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Leonov, Gennadii Alekseevich
(2947–2018)

Statistics Math-Net.Ru
Total publications: 84
Scientific articles: 72
Presentations: 2

Number of views:
This page:2912
Abstract pages:15726
Full texts:5560
References:600
Corresponding member of RAS
Professor
Doctor of physico-mathematical sciences (1983)
Keywords: dynamcal systems, control theory, synchronization
UDC: 531.36, 517.91, 517.977, 62-50, 517.938.5

Subject:

dynamcal systems, control theory, synchronization

   
Main publications:
  1. A.Kh. Gelig and G.A. Leonov and V.A. Yakubovich, Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities, World Scientific, 2004  mathscinet

http://www.mathnet.ru/eng/person20107
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/191338

Publications in Math-Net.Ru
2018
1. G. A. Leonov, M. M. Shumafov, “Pyragas stabilizability of unstable equilibria by nonstationary time-delayed feedback”, Avtomat. i Telemekh., 2018, 6,  87–98  mathnet  elib; Autom. Remote Control, 79:6 (2018), 1029–1039  isi  scopus
2016
2. B. R. Andrievsky, N. Kuznetsov, O. A. Kuznetsova, G. A. Leonov, T. N. Mokaev, “Localization of hidden oscillations in flight control systems”, Tr. SPIIRAN, 49 (2016),  5–31  mathnet  elib
3. G. A. Leonov, N. Kuznetsov, E. V. Kudryashova, “Tunisia 2011–2014. Bifurcation, revolution, and controlled stabilization”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2016, 4,  92–103  mathnet  elib
2012
4. G. A. Leonov, N. V. Kuznetsov, “Hidden oscillations in dynamical systems. 16 Hilbert's problem, Aizerman's and Kalman's conjectures, hidden attractors in Chua's circuits”, CMFD, 45 (2012),  105–121  mathnet  mathscinet; Journal of Mathematical Sciences, 201:5 (2014), 645–662  scopus
2011
5. G. A. Leonov, N. V. Kuznetsov, E. V. Kudryashova, O. A. Kuznetsova, “Modern symbolic computation methods: Lyapunov quantities and 16th Hilbert problem”, Tr. SPIIRAN, 16 (2011),  5–36  mathnet
2010
6. G. A. Leonov, N. V. Kuznetsov, E. V. Kudryashova, “A direct method for calculating Lyapunov values of two-dimensional dynamical systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:1 (2010),  119–126  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S119–S126  isi  scopus
2009
7. G. A. Leonov, “Analysis and synthesis of controlled delay lines”, Avtomat. i Telemekh., 2009, 10,  184–190  mathnet  mathscinet  zmath; Autom. Remote Control, 70:10 (2009), 1760–1766  isi  scopus
8. G. A. Leonov, “On the Aizerman problem”, Avtomat. i Telemekh., 2009, 7,  37–49  mathnet  mathscinet  zmath  elib; Autom. Remote Control, 70:7 (2009), 1120–1131  isi  elib  scopus
9. G. A. Leonov, “On the method of harmonic linearization”, Avtomat. i Telemekh., 2009, 5,  65–75  mathnet  mathscinet  zmath  elib; Autom. Remote Control, 70:5 (2009), 800–810  isi  elib  scopus
10. G. A. Leonov, “On the harmonic linearization method”, Dokl. Akad. Nauk, 424:4 (2009),  462–464  mathnet  mathscinet  elib; Dokl. Math., 79:1 (2009), 144–146  isi  scopus
2008
11. G. A. Leonov, “Mathematical models of phase syncronization systems with quadrature and phase-quadrature units”, Avtomat. i Telemekh., 2008, 9,  33–43  mathnet  mathscinet  zmath; Autom. Remote Control, 69:9 (2008), 1475–1485  isi  scopus
12. G. A. Leonov, “Dynamic principles of prediction and control”, Probl. Upr., 2008, 5,  31–35  mathnet
2006
13. G. A. Leonov, “Phase synchronization: Theory and applications”, Avtomat. i Telemekh., 2006, 10,  47–85  mathnet  mathscinet  zmath; Autom. Remote Control, 67:10 (2006), 1573–1609  scopus
14. G. A. Leonov, “Generalization of the Andronov–Vitt theorem”, Regul. Chaotic Dyn., 11:2 (2006),  281–289  mathnet  mathscinet  zmath
2005
