Relevant bibliographies by topics / Tangent

Contents

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

Academic literature on the topic 'Tangent'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 April 2022

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Journal articles on the topic "Tangent"

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Дмитриева, И., I. Dmitrieva, Геннадий Иванов, and Gennadiy Ivanov. "Competence Approach in Teaching the Topic "Tangent Plane and Normal"." Geometry & Graphics 6, no. 4 (January 29, 2019): 47–54. http://dx.doi.org/10.12737/article_5c21f80e2925c6.80568562.

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Qualified presentation of the topic "Tangent Plane and Surface Normal" in terms of competence approach is possible with the proper level for students' attention focusing on both intra-subject and inter-subject relations of descriptive geometry. Intra-subject connections follow from the position that the contingence is a particular (limit) case of intersection. Therefore, the line of intersection of the tangent plane and the surface, or two touching surfaces, has a special point at the tangency point. It is known from differential geometry [1] that this point can be nodal, return, or isolated one. In turn, this point’s appearance depends on differential properties of the surface(s) in this point’s vicinity. That's why, for the competent solution of the considered positional problem account must be also taken of the inter-subject connections for descriptive and differential geometry. In the training courses of descriptive geometry tangent planes are built only to the simplest surfaces, containing, as a rule, the frames of straight lines and circles. Therefore, the tangent plane is defined by two tangents drawn at the tangency point to two such lines. In engineering practice, as such lines are used cross-sections a surface by planes parallel to any two coordinate planes. That is, from the standpoints for the course of higher mathematics, the problem is reduced to calculation for partial derivatives. Although this topic is studied after the course of descriptive geometry, it seems possible to give geometric explanation for computation of partial derivatives in a nutshell. It also seems that the study of this topic will be stimulated by a story about engineering problems, which solution is based on construction of the tangent plane and the normal to the technical surface. In this paper has been presented an example for the use of surface curvature lines for programming of milling processing for 3D-harness surfaces.
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Koval, Galyna, Margarita Lazarchuk, and Liudmila Ovsienko. "APPLICATION OF CIRCLES FOR CONJUGATION OF FLAT CONTOURS OF THE FIRST ORDER OF SMOOTHNESS." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 100 (May 24, 2021): 162–71. http://dx.doi.org/10.32347/0131-579x.2021.100.162-171.

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In geometric modeling of contours, especially for conjugation of sections of flat contours of the first order of smoothness, arcs of circles can be applied. The article proposes ways to determine the equations of a circle for two ways of its problem: the problem of a circle with a point and two tangents, none of which contains a given point, and the problem of a circle with three tangents. The equations of the circles were determined in both cases using a projective coordinate system. In the first case, when a circle is given by a point and two tangents, neither of which contains this point, the center of the conjugation circle is defined as the point of intersection of two locus of points - the bisector of the angle between the tangents and the parabola, the focus of which is a given point. given tangents. In the general case, there are 2 conjugation circles for which canonical equations are defined. Parametric equations of conjugate circles, the parameters of which are equal to 0 and ∞ on tangents and equal to one at a given point, with the help of affine and projective coordinates of points of contact are determined first in the projective coordinate system, and then translated into affine system. For the second case, when specifying a circle using three tangent lines, the equation of the second-order curve tangent to these lines is first determined in the projective coordinate system. The tangent lines are taken as the coordinate lines of the projective coordinate system. The unit point of the projective coordinate system is selected in the metacenter of the thus obtained base triangle. The equation of the tangent to the base lines of the second order contains two unknown variables, positive or negative values ​​which determine the location of four possible tangents of the second order. After writing the vector-parametric equation of the tangent curve of the second order in the affine coordinate system, the equation is written to determine the parameters of cyclic points. In order for the equation of the tangent curve of the second order obtained in the projective plane to be an equation of a circle, it must satisfy the coordinates of the cyclic points of the plane, which allows to write the second equation to determine the parameters of cyclic points. By solving a system of two equations, we obtain the required equations of circles tangent to three given lines.
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Watkins, G. G. "Clarke's tangent vectors as tangents to lipschitz continuous curves." Journal of Optimization Theory and Applications 45, no. 2 (February 1985): 325–34. http://dx.doi.org/10.1007/bf00939984.

