Дисертації з теми "Finite geometry; projective geometry"
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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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Cook, Gary Russell. "Arcs in a finite projective plane." Thesis, University of Sussex, 2011. http://sro.sussex.ac.uk/id/eprint/7510/.
Повний текст джерелаАнотація:
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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Hamed, Zainab Shehab. "Arcs of degree four in a finite projective plane." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/77816/.
Повний текст джерелаАнотація:
The projective plane, PG(2;q), over a Galois field Fq is an incidence structure of points and lines. A (k;n)-arc K in PG(2;q) is a set of k points such that no n+1 of them are collinear but some n are collinear. A (k;n)-arc K in PG(2;q) is called complete if it is not contained in any (k+1;n)-arc. The existence of arcs for particular values of k and n pose interesting problems in finite geometry. It connects with coding theory and graph theory, with important applications in computer science. The main problem, known as the packing problem, is to determine the largest size mn(2;q) of K in PG(2;q). This problem has received much attention. Here, the work establishes complete arcs with a large number of points. In contrast, the problem to determine the smallest size tn(2;q) of a complete (k;n)-arc is mostly based on the lower bound arising from theoretical investigations. This thesis has several goals. The first goal is to classify certain (k;4)-arcs for k = 6,...,38 in PG(2;13). This classification is established through an approach in Chapter 2. This approach uses a new geometrical method; it is a combination of projective inequivalence of (k;4)-arcs up to k = 6 and certain sdinequivalent (k;4)-arcs that have sd-inequivalent classes of secant distributions for k = 7,...,38. The part related to projectively inequivalent (k;4)-arcs up to k=6 starts by fixing the frame points f1;2;3;88g and then classify the projectively inequivalent (5;4)-arcs. Among these (5;4)-arcs and (6;4)-arcs, the lexicographically least set are found. Now, the part regarding sd-inequivalent (k;4)-arcs in this method starts by choosing five sd-inequivalent (7;4)-arcs. This classification method may not produce all sd-inequivalent classes of (k;4)-arcs. However, it was necessary to employ this method due to the increasing number of (k;4)-arcs in PG(2;13) and the extreme computational difficulty of the problem. It reduces the constructed number of (k;4)-arcs in each process for large k. Consequently, it reduces the executed time for the computation which could last for years. Also, this method decreases the memory usage needed for the classification. The largest size of (k;4)-arc established through this method is k = 38. The classification of certain (k;4)-arcs up to projective equivalence, for k = 34,35,36,37,38, is also established. This classification starts from the 77 incomplete (34;4)-arcs that are constructed from the sd-inequivalent (33;4)-arcs given in Section 2.29, Table 2.35. Here, the largest size of (k;4)-arc is still k = 38. In addition, the previous process is re-iterated with a different choice of five sd-inequivalent (7;4)-arcs. The purpose of this choice is to find a new size of complete (k;4)-arc for k > 38. This particular computation of (k;4)-arcs found no complete (k;4)-arc for k > 38. In contrast, a new size of complete (k;4)-arc in PG(2;13) is discovered. This size is k = 36 which is the largest complete (k;4)-arc in this computation. This result raises the second largest size of complete (k;4)-arc found in the first classification from k = 35 to k = 36. The second goal is to discuss the incidence structure of the orbits of the groups of the projectively inequivalent (6;4)-arcs and also the incidence structures of the orbits of the groups other than the identity group of the sd-inequivalent (k;4)-arcs. In Chapter 3, these incidence structures are given for k = 6,7,8,9,10,11,12,13,14,38. Also, the pictures of the geometric configurations of the lines and the points of the orbits are described. The third goal is to find the sizes of certain sd-inequivalent complete (k;4)-arcs in PG(2;13). These sizes of complete (k;4)-arcs are given in Chapter 4 where the smallest size of complete (k;4)-arc is at most k = 24 and the largest size is at least k = 38. The fourth