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Journal articles on the topic 'Conic section'

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Published: 4 June 2021
Last updated: 18 February 2022

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1

Lipp, Alan. "Cubic Polynomials." Mathematics Teacher 93, no. 9 (December 2000): 788–92. http://dx.doi.org/10.5951/mt.93.9.0788.

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2

Rizal, Yusmet. "DIAGONALISASI BENTUK KUADRATIK IRISAN KERUCUT." EKSAKTA: Berkala Ilmiah Bidang MIPA 19, no. 1 (April 25, 2018): 83–90. http://dx.doi.org/10.24036/eksakta/vol19-iss1/132.

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In general, the conic section equation consists of three parts, namely quadratic, cross-product, and linear terms. A conic sections will be easily determined by its shape if it does not contain cross-product term, otherwise it is difficult to determine. Analytically a cone slice is a quadratic form of equation. A concept in linear algebraic discussion can be applied to facilitate the discovery of a shape of a conic section. The process of diagonalization can transform a quadratic form into another form which does not contain crosslinking tribes, ie by diagonalizing the quadrate portion. Hence this paper presents the application of an algebraic concept to find a form of conic sections.
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3

Cardona-Nunez, Octavio, Alejandro Cornejo-Rodriguez, Rufino Diaz-Uribe, Alberto Cordero-Davila, and Jesus Pedraza-Contreras. "Conic that best fits an off-axis conic section." Applied Optics 25, no. 19 (October 1, 1986): 3585. http://dx.doi.org/10.1364/ao.25.003585.

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4

Marinov, Marin, and Petya Asenova. "Teaching the Notion Conic Section with Computer." Mathematics and Informatics LXIV, no. 4 (August 30, 2021): 395–409. http://dx.doi.org/10.53656/math2021-4-5-pred.

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The article discusses the problem of introducing and constructing mathematical concepts using a computer. The Wolfram Mathematica 12 symbolic calculation system is used at each stage of the complex spiral process to form the notion of conic section and the related concepts of focus, directrix and eccentricity. The nature of these notions implies the use of appropriate animations, 3D graphics and symbolic calculations. Our vision of the process of formation of mathematical concepts is presented. The notions ellipse, parabola and hyperbola are defined as the intersection of a conical surface with a plane not containing the vertex of the conical surface. The conical section is represented as a geometric location of points on the plane for which the ratio of the distance to the focus to the distance to the directrix is a constant value. The lines of hyperbola and ellipse are determined by their foci. The equivalence of different definitions for conical sections is commented.
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5

Ayoub, Ayoub B. "The Eccentricity of a Conic Section." College Mathematics Journal 34, no. 2 (March 2003): 116. http://dx.doi.org/10.2307/3595784.

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6

Shklyar, Sergiy, Alexander Kukush, Ivan Markovsky, and Sabine Van Huffel. "On the conic section fitting problem." Journal of Multivariate Analysis 98, no. 3 (March 2007): 588–624. http://dx.doi.org/10.1016/j.jmva.2005.12.003.

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7

Ayoub, Ayoub B. "The Eccentricity of a Conic Section." College Mathematics Journal 34, no. 2 (March 2003): 116–21. http://dx.doi.org/10.1080/07468342.2003.11921994.

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8

Wilkins, Daniel. "The Tangent Lines of a Conic Section." College Mathematics Journal 34, no. 4 (September 2003): 296. http://dx.doi.org/10.2307/3595767.

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9

Hosseinyalmdary, S., and A. Yilmaz. "TRAFFIC LIGHT DETECTION USING CONIC SECTION GEOMETRY." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences III-1 (June 2, 2016): 191–200. http://dx.doi.org/10.5194/isprsannals-iii-1-191-2016.

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Traffic lights detection and their state recognition is a crucial task that autonomous vehicles must reliably fulfill. Despite scientific endeavors, it still is an open problem due to the variations of traffic lights and their perception in image form. Unlike previous studies, this paper investigates the use of inaccurate and publicly available GIS databases such as OpenStreetMap. In addition, we are the first to exploit conic section geometry to improve the shape cue of the traffic lights in images. Conic section also enables us to estimate the pose of the traffic lights with respect to the camera. Our approach can detect multiple traffic lights in the scene, it also is able to detect the traffic lights in the absence of prior knowledge, and detect the traffics lights as far as 70 meters. The proposed approach has been evaluated for different scenarios and the results show that the use of stereo cameras significantly improves the accuracy of the traffic lights detection and pose estimation.
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10

Hosseinyalmdary, S., and A. Yilmaz. "TRAFFIC LIGHT DETECTION USING CONIC SECTION GEOMETRY." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences III-1 (June 2, 2016): 191–200. http://dx.doi.org/10.5194/isprs-annals-iii-1-191-2016.

