Relevant bibliographies by topics / Finite fields (Algebra) Geometry

Contents

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

Academic literature on the topic 'Finite fields (Algebra) Geometry'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Finite fields (Algebra) Geometry"

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Dadarlat, Marius. "Fiberwise KK-equivalence of continuous fields of C*-algebras." Journal of K-Theory 3, no. 2 (May 28, 2008): 205–19. http://dx.doi.org/10.1017/is008001012jkt041.

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AbstractLet A and B be separable nuclear continuous C(X)-algebras over a finite dimensional compact metrizable space X. It is shown that an element σ of the parametrized Kasparov group KKX(A,B) is invertible if and only all its fiberwise components σx ∈ KK(A(x),B(x)) are invertible. This criterion does not extend to infinite dimensional spaces since there exist nontrivial unital separable continuous fields over the Hilbert cube with all fibers isomorphic to the Cuntz algebra . Several applications to continuous fields of Kirchberg algebras are given. It is also shown that if each fiber of a separable nuclear continuous C(X)-algebra A over a finite dimensional locally compact space X satisfies the UCT, then A satisfies the UCT.
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Bani-Ata, Mashhour, and Mariam Al-Rashed. "On certain finite dimensional algebras over finite fields." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 58, no. 1 (August 19, 2016): 195–200. http://dx.doi.org/10.1007/s13366-016-0312-8.

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RAFIE-RAD, M. "SPECIAL PROJECTIVE ALGEBRA OF RANDERS METRICS OF CONSTANT S-CURVATURE." International Journal of Geometric Methods in Modern Physics 09, no. 04 (May 6, 2012): 1250034. http://dx.doi.org/10.1142/s021988781250034x.

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The collection of all projective vector fields on a Finsler space (M, F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra. A specific Lie sub-algebra of projective algebra of Randers spaces (called the special projective algebra) of non-zero constant S-curvature is studied and it is proved that its dimension is at most [Formula: see text]. Moreover, a local characterization of Randers spaces whose special projective algebra has maximum dimension is established. The results uncover somehow the complexity of projective Finsler geometry versus Riemannian geometry.
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Lo, Catharine Wing Kwan, and Matilde Marcolli. "𝔽ζ-geometry, Tate motives, and the Habiro ring." International Journal of Number Theory 11, no. 02 (March 2015): 311–39. http://dx.doi.org/10.1142/s1793042115500189.

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In this paper, we propose different notions of 𝔽ζ-geometry, for ζ a root of unity, generalizing notions of 𝔽1-geometry (geometry over the "field with one element") based on the behavior of the counting functions of points over finite fields, the Grothendieck class, and the notion of torification. We relate 𝔽ζ-geometry to formal roots of Tate motives, and to functions in the Habiro ring, seen as counting functions of certain ind-varieties. We investigate the existence of 𝔽ζ-structures in examples arising from general linear groups, matrix equations over finite fields, and some quantum modular forms.
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Feng, Rongquan, Liwei Zeng, and Yang Zhang. "Constructions of 112-Designs from Unitary Geometry over Finite Fields." Algebra Colloquium 24, no. 03 (September 2017): 381–92. http://dx.doi.org/10.1142/s1005386717000232.

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In this paper, we construct some [Formula: see text]-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the unitary space. Furthermore, these [Formula: see text]-designs yield six infinite families of directed strongly regular graphs.
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Gao, Suogang, Zengti Li, Weili Wu, Panos M. Pardalos, and Dingzhu Du. "Group testing with geometry of classical groups over finite fields." Journal of Algebraic Combinatorics 49, no. 4 (June 6, 2018): 381–400. http://dx.doi.org/10.1007/s10801-018-0828-0.

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Camenga, Kristin A., Brandon Collins, Gage Hoefer, Jonny Quezada, Patrick X. Rault, James Willson, and Rebekah B. Johnson Yates. "On the geometry of numerical ranges over finite fields." Linear Algebra and its Applications 628 (November 2021): 182–201. http://dx.doi.org/10.1016/j.laa.2021.07.008.

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Koike, Masao. "Orthogonal matrices obtained from hypergeometric series over finite fields and elliptic curves over finite fields." Hiroshima Mathematical Journal 25, no. 1 (1995): 43–52. http://dx.doi.org/10.32917/hmj/1206127824.