goal is to give an example of an associated non-singular quartic curve C for each complete (k;4)-arc and to discuss the algebraic properties of each curve in terms of the number I of inflexion points, the number jC \K j of rational points on the corresponding arc, and the number N1 of rational points of C . These curves are given in Chapter 5. Also, the algebraic properties of complete arcs of the most interesting sizes investigated in this thesis are studied. In addition, there are two examples of quartic curves C (g0 1) and C (g0 2) attaining the Hasse-Weil- Serre upper bound for the number N1 of rational points on a curve over the finite field of order thirteen. This number is 32. The fifth goal is to classify the (k;4)-arcs in PG(2;13) up to projective inequivalence for k < 10. This classification is established in Chapter 6. It starts by fixing a triad, U1, on the projective line, PG(1;13). Here, the number of projectively inequivalent (k;4)-arcs are tested by using the tool given in Chapter 2. Then, among the number of the projectively inequivalent (10;4)-arcs found, the classification of sd-inequivalent (k;4)-arcs for k = 10 is made. The number of these sd-inequivalent arcs is 36. Then, the 36 sd-inequivalent arcs are extended. The aim here is to investigate if there is a new size of sd-inequivalent (k;4)-arc for k > 38 that can be obtained from these arcs. The largest size of sd-inequivalent (k;4)-arc in this process is the same as the largest size of the sd-inequivalent (k;4)-arc established in Chapter 2, that is, k = 38. In addition, the classification of (k;n)-arcs in PG(2;13) is extended from n = 4 to n = 6. This extension is given in Chapter 7 where some results of the classification of certain (k;6)-arcs for k = 9; : : : ;25 are obtained using the same method as in Chapter 2 for k = 7,...,38. This process starts by fixing a certain (8;6)-arc containing six collinear points in PG(2;13).
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Pichanick, E. V. D. "Bounds for complete arcs in finite projective planes." Thesis, University of Sussex, 2016. http://sro.sussex.ac.uk/id/eprint/63459/.
Повний текст джерелаАнотація:
This thesis uses algebraic and combinatorial methods to study subsets of the Desarguesian plane IIq = PG(2, q). Emphasis, in particular, is given to complete (k, n)-arcs and plane projective curves. Known Diophantine equations for subsets of PG(2, q), no more than n of which are collinear, have been applied to k-arcs of arbitrary degree. This yields a new lower bound for complete (k, n)-arcs in PG(2, q) and is a generalization of a classical result of Barlotti. The bound is one of few known results for complete arcs of arbitrary degree and establishes new restrictions upon the parameters of associated projective codes. New results governing the relationship between (k, 3)-arcs and blocking sets are also provided. Here, a sufficient condition ensuring that a blocking set is induced by a complete (k, 3)-arc in the dual plane q is established and shown to complement existing knowledge of relationships between k-arcs and blocking sets. Combinatorial techniques analyzing (k, 3)-arcs in suitable planes are then introduced. Utilizing the numeric properties of non-singular cubic curves, plane (k, 3)-arcs satisfying prescribed incidence conditions are shown not to attain existing upper bounds. The relative sizes of (k, 3)-arcs and non-singular cubic curves are also considered. It is conjectured that m3(2, q), the size of the largest complete (k, 3)-arc in PG(2, q), exceeds the number of rational points on an elliptic curve. Here, a sufficient condition for its positive resolution is given using combinatorial analysis. Exploiting its structure as a (k, 3)-arc, the elliptic curve is then considered as a method of constructing cubic arcs and results governing completeness are established. Finally, classical theorems relating the order of the plane q to the existence of an elliptic curve with a specified number of rational points are used to extend theoretical results providing upper bounds to t3(2, q), the size of the smallest possible complete (k, 3)-arc in PG(2, q).
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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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Giuzzi, Luca. "Hermitian varieties over finite fields." Thesis, University of Sussex, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326913.
