Thèses : « Geometric analysi »

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SOAVE, NICOLA. « Variational and geometric methods for nonlinear differential equations ». Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/49889.

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This thesis is devoted to the study of several problems arising in the field of nonlinear analysis. The work is divided in two parts: the first one concerns existence of oscillating solutions, in a suitable sense, for some nonlinear ODEs and PDEs, while the second one regards the study of qualitative properties, such as monotonicity and symmetry, for solutions to some elliptic problems in unbounded domains. Although the topics faced in this work can appear far away one from the other, the techniques employed in different chapters share several common features. In the firts part, the variational structure of the considered problems plays an essential role, and in particular we obtain existence of oscillating solutions by means of non-standard versions of the Nehari's method and of the Seifert's broken geodesics argument. In the second part, classical tools of geometric analysis, such as the moving planes method and the application of Liouville-type theorems, are used to prove 1-dimensional symmetry of solutions in different situations.

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Karlsson, Jesper. « Symplectic Automorphisms of C2n ». Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-144390.

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This essay is a detailed survey of an article from 1996 published by Franc Forstneric, where he studies symplectic automorphisms of C2n. The vision is to introduce the density property for holomorphic symplectic manifolds. Our idea is that of Dror Varolin when he in 2001 introduced the concept of density property for Stein manifolds. The main result here is the introduction of symplectic shears on C2n equipped with a holomorphic symplectic form and to show that the group generated by finite compositions of symplectic shears is dense in the group of symplectic automorphisms of C2n in the compact-open topology. We give a complete background of the tools from the theory of ordinary differential equations, smooth manifolds, and complex and symplectic geometry that is needed in order to prove this result.
Den här uppsatsen är en detaljerad undersökning av en artikel från 1996 publicerad av Franc Forstneric där han studerar symplektiska automorfismer av C2n. Visionen är att introducera täthetsegenskapen för holomorfa symplektiska mångfalder. Våran idé är som den av Dror Varolin när han 2001 introducerade täthetsegenskapen för Stein mångfalder. Huvudresultatet här är införandet av symplektiska skjuvningar på C2n med en holomorfisk symplektisk form och att visa att gruppen som genereras av ändliga sammansättningar av symplektiska skjuvningar är tät i gruppen av symplektiska automorfismer av C2n i den kompakt-öppna topologin. Vi ger en fullständig bakgrund av de verktyg från teorin om ordinära differentialekvationer, släta mångfalder och komplex och symplektisk geometri som behövs för att visa detta.

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Mascellani, Giovanni. « Fourth-order geometric flows on manifolds with boundary ». Doctoral thesis, Scuola Normale Superiore, 2017. http://hdl.handle.net/11384/85715.

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Litsgård, Malte. « The Orbit Method and Geometric Quantisation ». Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-351508.

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Lidén, Joel. « Stock Price Predictions using a Geometric Brownian Motion ». Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-353586.

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Dahl, Heidi. « Cantor minimal systems and AF-equivalence relations ». Doctoral thesis, Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-1897.

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Parra, Rodrigo. « Equidistribution towards the Green current in complex dynamics ». Doctoral thesis, KTH, Matematik (Inst.), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-34264.

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Given a holomorphic self-map of complex projective space of de-gree larger than one, we prove that there exists a finite collection oftotally invariant algebraic sets with the following property: given anypositive closed (1,1)-current of mass 1 with no mass on any element of this family, the sequence of normalized pull-backs of the current converges to the Green current. Under suitable geometric conditions on the collection of totally invariant algebraic sets, we prove a sharper equidistribution result.

QC 20110530

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Hedén, Isac. « Russell’s hypersurface from a geometric point of view ». Licentiate thesis, Uppsala universitet, Algebra, geometri och logik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-144688.

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Ahlman, Ove. « A zero-one law for l-colourable structures with a vectorspace pregeometry ». Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-168215.

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Skäremo, Holmberg Jonas. « Torsten Brodén och kontinuumhypotesen med en introduktion till naiv mängdlära ». Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-171975.

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Lidberg, Petter. « Barycentric and harmonic coordinates ». Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-179487.

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Bäck, Viktor. « Localization of Multiscale Screened Poisson Equation ». Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-180928.

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Strängberg, Dan. « Legendrian Approximations ». Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-187202.

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Näslund, Marcus. « The Hales-Jewett theorem and its application to further generalisations of m, n, k-games ». Thesis, Uppsala universitet, Algebra och geometri, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202188.

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Asplund, Teo. « Extremal Hypergraphs ». Thesis, Uppsala universitet, Algebra och geometri, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202192.

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Neovius, Sofia. « René Descartes’ Foundations of Analytic Geometry and Classification of Curves ». Thesis, Uppsala universitet, Algebra och geometri, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202147.

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Andréasson, Frida. « Barns sätt att benämna och uppfatta geometriska former : En observation och intervjustudie med förskolebarn ». Thesis, University of Gävle, Faculty of Engineering and Sustainable Development, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-6822.

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Syftet med arbetet är att undersöka hur barn i åldrarna tre till sex år uppfattar de geometriska formerna i sin närmiljö, utan att någon vuxen påvisar formerna. I undersökningen ingår även att se vilka former barnen känner till och hur de benämner formerna. Metoderna som använts i undersökningen är intervjuer och observationer. Huvudresultatet var att barnen såg olika geometriska former i sin förskolemiljö. Hur barnen benämnde formerna varierar mellan matematisk benämning och vardagsbenämning och även egen påhittad benämning. Att förskolorna arbetar olika med matematik gör ingen skillnad för hur barnen benämner formerna.

Viktig Slutsats: Barnen benämner de geometriska formerna med samma benämning som de vuxna i barnens omgivning använder sig av.

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Klisinska, Anna. « Clarkson type inequalities and geometric properties of banach spaces ». Licentiate thesis, Luleå tekniska universitet, Pedagogik, språk och Ämnesdidaktik, 1999. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25946.