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Traffic lights detection and their state recognition is a crucial task that autonomous vehicles must reliably fulfill. Despite scientific endeavors, it still is an open problem due to the variations of traffic lights and their perception in image form. Unlike previous studies, this paper investigates the use of inaccurate and publicly available GIS databases such as OpenStreetMap. In addition, we are the first to exploit conic section geometry to improve the shape cue of the traffic lights in images. Conic section also enables us to estimate the pose of the traffic lights with respect to the camera. Our approach can detect multiple traffic lights in the scene, it also is able to detect the traffic lights in the absence of prior knowledge, and detect the traffics lights as far as 70 meters. The proposed approach has been evaluated for different scenarios and the results show that the use of stereo cameras significantly improves the accuracy of the traffic lights detection and pose estimation.
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11

Wilkins, Daniel. "The Tangent Lines of a Conic Section." College Mathematics Journal 34, no. 4 (September 2003): 296–303. http://dx.doi.org/10.1080/07468342.2003.11922021.

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12

Хейфец and Aleksandr Kheyfets. "Conics As Sections of Quadrics by Plane (Generalized Dandelin Theorem)." Geometry & Graphics 5, no. 2 (July 4, 2017): 45–58. http://dx.doi.org/10.12737/article_5953f32172a8d8.94863595.

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Has been presented a geometrical proof of a theorem stating that when a plane section crosses second-order revolution surfaces (rotation quadrics, RQ), such types of conics as ellipse, hyperbola or parabola are formed. The theorem amplifies historically famous Dandelin theorem, which provides geometric proof only for the circular cone, and extends the proof to all RQ: ellipsoid, hyperboloid, paraboloid and cylinder. That is why the theorem described below has been called as Generalized Dandelin theorem (GDT). The GDT proof has been constructed on a little-known generalized definition (GDD) of the conic. This GDD defines the conic as a line, that is a geometrical locus of points (GLP) P, for which ratio q = PT / PD = const, where PT is tangential distance from the point to the circle inscribed in the line, and PD is distance from the point to the straight line passing through the tangency points of the circle and the line. Has been presented a proof of GDD for all types of conics as their necessary and sufficient condition. The proof is in the construction of a circular cone and inscribed in sphere which is tangent to a cutting plane line at two points. For this construction is defined the position of a cutting plane, giving in section the specified conic. On the GDD basis has been proved the GDT for all the RQ with the arbitrary position of the cutting plane. For the proving a tangent sphere is placed in the quadric. An auxiliary cutting plane passing through the quadric axis is introduced. It is proved that in a section by axial plane the GDD is performed as a necessary condition for the conic. The relationship between the axial section and the given one is established. This permits to make a conclusion that in the given section the GDD is performed as the conic’s sufficient condition. Visual stereometrical constructions that are necessary for the theorem proof have been presented. The implementation of constructions using 3D computer methods has been considered. The examples of constructions in AutoCAD package have been demonstrated. Some constructions have been carried out with implementation of 2D parameterization. With regard to affine transformations the possibility for application of Generalized Dandelin theorem to all elliptic quadrics has been demonstrated. This paper is meant for including the GDT in a new training course on theoretical basis for 3D engineering computer graphics as a part of students’ geometrical-graphic training.
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13

Thele, Kent. "Conic Connections with Polar Functions." Mathematics Teacher 110, no. 4 (November 2016): 320. http://dx.doi.org/10.5951/mathteacher.110.4.0320.

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14

Cardona-Nuñez, Octavio, Alejandro Cornejo-Rodriguez, Rufino Diaz-Uribe, Alberto Cordero-Dávila, and Jesús Pedraza-Contreras. "Comparison between toroidal and conic surfaces that best fit an off-axis conic section." Applied Optics 26, no. 22 (November 15, 1987): 4832. http://dx.doi.org/10.1364/ao.26.004832.

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15

Mahony, John D. "Locating parameters of interest in a conic section." Mathematical Gazette 103, no. 557 (June 6, 2019): 196–203. http://dx.doi.org/10.1017/mag.2019.50.

