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Explorando a dualidade em geometria de distâncias; Exploring the duality on distance geometry

Germano Abud de Rezende
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 28/08/2014 PT
Relevância na Pesquisa
36.09%
A geometria de distâncias é o estudo da geometria baseado no conceito de distância. Ela é útil em várias aplicações, onde os dados de entrada consistem de um conjunto incompleto de distâncias, e a saída é um conjunto de pontos no espaço euclidiano, que realiza as distâncias dadas. No Problema de Geometria de Distâncias (DGP), é dado um inteiro K > 0 e um grafo simples, não direcionado, G = (V,E,d), cujas arestas são ponderadas por uma função não negativa d. Queremos determinar se existe uma função (realização) que leva os vértices de V em coordenadas no espaço euclidiano K-dimensional, satisfazendo todas as restrições de distâncias dadas por d. Um DGPk (com K fixado) está fortemente relacionado a um outro tipo de problema, que trata dos possíveis completamentos de uma certa matriz de distâncias euclidianas. Este último pode ser visto, em um certo sentido, como o “dual do primeiro problema”. Neste trabalho, exploramos essa dualidade com a finalidade de propor melhorias no método Branch-and-Prune aplicado a uma versão discreta do DGPk.; Distance Geometry is the study of geometry based on the concept of distance. It is useful in many applications where the input data consists of an incomplete set of distances...

Geometria de distâncias euclidianas e aplicações; Euclidean distance geometry and applications

Jorge Ferreira Alencar Lima
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 23/01/2015 PT
Relevância na Pesquisa
36.09%
Geometria de Distâncias Euclidianas (GDE) é o estudo da geometria euclidiana baseado no conceito de distância. É uma teoria útil em diversas aplicações, onde os dados consistem em um conjunto de distâncias e as possíveis soluções são pontos em algum espaço euclidiano que realizam as distâncias dadas. O problema chave em GDE é conhecido como Problema de Geometria de Distâncias (PGD), em que é dado um inteiro K>0 e um grafo simples, não direcionado, ponderado G=(V,E,d), cujas arestas são ponderadas por uma função não negativa d, e queremos determinar se existe uma função (realização) que leva os vértices de V em coordenadas no espaço euclidiano K-dimensional, satisfazendo todas as restrições de distâncias dadas por d. Consideramos tanto problemas teóricos quanto aplicações da GDE. Em termos teóricos, demonstramos a quantidade exata de soluções de uma classe de PGDs muito importante para problemas de conformação molecular e, além disso, conseguimos condições necessárias e suficientes para determinar quando um grafo completo associado a um PGD é realizável e qual o espaço euclidiano com dimensão mínima para tal realização. Em termos práticos, desenvolvemos um algoritmo que calcula tal realização em dimensão mínima com resultados superiores a um algoritmo clássico da literatura. Finalmente...

In situ measured cross section geometry of old timber structures and its influence on structural safety

Lourenço, Paulo B.; Sousa, Hélder S.; Brites, Ricardo D.; Neves, L. C.
Fonte: Springer Publicador: Springer
Tipo: Artigo de Revista Científica
Publicado em /07/2013 ENG
Relevância na Pesquisa
36.09%
Old timber structures may show significant variation in the cross section geometry along the same element, as a result of both construction methods and deterioration. As consequence, the definition of the geometric parameters in situ may be both time consuming and costly. This work presents the results of inspections carried out in different timber structures. Based on the obtained results, different simplified geometric models are proposed in order to efficiently model the geometry variations found. Probabilistic modelling techniques are also used to define safety parameters of existing timber structures, when subjected to dead and live loads, namely self-weight and wind actions. The parameters of the models have been defined as probabilistic variables, and safety of a selected case study was assessed using the Monte Carlo simulation technique. Assuming a target reliability index, a model was defined for both the residual cross section and the time dependent deterioration evolution. As a consequence, it was possible to compute probabilities of failure and reliability indices, as well as, time evolution deterioration curves for this structure. The results obtained provide a proposal for definition of the cross section geometric parameters of existing timber structures with different levels of decay...

