Academic literature on the topic 'Computational algebraic geometry'

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Journal articles on the topic "Computational algebraic geometry"

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Shaska, T. "Computational algebraic geometry." Journal of Symbolic Computation 57 (October 2013): 1–2. http://dx.doi.org/10.1016/j.jsc.2013.05.001.

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Cox, David A. "Book Review: Computational algebraic geometry." Bulletin of the American Mathematical Society 42, no. 01 (October 5, 2004): 113–19. http://dx.doi.org/10.1090/s0273-0979-04-01038-9.

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Parker, Adam. "Computational Algebraic Geometry as a Computational Science Elective." Journal of Computational Science Education 1, no. 1 (December 2010): 2–7. http://dx.doi.org/10.22369/issn.2153-4136/1/1/1.

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Sturmfels, Bernd. "Computational algebraic geometry of projective configurations." Journal of Symbolic Computation 11, no. 5-6 (May 1991): 595–618. http://dx.doi.org/10.1016/s0747-7171(08)80121-6.

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Shaska, T. "Computational algebraic geometry and its applications." Applicable Algebra in Engineering, Communication and Computing 24, no. 5 (September 1, 2013): 309–11. http://dx.doi.org/10.1007/s00200-013-0204-1.

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Verschelde, J. "Basic algebraic geometry." Journal of Computational and Applied Mathematics 66, no. 1-2 (January 1996): N3—N4. http://dx.doi.org/10.1016/0377-0427(96)80471-7.

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He, Yang-Hui, Philip Candelas, Amihay Hanany, Andre Lukas, and Burt Ovrut. "Computational Algebraic Geometry in String and Gauge Theory." Advances in High Energy Physics 2012 (2012): 1–4. http://dx.doi.org/10.1155/2012/431898.

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Badger, Simon, Hjalte Frellesvig, and Yang Zhang. "Multi-loop Integrand Reduction with Computational Algebraic Geometry." Journal of Physics: Conference Series 523 (June 6, 2014): 012061. http://dx.doi.org/10.1088/1742-6596/523/1/012061.

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Segundo, F. San, J. R. Sendra, and Juana Sendra. "Offsets from the perspective of computational algebraic geometry." ACM SIGSAM Bulletin 39, no. 3 (September 2005): 87–90. http://dx.doi.org/10.1145/1113439.1113449.

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Wang, Ren-Hong. "Multivariate spline and algebraic geometry." Journal of Computational and Applied Mathematics 121, no. 1-2 (September 2000): 153–63. http://dx.doi.org/10.1016/s0377-0427(00)00344-7.

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Dissertations / Theses on the topic "Computational algebraic geometry"

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Shifler, Ryan M. "Computational Algebraic Geometry Applied to Invariant Theory." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/23154.

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Commutative algebra finds its roots in invariant theory and the connection is drawn from a modern standpoint. The Hilbert Basis Theorem and the Nullstellenstatz were considered lemmas for classical invariant theory. The Groebner basis is a modern tool used and is implemented with the computer algebra system Mathematica. Number 14 of Hilbert\'s 23 problems is discussed along with the notion of invariance under a group action of GLn(C). Computational difficulties are also discussed in reference to Groebner bases and Invariant theory.The straitening law is presented from a Groebner basis point of view and is motivated as being a key piece of machinery in proving First Fundamental Theorem of Invariant Theory.
Master of Science
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Jost, Christine. "Topics in Computational Algebraic Geometry and Deformation Quantization." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-87399.