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Lê, Công-Trình, and Tien-Son Phạm. "On tangent cones at infinity of algebraic varieties." Journal of Algebra and Its Applications 17, no. 08 (July 8, 2018): 1850143. http://dx.doi.org/10.1142/s0219498818501438.

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In this paper, we define the geometric and algebraic tangent cones at infinity of algebraic varieties and establish the following version at infinity of Whitney’s theorem [Local properties of analytic varieties, in Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse) (Princeton University Press, Princeton, N. J., 1965), pp. 205–244; Tangents to an analytic variety, Ann. of Math. 81 (1965) 496–549]: The geometric and algebraic tangent cones at infinity of complex algebraic varieties coincide. The proof of this fact is based on a geometric characterization of the geometric tangent cone at infinity using the global Łojasiewicz inequality with explicit exponents for complex algebraic varieties. Moreover, we show that the tangent cone at infinity of a complex algebraic variety is actually the part at infinity of this variety [G.-M. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra, 2nd extended edn. (Springer, Berlin, 2008)]. We also show that the tangent cone at infinity of a complex algebraic variety can be computed using Gröbner bases.
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Qi, Feng. "Derivatives of tangent function and tangent numbers." Applied Mathematics and Computation 268 (October 2015): 844–58. http://dx.doi.org/10.1016/j.amc.2015.06.123.

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Stanley, P. "Tangent Circles." Mathematical Gazette 86, no. 507 (November 2002): 386. http://dx.doi.org/10.2307/3621129.

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Simis, Aron, Bernd Ulrich, and Wolmer V. Vasconcelos. "Tangent algebras." Transactions of the American Mathematical Society 364, no. 2 (February 1, 2012): 571–94. http://dx.doi.org/10.1090/s0002-9947-2011-05161-5.

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Doris Devenport. "Another Tangent." Appalachian Heritage 36, no. 3 (2008): 55. http://dx.doi.org/10.1353/aph.2008.0032.

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Martin, D. H., and G. G. Watkins. "Cores of Tangent Cones and Clarke's Tangent Cone." Mathematics of Operations Research 10, no. 4 (November 1985): 565–75. http://dx.doi.org/10.1287/moor.10.4.565.

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Choi, Woocheol, and Raphaël Ponge. "Tangent maps and tangent groupoid for Carnot manifolds." Differential Geometry and its Applications 62 (February 2019): 136–83. http://dx.doi.org/10.1016/j.difgeo.2018.11.002.

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Dissertations / Theses on the topic "Tangent"

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Gargano, John Thomas. "A tangent between spheres." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1327001471.

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Martin, Adrian. "Density bounds and tangent measures." Thesis, University of Sussex, 2013. http://sro.sussex.ac.uk/id/eprint/45279/.

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A major theme in geometric measure theory is establishing global properties, such as rectifiability, of sets or measures from local ones, such as densities or tangent measures. In establishing sufficient conditions for rectifiability it is useful to know what local properties are possible in a given setting, and this is the theme of this thesis. It is known, for 1-dimensional subsets of the plane with positive lower density, that the tangent measures being concentrated on a line is sufficient to imply rectifiability. It is shown here that this cannot be relaxed too much by demonstrating the existence of a 1-dimensional subset of the plane with positive lower density whose tangent measures are concentrated on the union of two halflines, and yet the set is unrectiable. A class of metrics are also defined on R, which are functions of the Euclidean metric, to give spaces of dimension s (s > 1), where the lower density is strictly greater than 21-s, and a method for gaining an explicit lower bound for a given dimension is developed. The results are related to the generalised Besicovitch 1/2 conjecture. Set functions are defined that measure how easily the subsets of a set can be covered by balls (of any radius) with centres in the subset. These set functions are studied and used to give lower bounds on the upper density of subsets of a normed space, in particular Euclidean spaces. Further attention is paid to subsets of R, where more explicit bounds are given.
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Franch, Bullich Jaume. "Flatness, tangent systems and flat outputs." Doctoral thesis, Universitat Politècnica de Catalunya, 1999. http://hdl.handle.net/10803/6730.

