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1
Bosch, i. Bastardas Roger. "Projective forcing / Forcing projectiu." Doctoral thesis, Universitat de Barcelona, 2002. http://hdl.handle.net/10803/2097.
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2
Winroth, Harald. "Dynamic projective geometry." Doctoral thesis, Stockholm : Tekniska högsk, 1999. http://www.lib.kth.se/abs99/winr0324.pdf.
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3
Alexiou, John. "Projective articulated dynamics." Thesis, Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/19658.
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4
Rejoub, Riad A. "Projective and non-projective systems of first order nonlinear differential equations." Scholarly Commons, 1992. https://scholarlycommons.pacific.edu/uop_etds/2228.
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It is well established that many physical and chemical phenomena such as those in chemical reaction kinetics, laser cavities, rotating fluids, and in plasmas and in solid state physics are governed by nonlinear differential equations whose solutions are of variable character and even may lack regularities. Such systems are usually first studied qualitatively by examining their temporal behavior near singular points of their phase portrait.
In this work we will be concerned with systems governed by the time evolution equations [see PDF for mathematical formulas]
The xi may generally be considered to be concentrations of species in a chemical reaction, in which case the k's are rate constants. In some cases the xi may be considered to be position and momentum variables in a mechanical system. We will divide the equations into two classes: those in which the evolution can be carried out by the action of one of Lie's transformation groups of the plane, and those for which this is not possible. Members of the first class can be integrated by quadrature either directly or by use of an integrating factor; those in the second class cannot. Of those in the first class the most interesting evolve by transformations of the projective group, and these, as well as the equations that cannot be integrated by quadrature, we study in some detail. We seek a qualitative analysis of systems which have no linear terms in their evolution equations when the origin from which the xi are measured is a critical point. The standard, linear, phase plane analysis is of course not adequate for our purposes.
5
Chomenko, Aleksandr. "Categories with projective functors." [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=970362048.
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6
Rothwell, Charles Andrew. "Recognition using projective invariance." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334849.
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7
Charnes, C. "Invariants and projective planes." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.597502.
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In this thesis we study the isomorphism problem for finite projective planes and in particular for translation planes by using newly defined isomorphism invariants for projective planes. We consider two invariants; one which was proposed by J. H. Conway and is applicable to general projective planes, and another invariant defined only for translation planes. The isomorphism problem poses a serious obstacle in investigations of projective planes, as illustrated by the following remarks (contained in a paper by Hall, Swift and Killgrove). '<i>No satisfactory mechanical way to identify two isomorphic planes exists whether they be presented by a coordinate system or by an incidence matrix. The preparation of such a method is an interesting question</i>.' The approach developed in this thesis provides a partial solution to this problem. We also study the related problem of determining the automorphism group of a projective plane. It turns out that for two-dimensional translation planes of odd order, the methods developed here reduce this problem to a routine calculation of an invariant. We have implemented the above invariants (and a variant) for computation, and used them to study the translation planes of orders: 5<SUP>2</SUP>, 7<SUP>2</SUP>, 8<SUP>2</SUP>, 11<SUP>2</SUP> and 17<SUP>2</SUP> arising from the families of 8-dimensional ovoids defined by Conway <i>et al</i> and others. As a consequence of this investigation we obtain a number of new translation planes and determine their groups. We have also established previously unknown isomorphisms between certain translation planes occurring in the literature. We have found that the invariants have certain interesting properties and I have formulated a number of conjectures regarding these. The conjectures have been verified for all projective planes considered in this thesis, and we offer some comments regarding possibilities for their proof.
8
Hefez, Abramo. "Duality for projective varieties." Thesis, Massachusetts Institute of Technology, 1985. http://hdl.handle.net/1721.1/86249.
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Mainetti, Matteo 1970. "Studies in projective combinatorics." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47426.
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10
Pastor, Pierre. "Communication projective et prevention." Montpellier 3, 1995. http://www.theses.fr/1995MON30041.
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Nous etudions l'impact de communication d'un lieu de prevention contre le cancer : l'espace epidaure a val d'aurelle (montpellier, france) qui accueille un large public, dont l'essentiel est constitue d'enfants. Le principe de ce centre est l'education precoce a la prevention sante. En observant, sur trois ans, deux groupes de 50 enfants : un groupe d'enfants visiteurs, et un groupe temoin, nous avons voulu savoir si la situation de communication vecue, changeait le systeme de pertinence et les attitudes qui sous-tendent les comportements des enfants visiteurs en matiere de sante, et de prevention du cancer. Nous analysons les situations de communication de l'espace epidaure, en utilisant : la recherche des elements situationnels inducteurs (methode proposee par alex mucchielli) et les concepts systemiques de l'ecole de palo alto. Pour l'approche du systeme de pertinence et des attitudes sous-jacentes aux comportements, la voie choisie a ete celle de la communication projective. Nous montrons qu'une visite de deux heures, dans cet espace, permet a 70% du groupe "visiteurs", la restitution des messages-clefs, trois ans apres; mais leur niveau de conscience en matiere de sante n'est pas plus eleve. Le passage des messages preventifs dans les comportements est tres faible et subit une erosion due a la pression ambiante. Les systemes de pertinence des eleves visiteurs ne varient pas dans le sens d'une plus grande attention au probleme de prevention du cancer<br>We are studying the communications impact of a place where cancer is prevented : espace epidaure in val d'aurelle (montpellier, france), that welcomes a general public, mainly children. The principle of this center is early education in order to prevent health. During three years, we observed two groups of fifty children : a visitor group and a witness group, we wanted to know if the situation of real communication changed the significance system and the attitudes that imply the children's behaviour towards health and prvention of cancer. We analyse the situations of communications in epidaure espace using : research of situational inductives elements (from alex mucchielli method) and the systemics concepts of palo alto school. For the approach of the significance system and attitudes that imply the children behaviour, we chose the projective communication. We show that a two-hour visit in this space permits 70% of the visitors group to give the key messages back, three years later. But their level of conciousness about health does not improve. On the other hand, the passage from preventing messages to behaviours is weak because of an erosion due to surrounding pressure. The system of sifnificance of pupils visitors don't vary towards a fuller attention to the problem of prevention of cancer
11
Semenov, Nikita. "Motives of projective homogeneous varieties." Diss., lmu, 2007. http://nbn-resolving.de/urn:nbn:de:bvb:19-70866.