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White, Clinton T. Wilson R. M. "Two cyclic arrangement problems in finite projective geometry : parallelisms and two-intersection sets /." Diss., Pasadena, Calif. : California Institute of Technology, 2002. http://resolver.caltech.edu/CaltechETD:etd-06052006-143933.
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Culbert, Craig W. "Spreads of three-dimensional and five-dimensional finite projective geometries." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 101 p, 2009. http://proquest.umi.com/pqdweb?did=1891555371&sid=3&Fmt=2&clientId=8331&RQT=309&VName=PQD.
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Vereecke, Sam K. J. "Some properties of arcs, caps and quadrics in projective spaces in finite order." Thesis, University of Sussex, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263915.
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Grout, Jason Nicholas. "The Minimum Rank Problem Over Finite Fields." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1995.pdf.
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Braun, David. "Approche combinatoire pour l'automatisation en Coq des preuves formelles en géométrie d'incidence projective." Thesis, Strasbourg, 2019. http://www.theses.fr/2019STRAD020.
Повний текст джерелаАнотація:
Ce travail de thèse s’inscrit dans le domaine de la preuve assistée par ordinateur et se place d'un point de vue méthodologique. L’objectif premier des assistants de preuves est de vérifier qu’une preuve écrite à la main est correcte; la question ici est de savoir comment à l’intérieur d’un tel système, il est possible d'aider un utilisateur à fabriquer une preuve formelle du résultat auquel il s'intéresse. Ces questions autour de la vérification de preuves, en particulier en certification du logiciel, et au delà de leur traçabilité et de leur lisibilité sont en effet devenues prégnantes avec l’importance qu’ont prise les algorithmes dans notre société. Bien évidemment, répondre à la question de l’aide à la preuve dans toute sa généralité dépasse largement le cadre de cette thèse. C’est pourquoi nous focalisons nos travaux sur la preuve en mathématiques dans un cadre particulier qui est bien connu dans notre équipe : la géométrie et sa formalisation dans le système Coq. Dans ce domaine, nous mettons premièrement en évidence les niveaux auxquels on peut oeuvrer à savoir le contexte scientifique à travers les méthodes de formalisation mais aussi le contexte méthodologique et technique au sein de l'assistant de preuve Coq. Dans un second temps, nous essayons de montrer comment nos méthodes et nos idées sont généralisables à d'autres disciplines. Nous mettons ainsi en place dans nos travaux les premiers jalons pour une aide à la preuve efficace dans un contexte géométrique simple mais omniprésent. À travers une approche classique fondée sur la géométrie synthétique et une approche combinatoire complémentaire utilisant le concept de rang issu de la théorie des matroïdes, nous fournissons à l'utilisateur des principes généraux et des outils facilitant l'élaboration de preuves formelles. Dans ce sens, nous comparons les capacités d'automatisation de ces deux approches dans le contexte précis des géométries finies avant de finalement construire un prouveur automatique de configuration géométrique d'incidenceThis thesis work is part of the general field of computer-assisted proof and is methodologically based. The primary objective of proof assistants is to verify that handwritten demonstration is correct; the question here is how within such a system, it is possible to help a user to make a formal proof of the result in which he is interested. These questions around the verification of proofs, in particular in software certification, and beyond their traceability and readability have indeed become significant with the importance that algorithms have taken on in our society. Obviously, answering the question of proof assistance in all its generality goes far beyond the scope of this thesis. This is why we focus our work on proof in mathematics in a particular framework that is well known in our team: geometry and its formalization in the Coq system. In this field, we first highlight the levels at which we can work, namely the scientific context through the formalization methods but also the methodological and technical context within the Coq proof assistant. In a second step, we try to show how our methods and ideas can be generalized to other disciplines. In this way, we are putting in place the first steps towards effective proof assistance in a simple but omnipresent geometric context. Through a classical approach based on synthetic geometry and a complementary combinatorial approach using the concept of rank from matroid theory, we provide the user with general principles and tools to facilitate the development of formal proof. In this sense, we compare the automation capabilities of these two approaches in the specific context of finite geometries before finally constructing an automatic prover of geometric configurations of incidence
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Winroth, Harald. "Dynamic projective geometry." Doctoral thesis, Stockholm : Tekniska högsk, 1999. http://www.lib.kth.se/abs99/winr0324.pdf.
