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Dissertations / Theses on the topic 'Affine'
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Chen, Zongbin. "Pureté des fibres de Springer affines pour GL_4." Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112266/document.
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La thèse consiste de deux parties. Dans la première partie, on montre la pureté des fibres de Springer affines pour $\gl_{4}$ dans le cas non-ramifié. Plus précisément, on construit une famille de pavages non standard en espaces affines de la grassmannienne affine, qui induisent des pavages en espaces affines de la fibre de Springer affine. Dans la deuxième partie, on introduit une notion de $\xi$-stabilité sur la grassmannienne affine $\xx$ pour le groupe $\gl_{d}$, et on calcule le polynôme de Poincaré du quotient $\xx^{\xi}/T$ de la partie $\xi$-stable $\xxs$ par le tore maximal $T$ par une processus analogue de la réduction de Harder-NarasimhanThis thesis consists of two parts. In the first part, we prove the purity of affine Springer fibers for $\gl_{4}$ in the unramified case. More precisely, we have constructed a family of non standard affine pavings for the affine grassmannian, which induce an affine paving for the affine Springer fiber. In the second part, we introduce a notion of $\xi$-stability on the affine grassmannian $\xx$ for the group $G=\gl_{d}$, and we calculate the Poincaré polynomial of the quotient $\xx^{\xi}/T$ of the stable part $\xxs$ by the maximal torus $T$ by a process analogue to the Harder-Narasimhan reduction
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Azam, Saeid. "Extended affine Lie algebras and extended affine Weyl groups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ27440.pdf.
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Li, Yiqiang. "Affine canonical bases /." Search for this dissertation online, 2006. http://wwwlib.umi.com/cr/ksu/main.
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Deconchy, Vincent. "Géométrie affine symplectique." Montpellier 2, 1999. http://www.theses.fr/1999MON20076.
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La geometrie affine symplectique consiste en l'etude des invariants des hypersurfaces de l'espace symplectique standard sous l'action du groupe affine symplectique. On peut considerer qu'il s'agit d'une generalisation aux dimensions superieures de la geometrie equiaffine des courbes dans le plan, en notant que dans ce cas le groupe symplectique et le groupe special lineaire coincident. Sachant qu'il existe sur une hypersurface d'un espace symplectique un champ de droites privilegie, on construit un champ transverse adapte (le vecteur normal (affine) symplectique) dont on donne une interpretation geometrique, et une serie d'autres invariants affines symplectiques qui caracterisent les hypersurfaces a transformations affines symplectiques pres. Le vecteur normal affine symplectique induit sur l'hypersurface une forme volume permettant de calculer son volume symplectique. Apres avoir traite une serie d'exemple dont les spheres symplectiques, on etudie l'existence eventuelle d'une inegalite isoperimetrique en geometrie affine symplectique, en s'interessant aux variations successives du volume symplectique. L'etude de la variation seconde pour les spheres symplectiques montre que tres certainement il n'y a pas d'inegalite isoperimetrique en geometrie affine symplectique.
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Kohl, Stefan. "Restklassenweise affine Gruppen." [S.l. : s.n.], 2005. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB12168144.
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Fring, A. "Affine Toda field theory." Thesis, Imperial College London, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.295149.
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Holtom, Paul Andrew. "Affine-invariant symmetry sets." Thesis, University of Liverpool, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367704.
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Moakes, Matthew George. "On quantum affine algebras." Thesis, King's College London (University of London), 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.406170.
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Andrei, Octavian. "3D affine coordinate transformations." Thesis, KTH, Geodesi och satellitpositionering, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-199846.
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This thesis investigates the three-dimensional (3D) coordinate transformation from a globalgeocentric coordinate system to a national terrestrial coordinate system. Numerical studies arecarried out using the Swedish geodetic data SWEREF 93 and RT90/RH70. Based on theHelmert transformation model with 7-parameters, two new models have been studied: firstly ageneral 3D affine transformation model has been developed using 9-parameters (threetranslations, three rotations and three scale factors) and secondly the model with 8-parameters(three translations, three rotations and two scale factors) has been derived. To estimate the 3Dtransformation parameters from given coordinates in the two systems, the linearizedobservation equations were derived. Numerical tests were carried out using a local (North,East, Up) topocentric coordinate system derived from the given global geocentric system. Thetransformation parameters and the residuals of the coordinates of the common points werecomputed. The investigation shows the horizontal scale factor is significantly different by thevertical scale factor. The residuals of the control points were expressed in a separate (North,East, Up) coordinate system for each control point. Some investigations on the weightingprocess between horizontal and vertical components were also carried out, and an optimalweighting model was derived in order to reduce the residuals in horizontal componentswithout changing the coordinates.
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Welch, Amanda Renee. "Double Affine Bruhat Order." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/89366.
