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

Contents

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

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

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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

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Yoshihara, Hisao. "Families of Galois closure curves for plane quartic curves." Journal of Mathematics of Kyoto University 43, no. 3 (2003): 651–59. http://dx.doi.org/10.1215/kjm/1250283700.

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Baker, Matthew, Yoav Len, Ralph Morrison, Nathan Pflueger, and Qingchun Ren. "Bitangents of tropical plane quartic curves." Mathematische Zeitschrift 282, no. 3-4 (November 16, 2015): 1017–31. http://dx.doi.org/10.1007/s00209-015-1576-7.

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Watanabe, S. "The genera of Galois closure curves for plane quartic curves." Hiroshima Mathematical Journal 38, no. 1 (March 2008): 125–34. http://dx.doi.org/10.32917/hmj/1207580347.

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Fernández, Julio, Josep González, and Joan-C. Lario. "Plane Quartic Twists of X(5, 3)." Canadian Mathematical Bulletin 50, no. 2 (June 1, 2007): 196–205. http://dx.doi.org/10.4153/cmb-2007-021-8.

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AbstractGiven an odd surjective Galois representation ϱ: Gℚ → PGL2(3) and a positive integer N, there exists a twisted modular curve X(N, 3)ϱ defined over ℚ whose rational points classify the quadratic ℚ-curves of degree N realizing ϱ. This paper gives a method to provide an explicit plane quartic model for this curve in the genus-three case N = 5.
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Vakil, Ravi. "The Characteristic Numbers of Quartic Plane Curves." Canadian Journal of Mathematics 51, no. 5 (October 1, 1999): 1089–120. http://dx.doi.org/10.4153/cjm-1999-048-1.

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AbstractThe characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen’s prediction of characteristic numbers of smooth plane curves. A short sketch of a computation of the characteristic numbers of plane cubics is also given as an illustration.
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Miura, Kei. "Galois points on singular plane quartic curves." Journal of Algebra 287, no. 2 (May 2005): 283–93. http://dx.doi.org/10.1016/j.jalgebra.2005.02.015.

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Miura, Kei. "Field theory for function fields of singular plane quartic curves." Bulletin of the Australian Mathematical Society 62, no. 2 (October 2000): 193–204. http://dx.doi.org/10.1017/s0004972700018669.

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We study the structure of function fields of plane quartic curves by using projections. Taking a point P ∈ ℙ2, we define the projection from a curve C to a line l with the centre P. This projection induces and extension field k (C)/k (ℙ1). By using this fact, we study the field extension k (C)/k (ℙ1) from a geometrical point of view. In this note, we take up quartic curves with singular points.
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Bruin, Nils. "The arithmetic of Prym varieties in genus 3." Compositio Mathematica 144, no. 2 (March 2008): 317–38. http://dx.doi.org/10.1112/s0010437x07003314.

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AbstractGiven a curve of genus 3 with an unramified double cover, we give an explicit description of the associated Prym variety. We also describe how an unramified double cover of a non-hyperelliptic genus 3 curve can be mapped into the Jacobian of a curve of genus 2 over its field of definition and how this can be used to perform Chabauty- and Brauer–Manin-type calculations for curves of genus 5 with an fixed-point-free involution. As an application, we determine the rational points on a smooth plane quartic and give examples of curves of genus 3 and 5 violating the Hasse principle. The methods are, in principle, applicable to any genus 3 curve with a double cover. We also show how these constructions can be used to design smooth plane quartics with specific arithmetic properties. As an example, we give a smooth plane quartic with all 28 bitangents defined over $\mathbb {Q}(t)$. By specialization, this also gives examples over $\mathbb {Q}$.
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Kamel, Alwaleed, and Waleed Khaled Elshareef. "Weierstrass points of order three on smooth quartic curves." Journal of Algebra and Its Applications 18, no. 01 (January 2019): 1950020. http://dx.doi.org/10.1142/s0219498819500208.

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In this paper, we study the [Formula: see text]-Weierstrass points on smooth projective plane quartic curves and investigate their geometry. Moreover, we use a technique to determine in a very precise way the distribution of such points on any smooth projective plane quartic curve. We also give a variety of examples that illustrate and enrich the subject.
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Elsenhans, Andreas-Stephan. "Explicit computations of invariants of plane quartic curves." Journal of Symbolic Computation 68 (May 2015): 109–15. http://dx.doi.org/10.1016/j.jsc.2014.09.006.

