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 Total publications: 75 (75) in MathSciNet: 72 (72) in zbMATH: 58 (58) in Web of Science: 40 (40) in Scopus: 49 (49) Cited articles: 65 Citations in Math-Net.Ru: 165 Citations in MathSciNet (by Sep 2017): 270 Citations in Web of Science: 170 Citations in Scopus: 216

 Number of views: This page: 4850 Abstract pages: 7329 Full texts: 2005 References: 414
Professor
Doctor of physico-mathematical sciences (2004)
Speciality: 01.01.04 (Geometry and topology)
Birth date: 6.05.1971
E-mail:
Keywords: integral mean value theorems, integral inequalities with deviating argument, convex geometry, differential geometry, global Riemannian geometry, homogeneous spaces, Einstein homogeneous manifolds, geodesic orbit spaces, Killing vector fields of constant length.
UDC: 511.26, 512.812, 513, 514, 514.74, 514.752.7, 514.76, 514.765, 515.143, 515.143.28, 517, 517.26, 517.383, 517.98, 514.752.22
MSC: 52A, 52B, 53C25, 53C30, 26A24

Subject:

A positive solution of V. K. Ionin's conjecture was obtained. Namely, let $f$ be a continuous real-valued function defined on the segment $[0,1]$. For all $x\in(0,1]$, consider a value $\xi(x)$ that is the maximum of $\tau\in[0,x]$ with the property $xf(\tau)=\int_0^xf(t)\,dt$. Then $\varlimsup_{x\to 0}\frac{\xi(x)}{x}\ge\frac{1}{e}$. Some generalizations of this result are obtained (particularly, in a joint paper with V. V. Ivanov). Some problems of convex geometry are solved. New examples of Einstein homogeneous metrics are found with using various methods. Compact seven-dimensional and non-compact five-dimensional homogeneous Einstein manifolds are classified. The classes of $\delta$-homogeneous and Clifford-Wolf homogeneous Riemannian manifolds are studied, in particular, the classification of simply connected Clifford-Wolf homogeneous Riemannian manifolds is obtained (joint with V. N. Berestovskii). The structure of geodesic orbit Riemannian spaces is studied. The classification of simply connected compact geodesic orbit spaces of positive Euler characteristic is obtained (joint with D. V. Alekseevsky). The classification of generalized Wallach spaces is obtained. The structure of Killing vector fields of constant length on compact homogeneous Riemennian manifolds is studied.

Biography

Graduated from Faculty of Mathematics and Mechanics of Novosibirsk State University (NSU) in 1993 (department of mathematical analysis). Ph. D. thesis was defended in 1995, Doctor of Science thesis was defended in 2004. The list of my publications contains more than 70 titles.

Main publications:
1. Ivanov V. V., Nikonorov Yu. G., “Asymptotic behavior of the Lagrange points in the Taylor formula”, Siberian Math. J., 36:1 (1995), 78–83
2. Nikonorov Yu. G., “Compact homogeneous Einstein 7-manifolds”, Geom. Dedicata, 109 (2004), 7–30
3. Nikonorov Yu. G., “Noncompact homogeneous Einstein 5-manifolds”, Geom. Dedicata, 113:1 (2005), 107–143
4. Berestovskii V. N., Nikonorov Yu. G., “On $\delta$-homogeneous Riemannian manifolds”, Differential Geom. Appl., 26:5 (2008), 514–535
5. Berestovskii V. N., Nikonorov Yu. G., “Clifford-Wolf homogeneous Riemannian manifolds”, J. Differ. Geometry, 82:3 (2009), 467–500

http://www.mathnet.ru/eng/person17720