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Given a finite Weyl group W_fin with root system Phi_fin, one can create the affine Weyl group W_aff by taking the semidirect product of the translation group associated to the coroot lattice for Phi_fin, with W_fin. The double affine Weyl semigroup W can be created by using a similar semidirect product where one replaces W_fin with W_aff and the coroot lattice with the Tits cone of W_aff. We classify cocovers and covers of a given element of W with respect to the Bruhat order, specifically when W is associated to a finite root system that is irreducible and simply laced. We show two approaches: one extending the work of Lam and Shimozono, and its strengthening by Milicevic, where cocovers are characterized in the affine case using the quantum Bruhat graph of W_fin, and another, which takes a more geometrical approach by using the length difference set defined by Muthiah and Orr.Doctor of Philosophy
The Bruhat order is a way of organizing elements of the double affine Weyl semigroup so that we have a better understanding of how the elements interact. In this dissertation, we study the Bruhat order, specifically looking for when two elements are separated by exactly one step in the order. We classify these elements and show that there are only finitely many of them.
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Smilga, Ilia. "Pavages de l'espace affine." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112298/document.
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Pour tout entier naturel impair d, on construit un domaine fondamental pour l'action sur l'espace affine de dimension 2d+1 de certains groupes de transformations affines libres non abéliens, discrets, agissant proprement et de partie linéaire Zariski-dense dans SO(d+1, d). Pour tout groupe de Lie semisimple réel non compact G, on construit ensuite un groupe de transformations affines de son algèbre de Lie g qui est libre non abélien, discret, agit proprement sur g et a sa partie linéaire Zariski-dense dans Ad G. Enfin, on donne quelques résultats sur le comportement local des fonctions harmoniques sur le triangle de Sierpinski, plus précisément de leur restriction à un bord du triangleFor every odd positive integer d, we construct a fundamental domain for the action on the 2d+1-dimensional space of certain groups of affine transformations which are free, nonabelian, act properly discontinuously and have linear part Zariski-dense in SO(d+1,d). Next for every semisimple noncompact real Lie group G, we construct a group of affine transformations of its Lie algebra g which is free, nonabelian, acts properly discontinuously and has linear part Zariski-dense in Ad G. Finally, we give some results about the local behavior of harmonic functions on the Sierpinski triangle restricted to a side of the triangle
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Barucchieri, Bianca. "Affine Hermite-Lorentz manifolds." Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0153/document.
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Dans ce travail nous nous intéressons aux groupes cristallographiques, i.e. aux sous-groupes du groupe des transformations affines qui agissent proprement discontinûment et de façon cocompacte sur l’espace affine. Ce sont les groupes fondamentaux des variétés affines compactes et complètes. Nous classifions les groupes cristallographiques dont la partie linéaire préserve une forme hermitienne de signature (n,1). Grunewald et Margulis ont prouvé que ces groupes cristallographiques sont virtuellement résolubles (la conjecture d’Auslander affirme que c’est toujours le cas). Notre classification est effectuée pour n ≤ 3. Elle correspond à la classification, à revêtement fini près, des variétés Hermite-Lorentz plates, compactes et complètes en dimension complexe inférieure ou égale à4. Ce travail est inspiré par ceux menés par Bieberbach, puis Fried, et enfin Grunewald et Margulis sur les groupes cristallographiques dont la partie linéaire préserve une forme quadratique définie positive ou lorentzienne. En effectuant cette classification, nous avons été amené à étudier certains familles d’algèbres de Lie nilpotentes de dimension 8. Nous avons ensuite étendu cette classification à celle de toutes les algèbres de Lie 3-nilpotentes de dimension 8 ayant l’algèbre de Lie libre 3-nilpotente à 3générateurs pour quotient. Ce résultat peut être vu comme un pas dans la direction d’une classification des algèbres de Lie nilpotentes de dimension 8. Ensuite nous nous sommes demandé lesquelles de ces algèbres admettent une métrique pseudo-riemannienne plate et nous avons donné une réponse partielleIn this work we deal with crystallographic groups, i.e. the subgroups of the group of affine transformations that act properly discontinuously and cocompactly on affine space. In otherwords they are the fundamental groups of compact and complete affine manifolds. In this thesis we classify such groups with the additional hypothesis that the linear part preserves a Hermitian form of signature (n,1). Grunewald and Margulis proved that such crystallographic groups are virtually solvable (the Auslander conjecture states that this is always true). Our classification is for n ≤ 3. It corresponds to a classification, up to finite covering, and for complex dimension at most 4, of flat compact complete Hermite-Lorentz manifolds. This is inspired by the works done by Bieberbach,then Fried, and finally Grunewald and Margulis who classified crystallographic groups whose line arpart preserves a positive definite or Lorentzian quadratic form. Making this classification we had to classify a family of 8-dimensional nilpotent Lie algebras. We then extended this classification toall the 8-dimensional 3-step nilpotent Lie algebras having the free 2-step nilpotent Lie algebra on 3generators as quotient. This result can be seen as a step in the direction of a general classification of nilpotent Lie algebras of dimension 8. We then wondered which of these Lie algebras admit flat pseudo-Riemannian metrics and gave a partial answer to this question
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Al, Harbat Sadek. "Groupe de tresses affine, algèbre de Temperley-Lieb affine et trace de Markov." Paris 7, 2013. http://www.theses.fr/2013PA077204.