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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.
Повний текст джерелаАнотація:
[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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Romano, Raquel Andrea. "Projective minimal analysis of camera geometry." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/29231.
Повний текст джерелаАнотація:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 115-120).
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.
(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.
by Raquel A. Romano.
Ph.D.
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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.
Повний текст джерелаАнотація:
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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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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Beardsley, Paul Anthony. "Applications of projective geometry to robot vision." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.316854.
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O'Keefe, Christine M. "Concerning t-spreads of PG ((s + 1) (t + 1)- 1, q)." Title page, contents and summary only, 1987. http://web4.library.adelaide.edu.au/theses/09PH/09pho41.pdf.
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Ellis, Amanda. "Classification of conics in the tropical projective plane /." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1104.pdf.
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Caullery, Florian. "Polynomes sur les corps finis pour la cryptographie." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4013/document.
Повний текст джерелаАнотація:
Les fonctions de F_q dans lui-même sont des objets étudiés dans de divers domaines tels que la cryptographie, la théorie des codes correcteurs d'erreurs, la géométrie finie ainsi que la géométrie algébrique. Il est bien connu que ces fonctions sont en correspondance exacte avec les polynômes en une variable à coefficients dans F_q. Nous étudierons trois classes de polynômes particulières: les polynômes Presque Parfaitement Non linéaires (Almost Perfect Nonlinear (APN)), les polynômes planaires ou parfaitement non linéaire (PN) et les o-polynômes.Les fonctions APN sont principalement étudiées pour leurs applications en cryptographie. En effet, ces fonctions sont celles qui offre la meilleure résistance contre la cryptanalyse différentielle.Les polynômes PN et les o-polynômes sont eux liés à des problèmes célèbres de géométrie finie. Les premiers décrivent des plans projectifs et les seconds sont en correspondance directe avec les ovales et hyperovales de P^2(F_q). Néanmoins, leurs champ d'application a été récemment étendu à la cryptographie symétrique et à la théorie des codes correcteurs d'erreurs.L'un des moyens utilisé pour compléter la classification est de considérer les polynômes présentant l'une des propriétés recherchées sur une infinité d'extension de F_q. Ces fonctions sont appelées fonction APN (respectivement PN ou o-polynômes) exceptionnelles.Nous étendrons la classification des polynômes APN et PN exceptionnels et nous donneront une description complète des o-polynômes exceptionnels. Les techniques employées sont basées principalement sur la borne de Lang-Weil et sur des méthodes élémentairesFunctions from F_q to itself are interesting objects arising in various domains such as cryptography, coding theory, finite geometry or algebraic geometry. It is well known that these functions admit a univariate polynomial representation. There exists many interesting classes of such polynomials with plenty of applications in pure or applied maths. We are interested in three of them: Almost Perfect Nonlinear (APN) polynomials, Planar (PN) polynomials and o-polynomials. APN polynomials are mostly used in cryptography to provide S-boxes with the best resistance to differential cryptanalysis and in coding theory to construct double error-correcting codes. PN polynomials and o-polynomials first appeared in finite geometry. They give rise respectively to projective planes and ovals in P^2(F_q). Also, their field of applications was recently extended to symmetric cryptography and error-correcting codes.A complete classification of APN, PN and o-polynomials is an interesting open problem that has been widely studied by many authors. A first approach toward the classification was to consider only power functions and the studies were recently extended to polynomial functions.One way to face the problem of the classification is to consider the polynomials that are APN, PN or o-polynomials over infinitely many extensions of F_q, namely, the exceptional APN, PN or o-polynomials.We improve the partial classification of exceptional APN and PN polynomials and give a full classification of exceptional o-polynomials. The proof technique is based on the Lang-Weil bound for the number of rational points in algebraic varieties together with elementary methods
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McCallum, Rupert Gordon Mathematics & Statistics Faculty of Science UNSW. "Generalisations of the fundamental theorem of projective geometry." Publisher:University of New South Wales. Mathematics & Statistics, 2009. http://handle.unsw.edu.au/1959.4/43385.