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http://zbmath.org/authors/?q=ai:nikonorov.yurii-g
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http://orcid.org/0000-0002-9671-2314
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http://arxiv.org/a/nikonorov_y_1

Full list of publications:
 | by years | by types | by times cited | scientific publications | common list |

 2017 1. Z. Chen, Yu. G. Nikonorov, Yu. V. Nikonorova, “Invariant Einstein metrics on Ledger–Obata spaces”, Differential Geometry and its Applications, 50 (2017), 71–87         (cited: 1)   (cited: 1) 2. Yu. G. Nikonorov, “On the structure of geodesic orbit Riemannian spaces”, Ann. Glob. Anal. Geom., 52:3 (2017), 289–311 2016 3. Yu. G. Nikonorov, “Classification of generalized Wallach spaces”, Geometriae Dedicata, 181:1 (2016), 193–212     (cited: 4)     (cited: 6)   (cited: 5) 4. N. A. Abiev, Yu. G. Nikonorov, “The evolution of positively curved invariant Riemannian metrics on the Wallach spaces under the Ricci flow”, Ann. Glob. Anal. Geom., 50:1 (2016), 65–84     (cited: 1) 2015 5. Y. Nikolayevsky, Yu. G. Nikonorov, “On solvable Lie group of negative Ricci curvature”, Mathematische Zeitschrift, 280:1–2 (2015), 1–16     (cited: 1)     (cited: 3)   (cited: 3) 6. Yu. G. Nikonorov, “Killing vector fields of constant length on compact homogeneous Riemannian manifolds”, Ann. Glob. Anal. Geom., 48:4 (2015), 305–330         (cited: 1)   (cited: 1)   (cited: 1) 7. Yu. G. Nikonorov, Asymptotics of the mean value points, SMI VSC RAS, Vladikavkaz, 2015 , 200 pp. 2014 8. V. N. Berestovskii, Yu. G. Nikonorov, “Generalized normal homogeneous Riemannian metrics on spheres and projective spaces”, Ann. Glob. Anal. Geom., 45:3 (2014), 167–196     (cited: 2)     (cited: 3)   (cited: 2)   (cited: 2) 9. Yu. G. Nikonorov, “Asimptotika tochek srednego znacheniya v teoreme Shvartsa dlya razdelennykh raznostei”, Matem. tr., 17:1 (2014), 145–174   (cited: 1)   (cited: 1)     (cited: 5)  ; Yu. G. Nikonorov, “Asymptotics of mean value points in the Schwarz theorem for divided differences”, Siberian Adv. Math., 25:1 (2015), 56–75 10. Yu. G. Nikonorov, “Negative eigenvalues of the Ricci operator of solvable metric Lie algebras”, Geometriae Dedicata, 170:1 (2014), 119–133     (cited: 1)     (cited: 2)   (cited: 1)   (cited: 2) 11. N. A. Abiev, A. Arvanitoyeorgos, Yu. G. Nikonorov, P. Siasos, “The dynamics of the Ricci flow on generalized Wallach spaces”, Differential Geometry and its Applications, 35:Supplement (2014), 26–43     (cited: 3)     (cited: 7)   (cited: 7) 12. N. A. Abiev, A. Arvanitoyeorgos, Yu. G. Nikonorov, P. Siasos, “The Ricci flow on some generalized Wallach spaces”, Geometry and its Applications, Springer Proceedings in Mathematics & Statistics, Vol. 72, eds. V. Rovenski, P. Walczak, Springer, 2014, 3–37     (cited: 3)     (cited: 4) 13. N. V. Abrosimov, E. Makai, Jr., A. D. Mednih, Yu. G. Nikonorov, G. Rote, “The infinum of the volumes of convex polytops of any given facet areas is $0$”, Studia Scientiarum Mathematicarum Hungarica, 51:4 (2014), 466–519         (cited: 1) 14. Yu. G. Nikonorov, “Teorema Peano i tochki komplanarnosti prostranstvennykh krivykh”, Matem. tr., 17:2 (2014), 163–183      ; Yu. G. Nikonorov, “Peano's theorem and coplanarity