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Parra, Rodrigo. "Lelong numbers on projective varieties." Licentiate thesis, KTH, Matematik (Inst.), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-25285.
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Glesser, Adam M. "Refinements of Dade's projective conjecture /." Diss., Digital Dissertations Database. Restricted to UC campuses, 2006. http://uclibs.org/PID/11984.
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Mroczkowski, Maciej. "Projective links and their invariants /." Uppsala : Matematiska institutionen, Univ. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4519.
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15
Niall, Keith. "Projective invariance and visual perception." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75782.
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Six experiments tested the assumption that, in visual perception, observers have reliable and direct access to the equivalence of shapes in projective geometry (I call this "the invariance hypothesis in the theory of shape constancy"). This assumption has been made in the study of vision since Helmholtz's time. Two experiments tested recognition of the projective equivalence of planar shapes. In another four experiments, subjects estimated the apparent shape of a solid object from different perspectives. Departure from projective equivalence was assessed in each study by measuring the cross ratio for the plane. This measure of projective invariance is new to perceptual research. Projective equivalence was not found to be perceived uniformly in any of the studies. A significant effect of change in perspective was found in each study. These results were construed as supporting the classical theory of depth cues against the invariance hypothesis.
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Malkoun, Joseph. "Holomorphic curves in projective spaces." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=99350.
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If f : C → Pn is a holomorphic curve in complex projective n-space whose image does not lie in a hyperplane, and if xi1, . . . xin+2 are n + 2 hyperplanes of Pn in general position, then the curve f must intersect one of them. We will prove a quantitative refinement of this theorem for n ≤ 2, the so-called defect relations, by expanding the material in Chern's paper [4].
17
Smith, D. J. "Homology modules in projective space." Thesis, University of East Anglia, 2007. https://ueaeprints.uea.ac.uk/38270/.
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Charnes, Christopher. "Isomorphism invariants and projective planes." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386921.
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Bradonjić, Kaća. "Unimodular conformal and projective relativity." Thesis, Boston University, 2012. https://hdl.handle.net/2144/31513.
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Thesis (Ph.D.)--Boston University<br>PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.<br>Existing approaches to quantum gravity fail to fully reconcile the background independence of general relativity and the role of the quantum of action in quantum-mechanical theories. They disagree as to which classical space-time quantities (or observables) should be quantized, and use quantization techniques without taking into consideration the role of measurability analysis in assuring consistency between the definability of these observables and their individual measurability and joint co-measurability by some idealized process. This thesis outlines the framework of a new approach, called Unimodular Conformal and Projective Relativity (UCPR), discusses the classical measurability of all of its basic observables, and examines the problem of extending this analysis to a physically motivated theory of quantum gravity. We consider the unimodular group of transformations (i.e., those with the unit determinant), rather than the full diffeomorphism group, as the basic symmetry group of the theory. This reduction leads to a natural decomposition of the linear affine connection into a projective connection and an affine one-form, and of the Riemannian pseudo-metric into a conformal metric and a volume-element. The geometric representation of all four structures is motivated by their physical interpretation. The projective connection and affine one-form are motivated by the law of inertia; the first determines the paths traversed by massive particles moving only under the combined influence of inertia and gravitation, while the second assures that these particles move at constant speed. The conformal metric determines constant-phase wave-fronts of zero rest-mass fields, while the volume-element permits the averaging of physical fields independently of other space-time structures. Using the UCPR framework, we decompose the usual general-relativistic Lagrangian, and derive the homogenous and inhomogenous field equations and compatibility conditions for the four fundamental fields. The application of this formalism to systems including only zero rest-mass fields is presented. Finally, we outline some approaches to classical measurability analysis of all the relevant structures, and their possible extension to phenomena in which the quantum of action plays a significant role.<br>2031-01-01
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Smith, Nathan A. "Syzygy Decompositions and Projective Resolutions." Diss., Virginia Tech, 1999. http://hdl.handle.net/10919/37649.
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We give a projective resolution of a finite dimensional
<I>K</I>-algebra <I>A</I> over its enveloping
algebra <I>A</I><SUP><I>e</I></SUP> = <I>A</I><SUP><I>op</I></SUP>
<FONT FACE="Symbol">Ã </FONT><SUB><I>K</I></SUB><I>A</I>. The description
of
this resolution is related to decompositions of
the first syzygy module of <I>A</I> as an <I>A</I><SUP><I>e</I></SUP> module.