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In this thesis Clarkson's inequalities and their generalizations are the main tools. The technique that can be used to prove Clarkson type inequalities in more dimensions is shown. We also establish Clarkson type inequalities in general Banach spaces and point out the connections between Clarkson's inequalities and the concept of type and cotype. The classical results on the von Neumann-Jordan constant, closely related to Clarkson's inequalities, are shortly presented. The concepts of moduli of convexity and smoothness, which are connected with the geometry of Banach spaces, are discussed. Some equivalent ways of describing modulus of convexity and some properties of this function are formulated. The estimation of the modulus of convexity for L(p)-spaces is presented as well. Finally, several examples of moduli of convexity and smoothness for different spaces are described.

Godkänd; 1999; 20070320 (ysko)

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Yaskina, Maryna. « Topics in functional analysis and convex geometry ». Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4346.

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Thesis (Ph.D.)--University of Missouri-Columbia, 2006.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (March 1, 2007) Vita. Includes bibliographical references.

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Roysdon, Michael A. « ON SOME GEOMETRIC AND FUNCTIONAL INEQUALITIES INASYMPTOTIC GEOMETRIC ANALYSIS ». Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1599821442510494.

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Ivarsson, Emmy, et Louise Karlesand. « Höjden gånger bredden gånger antal : Gymnasielevers begreppsuppfattnig i gymnasieskolan ». Thesis, University of Kalmar, School of Human Sciences, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:hik:diva-1218.

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Wink, Matthias. « Ricci solitons and geometric analysis ». Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:3aae2c5e-58aa-42da-9a1b-ec15cacafdad.

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This thesis studies Ricci solitons of cohomogeneity one and uniform Poincaré inequalities for differentials on Riemann surfaces. In the two summands case, which assumes that the isotropy representation of the principal orbit consists of two inequivalent Ad-invariant irreducible summands, complete steady and expanding Ricci solitons have been detected numerically by Buzano-Dancer-Gallaugher-Wang. This work provides a rigorous construction thereof. A Lyapunov function is introduced to prove that the Ricci soliton metrics lie in a bounded region of an associated phase space. This also gives an alternative construction of non-compact Einstein metrics of non-positive scalar curvature due to Böhm. It is explained how the asymptotics of the Ricci flat trajectories induce Böhm's Einstein metrics on spheres and other low dimensional spaces. A numerical study suggests that all other Einstein metrics of positive scalar curvature which are induced by the generalised Hopf fibrations occur in an entirely non-linear regime of the Einstein equations. Extending the theory of cohomogeneity one steady and expanding Ricci solitons, an estimate which allows to prescribe the growth rate of the soliton potential at any given time is shown. As an application, continuous families of Ricci solitons on complex line bundles over products of Fano Kähler Einstein manifolds are constructed. This generalises work of Appleton and Stolarski. The method also applies to the Lü-Page-Pope set-up and allows to cover an optimal parameter range in the two summands case. The Ricci soliton equation on manifolds foliated by torus bundles over products of Fano Kähler Einstein manifolds is discussed. A rigidity theorem is obtained and a preserved curvature condition is discovered. The cohomogeneity one initial value problem is solved for m-quasi-Einstein metrics and complete metrics are described. L^p-Poincaré inequalities for k-differentials on closed Riemann surfaces are shown. The estimates are uniform in the sense that the Poincaré constant only depends on p &GE;1, k ≥ 2 and the genus γ ≥ 2 of the surface but not on its complex structure. Examples show that the analogous estimate for 1-differentials cannot be uniform. This part is based on joint work with Melanie Rupflin.

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Billing, Annika, et Lotta Linton. « En learning study i geometriEn learning study i geometri : Hur elever i årskurs 2 kan lära sig förstå skillnaderna och likheterna mellan kvadrat, rektangel, romb och parallellogram ». Thesis, Stockholm University, Department of Mathematics and Science Education, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-37159.

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Syftet med denna studie har varit att hitta de kritiska aspekterna för eleverna att lära sig särskilja fyrhörningarna, kvadrat, rektangel, romb och parallellogram. Vidare har vi undersökt hur undervisningen kan genomföras för att eleverna ska ha möjlighet att känna igen och korrekt namnge fyrhörningarna samt hur läraren kan ge eleverna möjlighet att erfara variation av vårt valda lärandeobjekt. För att besvara ovanstående frågor har vi använt oss av learning study som forskningsmetod. De 3 momenten som har ingått i vår studie är förtest, lektion och eftertest. Studien har genomförts i årskurs 2 i 3 relativt kunskapshomogena elevgrupper som vi i studien kallar grupp 1, 2 och 3. Alla grupper har efter genomförd undervisning förbättrat sina kunskaper avsevärt. Grupp 1 var den grupp som hade den största kunskapsökningen samt visade det totalt bästa resultatet.

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Jesus, Antonio Batista de. « Estudo numerico da solidificação em geometria anular ». [s.n.], 1998. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263442.

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Orientador: Kamal Abdel Radi Ismail
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
Made available in DSpace on 2018-07-24T15:15:51Z (GMT). No. of bitstreams: 1 Jesus_AntonioBatistade_M.pdf: 6229768 bytes, checksum: 61cd2624ecc0457d83d065bb7385e84a (MD5) Previous issue date: 1998
Resumo: O processo de solidificação de um material de mudança de fase em região anular ao redor de um cilindro resfriado pela passagem de um fluido em seu interior é estudado numericamente com vistas à aplicação em sistemas de armazenamento de calor latente. A solução do problema de mudança de fase é feita utilizando a técnica de imobilização de fronteira, onde aplica-se uma transformação de coordenadas, de maneira que no novo sistema a fronteira móvel e irregular seja fixa e paralela às demais. A condução de calor no material de mudança de fase é acoplada à condução na parede do cilindro e à convecção no interior deste. O método de volumes finitos é utilizado para a discretização das equações do modelo matemático que são em seguida resolvidas computacionalmente. São analisados aspectos relativos à implementação da técnica de imobilização, como o surgimento de termos pseudo-convectivos e pesudo-anisotrópicos por conseqüência da mudança de variáveis. Também são estudados aspectos relacionados com o acoplamento da condução de calor no cilindro e no material de mudança de fase e a convecção no fluido refrigerante. São apresentadas comparações com outros trabalhos da literatura e um conjunto de resultados para o caso de água como material de mudança de fase
Abstract: Solidification of a phase-change material in an annulus around a cylinder, which carries inside it a coolant fluid, is studied numerically for application in latent heat thermal energy storage. The boundaryimmobilization technique is used for solving the phase-change problem. A coordinate transformation is performed so that in the new system the moving and irregular boundary becomes fixed and parallel to the others. Heat conduction in the phase-change material is coupled with conduction in the inner tube wall and convection in the coolant. The fmite-volume methodology is used for discretization of the equations from the mathematical model which are then solved by a computer programo Some aspects related with the application of the boundaryimmobilization technique are analyzed such as the appearance of pseudo-convective and pseudo-anisotropic terms as a consequence of the change of variables. Aspects related to the coupling of conduction ill the cylinder wall and phase-change material with convection in the coolant fluid are also studied. Comparisons with other solutions available in the literature are presented as well results for the specific case of water being the phasechange material
Mestrado
Termica e Fluidos
Mestre em Engenharia Mecânica

