Edit Profile Bishop, Richard L. Compute Distance To: Compute Author ID: bishop.richard-l Published as: Bishop, R.; Bishop, R. L.; Bishop, Richard; Bishop, Richard L. External Links: MGP · Wikidata · GND Documents Indexed: 48 Publications since 1963, including 4 Books all top 5 Co-Authors 11 single-authored 24 Alexander, Stephanie B. 8 Goldberg, Samuel I. 5 Berg, I. David 3 Crittenden, Richard J. 2 Ghrist, Robert W. 1 Menn, Michael 1 O’Neill, Barrett all top 5 Serials 4 Transactions of the American Mathematical Society 3 Geometriae Dedicata 3 Proceedings of the American Mathematical Society 2 American Mathematical Monthly 2 Advances in Mathematics 2 Illinois Journal of Mathematics 2 Indiana University Mathematics Journal 2 Journal of Differential Geometry 2 Manuscripta Mathematica 2 Michigan Mathematical Journal 2 Tohoku Mathematical Journal. Second Series 2 L’Enseignement Mathématique. 2e Série 1 Mathematics Magazine 1 Canadian Journal of Mathematics 1 Mathematische Annalen 1 Pacific Journal of Mathematics 1 Tensor. New Series 1 Annals of Global Analysis and Geometry 1 Differential Geometry and its Applications 1 Geometric and Functional Analysis. GAFA 1 Proceedings of the National Academy of Sciences of the United States of America 1 Communications in Analysis and Geometry 1 Regular and Chaotic Dynamics 1 Bulletin of the American Mathematical Society 1 International Electronic Journal of Geometry all top 5 Fields 35 Differential geometry (53-XX) 3 Convex and discrete geometry (52-XX) 2 Geometry (51-XX) 2 Manifolds and cell complexes (57-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 45 Publications have been cited 1,170 times in 1,078 Documents Cited by ▼ Year ▼ Manifolds of negative curvature. Zbl 0191.52002Bishop, R. L.; O’Neill, B. 289 1969 Geometry of manifolds. (Pure and Applied Mathematics. Vol. 15). Zbl 0132.16003Bishop, R. L.; Crittenden, R. J. 288 1964 There is more than one way to frame a curve. Zbl 0298.53001Bishop, Richard L. 149 1975 Tensor analysis on manifolds. Zbl 0218.53021Bishop, R. L.; Goldberg, S. I. 72 1968 Geometry of manifolds. Reprint of the 1964 original. Zbl 0984.53001Bishop, Richard L.; Crittenden, Richard J. 65 2001 On the second cohomology group of a Kaehler manifold of positive curvature. Zbl 0125.39403Bishop, R. L.; Goldberg, S. I. 25 1965 The Hadamard-Cartan theorem in locally convex metric spaces. Zbl 0718.53055Alexander, Stephanie B.; Bishop, Richard L. 24 1990 Some implications of the generalized Gauss-Bonnet theorem. Zbl 0133.15101Bishop, R. L.; Goldberg, S. I. 24 1964 The Riemannian obstacle problem. Zbl 0625.53045Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L. 17 1987 Comparison theorems for curves of bounded geodesic curvature in metric spaces of curvature bounded above. Zbl 0859.53053Alexander, Stephanie B.; Bishop, Richard L. 16 1996 Decomposition of cut loci. Zbl 0373.53019Bishop, Richard L. 15 1977 Geometry of manifolds. Zbl 0146.43304Bishop, R. L.; Crittenden, R. J. 14 1967 Curvature bounds for warped products of metric spaces. Zbl 1087.53064Alexander, S. B.; Bishop, R. L. 13 2004 Geometric curvature bounds in Riemannian manifolds with boundary. Zbl 0793.53039Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L. 13 1993 Capture pursuit games on unbounded domains. Zbl 1177.91048Alexander, S.; Bishop, R.; Ghrist, R. 12 2009 Total curvature and simple pursuit on domains of curvature bounded above. Zbl 1210.53008Alexander, S.; Bishop, R.; Ghrist, R. 9 2010 Warped products of Hadamard spaces. Zbl 0909.53050Alexander, Stephanie B.; Bishop, Richard L. 9 1998 Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above. Zbl 1094.53073Alexander, Stephanie B.; Bishop, Richard L. 8 2006 Infinitesimal convexity implies local convexity. Zbl 0268.53011Bishop, Richard L. 8 1974 Characterizing motions by unit distance invariance. Zbl 