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This thesis consists of two parts, a first part on computations in algebraic geometry, and a second part on deformation quantization. More specifically, it is a collection of four papers. In the papers I, II and III, we present algorithms and an implementation for the computation of degrees of characteristic classes in algebraic geometry. Paper IV is a contribution to the field of deformation quantization and actions of the Grothendieck-Teichmüller group. In Paper I, we present an algorithm for the computation of degrees of Segre classes of closed subschemes of complex projective space. The algorithm is based on the residual intersection theorem and can be implemented both symbolically and numerically. In Paper II, we describe an algorithm for the computation of the degrees of Chern-Schwartz-MacPherson classes and the topological Euler characteristic of closed subschemes of complex projective space, provided an algorithm for the computation of degrees of Segre classes. We also explain in detail how the algorithm in Paper I can be implemented numerically. Together this yields a symbolical and a numerical version of the algorithm. Paper III describes the Macaulay2 package CharacteristicClasses. It implements the algorithms from papers I and II, as well as an algorithm for the computation of degrees of Chern classes. In Paper IV, we show that L-infinity-automorphisms of the Schouten algebra T_poly(R^d) of polyvector fields on affine space R^d which satisfy certain conditions can be globalized. This means that from a given L-infinity-automorphism of T_poly(R^d) an L-infinity-automorphism of T_poly(M) can be constructed, for a general smooth manifold M. It follows that Willwacher's action of the Grothendieck-Teichmüller group on T_poly(R^d) can be globalized, i.e., the Grothendieck-Teichmüller group acts on the Schouten algebra T_poly(M) of polyvector fields on a general manifold M.

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 3: Manuscript. Paper 4: Accepted.

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Garcia-Puente, Luis David. "Algebraic Geometry of Bayesian Networks." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11133.

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We develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry--statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification, in terms of primary decomposition of polynomial ideals, is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties. Moreover, a complete algebraic classification, in terms of generating sets of polynomial ideals, is given for Bayesian networks on at most three random variables and one hidden variable. The relevance of these results for model selection is discussed.
Ph. D.
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Dandekar, Pranav. "Algebraic-geometric methods for complexity lower bounds." [Gainesville, Fla.] : University of Florida, 2004. http://purl.fcla.edu/fcla/etd/UFE0008843.

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Byrnes, Sean. "Some computational and geometric aspects of generalized Weyl algebras /." [St. Lucia, Qld.], 2004. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe18765.pdf.

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Vonk, Jan Bert. "The Atkin operator on spaces of overconvergent modular forms and arithmetic applications." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:081e4e46-80c1-41e7-9154-3181ccb36313.

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We investigate the action of the Atkin operator on spaces of overconvergent p-adic modular forms. Our contributions are both computational and geometric. We present several algorithms to compute the spectrum of the Atkin operator, as well as its p-adic variation as a function of the weight. As an application, we explicitly construct Heegner-type points on elliptic curves. We then make a geometric study of the Atkin operator, and prove a potential semi-stability theorem for correspondences. We explicitly determine the stable models of various Hecke operators on quaternionic Shimura curves, and make a purely geometric study of canonical subgroups.
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Wilcox, Nicholas. "A Computational Introduction to Elliptic and Hyperelliptic Curve Cryptography." Oberlin College Honors Theses / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528649455201473.

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Eklund, David. "Topics in computation, numerical methods and algebraic geometry." Doctoral thesis, KTH, Matematik (Avd.), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-25941.

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This thesis concerns computation and algebraic geometry. On the computational side we have focused on numerical homotopy methods. These procedures may be used to numerically solve systems of polynomial equations. The thesis contains four papers. In Paper I and Paper II we apply continuation techniques, as well as symbolic algorithms, to formulate methods to compute Chern classes of smooth algebraic varieties. More specifically, in Paper I we give an algorithm to compute the degrees of the Chern classes of smooth projective varieties and in Paper II we extend these ideas to cover also the degrees of intersections of Chern classes. In Paper III we formulate a numerical homotopy to compute the intersection of two complementary dimensional subvarieties of a smooth quadric hypersurface in projective space. If the two subvarieties intersect transversely, then the number of homotopy paths is optimal. As an application we give a new solution to the inverse kinematics problem of a six-revolute serial-link mechanism. Paper IV is a study of curves on certain special quartic surfaces in projective 3-space. The surfaces are invariant under the action of a finite group called the level (2,2) Heisenberg group. In the paper, we determine the Picard group of a very general member of this family of quartics. We have found that the general Heisenberg invariant quartic contains 320 smooth conics and we prove that in the very general case, this collection of conics generates the Picard group.
QC 20101115
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Lundqvist, Samuel. "Computational algorithms for algebras." Doctoral thesis, Stockholm : Department of Mathematics, Stockholm University, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-31552.