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Dans cette thèse, on définit une tour d'algèbres de Temperley-Lieb affines de type à sur laquelle on définit une trace de Markov et on montre qu'il y a une unique telle trace. Pour y parvenir, on travaille sur quatre niveaux de type  : groupes de tresses affines, groupes de Coxeter affines, algèbres de Hecke affines et algèbres de Temperley-Lieb affines. Au niveau des tresses, on montre que le groupe de tresses affine de type À à n+1 générateurs se surjecte sur le groupe de tresses affine de type A à n générateurs, on montre que cette surjection provient d'un quotient sur un certain sous groupe et on définit une fermeture d'un élément de ce groupe que l'on appelle un lien affine. Au niveau Coxeter, on étudie le groupe de Coxeter affine de type à à n+1 générateurs, on donne un système complet de représentants des classes à gauche et des double-classes du groupe de Coxeter affine de type À à n générateurs, puis on classifie les éléments pleinement commutatifs et on en donne une forme normale. Au niveau Hecke, on définit une tour d'algèbres de Hecke affines de type À, on montre que cette tour est une tour d'inclusions, et on montre que cette tour "se surjecte" sur la tour d'algèbres de Hecke de type Ã. Au niveau Temperley-Lieb, on définit une tour d'algèbres de Temperley-Lieb affines de type À, on définit une trace de Markov comme une collection de traces sur cette tour dans sa forme la plus générale (compatibilité avec les liens affines). On obtient l'existence d'une telle trace en montrant que la tour mentionnée "se surjecte" sur la tour d'algèbres de Temperley-Lieb de type À et finalement on montre que cette trace est unique en utilisant la forme normale des éléments pleinement commutatifsIn this thesis we define a tower of affine Temperley-Lieb algebras of Type  on which we define a Markov trace and we show that there is a unique such trace. In order to do so, we work on four levels of type À : affine braid groups, affine Coxeter groups, affine Hecke algebras and affine Temperley-Lieb algebras On the braid level, we show that À-type affine braid group with n+1 generators surjects onto A-type affine braid group with n generators, we prove that this surjection cornes from a quotient on a certain subgroup and we define a closure of an element of this group which is to be called an affine link. On the Coxeter level, we study the À-type affine Coxeter group with n+1 generators, we give a full set of representatives of left cosets and double cosets of the À-type affine Coxeter group with n generators, then we classify fully commutative elements and we give a normal form for such elements. On the Hecke level, we define a tower of A-type affine Hecke algebras, we show that this tower is a tower of inclusions, and we show that this tower surjects onto the tower of A-type Hecke algebras. On the Temperley-Lieb level, we define a tower of Â-type affine Temperley-Lieb, we define a Markov trace as a collection of traces on this tower in its most general form (compatibrirty with affine links). We get the existence of such trace by showing that the mentioned tower surjects onto the tower of A-type Temperley-Lieb algebras and finally we show that this trace is unique by making use of the normal form of the fully commutative elements
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Arzhantsev, I. V., D. A. Timashev, and Andreas Cap@esi ac at. "Affine Embeddings of Homogeneous Spaces." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi929.ps.
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Kessari, Smaragda. "The Journey to Affine Histories." Thesis, Lancaster University, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.485229.
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Two problems are tackled in this thesis, both involving modern approaches to the 'problem of time' in canonical quantum. gravity. The first task involves applying the recently introduced 'parametric theory' of Charles Wang to the Bianchi IX. cosmological model. The second task involves showing how consistent histories quantum cosmology can be realised in the context of Chris Isham's Histories Projection Operator (HPO) consistent histories scheme. This involves using an 'affine histories' approach in which, in or:der to better reflect the positivity proper- ..... ties of a classical spatial metric, I use an affine algebra instead of a canonical one. In particular, this algebra is discussed for the case of a Friedmann Robertson-Walker (FRW) universe coupled to a scalar field. I then study the properties of some appropriate cocycle representations of this algebra that are ·obtained using old ideas of Gel'fand. Because of the use of a continuous time variable, certain divergences arise in quantities of physical interest, and these need to be removed. I do this by introducing a regularisation scheme that is closely adapted to the representations in use, and I then show how this leads to a well-defined history Hamiltonian that exists as a genuine, positive, self-adjoint operator. The role of the choice of cocycle is discussed and it is shown how it is related to a type of ground-state energy.
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Kutyniok, Gitta. "Affine density in wavelet analysis /." Berlin [u.a.] : Springer, 2007. http://www.gbv.de/dms/ilmenau/toc/529512874.PDF.
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Curnock, Audrey Geraldine. "Isomorphisms of affine function spaces." Thesis, Goldsmiths College (University of London), 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.412519.
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Shapiro, Larry Saul. "Affine analysis of image sequences." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358752.
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Low, David J. "Affine symmetry in general relativity." Thesis, University of Aberdeen, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386299.
