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Zelikin Mikhail Il'ich

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Total publications: 77
Scientific articles: 68
Citations to the author: 61
Cited articles: 20
Presentations: 10

Number of views:
This page:2923
Abstract pages:11762
Full texts:3448
References:399
Zelikin Mikhail Il'ich
Corresponding member of RAS
Professor
Doctor of physico-mathematical sciences
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 11.02.1936
E-mail:
Keywords: Optimal Control Theory, Chattering control, multiple integrals, cross ratio, Riccati equation, phase constraints, Pontryagin's maximum principle, Lagrangian manifolds, blow up.
UDC: 512.542, 517.551, 517.958, 517.977, 517.977.5, 519.9, 517
MSC: 37K10, 37K20

Subject

Optimal control theory, differential equations, differential games.

   
Main publications:
  1. M. I. Zelikin, Control Theory and Optimization I. Homogeneous Spaces and the Riccati Equation in the Calculus of Veriations, Springer-Verlag, Berlin, 2000  mathscinet
  2. M. I. Zelikin, V. F. Borisov, Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering, Birkhäuser, Boston, MA, 1994  mathscinet  zmath
  3. M. I. Zelikin, Optimal control and variational calculus., URSS, Moscow, 2004
  4. M. I. Zelikin, “Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems”, Mat. Sb., 195:6 (2004), 57–70  mathnet  mathscinet  zmath
  5. M. I. Zelikin, “Superconductivity of Plasma and Fireballs”, CMFD, 19, 2006, 45–69  mathnet

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Full list of publications:
1. M. I. Zelikin, D. D. Kiselev, L. V. Lokutsievskii, “Optimal control and Galois theory”, Sb. Math., 204:11 (2013), 1624–1638  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
2. V. F. Borisov, V. V. Gael, M. I. Zelikin, “Chattering regimes and Lagrangian manifolds in problems with phase constraints”, Izv. Math., 76:1 (2012), 1–38  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
3. M. I. Zelikin, “Theory and applications of the problem of Euler elastica”, Russian Math. Surveys, 67:2 (2012), 281–296  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
4. M. I. Zelikin, L. V. Lokutsievskiy, R. Hildebrand, “Geometry of neighborhoods of singular trajectories in problems with multidimensional control”, Proc. Steklov Inst. Math., 277 (2012), 67–83  mathnet  crossref  mathscinet  isi  elib
5. M. I. Zelikin, “Theory of fields of extremals for multiple integrals”, Russian Math. Surveys, 66:4 (2011), 733–765  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
6. V. F. Borisov, M. I. Zelikin, L. A. Manita, “Optimal synthesis in an infinite-dimensional space”, Proc. Steklov Inst. Math., 271 (2010), 34–52  mathnet  crossref  mathscinet  isi  elib  elib
7. M. I. Zelikin, V. F. Borisov, “Geometry of extremals with a countable number of contact points with the boundary of the phase constraint”, Dokl. Akad. Nauk, 430:1 (2010), 7–12  mathscinet  zmath
8. M. I. Zelikin, “Chattering control in infinite-dimensional spaces”, Tezisy dokladov, Suzdal, 2009, 186
9. M. I. Zelikin, “A criterion for the symmetry of a spectrum”, Dokl. Akad. Nauk, 418:6 (2008), 737–740  mathnet  mathscinet
