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Relevant bibliographies by topics / Curves, Algebraic. Curves, Plane

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Academic literature on the topic 'Curves, Algebraic. Curves, Plane'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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Journal articles on the topic "Curves, Algebraic. Curves, Plane"

1

de la Puente, Maria Jesus. "Real plane algebraic curves." Expositiones Mathematicae 20, no. 4 (2002): 291–314. http://dx.doi.org/10.1016/s0723-0869(02)80009-3.

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Гирш and A. Girsh. "Foci of Algebraic Curves." Geometry & Graphics 3, no. 3 (2015): 4–17. http://dx.doi.org/10.12737/14415.

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Curves have always been part geometry. Initially, there were lines and circle, then it was added to a conic section and later, with the advent of analytic geometry, they added more complex curves. Particularly in a number of lines are algebraic curves that are described by algebraic equations. Curves found application mostly in mechanics. Today algebraic curves used in engineering and in mathematics, in number theory, knot theory, computer science, criminology, etc. With the bringing to account of complex numbers became possible to consider curve

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KAUL, ANIL, and RIDA T. FAROUKI. "COMPUTING MINKOWSKI SUMS OF PLANE CURVES." International Journal of Computational Geometry & Applications 05, no. 04 (1995): 413–32. http://dx.doi.org/10.1142/s0218195995000258.

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The Minkowski sum of two plane curves can be regarded as the area generated by sweeping one curve along the other. The boundary of the Minkowski sum consists of translated portions of the given curves and/or portions of a more complicated curve, the “envelope” of translates of the swept curve. We show that the Minkowski-sum boundary is describable as an algebraic curve (or subset thereof) when the given curves are algebraic, and illustrate the computation of its implicit equation. However, such equations are typically of high degree and do not offer a practical basis for tracing the boundary.

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Hillman, Jonathan A. "Singularities of plane algebraic curves." Expositiones Mathematicae 23, no. 3 (2005): 233–54. http://dx.doi.org/10.1016/j.exmath.2005.01.007.

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Treger, Robert. "Plane Curves With Nodes." Canadian Journal of Mathematics 41, no. 2 (1989): 193–212. http://dx.doi.org/10.4153/cjm-1989-010-x.

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A smooth algebraic curve is birationally equivalent to a nodal plane curve. One of the main problems in the theory of plane curves is to describe the situation of nodes of an irreducible nodal plane curve (see [16, Art. 45], [10], [7, Book IV, Chapter I, §5], [12, p. 584], and [3]).Let n denote the degree of a nodal curve and d the number of nodes. The case (AZ, d) — (6,9) has been analyzed by Halphen [10]. It follows from Lemma 3.5 and Proposition 3.6 that this is an exceptional case. The case d ≦n(n + 3)/6, d ≦(n — 1)(n — 2)/2, and (n, d) ≠ (6,9) was investigated by Arbarello and Cornalba [3

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Cossidente, A., and A. Siciliano. "Plane algebraic curves with Singer automorphisms." Journal of Number Theory 99, no. 2 (2003): 373–82. http://dx.doi.org/10.1016/s0022-314x(02)00070-7.

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Boileau, Michel, and Laurence Fourrier. "Knot theory and plane algebraic curves." Chaos, Solitons & Fractals 9, no. 4-5 (1998): 779–92. http://dx.doi.org/10.1016/s0960-0779(97)00103-3.

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Borodzik, Maciej. "Morse theory for plane algebraic curves." Journal of Topology 5, no. 2 (2012): 341–65. http://dx.doi.org/10.1112/jtopol/jts006.

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Kulikov, Vik S. "ALEXANDER POLYNOMIALS OF PLANE ALGEBRAIC CURVES." Russian Academy of Sciences. Izvestiya Mathematics 42, no. 1 (1994): 67–89. http://dx.doi.org/10.1070/im1994v042n01abeh001534.

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Moura, Claire. "Local intersections of plane algebraic curves." Proceedings of the American Mathematical Society 132, no. 3 (2003): 687–90. http://dx.doi.org/10.1090/s0002-9939-03-07178-8.

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Dissertations / Theses on the topic "Curves, Algebraic. Curves, Plane"

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Nichols, Margaret E. "Intersection Number of Plane Curves." Oberlin College Honors Theses / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1385137385.

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Hilmar, Jan. "Intersection of algebraic plane curves : some results on the (monic) integer transfinite diameter." Thesis, University of Edinburgh, 2008. http://hdl.handle.net/1842/3843.

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Part I discusses the problem of determining the set of intersection points, with corresponding multiplicities, of two algebraic plane curves. We derive an algorithm based on the Euclidean Algorithm for polynomials and show how to use it to find the intersection points of two given curves. We also show that an easy proof of Bézout’s Theorem follows. We then discuss how, for curves with rational coefficients, this algorithm can bemodified to find the intersection points with coordinates expressed in terms of algebraic extensions of the rational numbers. Part II deals with the problem of determi

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Jaramillo, Puentes Andrés. "Rigid isotopy classification of real quintic rational plane curves." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066116/document.

