Relevant bibliographies by topics / Alexandrov Theorem

Contents

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

Academic literature on the topic 'Alexandrov Theorem'

Author: Grafiati
Published: 4 June 2021
Last updated: 8 June 2024

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Journal articles on the topic "Alexandrov Theorem"

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Hijazi, Oussama, Sebastián Montiel, and Simon Raulot. "An Alexandrov theorem in Minkowski spacetime." Asian Journal of Mathematics 23, no. 6 (2019): 933–52. http://dx.doi.org/10.4310/ajm.2019.v23.n6.a3.

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Mashiko, Yukihiro. "A splitting theorem for Alexandrov spaces." Pacific Journal of Mathematics 204, no. 2 (June 1, 2002): 445–58. http://dx.doi.org/10.2140/pjm.2002.204.445.

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Shen, Zhongmin. "A Regularity Theorem for Alexandrov Spaces." Mathematische Nachrichten 164, no. 1 (1993): 91–102. http://dx.doi.org/10.1002/mana.19931640108.

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Lang, Urs, and Viktor Schroeder. "On Toponogov's comparison theorem for Alexandrov spaces." L’Enseignement Mathématique 59, no. 3 (2013): 325–36. http://dx.doi.org/10.4171/lem/59-3-6.

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Alexander, Stephanie, and Richard Bishop. "A cone splitting theorem for Alexandrov spaces." Pacific Journal of Mathematics 218, no. 1 (January 1, 2005): 1–15. http://dx.doi.org/10.2140/pjm.2005.218.1.

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Chen, Wen-Haw, and Jyh-Yang Wu. "A rigidity theorem for discrete groups." Bulletin of the Australian Mathematical Society 73, no. 1 (February 2006): 1–8. http://dx.doi.org/10.1017/s0004972700038569.

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This work considers the discrete subgroups of group of isometries of an Alexandrov space with a lower curvature bound. By developing the notion of Hausdorff distance in these groups, a rigidity theorem for the close discrete groups was proved.
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Su, Xiaole, Hongwei Sun, and Yusheng Wang. "Generalized packing radius theorems of Alexandrov spaces with curvature ≥ 1." Communications in Contemporary Mathematics 19, no. 03 (April 5, 2017): 1650049. http://dx.doi.org/10.1142/s0219199716500498.

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In this paper, we give some generalized packing radius theorems of an [Formula: see text]-dimensional Alexandrov space [Formula: see text] with curvature [Formula: see text]. Let [Formula: see text] be any [Formula: see text]-separated subset in [Formula: see text] (i.e. the distance [Formula: see text] for any [Formula: see text]). Under the condition “[Formula: see text]” (after [K. Grove and F. Wilhelm, Hard and soft packing radius theorems, Ann. of Math. 142 (1995) 213–237]), we give the upper bound of [Formula: see text] (which depends only on [Formula: see text]), and classify the geometric structure of [Formula: see text] when [Formula: see text] attains the upper bound. As a corollary, we get an isometrical sphere theorem in Riemannian case.
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Kuwae, Kazuhiro, and Takashi Shioya. "A topological splitting theorem for weighted Alexandrov spaces." Tohoku Mathematical Journal 63, no. 1 (2011): 59–76. http://dx.doi.org/10.2748/tmj/1303219936.

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Wörner, Andreas. "A splitting theorem for nonnegatively curved Alexandrov spaces." Geometry & Topology 16, no. 4 (December 31, 2012): 2391–426. http://dx.doi.org/10.2140/gt.2012.16.2391.

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Hua, Bobo. "Generalized Liouville theorem in nonnegatively curved Alexandrov spaces." Chinese Annals of Mathematics, Series B 30, no. 2 (February 18, 2009): 111–28. http://dx.doi.org/10.1007/s11401-008-0376-3.

