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Dissertations / Theses on the topic 'Differential topology'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Anderson, Laura Marie. "Topology of combinatorial differential manifolds." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28093.

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2

Cox, Anna Lee. "A categorization of piecewise-linear surfaces." Virtual Press, 1994. http://liblink.bsu.edu/uhtbin/catkey/902464.

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Any Piecewise-Linear (PL) surface can be formed from a regular polygon (including the interior) with an even number of edges, where the edges are identified in pairs to form a two-dimensional manifold. The resulting surfaces can be distinguished by algebraic means. An analysis of the construction algorithm can also be used to determine the resulting surface. Knowledge of the polygon used can also yield information about the surfaces formed.In this thesis, an algorithm is developed that will analyze all possible edge pairings for an arbitrary regular polygon. The combination of this data, along

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3

Vetere, Elmiro [Verfasser], Annette [Akademischer Betreuer] Huber, and Stefan [Akademischer Betreuer] Kebekus. "Cohomological descent for logarithmic differential forms in the log etale topology." Freiburg : Universität, 2018. http://d-nb.info/1182894941/34.

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4

Walsh, Mark. "Metrics of positive scalar curvature and generalised Morse functions /." Connect to title online (Scholars' Bank) Connect to title online (ProQuest), 2009. http://hdl.handle.net/1794/10265.

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5

Sperança, Llohann Dallagnol 1986. "Fenomenos exoticos em geometria e topologia." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306815.

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Orientador: Carlos Eduardo Duran Fernandez<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-14T00:21:52Z (GMT). No. of bitstreams: 1 Speranca_LlohamDallagnol_M.pdf: 1442574 bytes, checksum: eec573204734790dd464f4ba0a79d6c5 (MD5) Previous issue date: 2009<br>Resumo: Apresentaremos neste trabalho alguns dos modelos clássicos em geometria e topologia diferencial para algumas variedades diferenciáveis com o mesmo tipo homotópico de uma esfera. Em seguida apresentaremos construções ma

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6

Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Differential operators on manifolds with singularities : analysis and topology : Chapter 4: Pseudodifferential operators." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2658/.

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Contents: Chapter 4: Pseudodifferential Operators 4.1. Preliminary Remarks 4.1.1. Why are pseudodifferential operators needed? 4.1.2. What is a pseudodifferential operator? 4.1.3. What properties should the pseudodifferential calculus possess? 4.2. Classical Pseudodifferential Operators on Smooth Manifolds 4.2.1. Definition of pseudodifferential operators on a manifold 4.2.2. Hörmander’s definition of pseudodifferential operators 4.2.3. Basic properties of pseudodifferential operators 4.3. Pseudodifferential Operators in Sections of Hilbert Bundles 4.3.1. Hilbert bundles 4.3.2. Operator-va

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7

Perlmutter, Nathan. "Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds." Thesis, University of Oregon, 2015. http://hdl.handle.net/1794/19241.

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Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n-1)-connected, (4n+1)-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the action of the diffeomorphism group of a manifold M on the linking form associated to the homology groups of M. In order to study this action we construct a geometric model for the linking form using the intersections of embedded and immersed Z/k-manifolds. In addition to our main homological sta

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8

Tang, Shouchun (Terry), and University of Lethbridge Faculty of Arts and Science. "A rapid method for approximating invariant manifolds of differential equations." Thesis, Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2006, 2006. http://hdl.handle.net/10133/356.

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The Intrinsic Low-Dimensional Manifold (ILDM) has been adopted as an approximation to the slow manifold representing the long-term evolution of a non-linear chemical system. The computation of the slow manifold simplifies the model without sacrificing accuracy because the trajectories are rapidly attracted to it. The ILDM has been shown to be a highly accurate approximation to the manifold when the curvature of the manifold is not too large. An efficient method of calculating an approximation to the slow manifold which may be equivalent to the ILDM is presented. This method, called Functional

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9

Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Differential operators on manifolds with singularities : analysis and topology : Chapter 5: Manifolds with isolated singularities." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2665/.