In situ measured cross section geometry of old timber structures and its influence on structural safety

Lourenço, PB; Sousa, HS; Brites, RD; Neves, LC
Fonte: Springer Publicador: Springer
Tipo: Artigo de Revista Científica
Publicado em //2012 ENG
Relevância na Pesquisa
36.09%
Old timber structures may show significant variation in the cross section geometry along the same element, as a result of both construction methods and deterioration. As consequence, the definition of the geometric parameters in situ may be both time consuming and costly. This work presents the results of inspections carried out in different timber structures. Based on the obtained results, different simplified geometric models are proposed in order to efficiently model the geometry variations found. Probabilistic modelling techniques are also used to define safety parameters of existing timber structures, when subjected to dead and live loads, namely self-weight and wind actions. The parameters of the models have been defined as probabilistic variables, and safety of a selected case study was assessed using the Monte Carlo simulation technique. Assuming a target reliability index, a model was defined for both the residual cross section and the time dependent deterioration evolution. As a consequence, it was possible to compute probabilities of failure and reliability indices, as well as, time evolution deterioration curves for this structure. The results obtained provide a proposal for definition of the cross section geometric parameters of existing timber structures with different levels of decay...

Left Ventricular Diastolic Function in Essential Hypertensive Patients: Influence of Age and Left Ventricular Geometry

Rosa,Eduardo Cantoni; Moysés,Valdir Ambrósio; Rivera,Ivan; Sesso,Ricardo da Cintra; Kohlmann,Nárcia; Zanella,Maria Tereza; Ribeiro,Artur Beltrame; Kohlmann Jr.,Osvaldo
Fonte: Sociedade Brasileira de Cardiologia - SBC Publicador: Sociedade Brasileira de Cardiologia - SBC
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/05/2002 EN
Relevância na Pesquisa
36.09%
PURPOSE - To evaluate diastolic dysfunction (DD) in essential hypertension and the influence of age and cardiac geometry on this parameter. METHODS - Four hundred sixty essential hypertensive patients (HT) underwent Doppler echocardiography to obtain E/A wave ratio (E/A), atrial deceleration time (ADT), and isovolumetric relaxation time (IRT). All patients were grouped according to cardiac geometric patterns (NG - normal geometry; CR - concentric remodeling; CH- concentric hypertrophy; EH - eccentric hypertrophy) and to age (<40; 40 - 60; >60 years). One hundred six normotensives (NT) persons were also evaluated. RESULTS - A worsening of diastolic function in the HT compared with the NT, including HT with NG (E/A: NT - 1.38±0.03 vs HT - 1.27±0.02, p<0.01), was observed. A higher prevalence of DD occurred parallel to age and cardiac geometry also in the prehypertrophic groups (CR). Multiple regression analysis identified age as the most important predictor of DD (r²=0.30, p<0.01). CONCLUSION - DD was prevalent in this hypertensive population, being highly affected by age and less by heart structural parameters. DD is observed in incipient stages of hypertensive heart disease, and thus its early detection may help in the risk stratification of hypertensive patients.

Functional Differential Geometry

Sussman, Gerald Jay; Wisdom, Jack
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
Formato: 77 p.; 38556269 bytes; 1665777 bytes; application/postscript; application/pdf
EN_US
Relevância na Pesquisa
36.09%
Differential geometry is deceptively simple. It is surprisingly easyto get the right answer with unclear and informal symbol manipulation.To address this problem we use computer programs to communicate aprecise understanding of the computations in differential geometry.Expressing the methods of differential geometry in a computer languageforces them to be unambiguous and computationally effective. The taskof formulating a method as a computer-executable program and debuggingthat program is a powerful exercise in the learning process. Also,once formalized procedurally, a mathematical idea becomes a tool thatcan be used directly to compute results.

On geometry along grafting rays in Teichmuller space

Laverdiere, Renee
Fonte: Universidade Rice Publicador: Universidade Rice
ENG
Relevância na Pesquisa
36.09%
In this work, we investigate the mid-range behavior of geometry along a grafting ray in Teichm"{u}ller space. The main technique is to describe the hyperbolic metric $sigma_{t}$ at a point along the grafting ray in terms of a conformal factor $g_{t}$ times the Thurston (grafted) metric and study solutions to the linearized Liouville equation. We give a formula that describes, at any point on a grafting ray, the change in length of a sum of distinguished curves in terms of the hyperbolic geometry at the point. We then make precise the idea that once the length of the grafting locus is small, local behavior of the geometry for grafting on a general manifold is like that of grafting on a cylinder. Finally, we prove that the sum of lengths of is eventually monotone decreasing along grafting rays.

