Дисертації з теми "Symplectic and Poisson geometry"
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Martino, Maurizio. "Symplectic reflection algebras and Poisson geometry." Thesis, University of Glasgow, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.426614.
Повний текст джерелаRemsing, Claidiu Cristian. "Tangentially symplectic foliations." Thesis, Rhodes University, 1994. http://hdl.handle.net/10962/d1005233.
Повний текст джерелаKirchhoff-Lukat, Charlotte Sophie. "Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283007.
Повний текст джерелаCosta, Paulo Henrique Pereira da 1983. "Difusões em variedades de poisson." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306283.
Повний текст джерелаDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-13T23:01:19Z (GMT). No. of bitstreams: 1 Costa_PauloHenriquePereirada_M.pdf: 875708 bytes, checksum: 8862a1813f1bb85b5d0269462a80501e (MD5) Previous issue date: 2009
Resumo: O objetivo desse trabalho é estudar as equações de Hamilton no contexto estocástico. Sendo necessário para tal um pouco de conhecimento a cerca dos seguintes assuntos: cálculo estocástico, geometria de segunda ordem, estruturas simpléticas e de Poisson. Abordamos importantes resultados, dentre eles o teorema de Darboux (coordenadas locais) em variedades simpléticas, teorema de Lie-Weinstein que de certa forma generaliza o teorema de Darboux em variedades de Poisson. Veremos que apesar de o ambiente natural para se estudar sistemas hamiltonianos ser variedades simpléticas, no caso estocástico esses sistemas se adaptam bem em variedades de Poisson. Além disso, para atingir a nossa meta, estudaremos equações diferenciais estocásticas em variedades de dimensão finita usando o operador de Stratonovich
Abstract: This dissertation deals with transfering Hamilton's equations in stochastic context. This requires some knowledge about the following: stochastic calculus, second order geometry and Poisson and simplectic structures. Important results that will be discussed in this theory are Darboux's theorem (local coordinates) for simplectic manifolds, and Lie-Weintein's theorem that is in a certain way of Darboux's theorem on Poisson manifolds. We will see that although the natural environment for studying hamiltonian systems is symplectic manifolds, if we have a Poisson structure we will still be able to study them. Moreover, to achieve our goal, we will study stochastic differential equations on finite dimensional manifolds using the Stratonovich operator
Mestrado
Geometria Estocastica
Mestre em Matemática
Van, De Ven Christiaan Jozef Farielda. "Quantum Systems and their Classical Limit A C*- Algebraic Approach." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/324358.
Повний текст джерелаMartin, Shaun K. "Symplectic geometry and gauge theory." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.389209.
Повний текст джерелаSmith, Ivan. "Symplectic geometry of Lefschetz fibrations." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299234.
Повний текст джерелаBoalch, Philip Paul. "Symplectic geometry and isomonodromic deformations." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301848.
Повний текст джерелаat, Andreas Cap@esi ac. "Equivariant Symplectic Geometry of Cotangent Bundles." Moscow Math. J. 1, No.2 (2001) 287-299, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi996.ps.
Повний текст джерелаRødland, Lukas. "Symplectic geometry and Calogero-Moser systems." Thesis, Uppsala universitet, Teoretisk fysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-256742.
Повний текст джерелаKarlsson, 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.
Повний текст джерелаDen 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.
Ishikawa, Suguru. "Construction of general symplectic field theory." Kyoto University, 2019. http://hdl.handle.net/2433/242575.
Повний текст джерелаBalleier, Carsten. "Geometry and quantization of Howe pairs of symplectic actions." Thesis, Metz, 2009. http://www.theses.fr/2009METZ016S/document.
Повний текст джерелаMotivated by the representation-theoretic notion of Howe duality, we seek an analogous construction in symplectic geometry in the sense that its geometric quantization decomposes in a Howe dual fashion. We find that in the symplectic context, the correct setting is given by two Lie groups acting on a symplectic manifold when these two actions commute and satisfy the symplectic Howe ondition, i. e., these actions are Hamiltonian and their collective functions are their mutual centralizers in the Poisson algebra of smooth functions on the symplectic manifold. Once this condition is satisfied, we can describe the orbit structure in detail. In particular, there is a bijection between the coadjoint orbits in one moment image and those in the other moment image – this bijection is what we call the coadjoint orbit correspondence. We study the coadjoint orbit correspondence further and show, if the acting Lie groups are compact and the symplectic manifold is prequantizable, that it preserves integrality of the coadjoint orbits, so to both coadjoint orbits in the correspondence an irreducible representation can be associated. We thus have a bijection between certain parts of the unitary duals of both Lie groups acting on the symplectic manifold. Applying known results about the interchangeability of quantization and reduction, we see that for a Kähler manifold, its quantization (as a representation of the product of both groups acting on the manifold) decomposes into a multiplicity-free direct sum of tensor products of irreducibles of the individual groups, the pairs being given by the bijection obtained before – as one would expect according to Howe duality. This main result is accompanied by a study of the local structure of a manifold carrying two commuting Hamiltonian action which proves a local version of the orbit correspondence and by a discussion about the relation of the coadjoint orbit correspondence to the generalized symplectic leaf correspondence in singular dual pairs
Distexhe, Julie. "Triangulating symplectic manifolds." Doctoral thesis, Universite Libre de Bruxelles, 2019. https://dipot.ulb.ac.be/dspace/bitstream/2013/287522/3/toc.pdf.