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Affine vector fields in 4-dimensional Lorentz manifolds have recently been investigated in some detail by Hall and da Costa. The picture is completed in this thesis by studying the zeros of affine vector fields. Hall and da Costa show that the problem of finding affine vector fields in non-degenerately reducible 4-dimensional Lorentz manifolds can be reduced, with one exceptional case, to the problem of finding homothetic vector fields in lower dimensional manifolds. This means that the study of affine vector fields with zeros in 4-dimensional Lorentz manifolds is aided by investigating proper homothetic and Killing vector fields with zeros in 2- or 3-dimensional manifolds. To this end proper homothetic vector fields with zeros are investigated in 2- and 3-dimensional Manifolds using techniques similar to those used by Hall. It is shown that in the 2-dimensional case the zero is necessarily isolated, whereas in the 3-dimensional case the zero set may either be isolated or 1-dimensional. In the latter case the manifold is shown to be a 3-dimensional plane wave space-time, and all of the affine and conformal vector fields that it admits are found. These results are then used to determine the nature of the zero sets of affine vector fields in 4-dimensional Lorentz manifolds. The algebraic structure of the Riemann, Ricci and Weyl tensors at such zeros is also described. This work is extended by studying affine vector fields, and their zero sets, in 3-dimensional Lorentz manifolds. An investigation of the zero sets of affine vector fields in 3- and 4-dimensional positive-definite manifolds is included for comparison.
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HUAMANI, EDISON FAUSTO CUBA. "AFFINE MINIMAL SURFACES WITH SINGULARITIES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32452@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
Neste trabalho, estudamos superfícies com curvatura média afim zero. Elas são chamadas de superfícies mínimas afins e para superfícies convexas, também são chamadas de superfícies máximas afins. Provamos que uma superfície mínima euclidiana também é uma superfície mínima afim se, e somente se, as linhas de curvatura da superfície mínima euclidiana conjugada são planas. Para uma superfície máxima afim, descrevemos como recuperá-la do campo de vetor conormal ao longo de uma determinada curva. Para algumas escolhas do vector conormal, a superfície máxima é singular e descrevemos as condições sob as quais as singularidades são arestas cuspidais ou swallowtails.
In this work we study surfaces with zero affine mean curvature. They are called affine minimal surfaces and for convex surfaces, they are also called affine maximal surfaces. We prove that an euclidean minimal surface is also an affine minimal surface if and only if the curvature lines of the conjugate euclidean minimal surface are planar. For an affine maximal surface, we describe how to recover it from the conormal vector field along a given curve. For some choices of the conormal vector, the maximal surface is singular and we describe conditions under which the singularities are cuspidal edges or swallowtails.
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Mitankin, Vladimir. "Integral points on affine surfaces." Thesis, University of Bristol, 2017. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730897.
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Papathanasiou, Dimitrios. "Hypercyclic Algebras and Affine Dynamics." Bowling Green State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1490913276727982.
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Wiehe, Martin. "Deformations in affine hypersurface theory /." Aachen : Shaker, 1999. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=008461776&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Benine-Neto, André. "Trajectory control in curves, towards the perceptive-ESC : through a piecewise affine approach." Thesis, Evry-Val d'Essonne, 2011. http://www.theses.fr/2011EVRY0021/document.
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Les avancées dans les technologies ont permis le développement de systèmes d’aide à la conduite (ADAS) pour prévenir les accidents routiers causés par les erreurs de conduite au manque d’attention de conducteurs. Plusieurs types sont déjà disponibles sur le marché, comme l’ABS et l’ESC (ou ESP), utilisant uniquement des capteurs proprioceptifs. Les capteurs extéroceptifs sont présents dans les ADAS plus récents, comme LKAS (maintien dans la voie) et LDWS. Cependant, l‘ESC agit dans la dynamique du véhicule en situations d¹urgence alors que les systèmes d’alerte de sortie de voie sont conçus pour les situations de faible sollicitation latérale. Cette thèse traite le développement d’un ADAS, nommé ESC-perceptif, qui intègre les informations des capteurs extéroceptifs (camera vidéo) avec le contrôle de la vitesse de lacet afin d’éviter les sorties de voie, y compris pour des conditions de fortes sollicitations latérales. La prise en compte de la saturation de forces de contact pneumatiques-chaussée est essentielle pour la conception de ce système. La non-linéairité des efforts pneumatiques est traité par l'approche des systèmes affines par morceaux (PWA). Cela permet de mener l'analyse et la synthèse de contrôleurs en combinant les fonctions de Lyapunov avec la résolution de problèmes d’optimisations sous contraintes d¹inégalités matricielles linéaires et bilinéaires. Au long de la thèse, plusieurs contrôleurs PWA pour le développement de ADAS sont présentés. L’ESC-perceptif, basé uniquement sur les capteurs disponibles sur les véhicules commercialisés est validé expérimentalement sur véhicule prototypeAdvances in the technology of sensors and actuators have enabled the development of driver assistance systems (ADAS) to prevent road accidents due to drivers mistakes or inattention. Several types are already deployed in the commercialised vehicles, such as, ABS and ESC by means of proprioceptive sensors. Exteroceptive sensors can be seen in systems such as, LKAS (Lane Keeping Assistance Systems) and LDWS (Lane Departure Warning Systems). While the ESC deals with the vehicle dynamics in emergency situations, the systems to avoid lane departure are currently designed to work in conditions of weak lateral solicitation. This thesis deals with the development of a ADAS, named perceptive-ESC, which integrates the information from the exteroceptive sensors (provided by a video camera) with the yaw rate control in order to avoid unintended lane departure even in situation of strong lateral solicitation or degraded road adhesion. Considering the saturation of the lateral tyre forces is essential for the conception of the perceptive-ESC, therefore the nonlinear behaviour of the lateral tyre forces is taken into account by the use of Piecewise Affine (PWA) Systems which analysis and control synthesis are based on quadratic Lyapunov functions casted as optimisation problems with linear and bilinear matrix inequalities constraints. Throughout the thesis, several PWA controllers for driver assistance systems are presented in which the complexity is gradually increased from simply enhancing the vehicle handling to the perceptive-ESC based only on sensors available in the currently commercialised passenger cars, which has been validated by practical experiments on a prototype vehicle
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Miao, Jun Jie. "The geometry of self-affine fractals." Thesis, St Andrews, 2008. http://hdl.handle.net/10023/838.