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Diss. (sammanfattning) Stockholm : Stockholms universitet, 2009.
At the time of doctoral defence, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript. Paper 5: Manuscript. Paper 6: Manuscript. Härtill 6 uppsatser.
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Berthomieu, Jérémy. "Contributions à la résolution des systèmes algébriques : réduction, localisation, traitement des singularités ; implantations." Phd thesis, Ecole Polytechnique X, 2011. http://pastel.archives-ouvertes.fr/pastel-00670436.

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Cette thèse traite de certains aspects particuliers de la résolution des systèmes algébriques. Dans un premier temps, nous présentons une façon de minimiser le nombres de variables additives apparaissant dans un système algébrique. Nous utilisons pour cela deux invariants de variété introduits par Hironaka : le faîte et la directrice. Dans un second temps, nous proposons une arithmétique rapide, dite détendue, pour les entiers p-adiques. Cette arithmétique nous permet ensuite de résoudre efficacement un système algébrique à coefficients rationnels localement, c'est-à-dire sur les entiers p-adiques. En quatrième partie, nous nous intéressons à la factorisation d'un polynôme à deux variables qui est une brique élémentaire pour la décomposition en composantes irréductibles des hypersurfaces. Nous proposons un algorithme réduisant la factorisation du polynôme donné en entrée à celle d'un polynôme dont la taille dense est essentiellement équivalente à la taille convexe-dense de celui donné en entrée. Dans la dernière partie, nous considérons la résolution en moyenne des systèmes algébriques réels. Nous proposons un algorithme probabiliste calculant un zéro approché complexe du système algébrique réel donné en entrée.
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Books on the topic "Computational algebraic geometry"

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Schenck, Hal. Computational algebraic geometry. Cambridge, UK: Cambridge University Press, 2003.

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Eyssette, Frédéric, and André Galligo, eds. Computational Algebraic Geometry. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-2752-6.

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Cox, David, and Bernd Sturmfels, eds. Applications of Computational Algebraic Geometry. Providence, Rhode Island: American Mathematical Society, 1997. http://dx.doi.org/10.1090/psapm/053.

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Seppälä, Mika, and Emil Volcheck, eds. Computational Algebraic and Analytic Geometry. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/conm/572.

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Tanush, Shaska, ed. Computational aspects of algebraic curves. Singapore: World Scientific, 2005.

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Emiris, Ioannis Z. Nonlinear computational geometry. Edited by Theobald Thorsten 1971- and Institute of Mathematics and Its Applications. New York, N.Y: Springer, 2010.

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Idaho), Conference on Computational Aspects of Algebraic Curves (2005 University of. Computational aspects of algebraic curves: [proceedings]. Hackensack, NJ: World Scientific, 2005.

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Decker, W. A first course in computational algebraic geometry. New York: Cambridge University Press, 2013.

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David, Eisenbud, ed. Computational methods in commutative algebra and algebraic geometry. Berlin: Springer, 1998.

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Joswig, Michael. Polyhedral and Algebraic Methods in Computational Geometry. London: Springer London, 2013.

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Book chapters on the topic "Computational algebraic geometry"

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Decker, W., and F. O. Schreyer. "Computational Algebraic Geometry Today." In Applications of Algebraic Geometry to Coding Theory, Physics and Computation, 65–119. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-1011-5_6.

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Husty, Manfred L., and Hans-Peter Schröcker. "Algebraic Geometry and Kinematics." In Nonlinear Computational Geometry, 85–107. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-0999-2_4.