0262.50001Bishop, Richard L. 8 1973 On the topology of positively curved Kaehler manifolds. II. Zbl 0134.17906Bishop, R. L.; Goldberg, S. I. 8 1965 Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds. Zbl 1149.53040Alexander, Stephanie B.; Bishop, Richard L. 7 2008 A cone splitting theorem for Alexandrov spaces. Zbl 1125.53023Alexander, Stephanie B.; Bishop, Richard L. 7 2005 \(\mathcal FK\)-convex functions on metric spaces. Zbl 1020.53049Alexander, Stephanie; Bishop, Richard L. 6 2003 Thin Riemannian manifolds with boundary. Zbl 0923.53013Alexander, Stephanie B.; Bishop, Richard L. 6 1998 Clairaut submersions. Zbl 0246.53048Bishop, R. L. 6 1972 The holonomy algebra of immersed manifolds of codimension two. Zbl 0177.50101Bishop, R. L. 6 1968 On the topology of positively curved Kaehler manifolds. Zbl 0116.38802Bishop, R. L.; Goldberg, S. I. 6 1963 On conformally flat spaces with commuting curvature and Ricci transformations. Zbl 0246.53046Bishop, R. L.; Goldberg, S. I. 5 1972 The Fary-Milnor theorem in Hadamard manifolds. Zbl 0911.57007Alexander, Stephanie B.; Bishop, Richard L. 4 1998 Infinitesimal convexity implies local convexity. Zbl 0281.53010Bishop, Richard L. 4 1974 Spines and homology of thin Riemannian manifolds with boundary. Zbl 0992.53026Alexander, Stephanie B.; Bishop, Richard L. 3 2000 Cauchy uniqueness in the Riemannian obstacle problem. Zbl 0621.53036Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L. 3 1986 A characterization of the Euclidean sphere. Zbl 0136.18703Bishop, R. L.; Goldberg, S. I. 3 1966 Warped products admitting a curvature bound. Zbl 1352.53027Alexander, Stephanie B.; Bishop, Richard L. 2 2016 Extrinsic curvature of semiconvex subspaces in Alexandrov geometry. Zbl 1190.53073Alexander, Stephanie B.; Bishop, Richard L. 2 2010 The intrinsic geometry of a Jordan domain. Zbl 1170.53059Bishop, Richard L. 2 2008 Circular billiard tables, conjugate loci, and a cardioid. Zbl 1023.37020Bishop, R. L. 2 2003 Spines and topology of thin Riemannian manifolds. Zbl 1035.53047Alexander, Stephanie B.; Bishop, Richard L. 2 2003 Racetracks and extremal problems for curves of bounded curvature in metric spaces. Zbl 0920.53019Alexander, Stephanie B.; Bishop, Richard L. 2 1997 Convex-supporting domains on spheres. Zbl 0272.53026Alexander, S.; Bishop, R. L. 2 1974 Cut loci, minimizers, and wavefronts in Riemannian manifolds with boundary. Zbl 0817.53023Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L. 1 1993 An infinitesimal cylindricity theorem. Zbl 0508.53059Bishop, Richard L. 1 1982 Generic surfaces in \(E^4\). Zbl 0295.53031Bishop, Richard L.; Menn, Michael 1 1975 On curvature and Euler-Poincaré characteristic. Zbl 0173.49805Bishop, R. L.; Goldberg, S. I. 1 1963 Warped products admitting a curvature bound. Zbl 1352.53027Alexander, Stephanie B.; Bishop, Richard L. 2 2016 Total curvature and simple pursuit on domains of curvature bounded above. Zbl 1210.53008Alexander, S.; Bishop, R.; Ghrist, R. 9 2010 Extrinsic curvature of semiconvex subspaces in Alexandrov geometry. Zbl 1190.53073Alexander, Stephanie B.; Bishop, Richard L. 2 2010 Capture pursuit games on unbounded domains. Zbl 1177.91048Alexander, S.; Bishop, R.; Ghrist, R. 12 2009 Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds. Zbl 1149.53040Alexander, Stephanie B.; Bishop, Richard L. 7 2008 The intrinsic geometry of a Jordan domain. Zbl 1170.53059Bishop, Richard L. 2 2008 Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above. Zbl 1094.53073Alexander, Stephanie B.; Bishop, Richard L. 8 2006 A cone splitting theorem for Alexandrov spaces. Zbl 1125.53023Alexander, Stephanie B.; Bishop, Richard L. 7 2005 Curvature bounds for warped products of metric spaces. Zbl 1087.53064Alexander, S. B.; Bishop, R. L. 13 2004 \(\mathcal FK\)-convex functions on metric spaces. Zbl 1020.53049Alexander, Stephanie; Bishop, Richard