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In an interesting Note [1] a method for constructing the directrices of a conic section using simple tools, viz. a pencil, a pair of compasses and a straight edge, was presented and it was wondered if the method might have been known before. From earlier days at school this author was aware that for a specific conic section (parabola, ellipse or hyperbola) displayed without reference on a piece of paper it was possible to determine not just the directrices but also the focal points and the usual axis set, again using just the simple tools. Others might also be aware of these facts, but if they are not so well known it might be of interest to present an argument in recipe format that will enable readers to appreciate a route to fathom the business, although there might well be other paths leading also to the same end-result, depending on the starting point.
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16

HERR, DAVID LINCOLN. "CONIC-SECTION ORBITS DERIVED FROM THE GRAVITATIONAL POTENTIAL." Journal of the American Society for Naval Engineers 70, no. 4 (March 18, 2009): 595–98. http://dx.doi.org/10.1111/j.1559-3584.1958.tb01775.x.

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17

Bétend-Bon, Jean-Pierre, Lech Wosinski, Magnus Breidne, and Lennart Robertsson. "Fiber optic interferometer for testing conic section surfaces." Applied Optics 30, no. 13 (May 1, 1991): 1715. http://dx.doi.org/10.1364/ao.30.001715.

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18

Yildirim, Tulay, and Lale Ozyilmaz. "Dimensionality reduction in conic section function neural network." Sadhana 27, no. 6 (December 2002): 675–83. http://dx.doi.org/10.1007/bf02703358.

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19

Srestasathiern, P., and N. Soontranon. "A novel camera calibration method for fish-eye lenses using line features." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-3 (August 11, 2014): 327–32. http://dx.doi.org/10.5194/isprsarchives-xl-3-327-2014.

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In this paper, a novel method for the fish-eye lens calibration is presented. The method required only a 2D calibration plane containing straight lines i.e., checker board pattern without a priori knowing the poses of camera with respect to the calibration plane. The image of a line obtained from fish-eye lenses is a conic section. The proposed calibration method uses raw edges, which are pixels of the image line segments, in stead of using curves obtained from fitting conic to image edges. Using raw edges is more flexible and reliable than using conic section because the result from conic fitting can be unstable. The camera model used in this work is radially symmetric model i.e., bivariate non-linear function. However, this approach can use other single view point camera models. The geometric constraint used for calibrating the camera is based on the coincidence between point and line on calibration plane. The performance of the proposed calibration algorithm was assessed using simulated and real data.
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20

Kung, Sidney H. "Finding the Tangent to a Conic Section without Calculus." College Mathematics Journal 34, no. 5 (November 2003): 394. http://dx.doi.org/10.2307/3595824.

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21

Mathews, John H. "The Five Point Conic Section: Exploration with Computer Software." School Science and Mathematics 95, no. 4 (April 1995): 206–8. http://dx.doi.org/10.1111/j.1949-8594.1995.tb15764.x.

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22

O¨zylmaz, Lale, and Tu¨lay Yldrm. "Reduction of complexity in conic section function neural network." Kybernetes 32, no. 4 (June 2003): 540–47. http://dx.doi.org/10.1108/03684920310463920.

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23

Jaiswal, Sushma, Sarita Singh Bhad, and Rakesh Singh Jado. "Creation 3D Animatable Face Methodology Using Conic Section-Algorithm." Information Technology Journal 7, no. 2 (February 1, 2008): 292–98. http://dx.doi.org/10.3923/itj.2008.292.298.

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24

GATES, J. "A New Conic Section Extraction Approach and Its Applications." IEICE Transactions on Information and Systems E88-D, no. 2 (February 1, 2005): 239–51. http://dx.doi.org/10.1093/ietisy/e88-d.2.239.

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25

배동훈. "Study on Conic Section Implementation for Product Design Technical Drawing." Journal of Digital Design 11, no. 2 (April 2011): 83–91. http://dx.doi.org/10.17280/jdd.2011.11.2.009.

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26

Cardona-Nuñez, O., A. Cornejo-Rodriguez, A. Cordero-Davila, and J. Pedraza-Contreras. "Inclined toroidal surface that fits an off-axis conic section." Applied Optics 35, no. 19 (July 1, 1996): 3559. http://dx.doi.org/10.1364/ao.35.003559.

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27

Zhu, Qiuming, and Lu Peng. "A new approach to conic section approximation of object boundaries." Image and Vision Computing 17, no. 9 (July 1999): 645–58. http://dx.doi.org/10.1016/s0262-8856(98)00148-6.

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28

王, 幼宁. "Metrical Geometry Classification of Conic Section in Hyperbolic Space Form." Pure Mathematics 02, no. 02 (2012): 97–102. http://dx.doi.org/10.12677/pm.2012.22016.