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Gasparini, Riccardo. « Engineering Analysis in Imprecise Geometric Models ». FIU Digital Commons, 2014. http://digitalcommons.fiu.edu/etd/1793.

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Engineering analysis in geometric models has been the main if not the only credible/reasonable tool used by engineers and scientists to resolve physical boundaries problems. New high speed computers have facilitated the accuracy and validation of the expected results. In practice, an engineering analysis is composed of two parts; the design of the model and the analysis of the geometry with the boundary conditions and constraints imposed on it. Numerical methods are used to resolve a large number of physical boundary problems independent of the model geometry. The time expended due to the computational process are related to the imposed boundary conditions and the well conformed geometry. Any geometric model that contains gaps or open lines is considered an imperfect geometry model and major commercial solver packages are incapable of handling such inputs. Others packages apply different kinds of methods to resolve this problems like patching or zippering; but the final resolved geometry may be different from the original geometry, and the changes may be unacceptable. The study proposed in this dissertation is based on a new technique to process models with geometrical imperfection without the necessity to repair or change the original geometry. An algorithm is presented that is able to analyze the imperfect geometric model with the imposed boundary conditions using a meshfree method and a distance field approximation to the boundaries. Experiments are proposed to analyze the convergence of the algorithm in imperfect models geometries and will be compared with the same models but with perfect geometries. Plotting results will be presented for further analysis and conclusions of the algorithm convergence

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Raub, Corey Bevan. « Geometric analysis of axisymmetric disk forging ». Ohio : Ohio University, 2000. http://www.ohiolink.edu/etd/view.cgi?ohiou1172778393.

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Benkert, Marc. « Construction and Analysis of Geometric Networks ». [S.l. : s.n.], 2007. http://digbib.ubka.uni-karlsruhe.de/volltexte/1000007167.

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Jonsson, Johan. « Elliptiska kurvor och Lenstras faktoriseringsalgoritm ». Thesis, Karlstad University, Karlstad University, Faculty of Technology and Science, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-4347.

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En elliptisk kurva består av nollställena till ett kubisk polynom i två variabler, sådant att det existerar åtminstone en punkt på kurvan och kurvan är icke-singulär. Punkterna på en sådan kurva bildar en abelsk grupp och olika egenskaper hos dessa grupper beskrivs i den här uppsatsen. Bland annat presenteras Mordell-Weils sats som säger att en elliptisk kurva över en talkropp är en ändligt genererad grupp. Nagell-Lutz sats ger nödvändiga villkor för att en punkt på en rationell elliptisk kurva ska ha ändlig ordning. Resultatet att en elliptisk kurva över de komplexa talen är isomorf med en torus presenteras också. Tillämpningen heltalsfaktorisering presenteras genom en beskrivning av Lenstras algoritm. En implementation av denna algoritm i form av ett datorprogram görs och denna implementation jämförs med den triviala algoritmen för heltalsfaktorisering.

An elliptic curve consists of the zeros of a cubic polynomial i two variables, such that there exists at least one point on the curve and the curve is non-singular. The points on such a curve form an abelian group and various properties of these groups are described in this thesis. Among other things the Mordell-Weil theorem, which states that an elliptic curve over a number field is a finitely generated group, is presented. The Nagell-Lutz theorem gives necessary conditions for a point on a rational elliptic curve to have finite order. Another presented result is that an elliptic curve over the complex numbers is a torus. The application of elliptic curves in integer factorization is presented by describing Lenstra's algorithm. A computer program implementing this algorithm is made and this implementation is compared to the trivial algorithm for integer factorization.

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Lescoat, Thibault. « Geometric operators for 3D modeling using dictionary-based shape representations ». Electronic Thesis or Diss., Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAT005.

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Dans cette thèse, nous étudions les représentations haut-niveau de formes 3D et nous développons les primitives algorithmiques nécessaires à la manipulation d'objets représentés par composition d'éléments. Nous commençons par une revue de l'état de l'art, des représentations bas-niveau usuelles jusqu'à celles haut-niveau, utilisant des dictionnaires. En particulier, nous nous intéressons à la représentation de formes via la composition discrète d'atomes tirés d'un dictionnaire de formes.Nous observons qu'il n'existe aucune méthode permettant de fusionner des atomes (placés sans intersection) de manière plausible ; en effet, la plupart des méthodes requiert des intersections ou alors ne préservent pas les détails grossiers. De plus, très peu de techniques garantissent la préservation de l'entrée, une propriété importante lors du traitement de formes créées par des artistes. Nous proposons donc un opérateur de composition qui propage les détails grossiers tout en conservant l'entrée dans le résultat.Dans le but de permettre une édition interactive, nous cherchons à prévisualiser la composition d'objets lourds. Pour cela, nous proposons de simplifier les atomes avant de les composer. Nous introduisons donc une méthode de simplification de maillage qui préserve les détails grossiers. Bien que notre méthode soit plus contrainte que les approches précédentes qui ne produisent pas de maillage, elle résulte en des formes simplifiées fidèles aux formes détaillées
In this thesis, we study high-level 3D shape representations and developed the algorithm primitives necessary to manipulate shapes represented as a composition of several parts. We first review existing representations, starting with the usual low-level ones and then expanding on a high-level family of shape representations, based on dictionaries. Notably, we focus on representing shapes via a discrete composition of atoms from a dictionary of parts.We observe that there was no method to smoothly blend non-overlapping atoms while still looking plausible. Indeed, most methods either required overlapping parts or do not preserve large-scale details. Moreover, very few methods guaranteed the exact preservation of the input, which is very important when dealing with artist-authored meshes to avoid destroying the artist's work. We address this challenge by proposing a composition operator that is guaranteed to exactly keep the input while also propagating large-scale details.To improve the speed of our composition operator and allow interactive edition, we propose to simplify the input parts prior to completing them. This allow us to interactively previsualize the composition of large meshes. For this, we introduce a method to simplify a detailed mesh to a coarse one by preserving the large details. While more constrained than related approaches that do not produce a mesh, our method still yields faithful outputs