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En esta tesis doctoral se presentan diversos métodos para la linealización de sistemas de control no lineales o para el estudio de la platitud. Se utilizan dos aproximaciones diferentes, en concreto: geometría diferencial y álgebra diferencial.

En el marco de álgebra diferencial, se presenta un estudio de los sistemas lineales de control desde la perspectiva de la teoría de módulos. A pesar de que los resultados han sido establecidos previamente por otros autores, algunas demostraciones y ejemplos son originales.

Entre las nuevas demostraciones cabe resaltar la que se refiere a la equivalencia entre sistemas de control lineales en representación de variables de estado, y los módulos sobre un anillo de operadores diferenciales. Los resultados de este estudio son ampliamente utilizados en el desarrollo de otros capítulos de la tesis en los que se usa el álgebra diferencial. En este contexto las principales contribuciones son:

Una nueva demostración del hecho, bien conocido, que la linealización por realimentación estática y la linealización por realimentación dinámica son equivalentes en el caso de sistemas de entrada simple. Para la linealización de este tipo de sistemas, se desarrolla un nuevo algoritmo.

Un procedimiento teórico para linealizar sistemas de entrada múltiple, basado en el cociente de módulos. También se ha hecho un paquete informático para llevar a cabo los cálculos necesarios. Debe mencionarse que este procedimiento es válido para linealizar sistemas mediante realimentación estática, así como para sistemas que sólo puedan linealizarse mediante realimentación dinámica.

Una condición para comprobar si las salidas linealizantes encontradas pueden obtenerse mediante prolongaciones. Como aplicación, se muestran algunos ejemplos de sistemas linealizables por prolongaciones. Algunos de estos sistemas se creían que no eran linealizables mediante esta técnica.
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Whited, Brian Scott. "Tangent-ball techniques for shape processing." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31670.

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Thesis (Ph.D)--Computing, Georgia Institute of Technology, 2010.
Committee Chair: Jarek Rossignac; Committee Member: Greg Slabaugh; Committee Member: Greg Turk; Committee Member: Karen Liu; Committee Member: Maryann Simmons. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Lokteva, Elizaveta. "On Smooth Knots and Tangent Lines." Thesis, Uppsala universitet, Algebra och geometri, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-354484.

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Knight, R. W. "Generalized tangent-disc spaces and Q-sets." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257958.

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Hennion, Benjamin. "Formal loops spaces and tangent Lie algebras." Thesis, Montpellier, 2015. http://www.theses.fr/2015MONTS160/document.

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L'espace des lacets lisses C(S^1,M) associé à une variété symplectique M se voit doté d'une structure (quasi-)symplectique induite par celle de M.Nous traiterons dans cette thèse d'un analogue algébrique de cet énoncé.Dans leur article, Kapranov et Vasserot ont introduit l'espace des lacets formels associé à un schéma. Il s'agit d'un analogue algébrique à l'espace des lacets lisses.Nous generalisons ici leur construction à des lacets de dimension supérieure. Nous associons à tout schéma X -- pas forcément lisse -- l'espace L^d(X) de ses lacets formels de dimension d.Nous démontrerons que ce dernier admet une structure de schéma (dérivé) de Tate : son espace tangent est de Tate, c'est-à-dire de dimension infinie mais suffisamment structuré pour se soumettre à la dualité.Nous définirons également l'espace B^d(X) des bulles de X, une variante de l'espace des lacets, et nous montrerons que le cas échéant, il hérite de la structure symplectique de X. Notons que ces résultats sont toujours valides dans des cas plus généraux : X peut être un champs d'Artin dérivé.Pour démontrer nos résultats, nous définirons ce que sont les objets de Tate dans une infinie-catégorie C stable et complète par idempotence.Nous prouverons au passage que le spectre de K-théorie non-connective de Tate(C) est équivalent à la suspension de celui de C, donnant une version infini-catégorique d'un résultat de Saito.Dans le dernier chapitre, nous traiterons d'un problème différent. Nous démontrerons l'existence d'une structure d'algèbre de Lie sur le tangent décalé de n'importe quel champ d'Artin dérivé X. Qui plus est, ce tangent agit sur tout quasi-cohérent E, l'action étant donnée par la classe d'Atiyah de E.Ces résultats sont par exemple valides dans le cas d'un schéma X sans hypothèse de lissité
If M is a symplectic manifold then the space of smooth loops C(S^1,M) inherits of a quasi-symplectic form. We will focus in this thesis on an algebraic analogue of that result.In their article, Kapranov and Vasserot introduced and studied the formal loop space of a scheme X. It is an algebraic version of the space of smooth loops in a differentiable manifold.We generalize their construction to higher dimensional loops. To any scheme X -- not necessarily smooth -- we associate L^d(X), the space of loops of dimension d. We prove it has a structure of (derived) Tate scheme -- ie its tangent is a Tate module: it is infinite dimensional but behaves nicely enough regarding duality.We also define the bubble space B^d(X), a variation of the loop space.We prove that B^d(X) is endowed with a natural symplectic form as soon as X has one.To prove our results, we develop a theory of Tate objects in a stable infinity category C. We also prove that the non-connective K-theory of Tate(C) is the suspension of that of C, giving an infinity categorical version of a result of Saito.The last chapter is aimed at a different problem: we prove there the existence of a Lie structure on the tangent of a derived Artin stack X. Moreover, any quasi-coherent module E on X is endowed with an action of this tangent Lie algebra through the Atiyah class of E. This in particular applies to not necessarily smooth schemes X
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Webber, Nicholas Jon. "Local tangent space approximation in canonical quantization." Thesis, Imperial College London, 1986. http://hdl.handle.net/10044/1/38183.

