Relevant bibliographies by topics / Semialgebraic and subanalytic geometry

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Semialgebraic and subanalytic geometry'

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Published: 1 September 2023

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Journal articles on the topic "Semialgebraic and subanalytic geometry"

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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.

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Loi, Ta Lê. "Transversality theorem in o-minimal structures." Compositio Mathematica 144, no. 5 (September 2008): 1227–34. http://dx.doi.org/10.1112/s0010437x08003503.

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AbstractIn this paper we present Thom’s transversality theorem in o-minimal structures (a generalization of semialgebraic and subanalytic geometry). There are no restrictions on the differentiability class and the dimensions of manifolds involved in comparison withthe general case.
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Figueiredo, 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.

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AbstractO-minimal geometry generalizes both semialgebraic and subanalytic geometries, and has been very successful in solving special cases of some problems in arithmetic geometry, such as André–Oort conjecture. Among the many tools developed in an o-minimal setting are cohomology theories for abstract-definable continuous manifolds such as singular cohomology, sheaf cohomology and Čech cohomology, which have been used for instance to prove Pillay’s conjecture concerning definably compact groups. In the present thesis we elaborate an o-minimal de Rham cohomology theory for abstract-definable $C^{\infty }$ manifolds in an o-minimal expansion of the real field which admits smooth cell decomposition and defines the exponential function. We can specify the o-minimal cohomology groups and attain some properties such as the existence of Mayer–Vietoris sequence and the invariance under abstract-definable $C^{\infty }$ diffeomorphisms. However, in order to obtain the invariance of our o-minimal cohomology under abstract-definable homotopy we must work in a tame context that defines sufficiently many primitives and assume the validity of a statement related to Bröcker’s question.Abstract prepared by Rodrigo Figueiredo.E-mail: rodrigo@ime.usp.brURL: https://doi.org/10.11606/T.45.2019.tde-28042019-181150
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KOVACSICS, 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.

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AbstractWe show there are intermediate P-minimal structures between the semialgebraic and subanalytic languages which do not have definable Skolem functions. As a consequence, by a result of Mourgues, this shows there are P-minimal structures which do not admit classical cell decomposition.
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Kaiser, Tobias. "Capacity in subanalytic geometry." Illinois Journal of Mathematics 49, no. 3 (July 2005): 719–36. http://dx.doi.org/10.1215/ijm/1258138216.

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Niederman, 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.

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Zeng, 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.

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Łojasiewicz, 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.

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Qi, 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.

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Solernó, 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.

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Dissertations / Theses on the topic "Semialgebraic and subanalytic geometry"

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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.

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Dans cette thèse, nous abordons des questions autour de la structure métrique des ensembles définissables dans les structures o-minimales.Dans la première partie, nous étudions les projections régulières au sens de Mostowski, nous prouvons que ces projections n'existent que pour les structures polynomialement bornées, nous utilisons les projections régulières pour refaire la preuve de Parusinski de l'existence des recouvrements réguliers. Dans la deuxième partie de cette thèse, nous étudions les faisceaux de Sobolev (au sens de Lebeau). Pour les fonctions de Sobolev de régularité entière positive, nous construisons ces faisceaux sur le site définissable d'une surface en nous basant sur des observations de base des domaines définissables dans le plan
In 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
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Rivard-Cooke, Martin. "Parametric Geometry of Numbers." Thesis, Université d'Ottawa / University of Ottawa, 2019. http://hdl.handle.net/10393/38871.