Resolutions of right <I>A</I>
modules <I>M</I><SUB><I>A</I></SUB> may be obtained by tensoring <I>M</I>
over <I>A</I> with this bimodule resoution. We
describe how to obtain such a resolution when <I>M</I> is simple or when <I>M</I>
is given in the form
of a projective presentation. Computations of
<I>Ext</I><SUP><I>n</I></SUP><SUB><I>A</I></SUB>(<I>S</I><SUB><I>v</I></SUB>,<I>S</I><SUB><I>w</I></SUB>) for
certain classes of algebras <I>A</I> are
made using these resolutions, and applied to obtain results on global
dimension.<br>Ph. D.
21
Marino, Nicholas John. "Vector Bundles and Projective Varieties." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1544457943307018.
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Lukyanenko, Anton Valerievich. "Projective deformations of triangle tilings." College Park, Md. : University of Maryland, 2008. http://hdl.handle.net/1903/8242.
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Thesis (M.A.) -- University of Maryland, College Park, 2008.<br>Thesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Leslie, Nathaniel. "Maximal LELM Distinguishability of Qubit and Qutrit Bell States using Projective and Non-Projective Measurements." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/hmc_theses/108.
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Many quantum information tasks require measurements to distinguish between different quantum-mechanically entangled states (Bell states) of a particle pair. In practice, measurements are often limited to linear evolution and local measurement (LELM) of the particles. We investigate LELM distinguishability of the Bell states of two qubits (two-state particles) and qutrits (three-state particles), via standard projective measurement and via generalized measurement, which allows detection channels beyond the number of orthogonal single-particle states. Projective LELM can only distinguish 3 of 4 qubit Bell states; we show that generalized measurement does no better. We show that projective LELM can distinguish only 3 of 9 qutrit Bell states that generalized LELM allows at most 5 of 9. We have also made progress on distinguishing qubit $\times$ qutrit hyperentangled Bell states, which are made up of tensor products of the qubit Bell states and the qutrit Bell states, showing that the maximum number distinguishable with projective LELM measurements is between 9 and 11.
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Fleming, Patrick Scott. "Finite projective planes and related topics." Laramie, Wyo. : University of Wyoming, 2006. http://proquest.umi.com/pqdweb?did=1225126281&sid=1&Fmt=2&clientId=18949&RQT=309&VName=PQD.
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Gabriel, Rui José. "A identificação projectiva e a psicologia da relação humana." Master's thesis, Instituto Superior de Psicologia Aplicada, 2008. http://hdl.handle.net/10400.12/2714.
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Dissertação de Mestrado em Psicologia Clínica, apresentada ao Instituto Superior de Psicologia Aplicada<br>O mecanismo da Identificação Projectiva foi descrito por Klein como um processo
através do qual partes do self de um indivíduo são clivadas e projectadas num outro.
Este conceito tem sido marcado por uma perspectiva eminentemente intrapsíquica. Com
os avanços da corrente Psicanalítica sobre a natureza relacional dos problemas
psicopatológicos, defendemos que o fenómeno da Identificação Projectiva está
associado a objectos interiorizados incapazes da experiência emocional correspondente
aos aspectos projectados. A Identificação Projectiva conduz a uma interacção humana
em que o receptor é coagido a sentir, pensar ou comportar-se de um modo congruente
com os estados induzidos pelo projector. Este trabalho salienta a importância deste
acontecimento, colocando o ênfase nas capacidades emocionais do terapeuta em
responder emocionalmente ao que o paciente pretende, e problematiza a complexidade
do fenómeno normalmente descrito por contenção.<br>ABSTRACT: Projective Identification is a mechanism described by Klein as a process in which there
is a splitting and projection of parts of the self into another person. This concept is
marked by an eminently intrapsychic perspective. With current advances in the
Psycoanalytic trends about the relational nature of the psycopatological issues we
support that the Projective Identification is a phenomenon associated with internalised
objects that do not allow the experiencing of the emotional contents corresponding to
the projected aspects. Due to this phenomenon there is a human interaction in which the
receptor is pursued to feel, think ou behave in a manner that is congruent with the
emotional state incited by the projector. This paper highlights the importance of this
occurence, emphasising the emotional capacities of the therapyst answering emotionally
to what the patient seeks and the complexities of the phenomenon currently described as
containment.
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Lam, Wai-hung. "Projective embeddings of compact Kähler manifolds." Click to view the E-thesis via HKUTO, 2004. http://sunzi.lib.hku.hk/hkuto/record/B31313620.
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Wong, Tzu Yen. "Image transition techniques using projective geometry." University of Western Australia. School of Computer Science and Software Engineering, 2009. http://theses.library.uwa.edu.au/adt-WU2009.0149.
