Relevant bibliographies by topics / Symmetric products of curves

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

Academic literature on the topic 'Symmetric products of curves'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Symmetric products of curves"

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Harris, Joe, and Joe Silverman. "Bielliptic curves and symmetric products." Proceedings of the American Mathematical Society 112, no. 2 (1991): 347. http://dx.doi.org/10.1090/s0002-9939-1991-1055774-0.

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Bastianelli, F. "On symmetric products of curves." Transactions of the American Mathematical Society 364, no. 5 (2012): 2493–519. http://dx.doi.org/10.1090/s0002-9947-2012-05378-5.

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Biswas, Indranil, and Shane D’Mello. "M-curves and symmetric products." Proceedings - Mathematical Sciences 127, no. 4 (2017): 615–24. http://dx.doi.org/10.1007/s12044-017-0347-2.

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Kouvidakis, Alexis. "Divisors on symmetric products of curves." Transactions of the American Mathematical Society 337, no. 1 (1993): 117–28. http://dx.doi.org/10.1090/s0002-9947-1993-1149124-5.

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Ross, J. "Seshadri constants on symmetric products of curves." Mathematical Research Letters 14, no. 1 (2007): 63–75. http://dx.doi.org/10.4310/mrl.2007.v14.n1.a5.

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Vanhaecke, Pol. "Integrable systems and symmetric products of curves." Mathematische Zeitschrift 227, no. 1 (1998): 93–127. http://dx.doi.org/10.1007/pl00004370.

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MEJÍA, ISRAEL MORENO. "CHARACTERISTIC CLASSES ON SYMMETRIC PRODUCTS OF CURVES." Glasgow Mathematical Journal 46, no. 3 (2004): 477–88. http://dx.doi.org/10.1017/s0017089504001946.

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Wang, Zhi Lan. "Tautological integrals on symmetric products of curves." Acta Mathematica Sinica, English Series 32, no. 8 (2016): 901–10. http://dx.doi.org/10.1007/s10114-016-5565-5.

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Krug, Andreas. "Stability of tautological bundles on symmetric products of curves." Mathematical Research Letters 27, no. 6 (2020): 1785–800. http://dx.doi.org/10.4310/mrl.2020.v27.n6.a9.

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Elencwajg, Georges. "Brauer group of fibrations and symmetric products of curves." Proceedings of the American Mathematical Society 94, no. 4 (1985): 597. http://dx.doi.org/10.1090/s0002-9939-1985-0792268-9.

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Dissertations / Theses on the topic "Symmetric products of curves"

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BASTIANELLI, FRANCESCO. "The geometry of second symmetric product of curves." Doctoral thesis, Università degli Studi di Pavia, 2009. http://hdl.handle.net/10281/21080.

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We deal with several problems on the surfaces obtained as second symmetric products of smooth projective curves. In particular, we treat both some attempts at extending the notion of gonality for curves and some classical problems, as the study of the ample cone in the Néron-Severi group. Moreover, we develop a family of examples of Lagrangian surfaces having particular topological properties.
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Ivey, law Hamish. "Algorithmic aspects of hyperelliptic curves and their jacobians." Thesis, Aix-Marseille, 2012. http://www.theses.fr/2012AIXM4084/document.