Повний текст джерелаIn this thesis, we study symplectic structures in a piecewise linear (PL) setting. The central question is to determine whether a smooth symplectic manifold can be triangulated symplectically, in the sense that there exists a triangulation $h :K -> M$ such that $h^*omega$ is a piecewise constant symplectic form on $K$. We first focus on a simpler related problem, and show that any smooth volume form $Omega$ on $M$ can be triangulated. This means that there always exists a triangulation $h :K -> M$ such that $h^*Omega$ is a piecewise constant volume form. In particular, symplectic surfaces admit symplectic triangulations. Given a closed symplectic manifold $(M,omega)$, we then prove that there exists triangulations $h :K -> M$ for which the piecewise smooth form $h^*omega$ has maximal rank along all the simplices of $K$. This result allows to approximate arbitrarily closely any closed symplectic manifold by a PL one. Finally, we investigate the case of a symplectic submanifold $M$ of an ambient space which is itself symplectically triangulated, and give the construction of a cobordism between $M$ and a piecewise smooth approximation of $M$, triangulated by a symplectic complex.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
CATTANEO, ALBERTO. "NON-SYMPLECTIC AUTOMORPHISMS OF IRREDUCIBLE HOLOMORPHIC SYMPLECTIC MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/606455.
Повний текст джерелаWe study automorphisms of irreducible holomorphic symplectic manifolds of type K3^[n], i.e. manifolds which are deformation equivalent to the Hilbert scheme of n points on a K3 surface, for some n > 1. In the first part of the thesis we describe the automorphism group of the Hilbert scheme of n points on a generic projective K3 surface, i.e. a K3 surface whose Picard lattice is generated by a single ample line bundle. We show that, if it is not trivial, the automorphism group is generated by a non-symplectic involution, whose existence depends on some arithmetic conditions involving the number of points n and the polarization of the surface. We also determine necessary and sufficient conditions on the Picard lattice of the Hilbert scheme for the existence of the involution. In the second part of the thesis we study non-symplectic automorphisms of prime order on manifolds of type K3^[n]. We investigate the properties of the invariant lattice and its orthogonal complement inside the second cohomology lattice of the manifold, providing a classification of their isometry classes. We then approach the problem of constructing examples (or at least proving the existence) of manifolds of type K3^[n] with a non-symplectic automorphism inducing on cohomology each specific action in our classification. In the case of involutions, and of automorphisms of odd prime order for n=3,4, we are able to realize all possible cases. In order to do so, we present a new non-symplectic automorphism of order three on a ten-dimensional family of Lehn-Lehn-Sorger-van Straten eightfolds of type K3^[4]. Finally, for n < 6 we describe deformation families of large dimension of manifolds of type K3^[n] equipped with a non-symplectic involution.
Nous allons étudier les automorphismes des variétés symplectiques holomorphes irréductibles de type K3^[n], c'est-à-dire des variétés équivalentes par déformation au schéma de Hilbert de n points sur une surface K3, pour n > 1. Dans la première partie de la thèse, nous classifions les automorphismes du schéma de Hilbert de n points sur une surface K3 projective générique, dont le réseau de Picard est engendré par un fibré ample. Nous montrons que le groupe des automorphismes est soit trivial soit engendré par une involution non-symplectique et nous déterminons des conditions numériques et géométriques pour l’existence de l’involution. Dans la deuxième partie, nous étudions les automorphismes non-symplectiques d’ordre premier des variétés de type K3^[n]. Nous déterminons les propriétés du réseau invariant de l'automorphisme et de son complément orthogonal dans le deuxième réseau de cohomologie de la variété et nous classifions leurs classes d’isométrie. Dans le cas des involutions, e des automorphismes d’ordre premier impair pour n = 3, 4, nous montrons que toutes les actions en cohomologie dans notre classification sont réalisées par un automorphism non-symplectique sur une variété de type K3^[n]. Nous construisons explicitement l’immense majorité de ces automorphismes et, en particulier, nous présentons la construction d’un nouvel automorphisme d’ordre trois sur une famille de dimension dix de variétés de Lehn-Lehn-Sorger-van Straten de type K3^[4]. Pour n < 6, nous étudions aussi les espaces de modules de dimension maximal des variétés de type K3^[n] munies d’une involution non-symplectique.
Bussi, Vittoria. "Derived symplectic structures in generalized Donaldson-Thomas theory and categorification." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:54896cc4-b3fa-4d93-9fa9-2a842ad5e4df.
Повний текст джерелаLozano, Guadalupe I. "Poisson geometry of the Ablowitz-Ladik equations." Diss., The University of Arizona, 2004. http://hdl.handle.net/10150/290120.
Повний текст джерелаKourliouros, Konstantinos. "Boundary singularities of functions in symplectic and volume-preserving geometry." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/32268.
Повний текст джерелаde, Gosson de Varennes Serge. "Multi-oriented Symplectic Geometry and the Extension of Path Intersection Indices." Doctoral thesis, Växjö universitet, Matematiska och systemtekniska institutionen, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-400.
Повний текст джерелаMelani, Valerio. "Poisson and coisotropic structures in derived algebraic geometry." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC299/document.