L. 6 2003 Circular billiard tables, conjugate loci, and a cardioid. Zbl 1023.37020Bishop, R. L. 2 2003 Spines and topology of thin Riemannian manifolds. Zbl 1035.53047Alexander, Stephanie B.; Bishop, Richard L. 2 2003 Geometry of manifolds. Reprint of the 1964 original. Zbl 0984.53001Bishop, Richard L.; Crittenden, Richard J. 65 2001 Spines and homology of thin Riemannian manifolds with boundary. Zbl 0992.53026Alexander, Stephanie B.; Bishop, Richard L. 3 2000 Warped products of Hadamard spaces. Zbl 0909.53050Alexander, Stephanie B.; Bishop, Richard L. 9 1998 Thin Riemannian manifolds with boundary. Zbl 0923.53013Alexander, Stephanie B.; Bishop, Richard L. 6 1998 The Fary-Milnor theorem in Hadamard manifolds. Zbl 0911.57007Alexander, Stephanie B.; Bishop, Richard L. 4 1998 Racetracks and extremal problems for curves of bounded curvature in metric spaces. Zbl 0920.53019Alexander, Stephanie B.; Bishop, Richard L. 2 1997 Comparison theorems for curves of bounded geodesic curvature in metric spaces of curvature bounded above. Zbl 0859.53053Alexander, Stephanie B.; Bishop, Richard L. 16 1996 Geometric curvature bounds in Riemannian manifolds with boundary. Zbl 0793.53039Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L. 13 1993 Cut loci, minimizers, and wavefronts in Riemannian manifolds with boundary. Zbl 0817.53023Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L. 1 1993 The Hadamard-Cartan theorem in locally convex metric spaces. Zbl 0718.53055Alexander, Stephanie B.; Bishop, Richard L. 24 1990 The Riemannian obstacle problem. Zbl 0625.53045Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L. 17 1987 Cauchy uniqueness in the Riemannian obstacle problem. Zbl 0621.53036Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L. 3 1986 An infinitesimal cylindricity theorem. Zbl 0508.53059Bishop, Richard L. 1 1982 Decomposition of cut loci. Zbl 0373.53019Bishop, Richard L. 15 1977 There is more than one way to frame a curve. Zbl 0298.53001Bishop, Richard L. 149 1975 Generic surfaces in \(E^4\). Zbl 0295.53031Bishop, Richard L.; Menn, Michael 1 1975 Infinitesimal convexity implies local convexity. Zbl 0268.53011Bishop, Richard L. 8 1974 Infinitesimal convexity implies local convexity. Zbl 0281.53010Bishop, Richard L. 4 1974 Convex-supporting domains on spheres. Zbl 0272.53026Alexander, S.; Bishop, R. L. 2 1974 Characterizing motions by unit distance invariance. Zbl 0262.50001Bishop, Richard L. 8 1973 Clairaut submersions. Zbl 0246.53048Bishop, R. L. 6 1972 On conformally flat spaces with commuting curvature and Ricci transformations. Zbl 0246.53046Bishop, R. L.; Goldberg, S. I. 5 1972 Manifolds of negative curvature. Zbl 0191.52002Bishop, R. L.; O’Neill, B. 289 1969 Tensor analysis on manifolds. Zbl 0218.53021Bishop, R. L.; Goldberg, S. I. 72 1968 The holonomy algebra of immersed manifolds of codimension two. Zbl 0177.50101Bishop, R. L. 6 1968 Geometry of manifolds. Zbl 0146.43304Bishop, R. L.; Crittenden, R. J. 14 1967 A characterization of the Euclidean sphere. Zbl 0136.18703Bishop, R. L.; Goldberg, S. I. 3 1966 On the second cohomology group of a Kaehler manifold of positive curvature. Zbl 0125.39403Bishop, R. L.; Goldberg, S. I. 25 1965 On the topology of positively curved Kaehler manifolds. II. Zbl 0134.17906Bishop, R. L.; Goldberg, S. I. 8 1965 Geometry of manifolds. (Pure and Applied Mathematics. Vol. 15). Zbl 0132.16003Bishop, R. L.; Crittenden, R. J. 288 1964 Some implications of the generalized Gauss-Bonnet theorem. Zbl 0133.15101Bishop, R. L.; Goldberg, S. I. 24 1964 On the topology of positively curved Kaehler manifolds. Zbl 0116.38802Bishop, R. L.; Goldberg, S. I. 6 1963 On curvature and Euler-Poincaré characteristic. Zbl 0173.49805Bishop, R. L.; Goldberg, S. I. 1 1963 all cited Publications top 5 cited Publications all top 5 Cited by 1,299 Authors 20 