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Arroyave-Tobón, Santiago. « Polyhedral models reduction in geometric tolerance analysis ». Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0720/document.

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L’analyse de tolérances par des ensembles de contraintes repose sur la détermination de l’accumulation de variations géométriques par des sommes et intersections d’ensembles opérandes 6d. Les degrés de liberté des liaisons et les degrés d’invariance des surfaces génèrent des opérandes non-bornés (polyèdres), posant des problèmes de simulation. En 2014, L. Homria proposé une méthode pour résoudre ce problème, consistant à ajouter des limites artificielles(contraintes bouchon) sur les déplacements non-bornés. Même si cette méthode permet la manipulation d’objets bornés (polytopes), les contraintes bouchon augmentent la complexité des simulations. En réponse à cette difficulté, une méthode dérivée est proposée dans cette thèse.Cette méthode consiste à tracer et simplifier les contraintes bouchon au travers des opérations.Puis une seconde stratégie basée sur la décomposition d’un polyèdre en une somme d’un polytope et de lignes droites (associées aux déplacements non-bornés). Cette stratégie consiste à simuler d’une part les sommes de droites, et d’autre part, à déterminer la somme de polytopes dans un sous-espace de dimension inférieur à 6. Ces trois stratégies sont comparées au travers d’une application industrielle. Cela montre que la traçabilité des contraintes bouchons est un aspect fondamental pour contrôler leur propagation et pour réduire le temps de calcul des simulations. Toutefois, cette méthode exige encore de déterminer les limites des déplacements non-bornés. La deuxième méthode, adaptant systématiquement la dimension de l’espace de calcul, elle permet de diminuer davantage le temps de calcul. Ce travail permet d’envisager la mise en oeuvre de cette méthode selon des formulations statistiques avec la prise en compte des défauts de forme des surfaces
The cumulative stack-up of geometric variations in mechanical systems can be modelled summing and intersecting sets of constraints. These constraints derive from tolerance zones or from contact restrictions between parts. The degrees of freedom (DOF) of jointsgenerate unbounded sets (i.e. polyhedra) which are difficult to deal with. L. Homri presented in 2014 a solution based on the setting of fictitious limits (called cap constraints) to each DOFto obtain bounded 6D sets (i.e. polytopes). These additional constraints, however, increase the complexity of the models, and therefore, of the computations. In response to this situation,we defined a derived strategy to control the effects of the propagation of the fictitious limits by tracing and simplifying the generated, new cap constraints. We proposed a second strategy based on the decomposition of polyhedra into the sum of a polytope and a set of straight lines.The strategy consists in isolating the straight lines (associated to the DOF) and summing the polytopes in the smallest sub-space. After solving an industrial case, we concluded that tracing caps constraints during the operations allows reducing the models complexity and,consequently, the computational time; however, it still involves working in 6d even in caseswhere this is not necessary. In contrast, the strategy based on the operands decompositionis more efficient due to the dimension reduction. This study allowed us to conclude that the management of mechanisms’ mobility is a crucial aspect in tolerance simulations. The gain on efficiency resulting from the developed strategies opens up the possibility for doing statistical treatment of tolerances and tolerance synthesis

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Kurtovic, Alen, et Kornelija Gros. « Analys av läroböcker i matematik för lågstadiet : med fokus på geometriska begrepp ». Thesis, Linköpings universitet, Institutionen för beteendevetenskap och lärande, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-176690.

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Syftet med denna studie var att ge förståelse för vilka möjligheter för elevers begreppsutveckling och lärande inom området geometri som finns i elevers matematikläroböcker. Begreppsinlärningen, med hjälp av läroboken, belystes utifrån olika representationsformer som hittades i läroböckernas uppgifter. En läromedelsanalys gjordes med hjälp av den kvalitativa innehållsanalysen. De olika representationsformerna som är bildmodell, språk, konkret modell, symbol och verklighet, användes för att analysera geometriska begrepp i två olika matematikläroböcker för åk 1, 2 och 3. I resultat kom det fram att matematikläroböckerna Prima Matematik och Mästerkatten genom sitt upplägg och sin variation av representationsformer till stor del ger möjlighet till begreppsutveckling av tvådimensionella geometriska begrepp. Mest förekommande representationsformer av geometriska begrepp var dock i bildform vilket tyder på att begreppsutveckling enligt matematikläroboken sker mest via bilder. Om begreppsutvecklingen ska ske på tillfredsställande sätt behöver begreppen angripas utifrån olika representationsformer som verklighetsanknytning, kommunikation mellan elever samt laboration.

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Hochard, Raphaël. « Théorèmes d’existence en temps court du flot de Ricci pour des variétés non-complètes, non-éffondrées, à courbure minorée ». Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0006/document.