Повний текст джерелаАнотація:
The fundamental theorem of projective geometry states that a mapping from a projective space to itself whose range has a sufficient number of points in general position is a projective transformation possibly combined with a self-homomorphism of the underlying field. We obtain generalisations of this in many directions, dealing with the case where the mapping is only defined on an open subset of the underlying space, or a subset of positive measure, and dealing with many different spaces over many different rings.
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Herman, Ivan. "The use of projective geometry in computer graphics /." Berlin ;Heidelberg ;New York ;London ;Paris ;Tokyo ;Hong Kong ;Barcelona ;Budapest : Springer, 1992. http://www.loc.gov/catdir/enhancements/fy0815/91043253-d.html.
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Goetz, Peter D. "The noncommutative algebraic geometry of quantum projective spaces /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3102165.
Повний текст джерелаАнотація:
Thesis (Ph. D.)--University of Oregon, 2003.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 106-108). Also available for download via the World Wide Web; free to University of Oregon users.
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Frost, George. "The projective parabolic geometry of Riemannian, Kähler and quaternion-Kähler metrics." Thesis, University of Bath, 2016. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690742.
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We present a uniform framework generalising and extending the classical theories of projective differential geometry, c-projective geometry, and almost quaternionic geometry. Such geometries, which we call \emph{projective parabolic geometries}, are abelian parabolic geometries whose flat model is an R-space $G\cdot\mathfrak{p}$ in the infinitesimal isotropy representation $\mathbb{W}$ of a larger self-dual symmetric R-space $H\cdot\mathfrak{q}$. We also give a classification of projective parabolic geometries with $H\cdot\mathfrak{q}$ irreducible which, in addition to the aforementioned classical geometries, includes a geometry modelled on the Cayley plane $\mathbb{OP}^2$ and conformal geometries of various signatures. The larger R-space $H\cdot\mathfrak{q}$ severely restricts the Lie-algebraic structure of a projective parabolic geometry. In particular, by exploiting a Jordan algebra structure on $\mathbb{W}$, we obtain a $\mathbb{Z}^2$-grading on the Lie algebra of $H$ in which we have tight control over Lie brackets between various summands. This allows us to generalise known results from the classical theories. For example, which riemannian metrics are compatible with the underlying geometry is controlled by the first BGG operator associated to $\mathbb{W}$. In the final chapter, we describe projective parabolic geometries admitting a $2$-dimensional family of compatible metrics. This is the usual setting for the classical projective structures; we find that many results which hold in these settings carry over with little to no changes in the general case.
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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.
Повний текст джерелаАнотація:
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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Heuel, Stephan. "[Uncertain projective geometry] [statistical reasoning for polyhedral object reconstruction]." [Berlin Heidelberg] [Springer], 2002. http://dx.doi.org/10.1007/b97201.
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Heuel, Stephan. "Uncertain projective geometry : statistical reasoning for polyhedral object reconstruction /." Berlin [u.a.] : Springer, 2004. http://www.loc.gov/catdir/enhancements/fy0813/2004104982-d.html.
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Eskeland, II John T. "Searching for Constructed Form: A Station for Projective Geometry." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/78192.
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The project is dreamed as a monumental edifice standing beside the rail corridor of South-Western Virginia. Two pairs of towers rise from the earth transitioning from squares to ellipses. The towers are cut mid-ascent to shape an eastern face, orienting the project and the rail traffic beneath.Master of Architecture
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Strawn, Nathaniel Kirk. "Geometry and constructions of finite frames." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1335.
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Raineri, Emanuele. "Quantum Riemannian geometry of finite sets." Thesis, Queen Mary, University of London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.414738.