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Contents: Chapter 5: Manifolds with Isolated Singularities 5.1. Differential Operators and the Geometry of Singularities 5.1.1. How do isolated singularities arise? Examples 5.1.2. Definition and methods for the description of manifolds with isolated singularities 5.1.3. Bundles. The cotangent bundle 5.2. Asymptotics of Solutions, Function Spaces,Conormal Symbols 5.2.1. Conical singularities 5.2.2. Cuspidal singularities 5.3. A Universal Representation of Degenerate Operators and the Finiteness Theorem 5.3.1. The cylindrical representation 5.3.2. Continuity and compactness 5.3.3. Elliptic

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10

Ankele, Michael Peter [Verfasser]. "Higher-Order Tensors and Differential Topology in Diffusion MRI Modeling and Visualization / Michael Peter Ankele." Bonn : Universitäts- und Landesbibliothek Bonn, 2019. http://d-nb.info/1188731769/34.

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11

Williamson, William Iain. "Differential chromatin topology and transcription factor enhancer binding regulate spatiotemporal gene expression in limb development." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8056.

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Many developmental genes are located in gene-poor genomic regions and are activated by long-range enhancers located up to 1Mb away. Modification and reorganisation of chromatin structure is pivotal to such long-range gene regulation. A prerequisite for enhancer activity is the binding of transcription factors and co-factors with the interplay between activating and repressive factors determining tissue, spatial and temporal specificity. Spatiotemporal control of sonic hedgehog (Shh) and the 5′ Hoxd genes (especially Hoxd13) is crucial for vertebrate limb anterior-posterior (A-P) axis and autop

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12

Ankele, Michael [Verfasser]. "Higher-Order Tensors and Differential Topology in Diffusion MRI Modeling and Visualization / Michael Peter Ankele." Bonn : Universitäts- und Landesbibliothek Bonn, 2019. http://d-nb.info/1188731769/34.

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13

Silva, Paul Jerome. "Investigation of the effectiveness of interface constraints in the solution of hyperbolic second-order differential equations." CSUSB ScholarWorks, 2000. https://scholarworks.lib.csusb.edu/etd-project/1953.

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Solutions to differential equations describing the behavior of physical quantities (e.g., displacement, temperature, electric field strength) often only have finite range of validity over a subdomain. Interest beyond the subdomain often arises. As a result, the problem of making the solution compatible across the connecting subdomain interfaces must be dealt with. Four different compatibility methods are examined here for hyperbolic (time varying) second-order differential equations. These methods are used to match two different solutions, one in each subdomain along the connecting interface.

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14

Pena, Moises. "Geodesics on Generalized Plane Wave Manifolds." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/866.

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A manifold is a Hausdorff topological space that is locally Euclidean. We will define the difference between a Riemannian manifold and a pseudo-Riemannian manifold. We will explore how geodesics behave on pseudo-Riemannian manifolds and what it means for manifolds to be geodesically complete. The Hopf-Rinow theorem states that,“Riemannian manifolds are geodesically complete if and only if it is complete as a metric space,” [Lee97] however, in pseudo-Riemannian geometry, there is no analogous theorem since in general a pseudo-Riemannian metric does not induce a metric space structure on the man

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15

Pinsky, Nathan. "Mathematical Knowledge for Teaching and Visualizing Differential Geometry." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/hmc_theses/49.

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In recent decades, education researchers have recognized the need for teachers to have a nuanced content knowledge in addition to pedagogical knowledge, but very little research was conducted into what this knowledge would entail. Beginning in 2008, math education researchers began to develop a theoretical framework for the mathematical knowledge needed for teaching, but their work focused primarily on elementary schools. I will present an analysis of the mathematical knowledge needed for teaching about the regular curves and surfaces, two important concepts in differential geometry which gene

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16

Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Differential operators on manifolds with singularities : analysis and topology : Chapter 1: Localization (surgery) in elliptic theory." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2654/.