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Le flot de Ricci est une équation aux dérivées partielles qui régit l’évolution d’une métrique riemannienne dépendant d’un paramètre de temps sur une variété différentielle. D’abord introduit et étudié par R. Hamilton, il est à l’origine de la solution de la conjecture de géométrisation des variétés compactes de dimension 3 par G. Perelman en 2001. La théorie classique concernant l’existence en temps court des solutions, due à Hamilton et à Shi, garantit (en dimension quelconque) l’existence d’un flot soit sur une variété compacte, soit lorsque la métrique initiale est complète avec une borne sur la norme du tenseur de courbure. En l’absence de cette borne, on conjecture qu’on peut trouver, à partir de la dimension 3, des données initiales pour lesquelles il n’existe pas de solution. Dans cette thèse, on démontre des théorèmes d’existence en temps court du flot sous des hypothèses plus faibles qu’une borne sur la norme du tenseur de courbure. Pour cela, on introduit une construction générale qui, pour une métrique riemannienne g quelconque sur une variété M, pas nécessairement complète, permet de produire une solution de l’équation du flot sur un domaine ouvert D de l’espace-temps M * [0,T] qui contient la tranche de temps initiale, avec g pour donnée initiale. On montre ensuite que sous des hypothèses adaptées sur la métrique g, on contrôle la forme du domaine D. En particulier, lorsque la métrique g est complète, D contient un ensemble de la forme M * [0,t], avec t>0, ce qui revient à dire qu’il existe un flot au sens classique dont la donnée initiale est g. Les « hypothèses adaptées » qui conduisent à des théorèmes d’existence sont de trois types. Dans tout les cas, on suppose une minoration uniforme du volume des boules de rayon au plus 1, à quoi on ajoute : a) en dimension 3, une minoration du tenseur de Ricci, b) en dimension n, une minoration d’une notion de courbure dite « courbure isotrope I » ou bien c) en dimension n, une borne sur la norme du tenseur de Ricci et une hypothèse qui garantit la proximité au sens métrique des boules de rayon au plus 1 avec une boule de même rayon dans un espace métrique obtenu comme le produit cartésien d’un espace de dimension 3 et d’un facteur euclidien de dimension n-3. De plus, avec ces résultats d’existence viennent des estimations sur les propriétés de régularisation du flot quantifiées en fonction des hypothèses sur la donnée initiale. La possibilité ainsi offerte de régulariser, globalement ou localement, pour un temps et avec des estimations quantifiés, une métrique initiale a des conséquence sur les espaces métriques singuliers obtenus comme limites, pour la distance de Gromov-Hausdorff, de suites de variétés satisfaisant uniformément aux conditions a), b) ou c). En effet, des théorèmes de compacité classiques pour le flot de Ricci permettent d’extraire un flot limite, étant donnée une suite de métriques initiales satisfaisant uniformément à ces hypothèses, et possédant donc toutes un flot pour un temps contrôlé. Lorsque les métriques en question approchent, pour la topologie de Gromov-Hausdorff, un espace singulier, cette solution limite s’interprète comme un flot régularisant l’espace singulier en question, et son existence contraint la topologie de cet espace singulier
The Ricci Flow is a partial differential equation governing the evolution of a Riemannian metric depending on a time parameter t on a differential manifold. It was first introduced and studied by R. Hamilton, and eventually led to the solution of the Geometrization conjecture for closed three-dimensional manifolds by G. Perelman in 2001. The classical short-time existence theory for the Ricci Flow, due to Hamilton and Shi, asserts, in any dimension, the existence of a flow starting from any initial metric when the underlying manifold in compact, or for any complete initial metric with a bound on the norm of the curvature tensor otherwise. In the absence of such a bound, though, the conjecture is that starting from dimension 3 one can find such initial data for which there is no solution. In this thesis, we prove short-time existence theorems under hypotheses weaker than a bound on the norm of the curvature tensor. To do this, we introduce a general construction which, for any Riemannian metric g (not necessarily complete) on a manifold M, allows us to produce a solution to the equation of the flow on an open domain D of the space-time M * [0,T] which contains the initial time slice, with g as an initial datum. We proceed to show that under suitable hypotheses on g, one can control the shape of the domain D, so that in particular, D contains a subset of the form M * [0,t] with t>0 if g is complete. By « suitable hypothesis », we mean one of the following. In any case, we assume a lower bound on the volume of balls of radius at most 1, plus a) in dimension 3, a lower bound on the Ricci tensor, b) in dimension n, a lower bound on the so-called « isotropic curvature I » or c) in dimension n, a bound on the norm of the Ricci tensor, as well as a hypothesis which garanties the metric proximity of every ball of radius at most $1$ with a ball of the same radius in a metric product between a three-dimensional metric space and a $n-3$ dimensional Euclidian factor. Moreover, with these existence results come estimates on the existence time and regularization properties of the flow, quantified in term of the hypotheses on the initial data. The possibility to regularize metrics, locally or globally, with such estimates has consequences in terms of the metric spaces obtained as limits, in the Gromov-Hausdorff topology, of sequences of manifolds uniformly satisfying a), b) or c). Indeed, the classical compactness theorems for the Ricci Flow allow for the extraction of a limit flow for any sequence of initial metrics uniformly satisfying the hypotheses and thus possessing a flow for a controlled amount of time. In the case when these metrics approach a singular space in the Gromov-Hausdorff topology, such a limit solution can be interpreted as a flow regularizing the singular limit space, the existence of which puts constraints on the topology of this space

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Lind, Andreas. « Holomorphic automorphisms of Danielewski surfaces ». Doctoral thesis, Sundsvall : Dep. of Natural Sciences, Engineering and Mathematics, Mid Sweden University, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-10360.

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Lindgren, Natalia. « Geometric and Mechanical Analysis of Aortic Aneurysm ». Thesis, KTH, Hållfasthetslära, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-284352.