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Fahlaoui, Rachid. "Stabilité du fibré tangent des surfaces algébriques." Paris 11, 1989. http://www.theses.fr/1989PA112170.

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Cette thèse a pour sujet la stabilité du fibré tangent des surfaces algébriques. On y étudie les deux notions de stabilité, à savoir, la stabilité au sens de Mumford-Takemoto et la T­stabilité (ou stabilité au sens de Bogomolov). Pour les surfaces à fibré canonique (resp anti-canonique) positif, l'existence d'une métrique de Kähler-Einstein implique la semi­stabilité du fibré tangent par rapport à la classe canonique (resp anti-canonique). Si K est positif, une telle métrique existe, ce qui implique la K-semi-stabilité du fibré tangent. Ceci nous conduit à étudier le cas des surfaces à fibré canonique négatif. Nous donnons une démonstration algébrique valable en caractéristique quelconque, de la semi-stabilité du fibré tangent par rapport à la classe anti-canonique. Nous généralisons ce résultat aux surfaces à fibré canonique numériquement négatif vérifiant : si le rang du groupe de Picard de S est 9, alors le système linéaire anti­canonique est à modules variables. Puis nous passons à l'étude de la T-stabilité en distinguant trois cas : les surfaces elliptiques, les surfaces à première classe de Chern nulle et les surfaces géométriquement réglées. On caractérise celles dont le fibré tangent est T-semi-stable et dans les deux derniers cas celles dont le fibré tangent est T-stable
This thesis is concerned with the stability of the tangent bundle of algebraic surfaces. We consider two notions of stability: stability in the sense of Mumford-Takemoto and T-stability (Bogomolov stability). For surfaces with positive canonical (resp. Anti-canonical) bundle, the existence of a Kähler-Einstein metric implies the semi-stability of the tangent bundle with respect to the canonical (resp. Anti-canonical) class. If K is positive, such a metric exists, which implies K-semi-stability. This leads us to study the case of surfaces with negative canonical bundle. We give an algebraic proof, valid in any characteristic, of the semi-stability of the tangent bundle with respect to the canonical class. We generalize this result to surfaces with numerically negative canonical bundle satisfying: if the rank of the Picard group is nine, the anti-canonical linear system contains a singular semi-stable curve. Then we turn to T-stability, distinguishing three cases: elliptic surfaces, surfaces with vanishing first Chern class and geometrically ruled surfaces. We characterize the ones for which the tangent bundle is T-semi-stable and, in the last two cases, the ones for which the tangent bundle is T-stable
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Moerters, Peter. "Tangent measure distributions and the geometry of measures." Thesis, University College London (University of London), 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307661.