15. G. A. Leonov, “Necessary and sufficient conditions for the absolute stability of two-dimensional time-varying systems”, Avtomat. i Telemekh., 2005, 7,  43–53  mathnet  mathscinet  zmath; Autom. Remote Control, 66:7 (2005), 1059–1068  scopus
16. G. A. Leonov, “Estimating the oscillation period of nonlinear discrete systems”, Avtomat. i Telemekh., 2005, 6,  147–152  mathnet  mathscinet  zmath; Autom. Remote Control, 66:6 (2005), 982–987  scopus
17. G. A. Leonov, S. M. Seledzhi, “An astatic phase-locked system for digital signal processors: circuit design and stability”, Avtomat. i Telemekh., 2005, 3,  11–19  mathnet  mathscinet  zmath; Autom. Remote Control, 66:3 (2005), 348–355  scopus
2003
18. G. A. Leonov, “A Modification of Perron's Counterexample”, Differ. Uravn., 39:11 (2003),  1566–1567  mathnet  mathscinet; Differ. Equ., 39:11 (2003), 1651–1652
2002
19. G. A. Leonov, “The Brockett Problem for Linear Discrete Control Systems”, Avtomat. i Telemekh., 2002, 5,  92–96  mathnet  mathscinet  zmath; Autom. Remote Control, 63:5 (2002), 777–781  isi  scopus
2001
20. G. A. Leonov, “The Brockett problem in the stability theory for linear differential equations”, Algebra i Analiz, 13:4 (2001),  134–155  mathnet  mathscinet  zmath; St. Petersburg Math. J., 13:4 (2002), 613–628
21. G. A. Leonov, “Lyapunov dimension formulas for Hénon and Lorentz attractors”, Algebra i Analiz, 13:3 (2001),  155–170  mathnet  mathscinet  zmath; St. Petersburg Math. J., 13:3 (2002), 453–464
22. G. A. Leonov, “Circular Criteria for Linear Systems”, Avtomat. i Telemekh., 2001, 6,  41–46  mathnet  mathscinet  zmath; Autom. Remote Control, 62:6 (2001), 896–900  isi  scopus
23. G. A. Leonov, “The Brocket Stabilization Problem”, Avtomat. i Telemekh., 2001, 5,  190–193  mathnet  mathscinet  zmath; Autom. Remote Control, 62:5 (2001), 847–849  isi  scopus
2000
24. G. A. Leonov, “Lyapunov functions in the estimation of dimensions of attractors of dynamical systems”, Zap. Nauchn. Sem. POMI, 266 (2000),  131–154  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 113:4 (2003), 614–628
1999
25. G. A. Leonov, “A frequency criterion for the existence of strange attractors of discrete systems”, Avtomat. i Telemekh., 1999, 5,  113–121  mathnet  mathscinet; Autom. Remote Control, 60:5 (1999), 697–703  isi
1997
26. G. A. Leonov, S. A. Lyashko, “The direct Lyapunov method in estimates for the fractal dimension of attractors”, Differ. Uravn., 33:1 (1997),  68–74  mathnet  mathscinet; Differ. Equ., 33:1 (1997), 67–74
1996
27. N. E. Barabanov, A. Kh. Gelig, G. A. Leonov, A. L. Likhtarnikov, A. S. Matveev, V. B. Smirnova, A. L. Fradkov, “The Frequency Theorem (Kalman–Yakubovich Lemma) in Control Theory”, Avtomat. i Telemekh., 1996, 10,  3–40  mathnet  mathscinet  zmath; Autom. Remote Control, 57:10 (1996), 1377–1407
1995
28. A. Yu. Kravchuk, G. A. Leonov, D. V. Ponomarenko, “Criteria for strong orbital stability of trajectories of dynamical systems. II”, Differ. Uravn., 31:3 (1995),  440–445  mathnet  mathscinet; Differ. Equ., 31:3 (1995), 405–410
29. V. A. Boichenko, G. A. Leonov, “Lyapunov's direct method in estimates of topological entropy”, Zap. Nauchn. Sem. POMI, 231 (1995),  62–75  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 91:6 (1998), 3370–3379
1993
30. G. A. Leonov, D. V. Ponomarenko, “Criteria for the orbital stability of trajectories of dynamical systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, 4,  88–94  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 37:4 (1993), 85–91
1992
31. A. Yu. Kravchuk, G. A. Leonov, D. V. Ponomarenko, “Criteria for strong orbital stability of trajectories of dynamical systems. I”, Differ. Uravn., 28:9 (1992),  1507–1520  mathnet  mathscinet; Differ. Equ., 28:9 (1992), 1230–1241
1991