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

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Jones, Andrew. "Modular elliptic curves over quartic CM fields." Thesis, University of Sheffield, 2015. http://etheses.whiterose.ac.uk/8791/.

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In this thesis I establish the modularity of a number of elliptic curves defined over quartic CM fields, by showing that the Galois representation attached to such curves (arising from the natural Galois action on the l-adic Tate module) is isomorphic to a representation attached to a cuspidal automorphic form for GL(2) over the CM field in question. This is achieved through the study of the Hecke action on the cohomology of certain symmetric spaces, which are known to be isomorphic to spaces of cuspidal automorphic forms by a generalization of the Eichler-Shimura isomorphism.
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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 Riemannian manifold (N, g), modulo the group of diffeomorphisms on M.
Dans cette thése, nous étudierons l'espace d'immersions d'un cercle au plan Imm(S¹,R²), modulo le groupe de difféomorphisme sur S¹. Nous discuterons de divers métriques riemanniennes et monterons la surprenante impossibilité de séparer des points dans la métrique L². Nous présenterons deux méthodes de renforcer cette métrique, une pour obtenir une métrique non-nulle, et une autre pour stabiliser le flot d'énergie. Nous donnerons les formules pour les géodésiques et l'énergie, et donnerons un exemple de calcul de géodésiques dans le cas des cercles concentriques. Nous étendrons alors nos résultats sur la plus grande espace d'immersion d'une variété M compacte à une variété riemannienne (N,g), modulo le groupe de difféomorphisme sur M.
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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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Debrecht, Johanna M. "Plane Curves, Convex Curves, and Their Deformation Via the Heat Equation." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278501/.

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We study the effects of a deformation via the heat equation on closed, plane curves. We begin with an overview of the theory of curves in R3. In particular, we develop the Frenet-Serret equations for any curve parametrized by arc length. This chapter is followed by an examination of curves in R2, and the resultant adjustment of the Frenet-Serret equations. We then prove the rotation index for closed, plane curves is an integer and for simple, closed, plane curves is ±1. We show that a curve is convex if and only if the curvature does not change sign, and we prove the Isoperimetric Inequality, which gives a bound on the area of a closed curve with fixed length. Finally, we study the deformation of plane curves developed by M. Gage and R. S. Hamilton. We observe that convex curves under deformation remain convex, and simple curves remain simple.
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Markwig, Hannah. "The enumeration of plane tropical curves." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980700736.

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Granholm, Jonas. "Remarkable curves in the Euclidean plane." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-112576.

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An important part of mathematics is the construction of good definitions. Some things, like planar graphs, are trivial to define, and other concepts, like compact sets, arise from putting a name on often used requirements (although the notion of compactness has changed over time to be more general). In other cases, such as in set theory, the natural definitions may yield undesired and even contradictory results, and it can be necessary to use a more complicated formalization.    The notion of a curve falls in the latter category. While it is intuitively clear what a curve is – line segments, empty geometric shapes, and squiggles like this: – it is not immediately clear how to make a general definition of curves. Their most obvious characteristic is that they have no width, so one idea may be to view curves as what can be drawn with a thin pen. This definition, however, has the weakness that even such a line has the ability to completely fill a square, making it a bad definition of curves. Today curves are generally defined by the condition of having no width, that is, being one-dimensional, together with the conditions of being compact and connected, to avoid strange cases.    In this thesis we investigate this definition and a few examples of curves.
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Peternell, Carolin Susanne [Verfasser]. "Birational models for moduli of quartic rational curves / Carolin Susanne Peternell." Mainz : Universitätsbibliothek Mainz, 2018. http://d-nb.info/1164037919/34.

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Radzimski, Vanessa Elena. "Points of small height on plane curves." Thesis, University of British Columbia, 2014. http://hdl.handle.net/2429/46341.