Повний текст джерелаIn this thesis, we define and study Poisson and coisotropic structures on derived stacks in the framework of derived algebraic geometry. We consider two possible presentations of Poisson structures of different flavour: the first one is purely algebraic, while the second is more geometric. We show that the two approaches are in fact equivalent. We also introduce the notion of coisotropic structure on a morphism between derived stacks, once again presenting two equivalent definitions: one of them involves an appropriate generalization of the Swiss Cheese operad of Voronov, while the other is expressed in terms of relative polyvector fields. In particular, we show that the identity morphism carries a unique coisotropic structure; in turn, this gives rise to a non-trivial forgetful map from n-shifted Poisson structures to (n-1)-shifted Poisson structures. We also prove that the intersection of two coisotropic morphisms inside a n-shifted Poisson stack is naturally equipped with a canonical (n-1)-shifted Poisson structure. Moreover, we provide an equivalence between the space of non-degenerate coisotropic structures and the space of Lagrangian structures in derived geometry, as introduced in the work of Pantev-Toën-Vaquié-Vezzosi
Richard, Nicolas. "Extrinsic symmetric symplectic spaces." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210064.
Повний текст джерелаPar analogie à la théorie standard des espaces symétriques, nous démontrons un théorème d'équivalence entre les espaces symétriques symplectiques extrinsèques d'une variété qui est elle-même un espace symétrique symplectique.
La définition d'un espace symétrique symplectique extrinsèque fait intervenir l'existence d'affinités globales de la variété ambiante, les ``symétries extrinsèques', qui induisent la structure symétrique de la sous-variété ;ceci mène à poser une question du type :quelles sont les variétés possédant ``beaucoup' de ces affinités~? Une question précise ainsi qu'une réponse sont fournies dans un contexte où la variété ambiante est seulement supposée munie d'une structure
symplectique et d'une connexion symplectiques. Nous considérons également le cas où ces symétries commutent avec un champ $K$ d'endomorphismes symplectiques fixé de la variété, de carré $pmId$. Nous définissons une notion de courbure sectionnelle pour plans $K$-stables et montrons que les espaces à $K$-courbure sectionnelle constantes sont localement symétriques de type Ricci.
Par suite nous étudions les espaces symétriques symplectiques extrinsèques dans un espace vectoriel symplectique. Nous montrons par exemple qu'un tel espace, s'ils est de dimension deux, est forcément intrinsèquement plat (c.-à-d. à courbure intrinsèque nulle), mais que son image n'est pas forcément un plan affin de l'espace vectoriel ambiant. Nous décrivons en fait explicitement tous les espaces
symétriques symplectiques extrinsèques, dans un espace vectoriel, dont la courbure intrinsèque s'annule identiquement. Nous décrivons également une famille d'exemples d'espaces extrinsèques, dont nous montrons qu'elle fournit la totalité des espaces extrinsèques de codimension $2$, dans un espace vectoriel.
Enfin, nous décrivons quelques exemples d'espaces symétriques symplectiques extrinsèques qui sont totalement géodésiques, dans un espace de type Ricci particulier.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
Cattaneo, Alberto. "Non-symplectic automorphisms of irreducible holomorphic symplectic manifolds." Thesis, Poitiers, 2018. http://www.theses.fr/2018POIT2322/document.
Повний текст джерелаWe study automorphisms of irreducible holomorphic symplectic manifolds of type K3^[n], i.e. manifolds which are deformation equivalent to the Hilbert scheme of n points on a K3 surface, for some n > 1. In the first part of the thesis we describe the automorphism group of the Hilbert scheme of n points on a generic projective K3 surface, i.e. a K3 surface whose Picard lattice is generated by a single ample line bundle. We show that, if it is not trivial, the automorphism group is generated by a non-symplectic involution, whose existence depends on some arithmetic conditions involving the number of points n and the polarization of the surface. We also determine necessary and sufficient conditions on the Picard lattice of the Hilbert scheme for the existence of the involution.In the second part of the thesis we study non-symplectic automorphisms of prime order on manifolds of type K3^[n]. We investigate the properties of the invariant lattice and its orthogonal complement inside the second cohomology lattice of the manifold, providing a classification of their isometry classes. We then approach the problem of constructing examples (or at least proving the existence) of manifolds of type K3^[n] with a non-symplectic automorphism inducing on cohomology each specific action in our classification. In the case of involutions, and of automorphisms of odd prime order for n=3,4, we are able to realize all possible cases. In order to do so, we present a new non-symplectic automorphism of order three on a ten-dimensional family of Lehn-Lehn-Sorger-van Straten eightfolds of type K3^[4]. Finally, for n < 6 we describe deformation families of large dimension of manifolds of type K3^[n] equipped with a non-symplectic involution
Gosson, Maurice A. de. "Symplectic geometry, Wigner-Weyl-Moyal calculus, and quantum mechanics in phase space." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2009/3021/.
Повний текст джерелаRussell, Neil Eric. "Aspects of the symplectic and metric geometry of classical and quantum physics." Thesis, Rhodes University, 1993. http://hdl.handle.net/10962/d1005237.
Повний текст джерелаNarayanan, Vivek. "Some aspects of the geometry of Poisson dynamical systems." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3038192.
Повний текст джерелаGardell, Fredrik. "Geometric Quantization." Thesis, Uppsala universitet, Teoretisk fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-296618.
Повний текст джерелаPrüfer, Sven [Verfasser], and Kai [Akademischer Betreuer] Cieliebak. "Symplectic Geometry of Moduli Spaces of Hurwitz Covers / Sven Prüfer ; Betreuer: Kai Cieliebak." Augsburg : Universität Augsburg, 2017. http://d-nb.info/114485797X/34.
Повний текст джерелаZinger, Aleksey 1975. "Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/8402.