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[Truncated abstract] Image transition effects are commonly used on television and human computer interfaces. The transition between images creates a perception of continuity which has aesthetic value in special effects and practical value in visualisation. The work in this thesis demonstrates that better image transition effects are obtained by incorporating properties of projective geometry into image transition algorithms. Current state-of-the-art techniques can be classified into two main categories namely shape interpolation and warp generation. Many shape interpolation algorithms aim to preserve rigidity but none preserve it with perspective effects. Most warp generation techniques focus on smoothness and lack the rigidity of perspective mapping. The affine transformation, a commonly used mapping between triangular patches, is rigid but not able to model perspective effects. Image transition techniques from the view interpolation community are effective in creating transitions with the correct perspective effect, however, those techniques usually require more feature points and algorithms of higher complexity. The motivation of this thesis is to enable different views of a planar surface to be interpolated with an appropriate perspective effect. The projective geometric relationship which produces the perspective effect can be specified by two quadrilaterals. This problem is equivalent to finding a perspectively appropriate interpolation for projective transformation matrices. I present two algorithms that enable smooth perspective transition between planar surfaces. The algorithms only require four point correspondences on two input images. ...The second algorithm generates transitions between shapes that lie on the same plane which exhibits a strong perspective effect. It recovers the perspective transformation which produces the perspective effect and constrains the transition so that the in-between shapes also lie on the same plane. For general image pairs with multiple quadrilateral patches, I present a novel algorithm that is transitionally symmetrical and exhibits good rigidity. The use of quadrilaterals, rather than triangles, allows an image to be represented by a small number of primitives. This algorithm uses a closed form force equilibrium scheme to correct the misalignment of the multiple transitional quadrilaterals. I also present an application for my quadrilateral interpolation algorithm in Seitz and Dyer's view morphing technique. This application automates and improves the calculation of the reprojection homography in the postwarping stage of their technique. Finally I unify different image transition research areas into a common framework, this enables analysis and comparison of the techniques and the quality of their results. I highlight that quantitative measures can greatly facilitate the comparisons among different techniques and present a quantitative measure based on epipolar geometry. This novel quantitative measure enables the quality of transitions between images of a scene from different viewpoints to be quantified by its estimated camera path.
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Ding, Yufeng. "Lottery problems, configurations and projective spaces." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0003/NQ42511.pdf.
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Quinlan, Rachel. "Irreducible projective representations of finite groups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ59658.pdf.
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Kermes, Jeremiah Mitchell Mr. "Fermat Curves on Weighted Projective Planes." NCSU, 2007. http://www.lib.ncsu.edu/theses/available/etd-03302007-160623/.
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Hønsen, Morten. "Compactifying locally Cohen-Macaulay projective curves." Doctoral thesis, Stockholm, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-470.
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Penttila, T. "Collineations and configurations in projective spaces." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355767.
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Lam, Wai-hung, and 林偉雄. "Projective embeddings of compact Kähler manifolds." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B31313620.
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Brotbek, Damian. "Variétés projective à fibré cotangent ample." Phd thesis, Université Rennes 1, 2011. http://tel.archives-ouvertes.fr/tel-00677065.
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Nous étudions différentes propriétés d'hyperbolicité pour les variétés intersection complète. Étant donnée une variété intersection complète lisse X ⊂ M dans une variété projective complexe lisse, nous démontrons que si k est plus grand que dim X/ codimM X et si le multidegré de X est suffisamment grand alors il existe sur X des équations différentielles de jets d'ordre k et de degré m pour m suffisamment grand. Ensuite nous étudions une conjecture de O. Debarre : si X ⊂ P^N est l'intersection d'au moins N/2 hypersurfaces génériques de degré suffisamment grand, alors le fibré cotangent de X est ample. Nous donnons différents résultats partiels en direction de cette conjecture. Nous démontrons que si X vérifie les hypothèses de la conjecture alors X est hyperbolique et le fibré cotangent de X est numériquement positif, gros, et ample en dehors d'un lieu de codimension au moins 2. Nous donnons ensuite une stratégie pour calculer explicitement des formes différentielles symétriques sur des variétés intersection complète particulières. Enfin, nous démontrons un théorème d'annulation pour la cohomologie des fibrés de différentielles de jets de Green-Griffiths, généralisant ainsi un théorème de Schneider et un théorème de Diverio. Pour finir, nous étudions la cohomologie des fibrés en droites sur l'hypersurface universelle des diviseurs dans P^1.
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Al-Thani, Huda Mohommed Jaber. "Projective and injective semimodules over semirings." Thesis, University of East London, 1998. http://roar.uel.ac.uk/679/.
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In this thesis general notions of projectivity and injectivity for semimodules are defined. This is done by introducing what we call k-projective and i-injective semimodules. The concepts of cogenerator and flatness have also been introduced. In chapter I we give an equivalent definition to projective semimodule. It is shown that the class of all semirnodules such that P is Mk-projective [P is M-injective (P is Mi-injective)] is closed under subsemimodules, factor semimodules and under taking homomorphic images for a k-regular homomorphism. We also characterize the projective, k-projective, injective and i-injective semimodulesi n terms of the Hom functor (chapters I and 111) Also we relate types of injectivity with several types of semi-cogenerators (chapter 111). In chapter 11 we prove that the contravariat functor Hom(-, C) is faithful (semi-faithful) if and only if C is a cogenerator (semi-cogenerator). We introduce the concept of reject for semimodules which plays the important role of radicals in module theory. We show that for any semimodule M and any class μ of semimodules, there is a unique largest factor semimodule of M semi-cogenerated [k-strongly semi-cogenerated (strongly semi-cogenerated)] by μ irrespective of μ semi-cogenerating [k-strongly semi-cogenerating (strongly semi-cogenerating)] M or not. We also characterize semicogenerators in terrns of the Hom functor. Finally, in chapter IV we introduce and investigate flat semimodules and k-flat semimodules. We prove that the semimodule V is flat if and only if the functor (V⊗R-) preserves the exactness of all right regular short exact sequences. We describe the relationship between projectivity and flatness for a certain restricted class of semirings and semimodules. The relationship between flatness and injectivity is also investigated.
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Cook, Gary Russell. "Arcs in a finite projective plane." Thesis, University of Sussex, 2011. http://sro.sussex.ac.uk/id/eprint/7510/.