10. V. F. Borisov, M. I. Zelikin, L. A. Manita, “Extremals with accumulation of switchings in infinite-dimensional spaces”, Optimalnoe upravlenie, Sovremennaya matematika i eë prilozheniya, 58, Tbilisi, 2008, 3–55  mathscinet; V. F. Borisov, M. I. Zelikin, L. A. Manita, “Extremals with accumulation of switchings in infinite-dimensional spaces”, J. Math. Sci., 160:2 (2009), 139–196  crossref  mathscinet  zmath  elib
11. M. I. Zelikin, L. V. Lokutsievskii, R. A. Usachev, “Vortex singularities of optimal strategies in search games”, Optimalnoe upravlenie, Sovremennaya matematika i eë prilozheniya, 58, Tbilisi, 2008, 56–78  mathscinet; M. I. Zelikin, L. V. Lokutsievskii, R. A. Usachev, “Vortex singularities of optimal strategies in search games”, J. Math. Sci., 160:2 (2009), 197–220  crossref  mathscinet  zmath  elib
12. J. Appl. Math. Mech., 70:2 (2006), 264–273  crossref  mathscinet  zmath  isi
13. M. I. Zelikin, L. A. Manita, “Accumulation of Switchings in Distributed Parameter Problems”, Optimalnoe upravlenie, SMFN, 19, RUDN, M., 2006, 78–113  mathnet  mathscinet  zmath; M. I. Zelikin, L. A. Manita, “Accumulation of Switchings in Distributed Parameter Problems”, Journal of Mathematical Sciences, 151:6 (2008), 3506–3542  crossref  mathscinet  zmath
14. M. I. Zelikin, “Superconductivity of Plasma and Fireballs”, Optimalnoe upravlenie, SMFN, 19, RUDN, M., 2006, 45–69  mathnet  zmath; M. I. Zelikin, “Superconductivity of Plasma and Fireballs”, Journal of Mathematical Sciences, 151:6 (2008), 3473–3496  crossref  zmath
15. M. I. Zelikin, N. B. Melnikov, “The Bellman function and optimal synthesis in control problems with nonsmooth constraints”, Optimalnoe upravlenie i dinamicheskie sistemy, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 110, VINITI, M., 2006, 134–154  mathnet  mathscinet  zmath; M. I. Zelikin, N. B. Melnikov, “The Bellman function and optimal synthesis in control problems with nonsmooth constraints”, J. Math. Sci. (N. Y.), 121:2 (2004), 2281–2294  crossref  mathscinet  zmath
16. M. I. Zelikin, “Optimal problems on Hölder function spaces”, Optimalnoe upravlenie i dinamicheskie sistemy, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 110, VINITI, M., 2006, 109–133  mathnet  mathscinet  zmath; M. I. Zelikin, “Optimal problems on Hölder function spaces”, J. Math. Sci. (N. Y.), 121:2 (2004), 2265–2280  crossref  mathscinet  zmath
17. M. I. Zelikin, “Geometry of operator cross ratio”, Sb. Math., 197:1 (2006), 37–51  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
18. M. I. Zelikin, “An efficient criterion for optimality in terms of two solutions of the Riccati equation”, Dokl. Akad. Nauk, 397:3 (2004), 300–303  mathnet  mathscinet
19. J. Appl. Math. Mech., 68:4 (2004), 617–622  crossref  mathscinet  zmath  isi
20. M. I. Zelikin, “Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems”, Sb. Math., 195:6 (2004), 819–831  mathnet  crossref  crossref  mathscinet  zmath  isi
21. M. I. Zelikin, V. F. Borisov, “Singular optimal regimes in problems of mathematical economics”, Optimalnoe upravlenie, Sovremennaya matematika i eë prilozheniya, 11, Tbilisi, 2003, 3–161  mathscinet  zmath; M. I. Zelikin, V. F. Borisov, “Singular optimal regimes in problems of mathematical economics”, J. Math. Sci. (N. Y.), 130:1 (2005), 4409–4570  crossref  mathscinet
22. M. I. Zelikin, “Hölderian extremal problems”, Patterns and waves (Saint Petersburg, 2002), AkademPrint, St. Petersburg, 2003, 412–432  mathscinet