points of space curves”, Siberian Adv. Math., 25, No 2, 124–137 (2015), Siberian Adv. Math., 25:2 (2015), 124–137 2013 15. Yu. G. Nikonorov, “Vektornye polya Killinga i tenzor krivizny rimanova mnogoobraziya”, Matem. tr., 16:1 (2013), 141–149        ; Yu. G. Nikonorov, “Killing vector fields and the curvature tensor of a Riemannian manifold”, Siberian Adv. Math., 24:3 (2014), 187–192 16. Yu. G. Nikonorov, “Geodesic orbit manifolds and Killing fields of constant length”, Hiroshima Math. J., 43:1 (2013), 129–137 Project Euclid   (cited: 1)     (cited: 2)   (cited: 1)   (cited: 2) 17. Yu. G. Nikonorov, “Geodesic orbit Riemannian metrics on spheres”, Vladikavkaz. Mat. Zh., 15:3 (2013), 67-76   (cited: 1) 2012 18. Yu. G. Nikonorov, “Asymptotic behavior of support points for planar curves”, J. Math. Anal. Appl., 391:1 (2012), 147–158     (cited: 2)       (cited: 8)   (cited: 2) 19. Yu. G. Nikonorov, “Dvoinoe eksponentsialnoe otobrazhenie na simmetricheskikh prostranstvakh”, Matem. tr., 15:1 (2012), 141–154       (cited: 5); Yu. G. Nikonorov, “Double exponential map on symmetric spaces”, Siberian Adv. Math., 23:3 (2013), 210–218 20. V. N. Berestovskii, Yu. G. Nikonorov, Riemannian manifolds and homogeneous geodesics, SMI VSC RAS, Vladikavkaz, 2012 , 414 pp. 21. Yu. G. Nikonorov, M. S. Chebarykov, “Operator Richchi vpolne razreshimykh metricheskikh algebr Li”, Matem. tr., 15:2 (2012), 146–158   (cited: 2)   (cited: 2)  ; Yu. G. Nikonorov, M. S. Chebarykov, “The Ricci operator of completely solvable metric Lie algebras”, Siberian Adv. Math., 24:1 (2014), 18–25 2011 22. Yu. G. Nikonorov, “Asimptotika tochek kasaniya ploskikh krivykh”, Matem. tr., 14:1 (2011), 141–157   (cited: 3)   (cited: 3)   (cited: 5); Yu. G. Nikonorov, “Asymptotics of tangent points for planar curves”, Siberian Adv. Math., 22:3 (2012), 192–203 23. V. N. Berestovskii, E. V. Nikitenko, Yu. G. Nikonorov, “Classification of generalized normal homogeneous Riemannian manifolds of positive Euler characteristic”, Differential Geometry and its Applications, 29:4 (2011), 533–546     (cited: 4)     (cited: 4)   (cited: 4) 24. Yu. G. Nikonorov, Yu. V. Nikonorova, “On an approach to the solution of the J. W. Fickett problem of overlapping congruent polygons”, Vladikavkaz. Mat. Zh., 13:4 (2011), 52–59 2009 25. A. G. Kremlev, Yu. G. Nikonorov, “Signatura krivizny Richchi levoinvariantnykh rimanovykh metrik na chetyrekhmernykh gruppakh Li. Neunimodulyarnyi sluchai”, Matem. tr., 12:1 (2009), 40–116   (cited: 16)   (cited: 4)   (cited: 30); A. G. Kremlyov, Yu. G. Nikonorov, “The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case”, Siberian Adv. Math., 20:1 (2010), 1–57       (cited: 4)   (cited: 6) 26. Dmitrii V. Alekseevsky, Yurii G. Nikonorov, “Compact Riemannian Manifolds with Homogeneous Geodesics”, SIGMA, 5 (2009), 93–16   (cited: 11)     (cited: 8)   (cited: 9)   (cited: 10) 27. V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta$-homogeneous Riemannian manifolds. II”, Siberian Math. J., 50:2 (2009), 214–222           (cited: 6)   (cited: 10)   (cited: 10)   (cited: 7) 28. V. N. Berestovskii, Yu. G. Nikonorov, “Clifford-Wolf homogeneous Riemannian manifolds”, Journal of Differential Geometry, 82:3 (2009), 467–500 Project Euclid   (cited: 17)     (cited: 17)   (cited: 20) 29. A. Arvanitoyeorgos, V. V. Dzhepko, Yu. G. Nikonorov, “Invariant Einstein metrics on some homogeneous spaces of classical Lie groups”, Canadian Journal of Mathematics, 61:6 (2009), 1201–1213     (cited: 6)     (cited: 5)   (cited: 5) 2008 30. A. G. Kremlev, Yu. G. Nikonorov, “Signatura krivizny Richchi levoinvariantnykh rimanovykh metrik na chetyrekhmernykh gruppakh Li. Unimodulyarnyi sluchai”, Matem. tr., 11:2 (2008), 115–147   (cited: 19)   (cited: 6)   (cited: 35); A. G. Kremlyov, Yu. G. Nikonorov, “The Signature of the Ricci Curvature of Left-Invariant Riemannian Metrics on Four-Dimensional Lie Groups. The Unimodular Case”, Siberian Adv. Math., 19:4 (2009), 245–267       (cited: 3)   (cited: 5) 31. V. N. Berestovskii, Yu. G. Nikonorov, “Killing vector fields of constant length on Riemannian manifolds”, Siberian Math. J., 49:3 (2008), 395–407           (cited: 18)   (cited: 15)   (cited: 15)   (cited: 20) 32. V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta$-homogeneous Riemannian manifolds”, Differential Geometry and its Applications, 26:5 (2008), 514–535     (cited: 19)   (cited: 18)   (cited: 18) 33. Yu. G. Nikonorov, Yu. V. Nikonorova, “The intrinsic diameter of the surface of a parallelepiped”, Discrete and Computational Geometry, 40:4 (2008), 504–527     (cited: 2)     (cited: 2)   (cited: 2) 34. A. Arvanitoyeorgos, V. V. Dzhepko, Yu. G. Nikonorov, “Invariant Einstein metrics on certain Stiefel manifolds”, Kowalski, Oldrich (ed.) et al., Differential geometry and its applications. Proceedings of the 10th international conference on differential geometry and its applications, DGA 2007 (Olomouc, Czech Republic, August 27–31, 2007), World Scientific, Hackensack, NJ, 2008, 35–44   (cited: 3) 35. V. V. Balaschenko, Yu. G. Nikonorov, E. D. Rodionov, V. V. Slavskii, Odnorodnye prostranstva: teoriya i prilozheniya, Poligrafist, Khanty-Mansiisk, 2008 , 280 pp. 36. V. N. Berestovskii, Yu. G. Nikonorov, “Killing vector fields of constant length on locally symmetric Riemannian manifolds”, Transform. Groups, 13:1 (2008), 25–45     (cited: 15)     (cited: 14)   (cited: 14)   (cited: 14) 37. V. N. Berestovskii, Yu. G. Nikonorov, “Chebyshevskaya norma na algebre Li gruppy dvizhenii kompaktnogo odnorodnogo finslerova mnogoobraziya”, Sovremennaya matematika i ee prilozheniya. Algebra, 60, VINITI RAN, 2008, 99–122; V. N. Berestovskii, Yu. G. Nikonorov, “The Chebyshev norm on the Lie algebra of the motion group of a compact homogeneous Finsler manifold”, Journal of Mathematical Sciences (New York), 161:1 (2009), 97–121     (cited: 4)     (cited: 2) 38. V. N. Berestovskii, Yu. G. Nikonorov, “On Clifford-Wolf homogeneous Riemannian manifolds”, Doklady Mathematics, 78:3 (2008), 807–810           (cited: 3)   (cited: 1)   (cited: 1)   (cited: 2) 2007 39. V. N. Berestovskii, Yu. G. Nikonorov, “Regulyarnye i kvaziregulyarnye izometricheskie potoki na rimanovykh mnogoobraziyakh”, Matem. tr., 10:2 (2007), 3–18   (cited: 3)   (cited: 1)   (cited: 2); V. N. Berestovskii, Yu. G. Nikonorov, “Regular and Quasiregular Isometric Flows on Riemannian Manifolds”, Siberian Adv. Math., 18:3 (2008), 153–162       (cited: 2)   (cited: 1) 40. Yu. G. Nikonorov, “On Einstein Extensions of Nilpotent Metric