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Vichiansin, Bovorn. "Essays on affine term structure models /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/7448.
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Popov, Vladimir L., and popov@ppc msk ru. "On Polynomial Automorphisms of Affine Spaces." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi938.ps.
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Duffie, D., D. Filipovic, and Walter Schachermayer. "Affine processes and applications in finance." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 2001. http://epub.wu.ac.at/798/1/document.pdf.
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We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuous-state branching processes with immigration and Ornstein-Uhlenbeck type processes. We show, and provide foundations for, a wide range of financial applications for regular affine processes. (author's abstract)Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
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Leclerc, Marc-Antoine. "The Hyperbolic Formal Affine Demazure Algebra." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35218.
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In this thesis, we extend the construction of the formal (affine) Demazure algebra due to Hoffnung, Malagón-López, Savage and Zainoulline in two directions. First, we introduce and study the notion of formal Demazure lattices of a Kac-Moody root system and show that the definitions and properties of the formal (affine) Demazure operators and algebras hold for such lattices. Second, we show that for the hyperbolic formal group law the formal Demazure algebra is isomorphic (after extending the coefficients) to the Hecke algebra.
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Hedén, Isac. "Ga-actions on Complex Affine Threefolds." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-203708.
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This thesis consists of two papers and a summary. The papers both deal with affine algebraic complex varieties, and in particular such varieties in dimension three that have a non-trivial action of one of the one-dimensional algebraic groups Ga := (C, +) and Gm := (C*, ·). The methods used involve blowing up of subvarieties, the correspondances between Ga - and Gm - actions on an affine variety X with locally nilpotent derivations and Z-gradings respectively on O(X) and passing from a filtered algebra A to its associated graded algebra gr(A). In Paper I, we study Russell’s hypersurface X , i.e. the affine variety in the affine space A4 given by the equation x + x2y + z3 + t2 = 0. We reprove by geometric means Makar-Limanov’s result which states that X is not isomorphic to A3 – a result which was crucial to Koras-Russell’s proof of the linearization conjecture for Gm -actions on A3. Our method consist in realizing X as an open part of a blowup M −→ A3 and to show that each Ga -action on X descends to A3 . This follows from considerations of the graded algebra associated to O(X ) with respect to a certain filtration. In Paper II, we study Ga-threefolds X which have as their algebraic quotient the affine plane A2 = Sp(C[x, y]) and are a principal bundle above the punctured plane A2 := A2 \ {0}. Equivalently, we study affine Ga -varieties Pˆ that extend a principal bundle P over A2, being P together with an extra fiber over the origin in A2. First the trivial bundle is studied, and some examples of extensions are given (including smooth ones which are not isomorphic to A2 × A). The most basic among the non-trivial principal bundles over A2 is SL2 (C) −→ A2, A 1→ Ae1 where e1 denotes the first unit vector, and we show that any non-trivial bundle can be realized as a pullback of this bundle with respect to a morphism A2 −→ A2. Therefore the attention is then restricted to extensions of SL2(C) and find two families of such extensions via a study of the graded algebras associated with the coordinate rings O(Pˆ) '→ O(P ) with respect to a filtration which is defined in terms of the Ga -actions on P and Pˆ respectively.
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Daigle, Daniel. "Birational endomorphisms of the affine plane." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75337.
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Birational morphisms f: X $ to$ Y of nonsingular surfaces are studied first. Properties of the surfaces X and Y are shown to be related to certain numerical data extracted from the configuration of "missing curves" of f, that is, the curves in Y whose generic point is not in f (X). These results are then applied to the problem of decomposing birational endomorphisms of the plane into a succession of irreducible ones.A graph-theoretic machinery is developed to keep track of the desingularization of the divisors at infinity of the plane. That machinery is then used to investigate the problem of classifying all birational endomorphisms of the plane, and a complete classification is given in the case of two fundamental points.
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Sepe, Daniele. "Integral affine geometry of Lagrangian bundles." Thesis, University of Edinburgh, 2011. http://hdl.handle.net/1842/5279.
