sågad planka, som indikativparameter (IP). Sådan hållfasthetssortering ger en noggrannhet i termer avförklaringsgrad på R2 ≈ 0.5, vilket är ganska lågt. Arbetet i denna studiemotiveras av en önskan att öka noggrannheten i hållfasthetssorteringen. Syftetmed denna studie är att bidra med kunskap om lokala variationer iböjstyvhet/MOE med hög upplösning och att lokalisera veka snitt (där kvistarär den viktigaste försvagande faktorn) för konstruktionsvirke.Den aktuella studien introducerar tre metoder som omfattar strukturdynamik,klassisk balkteori och optisk mätning vid bedömningen av lokal styvhet imaterialet. Specifikt: Metod I, där den lokala böjstyvheten studerades genom de dynamiskaegenskaperna såsom egenfrekvens och modform. Metod II, där en MOE profil beräknas på basis av information om lokalafibervinklar på ett virkesstyckes ytor. Den lokala fiberorienteringen mätsmed högupplöst laserskanning baserad på den så kallade trakeideffekten. Metod III, där en MOE-profil fastställdes med hjälp avtöjningsinformation för en hel flatsida av en planka belastad med konstantböjmoment. Det högupplösta töjningsfältet erhölls med hjälp av teknikför Digital Image Correlation (DIC). Studien visar att de två sistnämnda metoderna är mycket lämpade för attutvärdera den lokala styvheten i ett virkesstycke. Dessutom visar studien att deMOE-profiler som togs fram med hjälp av de två sistnämnda metoderna,vilka baseras på information om lokala fibervinklar och töjningsfältet på ytan,stämde överens för större delen av virkesstycket. För visa kvistgrupper kan dock den lokala böjstyvheten högre med metoden baserad på fibervinklar.
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Freitas, Pires Juliana. "Influência local através da curvatura normal em modelos multiníveis." Universidade Federal de Pernambuco, 2009. https://repositorio.ufpe.br/handle/123456789/6079.
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Previous issue date: 2009Conselho Nacional de Desenvolvimento Científico e Tecnológico
Os modelos lineares hierárquicos foram desenvolvidos para análise de dados que possuem uma estrutura de grupo, ou seja, uma estrutura de hierarquia, por levarem em consideração a dependência dos dados existente dentro de cada nível hierárquico. As estimativas dos parâmetros dos modelos hierárquicos são apresentadas separando os efeitos fixos dos aleatórios. O modelo linear hierárquico com dois níveis é apresentado e ilustrado através de um exemplo, juntamente com a sua teoria de estimação e testes de hipóteses. Para avaliar este modelo com respeito a sensibilidade sob pequenas perturbações, uma técnica de influência local sob a curvatura normal foi desenvolvida. Os dados do SAEPE 2005 foram estudados sob este enfoque
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LOBATO, JÚNIOR Dorival. "Influência local em modelos de regressão." Universidade Federal de Campina Grande, 2005. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1109.
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DORIVAL LOBATO JÚNIOR - DISSERTAÇÃO PPGMAT 2005..pdf: 658187 bytes, checksum: 934af5bed920aceba4c0f48a5fbca2d6 (MD5)Made available in DSpace on 2018-07-05T20:12:22Z (GMT). No. of bitstreams: 1 DORIVAL LOBATO JÚNIOR - DISSERTAÇÃO PPGMAT 2005..pdf: 658187 bytes, checksum: 934af5bed920aceba4c0f48a5fbca2d6 (MD5) Previous issue date: 2005-08
Neste trabalho, estudamos a influência local em modelos de regressão.Este método foi proposto inicialmente por Cook (1986) e tem se mostrado como um poderoso instrumento da análise de diagnóstico. A proposta de Cook consiste em avaliar a curvatura normal de uma superfície, baseada na medida Likelihood Displacement, sob uma pequena peturbação no modelo. Em seguida apresentamos a abordagem de Billor e Loynes (1993), que aplicam uma medida Likelihood Displacement modificada, cuja primeira deriva da não se anula, exceto em casos triviais, com isso a inclinação máxima é usada como medida de influência local. No final, discutimos três aplicações onde utilizamos algumas técnicas gráficas de diagnóstico e as duas propostas de influência local aqui referidas.
In this work, we study the local influence in regression models, this method was offer first of all by Cook(1986) and have show how an important instrument of the diagnostics analysis. The Cook's approach consist in assessing the normal curvature of the geometric surface, using the measure Likelihood Displacement, under an minor perturbations of statistical model. After we present the approach of the Billor and Loynes (1993), that apply an measure Likelihood Displacement changes whose first derivative does not, except in trivial cases, vanish.Thus the maximum slop is using how measure of the local influuence. In finish, we present three apply where use any technic graphics of the diagnostics and the two proposed of the local influence here reported.