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Let K be an algebraically closed field, and let C be an irreducible plane curve, defined over the algebraic closure of K(t), which is not defined over K. We show that there exists a positive real number c??? such that if P is any point on the curve C whose Weil height is bounded above by c???, then the coordinates of P belong to K.
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Holanda, Felipe D'Angelo. "Introduction to differential geometry of plane curves." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=15052.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
A intenÃÃo desse trabalho serà de abordar de forma bÃsica e introdutÃria o estudo da Geometria Diferencial, que por sua vez tem seus estudos iniciados com as Curvas Planas. Serà necessÃrio um conhecimento de CÃlculo Diferencial, Integral e Geometria AnalÃtica para melhor compreensÃo desse trabalho, pois como seu prÃprio nome nos transparece Geometria Diferencial vem de uma junÃÃo do estudo da Geometria envolvendo CÃlculo. Assim abordaremos subtemas como curvas suaves, vetor tangente, comprimento de arco passando por fÃrmulas de Frenet, curvas evolutas e involutas e finalizaremos com alguns teoremas importantes, como o teorema fundamental das curvas planas, teorema de Jordan e o teorema dos quatro vÃrtices. O que, basicamente representa, o capÃtulo 1, 4 e 6 do livro IntroduÃÃo Ãs Curvas Planas de HilÃrio Alencar e Walcy Santos.
The intention of this work is to address in basic form and introductory study of Differential Geometry, which in turn has started his studies with Planas curves. It will require a knowledge of Differential Calculus, Integral and Analytic Geometry for better understanding of this work, because as its name says in Differential Geometry comes from the joint study of geometry involving Calculation. So we discuss sub-themes as smooth curves, tangent vector, arc length through formulas of Frenet, evolutas curves and involute and conclude with some important theorems, as the fundamental theorem of plane curves, Jordan 's theorem and the theorem of four vertices. What basically is, Chapter 1, 4 and 6 of the book Introduction to Plane Curves HilÃrio Alencar and Walcy Santos.
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Al-Shammari, Fahd M. "Jacobians of plane quintic curves of genus one." Diss., The University of Arizona, 2002. http://hdl.handle.net/10150/289840.

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Let K be a number field. By representing genus one curves as plane quintic curves with 5 double points, we construct (up to birational equivalence) the universal elliptic curves defined over the modular curves X₁(5) and X(μ)(5) (X(μ)(5) is the modular curve parameterizing pairs (E, i : (μ)₅ → E) where E is an elliptic curve over Q). We then twist the latter by elements coming from H¹(Gal(K̅/K), (μ)₅) to construct universal families of principal homogeneous spaces for the curves E. Finally we show that every principal homogeneous space arising this way is visible in some abelian variety.
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Books on the topic "Curves, Plane. Curves, Quartic"

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Plane algebraic curves. Providence, R.I: American Mathematical Society, 2001.

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

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

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A, Palagallo Judith, and Price Thomas E, eds. Curious curves. Hackensack, NJ: World Scientific, 2010.

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Tricot, Claude. Curves and fractal dimension. New York: Springer-Verlag, 1995.

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Tookey, Richard Mark. Automatic filleting of plane curves. Birmingham: University of Birmingham, 1991.

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Tricot, Claude. Courbes et dimension fractale. Paris: Springer-Verlag, 1993.

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Brunnett, Guido. The curvature of plane elastic curves. Monterey, Calif: Naval Postgraduate School, 1993.

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The moduli problem for plane branches. Providence, R.I: American Mathematical Society, 2006.

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

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Gudkov, D. A. "Plane real projective quartic curves." In Lecture Notes in Mathematics, 341–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0082782.

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Pellikaan, Ruud. "The Klein Quartic, the Fano Plane and Curves Representing Designs." In Codes, Curves, and Signals, 9–20. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-5121-8_2.

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Aarts, J. M., and R. Erne. "Curves." In Plane and Solid Geometry, 1–109. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-78241-6_4.

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Berger, Marcel. "Plane curves." In Geometry Revealed, 249–340. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-540-70997-8_5.

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Arapura, Donu. "Plane Curves." In Universitext, 3–17. Boston, MA: Springer US, 2012. http://dx.doi.org/10.1007/978-1-4614-1809-2_1.

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Borceux, Francis. "Plane Curves." In A Differential Approach to Geometry, 55–138. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-01736-5_2.