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LARSSON, T. A. "CONFORMAL FIELDS: A CLASS OF REPRESENTATIONS OF Vect(N)." International Journal of Modern Physics A 07, no. 26 (October 20, 1992): 6493–508. http://dx.doi.org/10.1142/s0217751x92002970.

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Vect (N), the algebra of vector fields in N dimensions, is studied. Some aspects of local differential geometry are formulated as Vect(N) representation theory. There is a new class of modules, conformal fields, whose restrictions to the subalgebra sl(N+1)⊂ Vect (N) are finite-dimensional sl (N+1) representations. In this regard they are simpler than tensor fields. Fock modules are also constructed. Infinities, which are unremovable even by normal ordering, arise unless bosonic and fermionic degrees of freedom match.
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Evans, Ron, and John Greene. "Evaluations of hypergeometric functions over finite fields." Hiroshima Mathematical Journal 39, no. 2 (July 2009): 217–35. http://dx.doi.org/10.32917/hmj/1249046338.

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Dissertations / Theses on the topic "Finite fields (Algebra) Geometry"

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Rovi, Carmen. "Algebraic Curves over Finite Fields." Thesis, Linköping University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56761.

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This thesis surveys the issue of finding rational points on algebraic curves over finite fields. Since Goppa's construction of algebraic geometric codes, there has been great interest in finding curves with many rational points. Here we explain the main tools for finding rational points on a curve over a nite eld and provide the necessary background on ring and field theory. Four different articles are analyzed, the first of these articles gives a complete set of table showing the numbers of rational points for curves with genus up to 50. The other articles provide interesting constructions of covering curves: covers by the Hemitian curve, Kummer extensions and Artin-Schreier extensions. With these articles the great difficulty of finding explicit equations for curves with many rational points is overcome. With the method given by Arnaldo García in [6] we have been able to nd examples that can be used to define the lower bounds for the corresponding entries in the tables given in http: //wins.uva.nl/~geer, which to the time of writing this Thesis appear as "no information available". In fact, as the curves found are maximal, these entries no longer need a bound, they can be given by a unique entry, since the exact value of Nq(g) is now known.

At the end of the thesis an outline of the construction of Goppa codes is given and the NXL and XNL codes are presented.

 

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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 principale
In 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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Jogia, Danesh Michael Mathematics &amp Statistics Faculty of Science UNSW. "Algebraic aspects of integrability and reversibility in maps." Publisher:University of New South Wales. Mathematics & Statistics, 2008. http://handle.unsw.edu.au/1959.4/40947.

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We study the cause of the signature over finite fields of integrability in two dimensional discrete dynamical systems by using theory from algebraic geometry. In particular the theory of elliptic curves is used to prove the major result of the thesis: that all birational maps that preserve an elliptic curve necessarily act on that elliptic curve as addition under the associated group law. Our result generalises special cases previously given in the literature. We apply this theorem to the specific cases when the ground fields are finite fields of prime order and the function field $mathbb{C}(t)$. In the former case, this yields an explanation of the aforementioned signature over finite fields of integrability. In the latter case we arrive at an analogue of the Arnol'd-Liouville theorem. Other results that are related to this approach to integrability are also proven and their consequences considered in examples. Of particular importance are two separate items: (i) we define a generalization of integrability called mixing and examine its relation to integrability; and (ii) we use the concept of rotation number to study differences and similarities between birational integrable maps that preserve the same foliation. The final chapter is given over to considering the existence of the signature of reversibility in higher (three and four) dimensional maps. A conjecture regarding the distribution of periodic orbits generated by such maps when considered over finite fields is given along with numerical evidence to support the conjecture.
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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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Hart, Derrick. "Explorations of geometric combinatorics in vector spaces over finite fields." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/5585.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2008.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 8, 2009) Vita. Includes bibliographical references.
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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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Marseglia, Stefano. "Isomorphism classes of abelian varieties over finite fields." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-130316.

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Deligne and Howe described polarized abelian varieties over finite fields in terms of finitely generated free Z-modules satisfying a list of easy to state axioms. In this thesis we address the problem of developing an effective algorithm to compute isomorphism classes of (principally) polarized abelian varieties over a finite field, together with their automorphism groups. Performing such computations requires the knowledge of the ideal classes (both invertible and non-invertible) of certain orders in number fields. Hence we describe a method to compute the ideal class monoid of an order and we produce concrete computations in dimension 2, 3 and 4.
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Castilho, Tiago Nunes 1983. "Sobre o numero de pontos racionais de curvas sobre corpos finitos." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307074.