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Contents: Chapter 1: Localization (Surgery) in Elliptic Theory 1.1. The Index Locality Principle 1.1.1. What is locality? 1.1.2. A pilot example 1.1.3. Collar spaces 1.1.4. Elliptic operators 1.1.5. Surgery and the relative index theorem 1.2. Surgery in Index Theory on Smooth Manifolds 1.2.1. The Booß–Wojciechowski theorem 1.2.2. The Gromov–Lawson theorem 1.3. Surgery for Boundary Value Problems 1.3.1. Notation 1.3.2. General boundary value problems 1.3.3. A model boundary value problem on a cylinder 1.3.4. The Agranovich–Dynin theorem 1.3.5. The Agranovich theorem 1.3.6. Bojarski’s theor

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17

Botnan, Magnus Bakke. "Three Approaches in Computational Geometry and Topology : Persistent Homology, Discrete Differential Geometry and Discrete Morse Theory." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-14201.

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We study persistent homology, methods in discrete differential geometry and discrete Morse theory. Persistent homology is applied to computational biology and range image analysis. Theory from differential geometry is used to define curvature estimates of triangulated hypersurfaces. In particular, a well-known method for triangulated surfacesis generalised to hypersurfaces of any dimension. The thesis concludesby discussing a discrete analogue of Morse theory.

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18

Sperança, Llohann Dallagnol 1986. "Geometria e topologia de cobordos." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307262.

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Orientadores: Alcibiades Rigas, Carlos Eduardo Duran Fernandez<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-20T13:56:12Z (GMT). No. of bitstreams: 1 Speranca_LlohamDallagnol_D.pdf: 994466 bytes, checksum: 472919d7eec0f563b673a0307450dc49 (MD5) Previous issue date: 2012<br>Resumo: Nesse trabalho estudaremos a geometria e a topologia de algumas variedades homeomorfas, porém não difeomorfas, à esfera padrão Sn, chamadas esferas exóticas. Realizaremos duas dessas variedades como quocie

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19

Rayzaro, Oyran Silva [UNESP]. "Estimativas inferiores para dimensão de Hausdorff de repulsores não-uniformemente expansores." Universidade Estadual Paulista (UNESP), 2014. http://hdl.handle.net/11449/110599.

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Made available in DSpace on 2014-11-10T11:09:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-08-04Bitstream added on 2014-11-10T11:57:47Z : No. of bitstreams: 1 000788978.pdf: 408960 bytes, checksum: 1cfcc35354bc50d787e5fb17deef1134 (MD5)<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Estudamos a dimensão de Hausdorff de certos conjuntos invariantes obtidos como repulsores de aplicações com buraco. Neste trabalho relacionamos a dimensão de Hausdorff do repulsor ¤ com o volume do buraco H, em particular mostramos que a dimensão de Hausdorff de ¤ pode ser t

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20

Rayzaro, Oyran Silva. "Estimativas inferiores para dimensão de Hausdorff de repulsores não-uniformemente expansores /." São José do Rio Preto, 2014. http://hdl.handle.net/11449/110599.

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Orientador: Vanderlei Minori Horita<br>Banca: Ali Messaoudi<br>Banca: Marcio Ricardo Alves Gouveia<br>Banca: Thiago Aparecido Catalan<br>Banca: Nivaldo Costa Muniz<br>Resumo: Estudamos a dimensão de Hausdorff de certos conjuntos invariantes obtidos como repulsores de aplicações com buraco. Neste trabalho relacionamos a dimensão de Hausdorff do repulsor ¤ com o volume do buraco H, em particular mostramos que a dimensão de Hausdorff de ¤ pode ser tomada arbitrariamente próxima da dimensão do ambiente desde que o volume de H seja suficientemente pequeno. Como aplicação dos resultados, mostramos q

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21

Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Differential operators on manifolds with singularities : analysis and topology : Chapter 3: Eta invariant and the spectral flow." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2659/.