A Parametric Approach to 3D Dynamic Geometry

Botana Ferreiro, Francisco Ramón
Fonte: Elsevier Publicador: Elsevier
Tipo: info:eu-repo/semantics/article; acceptedVersion
ENG
Relevância na Pesquisa
36.09%
Dynamic geometry systems are computer applications allowing the exact on-screen drawing of geometric diagrams and their interactive manipulation by mouse dragging. Whereas there exists an extensive list of 2D dynamic geometry environments, the number of 3D systems is reduced. Most of them, both in 2D and 3D, share a common approach, using numerical data to manage geometric knowledge and elementary methods to compute derived objects. This paper deals with a parametric approach for automatic management of 3D Euclidean constructions. An open source library, implementing the core functions in a 3D dynamic geometry system, is described here. The library deals with constructions by using symbolic parameters, thus enabling a full algebraic knowledge about objects such as loci and envelopes. This parametric approach is also a prerequisite for performing automatic proof. Basic functions are defined for symbolically checking the truth of statements. Using recent results from the theory of parametric polynomial systems solving, the bottleneck in the automatic determination of geometric loci and envelopes is solved. As far as we know, there is no comparable library in the 3D case, except the paramGeo3D library (designed for computing equations of simple 3D geometric objects...

Internal connectivity of meandering rivers: Statistical generalization of channel hydraulic geometry

Czapiga, M.J.; Smith, V.B.; Nittrouer, J.A.; Mohrig, D.; Parker, G.
Fonte: Universidade Rice Publicador: Universidade Rice
Tipo: Journal article; Text; publisher version
ENG
Relevância na Pesquisa
36.09%
The geometry of rivers has been characterized in terms of downstream and at-a-station hydraulic geometry, based on individual cross sections. Such analyses do not, however, provide insight as to how these cross sections are connected. We generalize the concept of hydraulic geometry, using data on bathymetry from four reaches of meandering rivers that include at least five bends. We quantify connectivity in terms of the probability that a connected path exists such that a given attribute remains within specified bounds along it. While the concept is general, here we apply it to vessel navigability. We develop a predictor for navigability in meandering rivers, which requires only the following, relatively easily obtained input: vessel draft, vessel width, bankfull depth, bankfull width, relative difference between current and bankfull water surface elevation, and length of desired navigation path. The predictor is applicable to both bankfull and below-bankfull stage. A key input parameter is the standard deviation of the probability distribution of depth. This parameter, in and of itself, yields no information on connectivity as it does not capture the spatial orientation of depth variation. We find, however, that (a) the probability function for connectivity does depend on this parameter...

Aspects of overdetermined systems of partial differential equations in projective and conformal geometry

Randall, Matthew
Fonte: Universidade Nacional da Austrália Publicador: Universidade Nacional da Austrália
Tipo: Thesis (PhD); Doctor of Philosophy (PhD)
EN_AU
Relevância na Pesquisa
36.09%
This thesis discusses aspects of overdetermined systems of partial differential equations (PDEs) in projective and conformal geometry. The first part deals with projective differential geometry. A projective surface is a 2-dimensional smooth manifold equipped with a projective structure i.e. a class of torsion-free affine connections that have the same geodesics as unparameterised curves. Given any projective surface we can ask whether it admits a torsion-free affine connection (in its projective class) that has skew-symmetric Ricci tensor. This is equivalent to solving a particular overdetermined system of semi-linear partial differential equations. It turns out that there are local obstructions to solving the system of PDEs in two dimensions. These obstructions are constructed out of local invariants of the projective structure. We give examples of projective surfaces that admit skew-symmetric Ricci tensor and examples that do not because of nonvanishing obstructions. We relate projective surfaces admitting skew-symmetric Ricci tensor to 3-webs in 2 dimensions. We also give examples of projective structures in higher dimensions that admit skew-symmetric Ricci tensor. The second part of the thesis deals with conformal differential geometry. On Mobius surfaces introduced in [5]...