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The aorta, the main and largest artery in the human body, is susceptible for many types of problems. One of the most common aortic disease is the formation of an aneurysm. Endovascular aortic aneurysm repair (EVAR) is a minimally invasive treatment option for aortic aneurysms, involving the deployment of an expandable stent graft within the aorta without operating the aneurysm directly. With 1.5 to 43 % of EVAR patients having postoperative complications, research to help predict these complications of EVAR is of essence. In this study, the deformations of the aorta induced by a deployed stent graft have been investigated and visualized in order to aid understanding of the geometrical behaviour of the aorta post EVAR. This has been carried out by the development and analysis of patient-specific aortic 3D reconstruction models, 3D printed physical models and FE simulation models. A qualitative assessment of the deformations was achieved by superimposing reconstructed geometries, revealing a light straightening of the aorta and iliac vessels, as well as anterior movement of the iliac branches. Based on the good agreement between the simulated and reconstructed geometries, the findings suggest that such deformations could be derived from the pressure being removed from the aneurysm due to the deployed stent graft, in combination with stent radial forces from the proximal and distal landing zones. Despite that the simulation seemed to underestimate distal movement of the iliac vessel, this study emphasizes the potential of 3D printing and FE analysis as promising tools for planning and research of EVAR.
Den stora kroppspulsådern, aortan, kan drabbas av flera olika sjukdomstillstånd. En av de vanligaste är bildandet av en aortaaneurysm. Endovaskulär Aneruysm Reparation (EVAR) är en operationsteknik för att behandla aortaaneurysmer och involverar positionering av ett rörformat, självexpanderande stentgraft innanför aortaaneurysmen via ljumskartärerna. Eftersom 1,5 till 43 % av EVAR-patienter råkar ut för postoperativa komplikationer är det väsentligt att bedriva vidare studier för att förutse dessa. I denna studie har deformationerna av en aorta på grund av positionerade stentar undersökts och visualiserade för att underlätta förståelsen av aortans geometriska beteende efter EVAR. Detta har gjorts genom att utveckla och analysera patientspecifika 3D-rekonstruktioner, 3D-printade fysiska modeller och simulerade modeller av en aorta. En kvalitativ bedömning av deformationerna uppnåddes genom att superpositionering av rekonstruerade geometrier, vilket avslöjade en lätt uträtning av aortan och tarmbensartärerna, samt en framförflyttning av de senare. Baserat på den goda överensstämmelsen mellan de simulerade och rekonstruerade modellerna, antyder resultaten att sådana deformationer kan härledas av att trycket avlägsnats från aneurysmen på grund av stentgraften, i kombination med radiellt tryck från stentar över och under aneurysmen. Trots att simuleringen underskattade framförflyttningen av tarmbensartärerna, belyser denna studie potentialen hos 3D-printing och FE-analyser som ett värdefullt verktyg för att planera och studera EVAR.

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Tiwari, Abhishek Murray Richard M. Murray Richard M. « Geometric analysis of spatio-temporal planning problems / ». Diss., Pasadena, Calif. : Caltech, 2007. http://resolver.caltech.edu/CaltechETD:etd-05202007-135411.

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Gautam, Sushrut Zubin Sulaksh. « Two geometric obstruction results in harmonic analysis ». Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=1872162601&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.

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Zaidi, Syed Ali Raza. « Stochastic geometric analysis of cognitive wireless networks ». Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/5490/.

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The prime objective of this thesis is to study these interference management mechanisms for quantifying the potential gains of CRs in terms of spectral utility. Interference modeling is the most important aspect of this extensive evaluation. Accurate modeling of the cognitive network interference, accommodating its stochastic nature (triggered by both spatial and propagation dynamics) is therefore a central contribution of this thesis. Since the aggregate interference from CRs is a function of the access strategy, two wellknown access paradigms, namely, spectrum underlay and interweave, are thoroughly analyzed. For the spectrum underlay access mechanism, a guard-zone based interference control mechanism is examined. Specifically, CRs are obliged to maintain silence in a spatial no-talk zone of a certain radius which is centered on a primary receiver. It is shown that the radius of the guard-zone is strongly coupled with the medium access and routing strategies employed by the CRs. While the guard-zone provides a robust mechanism to protect a single primary user, it is a challenging task to achieve the same for a large scale primary network. An alternative degree of freedom, i.e., medium access probability (MAP), can easily address this issue. Furthermore, for a large CR network (CRN), significant gains can be harnessed by furnishing nodes with multiple antennas. Performance evaluation of such a network with MAP adaptation is one of the key contributions of this dissertation. It is shown that the multi-antenna paradigm results in a “win-win” situation for both primary and secondary users. In order to facilitate multi-hop communication between CRs, a quality-of-service (QoS) aware routing is also devised. We show that there exists an optimal MAP which maximizes the spectral utility of the secondary network. However, such an optimal point often lies outside the permissible operational regime dictated by the primary user’s co-existence constraint. Another approach can be adopted where we exploit a different degree of freedom, i.e., the transmit power employed by the CRs. Thus CRs can extend their operational regime by adapting one degree of freedom and selecting an optimal value for another. The optimality of this adapt-and-optimize strategy is shown for a variety of networking paradigms. Finally, the performance of the primary user in the presence of the interference-channel-aware CRs is quantified. For a CRN employing an interweave configuration, the performance of a legacy user is investigated. The impact of different network parameters is explored. It is shown that the cooperation between the CR transmitter and receiver can significantly improve the performance of the interference avoidance mechanism. Furthermore,we highlight that ignoring the self-coexistence criteria for the secondary network leads to an over-estimation of the aggregate interference and consequently results in pessimistic design strategies. The analysis is extended to consider the performance of a large primary network. Finally, a novel modification in the analytical approach is proposed so that performance guarantees can be provided to the existing users. Another contribution of this dissertation is to evaluate (currently very topical and very important) the energy efficiency of an ad hoc wireless network. The key motivation is to investigate the impact of the co-channel interference on the network-wide energy consumption. Both energy and spectral efficiency problems have a common origin, i.e., growing bandwidth demand. Also the design of both problems require understanding of co-channel interference management strategies. Finally,we try to put pull together all the analysis and simulation results to look at both open problems and directions for future research in this highly topical, and strategically important research areas of enabling high speed, future wireless networks.

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SEMOLA, DANIELE. « Recent developments about Geometric Analysis on RCD(K,N) spaces ». Doctoral thesis, Scuola Normale Superiore, 2020. http://hdl.handle.net/11384/94195.