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Contents: Chapter 3: Eta Invariant and the Spectral Flow 3.1. Introduction 3.2. The Classical Spectral Flow 3.2.1. Definition and main properties 3.2.2. The spectral flow formula for periodic families 3.3. The Atiyah–Patodi–Singer Eta Invariant 3.3.1. Definition of the eta invariant 3.3.2. Variation under deformations of the operator 3.3.3. Homotopy invariance. Examples 3.4. The Eta Invariant of Families with Parameter (Melrose’s Theory) 3.4.1. A trace on the algebra of parameter-dependent operators 3.4.2. Definition of the Melrose eta invariant 3.4.3. Relationship with the Atiyah–Patodi

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22

Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Differential operators on manifolds with singularities : analysis and topology : Chapter 6: Elliptic theory on manifolds with edges." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2675/.

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Contents: Chapter 6: Elliptic Theory on Manifolds with Edges Introduction 6.1. Motivation and Main Constructions 6.1.1. Manifolds with edges 6.1.2. Edge-degenerate differential operators 6.1.3. Symbols 6.1.4. Elliptic problems 6.2. Pseudodifferential Operators 6.2.1. Edge symbols 6.2.2. Pseudodifferential operators 6.2.3. Quantization 6.3. Elliptic Morphisms and the Finiteness Theorem 6.3.1. Matrix Green operators 6.3.2. General morphisms 6.3.3. Ellipticity, Fredholm property, and smoothness Appendix A. Fiber Bundles and Direct Integrals A.1. Local theory A.2. Globalization A.3. Versions

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23

Khomo, M. T. "Topological policy analysis : the application of differential topology to the technological analysis of industrialisation and economic development." Thesis, City University London, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306684.

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24

Garrisi, Daniele. "Ordinary differential equations in Banach spaces and the spectral flow." Doctoral thesis, Scuola Normale Superiore, 2008. http://hdl.handle.net/11384/85668.

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25

Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Differential operators on manifolds with singularities : analysis and topology : Chapter 7: The index problem on manifolds with singularities." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2670/.

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Contents: Chapter 7: The Index Problemon Manifolds with Singularities Preface 7.1. The Simplest Index Formulas 7.1.1. General properties of the index 7.1.2. The index of invariant operators on the cylinder 7.1.3. Relative index formulas 7.1.4. The index of general operators on the cylinder 7.1.5. The index of operators of the form 1 + G with a Green operator G 7.1.6. The index of operators of the form 1 + G on manifolds with edges 7.1.7. The index on bundles with smooth base and fiber having conical points 7.2. The Index Problem for Manifolds with Isolated Singularities 7.2.1. Statement of

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26

Williams, Jason Daniel. "Tightening and blending subject to set-theoretic constraints." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44742.

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Our work applies techniques for blending and tightening solid shapes represented by sets. We require that the output contain one set and exclude a second set, and then we optimize the boundary separating the two sets. Working within that framework, we present mason, tightening, tight hulls, tight blends, and the medial cover, with details for implementation. Mason uses opening and closing techniques from mathematical morphology to smooth small features. By contrast, tightening uses mean curvature flow to minimize the measure of the boundary separating the opening of the interior of the closed

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27

Chaparro, Maria Guadalupe. "Minimal surfaces." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3118.

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The focus of this project consists of investigating when a ruled surface is a minimal surface. A minimal surface is a surface with zero mean curvature. In this project the basic terminology of differential geometry will be discussed including examples where the terminology will be applied to the different subjects of differential geometry. In addition the focus will be on a classical theorem of minimal surfaces referred to as the Plateau's Problem.

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28

Topkara, Mustafa. "Exotic Smooth Structures On Non-simply Connected 4-manifolds." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12611752/index.pdf.

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In this thesis, we study exotic smooth structures on 4-manifolds with finite fundamental groups. For an arbitrary finite group G, we construct an infinite family of smooth 4-manifolds with fundamental group G, which are all homeomorphic but mutually non-diffeomorphic, using the small symplectic manifold with arbitrary fundamental group constructed by S. Baldridge and P. Kirk, together with the methods of A. Akhmedov, R.&amp<br>#221<br>. Baykur and D. Park for constructing infinite families of exotic simply connected 4-manifolds. In the final chapter, pairs of small exotic 4-manifolds with a cy

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29

Chang, Wenli. "Geodesics of surface of revolution." CSUSB ScholarWorks, 2011. https://scholarworks.lib.csusb.edu/etd-project/3321.