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Dissertations / Theses on the topic "Alexandrov Theorem"

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Silva, Neto Gregorio Manoel da. "O teorema de Alexandrov." Universidade Federal de Alagoas, 2009. http://repositorio.ufal.br/handle/riufal/1026.

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The goal of this dissertation is to present a R. Reilly's demonstration of the theorem of Alexandrov . The theorem states that The only compact hypersurfaces, conected, of constant mean curvature, immersed in Euclidean space are spheres. The theorem of Alexandrov was proved by A. D. Alexandrov in the article Uniqueness Theorems for Surfaces in the Large V, published in 1958 by Vestnik Leningrad University, volume 13, number 19, pages 5 to 8. In his demonstration, Alexandrov used the famous Principle of tangency, introduced by him in that article. In the year 1962, M. Obata shown in Certain Conditions for a Riemannian Manifold to be isometric With the Sphere, published by the Journal of Mathematical Society of Japan, volume 14, pages 333 to 340, that a Riemannian Manifold M, compact, connected and without boundary, is isometric to a sphere, since the Ricci curvature of M satisfies certain lower bound. This theorem solves the problem of finding manifolds that reach equality in the estimate of Lichnerowicz for the first eigenvalue. In 1977, R. Reilly, in the article Applications of the Hessian operator in a Riemannian Manifold, published in Indianna University Mathematical Journal, volume 23, pages 459 to 452, showed a generalization of the Obata theorem for compact manifolds with boundary. As an example of the technique developed in this demonstration, he presents a new demonstration of the theorem of Alexandrov. This demonstration, as well as the techniques involved are the object of study of this work.
Conselho Nacional de Desenvolvimento Científico e Tecnológico
O objetivo desta dissertação é apresentar uma demonstração de R. Reilly para o Teorema de Alexandrov. O teorema estabelece que As únicas hipersuperfícies compactas, conexas, de curvatura média constante, mergulhadas no espaço Euclidiano são as esferas. O teorema de Alexandrov foi provado por A. D. Alexandrov no artigo Uniqueness Theorems for Surfaces in the Large V, publicado em 1958 pela Vestnik Leningrad University, volume 13, número 19, páginas 5 a 8. Em sua demonstração, Alexandrov usou o famoso Princípio de Tangência, introduzido por ele no citado artigo. No ano de 1962, M. Obata demonstrou em Certain Conditions for a Riemannian Manifold to be Isometric With a Sphere, publicado pelo Journal of Mathematical Society of Japan, volume 14, páginas 333 a 340, que uma variedade Riemanniana M, compacta, conexa e sem bordo, é isométrica a uma esfera, desde que a curvatura de Ricci de M satisfaça determinada limitação inferior. Este teorema resolve o problema de encontrar as variedades que atingem a igualdade na estimativa de Lichnerowicz para o primeiro autovalor. Em 1977, R. Reilly, no artigo Applications of the Hessian Operator in a Riemannian Manifold, publicado no Indianna University Mathematical Journal, volume 23, páginas 459 a 452, demonstrou uma generalização do Teorema de Obata para variedades compactas com bordo. Como exemplo da técnica desenvolvida nesta demonstração, ele apresenta uma nova demonstração do Teorema de Alexandrov. Esta demonstração, bem como as técnicas envolvidas, são o objeto de estudo deste trabalho.
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Debin, Clément. "Géométrie des surfaces singulières." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAM078/document.