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De, Lorenzi Diego. "La rigidità della sfera." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18241/.
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La curvatura gaussiana K(p) di una superficie S dello spazio euclideo tridimensionale in un suo punto p misura di quanto la superficie si discosta dal proprio piano tangente in p e fornisce informazioni sul comportamento di S in un intorno di p. Quando K è costante su tutta la superficie, essa fornisce informazioni globali di notevole rilevanza. L'esempio più semplice di superficie a curvatura costante positiva è la sfera, ma non è l'unico esempio. Un famoso teorema di Liebmann ci dice che se S è una superficie regolare compatta e connessa con curvatura gaussiana K costante, allora S è una sfera. Questo risultato viene spesso citato come un risultato sulla rigidità della sfera. Questa tesi è dedicata allo studio di condizioni su una superficie regolare S che implicano che S è una sfera.
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Nguyen, Xuan Viet Nhan. "Structure métrique et géométrie des ensembles définissables dans des structures o-minimales." Thesis, Aix-Marseille, 2015. http://www.theses.fr/2015AIXM4742/document.
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L'objectif de la thèse est l'étude des propriétés géométriques des ensembles définissables dans les structures o-minimales et de ses applications. Il existe trois principaux résultats présentés dans cette thèse. Le premier est une preuve géométrique de l'existence de stratifications vérifiant les conditions (a) et (b) de Whitney d'ensembles définissables. Ce résultat fut d'abord prouvé par T. L. Loi en 1994 par une autre méthode. Le second est une preuve de l'existence de stratifications de Lipschitz (dans le sens de Mostowski) pour les ensembles définissables dans une structure o-minimale polynomialement bornée. Ceci est une généralisation de résultats de Parusin'ski en 1994 pour les ensembles sous-analytiques. Le troisième résultat est au sujet de la continuité des variations de géométrie intégrale appelées courbures de Lipschitz Killing locales, qui ont été introduites par A. Bernig et L. Broker en 2002. Nous prouvons que les courbures de Lipschitz Killing locales sont continues le long de strates de stratifications de Whitney d'ensembles définissable dans une structure o-minimale polynomialement bornée, et si les stratifications sont (w) régulières alors les courbures de Lipschitz Killing locales sont localement lipschitziennes le long des stratesThe thesis focus on study geometric properties of definable sets in o-minimal structures and its applications. There are three main results presented in this thesis. The first is a geometric proof of the existence of Whitney (a) and (b)-regular stratifications of definable sets. The result was initially proved by T. L. Loi in 1994 by using another method. The second is a proof of existence of Lipschitz stratifications (in the sense of Mostowski) of definable sets in a polynomially bounded o-minimal structure. This is a generalization of Parusinski's 1994 result for subanalytic sets. The third result is about the continuity of of variations of integral geometry called local Lipschitz Killing curvatures which were introduced by A. Bernig and L. Broker in 2002. We prove that Lipschitz Killing curvatures are continuous along strata of Whiney stratifications of definable sets in a polynomially bounded o-minimal structure. Moreover, if the stratifications are (w)-regular the Lipspchitz Killing curvatures are locally Lipschitz
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Melo, Fábio Silva. "Teoria de curvas para métricas não-euclidianas." reponame:Repositório Institucional da UNILA, 2016. http://dspace.unila.edu.br/123456789/560.
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Dissertação de Mestrado apresentada ao Instituto de Matemática, Estatística e Computação Científica, Unicamp, como requisito parcial para obtenção do título de Mestre em Matemática. 2010Submitted by Nilson Junior (nilson.junior@unila.edu.br) on 2016-07-08T20:28:03Z No. of bitstreams: 1 MeloFabioSilva_MP.pdf: 3864560 bytes, checksum: 704d21404c48a187914a0238b121d30e (MD5)
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A teoria local de curvas da Geometria Diferencial no plano e no espaço euclidiano é bem conhecida (vide referências como [4] e [13]). Este trabalho consiste de uma generalização desta teoria usando métricas arbitrárias. Tal generalização é feita substituindo a matriz identidade que define o produto interno usual por outra matriz quadrada, simétrica e positiva definida. Com este novo produto interno, são estudados conceitos como vetor tangente, vetor normal, vetor binormal, fórmulas de Frenet, curvatura e torção
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Kung, David T. "Local smoothing phenomena for operators failing the cinematic curvature condition." 2000. http://www.library.wisc.edu/databases/connect/dissertations.html.
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Lin, Ber Shiou. "A Local Geometric Constructive Method for Generating Curvature Continuous Shape Preserving Curves." 1993. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0009-0112200611361167.