23. M. I. Zelikin, “The $\zeta$-function of the cross-ratio on Sato's Grassmannian as an integral invariant of the Kadomtsev-Petviashvili hierarchy”, Dokl. Akad. Nauk, 389:2 (2003), 159–163  mathnet  mathscinet  zmath
24. M. I. Zelikin, V. F. Borisov, “Optimal chattering feedback control”, Optimalnoe upravlenie – 4, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 90, VINITI, M., 2002, 5–189  mathnet  mathscinet  zmath; M. I. Zelikin, V. F. Borisov, “Optimal chattering feedback control”, J. Math. Sci. (N. Y.), 114:3 (2003), 1227–1344  crossref  mathscinet  zmath
25. M. I. Zelikin, “Chattering on optimal trajectories of Hölder problems”, Sb. Math., 193:5 (2002), 669–683  mathnet  crossref  crossref  mathscinet  zmath  isi
26. M. I. Zelikin, “The Structure of Optimal Synthesis in the Vicinity of Singular Manifolds for Problems Affine with Respect to Control”, Proc. Steklov Inst. Math., 236 (2002), 164–185  mathnet  mathscinet  zmath
27. Differ. Equ., 37:9 (2001), 1217–1223  crossref  mathscinet  zmath  isi
28. M. I. Zelikin, “Optimal control in Hölder classes of functions”, Dokl. Akad. Nauk, 378:6 (2001), 733–736  mathnet  mathscinet  zmath
29. M. I. Zelikin, N. B. Melnikov, R. Hildebrand, “The Topological Structure of the Phase Portrait of a Typical Fiber of Optimal Synthesis for Chattering Problems”, Proc. Steklov Inst. Math., 233 (2001), 116–142  mathnet  mathscinet  zmath
30. M. I. Zelikin, L. F. Zelikina, R. Hildebrand, “Asymptotics of Optimal Synthesis for One Class of Extremal Problems”, Proc. Steklov Inst. Math., 233 (2001), 87–115  mathnet  mathscinet  zmath
31. M. I. Zelikin, “Synthesis of Optimal Trajectories That Defines the Reeb Foliation”, Proc. Steklov Inst. Math., 233 (2001), 81–86  mathnet  mathscinet  zmath
32. V. F. Borisov, M. I. Zelikin, “Approaching the intermediate thrust modes in control problems of space navigation”, Russ. J. Math. Phys., 7:2 (2000), 127–146  mathscinet  zmath  isi
33. M. I. Zelikin, “To the theory of chattering control”, Spectral and evolution problems (Sevastopol', 1999), Vol. 10, Natl. Taurida Univ. “V. Vernadsky”, Simferopol', 2000, 170–172  mathscinet
34. M. I. Zelikin, Control theory and optimization. I, Homogeneous spaces and the Riccati equation in the calculus of variations, Encyclopaedia of Mathematical Sciences, 86, Springer-Verlag, Berlin, 2000, ISBN: 3-540-66741-5, xii+284 pp.  mathscinet  zmath
35. Differential Equations, 35:11 (1999), 1489–1493 (2000)  mathscinet  zmath  isi
36. M. I. Zelikin, “The asymptotics of the deviation of a functional from its optimal value when chattering is replaced by a suboptimal regime”, Russian Math. Surveys, 54:3 (1999), 662–664  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
37. M. I. Zelikin, L. F. Zelikina, “Exact Constants in Kolmogorov-Type Inequalities”, Proc. Steklov Inst. Math., 227 (1999), 131–139  mathnet  mathscinet  zmath
38. M. I. Zelikin, “Optimal Synthesis Containing Successively Inserted Chattering Bundles”, Proc. Steklov Inst. Math., 224 (1999), 137–148  mathnet  mathscinet  zmath
39. M. I. Zelikin, “Cartan–Siegel homogeneous domains as integral manifolds of the complex Riccati-type equation”, Proc. Steklov Inst. Math., 220 (1998), 126–137  mathnet  mathscinet  zmath