Повний текст джерелаIncludes bibliographical references (p. 239-240).
Enumerative geometry of algebraic varieties is a fascinating field of mathematics that dates back to the nineteenth century. We introduce new computational tools into this field that are motivated by recent progress in symplectic topology and its influence on enumerative geometry. The most straightforward applications of the methods developed are to enumeration of rational curves with a cusp of specified nature in projective spaces. A general approach for counting positive-genus curves with a fixed complex structure is also presented. The applications described include enumeration of rational curves with a (3,4)-cusp, genus-two and genus-three curves with a fixed complex structure in the two-dimensional complex projective space, and genus-two curves with a fixed complex structure in the three-dimensional complex projective space. Our constructions may be applicable to problems in symplectic topology as well.
by Aleksey Zinger.
Ph.D.
Caine, John Arlo. "Poisson Structures on U/K and Applications." Diss., The University of Arizona, 2007. http://hdl.handle.net/10150/195363.
Повний текст джерелаFOSSATI, Edoardo. "Symplectic fillings of virtually overtwisted contact structures on lens spaces." Doctoral thesis, Scuola Normale Superiore, 2020. http://hdl.handle.net/11384/90719.
Повний текст джерелаBott, Christopher James. "Mirror Symmetry for K3 Surfaces with Non-symplectic Automorphism." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/7456.
Повний текст джерелаBäck, 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.
Повний текст джерелаNOVARIO, SIMONE. "LINEAR SYSTEMS ON IRREDUCIBLE HOLOMORPHIC SYMPLECTIC MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/886303.
Повний текст джерелаIn this thesis we study some complete linear systems associated to divisors of Hilbert schemes of 2 points on complex projective K3 surfaces with Picard group of rank 1, together with the rational maps induced. We call these varieties Hilbert squares of generic K3 surfaces, and they are examples of irreducible holomorphic symplectic (IHS) manifold. In the first part of the thesis, using lattice theory, Nakajima operators and the model of Lehn–Sorger, we give a basis for the subvector space of the singular cohomology ring with rational coefficients generated by rational Hodge classes of type (2, 2) on the Hilbert square of any projective K3 surface. We then exploit a theorem by Qin and Wang together with a result by Ellingsrud, Göttsche and Lehn to obtain a basis of the lattice of integral Hodge classes of type (2, 2) on the Hilbert square of any projective K3 surface. In the second part of the thesis we study the following problem: if X is the Hilbert square of a generic K3 surface admitting an ample divisor D with q(D)=2, where q is the Beauville–Bogomolov–Fujiki form, describe geometrically the rational map induced by the complete linear system |D|. The main result of the thesis shows that such an X, except on the case of the Hilbert square of a generic quartic surface of P^3, is a double EPW sextic, i.e., the double cover of an EPW sextic, a normal hypersurface of P^5, ramified over its singular locus. Moreover, the rational map induced by |D| is a morphism and coincides exactly with this double covering. The main tools to obtain this result are the description of integral Hodge classes of type (2, 2) of the first part of the thesis and the existence of an anti-symplectic involution on such varieties due to a theorem by Boissière, Cattaneo, Nieper-Wißkirchen and Sarti.
Dans cette thèse, nous étudions certains systèmes linéaires complets associés aux diviseurs des schémas de Hilbert de 2 points sur des surfaces K3 projectives complexes avec groupe de Picard de rang 1, et les fonctions rationnelles induites. Ces variétés sont appelées carrés de Hilbert sur des surfaces K3 génériques, et sont un exemple de variété symplectique holomorphe irréductible (variété IHS). Dans la première partie de la thèse, en utilisant la théorie des réseaux, les opérateurs de Nakajima et le modèle de Lehn–Sorger, nous donnons une base pour le sous-espace vectoriel de l’anneau de cohomologie singulière à coefficients rationnels engendré par les classes de Hodge rationnels de type (2, 2) sur le carré de Hilbert de toute surface K3 projective. Nous exploitons ensuite un théorème de Qin et Wang ainsi qu’un résultat de Ellingsrud, Göttsche et Lehn pour obtenir une base du réseau des classes de Hodge intégraux de type (2, 2) sur le carré de Hilbert d’une surface K3 projective quelconque. Dans la deuxième partie de la thèse, nous étudions le problème suivant : si X est le carré de Hilbert d’une surface K3 générique tel que X admet un diviseur ample D avec q(D) = 2, où q est la forme quadratique de Beauville–Bogomolov–Fujiki, on veut décrire géométriquement la fonction rationnelle induite par le système linéaire complet |D|. Le résultat principal de la thèse montre qu’une telle X, sauf dans le cas du carré de Hilbert d’une surface quartique générique de P^3, est une double sextique EPW, c’est-à-dire le revêtement double d’une sextique EPW, une hypersurface normale de P^5, ramifié sur son lieu singulier. En plus la fonction rationnelle induite par |D| est exactement ce revêtement double. Les outils principaux pour obtenir ce résultat sont la description des classes de Hodge intégraux de type (2, 2) de la première partie de la thèse et l’existence d’une involution anti-symplectique sur de telles variétés par un théorème de Boissière, Cattaneo, Nieper-Wißkirchen et Sarti.
Saha, Chiranjib. "Advances in Stochastic Geometry for Cellular Networks." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99835.