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The purpose of this project was to study the differential geometry of curves and surfaces in three-dimensional Euclidean space. Some important concepts such as, Curvature, Fundamental Form, Christoffel symbols, and Geodesic Curvature and equations are explored.

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30

Mansouri, Ahmad, and David Norman. "Strategy Development of Structural Optimization in Design Processes." Thesis, Linköping University, Linköping University, Department of Management and Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-17418.

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<p><p><p>This thesis aims toward developing strategies in the area of structural optimization and to implement these strategies in design processes. At</p><p> </p><em>GM Powertrain Sweden </em>where powertrains are designed and developed, two designs of a differential housing have been chosen for this thesis. The main tasks have been to perform a topology optimization of a model early in a design process, and a shape optimization on a model late in a design process. In addition the shape optimization strategies have also been applied on a fork shifter. This thesis covers the theory of differen

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31

Cordier, Michelle Renee. "On Bodies Whose Shadows Are Related Via Rigid Motions." Kent State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=kent1429547907.

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Nguyenhuu, Rick Hung. "Torus embedding and its applications." CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/1572.

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33

Broersma, Heather Ann. "Gauss-Bonnet formula." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3044.

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From fundamental forms to curvatures and geodesics, differential geometry has many special theorems and applications worth examining. Among these, the Gauss-Bonnet Theorem is one of the well-known theorems in classical differential geometry. It links geometrical and topological properties of a surface. The thesis introduced some basic concepts in differential geometry, explained them with examples, analyzed the Gauss-Bonnet Theorem and presented the proof of the theorem in greater detail. The thesis also considered applications of the Gauss-Bonnet theorem to some special surfaces.

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34

Brusaferro, Doniray. "Series Solutions of Polarized Gowdy Universes." VCU Scholars Compass, 2017. http://scholarscompass.vcu.edu/etd/4777.

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Einstein's field equations are a system of ten partial differential equations. For a special class of spacetimes known as Gowdy spacetimes, the number of equations is reduced due to additional structure of two dimensional isometry groups with mutually orthogonal Killing vectors. In this thesis, we focus on a particular model of Gowdy spacetimes known as the polarized T3 model, and provide an explicit solution to Einstein's equations.

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35

Amiridis, Kiriakos. "THE USE OF 3-D HIGHWAY DIFFERENTIAL GEOMETRY IN CRASH PREDICTION MODELING." UKnowledge, 2019. https://uknowledge.uky.edu/ce_etds/85.

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The objective of this research is to evaluate and introduce a new methodology regarding rural highway safety. Current practices rely on crash prediction models that utilize specific explanatory variables, whereas the depository of knowledge for past research is the Highway Safety Manual (HSM). Most of the prediction models in the HSM identify the effect of individual geometric elements on crash occurrence and consider their combination in a multiplicative manner, where each effect is multiplied with others to determine their combined influence. The concepts of 3-dimesnional (3-D) representatio

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36

Chiek, Veasna. "Geodesic on surfaces of constant Gaussian curvature." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3045.

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The goal of the thesis is to study geodesics on surfaces of constant Gaussian curvature. The first three sections of the thesis is dedicated to the definitions and theorems necessary to study surfaces of constant Gaussian curvature. The fourth section contains examples of geodesics on these types of surfaces and discusses their properties. The thesis incorporates the use of Maple, a mathematics software package, in some of its calculations and graphs. The thesis' conclusion is that the Gaussian curvature is a surface invariant and the geodesics of these surfaces will be the so-called best path

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37

Pade, Jonas. "Analysis and waveform relaxation for a differential-algebraic electrical circuit model." Doctoral thesis, Humboldt-Universität zu Berlin, 2021. http://dx.doi.org/10.18452/23044.