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Ce travail se divise en deux parties. Dans la première partie, nous généralisons le travail de Khuri-Makdisi qui décrit des algorithmes pour l'arithmétique des diviseurs sur une courbe sur un corps. Nous montrons que les analogues naturelles de ses résultats se vérifient pour les diviseurs de Cartier relatifs effectifs sur un schéma projectif, lisse et de dimension relative un sur un schéma affine noetherien quelconque, et que les analogues naturelles de ses algorithmes se vérifient pour une certaine classe d'anneaux de base. Nous présentons un formalisme pour tels anneaux qui sont caractérisés par l'existence d'un certain sous-ensemble des opérations standards de l'algèbre linéaire pour les modules projectifs sur ces anneaux.Dans la deuxième partie de ce travail, nous considérons un type de problème de Riemann-Roch pour les diviseurs sur certaines surfaces algébriques. Plus précisément, nous analysons les surfaces algébriques qui émanent d'un produit ou d'un produit symétrique d'une courbe hyperelliptique de genre supérieur à un sur un corps (presque) arbitraire. Les résultats principaux sont une décomposition des espaces de sections globales de certains diviseurs sur telles surfaces et des formules explicites qui décrivent les dimensions des espaces de sections de ces diviseurs. Dans le dernier chapitre, nous présentons un algorithme qui produit une base pour l'espace de sections globales d'un tel diviseur<br>The contribution of this thesis is divided naturally into two parts. In Part I we generalise the work of Khuri-Makdisi (2004) on algorithms for divisor arithmetic on curves over fields to more general bases. We prove that the natural analogues of the results of Khuri-Makdisi continue to hold for relative effective Cartier divisors on projective schemes which are smooth of relative dimension one over an arbitrary affine Noetherian base scheme and that natural analogues of the algorithms remain valid in this context for a certain class of base rings. We introduce a formalism for such rings,which are characterised by the existence of a certain subset of the usual linear algebra operations for projective modules over these rings.Part II of this thesis is concerned with a type of Riemann-Roch problem for divisors on certain algebraic surfaces. Specifically we consider algebraic surfaces arising as the square or the symmetric square of a hyperelliptic curve of genus at least two over an (almost) arbitrary field. The main results are a decomposition of the spaces of global sections of certain divisors on such surfaces and explicit formulæ for the dimensions of the spaces of sections of these divisors. In the final chapter we present an algorithm which generates a basis for the space of global sections of such a divisor
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Bajracharya, Neeraj. "Level Curves of the Angle Function of a Positive Definite Symmetric Matrix." Thesis, University of North Texas, 2009. https://digital.library.unt.edu/ark:/67531/metadc28376/.

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Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following question: if A and B are commuting positive definite symmetric matrices such that p(A) + p(B) is obtuse, what is the minimal p(S) such that {A, SBS^(-1)} indefinite? In this dissertation we will describe the level curves of the angle function mapping a unit vector x to the angle between x and Ax for a 3 by 3 PDS matrix A, and discuss their interaction with those of a second such matrix.
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Park, Jennifer Mun Young. "Effective Chabauty for symmetric powers of curves." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90189.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 75-76).<br>Faltings' theorem states that curves of genus g > 2 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the upper bound on the number of rational points, XI, [paragraph]2, but this bound is too large to be used in any reasonable sense. In 1985, Coleman showed that Chabauty's method, which works when the Mordell-Weil rank of the Jacobian of the curve is smaller than g, can be used to give a good effective bound on the number of rational points of curves of genus g > 1. We draw ideas from nonarchimedean geometry to show that we can also give an effective bound on the number of rational points outside of the special set of Symd X, where X is a curve of genus g > d, when the Mordell-Weil rank of the Jacobian of the curve is at most g > d.<br>by Jennifer Mun Young Park.<br>Ph. D.
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Costello, Kevin Joseph. "Gromov-Witten invariants and symmetric products." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620044.

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Mostovoy, J. "Symmetric products and quaternion cycle spaces." Thesis, University of Edinburgh, 1997. http://hdl.handle.net/1842/11203.