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The projective plane of order 11 is the dominant focus of this work. The motivation for working in the projective plane of order 11 is twofold. First, it is the smallest projective plane of prime power order such that the size of the largest (n, r)-arc is not known for all r ∈ {2,...,q + 1}. It is also the smallest projective plane of prime order such that the (n; 3)-arcs are not classified. Second, the number of (n, 3)-arcs is significantly higher in the projective plane of order 11 than it is in the projective plane of order 7, giving a large number of (n, 3)-arcs for study. The main application of (n, r)-arcs is to the study of linear codes. As a forerunner to the work in the projective plane of order eleven two algorithms are used to raise the lower bound on the size of the smallest complete n-arc in the projective plane of order thirty-one from 12 to 13. This work presents the classification up to projective equivalence of the complete (n, 3)- arcs in PG(2, 11) and the backtracking algorithm that is used in its construction. This algorithm is based on the algorithm used in [3]; it is adapted to work on (n, 3)-arcs as opposed to n-arcs. This algorithm yields one representative from every projectively inequivalent class of (n, 3)-arc. The equivalence classes of complete (n, 3)-arcs are then further classified according to their stabilizer group. The classification of all (n, 3)-arcs up to projective equivalence in PG(2, 11) is the foundation of an exhaustive search that takes one element from every equivalence class and determines if it can be extended to an (n′, 4)-arc. This search confirmed that in PG(2, 11) no (n, 3)-arc can be extended to a (33, 4)-arc and that subsequently m4(2, 11) = 32. This same algorithm is used to determine four projectively inequivalent complete (32, 4)-arcs, extended from complete (n, 3)-arcs. Various notions under the general title of symmetry are defined both for an (n, r)-arc and for sets of points and lines. The first of these makes the classification of incomplete (n; 3)- arcs in PG(2, 11) practical. The second establishes a symmetry based around the incidence structure of each of the four projectively inequivalent complete (32, 4)-arcs in PG(2, 11); this allows the discovery of their duals. Both notions of symmetry are used to analyze the incidence structure of n-arcs in PG(2, q), for q = 11, 13, 17, 19. The penultimate chapter demonstrates that it is possible to construct an (n, r)-arc with a stabilizer group that contains a subgroup of order p, where p is a prime, without reference to an (m < n, r)-arc, with stabilizer group isomorphic to ℤ1. This method is used to find q-arcs and (q + 1)-arcs in PG(2, q), for q = 23 and 29, supporting Conjecture 6.7. The work ends with an investigation into the effect of projectivities that are induced by a matrix of prime order p on the projective planes. This investigation looks at the points and subsets of points of order p that are closed under the right action of such matrices and their structure in the projective plane. An application of these structures is a restriction on the size of an (n, r)-arc in PG(2, q) that can be stabilized by a matrix of prime order p.
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Granja, Gustavo 1971. "Self maps of quaternionic projective spaces." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/42690.
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Romano, Raquel Andrea. "Projective minimal analysis of camera geometry." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/29231.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.<br>Includes bibliographical references (p. 115-120).<br>This thesis addresses the general problem of how to find globally consistent and accurate estimates of multiple-view camera geometry from uncalibrated imagery of an extended scene. After decades of study, the classic problem of recovering camera motion from image correspondences remains an active area of research. This is due to the practical difficulties of estimating many interacting camera parameters under a variety of unknown imaging conditions. Projective geometry offers a useful framework for analyzing uncalibrated imagery. However, the associated multilinear models-the fundamental matrix and trifocal tensorare redundant in that they allow a camera configuration to vary along many more degrees of freedom than are geometrically admissible. This thesis presents a novel, minimal projective model of uncalibrated view triplets in terms of the dependent epipolar geometries among view pairs. By explicitly modeling the trifocal constraints among projective bifocal parameters-the epipoles and epipolar collineations-this model guarantees a solution that lies in the valid space of projective camera configurations. We present a nonlinear incremental algorithm for fitting the trifocally constrained epipolar geometries to observed image point matches. The minimal trifocal model is a practical alternative to the trifocal tensor for commonly found image sequences in which the availability of matched point pairs varies widely among different view pairs. Experimental results on synthetic and real image sequences with typical asymmetries in view overlap demonstrate the improved accuracy of the new trifocally constrained model.<br>(cont.) We provide an analysis of the objective function surface in the projective parameter space and examine cases in which the projective parameterization is sensitive to the Euclidean camera configuration. Finally, we present a new, numerically stable method for minimally parameterizing the epipolar geometry that gives improved estimates of minimal projective representations.<br>by Raquel A. Romano.<br>Ph.D.
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Wang, Zhixiang. "Projective structure on 4-dimensional manifolds." Thesis, University of Aberdeen, 2012. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=206987.