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Die Hauptthemen dieser Arbeit sind einerseits eine tiefgehende Analyse von nichtlinearen differential-algebraischen Gleichungen (DAEs) vom Index 2, die aus der modifizierten Knotenanalyse (MNA) von elektrischen Schaltkreisen hervorgehen, und andererseits die Entwicklung von Konvergenzkriterien für Waveform Relaxationsmethoden zum Lösen gekoppelter Probleme. Ein Schwerpunkt in beiden genannten Themen ist die Beziehung zwischen der Topologie eines Schaltkreises und mathematischen Eigenschaften der zugehörigen DAE. Der Analyse-Teil umfasst eine detaillierte Beschreibung einer Normalform für S

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38

Akteke-ozturk, Basak. "New Approaches To Desirability Functions By Nonsmooth And Nonlinear Optimization." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612649/index.pdf.

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Desirability Functions continue to attract attention of scientists and researchers working in the area of multi-response optimization. There are many versions of such functions, differing mainly in formulations of individual and overall desirability functions. Derringer and Suich&rsquo<br>s desirability functions being used throughout this thesis are still the most preferred ones in practice and many other versions are derived from these. On the other hand, they have a drawback of containing nondifferentiable points and, hence, being nonsmooth. Current approaches to their optimization, which a

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39

Niederkrüger, Klaus. "On fillability of contact manifolds." Habilitation à diriger des recherches, Université Paul Sabatier - Toulouse III, 2013. http://tel.archives-ouvertes.fr/tel-00922320.

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The aim of this text is to give an accessible overview to some recent results concerning contact manifolds and their symplectic fillings. In particular, we work out the weakest compatibility conditions between a symplectic manifold and a contact structure on its boundary to still be able to obtain a sensible theory (Chapter II), furthermore we prove two results (Theorem A and B in Section I.4) that show how certain submanifolds inside a contact manifold obstruct the existence of a symplectic filling or influence its topology. We conclude by giving several constructions of contact manifolds tha

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40

Peske, Wendy Ann. "A topological approach to nonlinear analysis." CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2779.

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A topological approach to nonlinear analysis allows for strikingly beautiful proofs and simplified calculations. This topological approach employs many of the ideas of continuous topology, including convergence, compactness, metrization, complete metric spaces, uniform spaces and function spaces. This thesis illustrates using the topological approach in proving the Cauchy-Peano Existence theorem. The topological proof utilizes the ideas of complete metric spaces, Ascoli-Arzela theorem, topological properties in Euclidean n-space and normed linear spaces, and the extension of Brouwer's fixed po

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41

Miick, Tonja. "Minimizing Travel Time Through Multiple Media With Various Borders." TopSCHOLAR®, 2013. http://digitalcommons.wku.edu/theses/1246.

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This thesis consists of two main chapters along with an introduction andconclusion. In the introduction, we address the inspiration for the thesis, whichoriginates in a common calculus problem wherein travel time is minimized across two media separated by a single, straight boundary line. We then discuss the correlation of this problem with physics via Snells Law. The first core chapter takes this idea and develops it to include the concept of two media with a circular border. To make the problem easier to discuss, we talk about it in terms of running and swimming speeds. We first address the

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Kloeckner, Benoît. "Géométrie des variétés, des espaces de mesures et des espaces de sous-groupes." Habilitation à diriger des recherches, Université de Grenoble, 2012. http://tel.archives-ouvertes.fr/tel-00785679.

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Ce mémoire présente des résultats dans trois directions. En géométrie riemannienne, on montre une généralisation de l'inégalité de Günther sur le volume, et en dimension 4 une inégalité isopérimétrique pour les variétés à courbure majorée. En géométrie des espaces de Wasserstein, issus du transport optimal, on montre des résultats plongement et de non-plongement, on calcule des groupes d'isométries, et on étudie la dynamique de l'action sur les mesures des applications dilatantes du cercle. En topologie de Chabauty, on montre que l'espace des sous-groupes fermés de $R^n$ est simplement connexe

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Kunz, Daniel. "Lieovy grupy a jejich fyzikální aplikace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-417088.