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Shiping, Liu. "Synthetic notions of curvature and applications in graph theory." Doctoral thesis, 2012. https://ul.qucosa.de/id/qucosa%3A11816.
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The interaction between the study of geometric and analytic aspects of Riemannian manifolds and that of graphs is a very amazing subject. The study of synthetic curvature notions on graphs adds new contributions to this topic. In this thesis, we mainly study two kinds of synthetic curvature notions: the Ollivier-Ricci cuvature on locally finite graphs and the combinatorial curvature on infinite semiplanar graphs.
In the first part, we study the Ollivier-Ricci curvature. As known in Riemannian geometry, a lower Ricci curvature bound prevents geodesics from diverging too fast on average. We translate this Riemannian idea into a combinatorial setting using the Olliver-Ricci curvature notion. Note that on a graph, the analogue of geodesics starting in different directions, but eventually approaching each other again, would be a triangle. We derive lower and upper Ollivier-Ricci curvature bounds on graphs in terms of number of triangles, which is sharp for instance for complete graphs. We then describe the relation between Ollivier-Ricci curvature and the local clustering coefficient, which is an important concept in network analysis introduced by Watts-Strogatz.
Furthermore, positive lower boundedness of Ollivier-Ricci curvature for neighboring vertices imply the existence of at least one triangle. It turns out that the existence of triangles can also improve Lin-Yau\''s curvature dimension inequality on graphs and then produce an implication from Ollivier-Ricci curvature lower boundedness to the curvature dimension inequality.
The existence of triangles prevents a graph from being bipartite. A finite graph is bipartite if and only if its largest eigenvalue equals 2. Therefore it is natural that Ollivier-Ricci curvature is closely related to the largest eigenvalue estimates. We combine Ollivier-Ricci curvature notion with the neighborhood graph method developed by Bauer-Jost to study the spectrum estimates of a finite graph. We can always obtain nontrivial estimates on a non-bipartite graph even if its curvature is nonpositive. This answers one of Ollivier\''s open problem in the finite graph setting.
In the second part of this thesis, we study systematically infinite semiplanar graphs with nonnegative combinatorial curvature. Unlike the previous Gauss-Bonnet formula approach, we explore an Alexandrov approach based on the observation that the nonnegative combinatorial curvature on a semiplanar graph is equivalent to nonnegative Alexandrov curvature on the surface obtained by replacing each face by a regular polygon of side length one with the same facial degree and gluing the polygons along common edges.
Applying Cheeger-Gromoll splitting theorem on the surface, we give a metric classification of infinite semiplanar graphs with nonnegative curvature. We also construct the graphs embedded into the projective plane minus one point. Those constructions answer a question proposed by Chen.
We further prove the volume doubling property and Poincare inequality which make the running of Nash-Moser iteration possible. We in particular explore the volume growth behavior on Archimedean tilings on a plane and prove that they satisfy a weak version of relative volume comparison with constant 1.
With the above two basic inequalities in hand, we study the geometric function theory of infinite semiplanar graphs with nonnegative curvature. We obtain the Liouville type theorem for positive harmonic functions, the parabolicity. We also prove a dimension estimate for polynomial growth harmonic functions, which is an extension of the solution of Colding-Minicozzi of a conjecture of Yau in Riemannian geometry.
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Fan, Yuan-Jia, and 范原嘉. "Structures of octahedral fullerenes and the application of discrete local curvature and continuum elastic theory to the study of fullerene''s stability." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/51728487455511815157.
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博士國立臺灣大學
化學研究所
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There are two chapters in this dissertation. In Chapter 1, a modified elastic theory for $ ext{sp}^2$ pure carbon molecules has been proposed. The theory includes high order term in curvature, the bond stretching term and the tight-binding correction. The validity of this model has been examined by various graphitic-like molecules with different topology. The model can be applied on DFT (Density Functional Theory) optimized geometry or AIREBO (Adaptive Intermolecular Reactive Empirical Bond-Order) optimized geometry. Finally the most stable fullerene was found by constructing the candidates via the new model first and then verifying by VASP. In Chapter 2, a construction scheme of octahedral fullerenes has been built. After investigating the topological constraint, a fundamental polygon compatible with the octahedral symmetry was found. The fundamental polygon can be specified by four integers called index. However, the octahedral fullerene does not specified by a unique index and there is redundancy in the indexes which we called index symmetries. Besides symmetries corresponded to the geometrical symmetries of the graphene, there are symmetries originated from different dissection ways of the octahedral fullerenes. Finally all the possible orbits are clarified and an algorithm to eliminate these redundancy has been suggested.