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The objects of study in this thesis are symmetric products and spaces of algebraic cycles. The first new result concerns symmetric products and it describes the geometry of truncated symmetric products (or, in other terminology, symmetric products modulo 2). We prove that if <I>M</I> is a closed compact connected triangulable manifold, a necessary and sufficient condition for its symmetric products modulo 2 to be manifolds is that <I>M</I> is a circle. We also show that the symmetric products of the circle modulo 2 are homeomorphic to real projective spaces and give an interpretation of this homeomorphism as a real topological analogue of Vieta's theorem. The second result concerns the spaces of real algebraic cycles, first studied by T.K. Lam. We describe a method of calculating the homotopy groups of the spaces of real cycles with integral coefficients on projective spaces; we give an explicit formula for the groups which lie in the "stable range". The third result (or, rather, a group of results) is the construction of a quaternionic analogue of Lawson's theory of algebraic cycles. We define quaternionic objects as those, which are invariant (in the case of varieties) or equivalent (in the case of polynomials) with respect to a free involution on CP<I><SUP>2n</SUP></I><SUP>+1</SUP>, induced by the action of the quaternion <I>j</I> on H<I><SUP>n</SUP></I>. Basic properties of quaternionic algebraic cycles are studied; a rational "quaternionic suspension theorem" is proved and the spaces of quaternionic cycles with rational coefficients on CP<I><SUP>2n</SUP></I><SUP>+1</SUP> are described. We also present a method of calculating the Betti numbers of the spaces of quaternionic cycles of degree 2 and odd codimension on CP<SUP>∞</SUP>. Some other results that are included in the thesis are a twisted version of the Dold-Thom theorem and an interpretation of the Kuiper-Massey theorem via symmetric products. After the main results on quaternionic cycles were proved, the author learned that similar results were obtained by Lawson, Lima-Filho and Michelson. Their version of the quaternionic suspension theorem is stronger and requires more sophisticated machinery for the proof.
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Ryba, Christopher(Christopher Jonathan). "Stable characters for symmetric groups and wreath products." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/126936.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020<br>Cataloged from the official PDF of thesis.<br>Includes bibliographical references (pages 145-147).<br>Given a Hopf algebra R, the Grothendieck group of C = R-mod inherits the structure of a ring. We define a ring [mathematical equation]), which is "the [mathematical equation] limit" of the Grothendieck rings of modules for the wreath products [mathematical equation]; it is the Grothendieck group of a certain wreath product Deligne category. The construction yields a basis of [mathematical equation] corresponding to irreducible objects. The structure constants of this basis are stable tensor product multiplicities for the wreath products [mathematical equation]. We generalise [mathematical equation], allowing an arbitrary ring to be substituted for the Grothendieck ring of C. Aside from being a Hopf algebra, [mathematical equation] is the algebra of distributions on a certain affine group scheme. In the special case where C is the category of vector spaces (over C, say), [mathematical equation] is the ring of symmetric functions. The basis obtained by our construction is the family of stable Specht polynomials, which is closely related to the problem of calculating restriction multiplicities from [mathematical equation]. We categorify the stable Specht polynomials by producing a resolution of irreducible representations of S[subscript n] by modules restricted from [mathematical equation].<br>by Christopher Ryba.<br>Ph. D.<br>Ph.D. Massachusetts Institute of Technology, Department of Mathematics
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Moreira, Rodriguez Rivera Walter. "Products of representations of the symmetric group and non-commutative versions." Texas A&M University, 2008. http://hdl.handle.net/1969.1/85938.

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We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following Malvenuto and Reutenauer, we pass from symmetric functions to non-commutative symmetric functions and from there to the algebra of permutations in order to relate the internal and external products to the composition and convolution of linear endomorphisms of the tensor algebra. The new product we construct corresponds to the Heisenberg product of endomorphisms of the tensor algebra. For symmetric functions, the Heisenberg product is given by a construction which combines induction and restriction of representations. For non-commutative symmetric functions, the structure constants of the Heisenberg product are given by an explicit combinatorial rule which extends a well-known result of Garsia, Remmel, Reutenauer, and Solomon for the descent algebra. We describe the dual operation among quasi-symmetric functions in terms of alphabets.
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Hausmann, Markus [Verfasser]. "Symmetric products, subgroup lattices and filtrations of global K-theory / Markus Hausmann." Bonn : Universitäts- und Landesbibliothek Bonn, 2016. http://d-nb.info/1113688408/34.

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Liou, Jiann-Haw. "Study of stress developments in axi-symmetric products fabricated by forging and machining /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9737869.

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Books on the topic "Symmetric products of curves"

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McCullough, Darryl. Symmetric automorphisms of free products. American Mathematical Society, 1996.

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Geometric analysis on symmetric spaces. 2nd ed. American Mathematical Society, 2008.

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Geometric analysis on symmetric spaces. American Mathematical Society, 1994.

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Mahmoud, Ibrahim Mahmoud Ibrahim. On the representations of wreath products of symmetric groups. University of Birmingham, 1985.

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Gurahick, Robert M. Symmetric and alternating groups as monodromy groups of Riemann surfaces I: Generic covers and covers with many branch points. American Mathematical Society, 2007.

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Conference on Hopf Algebras and Tensor Categories (2011 University of Almeria). Hopf algebras and tensor categories: International conference, July 4-8, 2011, University of Almería, Almería, Spain. Edited by Andruskiewitsch Nicolás 1958-, Cuadra Juan 1975-, and Torrecillas B. (Blas) 1958-. American Mathematical Society, 2013.

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Guichardet, Alain. Symmetric Hilbert Spaces and Related Topics: Infinitely Divisible Positive Definite Functions. Continuous Products and Tensor Products. Gaussian and Poissonian Stochastic Processes. Springer London, Limited, 2006.

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Kerber, A. Representations of Permutation Groups I: Representations of Wreath Products and Applications to the Representation Theory of Symmetric and Alternating Groups. Springer London, Limited, 2006.