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This thesis is primarily concerned in studying the relationship between different exponents of Diophantine approximation, which are quantities arising naturally in the study of rational approximation to a fixed n-tuple of real irrational numbers. As Khinchin observed, these exponents are not independent of each other, spurring interest in the study of the spectrum of a given family of exponents, which is the set of all possible values that can be taken by said family of exponents. Introduced in 2009-2013 by Schmidt and Summerer and completed by Roy in 2015, the parametric geometry of numbers provides strong tools with regards to the study of exponents of Diophantine approximation and their associated spectra by the introduction of combinatorial objects called n-systems. Roy proved the very surprising result that the study of spectra of exponents is equivalent to the study of certain quantities attached to n-systems. Thus, the study of rational approximation can be replaced by the study of n-systems when attempting to determine such spectra. Recently, Roy proved two new results for the case n=3, the first being that spectra are semi-algebraic sets, and the second being that spectra are stable under the minimum with respect to the product ordering. In this thesis, it is shown that both of these results do not hold in general for n>3, and examples are given. This thesis also provides non-trivial examples for n=4 where the spectra is stable under the minimum. An alternate and much simpler proof of a recent result of Marnat-Moshchevitin proving an important conjecture of Schmidt-Summerer is also given, relying only on the parametric geometry of numbers instead. Further, a conjecture which generalizes this result is also established, and some partial results are given towards its validity. Among these results, the simplest, but non-trivial, new case is also proven to be true. In a different vein, this thesis considers certain generalizations theta(q) of the classical theta q-series. We show under conditions on the coefficients of the series that theta(q) is neither rational nor quadratic irrational for each integer q>1.
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Tonelli, 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.

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Niederman, 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.

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L'étude de la stabilité et de l'instabilité des systèmes hamiltoniens proches de systèmes intégrables est un problème ancien et difficile en systèmes dynamiques.

Il 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.
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Skomra, Mateusz. "Tropical spectrahedra : Application to semidefinite programming and mean payoff games." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLX058/document.

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La programmation semi-définie est un outil fondamental d'optimisation convexe et polynomiale. Elle revient à optimiser une fonction linéaire sur un spectraèdre (un ensemble défini par des inégalités matricielles linéaires). En particulier, la programmation semi-définie est une généralisation de la programmation linéaire.Nous étudions l'analogue non-archimédien de la programmation semi-définie, en remplaçant le corps des nombres réels par le corps des séries de Puiseux. Notre approche est fondée sur des méthodes issues de la géométrie tropicale et, en particulier, sur l'étude de la tropicalisation des spectraèdres.En première partie de la thèse, nous analysons les images par la valuation des ensembles semi-algébriques généraux définis dans le corps des séries de Puiseux. Nous montrons que ces images ont une structure polyédrale, ce qui fournit un analogue réel du théorème de Bieri et Groves. Ensuite, nous introduisons la notion de spectraèdres tropicaux et nous montrons que, sous une hypothèse de généricité, ces objets sont décrits par des systèmes d'inégalités polynomiales de degré 2 sur le semi-corps tropical. Cela généralise un résultat de Yu sur la tropicalisation du cône des matrices positives.Une question importante relative à la programmation semi-définie sur les réels consiste à caractériser des projections de spectraèdres. Dans ce cadre, Helton et Nie ont conjecturé que tout ensemble semi-algébrique convexe est la projection d'un spectraèdre. La conjecture a été réfutée par Scheiderer. Néanmoins, nous montrons qu'elle est vraie ''à valuation près'' : dans le corps réel clos des séries de Puiseux, les ensembles semi-algébriques convexes et les spectraèdres projetés ont exactement les mêmes images par la valuation non-archimédienne.En seconde partie de la thèse, nous étudions des questions algorithmiques liées à la programmation semi-définie. Le problème algorithmique de base consiste à décider si un spectraèdre est vide. On ne sait pas si ce problème appartient à NP dans le modèle de la machine de Turing, et les algorithmes fondés sur la décomposition cylindrique algébrique ou la méthode de points critiques constituent l'état de l'art dans ce domaine. Nous montrons que, dans le cadre non-archimédien, les spectraèdres tropicaux génériques sont décrits par des opérateurs de Shapley associés aux jeux à paiement moyen stochastiques. Cela donne une méthode pour résoudre des problèmes de réalisabilité en programmation semi-définie non-archimédienne en utilisant les algorithmes combinatoires conçus pour les jeux stochastiques.Dans les chapitres finals de la thèse, nous établissons des bornes de complexité pour l'algorithme d'itération sur les valeurs qui exploitent la correspondance entre les jeux stochastiques et la convexité tropicale. Nous montrons que le nombre d'itérations est contrôlé par un nombre de conditionnement relié au diamètre intérieur du spectraèdre tropical associé.Nous fournissons des bornes supérieures générales sur le nombre de conditionnement. Pour cela, nous établissons des bornes optimales sur la taille en bits des mesures invariantes de chaînes de Markov. Comme corollaire, notre estimation montre que l'itération sur la valeur résout les jeux ergodiques à paiement moyen en temps pseudo-polynomial si le nombre de positions aléatoires est fixé. Enfin, nous expérimentons notre approche à la résolution de programmes semi-définis non-archimédiens aléatoires de grande taille
Semidefinite 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
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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.