Lie Algebras”, Siberian Adv. Math., 17:3 (2007), 153–170 41. V. V. Dzhepko, Yu. G. Nikonorov, “Dvoinoe eksponentsialnoe otobrazhenie na prostranstvakh postoyannoi krivizny”, Matem. tr., 10:1 (2007), 141–153   (cited: 1)   (cited: 1)   (cited: 1); V. V. Dzhepko, Yu. G. Nikonorov, “The Double Exponential Map on Spaces of Constant Curvature”, Siberian Adv. Math., 18:1 (2008), 21–29 42. V. N. Berestovskii, Yu. G. Nikonorov, “Continued Fractions, the Group $\mathrm{GL}(2,\mathbb Z)$, and Pisot Numbers”, Siberian Adv. Math., 17:4 (2007), 268–290 43. E. V. Volnikh, A. V. Kutishkin, Yu. G. Nikonorov, “Construction of the $\delta$-homogeneous VES production function”, Sib. Zh. Ind. Mat., 10:2 (2007), 31–44 44. A. Arvanitoyeorgos, V. V. Dzhepko, Yu. G. Nikonorov, “Invariant Einstein metrics on quaternionic Stiefel manifolds”, Bull. Greek Math. Soc., 53 (2007), 1–14   (cited: 2) 45. V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta$-homogeneous Riemannian manifolds”, Doklady Mathematics, 76:1 (2007), 596–598           (cited: 2)   (cited: 3)   (cited: 3)   (cited: 3) 2006 46. Yu. G. Nikonorov, E. D. Rodionov, V. V. Slavskii, “Geometriya odnorodnykh rimanovykh mnogoobrazii”, Sovremennaya matematika i ee prilozheniya. Geometriya, 37, VINITI RAN, 2006, 1–78; Yu. G. Nikonorov, E. D. Rodionov, V. V. Slavskii, “Geometry of homogeneous Riemannian manifolds”, Journal of Mathematical Sciences (New York), 146:7 (2007), 6313–6390     (cited: 17)     (cited: 22) 2005 47. E. V. Nikitenko, Yu. G. Nikonorov, “Shestimernye einshteinovy solvmnogoobraziya”, Matem. tr., 8:1 (2005), 71–121   (cited: 15)   (cited: 1)   (cited: 14); E. V. Nikitenko, Yu. G. Nikonorov, “Six-Dimensional Einstein Solvmanifolds”, Siberian Adv. Math., 16:1 (2006), 66–112 48. Yu. G. Nikonorov, “Noncompact homogeneous Einstein 5-manifolds”, Geometriae Dedicata, 113:1 (2005), 107–143     (cited: 12)     (cited: 11)   (cited: 11)   (cited: 10) 2004 49. Yu. G. Nikonorov, “Compact homogeneous Einstein 7-manifolds”, Geometriae Dedicata, 109:1 (2004), 7–30     (cited: 9)     (cited: 7)   (cited: 8) 2003 50. A. M. Lomshakov, Yu. G. Nikonorov, E. V. Firsov, “Invariantnye metriki Einshteina na tri-lokalno-simmetricheskikh prostranstvakh”, Matem. tr., 6:2 (2003), 80–101   (cited: 8)   (cited: 1)    ; A. M. Lomshakov, Yu. G. Nikonorov, E. V. Firsov, “Invariant Einstein Metrics on Three-Locally-Symmetric Spaces”, Siberian Adv. Math., 14:3 (2004), 43–62 51. D. V. Vasin, Yu. G. Nikonorov, “O zadache L. Feiesha Tota v mnogomernom evklidovom prostranstve”, Matem. tr., 6:2 (2003), 3–13        ; D. V. Vasin, Yu. G. Nikonorov, “A Problem of L. Fejes Tóth in a Multidimensional Euclidean Space”, Siberian Adv. Math., 14:2 (2004), 116–125 52. Yu. G. Nikonorov, E. D. Rodionov, “Compact homogeneous Einstein 6-manifolds”, Differential Geometry and its Applications, 19:3 (2003), 369–378     (cited: 8)     (cited: 8)   (cited: 11) 2002 53. Yu. G. Nikonorov, “Invariantnye metriki Einshteina na prostranstvakh Ledzhera–Obaty”, Algebra i analiz, 14:3 (2002), 169–185   (cited: 5)   (cited: 7)  ; Yu. G. Nikonorov, “Invariant Einstein metrics on the Ledger–Obata spaces”, St. Petersburg Math. J., 14:3 (2003), 487–497 54. Yu. G. Nikonorov, N. V. Rasskazova, “A Problem of Fejes L. Tóth”, Siberian