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Статті в журналах з теми "Semialgebraic and subanalytic geometry"
Coste, Michel. "Book Review: Geometry of subanalytic and semialgebraic sets." Bulletin of the American Mathematical Society 36, no. 04 (July 27, 1999): 523–28. http://dx.doi.org/10.1090/s0273-0979-99-00793-4.
Повний текст джерелаLoi, Ta Lê. "Transversality theorem in o-minimal structures." Compositio Mathematica 144, no. 5 (September 2008): 1227–34. http://dx.doi.org/10.1112/s0010437x08003503.
Повний текст джерелаFigueiredo, Rodrigo. "O-minimal de Rham Cohomology." Bulletin of Symbolic Logic 28, no. 4 (December 2022): 529. http://dx.doi.org/10.1017/bsl.2021.20.
Повний текст джерелаKOVACSICS, PABLO CUBIDES, and KIEN HUU NGUYEN. "A P-MINIMAL STRUCTURE WITHOUT DEFINABLE SKOLEM FUNCTIONS." Journal of Symbolic Logic 82, no. 2 (May 15, 2017): 778–86. http://dx.doi.org/10.1017/jsl.2016.58.
Повний текст джерелаKaiser, Tobias. "Capacity in subanalytic geometry." Illinois Journal of Mathematics 49, no. 3 (July 2005): 719–36. http://dx.doi.org/10.1215/ijm/1258138216.
Повний текст джерелаNiederman, Laurent. "Hamiltonian stability and subanalytic geometry." Annales de l’institut Fourier 56, no. 3 (2006): 795–813. http://dx.doi.org/10.5802/aif.2200.
Повний текст джерелаZeng, Guangxin. "Homogeneous Stellensätze in semialgebraic geometry." Pacific Journal of Mathematics 136, no. 1 (January 1, 1989): 103–22. http://dx.doi.org/10.2140/pjm.1989.136.103.
Повний текст джерелаŁojasiewicz, Stanisław. "On semi-analytic and subanalytic geometry." Banach Center Publications 34, no. 1 (1995): 89–104. http://dx.doi.org/10.4064/-34-1-89-104.
Повний текст джерелаQi, Yang, Pierre Comon, and Lek-Heng Lim. "Semialgebraic Geometry of Nonnegative Tensor Rank." SIAM Journal on Matrix Analysis and Applications 37, no. 4 (January 2016): 1556–80. http://dx.doi.org/10.1137/16m1063708.
Повний текст джерелаSolernó, Pablo. "Effective Łojasiewicz inequalities in semialgebraic geometry." Applicable Algebra in Engineering, Communication and Computing 2, no. 1 (March 1991): 1–14. http://dx.doi.org/10.1007/bf01810850.
Повний текст джерелаДисертації з теми "Semialgebraic and subanalytic geometry"
Oudrane, M'hammed. "Projections régulières, structure de Lipschitz des ensembles définissables et faisceaux de Sobolev." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4034.
Повний текст джерелаIn this thesis we address questions around the metric structure of definable sets in o-minimal structures. In the first part we study regular projections in the sense of Mostowski, we prove that these projections exists only for polynomially bounded structures, we use regular projections to re perform Parusinski's proof of the existence of regular covers. In the second part of this thesis, we study Sobolev sheaves (in the sense of Lebeau). For Sobolev functions of positive integer regularity, we construct these sheaves on the definable site of a surface based on basic observations of definable domains in the plane
Rivard-Cooke, Martin. "Parametric Geometry of Numbers." Thesis, Université d'Ottawa / University of Ottawa, 2019. http://hdl.handle.net/10393/38871.
Повний текст джерелаTonelli, Cueto Josué [Verfasser], Peter [Akademischer Betreuer] Bürgisser, Felipe [Akademischer Betreuer] Cucker, Peter [Gutachter] Bürgisser, Felipe [Gutachter] Cucker, and Pierre [Gutachter] Lairez. "Condition and homology in semialgebraic geometry / Josué Tonelli Cueto ; Gutachter: Peter Bürgisser, Felipe Cucker, Pierre Lairez ; Peter Bürgisser, Felipe Cucker." Berlin : Technische Universität Berlin, 2019. http://d-nb.info/120229703X/34.
Повний текст джерелаNiederman, Laurent. "STABILITE GENERIQUE DES SYSTEMES HAMILTONIENS QUASI-INTEGRABLES." Habilitation à diriger des recherches, Université Paris Sud - Paris XI, 2006. http://tel.archives-ouvertes.fr/tel-00124486.
Повний текст джерелаIl y a deux types de théorèmes :
i) Les résultats of stabilité sur des temps infinis obtenus avec la théorie K.A.M. qui sont valables sur un ensemble de Cantor de grande mesure mais on a très peu d'informations sur les autres trajectoires et même une instabilité importante peut se développer.
ii) D'autre part, des résultats de stabilité sur des ensembles ouverts mais seulement sur un temps exponentiellement long par rapport à la taille de la perturbation.