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Shartser, Leonid. "De Rham Theory and Semialgebraic Geometry." Thesis, 2011. http://hdl.handle.net/1807/29865.

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This thesis consists of six chapters and deals with four topics related to De Rham Theory on semialgebraic sets. The first topic deals with L-infinity cohomology on semialgebraic sets. We introduce smooth L-infinity differential forms on a singular (semialgebraic) space X in Rn. Roughly speaking, a smooth L-infinity differential form is a collection of smooth forms on disjoint smooth subsets (stratification) of X with matching tangential components on the adjacent strata and of bounded size (in the metric induced from Rn). We identify the singular homology of X as the homology of the chain complex generated by semialgebraic singular simplices, i.e. continuous semialgebraic maps from the standard simplex into X. Singular cohomology of X is defined as the homology of the Hom dual to the chain complex of the singular chains. Finally, we prove a De Rham type theorem establishing a natural isomorphism between the singular cohomology and the cohomology of smooth L-infinity forms. The second topic is a construction of a Lipschitz deformation retraction on a neighborhood of a point in a semialgebraic set with estimates on its derivatives. Such a deformation retraction is the key to the results of the first and the third topics. The third topic is related to Poincare inequality on a semialgebraic set. We study Poincare type Lp inequality for differential forms on a compact semialgebraic subset of Rn for p >> 1. First we derive a local inequality by using a Lipschitz deformation retraction with estimates on its derivatives from the second topic and then we extend it to a global inequality by employing a technique developed in the appendix. As a consequence we obtain an isomorphism between Lp cohomology and singular cohomology of a normal compact semialgebraic set. The final topic is in the appendix. It deals with an explicit proof of Poincare type inequality for differential forms on compact manifolds. We prove the latter inequality by means of a constructive 'globalization' method of a local Poincare inequality on convex sets. The appendix serves as a model case for the results of the third topic in Chapter 5.
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Parrilo, 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.

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In the first part of this thesis, we introduce a specific class of Linear Matrix Inequalities (LMI) whose optimal solution can be characterized exactly. This family corresponds to the case where the associated linear operator maps the cone of positive semidefinite matrices onto itself. In this case, the optimal value equals the spectral radius of the operator. It is shown that some rank minimization problems, as well as generalizations of the structured singular value ($mu$) LMIs, have exactly this property. In the same spirit of exploiting structure to achieve computational efficiency, an algorithm for the numerical solution of a special class of frequency-dependent LMIs is presented. These optimization problems arise from robustness analysis questions, via the Kalman-Yakubovich-Popov lemma. The procedure is an outer approximation method based on the algorithms used in the computation of hinf norms for linear, time invariant systems. The result is especially useful for systems with large state dimension. The other main contribution in this thesis is the formulation of a convex optimization framework for semialgebraic problems, i.e., those that can be expressed by polynomial equalities and inequalities. The key element is the interaction of concepts in real algebraic geometry (Positivstellensatz) and semidefinite programming. To this end, an LMI formulation for the sums of squares decomposition for multivariable polynomials is presented. Based on this, it is shown how to construct sufficient Positivstellensatz-based convex tests to prove that certain sets are empty. Among other applications, this leads to a nonlinear extension of many LMI based results in uncertain linear system analysis. Within the same framework, we develop stronger criteria for matrix copositivity, and generalizations of the well-known standard semidefinite relaxations for quadratic programming. Some applications to new and previously studied problems are presented. A few examples are Lyapunov function computation, robust bifurcation analysis, structured singular values, etc. It is shown that the proposed methods allow for improved solutions for very diverse questions in continuous and combinatorial optimization.
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Raclavský, Marek. "Algebraické nerovnice nad reálnými čísly." Master's thesis, 2017. http://www.nusl.cz/ntk/nusl-357111.