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In this thesis, a bundle F →(M,ω) → B is said to be Lagrangian if (M,ω) is a 2n- dimensional symplectic manifold and the fibres are compact and connected Lagrangian submanifolds of (M,ω), i.e. ω |F = 0 for all F. This condition implies that the fibres and the base space are n-dimensional. Such bundles arise naturally in the study of a special class of dynamical systems in Hamiltonian mechanics, namely those called completely integrable Hamiltonian systems. A celebrated theorem due to Liouville [39], Mineur [46] and Arnol`d [2] provides a semi-global (i.e. in the neighbourhood of a fibre) symplectic classification of Lagrangian bundles, given by the existence of local action-angle coordinates. A proof of this theorem, due to Markus and Meyer [41] and Duistermaat [20], shows that the fibres and base space of a Lagrangian bundle are naturally integral affine manifolds, i.e. they admit atlases whose changes of coordinates can be extended to affine transformations of Rn which preserve the standard cocompact lattice Zn Rn. This thesis studies the problem of constructing Lagrangian bundles from the point of view of affinely at geometry. The first step to study this question is to construct topological universal Lagrangian bundles using the affine structure on the fibres. These bundles classify Lagrangian bundles topologically in the sense that every such bundle arises as the pullback of one universal bundle. However, not all bundles which are isomorphic to the pullback of a topological universal Lagrangian bundle are Lagrangian, as there exist further smooth and symplectic invariants. Even for bundles which admit local action-angle coordinates (these are classified up to isomorphism by topological universal Lagrangian bundles), there is a cohomological obstruction to the existence of an appropriate symplectic form on the total space, which has been studied by Dazord and Delzant in [18]. Such bundles are called almost Lagrangian. The second half of this thesis constructs the obstruction of Dazord and Delzant using the spectral sequence of a topological universal Lagrangian bundle. Moreover, this obstruction is shown to be related to a cohomological invariant associated to the integral affine geometry of the base space, called the radiance obstruction. In particular, it is shown that the integral a ne geometry of the base space of an almost Lagrangian bundle determines whether the bundle is, in fact, Lagrangian. New examples of (almost) Lagrangian bundles are provided to illustrate the theory developed.
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Kao, Chang-Lung. "Affine invariant matching of noisy objects." Thesis, Monterey, California. Naval Postgraduate School, 1989. http://hdl.handle.net/10945/26852.
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Hall, Richard Andrew. "Affine Toda solitons and fusing rules." Thesis, Durham University, 1994. http://etheses.dur.ac.uk/5596/.
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This thesis is concerned with various soliton solutions to some of the affine Toda field theories. These are field theories in 1+1 dimensions that possess a rich underlying Lie algebraic structure and they are known to be integrable. The soliton solutions occur as a result of the multi-vacua that appear in the field theory when the coupling constant is taken to be purely imaginary. In chapter one a review of the affine Toda field theories is undertaken. This is meant to be a relatively complete and exhaustive survey of the literature that has appeared on the subject in recent years. A brief introduction to the theory of solitons and the methods of obtaining such solutions in field theory is given in chapter two, resulting in the construction of the relevant machinery for the Toda theories. In chapter three, Hi rota's method is used to construct single and double soliton solutions to these theories. As a consequence of these explicit formulae the fusing structure of the solitons may be investigated and shown to be equivalent to that found in the classical particle regime, supplemented by further 'annihilations' of 'soliton-antisoliton'. The calculations of the double soliton solutions are claimed to be original in this context. The fusing has also been examined by Olive, Turok and Underwood(^16) through an abstract group-theoretical approach to the affine Toda field theories, however very few explicit formulae are given by them, and hence all the solutions given here are important in their own right. An algebra-independent analysis of such phenomena is undertaken in chapter four where a vertex operator construction is given for the relevant interaction functions. Some properties of these functions are noted; (some of these facts correspond with those in [16] concerning the fusing structure of the solitons).
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Iskandar, Alexander Agustinus Popo. "On breathers in affine Toda theories." Thesis, Durham University, 1995. http://etheses.dur.ac.uk/5236/.
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Oscillating solitonic solutions, the breathers, of affine Toda theory are studied. These breather solutions are constructed from two solitons of the same mass with velocity opposite of each other; by analytically continuing its velocity or rapidity to a complex value, the resulting solution becomes a periodic solution. Generally, the parameters in the soliton solutions are restricted to a certain range of definition. In particular, it is shown for a(^(1))(_n) and d(^(1))(_4) cases, these restrictions can be calculated explicitly. To some cases of a(^(a))(_n) theories, one can show that there are sine-Gordon embedded solitons which give rise to a sine-Gordon breather. Furthermore, these breather solutions carry topological charges. These topological charges are calculated and it is found that they are exactly the same as the topological charges of some single soliton cases. Moreover, for the non-zero topological charges, one can show they belong to the irreducible fundamental representation component of the tensor product of two fundamental representations associated with the constituent solitons. This Clebsch-Gordan decomposition property is in agreement with the fusing rule of soliton which in turn is similar to the fusing rule of the fundamental Toda particles. One can also make a conjecture that the zero topological charge is always carried by a breather whose constituent solitons are associated with either conjugate or self-conjugate fundamental representations. Although it is not possible to know the individual topological charge carried by the constituent solitons in a breather, nevertheless using the crossing symmetry similar to that of the crossing symmetry of the S'-matrix, one can perform a superficial calculation to determine the constituent soliton's topological charges. Attempts to understand the exact scattering matrices of the sine-Gordon solitons and breathers from a root space point of . view is also discussed. This study tries to mimic the exact S-matrix construction of the real coupling regime affine Toda theory from the root space by Dorey. In this study, one replaces the ordinary Coxeter element, which plays an important role in the real coupling regime, with other transformations to incorporate the infinite product nature of the sine-Gordon soliton scattering matrix. However, the desired consistent construction seems to elude the author in this study.