Siraj-Uddin 18 Farouki, Rida T. 13 Al-Solamy, Falleh Rijaullah 13 Korpinar, Talat 12 Bishop, Richard L. 11 Donnelly, Harold 10 Alexander, Stephanie B. 9 Ali, Akram 9 Eberlein, Patrick B. 8 Khan, Meraj Ali 8 Schröder, Viktor M. H. 8 Turhan, Essin 7 Gliklikh, Yuriĭ Evgen’evich 7 Lytchak, Alexander 6 Ehrlich, Paul Ewing 6 Goldberg, Samuel I. 6 Greene, Robert Everist 6 Han, Chang Yong 6 Petrunin, Anton Mikhailovich 6 Sestini, Alessandra 6 Takahashi, Masatomo 6 Ünal, Bülent 6 Yau, Shing-Tung 5 Anco, Stephen C. 5 Giannelli, Carlotta 5 Moore, John Douglas 5 Noronha, Maria Helena 5 Pişcoran, Laurian-Ioan 5 Sánchez Caja, Miguel 5 Shenawy, Sameh 5 Tanno, Shukichi 5 Yayli, Yusuf 4 Alkhaldi, Ali H. 4 Berestovskiĭ, Valeriĭ Nikolaevich 4 Chen, Bang-Yen 4 Chen, Su-Shing 4 Dobarro, Fernando Ruben 4 Gomes, José Nazareno Vieira 4 Gray, Alfred 4 Haji-Badali, Ali 4 Holopainen, Ilkka 4 Hurder, Steven E. 4 Kendall, Wilfrid S. 4 Loboda, Alexander Vasil’evich 4 Nešović, Emilija 4 Ni, Lei 4 Othman, Wan Ainun Mior 4 Ṣahin, Bayram 4 Shiohama, Katsuhiro 4 Stadler, Stephan 4 Wu, Hung-Hsi 4 Yamaguchi, Takao 3 Abresch, Uwe 3 Adachi, Toshiaki 3 Alghanemi, Azeb 3 Anderson, Michael T. 3 Atçeken, Mehmet 3 Ballmann, Hans Werner 3 Bangert, Victor 3 Borisenko, Aleksandr Andreevich 3 Cao, Huai-Dong 3 Clark, Alex 3 da Silva, Luiz Carlos Barbosa 3 Faghfouri, Morteza 3 Foertsch, Thomas 3 Galloway, Gregory J. 3 Goriely, Alain 3 Grant, James D. E. 3 Honda, Shun’ichi 3 Hui, Shyamal Kumar 3 Ibragimov, Gafurjan I. 3 Iliev, Bozhidar Zakhariev 3 Itokawa, Yoe 3 Jost, Jürgen 3 Kalish, Diane 3 Karp, Leon 3 Kasue, Atsushi 3 Kawakubo, Satoshi 3 Ketterer, Christian 3 Khan, Viqar Azam 3 Kisi, İlim 3 Kunzinger, Michael 3 Kuzminykh, Alexandr V. 3 Lohoué, Noël 3 Lumiste, Ülo 3 Meyer, Daniel 3 Miquel, Vicente 3 Naghi, Monia Fouad 3 Ontaneda, Pedro 3 Ozel, Cenap 3 Öztürk, Günay 3 Pahan, Sampa 3 Panoskaltsis, Vassilis P. 3 Panov, Dmitri Alekseevich 3 Petrov, Nikolaĭ Nikandrovich 3 Rapcsák, Tamás 3 Sakai, Takashi 3 Sakkalis, Takis 3 Sämann, Clemens 3 Sariaydin, Muhammed Talat ...and 1,199 more Authors all top 5 Cited in 289 Serials 52 Proceedings of the American Mathematical Society 50 Transactions of the American Mathematical Society 33 Journal of Geometry and Physics 28 Mathematische Annalen 27 Mathematische Zeitschrift 25 International Journal of Geometric Methods in Modern Physics 24 Geometriae Dedicata 22 The Journal of Geometric Analysis 20 Tohoku Mathematical Journal. Second Series 20 Differential Geometry and its Applications 17 Annals of Global Analysis and Geometry 16 Inventiones Mathematicae 15 Journal of Mathematical Analysis and Applications 15 Journal of Geometry 14 Journal of Functional Analysis 13 Advances in Mathematics 13 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 13 Archiv der Mathematik 12 General Relativity and Gravitation 12 Duke Mathematical Journal 11 Computer Aided Geometric Design 11 Geometry & Topology 11 Boletim da Sociedade Paranaense de Matemática. Terceira Série 10 Communications in Mathematical Physics 10 Compositio Mathematica 10 Siberian Mathematical Journal 9 International Journal of Theoretical Physics 9 Journal of Soviet Mathematics 9 Manuscripta Mathematica 8 Kodai Mathematical Journal 8 Bulletin of the American Mathematical Society 7 Mathematical Notes 7 Reports on Mathematical Physics 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Journal of Mathematical Sciences (New York) 7 Kodai Mathematical Seminar Reports 6 Acta Mechanica 6 Archive for Rational Mechanics and Analysis 6 Israel Journal of Mathematics 6 Annales de l’Institut Fourier 6 Czechoslovak Mathematical Journal 6 Publications Mathématiques 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Results in Mathematics 6 Calculus of Variations and Partial Differential Equations 6 Abstract and Applied Analysis 6 Mediterranean Journal of