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La recherche d'une compactification de l'ensemble des métriques Riemanniennes à singularités coniques sur une surface amène naturellement à l'étude des "surfaces à Courbure Intégrale Bornée au sens d'Alexandrov". Il s'agit d'une géométrie singulière, développée par A. Alexandrov et l'école de Leningrad dans les années 1970, et dont la caractéristique principale est de posséder une notion naturelle de courbure, qui est une mesure. Cette large classe géométrique contient toutes les surfaces "raisonnables" que l'on peut imaginer.Le résultat principal de cette thèse est un théorème de compacité pour des métriques d'Alexandrov sur une surface ; un corollaire immédiat concerne les métriques Riemanniennes à singularités coniques. On décrit dans ce manuscrit trois hypothèses adaptées aux surfaces d'Alexandrov, à la manière du théorème de compacité de Cheeger-Gromov qui concerne les variétés Riemanniennes à courbure bornée, rayon d'injectivité minoré et volume majoré. On introduit notamment la notion de rayon de contractibilité, qui joue le rôle du rayon d'injectivité dans ce cadre singulier.On s'est également attachés à étudier l'espace (de module) des métriques d'Alexandrov sur la sphère, à courbure positive le long d'une courbe fermée. Un sous-ensemble intéressant est constitué des convexes compacts du plan, recollés le long de leurs bords. A la manière de W. Thurston, C. Bavard et E. Ghys, qui ont considéré l'espace de module des polyèdres et polygones (convexes) à angles fixés, on montre que l'identification d'un convexe à sa fonction de support fait naturellement apparaître une géométrie hyperbolique de dimension infinie, dont on étudie les premières propriétés
If we look for a compactification of the space of Riemannian metrics with conical singularities on a surface, we are naturally led to study the "surfaces with Bounded Integral Curvature in the Alexandrov sense". It is a singular geometry, developed by A. Alexandrov and the Leningrad's school in the 70's, and whose main feature is to have a natural notion of curvature, which is a measure. This large geometric class contains any "reasonable" surface we may imagine.The main result of this thesis is a compactness theorem for Alexandrov metrics on a surface ; a straightforward corollary concerns Riemannian metrics with conical singularities. We describe here three hypothesis which pair with the Alexandrov surfaces, following Cheeger-Gromov's compactness theorem, which deals with Riemannian manifolds with bounded curvature, injectivity radius bounded by below and volume bounded by above. Among other things, we introduce the new notion of contractibility radius, which plays the role of the injectivity radius in this singular setting.We also study the (moduli) space of Alexandrov metrics on the sphere, with non-negative curvature along a closed curve. An interesting subset is the set of compact convex sets, glued along their boundaries. Following W. Thurston, C. Bavard and E. Ghys, who considered the moduli space of (convex) polyhedra and polygons with fixed angles, we show that the identification between a convex set and its support function give rise to an infinite dimensional hyperbolic geometry, for which we study the first properties
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Fujioka, Tadashi. "Fibration theorems for collapsing Alexandrov spaces." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263435.

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Desmonts, Christophe. "Surfaces à courbure moyenne constante via les champs de spineurs." Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0073/document.