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Davis, Declan Denis Daniel. "Affine differential geometry and singularity theory." Thesis, University of Liverpool, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.479061.
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Hussin, Amran. "Characters of affine Kac-Moody algebras." Thesis, University of Southampton, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296515.
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Hyun, Yoonsuk. "On affine embeddings of reductive groups." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/68482.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 63-65).
In this thesis, we study the properties and the classification of embeddings of homogeneous spaces, especially the case of affine normal embeddings of reductive groups. We might guess that as in the case of toric varieties, some specific subset of one-parameter subgroups may contribute to the classification of affine embeddings of general reductive group. To check this, we review the theory of affine normal SL(2)-embeddings, and prove that the classification cannot be solved entirely based on one-parameter subgroups. We can also show that even though this set does not give a complete answer to the classification problem, but still contains useful information about varieties. We will also give examples of GL(2)- embeddings which had not previously been constructed in detail, which might be helpful in understanding the general classification of affine normal G-embeddings.
by Yoonsuk Hyun.
Ph.D.
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Thórhallsson, Torfi. "Symmetric objects in multiple affine views." Thesis, University of Oxford, 2000. http://ora.ox.ac.uk/objects/uuid:49ec4596-7086-4645-81f8-8dacf48b694a.
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This thesis is concerned with the utilization of object symmety as a cue for segmentation and object recognition. In particular it investigates the problem of detecting 3D bilaterally symmetric objects from affine views. The first part of the thesis investigates the problem of detecting 3D bilateral symmetry within a scene from known point correspondences across two or more affine views. We begin by extending the notion of skewed symmetry to three dimensions, and give a definition in terms of degenerate structure that applies equally to an affine 3D structure or to point correspondences across two or more affine views. We then consider the effects of measurement errors on symmetry detection, and derive an optimal statistical test of degenerate structure, and thereby of 3D-skewed symmetry. We then move on to the problem of searching for 3D skewed symmetric sets within a larger scene. We discuss two approaches to the problem, both of which we have implemented, and we demonstrate fully automatic detection of 3D skewed symmetry on images of uncluttered scenes. We conclude the first part by investing means of verifying the presence of bilateral rather than skewed symmetry in the Euclidean space, by enforcing mutual consistency between multiple skewed symmetric sets, and by drawing on partial knowledge about the camera calibration. The second part of the thesis is concerned with the problem of obtaining feature correspondences across multiple affine views, as required for the detection of symmetry. In particular we investigate the geometric matching constraints that exist between affine views. We start by specilizing the four projective multifocal tensors to the affine case, and use these to carry the bulk of all known projective multi-view matching relations to affine views, unearthing some new relations in the process. Having done that, we address the problem of estimating the affine tensors. We provide a minimal set of constraints on the affine trifocal tensor, and search for ways of estimating the affine tensors from point and line correspondences.
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Thapa, Magar Surya. "Skeleta of affine curves and surfaces." Diss., Kansas State University, 2015. http://hdl.handle.net/2097/20395.
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Doctor of PhilosophyMathematics
Ilia Zharkov
A smooth affine hypersurface of complex dimension n is homotopy equivalent to a real n-dimensional cell complex. We describe a recipe of constructing such cell complex for the hypersurfaces of dimension 1 and 2, i.e. for curves and surfaces. We call such cell complex a skeleton of the hypersurface. In tropical geometry, to each hypersurface, there is an associated hypersurface, called tropical hypersurface given by degenerating a family of complex amoebas. The tropical hypersurface has a structure of a polyhedral complex and it is a base of a torus fibration of the hypersurface constructed by Mikhalkin. We introduce on the edges of a tropical hypersurface an orientation given by the gradient flow of some piece-wise linear function. With the help of this orientation, we choose some sections and fibers of the fibration.These sections and fibers constitute a cell complex and we prove that this complex is the skeleton by using decomposition of the coemoeba of a classical pair-of-pants. We state and prove our main results for the case of curves and surfaces in Chapters 4 and 5.
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Lehébel, Patrick. "Surfaces et hypersurfaces de revolution affine." Nantes, 1995. http://www.theses.fr/1995NANT2025.