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Arnold, V. "Plane curves." In University Lecture Series, 5–23. Providence, Rhode Island: American Mathematical Society, 1994. http://dx.doi.org/10.1090/ulect/005/02.

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Lorenzini, Dino. "Plane curves." In Graduate Studies in Mathematics, 35–84. Providence, Rhode Island: American Mathematical Society, 1996. http://dx.doi.org/10.1090/gsm/009/03.

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Musili, C. "Plane Curves." In Algebraic Geometry for Beginners, 187–270. Gurgaon: Hindustan Book Agency, 2001. http://dx.doi.org/10.1007/978-93-86279-05-7_5.

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Fried, Michael D., and Moshe Jarden. "Plane Curves." In Field Arithmetic, 43–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-662-07216-5_4.

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

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Liu, Kuo-Chung, and Yuan-Fang Chou. "Identifying Intersections of Dispersion Curves for Phononic Crystals." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65754.

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Many methods have been developed to obtain the band structure of crystals. Generally, they all require numerical computation to construct the spectrum. Therefore, only discrete points instead of continuous lines provided for dispersion relations. This makes it difficult to distinguish the modes of nearby discrete points without calculating mode profiles. That is, more effort is required to determine whether two dispersion curves intersect each other or not. A new method of investigation for phononic crystals is proposed which takes advantage of finite group theory and symmetrized plane waves that can block-diagonalize secular equations. A system consisting of a periodic square array of nickel alloy cylinders and an aluminum alloy matrix is studied. Intersections between dispersion curves of different modes can be identified directly. The result contradicts that presented by Kushwaha in 1993. The method can not only distinguish different modes directly from the computed band structure but also saves computation time. Compared to plane wave expansion method, only one quarter of computation time is required for calculating the spectrum. The higher symmetry a group has, the shorter the computation time expected.
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Moody, Dustin. "Division polynomials for Jacobi quartic curves." In the 36th international symposium. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1993886.1993927.

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Haihua Gu, WenLu Xie, and Dawu Gu. "Differential addition on Jacobi quartic curves." In Symposium on ICT and Energy Efficiency and Workshop on Information Theory and Security (CIICT 2012). Institution of Engineering and Technology, 2012. http://dx.doi.org/10.1049/cp.2012.1890.

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Xu, Ping, and Desheng Yu. "Connections between Quartic Bezier Curves with Shape Parameters and Cubic H- Bezier Curves." In 3rd International Conference on Material, Mechanical and Manufacturing Engineering (IC3ME 2015). Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/ic3me-15.2015.240.

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Yang, Han, Qiang Li, and Xuezhang Liang. "Approximations of Circular Arcs by Quartic Bézier Curves." In 2019 6th International Conference on Information Science and Control Engineering (ICISCE). IEEE, 2019. http://dx.doi.org/10.1109/icisce48695.2019.00042.

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Lian Yang, Juncheng Li, and Zhilin Chen. "Trigonometric extension of quartic Bézier curves." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6001841.

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Latecki, Longin J., and Azriel Rosenfeld. "Differentialless geometry of plane curves." In Optical Science, Engineering and Instrumentation '97, edited by Robert A. Melter, Angela Y. Wu, and Longin J. Latecki. SPIE, 1997. http://dx.doi.org/10.1117/12.279677.

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Qin, Xinqiang, Dan Lv, Gang Hu, and Junli Wu. "Subdivision Algorithm of Quartic Q-Ball Curves with Shape Parameters." In 2018 IEEE 3rd International Conference on Image, Vision and Computing (ICIVC). IEEE, 2018. http://dx.doi.org/10.1109/icivc.2018.8492815.

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Sun, Xin, Yu Qiao, and Huinan Li. "Subdivision Algorithm of Quartic λ-Bézier Curves with Shape Parameters." In 2019 IEEE 4th International Conference on Image, Vision and Computing (ICIVC). IEEE, 2019. http://dx.doi.org/10.1109/icivc47709.2019.8981030.

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Ren, Yajuan. "Pairing Computation in Jacobi Quartic Curves Using Weight Projective Coordinates." In 2016 International Conference on Sensor Network and Computer Engineering. Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/icsnce-16.2016.18.

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

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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, August 2019. http://dx.doi.org/10.7546/crabs.2019.08.02.

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

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