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Bokowski, Jürgen, and Bernd Sturmfels. "Combinatorial and algebraic methods." In Computational Synthetic Geometry, 32–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0089256.

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Seppälä, M. "Computational conformal geometry." In Algorithms in Algebraic Geometry and Applications, 365–72. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9104-2_18.

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Jaworski, Piotr. "Arrangements of singularities and proper partitions of Dynkin diagrams." In Computational Algebraic Geometry, 129–42. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-2752-6_9.

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Becker, E., and R. Neuhaus. "Computation of Real Radicals of Polynomial Ideals." In Computational Algebraic Geometry, 1–20. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-2752-6_1.

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Kostov, V. P., and S. K. Lando. "Versal deformations of powers of volume forms." In Computational Algebraic Geometry, 143–62. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-2752-6_10.

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Lazard, D., and A. Valibouze. "Computing subfields: Reverse of the primitive element problem." In Computational Algebraic Geometry, 163–76. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-2752-6_11.

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Łȩcki, Andrzej, and Zbigniew Szafraniec. "Applications of the Eisenbud-Levine’s theorem to real algebraic geometry." In Computational Algebraic Geometry, 177–84. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-2752-6_12.

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Maybank, S. J. "Applications of Algebraic Geometry to Computer Vision." In Computational Algebraic Geometry, 185–94. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-2752-6_13.

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Conference papers on the topic "Computational algebraic geometry"

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Bürgisser, Peter, and Peter Scheiblechner. "Differential forms in computational algebraic geometry." In the 2007 international symposium. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1277548.1277558.

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Rodríguez Vega, Martín. "Computational algebraic geometry of epidemic models." In SPIE Sensing Technology + Applications, edited by Šárka O. Southern, Mark A. Mentzer, Isaac Rodriguez-Chavez, and Virginia E. Wotring. SPIE, 2014. http://dx.doi.org/10.1117/12.2049255.

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Buchberger, B. "Algebraic methods for non-linear computational geometry (invited address)." In the fourth annual symposium. New York, New York, USA: ACM Press, 1988. http://dx.doi.org/10.1145/73393.73402.

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Wang, L., R. R. Mettu, and B. R. Donald. "An algebraic geometry approach to protein structure determination from NMR data." In Proceedings. 2005 IEEE Computational Systems Bioinformatics Conference. IEEE, 2005. http://dx.doi.org/10.1109/csb.2005.11.

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Kavasseri, Rajesh G., and Parthasarathi Nag. "A Computational Algebraic Geometry Based Global Optimization Technique to Address Economic Dispatch." In 2007 IEEE Power Engineering Society General Meeting. IEEE, 2007. http://dx.doi.org/10.1109/pes.2007.386198.

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Ramirez Lopez, Adan, D. F. Muñoz-Negron, and J. A. Alcántara-Cardenas. "REINFORCEMENT OF MATHEMATICAL CONCEPTS FOR HIGH SCHOOL STUDENTS DURING ALGEBRAIC, GEOMETRY AND CALCULUS COURSES USING COMPUTATIONAL AIDS." In International Conference on Education and New Learning Technologies. IATED, 2017. http://dx.doi.org/10.21125/edulearn.2017.2141.

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Ge, Q. Jeffrey, and Pierre M. Larochelle. "Algebraic Motion Approximation With NURBS Motions and its Application to Spherical Mechanism Synthesis." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5881.