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Flórez, Rigoberto. "Four studies in geometry of biased graphs." Online access via UMI:, 2005.
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Neretin, Yurii A., and Andreas Cap@esi ac at. "Geometry of GL$_n$(C) on Infinity: Hinges, Projective Compactifications." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi971.ps.
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Gordon, Neil Andrew. "Finite geometry and computer algebra, with applications." Thesis, University of Hull, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262412.
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Heuel, Stephan [Verfasser]. "[Uncertain projective geometry] : [statistical reasoning for polyhedral object reconstruction] / [Stephan Heuel]." [Berlin, 2004. http://d-nb.info/972277110/34.
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Shabbir, Ghulam. "Curvature and projective symmetries in space-times." Thesis, University of Aberdeen, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364690.
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In this thesis a number of problems concerning proper curvature collineations, proper Weyl collineations and projective vector fields will be considered. The work on the above areas can be summarised as: (i) A study of proper curvature collineations in plane symmetric static, spherically symmetric static and Bianchi type I spacetimes will be presented by considering the rank of their 6 x 6 Riemann tensors and using a theorem which eliminates those space-times where proper curvature collineations can not exist; (ii) A study of proper Weyl collineations is given by using the algebraic classification and associated rank of the Weyl tensor and using a theorem similar to that used in (i); (iii) A technique is developed to study projective vector fields in the Friedmann Robertson-Walker models and plane symmetric static spacetimes; (iv) The situations when conformally flat spacetimes admit proper curvature collineations are fully explored.
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Yoon, Young-jin. "Characterizations of Some Combinatorial Geometries." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc277894/.
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We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a characterization of supersolvable signed graphs. Finally, we give the following characterization of non—splitting supersolvable signed-graphic geometries : If a non-splitting supersolvable ternary geometry does not contain the Reid geometry as a subgeometry, then it is signed—graphic.
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McKinnon, David N. R. "The multiple view geometry of implicit curves and surfaces /." [St. Lucia, Qld.], 2006. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe19677.pdf.
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Zeng, Rui. "Homography estimation: From geometry to deep learning." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/134132/1/Rui_Zeng_Thesis.pdf.
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Homography is an important area of computer vision for scene understanding and plays a key role in extracting relationships across different viewpoints of a scene. This thesis focuses on studying homography transformations between images from both geometric and deep learning perspectives. We have developed an accurate and effective homography estimation system for sports scenes analysis an efficient and novel 3D perspective feature to improve 3D object recognition especially for the vehicle recognition.
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Pun, Ying Anna, and 潘瑛. "On laguerre geometry and generalized quadrangles." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B46542280.
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Berardini, Elena. "Algebraic geometry codes from surfaces over finite fields." Thesis, Aix-Marseille, 2020. http://www.theses.fr/2020AIXM0170.
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Nous proposons, dans cette thèse, une étude théorique des codes géométriques algébriques construits à partir de surfaces définies sur les corps finis. Nous prouvons des bornes inférieures pour la distance minimale des codes sur des surfaces dont le diviseur canonique est soit nef soit anti-strictement nef et sur des surfaces sans courbes irréductibles de petit genre. Nous améliorons ces bornes inférieures dans le cas des surfaces dont le nombre de Picard arithmétique est égal à un, des surfaces sans courbes de petite auto-intersection et des surfaces fibrées. Ensuite, nous appliquons ces bornes aux surfaces plongées dans P3. Une attention particulière est accordée aux codes construits à partir des surfaces abéliennes. Dans ce contexte, nous donnons une borne générale sur la distance minimale et nous démontrons que cette estimation peut être améliorée en supposant que la surface abélienne ne contient pas de courbes absolument irréductibles de petit genre. Dans cette optique nous caractérisons toutes les surfaces abéliennes qui ne contiennent pas de courbes absolument irréductibles de genre inférieur ou égal à 2. Cette approche nous conduit naturellement à considérer les restrictions de Weil de courbes elliptiques et les surfaces abéliennes qui n'admettent pas de polarisation principaleIn this thesis we provide a theoretical study of algebraic geometry codes from surfaces defined over finite fields. We prove lower bounds for the minimum distance of codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus. We sharpen these lower bounds for surfaces whose arithmetic Picard number equals one, surfaces without curves with small self-intersection and fibered surfaces. Then we apply these bounds to surfaces embedded in P3. A special attention is given to codes constructed from abelian surfaces. In this context we give a general bound on the minimum distance and we prove that this estimation can be sharpened under the assumption that the abelian surface does not contain absolutely irreducible curves of small genus. In this perspective we characterize all abelian surfaces which do not contain absolutely irreducible curves of genus up to 2. This approach naturally leads us to consider Weil restrictions of elliptic curves and abelian surfaces which do not admit a principal polarization
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Ellis, Amanda. "Classifcation of Conics in the Tropical Projective Plane." BYU ScholarsArchive, 2005. https://scholarsarchive.byu.edu/etd/697.