Повний текст джерелаDoctor of Philosophy
The high speed global cellular communication network is one of the most important technologies, and it continues to evolve rapidly with every new generation. This evolution greatly depends on observing performance-trends of the emerging technologies on the network models through extensive system-level simulations. Since these simulation models are extremely time-consuming and error prone, the complementary analytical models of cellular networks have been an area of active research for a long time. These analytical models are intended to provide crisp insights on the network behavior such as the dependence of network performance metrics (such as coverage or rate) on key system-level parameters (such as transmission powers, base station (BS) density) which serve as the prior knowledge for more fine-tuned simulations. Over the last decade, the analytical modeling of the cellular networks has been driven by stochastic geometry. The main purpose of stochastic geometry is to endow the locations of the base stations (BSs) and users with probability distributions and then leverage the properties of these distributions to average out the spatial randomness. This process of spatial averaging allows us to derive the analytical expressions of the system-level performance metrics despite the presence of a large number of random variables (such as BS and user locations, channel gains) under some reasonable assumptions. The simplest stochastic geometry based model of cellular networks, which is also the most tractable, is the so-called Poisson point process (PPP) based network model. In this model, users and BSs are assumed to be distributed as independent homogeneous PPPs. This is equivalent to saying that the users and BSs independently and uniformly at random over a plane. The PPP-based model turned out to be a reasonably accurate representation of the yesteryear’s cellular networks which consisted of a single tier of macro BSs (MBSs) intended to provide a uniform coverage blanket over the region. However, as the data-hungry devices like smart-phones, tablets, and application like online gaming continue to flood the consumer market, the network configuration is rapidly deviating from this baseline setup with different spatial interactions between BSs and users (also termed spatial coupling) becoming dominant. For instance, the user locations are far from being homogeneous as they are concentrated in specific areas like residential and commercial zones (also known as hotspots). Further, the network, previously consisting of a single tier of macro BSs (MBSs), is becoming increasingly heterogeneous with the deployment of small cell BSs (SBSs) with small coverage footprints and targeted to serve the user hotspots. It is not difficult to see that the network topology with these spatial couplings is quite far from complete spatial randomness which is the basis of the PPP-based models. The key contribution of this dissertation is to enrich the stochastic geometry-based mathematical models so that they can capture the fine-grained spatial couplings between the BSs and users. More specifically, this dissertation contributes in the following three research directions. Direction-I: Modeling Spatial Clustering. We model the locations of users and SBSs forming hotspots as Poisson cluster processes (PCPs). A PCP is a collection of offspring points which are located around the parent points which belong to a PPP. The coupling between the locations of users and SBSs (due to their user-centric deployment) can be introduced by assuming that the user and SBS PCPs share the same parent PPP. The key contribution in this direction is the construction of a general HetNet model with a mixture of PPP and PCP-distributed BSs and user distributions. Note that the baseline PPP-based HetNet model appears as one of the many configurations supported by this general model. For this general model, we derive the analytical expressions of the performance metrics like coverage probability, BS load, and rate as functions of the coupling parameters (e.g. BS and user cluster size). Direction-II: Modeling Coupling in Wireless Backhaul Networks. While the deployment of SBSs clearly enhances the network performance in terms of coverage, one might wonder: how long network densification with tens of thousands of SBSs can meet the everincreasing data demand? It turns out that in the current network setting, where the backhaul links (i.e. the links between the BSs and core network) are still wired, it is not feasible to densify the network beyond some limit. This backhaul bottleneck can be overcome if the backhaul links also become wireless and the backhaul and access links (link between user and BS) are jointly managed by an integrated access and backhaul (IAB) network. In this direction, we develop the analytical models of IAB-enabled HetNets where the key challenge is to tackle new types of couplings which exist between the rates on the wireless access and backhaul links. Such couplings exist due to the spatial correlation of the signal qualities of the two links and the number of users served by different BSs. Two fundamental insights obtained from this work are as follows: (1) the IAB HetNets can support a maximum number of users beyond which the network performance drops below that of a single-tier macro-only network, and (2) there exists a saturation point of SBS density beyond which no performance gain is observed with the addition of more SBSs. Direction-III: Modeling Repulsion. In this direction, we focus on modeling another aspect of spatial coupling imposed by the intra-point repulsion. Consider a device-to-device (D2D) communication scenario, where some users are transmitting some on-demand content locally cached in their devices using a common channel. Any reasonable multiple access scheme will ensure that two nearly users are never simultaneously active as they will cause severe mutual interference and thereby reducing the network-wide sum rate. Thus the active users in the network will have some spatial repulsion. The locations of these users can be modeled as determinantal point processes (DPPs). The key property of DPP is that it forms a bridge between stochastic geometry and machine learning, two otherwise non-overlapping paradigms for wireless network modeling and design. The main focus in this direction is to explore the learning framework of DPP and bring together advantages of stochastic geometry and machine learning to construct a new class of data-driven analytical network models.
Miscione, Steven. "Loop algebras and algebraic geometry." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=116115.
Повний текст джерелаAravanis, Alexios. "Closed form analysis of Poisson cellular networks: a stochastic geometry approach." Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/667470.