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Afin d’étudier les classes d'isotopie rigide des courbes rationnelles nodales de degré 5 dans RPP, nous associons à chaque quintique avec un point double réel marque une courbe trigonale dans la surface de Hirzebruch Sigma3 et le dessin reel nodal correspondant dans CP/(z mapsto bar{z}). Les dessins sont des versions réelles, proposées par S. Orevkov dans cite{Orevkov}, des dessins d'enfants de Grothendieck. Un dessin est un graphe contenu dans une surface topologique, muni d'une certaine structure supplémentaire. Dans cette thèse, nous étudions les propriétés combinatoires et les recompositio

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Cohen, Camron Alexander Robey. "CURVING TOWARDS BÉZOUT: AN EXAMINATION OF PLANE CURVES AND THEIR INTERSECTION." Oberlin College Honors Theses / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin159345184740689.

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Killian, Kenneth. "Maxwell’s Problem on Point Charges in the Plane." Scholar Commons, 2008. https://scholarcommons.usf.edu/etd/333.

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This paper deals with approximating an upper bound for the number of equilibrium points of a potential field produced by point charges in the plane. This is a simplified form of a problem posed by Maxwell [4], who considered spatial configurations of the point charges. Using algebraic techniques, we will give an upper bound for planar charges that is sharper than the bound given in [6] for most general configurations of charges. Then we will study an example of a configuration of charges that has exactly the number of equilibrium points that Maxwell's conjecture predicts, and we will look into

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Rimmasch, Gretchen. "Complete Tropical Bezout's Theorem and Intersection Theory in the Tropical Projective Plane." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2507.pdf.

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Mialaret, Júnior Marco Aurélio Tomaz. "Folheações e Curvas Estáticas no Plano Projetivo." Universidade Federal da Paraíba, 2011. http://tede.biblioteca.ufpb.br:8080/handle/tede/7049.

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Made available in DSpace on 2015-05-14T13:21:10Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 422678 bytes, checksum: a7a607df8d67afa93aa6137919ecb1f5 (MD5) Previous issue date: 2011-08-17<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>The present work discusses a study of extactic curves in the projective plane, providing a method that guarantees the existence of first integrals for certain vector fields. To achieve this goal, this study covers the following topics: vector fields, first integrals (with the main result presented in Jouanolou's Theorem), holom

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de, Almeida Otterson James Joaquim. "Curves in algebraic surfaces." Thesis, Imperial College London, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.525234.

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Smilovic, Mikhail. "Curves on a plane." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=106605.

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In this thesis, we study the space of immersions from the circle to the plane Imm(S¹,R²), modulo the group of diffeomorphisms on S¹. We discuss various Riemannian metrics and find surprisingly that the L²-metric fails to separate points. We show two methods of strengthening this metric, one to obtain a non-vanishing metric, and the other to stabilize the minimizing energy flow. We give the formulas for geodesics, energy and give an example of computed geodesics in the case of concentric circles. We then carry our results over to the larger spaces of immersions from a compact manifold M to a Ri

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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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<p>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

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Books on the topic "Curves, Algebraic. Curves, Plane"

1

Plane algebraic curves. American Mathematical Society, 2001.

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Brieskorn, Egbert, and Horst Knörrer. Plane Algebraic Curves. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0493-6.

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Brieskorn, Egbert, and Horst Knörrer. Plane Algebraic Curves. Birkhäuser Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-5097-1.

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Horst, Knörrer, ed. Plane algebraic curves. Birkhäuser Verlag, 1986.

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The moduli problem for plane branches. American Mathematical Society, 2006.

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François, Kmety, Merle Michel, Teissier Bernard, and Ecole polytechnique (France). Centre de mathématiques., eds. Le problème des modules pour les branches planes: Cours donné au Centre de mathématiques de l'Ecole polytechnique. Hermann, 1986.

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Topology of algebraic curves: An approach via dessins d'enfants. De Gruyter, 2012.

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Zariski, Oscar. Le probleme des modules pour les branches planes: Cours donné au Centre de mathématiques de l'École polytechnique, octobre-novembre 1973. Hermann, 1986.

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1960-, Zaslavskiĭ A. A., ed. Geometry of conics. American Mathematical Society, 2007.

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Blahut, Richard E. Algebraic codes on lines, planes, and curves. Cambridge University Press, 2008.

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Book chapters on the topic "Curves, Algebraic. Curves, Plane"

1

Husemöller, Dale. "Plane Algebraic Curves." In Elliptic Curves. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-5119-2_3.

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Musili, C. "Plane Curves." In Algebraic Geometry for Beginners. Hindustan Book Agency, 2001. http://dx.doi.org/10.1007/978-93-86279-05-7_5.