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29

Erkmen, B., N. Kahraman, R. A. Vural, and T. Yildirim. "Conic Section Function Neural Network Circuitry for Offline Signature Recognition." IEEE Transactions on Neural Networks 21, no. 4 (April 2010): 667–72. http://dx.doi.org/10.1109/tnn.2010.2040751.

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30

Helsø, Martin. "Rational quartic symmetroids." Advances in Geometry 20, no. 1 (January 28, 2020): 71–89. http://dx.doi.org/10.1515/advgeom-2018-0037.

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31

Shpitalni, M., and H. Lipson. "Classification of Sketch Strokes and Corner Detection Using Conic Sections and Adaptive Clustering." Journal of Mechanical Design 119, no. 1 (March 1, 1997): 131–35. http://dx.doi.org/10.1115/1.2828775.

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This paper presents a method for classifying pen strokes in an on-line sketching system. The method, based on linear least squares fitting to a conic section equation, proposes using the conic equation’s natural classification property to help classify sketch strokes and identify lines, elliptic arcs, and corners composed of two lines with an optional fillet. The hyperbola form of the conic equation is used for corner detection. The proposed method has proven to be fast, suitable for real-time classification, and capable of tolerating noisy input, including cusps and spikes. The classification is obtained in o(n) time in a single path, where n is the number of sampled points. In addition, an improved adaptive method for clustering disconnected end-points is proposed. The notion of in-context analysis is discussed, and examples from a working implementation are given.
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32

Ahn, Young-Joon. "AN ERROR BOUND ANALYSIS FOR CUBIC SPLINE APPROXIMATION OF CONIC SECTION." Communications of the Korean Mathematical Society 17, no. 4 (October 1, 2002): 741–54. http://dx.doi.org/10.4134/ckms.2002.17.4.741.

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33

Sato, Eiichi. "Hyperplane section principle of Lefschetz on conic-bundle and blowing-down." Kodai Mathematical Journal 31, no. 3 (October 2008): 307–22. http://dx.doi.org/10.2996/kmj/1225980438.

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34

Salsabila, E., W. Rahayu, S. A. Kharis, and A. Putri. "Analysis of Mathematical Literacy on Students’ Metacognition in Conic Section Material." Journal of Physics: Conference Series 1417 (December 2019): 012057. http://dx.doi.org/10.1088/1742-6596/1417/1/012057.

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35

Fang, Guangyu, Li Huang, Li Xin, Haifa Zhao, Lei Huo, and Lili Wu. "Geometric explanation of conic-section interference fringes in a Michelson interferometer." American Journal of Physics 81, no. 9 (September 2013): 670–75. http://dx.doi.org/10.1119/1.4811780.

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36

Thompson, Samantha J., Richard Lang, Paul Rees, and Gareth W. Roberts. "Reconstruction of a conic-section surface from autocollimator-based deflectometric profilometry." Applied Optics 55, no. 10 (April 1, 2016): 2827. http://dx.doi.org/10.1364/ao.55.002827.

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37

Li, Yajun. "Laser beam scanning by rotary mirrors II Conic-section scan patterns." Applied Optics 34, no. 28 (October 1, 1995): 6417. http://dx.doi.org/10.1364/ao.34.006417.

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38

Zhu, Qiuming. "On the Geometries of Conic Section Representation of Noisy Object Boundaries." Journal of Visual Communication and Image Representation 10, no. 2 (June 1999): 130–54. http://dx.doi.org/10.1006/jvci.1999.0419.

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39

Brown, Matthew R. "Ovoids of PG(3,q ), q Even, with a Conic Section." Journal of the London Mathematical Society 62, no. 2 (October 2000): 569–82. http://dx.doi.org/10.1112/s0024610700001137.

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40

Duan, D. W., and Y. Rahmat-Samii. "Generalised formulas for beam squint prediction in conic-section reflector antennas." Electronics Letters 26, no. 11 (May 24, 1990): 722–24. http://dx.doi.org/10.1049/el:19900471.

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41

Dorffner, Georg. "UNIFIED FRAMEWORK FOR MLPs AND RBFNs: INTRODUCING CONIC SECTION FUNCTION NETWORKS." Cybernetics and Systems 25, no. 4 (July 1994): 511–54. http://dx.doi.org/10.1080/01969729408902340.

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42

Wang, Shuquan. "Patched Conic Section Maneuver Trajectory Planning For Two-Craft Coulomb Formation." IEEE Transactions on Aerospace and Electronic Systems 53, no. 1 (February 2017): 258–72. http://dx.doi.org/10.1109/taes.2017.2650098.