40. M. I. Zelikin, “A quadratic system of partial differential equations that is associated with the problem of minimizing a multiple integral”, Dokl. Akad. Nauk, 358:1 (1998), 7–9  mathnet  mathscinet  zmath  isi
41. M. I. Zelikin, Odnorodnye prostranstva i uravnenie Rikkati v variatsionnom ischislenii, Faktorial, M., 1998, ISBN: 5-88688-022-4, 250 pp.  zmath
42. M. I. Zelikin, L. F. Zelikina, “The structure of optimal synthesis in a neighbourhood of singular manifolds for problems that are affine in control”, Sb. Math., 189:10 (1998), 1467–1484  mathnet  crossref  crossref  mathscinet  zmath  isi
43. M. I. Zelikin, “One-parameter families of solutions to a class of PDE optimal control problems”, Optimization methods in partial differential equations (South Hadley, MA, 1996), Contemp. Math., 209, Amer. Math. Soc., Providence, RI, 1997, 339–349  mathscinet  zmath
44. M. I. Zelikin, “On the connection generated by the problem of minimizing a multiple integral”, Sb. Math., 188:1 (1997), 61–74  mathnet  crossref  crossref  mathscinet  zmath  isi
45. M. I. Zelikin, “The Fuller phenomenon in problems of vibration of two linked oscillators”, Dynamical systems, 1, J. Math. Sci., 78:5 (1996), 626–631  crossref  mathscinet  zmath
46. M. I. Zelikin, “Totally extremal manifolds for optimal control problems”, Semigroups in algebra, geometry and analysis (Oberwolfach, 1993), de Gruyter Exp. Math., 20, de Gruyter, Berlin, 1995, 339–354  mathscinet  zmath
47. M. I. Zelikin, “Irregularity of optimal control in regular extremal problems”, Fundam. Prikl. Mat., 1:2 (1995), 399–408  mathnet  mathscinet  zmath
48. M. I. Zelikin, V. F. Borisov, Theory of chattering control, With applications to astronautics, robotics, economics, and engineering, Systems & Control: Foundations & Applications, Birkhäuser Boston Inc., Boston, MA, 1994, ISBN: 0-8176-3618-8, xvi+242 pp.  mathscinet  zmath
49. M. I. Zelikin, “On the theory of the matrix Riccati equation. II”, Matem. sb., 183:10 (1992), 87–108  mathnet  mathscinet  zmath  adsnasa; M. I. Zelikin, “On the theory of the matrix Riccati equation. II”, Russian Acad. Sci. Sb. Math., 77:1 (1994), 213–230  crossref  mathscinet  zmath  isi
50. M. I. Zelikin, V. F. Borisov, “Regimes with frequented switches in the problems of optimal control”, Nekotorye voprosy teorii kolebanii i teorii optimalnogo upravleniya, Tr. MIAN SSSR, 197, Nauka, M., 1991, 85–166  mathnet  mathscinet  zmath; M. I. Zelikin, V. F. Borisov, “Regimes with frequented switches in the problems of optimal control”, Proc. Steklov Inst. Math., 197 (1993), 95–186  mathscinet  zmath
51. M. I. Zelikin, V. F. Borosov, “Optimal synthesis containing chattering arcs and singular arcs of the second order”, Nonlinear synthesis (Sopron, 1989), Progr. Systems Control Theory, 9, Birkhäuser Boston, Boston, MA, 1991, 283–296  mathscinet
52. M. I. Zelikin, “On the theory of the matrix Riccati equation”, Matem. sb., 182:7 (1991), 970–984  mathnet  mathscinet  zmath  adsnasa; M. I. Zelikin, “On the theory of the matrix Riccati equation”, Math. USSR-Sb., 73:2 (1992), 341–354  crossref  mathscinet  zmath  isi
53. M. I. Zelikin, V. F. Borisov, “Synthesis in problems of optimal control containing trajectories with participating switchings and singular trajectories of the second order”, Math. Notes, 47:1 (1990), 41–49  mathnet  crossref  mathscinet  zmath  isi
54. Soviet Math. Dokl., 39:1 (1989), 188–191  mathnet  mathscinet  isi