Mathematics 5 Periodica Mathematica Hungarica 5 Journal of Optimization Theory and Applications 5 Journal of the American Mathematical Society 5 Journal of Elasticity 5 Journal of the Egyptian Mathematical Society 5 Mathematical Problems in Engineering 5 Acta Mathematica Sinica. English Series 5 Dynamic Games and Applications 4 Computer Methods in Applied Mechanics and Engineering 4 Acta Mathematica 4 Journal of Differential Equations 4 Proceedings of the Japan Academy. Series A 4 Acta Applicandae Mathematicae 4 Physica D 4 Russian Mathematics 4 Turkish Journal of Mathematics 4 Journal of Inequalities and Applications 3 Journal of Computational Physics 3 Journal of Mathematical Physics 3 Reviews in Mathematical Physics 3 Chaos, Solitons and Fractals 3 Applied Mathematics and Computation 3 Automatica 3 Bulletin de la Société Mathématique de France 3 International Journal of Mathematics and Mathematical Sciences 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Tokyo Journal of Mathematics 3 Topology and its Applications 3 Acta Mathematica Hungarica 3 Journal of Symbolic Computation 3 Revista Matemática Iberoamericana 3 Journal of Global Optimization 3 Annals of Physics 3 Linear Algebra and its Applications 3 Bulletin of the American Mathematical Society. New Series 3 St. Petersburg Mathematical Journal 3 Advances in Applied Clifford Algebras 3 Advances in Computational Mathematics 3 Annales Henri Poincaré 3 Journal of Nonlinear Mathematical Physics 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Proceedings of the Japan Academy 3 Advances in Mathematical Physics 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 Afrika Matematika 2 Journal of Applied Mathematics and Mechanics 2 Journal of Fluid Mechanics 2 Journal of Mathematical Biology 2 Letters in Mathematical Physics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Physics Letters. A ...and 189 more Serials all top 5 Cited in 56 Fields 777 Differential geometry (53-XX) 201 Global analysis, analysis on manifolds (58-XX) 80 Partial differential equations (35-XX) 74 Manifolds and cell complexes (57-XX) 44 Dynamical systems and ergodic theory (37-XX) 43 Relativity and gravitational theory (83-XX) 37 Numerical analysis (65-XX) 33 Mechanics of deformable solids (74-XX) 31 Probability theory and stochastic processes (60-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 30 Quantum theory (81-XX) 29 Several complex variables and analytic spaces (32-XX) 25 Convex and discrete geometry (52-XX) 24 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 22 Topological groups, Lie groups (22-XX) 22 Geometry (51-XX) 21 Mechanics of particles and systems (70-XX) 20 Algebraic topology (55-XX) 20 Computer science (68-XX) 18 Potential theory (31-XX) 17 Group theory and generalizations (20-XX) 15 Algebraic geometry (14-XX) 15 Operations research, mathematical programming (90-XX) 15 Systems theory; control (93-XX) 14 Ordinary differential equations (34-XX) 13 Fluid mechanics (76-XX) 12 Operator theory (47-XX) 10 Functions of a complex variable (30-XX) 10 Optics, electromagnetic theory (78-XX) 10 Biology and other natural sciences (92-XX) 9 General topology (54-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Abstract harmonic analysis (43-XX) 7 Statistics (62-XX) 6 Nonassociative rings and algebras (17-XX) 6 Real functions (26-XX) 6 Measure and integration (28-XX) 5 Information and communication theory, circuits (94-XX) 4 Functional analysis (46-XX) 3 History and biography (01-XX) 3 Approximations and expansions (41-XX) 2 General and overarching topics; collections (00-XX) 2 Number theory (11-XX) 2 Difference and functional equations (39-XX) 2 Integral transforms, operational calculus (44-XX) 2 Astronomy and astrophysics (85-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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