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This thesis analyses the semialgebraic sets, that is, a finite union of solu- tions to a finite sequence of polynomial inequalities. We introduce a notion of cylindrical algebraic decomposition as a tool for the construction of a semialge- braic stratification and a triangulation of a semialgebraic set. On this basis, we prove several important and well-known results of real algebraic geometry, such as Hardt's semialgebraic triviality or Sard's theorem. Drawing on Morse theory, we finally give a proof of a Thom-Milnor bound for a sum of Betti numbers of a real algebraic set. 1
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Νταργαράς, Κωνσταντίνος. "Το θεώρημα Tarski-Seidenberg : συνέπειες και μία διδακτική έρευνα στη θεωρία πολυωνύμων με πραγματικούς συντελεστές." Thesis, 2014. http://hdl.handle.net/10889/8216.

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To αντικείμενο μελέτης της εργασίας αυτής είναι κατά μείζονα λόγο το θεώρημα Tarski-Seidenberg. Στο πρώτο κεφάλαιο μελετάμε το κίνητρο που ώθησε τον Tarski σε αυτή την έρευνα, εξιστορούμε την πορεία της ιδέας του από την ανακάλυψη μέχρι τη δημοσίευση και έπειτα προσπαθούμε να σκιαγραφήσουμε ευκρινώς τη συνολική επίδραση του θεωρήματος στα μαθηματικά και όχι μόνο. Για την ακρίβεια, αναφερόμαστε στην πληρότητα της Ευκλείδειας γεωμετρίας ως συνέπεια του θεωρήματος, στη συμβολή του θεωρήματος στην ανάπτυξη της ημιαλγεβρικής γεωμετρίας. Στο δεύτερο κεφάλαιο αποδικνύεται το εν λόγω θεώρημα, δηλαδή ότι η πρωτοβάθμια θεωρία των πραγματικώς κλειστών σωμάτων είναι πλήρης, με χρήση των θεωρημάτων Sturm και Sylvester. Στο τρίτο κεφάλαιο παρουσιάζεται μία διδακτική έρευνα με φοιτητές του τμήματος με σκοπό τη διάγνωση πιθανών γνωστικών κενών των φοιτητών σε θέματα της θεωρίας πολυωνύμων με πραγματικούς συντελεστές.
To 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.
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Books on the topic "Semialgebraic and subanalytic geometry"

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Shiota, Masahiro. Geometry of Subanalytic and Semialgebraic Sets. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2008-4.

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Shiota, Masahiro. Geometry of subanalytic and semialgebraic sets. Boston: Birkhäuser, 1997.

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Geometry of subanalytic and semialgebraic sets. Boston: Birkhäuser, 1997.

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Manfred, Knebusch, ed. Locally semialgebraic spaces. Berlin: Springer-Verlag, 1985.

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Andradas, Carlos. Algebraic and analytic geometry of fans. Providence, R.I: American Mathematical Society, 1995.

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Geometry of Subanalytic and Semialgebraic Sets. Birkhäuser, 2011.

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Shiota, Masahiro. Geometry of Subanalytic and Semialgebraic Sets. Springer, 2012.

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Shiota, Masahiro. Geometry of Subanalytic and Semialgebraic Sets. Birkhauser Verlag, 2012.

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Knebusch, Manfred, and Hans Delfs. Locally Semialgebraic Spaces. Springer London, Limited, 2006.

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Knebusch, Manfred, and Hans Delfs. Locally Semialgebraic Spaces. Springer Berlin Heidelberg, 1986.

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Book chapters on the topic "Semialgebraic and subanalytic geometry"

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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.

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Shiota, 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.

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Shiota, 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.

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Shiota, 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.

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Shiota, 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.

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Coste, 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.

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Briskin, 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.

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Shiota, 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.

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Andradas, 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.

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Conti, 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.

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Conference papers on the topic "Semialgebraic and subanalytic geometry"

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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.

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You might also be interested in the extended bibliographies on the topic 'Semialgebraic and subanalytic geometry' for particular source types:
Journal articles
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