Ce deuxième type de résultats est du à N.N. Nekhorochev qui a établi en 1977 un théorème de stabilité global en temps exponentiellement long dans le cas où le hamiltonien non perturbé (intégrable) est escarpé. C'est à dire s'il vérifie certaines conditions de transversalité qui sont génériquement satisfaites par les fonctions infiniment différentiables. Notamment, les fonctions convexes sont escarpées. L'étude de cette notion et ses conséquences n'a pas été reprise depuis la démonstration originale de Nekhorochev malgrés la densité de la classe des fonctions escarpées et différents exemples issus de la physique où le hamiltonien intégrable considéré est escarpé mais pas convexe.
Dans ce mémoire, on présente tout d'abord une démonstration notablement simplifiée du théorème de Nekhorochev. Ceci permet d'obtenir des estimations raffinées sur les temps de stabilité qui sont essentiellement optimales dans le cas convexe.
D'autre part, Y. Ilyashenko a donné une caractérisation géométrique des fonctions escarpées dans le cas holomorphe. On reprend cette étude à l'aide d'outils de géométrie sous analytique réelle (lemme de sélection de courbe et exposants de Lojaciewicz). Ceci permet d'étendre le résultat d'Ilyashenko au cas réel et de montrer clairement que les hypothèses d'escarpement sont presques minimales pour assurer la stabilité effective des systèmes hamiltoniens proches d'un système intégrable. On en déduit aussi des méthodes de calcul explicites des constantes intervenant dans ce type de théorème.
Enfin, on montre un théorème de stabilité en temps exponentiellement long pour des systèmes hamiltoniens presques-intégrables avec une condition de non-dégénérescence sur le hamiltonien non perturbé strictement plus faible que la raideur. L'intérêt de ce raffinement vient du fait qu'il permet d'établir un résultat de stabilité générique avec des exposants fixes. Il s'agit de généricité au sens de la mesure (ensembles prévalents suivant la terminologie de Kaloshin) parmi les fonctions réelle-analytiques. Ce résultat est obtenu grâce à l'application d'une version quantitative du théorème de Sard due à Yomdin.
Skomra, Mateusz. "Tropical spectrahedra : Application to semidefinite programming and mean payoff games." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLX058/document.
Повний текст джерелаSemidefinite programming (SDP) is a fundamental tool in convex and polynomial optimization. It consists in minimizing the linear functions over the spectrahedra (sets defined by linear matrix inequalities). In particular, SDP is a generalization of linear programming.The purpose of this thesis is to study the nonarchimedean analogue of SDP, replacing the field of real numbers by the field of Puiseux series. Our methods rely on tropical geometry and, in particular, on the study of tropicalization of spectrahedra.In the first part of the thesis, we analyze the images by valuation of general semialgebraic sets defined over the Puiseux series. We show that these images have a polyhedral structure, giving the real analogue of the Bieri--Groves theorem. Subsequently, we introduce the notion of tropical spectrahedra and show that, under genericity conditions, these objects can be described explicitly by systems of polynomial inequalities of degree 2 in the tropical semifield. This generalizes the result of Yu on the tropicalization of the SDP cone.One of the most important questions about real SDPs is to characterize the sets that arise as projections of spectrahedra. In this context, Helton and Nie conjectured that every semialgebraic convex set is a projected spectrahedron. This conjecture was disproved by Scheiderer. However, we show that the conjecture is true ''up to taking the valuation'': over a real closed nonarchimedean field of Puiseux series, the convex semialgebraic sets and the projections of spectrahedra have precisely the same images by the nonarchimedean valuation.In the second part of the thesis, we study the algorithmic questions related to SDP. The basic computational problem associated with SDP over real numbers is to decide whether a spectrahedron is nonempty. It is unknown whether this problem belongs to NP in the Turing machine model, and the state-of-the-art algorithms that certify the (in)feasibility of spectrahedra are based on cylindrical decomposition or the critical points method. We show that, in the nonarchimedean setting, generic tropical spectrahedra can be described by Shapley operators associated with stochastic mean payoff games. This provides a tool to solve nonarchimedean semidefinite feasibility problems using combinatorial algorithms designed for stochastic games.In the final chapters of the thesis, we provide new complexity bounds for the value iteration algorithm, exploiting the correspondence between stochastic games and tropical convexity. We show that the number of iterations needed to solve a game is controlled by a condition number, which is related to the inner radius of the associated tropical spectrahedron. We provide general upper bounds on the condition number. To this end, we establish optimal bounds on the bit-length of stationary distributions of Markov chains. As a corollary, our estimates show that value iteration can solve ergodic mean payoff games in pseudopolynomial time, provided that the number of random positions of the game is fixed. Finally, we apply our approach to large scale random nonarchimedean SDPs
Phillips, Laura Rose. "Some structures interpretable in the ring of continuous semi-algebraic functions on a curve." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/some-structures-interpretable-in-the-ring-of-continuous-semialgebraic-functions-on-a-curve(f5a52f43-1bf2-42da-85c0-22847a35dcfc).html.