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Les travaux présentés dans cette thèse portent sur le rôle que peuvent jouer les différentes courbures extrinsèques d’une hypersurface dans l’étude de sa géométrie, en particulier dans le cas des variétés spinorielles. Dans un premier temps, nous nous intéressons au cas de la courbure moyenne et construisons une nouvelle famille de surfaces minimales non simplement connexes dans le groupe de Lie Sol3, en adaptant une méthode déjà utilisée par Daniel et Hauswirth dans Nil3 et utilisant les propriétés de l’application de Gauss d’une surface. Ensuite, nous démontrons le Théorème d’Alexandrov généralisé aux Hr-courbures dans l’espace euclidien Rn+1 et dans l’espace hyperbolique Hn+1 en testant un spineur adéquat dans des inégalités de type holographiques établies récemment par Hijazi, Montiel et Raulot. Grâce à ces inégalités, nous démontrons également l'Inégalité de Heintze-Karcher dans l'espace euclidien. Enfin, nous donnons des majorations extrinsèques de la première valeur propre de l’opérateur de Dirac des surfaces de S2 x S1(r) et des sphères de Berger Sb3 (τ) grâce aux restrictions de spineurs ambiants construits par Roth, et nous en caractérisons les cas d’égalité
In this thesis we are interested in the role played by the extrinsic curvatures of a hypersurface in the study of its geometry, especially in the case of spin manifolds. First, we focus our attention on the mean curvature and construct a new family of non simply connected minimal surfaces in the Lie group Sol3, by adapting a method used by Daniel and Hauswirth in Nil3 based on the properties of the Gauss map of a surface. Then we give a new spinorial proof of the Alexandrov Theorem extended to all Hr-curvatures in the euclidean space Rn+1 and in the hyperbolic space Hn+1, using a well-chosen test-spinor in the holographic inequalities recently obtained by Hijazi, Montiel and Raulot. These inequalities lead to a new proof of the Heintze-Karcher Inequality as well. Finally we use restrictions of particular ambient spinor fields constructed by Roth to give some extrinsic upper bounds for the first nonnegative eigenvalue of the Dirac operator of surfaces immersed into S2 x S1(r) and into the Berger spheres Sb3 (τ), and we describe the equality cases
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Price, Gregory Nathan. "A pseudopolynomial algorithm for Alexandrov's theorem." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44738.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.
Includes bibliographical references (p. 43-44).
Alexandrov's Theorem states that every metric with the global topology and local geometry required of a convex polyhedron is in fact the intrinsic metric of some convex polyhedron. Recent work by Bobenko and Izmestiev describes a differential equation whose solution is the polyhedron corresponding to a given metric. We describe an algorithm based on this differential equation to compute the polyhedron given the metric, and prove a pseudopolynomial bound on its running time. This is joint work with Erik Demaine and Daniel Kane.
by Gregory Nathan Price.
S.M.
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Desmonts, Christophe. "Surfaces à courbure moyenne constante via les champs de spineurs." Electronic Thesis or Diss., Université de Lorraine, 2015. http://www.theses.fr/2015LORR0073.

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Les travaux présentés dans cette thèse portent sur le rôle que peuvent jouer les différentes courbures extrinsèques d’une hypersurface dans l’étude de sa géométrie, en particulier dans le cas des variétés spinorielles. Dans un premier temps, nous nous intéressons au cas de la courbure moyenne et construisons une nouvelle famille de surfaces minimales non simplement connexes dans le groupe de Lie Sol3, en adaptant une méthode déjà utilisée par Daniel et Hauswirth dans Nil3 et utilisant les propriétés de l’application de Gauss d’une surface. Ensuite, nous démontrons le Théorème d’Alexandrov généralisé aux Hr-courbures dans l’espace euclidien Rn+1 et dans l’espace hyperbolique Hn+1 en testant un spineur adéquat dans des inégalités de type holographiques établies récemment par Hijazi, Montiel et Raulot. Grâce à ces inégalités, nous démontrons également l'Inégalité de Heintze-Karcher dans l'espace euclidien. Enfin, nous donnons des majorations extrinsèques de la première valeur propre de l’opérateur de Dirac des surfaces de S2 x S1(r) et des sphères de Berger Sb3 (τ) grâce aux restrictions de spineurs ambiants construits par Roth, et nous en caractérisons les cas d’égalité
In this thesis we are interested in the role played by the extrinsic curvatures of a hypersurface in the study of its geometry, especially in the case of spin manifolds. First, we focus our attention on the mean curvature and construct a new family of non simply connected minimal surfaces in the Lie group Sol3, by adapting a method used by Daniel and Hauswirth in Nil3 based on the properties of the Gauss map of a surface. Then we give a new spinorial proof of the Alexandrov Theorem extended to all Hr-curvatures in the euclidean space Rn+1 and in the hyperbolic space Hn+1, using a well-chosen test-spinor in the holographic inequalities recently obtained by Hijazi, Montiel and Raulot. These inequalities lead to a new proof of the Heintze-Karcher Inequality as well. Finally we use restrictions of particular ambient spinor fields constructed by Roth to give some extrinsic upper bounds for the first nonnegative eigenvalue of the Dirac operator of surfaces immersed into S2 x S1(r) and into the Berger spheres Sb3 (τ), and we describe the equality cases
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Junck, Alexandra [Verfasser]. "Theory of Photocurrents in Topological Insulators / Alexandra Junck." Berlin : Freie Universität Berlin, 2015. http://d-nb.info/107049836X/34.