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Orientador: Fernando Eduardo Torres Orihuela
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-10T15:12:25Z (GMT). No. of bitstreams: 1 Castilho_TiagoNunes_M.pdf: 813127 bytes, checksum: 313e9951b003dcd0e0876813659d7050 (MD5) Previous issue date: 2008
Resumo: Nesta dissertacao estudamos cotas para o numero de pontos racionais de curvas definidas sobre corpos finitos tendo como ponto de partida a teoria de Stohr-Voloch
Abstract: In this work we study upper bounds on the number of rational points of curves over finite fields by using the Stohr-Voloch theory
Mestrado
Algebra Comutativa, Geometria Algebrica
Mestre em Matemática
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Ribeiro, Beatriz Casulari da Motta 1984. "O arco associado a uma generalização da curva Hermitiana." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307081.

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Orientadores: Fernando Eduardo Torres Orihuela, Herivelto Martins Borges Filho
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-19T05:54:38Z (GMT). No. of bitstreams: 1 Ribeiro_BeatrizCasularidaMotta_D.pdf: 51476410 bytes, checksum: 46cb0c7a6206a5f0683b23a73ff3938e (MD5) Previous issue date: 2011
Resumo: Obtemos novos arcos completos associados ao conjunto de pontos racionais de uma certa generalização da curva Hermitiana que é Frobenius não-clássica. A construção está relacionada ao cálculo do número de pontos racionais de uma classe de curvas de Artin-Schreier
Abstract: We obtain new complete arcs arising from the set of rational points of a certain generalization of the Hermitian plane curve which is Frobenius non-classical. Our construction is related to the computation of the number of rational points of a class of Artin-Schreier curves
Doutorado
Matematica
Doutor em Matemática
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Albuquerque, JoÃo Victor Maximiano. "Finitude do grupo das classes de um corpo de nÃmeros via empacotamentos reticulados." Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11247.

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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
Este trabalho à baseado no artigo Finiteness of the class group of a number field via lattice packings. Daremos aqui uma prova alternativa da finitude do grupo das classes de um corpo de nÃmeros de grau n. Ela à baseada apenas no fato de que a densidade de centro de um empacotamento reticulado n-dimensional à limitado fora do infinito.
This work is based on the article Finiteness of the class group of a number field via lattice packings. An alternative proof of the finiteness of the class group of a number field of the degree n is presented. It is based solely on the fact that the center density of an n-dimensional lattice packing is bounded away from infinity.
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Books on the topic "Finite fields (Algebra) Geometry"

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Dmitri, Kaledin, and Tschinkel Yuri, eds. Higher-dimensional geometry over finite fields. Amsterdam, Netherlands: IOS Press, 2008.

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Projective geometries over finite fields. 2nd ed. Oxford: Clarendon Press, 1998.

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Noll, W. Finite-dimensional spaces: Algebra, geometry, and analysis. Dordrecht: M. Nijhoff, 1987.

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1971-, Orlik Sascha, and Rapoport M. 1948-, eds. Period domains over finite and p-adic fields. Cambridge: Cambridge University Press, 2010.

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Hansen, Søren Have. Rational points on curves over finite fields. [Aarhus, Denmark: Aarhus Universitet, Matematisk Institut, 1995.

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Gary, McGuire, ed. Finite fields: Theory and applications : Ninth International Conference on Finite Fields and Applications, July 13-17, 2009, Dublin, Ireland. Providence, R.I: American Mathematical Society, 2010.

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A, Thas J., ed. General Galois geometries. Oxford: Clarendon Press, 1991.

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Many rational points: Coding theory and algebraic geometry. Dordrecht: Kluwer Academic Publishers, 2003.

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Germany) International Conference on Finite Fields and Applications (11th 2013 Magdeburg. Topics in finite fields: 11th International Conference on Finite Fields and Their Applications, July 22--26, 2013, Magdeburg, Germany. Edited by Kyureghyan Gohar 1974 editor, Mullen Gary L. editor, and Pott Alexander 1961 editor. Providence, Rhode Island: American Mathematical Society, 2015.