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The object of my thesis is to investigate projectively related metrics, that is, metrics whose Levi-Civita connections admit exactly the same family of unparametrised geodesics on 4-dimensional manifolds with positive de nite or neutral (+;+;;) signatures. The general idea is to study the relationship between projectively related metrics and the holonomy types of each metric. The main technique presented in the work requires a certain classification of the curvature map which has been developed by G. S. Hall and D. P. Lonie in the case of Lorentz signature. In chapter 1, some of the background theory will be given. This will include an introduction to bivector algebra, a revision of the Riemann curvature tensor and holonomy theory and, in particular, the fundamental equations for projective related metrics. A brief historical and bibliographical review is also given. The subsequent chapter gives the details of projective related metrics of positive definite signature. In x2.1, the structure of so(4) is described with an emphasis on the canonical decomposition of bivectors and then the subalgebras of so(4) follow. In x2.2., the problem of projective related metrics can be solved case by case decided by holonomy types. In many of these cases, the connections are found to be necessarily equal. A few cases with nontrivial projectively related metrics have been found by only in the rather special case of curvature class D, and the metrics are given in the appendices. An extension of this method to spaces of neutral signature (+;+;;) is made in chapter 3. The rst part of the chapter discusses the algebraic structure of a 4-dimensional vector space with such a metric. In contrast to metrics of the other two signatures (positive definite and Lorentz), this metric admits totally null planes. The structure of the Lie algebra so(2; 2) can be described through the action on totally null planes. The classification of all subalgebras of so(2,2) is then obtained in terms of self-dual and anti-self-dual bivectors. In most holonomy types and curvature classes, the problem has only trivial solutions. Nontrivial projectively related metrics can be found for four holonomy types with curvature class D and two holonomy types with curvature class A.
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Petrescu, Brindusa. "L'identification projective : les énigmes d'un concept." Paris 7, 2002. http://www.theses.fr/2002PA070051.
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La naissance et l'évolution du concept d'identification projective montrent que celui-ci était destiné dès le début à parler du contre-tranfert, étant créé par une défense à l'égard de l'étrangeté du contre-transfert pour la théorie psychanalytique. L'auteur propose que l'identification projective soit vue comme un concept-limite pour la théorie psychanalytique et, accompagnée par la notion de pulsion, comme un cadre théorique pour la pensée de l'analyste<br>The birth and evolution of the concept of projective identification show that this notion was destined from the beginning to speak about countertransference, being created by a defense against the peculiarity of countertransference for the psychoanalytic theory and, accompanied by the notion of drive, as a theoretical setting for the analytic thinking
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Brunson, Jason Cornelius. "On Projective Planes & Rational Identities." Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/32498.
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One of the marvelous phenomena of coordinate geometry is the equivalence of Desargues' Theorem to the presence of an underlying division ring in a projective plane. Supplementing this correspondence is the general theory of intersection theorems, which, restricted to desarguian projective planes P, corresponds precisely to the theory of integral rational identities, restricted to division rings D. The first chapter of this paper introduces projective planes, develops the concept of an intersection theorem, and expounds upon the Theorem of Desargues; the discussion culminates with a proof of the desarguian phenomenon in the second chapter. The third chapter characterizes the automorphisms of P and introduces the theory of polynomial identities; the fourth chapter expands this discussion to rational identities and cements the ``dictionary''. The last section describes a measure of complexity for these intersection theorems, and the paper concludes with a curious spawn of the correspondence.<br>Master of Science
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Mori, Izuru. "Some results on quantum projective planes /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/5790.
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Brelet-Foulard, Françoise. "Le TAT, fantasme et situation projective." Lille 3 : ANRT, 1989. http://catalogue.bnf.fr/ark:/12148/cb376123288.
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Contatto, Felipe. "Vortices, Painlevé integrability and projective geometry." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/275099.
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GaugThe first half of the thesis concerns Abelian vortices and Yang-Mills theory. It is proved that the 5 types of vortices recently proposed by Manton are actually symmetry reductions of (anti-)self-dual Yang-Mills equations with suitable gauge groups and symmetry groups acting as isometries in a 4-manifold. As a consequence, the twistor integrability results of such vortices can be derived. It is presented a natural definition of their kinetic energy and thus the metric of the moduli space was calculated by the Samols' localisation method. Then, a modified version of the Abelian–Higgs model is proposed in such a way that spontaneous symmetry breaking and the Bogomolny argument still hold. The Painlevé test, when applied to its soliton equations, reveals a complete list of its integrable cases. The corresponding solutions are given in terms of third Painlevé transcendents and can be interpreted as original vortices on surfaces with conical singularity. The last two chapters present the following results in projective differential geometry and Hamiltonians of hydrodynamic-type systems. It is shown that the projective structures defined by the Painlevé equations are not metrisable unless either the corresponding equations admit first integrals quadratic in first derivatives or they define projectively flat structures. The corresponding first integrals can be derived from Killing vectors associated to the metrics that solve the metrisability problem. Secondly, it is given a complete set of necessary and sufficient conditions for an arbitrary affine connection in 2D to admit, locally, 0, 1, 2 or 3 Killing forms. These conditions are tensorial and simpler than the ones in previous literature. By defining suitable affine connections, it is shown that the problem of existence of Killing forms is equivalent to the conditions of the existence of Hamiltonian structures for hydrodynamic-type systems of two components.
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Weilandt, Martin. "Isospectral metrics on weighted projective spaces." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2010. http://dx.doi.org/10.18452/16169.