Повний текст джерелаLas redes ultra densas (UDNs) permiten una reutilización espacial del espectro, proporcionando ventajas en términos de mejora de capacidad y ahorro de potencia. Para explotar estas ventajas se necesitan modelos matemáticos simples que permitan el análisis y la optimización de la operación de la red. Por esta razón, la geometría estocástica se ha convertido en una potente herramienta para el análisis de redes celulares. En particular, el empleo de la geometría estocástica ha sido fundamental para la caracterización del rendimiento de la red y para proporcionar información importante sobre la densificación de la misma. Sin embargo, hay problemas fundamentales que deben resolverse para utilizar estas herramientas de geometría estocástica, siendo el mayor desafío la falta de expresiones simples de forma cerrada para las funciones objetivo de interés. Por este motivo, la presente tesis examina la geometría estocástica y proporciona un marco novedoso con una doble contribución. La primera parte de la tesis se centra en la derivación de aproximaciones cerradas simples pero ajustadas para la capacidad ergódica de las redes de Poisson en escenarios limitados por ruido, por interferencia y por ambos. La capacidad ergódica constituye la figura de mérito más apropiada para caracterizar el rendimiento del sistema, pero no se ha formulado en forma cerrada debido a la complejidad inherente de las expresiones de geometría estocástica disponibles. Para demostrar el potencial de las expresiones simples propuestas, la presente tesis propone un paradigma de conectividad flexible y utiliza parte de las expresiones desarrolladas para optimizar la conectividad de la red. El paradigma de conectividad flexible propuesto explota la configuración de "Downlink Uplink Decoupling" (DUDe), que es un marco que proporciona ventajas sustanciales en términos de incremento de capacidad y reducción de la probabilidad de bloqueo en UDNs e introduce mejoras de conectividad DUDe en la era de 5G. Más adelante, la última parte de la tesis proporciona una formulación analítica de la función de densidad de probabilidad (PDF) de la interferencia agregada en las redes celulares de Poisson. La PDF desarrollada es una aproximación precisa de la PDF exacta que hasta ahora no se ha podido formular analíticamente, a pesar de que se trata de una herramienta crucial para el análisis y la optimización de las redes celulares. La falta de una expresión analítica para la PDF de la interferencia en las redes celulares de Poisson había impuesto el uso de fórmulas complejas, a fin de derivar funciones objetivas apropiadas empleando solo la función generadora de momentos (MGF). Por lo tanto, la presente tesis presenta un marco innovador capaz de simplificar el análisis de las redes celulares de Poisson y así resolver problemas fundamentales relacionados con la optimización y el diseño de la red.
Sugimoto, Yoshihiro. "Spectral spread and non-autonomous Hamiltonian diffeomorphisms." Kyoto University, 2019. http://hdl.handle.net/2433/242579.
Повний текст джерелаLamb, McKenzie Russell. "Ginzburg-Weinstein Isomorphisms for Pseudo-Unitary Groups." Diss., The University of Arizona, 2009. http://hdl.handle.net/10150/193755.
Повний текст джерелаChetlur, Ravi Vishnu Vardhan. "Stochastic Geometry for Vehicular Networks." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99954.
Повний текст джерелаDoctor of Philosophy
Vehicular communication networks are essential to the development of intelligent transportation systems (ITS) and improving road safety. As the in-vehicle sensors can assess only their immediate environment, vehicular nodes exchange information about critical events, such as accidents and sudden braking, with other vehicles, pedestrians, roadside infrastructure, and cellular base stations in order to make critical decisions in a timely manner. Considering the time-sensitive nature of this information, it is of paramount importance to design efficient communication networks that can support the exchange of this information with reliable and high-speed wireless links. Typically, prior to actual deployment, any design of a wireless network is subject to extensive analysis under various operational scenarios using computer simulations. However, it is not viable to rely entirely on simulations for the system design of highly complex systems, such as the vehicular networks. Hence, it is necessary to develop analytical methods that can complement simulators and also serve as a benchmark. One of the approaches that has gained popularity in the recent years for the modeling and analysis of large-scale wireless networks is the use of tools from stochastic geometry. In this approach, we endow the locations of wireless nodes with some distribution and analyze various aspects of the network by leveraging the properties of the distribution. Traditionally, wireless networks have been studied using simple spatial models in which the wireless nodes can lie anywhere on the domain of interest (often a 1D or a 2D plane). However, vehicular networks have a unique spatial geometry because the locations of vehicular nodes are restricted to roadways. Therefore, in order to model the locations of vehicular nodes in the network, we have to first model the underlying road systems. Further, we should also consider the randomness in the locations of vehicles on each road. So, we consider a doubly stochastic model called Poisson line Cox process (PLCP), in which the spatial layout of roads are modeled by random lines and the locations of vehicles on the roads are modeled by random set of points on these lines. As is usually the case in wireless networks, multiple vehicular nodes and roadside units (RSUs) operate at the same frequency due to the limited availability of radio frequency spectrum, which causes interference. Therefore, any receiver in the network obtains a signal that is a mixture of the desired signal from the intended transmitter and the interfering signals from the other transmitters. The ratio of the power of desired signal to the aggregate power of the interfering signals, which is called as the signal-to-interference ratio (SIR), depends on the locations of the transmitters with respect to the receiver. A receiver in the network is said to be in coverage if the SIR measured at the location of the receiver exceeds the required threshold to successfully decode the message. The probability of occurrence of this event is referred to as the coverage probability and it is one of the fundamental metrics that is used to characterize the performance of a wireless network. In our work, we have analytically characterized the coverage probability of the typical vehicular node in the network. This was the first work to present the coverage analysis of a vehicular network using the aforementioned doubly stochastic model. In addition to coverage probability, we have also explored other performance metrics such as data rate, which is the number of bits that can be successfully communicated per unit time, and spectral efficiency. Our analysis has revealed interesting trends in the coverage probability as a function of key system parameters such as the density of roads in a region (total length of roads per unit area), and the density of vehicles on the roads. We have shown that the vehicular nodes in areas with high density of roads have lower coverage than those in areas with sparsely distributed roads. On the other hand, the coverage probability of a vehicular node improves as the density of vehicles on the roads increases. Such insights are quite useful in the design and deployment of network infrastructure. While our research was primarily focused on communication networks, the utility of the spatial models considered in these works extends to other areas of engineering. For a special variant of the PLCP, we have derived the distribution of the shortest path distance between an arbitrary point and its nearest neighbor in the sense of path distance. The analytical framework developed in this work allows us to answer several important questions pertaining to infrastructure planning and personnel deployment.