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Menix, Jacob Scott. "Properties of Functionally Alexandroff Topologies and Their Lattice." TopSCHOLAR®, 2019. https://digitalcommons.wku.edu/theses/3147.

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This thesis explores functionally Alexandroff topologies and the order theory asso- ciated when considering the collection of such topologies on some set X. We present several theorems about the properties of these topologies as well as their partially ordered set. The first chapter introduces functionally Alexandroff topologies and motivates why this work is of interest to topologists. This chapter explains the historical context of this relatively new type of topology and how this work relates to previous work in topology. Chapter 2 presents several theorems describing properties of functionally Alexandroff topologies ad presents a characterization for the functionally Alexandroff topologies on a finite set X. The third and fourth chapters present facts about the lattice of functionally Alexandroff topologies, with Chapter 4 being dedicated to an algorithm which generates a complement in this lattice.
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Craveiro, Pedro Alexandre Albano Dias. "O conceito de arte em Alexandre Herculano." Master's thesis, Instituições portuguesas -- UL-Universidade de Lisboa -- -Faculdade de Belas Artes, 2001. http://dited.bn.pt:80/30104.

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Squillante, Maurizio. "'The Wings of Daedalus' and 'Alexandros' : two tragic operas inspired by the theory of the affections." Thesis, University of Birmingham, 2012. http://etheses.bham.ac.uk//id/eprint/7606/.

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This thesis presents the librettos, scores and CD recordings of two contemporary operas – The Wings of Daedalus and Alexandros – conceived, composed and, in the case of The Wings of Daedalus staged, by myself, along with detailed analysis of the development phases of various different aspects (such as dramaturgy, libretto, staging and characterisation, and particularly the composition of the vocal line and electronic accompaniment of each opera), following them from the initial idea to the final result. All this is paralleled with the period in the development of Western music four hundred years ago that led to the birth of opera. That transitional phase is correlated with my work and its contemporary context, as seen from various viewpoints. I have chosen The Theory of the Affections as an exemplary connecting point between these chronologically distant eras in music, and used it to identify important links between compositional intention and vocal practice in the years leading up to 1600 and those leading up to 2000. This in turn leads me to explain specifically my own compositional techniques - many of which are radically unusual and correlate them with The Theory of the Affections as approaches to creating opera.
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Books on the topic "Alexandrov Theorem"

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Wang, Ye-Kai. A Spacetime Alexandrov Theorem. [New York, N.Y.?]: [publisher not identified], 2014.

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Little, Heath Thomas. Diophantus of Alexandria: A study in the history of Greek algebra. Mansfield Center, CT: Martino Pub., 2009.

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Word and meaning in ancient Alexandria: Theories of language from Philo to Plotinus. Aldershot, England: Ashgate, 2008.

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1943-, Petersen Karl Endel, Salama Ibrahim A, and London Mathematical Society, eds. Ergodic theory and its connection with harmonic analysis: Proceedings of the 1993 Alexandria conference. Cambridge: Cambridge University Press, 1995.

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Little, Heath Thomas. Diophantus of Alexandria, a study in the history of Greek algebra: With a supplement containing an account of Fermat's theorems and problems connected with Diophantine analysis and some solutions of Diophantine problems by Euler. 2nd ed. [Charleston, S.C.]: Forgotten Books, 2011.

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IEEE-IMS Workshop on Information Theory and Statistics (1994 Alexandria, Va.). 1994 IEEE-IMS Workshop on Information Theory and Statistics: October 27-29, 1994, Holiday Inn Old Town, Alexandria, Virginia, USA. Piscataway, NJ: IEEE, 1995.