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Zagier, D. B. Equivariant Pontrjagin Classes and Applications to Orbit Spaces: Applications of the G-Signature Theorem to Transformation Groups, Symmetric Products and Number Theory. Springer London, Limited, 2006.

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(Contributor), R. Stafford, ed. Symmetric and Alternating Groups As Monodromy Groups of Riemann Surfaces 1: Generic Covers and Covers With Many Branch Points (Memoirs of the American Mathematical Society). Amer Mathematical Society, 2007.

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Book chapters on the topic "Symmetric products of curves"

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Dijkgraaf, Robbert. "Fields, Strings, Matrices and Symmetric Products." In Moduli of Curves and Abelian Varieties. Vieweg+Teubner Verlag, 1999. http://dx.doi.org/10.1007/978-3-322-90172-9_8.

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Vanhaecke, Pol. "Integrable Hamiltonian systems and symmetric products of curves." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-662-21535-7_3.

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Nakajima, Hiraku. "Symmetric products of an embedded curve, symmetric functions and vertex operators." In University Lecture Series. American Mathematical Society, 1999. http://dx.doi.org/10.1090/ulect/018/10.

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Cao, Tao, Khalegh Mamakani, and Frank Ruskey. "Symmetric Monotone Venn Diagrams with Seven Curves." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13122-6_32.

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Kaneta, Hitoshi, S. Marcugini, and F. Pambianco. "The Most Symmetric Non-Singular Plane Curves." In Proceedings of the Second ISAAC Congress. Springer US, 2000. http://dx.doi.org/10.1007/978-1-4613-0271-1_19.

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Hain, Richard. "Locally Symmetric Families of Curves and Jacobians." In Moduli of Curves and Abelian Varieties. Vieweg+Teubner Verlag, 1999. http://dx.doi.org/10.1007/978-3-322-90172-9_5.

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Curto, Carina, Joshua Paik, and Igor Rivin. "Betti Curves of Rank One Symmetric Matrices." In Lecture Notes in Computer Science. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80209-7_69.

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Farjoun, Emmanuel Dror. "Dold-Thom symmetric products and other colimits." In Cellular Spaces, Null Spaces and Homotopy Localization. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0094433.

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Caldana, Ruggero, Gianluca Fusai, and Andrea Roncoroni. "How to Build Electricity Forward Curves." In Handbook of Multi-Commodity Markets and Products. John Wiley & Sons, Ltd, 2015. http://dx.doi.org/10.1002/9781119011590.ch14.

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Kroon, Juan A. Valiente, and Christian Lübbe. "A Class of Conformal Curves on Spherically Symmetric Spacetimes." In Springer Proceedings in Physics. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06761-2_30.

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Conference papers on the topic "Symmetric products of curves"

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Ponce, M. A., E. R. Mendez, and V. Ruiz. "Scattering from symmetric surfaces and surfaces perpendicular to a mirror." In OSA Annual Meeting. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.thh3.

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Recent theoretical and experimental results on light scattering from randomly rough surfaces have shown the importance of coherent effects in the presence of multiple scattering and symmetries. These coherent effects give rise to enhancements in the back-scattering, antispecular, or specular directions. Here, we present some recent experimental results of scattering from one-dimensional randomly rough surfaces with an even profile and from two-dimensional rough surfaces perpendicular to a mirror. These systems produce, respectively, enhanced specular and enhanced backscattering phenomena and are closely related. The similarities and differences between the two cases will be discussed, and, where possible, theoretical curves will be presented. The fabrication and characterization of the symmetric surfaces in photoresist will also be described.
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Borthakur, Manash Pratim, Binita Nath, Gautam Biswas, and Dipankar Bandyopadhyay. "Formation and Breakup of Liquid Jets Curved by Gravity." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-71608.

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The formation and breakup of a liquid jet in air with gravity acting perpendicular to the direction of the jet is studied computationally. The liquid jet follows a parabolic path due to the influence of gravity which curves the jet trajectory. Both symmetric and asymmetric perturbations develop on the liquid surface which lead to jet breakup with varying droplet size distribution. The limiting length of the jet at breakup increases with increase in the Weber number and Ohnesorge number. At higher value of Weber number, the liquid jet traverses a longer horizontal distance when released from the same vertical height. Increasing the Bond number leads to a significant increase in the curvature of the jet trajectory. The volume of drops produced varies temporally for a given Weber number and decreases with the increasing value of Weber number. The detached drops undergo rolling motion as well as shape oscillations as they continue to fall on their trajectories.
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Voloch, José Felipe. "Symmetric Cryptography and Algebraic Curves." In Proceedings of the First SAGA Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812793430_0007.