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This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.
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Huang, Jen-Fa. "On finding generator polynomials and parity-check sums of binary projective geometry codes." Thesis, University of Ottawa (Canada), 1985. http://hdl.handle.net/10393/4800.
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Packer, S. "On sets of odd type and caps in Galois geometries of order four." Thesis, University of Sussex, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262299.
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Majid, Shahn, and Andreas Cap@esi ac at. "Riemannian Geometry of Quantum Groups and Finite Groups with." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi902.ps.
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Wong, Vui-Hong, and n/a. "Finite Element Analysis and Improvement of Impeller Blade Geometry." Griffith University. School of Engineering, 2003. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20030825.150853.
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Stratification of water in large reservoirs occurs in summer, or at anytime in hot climates where the water surface is exposed long-term to sunlight and the water surface is heated. Natural mixing will not occur due to the cooler and denser water always staying at the lower levels. Therefore, mechanical circulators are designed to prevent water quality problems related to stratification and depletion of dissolved oxygen. Impellers that produce the flow in mechanical circulators are available in different sizes and these impellers are designed to produce different flow rates. Due to hydraulic loadings, impellers have to be strong and durable. Loadings on impellers depend on their geometries and therefore, a durable impeller is a good combination of the use of correct materials and good geometry. Long and slender impellers are prone to failure when subjected to high hydrodynamic loadings. Nowadays, designers have very limited information on predicting the stresses on impellers and the deflection patterns of impellers because there are no design rules in designing these impeller blades and there is no such thing as "best geometry". A good impeller blade design is by guesswork and experience. In order to design the geometry that suits this application, trial-and-error finite element analyses have been conducted in this project to minimize stress levels on the blades. This research involves the use of finite element analysis (FEA) to predict stress and deflection of impeller blades used on large (5m diameter) ducted axial flow impellers as the first step in the design process. Then, based on the results, improvements have been done to the models until the final design was made. As far as the author has been able to determine, this has not been researched before. Finite Element Analysis has been used on wind turbine blades, rudders and hulls of boats but not on axial flow impeller blades of the type used in this project. For the purpose of this project, commercial finite element computer program packages STRAND6 and STRAND7 were used as the main analysis tools. A static line load increasing linearly with radius along the blade has been used to simulate the assumed hydrodynamic loading, and applied to all FEA blade models. The analysis results proved the stresses on blades are largely dependant on the blade geometry. From the analysis results, the author modified the stacking arrangement of the FEA elements in order to minimize both the tensile stresses and the displacements of the blades at the tip. Parametric studies have been done in order to obtain the best FEA impeller blade model.
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Strunk, Stefanie. "High performance adaptive finite elementmodeling of complex CAD geometry." Thesis, KTH, Numerisk analys, NA, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-127543.