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43

Ionescu, Paltin, and Francesco Russo. "Varieties with quadratic entry locus, II." Compositio Mathematica 144, no. 4 (July 2008): 949–62. http://dx.doi.org/10.1112/s0010437x08003539.

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AbstractWe continue the study, begun in [F. Russo, Varieties with quadratic entry locus. I, Preprint (2006), math. AG/0701889] , of secant defective manifolds having ‘simple entry loci’. We prove that such manifolds are rational and describe them in terms of tangential projections. Using also the work of [P. Ionescu and F. Russo, Conic-connected manifolds, Preprint (2006), math. AG/0701885], their classification is reduced to the case of Fano manifolds of high index, whose Picard group is generated by the hyperplane section class. Conjecturally, the former should be linear sections of rational homogeneous manifolds. We also provide evidence that the classification of linearly normal dual defective manifolds with Picard group generated by the hyperplane section should follow along the same lines.
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44

Kuhnke, Stefan, Felix Gensch, René Nitschke, Vidal Sanabria, and Soeren Mueller. "Influence of Die Surface Topography and Lubrication on the Product Quality during Indirect Extrusion of Copper-Clad Aluminum Rods." Metals 10, no. 7 (July 4, 2020): 888. http://dx.doi.org/10.3390/met10070888.

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Copper-clad aluminum rods are usually fabricated using hydrostatic extrusion, since during direct and indirect extrusion fracture of the copper sleeve is difficult to avoid. In this study, different die surface topographies and lubrication conditions were applied to improve the material flow during indirect extrusion of copper-clad aluminum rods. Thus, conic dies with different roughness (polished and sandblasted) and surfaces shapes (fine and coarse grooves) were tested. Additionally, the effects of a wax-graphite-based lubricant as well as a graphite-like carbon (GLC) coating of the die conic surfaces were investigated. The composite billets were made of aluminum EN AW-1080A cores and copper CW004A sleeves with an equivalent copper cross section of 0.24 of the total billet cross section. For all trials, an extrusion ratio of 14.8:1 and a conic die angle of 2α = 90° were chosen. Non-isothermal extrusion trials were carried out using a container at 330 °C and billet and tools at room temperature to reduce the flow stress ratio σCu/σAl. The extruded composite rods’ integrity, surface quality, interface integrity, and equivalent copper cross section were analyzed. In addition, a visual inspection of the sleeve-die contact surface was performed. The results showed that the GLC coating proved to be unsuitable due to a lack of lubrication, which causes accumulated sleeve fractures and longitudinal grooves on the extruded rods. The best results were achieved with the combination of the sandblasted die surface and the wax-graphite-based lubricant, observing a uniform material flow without sleeve fractures.
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45

Xu, Yinan, and Shuquan Wang. "Reconfiguration of Three-Craft Coulomb Formation Based on Patched-Conic-Section Trajectories." Journal of Guidance, Control, and Dynamics 39, no. 3 (March 2016): 474–86. http://dx.doi.org/10.2514/1.g001557.

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46

Duan, D. W., and Y. Rahmat-Samii. "Beam squint determination in conic-section reflector antennas with circularly polarized feeds." IEEE Transactions on Antennas and Propagation 39, no. 5 (May 1991): 612–19. http://dx.doi.org/10.1109/8.81488.

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47

Fuks, I. M. "High-frequency asymptotic solutions for backscattering by cylinders with conic section directrixes." IEEE Transactions on Antennas and Propagation 53, no. 5 (May 2005): 1653–62. http://dx.doi.org/10.1109/tap.2005.846803.

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48

Liu, Yu, and Chen-dong Xu. "Approximation of conic section by quartic Bézier curve with endpoints continuity condition." Applied Mathematics-A Journal of Chinese Universities 32, no. 1 (March 2017): 1–13. http://dx.doi.org/10.1007/s11766-017-3434-3.

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49

Lobontiu, Nicolae, Jeffrey S. N. Paine, Ephrahim Garcia, and Michael Goldfarb. "Design of symmetric conic-section flexure hinges based on closed-form compliance equations." Mechanism and Machine Theory 37, no. 5 (May 2002): 477–98. http://dx.doi.org/10.1016/s0094-114x(02)00002-2.

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50

Shenheng Xu and Y. Rahmat-Samii. "A Novel Beam Squint Compensation Technique for Circularly Polarized Conic-Section Reflector Antennas." IEEE Transactions on Antennas and Propagation 58, no. 2 (February 2010): 307–17. http://dx.doi.org/10.1109/tap.2009.2037711.

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