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This thesis is about some recent developments on Geometric Analysis and Geometric Measure Theory on RCD(K,N) metric measure spaces that have been obtained in [8,48,49,51,52,171]. After the preliminary Chapter 1, where we collect the basic notions of the theory relevant for our purposes, Chapter 2 is dedicated to the presentation of a simplified approach to the structure theory of RCD(K,N) spaces via δ- splitting maps developed in collaboration with Brué and Pasqualetto. The strategy is similar to the one adopted by Cheeger-Colding in the theory of Ricci limit spaces and it is suitable for adaptations to codimension one. Chapter 3 is devoted to the proof of the constancy of the dimension conjecture for RCD(K,N) spaces. This has been obtained in a joint work with Brué, where we proved that dimension of the tangent space is the same almost everywhere with respect to the reference measure, generalizing a previous result obtained by Colding-Naber for Ricci limits. The strategy is based on the study of regularity of flows of Sobolev vector fields on spaces with Ricci curvature bounded from below, which we find of independent interest. In Chapters 4 and 5 we present the structure theory for boundaries of sets of finite perimeter in this framework, as developed in collaboration with Ambrosio, Brué and Pasqualetto. An almost complete generalization of De Giorgi’s celebrated theorem is given, opening to further developments for Geometric Measure Theory in the setting of synthetic lower bounds on Ricci curvature. In Chapter 6 we eventually collect some results about sharp lower bounds on the first Dirichlet eigenvalue of the p-Laplacian based on a joint work with Mondino. We also address the problems of rigidity and almost rigidity, heavily relying on the compactness and stability properties of RCD spaces.

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Ammoura, Adnan. « Geometrie analagmatique et triangulation de delaunay : contribution de l'analyse des donnees aux etudes marketing sur les medicaments ». Paris 6, 1988. http://www.theses.fr/1988PA066022.

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Dans la partie theorique, nous presentons la contribution de la triangulation de delaunay a la classification ascendante hierarchique; nous montrons ici l'unicite de la decomposition de delaunay dans le cas generique ou les facettes de l'enveloppe convexe de l'ensemble a classer sont toutes des simplexes. Grace a cette recherche theorique, nous ponvons dire que la methode de triangulation de delaunay est a la base de l'algorithme accelere de la cah. Dans la partie appliquee, on presente la contribution de l'analyse des donnees aux etudes marketing sur les medicaments en appliquant l'afc sur le tableau de donnees qui contient 99 medicaments et qui a pour objectif: la recherche du medicament le plus utilise et le plus apprecie par les patientes interrogees, leurs conjoints et leurs enfants. Grace a la technique du regroupement des individus en categories semblables par combinaison lineaire des modalites du signalement, nous avons pu determiner clairement les medicaments les plus utilises et les plus apprecies par les patientes, leurs conjoints et leurs enfants en fonction des maux, de la region, de la classe d'age et de la classe sociale

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Rao, Arvind Satya. « Weak solutions to a Monge-Ampère type equation on Kähler surfaces ». Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/582.

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In the context of moment maps and diffeomorphisms of Kähler manifolds, Donaldson introduced a fully nonlinear Monge-Ampère type equation. Among the conjectures he made about this equation is that the existence of solutions is equivalent to a positivity condition on the initial data. Weinkove later affirmed Donaldson's conjecture using a gradient flow for the equation in the space of Kähler potentials of the initial data. The topic of this thesis is the case when the initial data is merely semipositive and the domain is a closed Kähler surface. Regularity techniques for degenerate Monge-Ampère equations, specifically those coming from pluripotential theory, are used to prove the existence of a bounded, unique, weak solution. With the aid of a Nakai criterion, due to Lamari and Buchdahl, it is shown that this solution is smooth away from some curves of negative self-intersection.

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Lindahl, Karl-Olof. « On the linearization of non-Archimedean holomorphic functions near an indifferent fixed point ». Doctoral thesis, Växjö : Växjö University Press, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1713.

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Enqvist, Per. « Spectral Estimation by Geometric, Topological and Optimization Methods ». Doctoral thesis, Stockholm, 2001. http://media.lib.kth.se:8080/kthdisseng.html.

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Bonelli, Rebeca Cristina [UNESP]. « Desigualdades matemáticas e aplicações ». Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/151180.

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Submitted by REBECA CRISTINA BONELLI (rebeca_bonelli@hotmail.com) on 2017-07-21T19:04:33Z No. of bitstreams: 1 bonelli_rebeca_rcl.pdf: 997675 bytes, checksum: deb5cde186de3e644c8b5ceaa2aef072 (MD5)
Approved for entry into archive by LUIZA DE MENEZES ROMANETTO (luizamenezes@reitoria.unesp.br) on 2017-07-21T20:52:28Z (GMT) No. of bitstreams: 1 bonelli_rebeca_me_rcla.pdf: 997675 bytes, checksum: deb5cde186de3e644c8b5ceaa2aef072 (MD5)
Made available in DSpace on 2017-07-21T20:52:28Z (GMT). No. of bitstreams: 1 bonelli_rebeca_me_rcla.pdf: 997675 bytes, checksum: deb5cde186de3e644c8b5ceaa2aef072 (MD5) Previous issue date: 2017-07-14
Este trabalho apresenta um estudo sobre importantes desigualdades matemáticas e explora aplicações na resolução de problemas de Geometria, Álgebra e Análise, que podem ser abordados no Ensino Médio.
This work presents a study on important mathematical inequalities and explores applications in solving problems of Geometry, Algebra and Analysis, which can be approached in High School.

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Aydin, Ayhan. « Geometric Integrators For Coupled Nonlinear Schrodinger Equation ». Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12605773/index.pdf.

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Multisymplectic integrators like Preissman and six-point schemes and a semi-explicit symplectic method are applied to the coupled nonlinear Schrö
dinger equations (CNLSE). Energy, momentum and additional conserved quantities are preserved by the multisymplectic integrators, which are shown using modified equations. The multisymplectic schemes are backward stable and non-dissipative. A semi-explicit method which is symplectic in the space variable and based on linear-nonlinear, even-odd splitting in time is derived. These methods are applied to the CNLSE with plane wave and soliton solutions for various combinations of the parameters of the equation. The numerical results confirm the excellent long time behavior of the conserved quantities and preservation of the shape of the soliton solutions in space and time.