Повний текст джерелаShartser, Leonid. "De Rham Theory and Semialgebraic Geometry." Thesis, 2011. http://hdl.handle.net/1807/29865.
Повний текст джерелаParrilo, Pablo A. "Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization." Thesis, 2000. https://thesis.library.caltech.edu/1647/1/Parrilo-Thesis.pdf.
Повний текст джерелаRaclavský, Marek. "Algebraické nerovnice nad reálnými čísly." Master's thesis, 2017. http://www.nusl.cz/ntk/nusl-357111.
Повний текст джерелаΝταργαράς, Κωνσταντίνος. "Το θεώρημα Tarski-Seidenberg : συνέπειες και μία διδακτική έρευνα στη θεωρία πολυωνύμων με πραγματικούς συντελεστές". Thesis, 2014. http://hdl.handle.net/10889/8216.
Повний текст джерелаTo study object of this work is a fortiori the Tarski-Seidenberg theorem. In the first chapter we study Tarski's motivation in this research, we recount the progress of the idea from the discovery until the publication, and then we try to outline clearly the overall effect of the theorem in mathematics and beyond. In fact, we refer to the completeness of Euclidean geometry as a consequence of the theorem, in its contribution to the development of semialgebraic geometry. In the second chapter we prove the Tarski-Seidenberg theorem, namely that the first order theory of real closed fields is actually complete, using the Sturm and Sylvester theorems. In the third chapter we present a teaching research on students of the Department in purpose to diagnose potential knowledge gaps of the students concerning the theory of polynomials with real coefficients.
Книги з теми "Semialgebraic and subanalytic geometry"
Shiota, Masahiro. Geometry of Subanalytic and Semialgebraic Sets. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2008-4.
Повний текст джерелаShiota, Masahiro. Geometry of subanalytic and semialgebraic sets. Boston: Birkhäuser, 1997.
Знайти повний текст джерелаGeometry of subanalytic and semialgebraic sets. Boston: Birkhäuser, 1997.
Знайти повний текст джерелаManfred, Knebusch, ed. Locally semialgebraic spaces. Berlin: Springer-Verlag, 1985.
Знайти повний текст джерелаAndradas, Carlos. Algebraic and analytic geometry of fans. Providence, R.I: American Mathematical Society, 1995.
Знайти повний текст джерелаGeometry of Subanalytic and Semialgebraic Sets. Birkhäuser, 2011.
Знайти повний текст джерелаShiota, Masahiro. Geometry of Subanalytic and Semialgebraic Sets. Springer, 2012.
Знайти повний текст джерелаShiota, Masahiro. Geometry of Subanalytic and Semialgebraic Sets. Birkhauser Verlag, 2012.
Знайти повний текст джерелаKnebusch, Manfred, and Hans Delfs. Locally Semialgebraic Spaces. Springer London, Limited, 2006.
Знайти повний текст джерелаKnebusch, Manfred, and Hans Delfs. Locally Semialgebraic Spaces. Springer Berlin Heidelberg, 1986.
Знайти повний текст джерелаЧастини книг з теми "Semialgebraic and subanalytic geometry"
Shiota, Masahiro. "Preliminaries." In Geometry of Subanalytic and Semialgebraic Sets, 1–94. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2008-4_1.
Повний текст джерелаShiota, Masahiro. "X-Sets." In Geometry of Subanalytic and Semialgebraic Sets, 95–269. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2008-4_2.
Повний текст джерелаShiota, Masahiro. "Hauptvermutung for Polyhedra." In Geometry of Subanalytic and Semialgebraic Sets, 270–304. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2008-4_3.
Повний текст джерелаShiota, Masahiro. "Triangulations of X-Maps." In Geometry of Subanalytic and Semialgebraic Sets, 305–87. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2008-4_4.
Повний текст джерелаShiota, Masahiro. "Y-Sets." In Geometry of Subanalytic and Semialgebraic Sets, 388–419. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2008-4_5.
Повний текст джерелаCoste, Michel. "Effective semialgebraic geometry." In Lecture Notes in Computer Science, 1–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51683-2_21.
Повний текст джерелаBriskin, M., and Y. Yomdin. "Semialgebraic geometry of polynomial control problems." In Computational Algebraic Geometry, 21–28. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-2752-6_2.
Повний текст джерелаShiota, Masahiro. "Piecewise linearization of subanalytic functions II." In Real Analytic and Algebraic Geometry, 247–307. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0083925.
Повний текст джерелаAndradas, Carlos, Ludwig Bröcker, and Jesús M. Ruiz. "A First Look at Semialgebraic Geometry." In Constructible Sets in Real Geometry, 5–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-80024-5_2.
Повний текст джерелаConti, Pasqualina, and Carlo Traverso. "Algebraic and Semialgebraic Proofs: Methods and Paradoxes." In Automated Deduction in Geometry, 83–103. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45410-1_6.
Повний текст джерелаТези доповідей конференцій з теми "Semialgebraic and subanalytic geometry"
Pleśniak, W. "Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods." In Approximation and Probability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2006. http://dx.doi.org/10.4064/bc72-0-16.
Повний текст джерела