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al-Handasah, Jāmiʻat al-Iskandarīyah Kullīyat, Akādīmīyat al-Ba hth al-ʻIlmī wa-al-Tiknūlūjiyā., National Radio Science Committee., IEEE Electron Devices Society, and International Union of Radio Science., eds. NRSC'2002: Proceedings of the Nineteenth National Radio Science Conference : Alexandra, Egypt, March 19-21, 2002. [Piscataway, N.J: IEEE, 2002.

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1939-, Tompazēs Alexandros N., Schmiedeknecht Torsten, and Grapheio Meletōn Alexandrou N. Tompazē., eds. Tombazis and associates architects: Less in beautiful. Milano: L'Arca Edizioni, 2002.

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Blandzi, Seweryn. Między aletjologią Parmenidesa a ontoteologia ̨Filona: Rekonstrukcyjne studia historyczno-genetyczne = Between Parmenides' Aletheiology and Philo's of Alexandria ontotheology : reconstructionist historical and genetic studies. Warszawa: Wydawnictwo IFiS PAN, 2013.

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Sprache, Erkennen und Schweigen in der Gedankenwelt des Philo von Alexandrien. Frankfurt am Main: P. Lang, 1996.

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Book chapters on the topic "Alexandrov Theorem"

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Kane, Daniel, Gregory N. Price, and Erik D. Demaine. "A Pseudopolynomial Algorithm for Alexandrov’s Theorem." In Lecture Notes in Computer Science, 435–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03367-4_38.

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Gavriluţ, Alina, Ioan Mercheş, and Maricel Agop. "Continuity properties and Alexandroff theorem in Vietoris topology." In Atomicity through Fractal Measure Theory, 83–103. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29593-6_7.

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Feldzamen, A. N. "The Alexandra Ionescu Tulcea Proof of Mcmillan'S Theorem." In Sistemi dinamici e teoremi ergodici, 179–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-10945-4_7.

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Markina, Irina, and Stephan Wojtowytsch. "On the Alexandrov Topology of sub-Lorentzian Manifolds." In Geometric Control Theory and Sub-Riemannian Geometry, 287–311. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02132-4_17.

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Huber, Alfred. "On the Potential Theoretic Aspect of Alexandrov Surface Theory." In Reshetnyak's Theory of Subharmonic Metrics, 341–72. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-24255-7_14.

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Troyanov, Marc. "On Alexandrov’s Surfaces with Bounded Integral Curvature." In Reshetnyak's Theory of Subharmonic Metrics, 9–34. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-24255-7_2.

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Barotsi, Rosa. "Not Yet." In Errans, 75–92. Berlin: ICI Berlin Press, 2022. http://dx.doi.org/10.37050/ci-24_3.

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Mafrouza is a twelve-hour-long documentary by French director Emanuelle Demoris, shot in a now-demolished neighbourhood in Alexandria, Egypt. Demoris is one of a long chain of western filmmakers who appeal to some form of ‘taking one’s time’ as an instrument for — morally, politically, epistemologically — adequate representation. Based on the work of Trinh T. Minh-ha, Eduard Glissant, and Poor Theory, this chapter evaluates what happens when a film adopts a strategy of deferral in cases in which it is not clear how questions of ‘doing justice’ could be resolved. Using long duration and an insistence on the quotidian, Demoris’s film forces us to think about the conditions that make pronouncements about character, situation, and narrative possible, continuously postponing the moment when it will become possible to say: ‘this film is about …’. By setting itself up for failure, the film proposes one possible approach to the ethics and politics of visibility.
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"A general uniqueness theorem for closed surfaces." In A. D. Alexandrov Selected Works Part I, 155–58. CRC Press, 2002. http://dx.doi.org/10.1201/9781482287172-12.

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"OTHER EXISTENCE THEOREMS." In A.D. Alexandrov, 291–314. Chapman and Hall/CRC, 2005. http://dx.doi.org/10.1201/9780203643846-13.