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Books on the topic "Tangent"

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Michel, Jacquelin, ed. L' art tangent. Arles: Actes sud, 2007.

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Dwayne, McDuffie, and Marz Ron, eds. Tangent: Superman's reign. New York: DC Comics, 2009.

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Patterson, Richard North. The Lasko tangent. Rockland, MA: Wheeler Pub., 2000.

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Jurgens, Dan. Tangent: Superman's reign. New York: DC Comics, 2009.

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1960-, Paiement Alain, and Amelunxen Hubertus von, eds. Tangent e: Alain Paiement. Montréal: Canadian Centre for Architecture, 2003.

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1953-, Brush Debra, and Samard Eileen, eds. History of Tangent, Oregon. Dallas, Tex: Curtis Media Corp., 1993.

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Settle, Ellis W. Ceremonies at Tangent Stone. Washington Depot, CT: Design to Printing, 1995.

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Rectifiable sets, densities and tangent measures. Zurich, Switzerland: European Mathematical Society, 2008.

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A simplified guide to custom stairbuilding and tangent handrailing. Fresno, CA: Linden Pub., 2000.

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A simplified guide to custom stairbuilding and tangent handrailing. Fresno, CA: Linden Pub., 1994.

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Book chapters on the topic "Tangent"

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Weik, Martin H. "tangent." In Computer Science and Communications Dictionary, 1734. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_19045.

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Casey, James. "Tangent." In Exploring Curvature, 100–112. Wiesbaden: Vieweg+Teubner Verlag, 1996. http://dx.doi.org/10.1007/978-3-322-80274-3_9.

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Khan, Akhtar A., Christiane Tammer, and Constantin Zălinescu. "Tangent Cones and Tangent Sets." In Vector Optimization, 109–211. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-54265-7_4.

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Russo, Francesco. "Tangent Cones, Tangent Spaces, Tangent Stars: Secant, Tangent, Tangent Star and Dual Varieties of an Algebraic Variety." In On the Geometry of Some Special Projective Varieties, 1–38. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-26765-4_1.

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Blair, David E. "Tangent Bundles and Tangent Sphere Bundles." In Riemannian Geometry of Contact and Symplectic Manifolds, 137–55. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4757-3604-5_9.

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Blair, David E. "Tangent Bundles and Tangent Sphere Bundles." In Riemannian Geometry of Contact and Symplectic Manifolds, 169–93. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4959-3_9.

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Dineen, Seán. "Tangent Planes." In Functions of Two Variables, 54–60. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-3250-1_8.

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Verruijt, Arnold. "Tangent Modulus." In An Introduction to Soil Mechanics, 109–14. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61185-3_13.

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Grøn, Øyvind, and Arne Næss. "Tangent vectors." In Einstein's Theory, 43–59. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0706-5_3.

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Sinha, Rajnikant. "Tangent Spaces." In Smooth Manifolds, 31–124. New Delhi: Springer India, 2014. http://dx.doi.org/10.1007/978-81-322-2104-3_2.

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Conference papers on the topic "Tangent"

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Onuma, Kensuke, Hanghang Tong, and Christos Faloutsos. "TANGENT." In the 15th ACM SIGKDD international conference. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1557019.1557093.

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Wong, Wai-Him, and Horace H. S. Ip. "Direction-dependent tangent: a new tangent representation." In IS&T/SPIE's Symposium on Electronic Imaging: Science & Technology, edited by Robert L. Stevenson and Sarah A. Rajala. SPIE, 1995. http://dx.doi.org/10.1117/12.205481.

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Mansouri, Behrooz, Shaurya Rohatgi, Douglas W. Oard, Jian Wu, C. Lee Giles, and Richard Zanibbi. "Tangent-CFT." In ICTIR '19: The 2019 ACM SIGIR International Conference on the Theory of Information Retrieval. New York, NY, USA: ACM, 2019. http://dx.doi.org/10.1145/3341981.3344235.

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Lee, Jianguo, Jingdong Wang, Changshui Zhang, and Zhaoqi Bian. "Probabilistic tangent subspace." In Twenty-first international conference. New York, New York, USA: ACM Press, 2004. http://dx.doi.org/10.1145/1015330.1015362.