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Seidel, Hans-Peter. "Symmetric algorithms for curves and surfaces." In SC - DL tentative, edited by Leonard A. Ferrari and Rui J. P. de Figueiredo. SPIE, 1990. http://dx.doi.org/10.1117/12.19727.

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Liu, Xueting, and Hongkui Li. "On the Kippenhahn Curves of Kronecker Products." In 2009 IITA International Conference on Control, Automation and Systems Engineering, CASE 2009. IEEE, 2009. http://dx.doi.org/10.1109/case.2009.150.

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Li, Hongkui, Zhaowei Meng, Yunming Zhou, and Xueting Liu. "The Kippenhahn Curves of Some Kronecker Products." In 2009 ETP International Conference on Future Computer and Communication (FCC). IEEE, 2009. http://dx.doi.org/10.1109/fcc.2009.55.

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Zhao, Wenling, and Daojin Song. "About the kippenhahn curves of some kronecker products." In 2009 ISECS International Colloquium on Computing, Communication, Control, and Management (CCCM). IEEE, 2009. http://dx.doi.org/10.1109/cccm.2009.5267910.

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González-Vega, L., and G. Trujillo. "Implicitization of parametric curves and surfaces by using symmetric functions." In the 1995 international symposium. ACM Press, 1995. http://dx.doi.org/10.1145/220346.220369.

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Liu, Fang. "Effects of Geometries on the Nonlinearity of Thermal Fluids in Curved Ducts of Heat Exchangers." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-51126.

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The present work is on comparison of bifurcation and stability of fully-developed forced convection in a curved duct with various aspect ratios and various curvature ratios. In this study, water was used as the fluid assuming the properties are constant. Boundary conditions are non-slip, impermeability and uniform peripheral temperature. The governing differential equations from the conservation laws are discretized by the finite volume method and then solved for parameter-dependence of flow and temperature fields by the Euler–Newton continuation. The Dk number and the local variable are used as the control parameters in tracing the branches. The Dk number is the ratio of the square root of the product of inertial and centrifugal forces to the viscous force. The test function and branch switching technique are used to detect the bifurcation points and switch the branch respectively. The flow stability on various branches is determined by direct transient computation on dynamic responses of the multiple solutions. For the curved ducts with of aspect ratio 1 and curvature ratio 5 × 10−6, ten solution branches (either symmetric or asymmetric) are found with eight symmetry-breaking bifurcation points and thirty-one limit points. Thus a rich solution structure exists with the co-existence of various flow states over certain ranges of governing parameters. Dynamic responses of the multiple steady flows to finite random disturbances are examined by the direct transient computation. It is found that possible physically realizable fully developed flows under the effect of unknown disturbances evolve, as the Dean number increases, from a stable steady 2-cell state at lower Dean number to a temporal periodic oscillation, another stable steady 2-cell state, a temporal intermittent oscillation, and a chaotic temporal oscillation. There exist no stable steady fully-developed flows in some ranges of governing parameters. For the curved ducts with of aspect ratio 1 and curvature ratio 0.5, ten solution branches, two symmetric and eight asymmetric, are found. Among them, one symmetric branch and seven asymmetric branches have not been reported in the literature. On these new branches, the flow has a structural 2-, 4-, 5-, 6-, 7- or 8-cell. The mean friction factor and Nusselt number are different on various solution branches. In tightly curved ducts, the secondary flow enhances the heat transfer more significantly than the friction increase. For the curved ducts with of aspect ratio 10 and curvature ratio 0.5, seven symmetric and four asymmetric solution branches were found. As Dean number increases, finite random disturbances lead the flows from a stable steady state to another stable steady state, a periodic oscillation, an intermittent oscillation, another periodic oscillation and a chaotic oscillation. The mean friction factor and the mean Nusselt number are obtained for all physically-realizable flows. Heat transfer enhancement potential of the flow and the evolution of stability as Dk increases in curved ducts with different aspect ratio and curvature ratio are compared. It is found that a significant enhancement of heat transfer can be achieved at the expense of a slight increase of flow friction, especially for the square curved ducts.
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Kallel, Sadok. "Symmetric products, duality and homological dimension of configuration spaces." In Groups, homotopy and configuration spaces, in honour of Fred Cohen's 60th birthday. Mathematical Sciences Publishers, 2008. http://dx.doi.org/10.2140/gtm.2008.13.499.

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