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Der Laplace-Operator auf kompakten Riemannschen Mannigfaltigkeiten besitzt eine natürliche Verallgemeinerung auf kompakte Riemannsche Orbifolds und das Spektrum des so gewonnenen Operators besteht ausschließlich aus Eigenwerten endlicher Vielfachheit. Die Feststellung, dass das Spektrum Informationen über die Geometrie einer Mannigfaltigkeit (oder, allgemeiner, einer Orbifold) enthält, begründete ein ganzes Teilgebiet der Mathematik. Es ist eine offene Frage der sogenannten Spektralgeometrie, ob eine Mannigfaltigkeit und eine singuläre Orbifold isospektral sein (d.h., dasselbe Spektrum mitsamt den Vielfachheiten der Eigenwerte besitzen) können. Angesichts diverser Obstruktionen zur Existenz eines solchen Beispiels für die bekannten Beispiele isospektraler guter Orbifolds, soll diese Arbeit die Spektralgeometrie schlechter Orbifolds erhellen. Zu diesem Zweck geben wir die ersten Beispiele für isospektrale Metriken auf schlechten Orbifolds an. Diese basieren auf bestimmten gewichteten projektiven Räumen, auf denen wir mittels einer Verallgemeinerung von Schüths Version der Torus-Methode nicht-trivial isospektrale Metriken konstruieren.<br>The Laplace Operator on compact Riemannian manifolds naturally generalizes to compact Riemannian orbifolds and the spectrum of the resulting operator consists only of eigenvalues with finite multiplicities. The observation that the spectrum contains information about the geometry of a manifold (and, more generally, an orbifold) gave rise to a whole field of mathematics. It is an open question of so-called spectral geometry, whether a manifold and a singular orbifold can be isospectral (i.e., have the same spectrum with the same multiplicities of the eigenvalues). Given the various obstructions to the existence of such an example for the known examples of isospectral good orbifolds, this work is an attempt to shed light on the spectral geometry of bad orbifolds by giving the first examples of isospectral Riemannian metrics on bad orbifolds. In our case these are particular fixed weighted projective spaces equipped with non-trivially isospectral metrics obtained by a generalization of Schüth''s version of the torus method.
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Baboin, Anne-Céline. "Calcul quantique : algèbre et géométrie projective." Phd thesis, Université de Franche-Comté, 2011. http://tel.archives-ouvertes.fr/tel-00600387.
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Cette thèse a pour première vocation d'être un état de l'art sur le calcul quantique, sinon exhaustif, simple d'accès (chapitres 1, 2 et 3). La partie originale de cet essai consiste en deux approches mathématiques du calcul quantique concernant quelques systèmes quantiques : la première est de nature algébrique et fait intervenir des structures particulières : les corps et les anneaux de Galois (chapitre 4), la deuxième fait appel à la géométrie dite projective (chapitre 5). Cette étude a été motivée par le théorème de Kochen et Specker et par les travaux de Peres et Mermin qui en ont découlé
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Baboin, Anne-Céline. "Calcul quantique : algèbre et géométrie projective." Electronic Thesis or Diss., Besançon, 2011. http://www.theses.fr/2011BESA2028.
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Cette thèse a pour première vocation d’être un état de l’art sur le calcul quantique, sinon exhaustif, simple d’accès (chapitres 1, 2 et 3). La partie originale de cet essai consiste en deux approches mathématiques du calcul quantique concernant quelques systèmes quantiques : la première est de nature algébrique et fait intervenir des structures particulières : les corps et les anneaux de Galois (chapitre 4), la deuxième fait appel à la géométrie dite projective (chapitre 5). Cette étude a été motivée par le théorème de Kochen et Specker et par les travaux de Peres et Mermin qui en ont découlé<br>The first vocation of this thesis would be a state of the art on the field of quantum computation, if not exhaustive, simple access (chapters 1, 2 and 3). The original (interesting) part of this treatise consists of two mathematical approaches of quantum computation concerning some quantum systems : the first one is an algebraic nature and utilizes some particular structures : Galois fields and rings (chapter 4), the second one calls to a peculiar geometry, known as projective one (chapter 5). These two approaches were motivated by the theorem of Kochen and Specker and by work of Peres and Mermin which rose from it
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Fléchelles, Balthazar. "Geometric finiteness in convex projective geometry." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM029.
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Cette thèse est consacrée à l’étude des orbivariétés projectives convexes géométriquement finies, et fait suite aux travaux de Ballas, Cooper, Crampon, Leitner, Long, Marquis et Tillmann sur le sujet. Une orbivariété projective convexe est le quotient d’un ouvert convexe et borné d’une carte affine de l’espace projectif réel (appelé aussi ouvert proprement convexe) par un groupe discret de transformations projectives préservant cet ouvert. S’il n’y a pas de segment dans le bord du convexe, on dit que l’orbivariété est strictement convexe, et si de plus il y a un unique hyperplan de support en chaque point du bord, on dit qu’elle est ronde. Suivant Cooper-Long-Tillmann et Crampon-Marquis, on dit qu’une orbivariété strictement convexe est géométriquement finie si son cœur convexe est l’union d’un compact et d’un nombre fini de bouts, appelés pointes, où le rayon d’injectivité est inférieur à une constante ne dépendant que de la dimension. Comprendre la géométrie des pointes est primordial pour l’étude des orbivariétés géométriquement finies. Dans le cas strictement convexe, la seule restriction connue sur l’holonomie des pointes vient d’une généralisation du lemme de Margulis due à Cooper-Long-Tillmann et Crampon-Marquis, qui implique que cette holonomie est virtuellement nilpotente. On donne dans cette thèse une caractérisation de l’holonomie des pointes des orbivariétés strictement convexes et des orbivariétés rondes. En généralisant la méthode de Cooper, qui a produit le seul exemple connu jusqu’ici d’une pointe de variété strictement