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Katcher, Pollatsek Harriet Suzanne, ed. Difference sets: Connecting algebra, combinatorics and geometry. Providence, Rhode Island: American Mathematical Society, 2013.

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Book chapters on the topic "Finite fields (Algebra) Geometry"

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Blake, Ian F., XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, and Tomik Yaghoobian. "Codes From Algebraic Geometry." In Applications of Finite Fields, 191–209. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4757-2226-0_10.

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Blake, Ian F., XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, and Tomik Yaghoobian. "Introduction to Algebraic Geometry." In Applications of Finite Fields, 173–90. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4757-2226-0_9.

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van Lint, Jacobus H., and Gerard van der Geer. "Finite fields." In Introduction to Coding Theory and Algebraic Geometry, 11–12. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9286-5_1.

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Farrán, J. I. "Asymptotics of Reduced Algebraic Curves Over Finite Fields." In Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, 511–23. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-96827-8_22.

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Gekeler, Ernst-Ulrich. "Asymptotically Optimal Towers of Curves over Finite Fields." In Algebra, Arithmetic and Geometry with Applications, 325–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18487-1_21.

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Wan, Daqing. "Pure L-Functions from Algebraic Geometry over Finite Fields." In Finite Fields and Applications, 437–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56755-1_34.

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Cafure, Antonio, Guillermo Matera, and Ariel Waissbein. "Efficient Inversion of Rational Maps Over Finite Fields." In Algorithms in Algebraic Geometry, 55–77. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-75155-9_4.

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Eick, Bettina, and Tobias Moede. "Classifying Nilpotent Associative Algebras: Small Coclass and Finite Fields." In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 213–29. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70566-8_9.

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van Lint, Jacobus H., and Gerard van der Geer. "Counting points on curves over finite fields." In Introduction to Coding Theory and Algebraic Geometry, 66–72. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9286-5_13.

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Geer, G. "Coding Theory and Algebraic Curves Over Finite Fields." In Applications of Algebraic Geometry to Coding Theory, Physics and Computation, 139–59. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-1011-5_8.

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Conference papers on the topic "Finite fields (Algebra) Geometry"

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Tsukanov, Igor, and Sudhir R. Posireddy. "Hybrid Method of Engineering Analysis: Combining Meshfree Method With Distance Fields and Collocation Technique." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12881.

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Most of the modern engineering analysis methods (Finite Element, Finite Difference, Finite Volume, etc.) rely on space discretizations of the underlying geometric model. Such spatial meshes have to conform to the geometric model in order to approximate boundary conditions, construct basis functions with good local properties as well as perform numerical integration and visualization of the modeling results. Despite recent advances in automatic mesh generation, spatial meshing still remains difficult problem which often requires geometry simplification and feature removal. Conforming spatial mesh also restricts motions and variations of the geometry and breaks design-analysis cycle. In order to overcome difficulties and restrictions of the mesh-based methods, the alternative analysis methods have been proposed. We present a numerical technique for solving engineering analysis problems that combines meshfree method with distance fields, radial basis functions and collocation technique. The proposed approach enhances the collocation method with exact treatment of boundary conditions at all boundary points. It makes it possible to exclude boundary conditions from the collocation equations. This reduces the size of the algebraic system which results in faster solutions. On another hand, the boundary collocation points can be used to enforce the governing equation of the problem which enhances the solutions accuracy. Ability to use unstructured grids empowers the meshfree method with distance fields with higher level of geometric flexibility. In our presentation we demonstrate comparisons of the numerical results given by the combined approach with results delivered by the traditional collocation technique and meshfree method with distance fields.
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Todorov, Ivan. "Jordan algebra approach to finite quantum geometry." In Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity". Trieste, Italy: Sissa Medialab, 2020. http://dx.doi.org/10.22323/1.376.0163.

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Coquereaux, R., and G. E. Schieber. "Action of finite quantum group on the algebra of complex N×N matrices." In Particles, fields and gravitation. AIP, 1998. http://dx.doi.org/10.1063/1.57119.

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Ferna´ndez, Manuel Rodri´guez, Evangelino Garrido Torres, and Ricardo Ortega Garci´a. "TrenSen: A New Way to Study the Unsteady Behaviour of Air Inside Tunnels—Application to High Speed Railway Lines." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62641.