Benedetti, Gabriele. "The contact property for magnetic flows on surfaces." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/247157.
Повний текст джерелаLemes, Ricardo Chicalé [UNESP]. "Propriedades genéricas de sistemas hamiltonianos." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/111007.
Повний текст джерелаCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Nosso objetivo neste trabalho é demonstrar o Teorema da Densidade Geral que é um resultado análogo ao Teorema de Kupka-Smale para campos de vetores hamiltonianos. O Teorema da Densidade Geral afirma que o conjuntos dos campos hamiltonianos em uma variedade simplética M que possuem a propriedade H2-N é residual em Xk H(M). Começamos estabelecendo as teorias simpléticas linear e não-linear básicas e depois estudamos suas conexões com os sistemas hamiltonianos, provando os principais resultados da teoria e alguns resultados relacionados. Recebem destaque o estudo das curvas genéricas de matrizes simpléticas, a noção de funções geradoras de difeomorfismos simpléticos e sua aplicação na questão da estabilidade dos pontos fixos elípticos de campos hamiltonianos, a qual é respondida parcialmente através da Forma Normal de Birkhoff. Depois de estabelecer os resultados necessários, passamos a estudar a dinâmica hamiltoniana do ponto de vista das famílias a um parâmetro de difeomorfismos simpléticos. Provamos um resultado devido a Pugh e consideramos a questão da estabilidade estrutural de certas famílias de difeomorfismos simpléticos. Finalmente, provamos o Teorema da Densidade Geral usando a noção de pseudotransversalidade dada no Apêndice C. Este trabalho é baseado nas notas de aula Lectures on Hamiltonian Systems do professor R. Clark Robinson
In this work our goal is to prove the General Density Theorem which is an analogous result for hamiltonian vector fields of the Kupka-Smale Theorem. The General Density Theorem states that the set of hamiltonian vector fields on a symplectic manifold M that has the property H2-N is a residual subset of Xk H(M). We begin by stating the basic linear and nonlinear symplectic theory and then we study its connections with hamiltonian systems, proving some of the main theorems of the theory and other related results. Here we give special attention to topics like generic curves of symplectic matrices, generating functions of symplectic diffeomorphisms and their applications in the problem of the stability of eliptic fixed points of hamiltonian systems, which is partially solved using the Birkhoff Normal Form. After stating the necessary results, we begin to study some hamiltonian dynamics using one-parameter families of symplectic diffeomorphisms. We prove a result stated by Pugh and consider the problem of structural stability of a certain type of one-parameter family. Finally we prove the General Density Theorem using the notion of pseudotransversality given in Appendix C. This work is based on the lecture notes Lectures on Hamiltonian Systems of professor R. Clark Robinson
Lemes, Ricardo Chicalé. "Propriedades genéricas de sistemas hamiltonianos /." São José do Rio Preto, 2013. http://hdl.handle.net/11449/111007.
Повний текст джерелаBanca: Thiago Aparecido Catalan
Banca: Claudio Aguinaldo Buzzi
Resumo: Nosso objetivo neste trabalho é demonstrar o Teorema da Densidade Geral que é um resultado análogo ao Teorema de Kupka-Smale para campos de vetores hamiltonianos. O Teorema da Densidade Geral afirma que o conjuntos dos campos hamiltonianos em uma variedade simplética M que possuem a propriedade H2-N é residual em Xk H(M). Começamos estabelecendo as teorias simpléticas linear e não-linear básicas e depois estudamos suas conexões com os sistemas hamiltonianos, provando os principais resultados da teoria e alguns resultados relacionados. Recebem destaque o estudo das curvas genéricas de matrizes simpléticas, a noção de funções geradoras de difeomorfismos simpléticos e sua aplicação na questão da estabilidade dos pontos fixos elípticos de campos hamiltonianos, a qual é respondida parcialmente através da Forma Normal de Birkhoff. Depois de estabelecer os resultados necessários, passamos a estudar a dinâmica hamiltoniana do ponto de vista das famílias a um parâmetro de difeomorfismos simpléticos. Provamos um resultado devido a Pugh e consideramos a questão da estabilidade estrutural de certas famílias de difeomorfismos simpléticos. Finalmente, provamos o Teorema da Densidade Geral usando a noção de pseudotransversalidade dada no Apêndice C. Este trabalho é baseado nas notas de aula Lectures on Hamiltonian Systems do professor R. Clark Robinson
Abstract: In this work our goal is to prove the General Density Theorem which is an analogous result for hamiltonian vector fields of the Kupka-Smale Theorem. The General Density Theorem states that the set of hamiltonian vector fields on a symplectic manifold M that has the property H2-N is a residual subset of Xk H(M). We begin by stating the basic linear and nonlinear symplectic theory and then we study its connections with hamiltonian systems, proving some of the main theorems of the theory and other related results. Here we give special attention to topics like generic curves of symplectic matrices, generating functions of symplectic diffeomorphisms and their applications in the problem of the stability of eliptic fixed points of hamiltonian systems, which is partially solved using the Birkhoff Normal Form. After stating the necessary results, we begin to study some hamiltonian dynamics using one-parameter families of symplectic diffeomorphisms. We prove a result stated by Pugh and consider the problem of structural stability of a certain type of one-parameter family. Finally we prove the General Density Theorem using the notion of pseudotransversality given in Appendix C. This work is based on the lecture notes Lectures on Hamiltonian Systems of professor R. Clark Robinson
Mestre
Guan, Peng. "Stochastic Geometry Analysis of LTE-A Cellular Networks." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLS252/document.