Geometria e habilidade de rotação mental : uma experiência de ensino com transformações isométricas no design; Geometry and mental rotation skill : an experience of teaching with isometric transformations in design

Fernando da Silva Ramos
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 23/02/2012 PT
Relevância na Pesquisa
36.09%
A geometria tem sido, ao longo da história, disciplina prescritiva de uma extensa série de atividades cientificas e artísticas, e modernamente, sabe se que é fundamento para diversas profissões como arquitetura, design, engenharias, química, física, geologia, astronomia, etc. Apesar da importância reconhecida, seu ensino regular ao longo da vida acadêmica do indivíduo tem passado por muitas transformações (nem sempre para melhor) desde a segunda metade do século XX, e é hoje, assunto complexo e controverso no Brasil e no mundo. Entretanto, parece consensual entre os pesquisadores que a capacidade de visualização - que para a Psicologia Cognitiva, está categorizada entre as habilidades espaciais do indivíduo - pode ser positivamente afetada através do treinamento adequado em geometria. Tal vocação é muitas vezes descrita como seu maior potencial e principal justificativa para seu ensino sistemático. Esta pesquisa descreve um experimento que envolveu um grupo de sessenta alunos de um curso de bacharelado em design, onde procurou se compreender o impacto causado sobre sua capacidade cognitiva de rotação mental, a partir da administração de uma série de conceitos e exercícios relacionados ao tópico das Transformações Isométricas. Os estudantes foram divididos em duas turmas...

Preservice teachers' knowledge on elementary geometry concepts

Couto, Angela; Vale, Isabel
Fonte: European Teacher Education Network Publicador: European Teacher Education Network
Tipo: Artigo de Revista Científica
Publicado em //2014 ENG
Relevância na Pesquisa
36.09%
This text is based on a research, which is still in progress, whose main objective is to identify and understand what are the main difficulties of future mathematics teachers of basic education are, regarding their content knowledge in geometry in the context of the curricular unit of Geometry during their undergraduate degree. We chose a qualitative approach in the form of case study, in which data collection was done through observation, interviews, a diverse set of tasks, a diagnostic test and other documents. This paper focuses on the test given to prospective teachers at the beginning of the course. The preliminary analysis of the data points to a weak performance of preservice teachers in the test issues addressing elementary knowledge of Geometry.

A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences

Loaiza Ossa, Gabriel Ignacio; Quiceno Echavarr??a, H??ctor Rom??n
Fonte: Springer Berlin Heidelberg; Grupo de Investigaci??n An??lisis Funcional y Aplicaciones; Escuela de Ciencias Publicador: Springer Berlin Heidelberg; Grupo de Investigaci??n An??lisis Funcional y Aplicaciones; Escuela de Ciencias
Tipo: info:eu-repo/semantics/conferenceObject; conferenceObject; Documento de conferencia; publishedVersion
ENG
Relevância na Pesquisa
36.09%
For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari???s ??-connections appears as special case of the q??????connections ??????(q). The main result is the expected one, namely the zero curvature of the manifold. Loading... Geometric Science of InformationGeometric Science of Information Look Inside Chapter Metrics Downloads1K Provided by Bookmetrix Other actions Export citation About this Book Reprints and Permissions Add to Papers Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn

A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.

Quiceno, H. R.; Loaiza, Gabriel
Fonte: Springer; Grupo de Investigaci??n An??lisis Funcional y Aplicaciones; Escuela de Ciencias y Humanidades Publicador: Springer; Grupo de Investigaci??n An??lisis Funcional y Aplicaciones; Escuela de Ciencias y Humanidades
Tipo: bookPart; Cap??tulo o parte de un libro; publishedVersion
ENG
Relevância na Pesquisa
36.09%
For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari???s ??-connections appears as special case of the q??????connections ??????(q). The main result is the expected one, namely the zero curvature of the manifold.