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During the last decades, high speed railway traffic system has achieved a great development all over the world. Increasing speed in the train circulation implies the apparition of new aerodynamic phenomena that need to be studied. One of these problems has to do with the entrance and exit of high speed (HS) trains in tunnels. When this occurs, pressure waves propagate and reflect through the tunnel at sound speed, generating a non-stationary movement of the air which depends greatly on the speed of the train and the geometry between train and tunnel. A study has been carried on to determine the pressure and velocity fields of air inside the tunnel when the train passes through. As a result of this study, a new software, “TrenSen”, has been developed. This program solves numerically a particular case of the Navier-Stokes equations, a hyperbolic system of partial differential equations which describe the flow behaviour inside the tunnel. In the first section of the paper presented hereby a description of the algebra for the fluid dynamics equations is conducted. The second section will explain some features of the software, ending with some numerical results obtained from the program. To finish the paper, the software is validated by comparing the numeric results with available experimental data and with some other commercial software.
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Lin, Dongdai, and Zhuojun Liu. "Some results on theorem proving in geometry over finite fields." In the 1993 international symposium. New York, New York, USA: ACM Press, 1993. http://dx.doi.org/10.1145/164081.164143.

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ADACHI, Toshiaki. "LAPLACIANS FOR FINITE REGULAR KÄHLER GRAPHS AND FOR THEIR DUAL GRAPHS." In 4th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814719780_0002.

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PIPERKOV, Paskal, Iliya BOUYUKLIEV, and Stefka BOUYUKLIEVA. "AN ALGORITHM FOR COMPUTING THE WEIGHT DISTRIBUTION OF A LINEAR CODE OVER A COMPOSITE FINITE FIELD WITH CHARACTERISTIC 2." In 6th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811206696_0011.

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Wang, Jian-Kang, and Han-Xiong Huang. "Analysis of Flow Fields in Foaming Die Using Finite Element Method." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79833.

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The morphology and properties of the extruded polymeric foams are affected by the geometry of extrusion die. In this paper, the flow in the slit die was simulated using POLYFLOW software package to predict the pressure distribution and residence time. Then the pressure drop rate in the die was calculated. The results for seven dies with different length (L) and gap (H) of the straight section were compared. The effects of the L and H on the nucleation position were analyzed. Based on the critical foaming pressure (Pf), the minimum length and maximum gap providing required pressure drop were determined under a constant gap and a constant length, respectively.
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9

Ketchel, John S., and Pierre M. Larochelle. "Collision Detection of Cylindrical Rigid Bodies Using Line Geometry." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84699.

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Abstract:
This paper presents a novel methodology for detecting collisions of cylindrically shaped rigid bodies moving in three dimensions. This algorithm uses line geometry and dual number algebra to exploit the geometry of right circular cylindrical objects to facilitate the detection of collisions. First, the rigid bodies are modelled with infinite length cylinders and a necessary condition for collision is evaluated. If the necessary condition is not satisfied then the two bodies are not capable of collision. If the necessary condition is satisfied then a collision between the bodies may occur and we proceed to the next stage of the algorithm. In the second stage the bodies are modelled with finite length cylinders and a definitive necessary and sufficient collision detection algorithm is employed. The result is a straight-forward and efficient means of detecting collisions of cylindrically shaped bodies moving in three dimensions. This methodology has applications in spatial mechanism design, robot motion planning, workspace analysis of parallel kinematic machines such as Stewart-Gough platforms, nuclear physics, medical research, computer graphics and well drilling. A case study examining a spatial 4C robotic mechanism for self collisions is included.
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10

Strozzi, Matteo, Francesco Pellicano, and Antonio Zippo. "Nonlinear Vibrations of Functionally Graded Cylindrical Shells: Effect of the Geometry." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70417.

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Abstract:
In this paper, the effect of the geometry on the nonlinear vibrations of functionally graded (FGM) cylindrical shells is analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. In the linear analysis, after spatial discretization, mass and stiff matrices are computed, natural frequencies and mode shapes of the shell are obtained. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions obtained by the linear analysis; specific modes are selected. The Lagrange equations reduce nonlinear partial differential equations to a set of ordinary differential equations. Numerical analyses are carried out in order to characterize the nonlinear response of the shell. A convergence analysis is carried out to determine the correct number of the modes to be used. The analysis is focused on determining the nonlinear character of the response as the geometry of the shell varies.
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