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"Uniqueness theorems for closed surfaces." In A. D. Alexandrov Selected Works Part I, 159–64. CRC Press, 2002. http://dx.doi.org/10.1201/9781482287172-13.

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Conference papers on the topic "Alexandrov Theorem"

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Zhang, Chuanyi. "Generalized Kronecker’s theorem and strong limit power functions." In ALEXANDRU MYLLER MATHEMATICAL SEMINAR CENTENNIAL CONFERENCE. AIP, 2011. http://dx.doi.org/10.1063/1.3546091.

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Ieşan, D. "On the grade consistent theories of micromorphic elastic solids." In ALEXANDRU MYLLER MATHEMATICAL SEMINAR CENTENNIAL CONFERENCE. AIP, 2011. http://dx.doi.org/10.1063/1.3546081.

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Bri^nzănescu, Vasile. "From string theory to algebraic geometry and back." In ALEXANDRU MYLLER MATHEMATICAL SEMINAR CENTENNIAL CONFERENCE. AIP, 2011. http://dx.doi.org/10.1063/1.3546073.

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Avdyev, M. "THE DIOPHANTINE EQUATION FROM THE EYE OF PHYSICIST." In X Международная научно-практическая конференция "Культура, наука, образование: проблемы и перспективы". Нижневартовский государственный университет, 2022. http://dx.doi.org/10.36906/ksp-2022/57.

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A Diophantine equation is an equation with integer coefficients, the solutions of which must be found among integers. The equation is named after the mathematician Diophantus of Alexandria (III century). Despite its simplicity, a Diophantine equation may have a nontrivial solution (several solutions) or has no solution at all. Fermat's Last Theorem and Pythagorean Theorem are the Diophantine equations too. In 1900 The German mathematician David Hilbert formulated the Tenth problem. After 70 years, the answer turned out to be negative: there is no general algorithm. Nevertheless, for some cases, schoolchildren can understand whether a Diophantine equation is solvable without resorting to calculations, relying on the methods of physics, symmetry and set theory.
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Arruda, Amilton, Celso Hartkopf, and Rodrigo Balestra. "City branding: strategic planning and communication image in the management of contemporary cities." In Systems & Design: Beyond Processes and Thinking. Valencia: Universitat Politècnica València, 2016. http://dx.doi.org/10.4995/ifdp.2016.3288.

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Over the past decade, one can observe a steady growth in the use of terms such as Place Branding, Nation Branding, Destination Branding and City Branding. Both in academic research and in the practical applications in large cities management and urban spaces, this new paradigm takes shape and, along with it, the need for definitions and concepts, methods and methodologies and the establishment of technical and theoretical standards. This approach was born in the Marketing field, specifically in what was called Place Marketing. In this context the Branding stood out as a development tool solutions to the need for differentiation, generation of solid images and the establishment of symbols and identity signs, in order to leverage economic benefits for countries, cities and regions. In a way, fulfilling, in the first instance, a similar role to the branding of products and services. But it was specifically in Branding corporations that were found the biggest matches to adapt this knowledge to management positions. Ashworth & Kavaratzis (2010) highlight the fact that both present multidisciplinary roots, a multiple number of strategic actors (stakeholders), high degree of intangibility and complexity of social responsibility, the multiplicity of identities and the long-term development needs are strong examples their similarities. The development and management of corporate identities, here expanded to the Branding corporations, it is a prolific field of Design. It great names of the area said their careers and built great legacy. The time of greater proficiency in the area were the 50s and 60s, dominated by modernist thought, and, coincidentally or not, exactly the time that focused efforts to assert the identity of the designer as a professional (STOLARSKI, 2006) . Nationally stand out names like Alexandre Wollner, Ruben Martins, the duo Carlos Cauduro and Ludovico Martino and Aloisio Magalhaes. In contrast, in the literature produced in the marketing field, often the role of design in this context is reduced to merely promotional measures, such as creating logos or advertising campaigns. In other words, defined as a work of low complexity and low social prägnanz. This approach comes at odds with contemporary theories of design, such as MetaDesign, Design Thinking and Design Collaborative, in which are presented motodológicos models of high relevance for the identification, analysis and solution of complex problems involving multiple elements and agents. The proposed article aims to survey the state of the art City Branding / Place Branding focused on publications produced in the disciplinary field of design. The literature review will grant that, before the above presented context, is analyzed as designers and researchers design face the contributions that the field can offer to the practice and theory of Branding places. Finally, Article yearns assess whether the pre-established hypothesis that there are possible and fruitful connections between contemporary theories of design and the City Branding, is being addressed in articles and publications area.DOI: http://dx.doi.org/10.4995/IFDP.2016.3288
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Reports on the topic "Alexandrov Theorem"