Adv. Math., 12:4 (2002), 34–43 55. Yu. G. Nikonorov, “On the asymptotics of mean value points for some finite-difference operators”, Siberian Math. J., 43:3 (2002), 518–524           (cited: 1)   (cited: 3) 56. E. V. Lomshakov, Yu. G. Nikonorov, E. V. Firsov, “On invariant Einstein metrics on three-locally-symmetric spaces”, Doklady Mathematics, 66:2 (2002), 224–227         (cited: 1) 2001 57. Yu. G. Nikonorov, “On the asymptotic of the mean value points for some finite difference operators”, Fundam. Prikl. Mat., 7:3 (2001), 829–838 2000 58. Yu. G. Nikonorov, “Kompaktnye semimernye odnorodnye mnogoobraziya Einshteina”, Matem. tr., 3:2 (2000), 129–145   (cited: 1)    ; Yu. G. Nikonorov, “Compact Homogeneous Einstein 7-Manifolds”, Siberian Adv. Math., 11:1 (2001), 84–99 59. Yu. G. Nikonorov, “Algebraic Structure of Standard Homogeneous Einstein Manifolds”, Siberian Adv. Math., 10:3 (2000), 59–82 60. Yu. G. Nikonorov, “Tessellations of many-dimensional parallelepipeds”, Siberian Math. J., 41:4 (2000), 760–762 61. Yu. G. Nikonorov, “On the Ricci curvature of homogeneous metrics on noncompact homogeneous spaces”, Siberian Math. J., 41:2 (2000), 329–346           (cited: 3) 62. Yu. G. Nikonorov, “On a class of homogeneous compact Einstein manifolds”, Siberian Math. J., 41:1 (2000), 168–172           (cited: 8) 63. Yu. G. Nikonorov, “New series of Einstein homogeneous metrics”, Differential Geometry and its Applications, 12:1 (2000), 25–34     (cited: 2) 64. Yu. G. Nikonorov, “On homogeneous Einstein manifolds”, Doklady Mathematics, 61:3 (2000), 328–331     (cited: 2) 65. Yu. G. Nikonorov, “On compact seven-dimensional homogeneous Einstein manifolds”, Doklady Mathematics, 61:3 (2000), 403–405     (cited: 2)   (cited: 2) 1999 66. Yu. G. Nikonorov, “On Two Problems of Convex Geometry”, Siberian Adv. Math., 9:4 (1999), 59–65 67. Yu. G. Nikonorov, E. D. Rodionov, “Six-dimensional compact homogeneous Einstein manifolds”, Doklady Mathematics, 59:3 (1999), 451–453     (cited: 1) 1998 68. Yu. G. Nikonorov, “The scalar curvature functional and homogeneous Einstein metrics on Lie groups”, Siberian Math. J., 39:3 (1998), 504–509           (cited: 4) 1997 69. Yu. G. Nikonorov, “Inscribed balls and the Lyusternik–Shnirel'man category”, Siberian Math. J., 38:5 (1997), 957–959 1996 70. Yu. G. Nikonorov, E. D. Rodionov, “Standard homogeneous Einstein manifolds and diophantine equations”, Archivum Mathematicum, 32:2 (1996), 123–136   (cited: 2) 1995 71. V. V. Ivanov, Yu. G. Nikonorov, “Asymptotic behavior of the Lagrange points in the Taylor formula”, Siberian Math. J., 36:1 (1995), 78–83           (cited: 1)   (cited: 4) 1994 72. Yu. G. Nikonorov, “A homotopic analog of Helly's theorem and the existence of quasi-invariant points”, Siberian Math. J., 35:3 (1994), 577–579 73. Yu. G. Nikonorov, “On sharp estimates in the first mean value theorem”, Doklady Mathematics, 49:3 (1994), 493–496 1993 74. Yu. G. Nikonorov, “On the integral mean value theorem”, Siberian Math. J., 34:6 (1993), 1135–1137           (cited: 2)   (cited: 7) 75. V. K. Ionin, Yu. G. Nikonorov, “An uncountable family of disjoint spatial continua in Euclidean space”, Siberian Math. J., 34:5 (1993), 848–851

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