convexe dont l’holonomie n’est pas virtuellement abélienne, on construit des pointes de variétés strictement convexes et de variétés rondes dont l’holonomie est isomorphe à n’importe quel groupe nilpotent sans torsion de type fini. En collaboration avec M. Islam et F. Zhu, on démontre que dans le cas des groupes relativement hyperboliques sans torsion, les représentations relativement P1-anosoviennes (au sens de Kapovich-Leeb, Zhu et Zhu-Zimmer) qui préservent un ouvert proprement convexe sont exactement les holonomies des variétés rondes géométriquement finies.Dans le cas des orbivariétés projectives convexes non strictement convexes, il n’y a pas pour l’instant de définition satisfaisante de la finitude géométrique. Toutefois, Cooper-Long-Tillmann puis Ballas-Cooper-Leitner ont proposé une définition de pointe généralisée dans ce contexte. Bien qu’ils demandent que l’holonomie des pointes généralisées soit virtuellement nilpotente, tous les exemples connus jusqu’à présent avaient une holonomie virtuellement abélienne. On construit des exemples de pointes généralisées dont l’holonomie peut être n’importe quel groupe nilpotent sans torsion de type fini. On s’autorise également à modifier la définition originale de Cooper-Long-Tillmann en affaiblissant l’hypothèse de nilpotence en une hypothèse naturelle de résolubilité, ce qui nous permet de construire de nouveaux exemples dont l’holonomie n’est pas virtuellement nilpotente.Une orbivariété géométriquement finie qui n’a pas de pointes, c’est-à-dire dont le cœur convexe est compact, est dite convexe cocompacte. On dispose par les travaux de Danciger-Guéritaud-Kassel d’une définition de la convexe cocompacité pour les orbivariétés projectives convexes sans hypothèse de stricte convexité, contrairement au cas géométriquement fini. Ils démontrent que l’holonomie d’une orbivariété projective convexe convexe cocompacte est Gromov hyperbolique si et seulement si la représentation associée est P1-anosovienne. À l’aide de ce résultat, de la théorie de Vinberg et des travaux d’Agol et Haglund-Wise sur les groupes hyperboliques cubulés, on construit en collaboration avec S. Douba, T. Weisman et F. Zhu des représentations P1-anosoviennes pour tout groupe hyperbolique cubulé. Ceci fournit de nouveaux exemples de groupes hyperboliques admettant des représentations anosoviennes<br>This thesis is devoted to the study of geometrically finite convex projective orbifolds, following work of Ballas, Cooper, Crampon, Leitner, Long, Marquis and Tillmann. A convex projective orbifold is the quotient of a bounded, convex and open subset of an affine chart of real projective space (called a properly convex domain) by a discrete group of projective transformations that preserve it. We say that a convex projective orbifold is strictly convex if there are no non-trivial segments in the boundary of the convex subset, and round if in addition there is a unique supporting hyperplane at each boundary point. Following work of Cooper-Long-Tillmann and Crampon-Marquis, we say that a strictly convex orbifold is geometrically finite if its convex core decomposes as the union of a compact subset and of finitely many ends, called cusps, all of whose points have an injectivity radius smaller than a constant depending only on the dimension. Understanding what types of cusps may occur is crucial for the study of geometrically finite orbifolds. In the strictly convex case, the only known restriction on cusp holonomies, imposed by a generalization of the celebrated Margulis lemma proven by Cooper-Long-Tillmann and Crampon-Marquis, is that the holonomy of a cusp has to be virtually nilpotent. We give a complete characterization of the holonomies of cusps of strictly convex orbifolds and of those of round orbifolds. By generalizing a method of Cooper, which gave the only previously known example of a cusp of a strictly convex manifold with non virtually abelian holonomy, we build examples of cusps of strictly convex manifolds and round manifolds whose holonomy can be any finitely generated torsion-free nilpotent group. In joint work with M. Islam and F. Zhu, we also prove that for torsion-free relatively hyperbolic groups, relative P1-Anosov representations (in the sense of Kapovich-Leeb, Zhu and Zhu-Zimmer) that preserve a properly convex domain are exactly the holonomies of geometrically finite round manifolds.In the general case of non strictly convex projective orbifolds, no satisfactory definition of geometric finiteness is known at the moment. However, Cooper-Long-Tillmann, followed by Ballas-Cooper-Leitner, introduced a notion of generalized cusps in this context. Although they only require that the holonomy be virtually nilpotent, all previously known examples had virtually abelian holonomy. We build examples of generalized cusps whose holonomy can be any finitely generated torsion-free nilpotent group. We also allow ourselves to weaken Cooper-Long-Tillmann’s original definition by assuming only that the holonomy be virtually solvable, and this enables us to construct new examples whose holonomy is not virtually nilpotent.When a geometrically finite orbifold has no cusps, i.e. when its convex core is compact, we say that the orbifold is convex cocompact. Danciger-Guéritaud-Kassel provided a good definition of convex cocompactness for convex projective orbifolds that are not necessarily strictly convex. They proved that the holonomy of a convex cocompact convex projective orbifold is Gromov hyperbolic if and only if the associated representation is P1-Anosov. Using these results, Vinberg’s theory and work of Agol and Haglund-Wise about cubulated hyperbolic groups, we construct, in collaboration with S. Douba, T. Weisman and F. Zhu, examples of P1-Anosov representations for any cubulated hyperbolic group. This gives new examples of hyperbolic groups admitting Anosov representations
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Sved, Marta. "On finite linear and baer structures /." Title page, contents and summary only, 1985. http://web4.library.adelaide.edu.au/theses/09PH/09phs9683.pdf.
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Oxenham, Martin Glen. "On n-covers of PG (3,q) and related structures /." Title page, contents and introduction only, 1991. http://web4.library.adelaide.edu.au/theses/09PH/09pho98.pdf.
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