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INFORMATION THEORY SOCIETY (IEEE) PASADENA CA. Proceedings of the IEEE-IMS Workshop on Information Theory and Statistics (1994) Alexandria, Virginia on October 27-29, 1994. Fort Belvoir, VA: Defense Technical Information Center, October 1994. http://dx.doi.org/10.21236/ada288808.

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Graham, Timothy, and Katherine M. FitzGerald. Bots, Fake News and Election Conspiracies: Disinformation During the Republican Primary Debate and the Trump Interview. Queensland University of Technology, 2023. http://dx.doi.org/10.5204/rep.eprints.242533.

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We used Alexandria Digital, a world leading disinformation detection technology, to analyse almost a million posts on X (formerly known as Twitter) and Reddit comments during the first Republican primary debate and counterprogrammed Tucker Carlson and Donald Trump interview on the 23rd of August. What we did: • Collected 949,259 posts from the platform X, formerly known as Twitter. These posts were collected if they contained one of 11 relevant hashtags or keywords and were posted between 8:45pm and 11:15pm EST on 23rd August 2023. • Collected 20,549 comments from two separate Reddit threads. Both were discussion threads dedicated to the first Republican primary Debate and the Tucker Carlson and Donald Trump interview from r/Conservative and r/politics. • This methodology allowed us to capture narratives and conduct analysis of coordinated behaviour that occurred immediately before, during, and after the Republican primary debate and the airing of the Tucker Carlson interview of Donald Trump. What we found: • A coordinated network of over 1200 accounts promoting the conspiracy theory that Donald Trump won the 2020 United States presidential election that received over 3 million impressions on the platform X; • A sprawling bot network consisting of 1,305 unique accounts with a variety of clusters; • Some of the largest clusters were coordinated troll networks in support of Donald Trump; a coordinated network of misleading news outlets, and a clickbait Pro-Trump bot network. • No coordinated activity was found on Reddit during the Republican Primary Debate or in discussion of the Tucker Carlson and Donald Trump interview. What does this mean? • X is flooded with platform manipulation of various kinds, is not doing enough to moderate content, and has no clear strategy for dealing with political disinformation. • A haven for disinformation. While pre-Musk Twitter previously managed to moderate harmful conspiracy theories such as QAnon, X is now a safe space for conspiracy theorists and political disinformation. • That no evidence of coordinated influence activity was found on Reddit suggests the extensive rules and moderation either prevented or removed coordinated activity from the platform. • Worrying trends. Given the prevalence of mis- and disinformation during the debate and interview, the leadup to the US 2024 Presidential Election is likely to witness a surge of information disorder on the platform. • Trump is back. The reinstatement of Donald Trump’s X account has emboldened conspiracy theorists and the far right, who are interpreting this as a sign that the reason why Trump was suspended (incitement to violence) validates election fraud disinformation and activism. • Anything goes. The lack of a freely available Twitter Application Programming Interface (API) means that researchers, journalists, and regulators cannot monitor disinformation on X and hold the platform to account.
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