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Rucci, Marco. « Geometric Surface Processing and Virtual Modeling ». Doctoral thesis, Università degli studi di Padova, 2013. http://hdl.handle.net/11577/3426305.

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In this work we focus on two main topics "Geometric Surface Processing" and "Virtual Modeling". The inspiration and coordination for most of the research work contained in the thesis has been driven by the project New Interactive and Innovative Technologies for CAD (NIIT4CAD), funded by the European Eurostars Programme. NIIT4CAD has the ambitious aim of overcoming the limitations of the traditional approach to surface modeling of current 3D CAD systems by introducing new methodologies and technologies based on subdivision surfaces in a new virtual modeling framework. These innovations will allow designers and engineers to transform quickly and intuitively an idea of shape in a high-quality geometrical model suited for engineering and manufacturing purposes. One of the objective of the thesis is indeed the reconstruction and modeling of surfaces, representing arbitrary topology objects, starting from 3D irregular curve networks acquired through an ad-hoc smart-pen device. The thesis is organized in two main parts: "Geometric Surface Processing" and "Virtual Modeling". During the development of the geometric pipeline in our Virtual Modeling system, we faced many challenges that captured our interest and opened new areas of research and experimentation. In the first part, we present these theories and some applications to Geometric Surface Processing. This allowed us to better formalize and give a broader understanding on some of the techniques used in our latest advancements on virtual modeling and surface reconstruction. The research on both topics led to important results that have been published and presented in articles and conferences of international relevance.
In questa tesi sono trattati due argomenti principali "Geometric Surface Processing" e "Virtual Modeling". L'ispirazione e la coordinazione di gran parte del lavoro di ricerca contenuto nella tesi e' dovuta al progetto New Interactive and Innovative Technologies for CAD (NIIT4CAD), finanziato dall'European Eurostars Programme. NIIT4CAD ha l'ambizioso obiettivo di superare le limitazioni degli approcci tradizionali alla modellazione di superfici dei moderni sistemi di progettazione assistita al calcolatore, introducendo nuove metodologie e tecnologie basate su superfici di suddivisione in un nuovo framework virtuale di modellazione. Tali innovazioni permetteranno progettisti ed ingegneri a trasformare velocemente ed intuitivamente l'idea di una forma in un modello geometrico ad alta qualita' adatto per scopi ingegneristici e di produzione. Uno degli obiettivi della tesi e' proprio la ricostruzione e modellazione di superfici, rappresentanti oggetti a topologia arbitraria, partendo da curve 3D irregolari acquisite tramite un dispositivo smart-pen sviluppato ad-hoc. La tesi e' organizzata in due parti: "Geometric Surface Processing" e "Virtual Modeling". Durante lo sviluppo della pipeline geometrica del nostro sistema di modellazione virtuale, abbiamo affrontato diverse problematiche che hanno attratto il nostro interesse ed aperto nuove aree di ricerca e sperimentazione. Nella prima parte, presentiamo tali teorie ed alcune applicazioni nell'ambito di Geometric Surface Processing. Questo ci permette di formalizzare meglio e dare una visione piu' ampia ad alcune delle tecniche usate nelle ultime versioni del nostro sistema ricostruzione di superfici e modellazione virtuale. Il lavoro di ricerca per entrambi gli argomenti ha portato al raggiungimento di importanti risultati che sono stati pubblicati e presentati in articoli e conferenze di rilevanza internazionale.

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Dimitrov, Darko [Verfasser]. « Geometric applications of principal component analysis / Darko Dimitrov ». Berlin : Freie Universität Berlin, 2009. http://d-nb.info/102346392X/34.

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Isgro, Francesco. « Geometric methods for video sequence analysis and applications ». Thesis, Heriot-Watt University, 2001. http://hdl.handle.net/10399/495.

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Kramer, Glenn Andrew. « Geometric reasoning in the kinematic analysis of mechanisms ». Thesis, University of Sussex, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.385673.

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McManigle, John E. « Three-dimensional geometric image analysis for interventional electrophysiology ». Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:2f36fa8e-9c64-4807-97c0-25e63398da7e.

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Improving imaging hardware, computational power, and algorithmic design are driving advances in interventional medical imaging. We lay the groundwork here for more effective use of machine learning and image registration in clinical electrophysiology. To achieve identification of atrial fibrosis using image data, we registered the electroanatomic map (EAM) data of atrial fibrillation (AF) patients undergoing pulmonary vein isolation (PVI) with MR (n = 16) or CT (n = 18) images. The relationship between image features and bipolar voltage was evaluated using single-parameter regression and random forest models. Random forest performed significantly better than regression, identifying fibrosis with area under the receiver operating characteristic curve (AUC) 0.746 (MR) and 0.977 (CT). This is the first evaluation of voltage prediction using image data. Next, we compared the character of native atrial fibrosis with ablation scar in MR images. Fourteen AF patients undergoing repeat PVI were recruited. EAM data from their first PVI was registered to the MR images acquired before the first PVI (‘pre-operative’) and before the second PVI ('post-operative' with respect to the first PVI). Non-ablation map points had similar characteristics in the two images, while ablation points exhibited higher intensity and more heterogeneity in post-operative images. Ablation scar is more strongly enhancing and more heterogeneous than native fibrosis. Finally, we addressed myocardial measurement in 3-D echocardiograms. The circular Hough transform was modified with a feature asymmetry filter, epicardial edges, and a search constraint. Manual and Hough measurements were compared in 5641 slices from 3-D images. The enhanced Hough algorithm was more accurate than the unmodified version (Dice coefficient 0.77 vs. 0.58). This method promises utility in segmentation-assisted cross-modality registration. By improving the information that can be extracted from medical images and the ease with which that information can be accessed, this progress will contribute to the advancing integration of imaging in electrophysiology.

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Thakkar, Kairavee K. « A Geometric Analysis of Time Varying Electroencephalogram Vectors ». University of Cincinnati / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1613745734396658.

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