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CAD (Computer Aided Design) and finite elementanalysis are of fundamental importance for numerical simulations. The generalapproach is to design a model using CAD software, create a mesh of a domainthat includes this model and use finite element analysis to perform simulationson that mesh. When using more advanced simulation techniques, like adaptivefinite element methods, it is more and more desired to use CAD information, notonly for the creation of the initial mesh but also during the simulation. Inthis thesis, an approach is presented how to use CAD data during adaptive mesh refinementin a finite element simulation. An error indicator is presented to find theelements in a mesh, which need to be improved for a better geometricapproximation and it is shown how to integrate the different approaches into anexisting high performance finite element solverCAD (Computer Aided Design)och finita-element-analys är grundläggande för numerisk simulering. Mankonstruerar en modell med CAD-program, skapar ett beräkningsnät på en domän sominnehåller modellen, och använder finita-elementanalys för beräkningar pånätet. I mer avancerade simuleringar, som för adaptiva finita-element-metoder,är det önskvärt att använda CAD information inte bara för att skapa det förstanätet utan under nätförfiningarna i adaptionen under simuleringen. I dettaarbete presenteras ett sätt att använda CAD-data för adaptiv nätförfining i enfinita-element-simulering. En fel-indikator ges för att hitta de element somska förfinas för att förbättra geometrisk approximation och vi beskriver hur deolika angreppssätten kan integreras i ett finita-element programpaket för högpresterandedatorer
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Ratcliffe, Diana. "On the classification and geometry of finite map-germs." Thesis, University of Warwick, 1990. http://wrap.warwick.ac.uk/2827/.
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Summary of Chapter I: 1. We use Samuel's theory of multiplicity to describe the structure of (f)/T [cal Af in terms of the multiplicity e((f)/T cal Af) and the dimension of the instability locus (this dimension is also the Krull dimension of (f)/T cal Af). 2. We extend the theory of trivial unfoldings of map-germs to the theory of k-trivial unfoldings of k-jets. 3. We develop a method for obtaining normal forms for the (k+1)-jets having a given k-jet f by inspection of certain submodules of T cal Af. We give a test for sufficiency of a normal form and a method for constructing a (k+1)-trivial unfolding of the normal form. 4. We show that if f is weighted homogeneous and the Krull dimension and multiplicity of (f)/T cal Af are both 1 then f is a weak stem and we can find an integer k and a complete list of normal forms for finitely determined map-germs whose k-jet is f. The list has many similarities with the series found by Arnold and Mond. Summary of Chapter II: We extend Mond's classification of map-germs f:(cal C^2,O)(cal C^3?O) under cal A-equivalence. This chapter also demonstrates the use of the classification theory developed in I.2 and provides a large number of examples for use in the rest of the thesis. Summary of Chapter III: 1. We prove that f is a geometric stem if and only if is irreducible and the localised module ((f)/T cal Af) has length char61 1 (localise with respect to the prime ideal defining ). 2. We also prove that if has transversal type A_2n or A_2n+1 for some n1 then char61 n. This makes it easier to determine n if has transversal type of A_2n or A_2n+1 since we shall calculate anyway. 3. If f is a stem we show that is irreducible and give a list of transversal types that may have (although having one of these transversal types does not necessarily indicate that f is a stem). 4. We look at how the numbers C, T and (D_2(f)/cal Z_2) behave for the families of map-germs associated with some weak stems. We observe that for a given family (f+p_s) the integer C(f+p_s)+T(f+p_s)+(D2(f+ps)/cal Z2)-cod(cal A,f+ps) appears to be a constant. Appendices A and B contain supplementary calculations. Appendix C is a description of the computer programs written to calculate the modules used in classifying the map-germs of Chapter II.
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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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Tuncer, Necibe Meir Amnon J. "A novel finite element discretization of domains with spheroidal geometry." Auburn, Ala., 2007. http://repo.lib.auburn.edu/Send%2011-10-07/TUNCER_NECIBE_24.pdf.
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Darling, Brian. "A finite element geometry method for Monte Carlo transport calculations." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47016.
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