Sub-Finsler geometry and finite propagation speed

Cowling, Michael G.; Martini, Alessio
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/05/2012
Relevância na Pesquisa
36.09%
We prove a number of results on the geometry associated to the solutions of evolution equations given by first-order differential operators on manifolds. In particular, we consider distance functions associated to a first-order operator, and discuss the associated geometry, which is sometimes surprisingly different to riemannian geometry.; Comment: 45 pages

Ideas of E.~Cartan and S.~Lie in modern geometry: $G$-structures and differential equations. Lecture 2

Arteaga, J. R.; Malakhaltsev, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/09/2011
Relevância na Pesquisa
36.09%
This is the lecture 2 of a mini-course of 4 lectures. Our purpose of this mini-curse is to explain some ideas of E. Cartan and S. Lie when we study differential geometry, particularly we will to explain the Cartan reduction method. The Cartan reduction method is a technique in Differential Geometry for determining whether two geometrical structure are the same up to a diffeomorphism. This method use new tools of differential geometry as principal bundles, $G$-structures and jets theory. We start with an example of a $G$-structure: the 3-webs in $\mathbb{R}^{2}$. Here we use the Cartan method to classify the differential equations but not to resolve. This is a classification can be a weak classification in the sense of not involving all the structural invariants.; Comment: Congreso Colombiano de Matem\'aticas, Bucaramanga, Colombia, July 2011

Ideas of E. Cartan and S. Lie in modern geometry: $G$-structures and differential equations. Lecture 1

Arteaga, J. R.; Malakhaltsev, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/09/2011
Relevância na Pesquisa
36.09%
This is the lecture 1 of a mini-course of 4 lectures. Our purpose of this mini-curse is to explain some ideas of E. Cartan and S. Lie when we study differential geometry, particularly we will to explain the Cartan reduction method. The Cartan reduction method is a technique in Differential Geometry for determining whether two geometrical structure are the same up to a diffeomorphism. This method use new tools of differential geometry as principal bundles, $G$-structures and jets theory. We start with an example of a $G$-structure: the 3-webs in $\mathbb{R}^{2}$. Here we use the Cartan method to classify the differential equations but not to resolve. This is a classification can be a weak classification in the sense of not involving all the structural invariants.; Comment: Congreso Colombiano de Matem\'aticas, Bucaramanga, Colombia, July 2011

Ideas of E.~Cartan and S.~Lie in modern geometry: $G$-structures and differential equations. Lecture 3

Arteaga, J. R.; Malakhaltsev, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/09/2011
Relevância na Pesquisa
36.09%
This is the lecture 3 of a mini-course of 4 lectures. Our purpose of this mini-curse is to explain some ideas of E. Cartan and S. Lie when we study differential geometry, particularly we will to explain the Cartan reduction method. The Cartan reduction method is a technique in Differential Geometry for determining whether two geometrical structure are the same up to a diffeomorphism. This method use new tools of differential geometry as principal bundles, $G$-structures and jets theory. We start with an example of a $G$-structure: the 3-webs in $\mathbb{R}^{2}$. Here we use the Cartan method to classify the differential equations but not to resolve. This is a classification can be a weak classification in the sense of not involving all the structural invariants.; Comment: Congreso Colombiano de Matem\'aticas, Bucaramanga, Colombia, July 2011

Ideas of E.~Cartan and S.~Lie in modern geometry: $G$-structures and differential equations. Lecture 4

Arteaga, J. R.; Malakhaltsev, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/09/2011
Relevância na Pesquisa
36.09%
This is the lecture 4 of a mini-course of 4 lectures. Our purpose of this mini-curse is to explain some ideas of E. Cartan and S. Lie when we study differential geometry, particularly we will to explain the Cartan reduction method. The Cartan reduction method is a technique in Differential Geometry for determining whether two geometrical structure are the same up to a diffeomorphism. This method use new tools of differential geometry as principal bundles, $G$-structures and jets theory. We start with an example of a $G$-structure: the 3-webs in $\mathbb{R}^{2}$. Here we use the Cartan method to classify the differential equations but not to resolve. This is a classification can be a weak classification in the sense of not involving all the structural invariants.; Comment: Congreso Colombiano de Matem\'aticas, Bucaramanga, Colombia, July 2011

Algorithmic Semi-algebraic Geometry and Topology -- Recent Progress and Open Problems

Basu, Saugata
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.09%
We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from describing these results, we discuss briefly the background as well as the importance of these problems, and also describe the main tools from algorithmic semi-algebraic geometry, as well as algebraic topology, which make these advances possible. We end with a list of open problems.; Comment: Survey article, 74 pages, 15 figures. Final revision. This version will appear in the AMS Contemporary Math. Series: Proceedings of the Summer Research Conference on Discrete and Computational Geometry, Snowbird, Utah (June, 2006). J.E. Goodman, J. Pach, R. Pollack Eds