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Ono, Takashi. "Plane Algebraic Curves." In Variations on a Theme of Euler. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4757-2326-7_4.

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Brieskorn, Egbert, and Horst Knörrer. "I History of algebraic curves." In Plane Algebraic Curves. Springer Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-0493-6_1.

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Brieskorn, Egbert, and Horst Knörrer. "2. Synthetic and analytic geometry." In Plane Algebraic Curves. Springer Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-0493-6_2.

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Brieskorn, Egbert, and Horst Knörrer. "3. The development of projective geometry." In Plane Algebraic Curves. Springer Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-0493-6_3.

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Brieskorn, Egbert, and Horst Knörrer. "II Investigation of curves by elementary algebraic methods." In Plane Algebraic Curves. Springer Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-0493-6_4.

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Brieskorn, Egbert, and Horst Knörrer. "5. Definition and elementary properties of plane algebraic curves." In Plane Algebraic Curves. Springer Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-0493-6_5.

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Brieskorn, Egbert, and Horst Knörrer. "6. The intersection of plane curves." In Plane Algebraic Curves. Springer Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-0493-6_6.

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Brieskorn, Egbert, and Horst Knörrer. "7. Some simple types of curves." In Plane Algebraic Curves. Springer Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-0493-6_7.

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Conference papers on the topic "Curves, Algebraic. Curves, Plane"

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Andreev, Fedor, and Iraj Kalantari. "Collinearity of Iterations and Real Plane Algebraic Curves." In 2012 Ninth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). IEEE, 2012. http://dx.doi.org/10.1109/isvd.2012.23.

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Stussak, Christian. "On exact rasterization of real algebraic plane curves." In the 27th Spring Conference. ACM Press, 2013. http://dx.doi.org/10.1145/2461217.2461243.

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Pach, János, and Frank de Zeeuw. "Distinct distances on algebraic curves in the plane." In Annual Symposium. ACM Press, 2014. http://dx.doi.org/10.1145/2582112.2582135.

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Liu, Yang, and J. Michael McCarthy. "Design of Mechanisms to Trace Plane Curves." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59689.

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This paper describes a mechanism design methodology that assembles standard components to trace plane curves that have a Fourier series parameterization. This approach can be used to approximate complex plane curves to interpolate image boundaries constructed from points. We describe three ways to construct a mechanism that generates a curve from a Fourier series parameterization. One uses Scotch yoke linkages for each term of Fourier series which are added using a belt drive. The second approach uses a coupled serial chain for each coordinate Fourier parameterization. The third method uses on

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Eigenwillig, Arno, Michael Kerber, and Nicola Wolpert. "Fast and exact geometric analysis of real algebraic plane curves." In the 2007 international symposium. ACM Press, 2007. http://dx.doi.org/10.1145/1277548.1277570.

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González-Vega, Laureano. "Working with real algebraic plane curves in REDUCE the GCUR package." In the 1991 international symposium. ACM Press, 1991. http://dx.doi.org/10.1145/120694.120755.

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KODAMA, YUJI, and BORIS G. KONOPELCHENKO. "DEFORMATIONS OF PLANE ALGEBRAIC CURVES AND INTEGRABLE SYSTEMS OF HYDRODYNAMIC TYPE." In Proceedings of the Workshop. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704467_0033.

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Welke, Stefan. "Visualization of Real Projective Algebraic Curves on Models of the Real Projective Plane." In Proceedings of the Fifth International Mathematica Symposium. PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO., 2003. http://dx.doi.org/10.1142/9781848161313_0047.

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Lu, Chung-Chin, Chih-Yen Yang, and Ti-Chung Lee. "Syndrome calculation for the decoding of algebraic-geometry codes on plane Garcia-Stichtenoth curves." In Its Applications (Isita2010). IEEE, 2010. http://dx.doi.org/10.1109/isita.2010.5649521.

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Ganter, M. A., and D. W. Storti. "Object Extent Determination for Algebraic Solid Models." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0176.

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Abstract This paper presents methods for determination of spatial extent of algebraic solid models. Algebraic solid models (ASM) are a variation of implicit solid models defined by implicit polynomial functions with rational coefficients. Spatial extent information, which can be used to enhance the performance of visualization and property evaluation, includes silhouettes, outlines and profiles. Silhouettes are curves on the surface of the solid which separate portions of the surface which face towards or away from a given viewpoint. The projection of the silhouette onto the viewing plane give

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Reports on the topic "Curves, Algebraic. Curves, Plane"

1

Hoffmann, Christoph M. Algebraic Curves. Defense Technical Information Center, 1987. http://dx.doi.org/10.21236/ada231940.

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Mehmood, Khawar, and Muhammad Ahsan Binyamin. Bimodal Singularities of Parametrized Plane Curves. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2019. http://dx.doi.org/10.7546/crabs.2019.08.02.

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Brunnett, Guido. The Curvature of Plane Elastic Curves. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada263198.

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