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In this thesis I describe construction of Lie group and Lie algebra and its following usage for physical problems. To be able to construct Lie groups and Lie algebras we need define basic terms such as topological manifold, tensor algebra and differential geometry. First part of my thesis is aimed on this topic. In second part I am dealing with construction of Lie groups and algebras. Furthermore, I am showing different properties of given structures. Next I am trying to show, that there exists some connection among Lie groups and Lie algebras. In last part of this thesis is used just for show

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Smith, John C. "The Computation of Ultrapowers by Supercompactness Measures." Thesis, University of North Texas, 1999. https://digital.library.unt.edu/ark:/67531/metadc2201/.

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The results from this dissertation are a computation of ultrapowers by supercompactness measures and concepts related to such measures. The second chapter gives an overview of the basic ideas required to carry out the computations. Included are preliminary ideas connected to measures, and the supercompactness measures. Order type results are also considered in this chapter. In chapter III we give an alternate characterization of 2 using the notion of iterated ordinal measures. Basic facts related to this characterization are also considered here. The remaining chapters are devoted to finding b

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Ngo, Fabien. "Quantum structures of some non-monotone Lagrangian submanifolds." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210039.

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In this thesis we present a slight generalisation of the Pearl complex or relative quantum homology to some non monotone Lagrangian submanifolds. First we develop the theory for the so called almost monotone Lagrangian submanifolds, We apply it to uniruling problems as well as estimates for the relative Gromov width. In the second part we develop the theory for toric fiber in toric Fano manifolds, recovering previous computaional results of Floer homology .<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished

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Konnerth, Reinhold. "Automorphism groups of differentially closed fields." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327406.

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Mazzoni, Michele. "A fibre bundle approach to U(1) symmetries in physics." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16776/.

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In questa tesi si utilizza il formalismo dei fibrati principali per descrivere le propriet`a topologiche globali di sistemi fisici classici e quantistici che presentano simmetrie legate all’azione del gruppo U(1). Nel primo capitolo `e contenuta una esposizione della teoria matematica dei fibrati, con un particolare riguardo ai fibrati principali ed alle strutture differenziali definibili su di essi (forme differenziali di connessione e curvatura). Nel secondo capitolo si impiega il formalismo precedentemente sviluppato per trattare le propriet`a del monopolo magnetico di Dirac e si otti

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Chaturapruek, Sorathan. "A Mathematical Framework for Unmanned Aerial Vehicle Obstacle Avoidance." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/60.

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The obstacle avoidance navigation problem for Unmanned Aerial Vehicles (UAVs) is a very challenging problem. It lies at the intersection of many fields such as probability, differential geometry, optimal control, and robotics. We build a mathematical framework to solve this problem for quadrotors using both a theoretical approach through a Hamiltonian system and a machine learning approach that learns from human sub-experts' multiple demonstrations in obstacle avoidance. Prior research on the machine learning approach uses an algorithm that does not incorporate geometry. We have developed tool

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Rocha, Kelvin Raymond. "A variational approach for viewpoint-based visibility maximization." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24816.

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Thesis (Ph.D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2008.<br>Committee Chair: Allen R. Tannenbaum; Committee Member: Anthony J. Yezzi; Committee Member: Gregory Turk; Committee Member: Joel R. Jackson; Committee Member: Patricio A. Vela

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Barazer, Simon. "Geometric recursion and volumes of moduli spaces : Oriented ribbon graphs, acyclic decomposion, “Cut-and-Join” operators." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM003.

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Dans cette thèse on étudie les liens entre les récurrences topologique et géométrique et les volumes de Masur-Veech des espaces des modules des différentielles quadratiques et Abéliennes. On a choisi de s'intéresser aux graphes en rubans car ils peuvent être utilisé pour calculer les volumes de Masur-Veech. Dans le cas des graphes trivalents on propose une formule de récurrence géométrique, qui a été donnée indépendamment dans "On the Kontsevich geometry of the combinatorial Teichmüller space". On étudie ensuite les graphes en rubans orientés, dans ce cas on propose une décomposition des graph

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