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Abstract In this work we bring together classical mechanism theory with recent works in the area of Computer Aided Geometric Design (CAGD) of rational motions as well as curve approximation techniques in CAGD to study the problem of mechanism motion approximation from a computational geometric viewpoint. We present a framework for approximating algebraic motions of spherical mechanisms with rational B-Spline spherical motions. Algebraic spherical motions and rational B-spline spherical motions are represented as algebraic curves and rational B-Spline curves in the space of quaternions (or the image space). Thus the problem of motion approximation is transformed into a curve approximation problem, where concepts and techniques in the field of Computer Aided Geometric Design and Computational Geometry may be applied. An example is included at the end to show how a NURBS motion can be used for synthesizing spherical four-bar linkages.
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Panta Pazos, Rube´n. "Behavior of a Sequence of Geometric Transformations for a Truncated Ellipsoid Geometry in Transport Theory." In 17th International Conference on Nuclear Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/icone17-75758.

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The neutron transport equation has been studied from different approaches, in order to solve different situations. The number of methods and computational techniques has increased recently. In this work we present the behavior of a sequence of geometric transformations evolving different transport problems in order to obtain solve a transport problem in a truncated ellipsoid geometry and subject to known boundary conditions. This scheme was depicted in 8, but now is solved for the different steps. First, it is considered a rectangle domain that consists of three regions, source, void and shield regions 5. Horseshoe domain: for that it is used the complex function: f:D→C,definedasf(z)=12ez+1ezwhereD=z∈C−0.5≤Re(z)≤0.5,−12π≤Im(z)≤12π(0.1) The geometry obtained is such that the source is at the focus of an ellipse, and the target coincides with the other focus. The boundary conditions are reflective in the left boundary and vacuum in the right boundary. Indeed, if the eccentricity is a number between 0,95 and 0,99, the distance between the source and the target ranges from 20 to 100 length units. The rotation around the symmetry axis of the horseshoe domain generates a truncated ellipsoid, such that a focus coincides with the source. In this work it is analyzed the flux in each step, giving numerical results obtained in a computer algebraic system. Applications: in nuclear medicine and others.
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Jorabchi, Kavous, Joshua Danczyk, and Krishnan Suresh. "Shape Optimization of Potentially Slender Structures." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-50001.

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Shape optimization lies at the heart of modern engineering design. Through shape optimization, computers can, in theory, ‘synthesize’ engineering artifacts in a fully automated fashion. However, a serious limitation today is that the evolving geometry (during optimization) may become slender, i.e., beam or plate-like. Under such circumstances, modern 3-D computational methods, such as finite element analysis (FEA), will fail miserably, and so will the shape optimization process. Indeed, the recommended method for analyzing slender artifacts is to replace them with 1-D beams/ 2-D plates, prior to discretization and computational analysis, a process referred to as geometric dimensional reduction. Unfortunately explicit geometric reduction is impractical and hard to automate during optimization since one cannot predict a priori when an artifact will become slender. In this paper, we develop an implicit dimensional reduction method where the reduction is achieved through an algebraic process. The proposed method of reduction is computationally equivalent to explicit geometric reduction for comparable computational cost. However, the proposed method can be easily automated and integrated within a shape optimization process, and standard off-the-shelf 3-D finite element packages can be used to implement the proposed methodology.
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Böhm, Janko, and Anne Frühbis-Krüger. "Massively Parallel Computations in Algebraic Geometry." In ISSAC '21: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3452143.3465510.

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Reports on the topic "Computational algebraic geometry"

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Stiller, Peter. Algebraic Geometry and Computational Algebraic Geometry for Image Database Indexing, Image Recognition, And Computer Vision. Fort Belvoir, VA: Defense Technical Information Center, October 1999. http://dx.doi.org/10.21236/ada384588.

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Thompson, David C., Joseph Maurice Rojas, and Philippe Pierre Pebay. Computational algebraic geometry for statistical modeling FY09Q2 progress. Office of Scientific and Technical Information (OSTI), March 2009. http://dx.doi.org/10.2172/984161.

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Yau, Stephen S. T. PDE, Differential Geometric, Algebraic, Wavelet and Parallel Computation Methods in Nonlinear Filtering. Fort Belvoir, VA: Defense Technical Information Center, June 2003. http://dx.doi.org/10.21236/ada415460.

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