Повний текст джерелаThe main focus of this thesis is on performance analysis and system optimization of Long Term Evolution - Advanced (LTE-A) cellular networks by using stochastic geometry. Mathematical analysis of cellular networks is a long-lasting difficult problem. Modeling the network elements as points in a Poisson Point Process (PPP) has been proven to be a tractable yet accurate approach to the performance analysis in cellular networks, by leveraging the powerful mathematical tools such as stochastic geometry. In particular, relying on the PPP-based abstraction model, this thesis develops the mathematical frameworks to the computations of important performance measures such as error probability, coverage probability and average rate in several application scenarios in both uplink and downlink of LTE-A cellular networks, for example, multi-antenna transmissions, heterogeneous deployments, uplink power control schemes, etc. The mathematical frameworks developed in this thesis are general enough and the accuracy has been validated against extensive Monte Carlo simulations. Insights on performance trends and system optimization can be done by directly evaluating the formulas to avoid the time-consuming numerical simulations
Spiegler, Adam. "Stability of Generic Equilibria of the 2n Dimensional Free Rigid Body Using the Energy-Casimir Method." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/194821.
Повний текст джерелаSáez, Calvo Carles. "Finite groups acting on smooth and symplectic 4-manifolds." Doctoral thesis, Universitat de Barcelona, 2019. http://hdl.handle.net/10803/667781.
Повний текст джерелаRoeser, Markus Karl. "The ASD equations in split signature and hypersymplectic geometry." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:7d46ffc8-6d12-4fec-9450-13d2c726885c.
Повний текст джерелаChapron, Aurélie. "Mosaïques de Poisson-Voronoï sur une variété riemannienne." Thesis, Paris 10, 2018. http://www.theses.fr/2018PA100098/document.
Повний текст джерелаA Poisson-Voronoi tessellation is a random partition of the Euclidean space intopolytopes, called cells, obtained from a discrete set of points called germs. To each germ corresponds a cell which is the set of the points of the space which are closer to this germ than to the other germs. These models are often used in several domains such as biology, telecommunication, astronomy, etc. The caracteristics of these tessellations and cells have been widely studied in the Euclidean space but only a few works concerns non-Euclidean Voronoi tessellation. In this thesis, we extend the definition of Poisson-Voronoi tessellation to a Riemannian manifold with finite dimension and we study the caracteristics of the associated cells. More precisely, we first measure the influence of the local geometry of the manifold, namely the curvatures, on the caracteristics of the cells, e.g. the mean volume or the mean number of vertices. Second, we aim to recover the local geometry of the manifold from the combinatorial properties of the tessellation on the manifolds. In particular, we establish limit theorems for the number of vertices of the tessellation, when the intensity of the process of the germs tends to infinity. This leads to the construction of an estimator of the curvature of the manifold and makes it possible to derive some properties of it. The main results of this thesis relies on the combination of stochastic methods and techniques from the differential geometry theory
Singh, Javed Kiran. "Topics in the geometry and physics of Galilei invariant quantum and classical dynamics." Thesis, University of Hull, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.342978.
Повний текст джерелаBergvall, Olof. "Cohomology of the moduli space of curves of genus three with level two structure." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-103062.
Повний текст джерелаMålet med denna uppsats är att undersöka modulirummet M3[2] av kurvor av genus 3 med symplektisk nivå 2 struktur. Mer specifikt vill vi hitta informationom kohomologin av detta rum. För att uppnå detta delar vi först upp M[2] i en disjunkt union av två naturliga delrum, Q[2] och H3[2], och räknar därefter punkterna av dessa rum S7- respektive S8-ekvivariant.
Song, Jian. "A Stochastic Geometry Approach to the Analysis and Optimization of Cellular Networks." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS545.
Повний текст джерелаThe main focus of this thesis is on modeling, performance evaluation and system-level optimization of next-generation cellular networks by using stochastic geometry. In addition, the emerging technology of Reconfigurable Intelligent Surfaces (RISs) is investigated for application to future wireless networks. In particular, relying on a Poisson-based abstraction model for the spatial distribution of nodes and access points, this thesis develops a set of new analytical frameworks for the computation of important performance metrics, such as the coverage probability and potential spectral efficiency, which can be used for system-level analysis and optimization. More specifically, a new analytical methodology for the analysis of three-dimensional cellular networks is introduced and employed for system optimization. A novel resource allocation problem is formulated and solved by jointly combining for the first time stochastic geometry and mixed-integer non-linear programming. The impact of deploying intelligent reflecting surfaces throughout a wireless network is quantified with the aid of line point processes, and the potential benefits of RISs against relaying are investigated with the aid of numerical simulations