55. J. Appl. Math. Mech., 52:6 (1988), 731–737 (1990)  crossref  mathscinet  zmath  isi
56. M. I. Zelikin, “Group symmetry in degenerate extremal problems”, Russian Math. Surveys, 43:2 (1988), 189–190  mathnet  crossref  mathscinet  zmath  adsnasa  isi
57. M. I. Zelikin, “Synthesis of optimal trajectories on representation spaces of Lie groups”, Matem. sb., 132(174):4 (1987), 541–555  mathnet  mathscinet  zmath; M. I. Zelikin, “Synthesis of optimal trajectories on representation spaces of Lie groups”, Math. USSR-Sb., 60:2 (1988), 533–546  crossref  mathscinet  zmath
58. M. I. Zelikin, “The search for singular extremals”, Stochastic optimization (Kiev, 1984), Lecture Notes in Control and Inform. Sci., 81, Springer, Berlin, 1986, 738–746  mathscinet
59. M. I. Zelikin, Optimalnoe upravlenie i variatsionnoe ischislenie, Izd-vo MGU, M., 1985, 96 pp.  mathscinet  zmath
60. M. I. Zelikin, “Minimization of integrals of differential forms, and degenerate variational problems”, Wiss. Z. Tech. Hochsch. Leuna-Merseburg, 27:5 (1985), 526–534  mathscinet  zmath
61. M. I. Zelikin, “On the singular arcs”, Problems Control Inform. Theory/Problemy Upravlen. Teor. Inform., 14:2 (1985), 75–88, R1–R15  mathscinet  zmath
62. M. I. Zelikin, “Necessary conditions for optimality of singular trajectories in problems that are linear with respect to control”, Some problems in modern analysis, Moskov. Gos. Univ. Mekh.-Mat. Fak., Moscow, 1984, 35–41  mathscinet  zmath
63. M. I. Zelikin, “Minimization of integrals of differential forms”, Dokl. Akad. Nauk SSSR, 278:5 (1984), 1057–1059  mathnet  mathscinet  zmath  isi
64. M. I. Zelikin, “On the theory of linear control problems”, Dokl. Akad. Nauk SSSR, 277:4 (1984), 782–785  mathnet  mathscinet  zmath  isi
65. M. I. Zelikin, “Optimality conditions for singular trajectories in a problem of curvilinear integral minimization”, Dokl. Akad. Nauk SSSR, 267:3 (1982), 528–531  mathscinet  zmath  isi
66. M. I. Zelikin, B. Ju. Sternin, “A system of integral equations that arises in the problem of S. L. Sobolev”, Sibirsk. Mat. Ž., 18:1 (1977), 97–102  mathscinet  zmath
67. M. I. Zelikin, “A certain differential game with incomplete information”, Dokl. Akad. Nauk SSSR, 202 (1972), 998–1000  mathscinet  zmath
68. M. I. Zelikin, N. T. Tynyanskii, “Determined differential games”, Uspekhi Mat. Nauk, 20:4(124) (1965), 151–157  mathnet  mathscinet  zmath

69. M. I. Zelikin, “Lev Semenovich Pontryagin: reminiscences and reflections”, Istor.-Mat. Issled. (2), 2011, no. 14(49), 77–84, 357–358  mathscinet
70. Yu. S. Osipov, V. V. Kozlov, L. D. Faddeev, D. V. Anosov, V. S. Vladimirov, R. V. Gamkrelidze, A. A. Gonchar, N. N. Krasovskii, A. V. Kryazhimskii, A. B. Kurzhanskii, S. P. Novikov, S. M. Aseev, A. B. Zhizhchenko, D. V. Treschev, A. A. Agrachev, E. A. Volkov, N. L. Grigorenko, A. A. Davydov, M. I. Zelikin, A. Yu. Kolesov, A. A. Mal'tsev, M. S. Nikol'skii, N. Kh. Rozov, A. G. Sergeev, K. O. Besov, S. P. Konovalov, “In memory of Evgenii Frolovich Mishchenko”, Proc. Steklov Inst. Math., 271 (2010), 1–2  mathnet  crossref  mathscinet  isi
71. V. I. Arnol'd, L. R. Volevich, A. A. Gonchar, S. S. Demidov, M. I. Zelikin, Yu. S. Ilyashenko, G. G. Magaril-Il'yaev, A. V. Mikhalev, S. P. Novikov, I. V. Yaschenko, “Vladimir Mikhailovich Tikhomirov (on his 70th birthday)”, Russian Math. Surveys, 61:1 (2006), 189–192  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