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George, Phillip. "Tangent @ 23 X." In ACM SIGGRAPH 97 Visual Proceedings: The art and interdisciplinary programs of SIGGRAPH '97. New York, New York, USA: ACM Press, 1997. http://dx.doi.org/10.1145/259081.259129.

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George, Phillip. "Tangent @ 23 fire." In ACM SIGGRAPH 97 Visual Proceedings: The art and interdisciplinary programs of SIGGRAPH '97. New York, New York, USA: ACM Press, 1997. http://dx.doi.org/10.1145/259081.259130.

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Takano, Gaku, Makoto Obayashi, and Keisuke Uto. "Path planning for autonomous car to avoid moving obstacles by steering using tangent-arc-tangent-arc-tangent model." In 2015 IEEE Conference on Control Applications (CCA). IEEE, 2015. http://dx.doi.org/10.1109/cca.2015.7320855.

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Hunt, Thomas, and Arthur J. Krener. "Principal tangent data reduction." In 2009 IEEE International Conference on Control and Automation (ICCA). IEEE, 2009. http://dx.doi.org/10.1109/icca.2009.5410162.

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Boulakradeche, M., S. Ait Aoudia, D. Michelucci, A. Farouzi, and K. Taibouni. "Segmentation By Tangent Filter." In the Mediterranean Conference. New York, New York, USA: ACM Press, 2016. http://dx.doi.org/10.1145/3038884.3038889.

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Pasa, Luca, Nicolò Navarin, and Alessandro Sperduti. "Tangent Graph Convolutional Network." In ESANN 2021 - European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. Louvain-la-Neuve (Belgium): Ciaco - i6doc.com, 2021. http://dx.doi.org/10.14428/esann/2021.es2021-143.

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Reports on the topic "Tangent"

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Zinkle, S. J., and R. H. Goulding. Loss tangent measurements on unirradiated alumina. Office of Scientific and Technical Information (OSTI), April 1996. http://dx.doi.org/10.2172/270454.

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Munteanu, Marian Ioan. Old and New Structures on the Tangent Bundle. GIQ, 2012. http://dx.doi.org/10.7546/giq-8-2007-264-278.

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Bivas, Mira, Nadezhda Ribarska, and Mladen Valkov. Properties of Uniform Tangent Sets and Lagrange Multiplier Rule. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, July 2018. http://dx.doi.org/10.7546/crabs.2018.07.02.

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4

Miller, Arthur J., and Bruce D. Cornuelle. ROMS Tangent Linear and Adjoint Models: Testing and Applications. Fort Belvoir, VA: Defense Technical Information Center, October 2001. http://dx.doi.org/10.21236/ada390458.

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Moore, Andrew M. ROMS/TOMS Tangent Linear and Adjoint Models:Testing and Applications. Fort Belvoir, VA: Defense Technical Information Center, September 2002. http://dx.doi.org/10.21236/ada626935.

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6

Arango, Hernan G. ROMS Tangent Linear and Adjoint Models: Testing and Applications. Fort Belvoir, VA: Defense Technical Information Center, September 2001. http://dx.doi.org/10.21236/ada625256.

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Miller, Arthur J., and Bruce D. Cornuelle. ROMS Tangent Linear and Adjoint Models: Testing and Applications. Fort Belvoir, VA: Defense Technical Information Center, September 2001. http://dx.doi.org/10.21236/ada625422.

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Miller, Arthur J., and Bruce D. Cornuelle. ROMS/TOMS Tangent Linear and Adjoint Models: Testing and Applications. Fort Belvoir, VA: Defense Technical Information Center, January 2004. http://dx.doi.org/10.21236/ada432421.

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9

Arango, Hernan G. ROMS/TOMS Tangent Linear and Adjoint Models: Testing and Applications. Fort Belvoir, VA: Defense Technical Information Center, September 2006. http://dx.doi.org/10.21236/ada630975.

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Miller, Arthur J., Bruce D. Cornuelle, and Andrew M. Moore. ROMS/TOMS Tangent Linear and Adjoint Models: Testing and Applications. Fort Belvoir, VA: Defense Technical Information Center, September 2003. http://dx.doi.org/10.21236/ada620406.

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