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Cette these est essentiellement un prolongement des travaux d'isaac c. Lee (these en 1993 sous la direction de k. Komizu) concernant les surfaces de revolution affine, c-a-d les surfaces invariantes par un sous-groupe a un parametre de sa (3) dont chaque element respecte la meme droite de points fixes. Apres avoir generalise la definition de lee aux dimensions superieures, nous classifions les hypersurfaces de revolution affine de dimension 3 dans r#4 en 16 modeles a equivalence affine pres et etudions les invariants affines de ces modeles. Une telle longue etude nous permet: 1) de montrer que 14 de ces 16 modeles sont des hypersurfaces de revolution affine au sens de sus (1928), c-a-d que leurs normales affines rencontrent toutes l'axe de revolution. 2) de decouvrir des modeles originaux (a notre connaissance) d'hyperspheres affines de dimension 3. On remarque de plus que 2 des 3 hyperspheres de dimension 3 de courbure constante et d'invariant de pick non nul decouvertes par magid et ryan (1992) sont justement des hypersurfaces de revolution en notre sens. Il en est d'ailleurs de meme pour un grand nombre des modeles construits par dillen et vrancken dans leur article sur la composition de type calabi des spheres affines (1994) 3) d'etudier pour ces hypersurfaces a quelles conditions sur la courbe profil l'invariant de pick est nul ou constant. En particulier, la nullite de cet invariant pour 5 de ces modeles entraine que les hypersurfaces correspondantes sont des hyperquadriques
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Pitsillis, Zachry Steven. "Estimating dynamic affine term structure models." Master's thesis, University of Cape Town, 2015. http://hdl.handle.net/11427/15731.
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Duffee and Stanton (2012) demonstrated some pointed problems in estimating affine term structure models when the price of risk is dynamic, that is, risk factor dependent. The risk neutral parameters are estimated with precision, while the price of risk parameters are not. For the Gaussian models they investigated, these problems are replicated and are shown to stem from a lack of curvature in the log-likelihood function. This geometric issue for identifying the maximum of an essentially horizontal log-likelihood has statistical meaning. The Fisher information for the price of risk parameters is multiple orders of magnitude smaller than that of the risk neutral parameters. Prompted by the recent results of Christoffersen et al. (2014) a remedy to the lack of curvature is attempted. An unscented Kalman filter is used to estimate models where the observations are portfolios of FRAs, Swaps and Zero Coupon Bond Options. While the unscented Kalman filter performs admirably in identifying the unobserved risk factor processes, there is little improvement in the Fisher information.
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Thorén, Jesper. "Irreductible representations of quantum affine algebras /." Lund : Center for mathematical sciences, Lund university, 2000. http://catalogue.bnf.fr/ark:/12148/cb39293499j.
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Bell, Jason Pierre. "Affine rings of low GK dimension /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2002. http://wwwlib.umi.com/cr/ucsd/fullcit?p3044791.
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Kusilek, Jonathan. "On representations of affine Hecke algebras." Thesis, The University of Sydney, 2011. http://hdl.handle.net/2123/12074.
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We introduce a C-algebra Ht corresponding to an affine Hecke algebra H and a central character t of H, and show that the irreducible representations of Ht are precisely the irreducible representations of H with central character t. For certain choices of t we give an explicit construction of a cellular basis of Ht in terms of elementary properties of t. We thus classify, and give a construction of, the irreducible representations of Ht. While the indexing sets appear similar to those given for calibrated representations, we obtain many representations which are not calibrated.
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Byun, Eui Won James. "Affine varieties, Groebner basis, and applications." CSUSB ScholarWorks, 2000. https://scholarworks.lib.csusb.edu/etd-project/1611.
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Chen, Zongbin. "Sur la pureté des fibres de Springer affines non-ramifiées pour GL4." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00656163.
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La thèse consiste de deux parties. Dans la première partie, on montre la pureté des fibres de Springer affines pour $\gl_{4}$ dans le cas non-ramifié. Plus précisément, on construit une famille de pavages non standard en espaces affines de la grassmannienne affine, qui induisent des pavages en espaces affines de la fibre de Springer affine. Dans la deuxième partie, on introduit une notion de $\xi$-stabilité sur la grassmannienne affine $\xx$ pour le groupe $\gl_{d}$, et on calcule le polynôme de Poincaré du quotient $\xx^{\xi}/T$ de la partie $\xi$-stable $\xxs$ par le tore maximal $T$ par une processus analogue de la réduction de Harder-Narasimhan.
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Schwarzenberger, Michael. "Affine Processes and Pseudo-Differential Operators with Unbounded Coefficients." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-211510.
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The concept of pseudo-differential operators allows one to study stochastic processes through their symbol. This approach has generated many new insights in recent years. However, most results are based on the assumption of bounded coefficients. In this thesis, we study Levy-type processes with unbounded coefficients and, especially, affine processes. In particular, we establish a connection between pseudo-differential operators and affine processes which are well-known from mathematical finance. Affine processes are an interesting example in this field since they have linearly growing and hence unbounded coefficients. New techniques and tools are developed to handle the affine case and then expanded to general Levy-type processes. In this way, the convergence of a simulation scheme based on a Markov chain approximation, results on path properties, and necessary conditions for the symmetry of operators were proven.
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Lugo, Michael Ruben. "A Combinatorially Explicit Relative Möbius Function on Affine Grassmannians and a Proposal for an Affine Infinite Symmetric Group." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/89477.
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For an affine Weyl group W, we explicitly determine the elements for which the Möbius function of the subposet of affine Grassmannians under the Bruhat order is non-zero by utilizing the quantum Bruhat graph of the classical Weyl group associated to W . Then we examine embedding stable and consistent statistics on the affine Weyl group of type A which permit the definition of an affine infinite symmetric group.Doctor of Philosophy
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Mierendorff, Eva. "On affine Deligne-Lusztig varieties for GLn." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=979018684.
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