72. V. I. Arnol'd, A. S. Demidov, Yu. S. Ilyashenko, G. G. Magaril-Il'yaev, E. F. Mishchenko, K. Yu. Osipenko, A. B. Sossinski, M. A. Tsfasman, V. A. Uspenskii, M. N. Vyalyi, I. V. Yaschenko, M. I. Zelikin, “Vladimir M. Tikhomirov”, Mosc. Math. J., 5:1 (2005), 295  mathnet  mathscinet
73. A. A. Bolibrukh, A. A. Irmatov, M. I. Zelikin, O. B. Lupanov, V. M. Maynulov, E. F. Mishchenko, M. M. Postnikov, Yu. P. Solov'ev, E. V. Troitskii, “Aleksandr Sergeevich Mishchenko (on his 60th birthday)”, Russian Math. Surveys, 56:6 (2001), 1187–1191  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
74. M. I. Zelikin, V. A. Il'in, N. N. Krasovskiĭ, et al., “Lyudmila Filippovna Zelikina”, Differential Equations, 35:6 (1999), 856–857  mathscinet  isi
75. N. S. Bakhvalov, M. I. Zelikin, A. S. Kalashnikov, V. L. Kamynin, O. A. Oleinik, E. Yu. Panov, N. S. Petrosyan, V. M. Tikhomirov, A. V. Faminskii, V. N. Chubarikov, “Stanislav Nikolaevich Kruzhkov (obituary)”, Russian Math. Surveys, 53:5 (1998), 1071–1078  mathnet  crossref  crossref  mathscinet  zmath  isi
76. A. G. Vitushkin, M. I. Zelikin, N. N. Krasovskii, S. P. Novikov, Yu. S. Osipov, K. A. Sitnikov, “Nicolai Terent'evich Tynyanskii (obituary)”, Russian Math. Surveys, 41:4 (1986), 173–174  mathnet  crossref  mathscinet  adsnasa  isi
77. D. V. Anosov, V. I. Arnol'd, M. I. Zelikin, A. N. Kolmogorov, O. V. Lokutsievskii, Yu. S. Osipov, Ya. G. Sinai, V. M. Tikhomirov, M. V. Jakobson, “Vladimir Mikhailovich Alekseev (obituary)”, Russian Math. Surveys, 36:4 (1981), 201–206  mathnet  crossref  mathscinet  zmath  adsnasa  isi

Presentations in Math-Net.Ru
1. Фрактальная структура оптимального синтеза
All-Moscow regular scientific seminar "Control Theory and Optimization"
December 2, 2014 11:30
2. Chaos in optimal synthesis in problems with multidimensional control (part I)
The International Conference "Geometric Control Theory and Analysis on Metric Structures"
August 4, 2014 15:00
3. Singular orbits in hamiltonian systems with discontinous right term
Differential geometry and applications
March 24, 2014 16:45
4. Chaotic dynamics of optimal trajectories in problems with multidimensional control
Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin
September 24, 2013 11:10   
5. Stochastic dynamics of Lie algebras of Poisson brackets in a neighbourhood of the points where the Hamiltonian is not smooth
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
April 3, 2013 16:45
6. Стохастическая динамика алгебр Ли скобок Пуассона в окрестности точек негладкости гамильтониана
Meetings of the Moscow Mathematical Society
February 12, 2013 18:30
7. Euler's elastics and elastic shells
Differential geometry and applications
November 26, 2012 16:45
8. Fields of extremals for multiple integrals
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
March 23, 2011 16:45
9. Теория поля экстремалей для функционалов типа кратных интегралов
Meetings of the Moscow Mathematical Society
March 23, 2010
10. Фазовый портрет с накоплением переключений в бесконечномерном пространстве
Seminar of the Department of Differential Equations, Steklov Mathematical Institute
April 2, 2008 12:00

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