32. G. A. Leonov, “An estimate for the Hausdorff dimension of the attractors of dynamical systems”, Differ. Uravn., 27:5 (1991),  767–771  mathnet  mathscinet; Differ. Equ., 27:5 (1991), 520–524
33. G. A. Leonov, “Instability in attractors that are close to two-dimensional surfaces”, Differ. Uravn., 27:3 (1991),  537–539  mathnet  mathscinet  zmath
1990
34. N. V. Kondrat'yeva, G. A. Leonov, “Dynamic stability of synchronous machines with strong control of excitation”, Avtomat. i Telemekh., 1990, 6,  57–67  mathnet  zmath; Autom. Remote Control, 51:6 (1990), 768–778
35. V. A. Boichenko, G. A. Leonov, “Frequency estimates for the Hausdorff dimension of the attractors of nonlinear systems”, Differ. Uravn., 26:4 (1990),  555–563  mathnet  mathscinet  zmath; Differ. Equ., 26:4 (1990), 399–406
36. I. M. Burkin, I. S. Dzesov, G. A. Leonov, “Estimates for domains of attraction of stationary solutions of differential equations of systems of frequency synchronization. II”, Differ. Uravn., 26:3 (1990),  381–386  mathnet  mathscinet; Differ. Equ., 26:3 (1990), 276–279
37. I. M. Burkin, I. S. Dzesov, G. A. Leonov, “Estimates for domains of attraction of stationary solutions of differential equations of systems of frequency synchronization. I”, Differ. Uravn., 26:2 (1990),  205–213  mathnet  mathscinet; Differ. Equ., 26:2 (1990), 152–159
1989
38. G. A. Leonov, “Asymptotic behavior of the solutions of the Lorenz system”, Differ. Uravn., 25:12 (1989),  2103–2109  mathnet  mathscinet  zmath; Differ. Equ., 25:12 (1989), 1492–1497
39. V. A. Boichenko, G. A. Leonov, “The Hausdorff dimension of attractors of the Lorenz system”, Differ. Uravn., 25:11 (1989),  1999–2000  mathnet  mathscinet  zmath
40. M. I. Lapachugina, G. A. Leonov, “A frequency criterion for instability in the large of nonlinear dynamical systems”, Differ. Uravn., 25:8 (1989),  1451–1453  mathnet  mathscinet  zmath
1988
41. G. A. Leonov, “A multidimensional analogue of a criterion for Poincaré orbital stability”, Differ. Uravn., 24:9 (1988),  1637–1639  mathnet  mathscinet  zmath
42. G. A. Leonov, “An estimate for the bifurcation parameters of the saddle separatrix loop of the Lorenz system”, Differ. Uravn., 24:6 (1988),  972–977  mathnet  mathscinet  zmath; Differ. Equ., 24:6 (1988), 634–638
43. G. A. Leonov, “Asymptotic behavior of the solutions of the Lorenz system”, Differ. Uravn., 24:5 (1988),  804–809  mathnet  mathscinet  zmath; Differ. Equ., 24:5 (1988), 527–531
44. G. A. Leonov, “On orbital stability of trajectories of autonomous systems”, Differ. Uravn., 24:4 (1988),  694–695  mathnet  mathscinet  zmath
45. G. A. Leonov, V. B. Smirnova, “Stability in the large of integro-differential equations of nondirect control systems”, Differ. Uravn., 24:3 (1988),  500–508  mathnet  mathscinet; Differ. Equ., 24:3 (1988), 359–366
46. G. A. Leonov, “On estimates of the bifurcation values of the parameters of a Lorentz system”, Uspekhi Mat. Nauk, 43:3(261) (1988),  189–190  mathnet  mathscinet  zmath; Russian Math. Surveys, 43:3 (1988), 216–217  isi
1987
47. G. A. Leonov, “A frequency criterion for the existence of limit cycles of dynamical systems with a cylindrical phase space”, Differ. Uravn., 23:12 (1987),  2047–2051  mathnet  mathscinet  zmath
48. G. A. Leonov, V. A. Teshev, “A frequency criterion for the stability of systems of differential equations with hysteresis functions”, Differ. Uravn., 23:4 (1987),  718–719  mathnet  mathscinet  zmath
1986
49. G. A. Leonov, “A frequency criterion in stabilization of nonlinear systems by a harmonic exogenous signal”, Avtomat. i Telemekh., 1986, 1,  169–174  mathnet
50. G. A. Leonov, “Dissipativity and global stability of the Lorenz system”, Differ. Uravn., 22:9 (1986),  1642–1644  mathnet  mathscinet  zmath
51. G. A. Leonov, “Estimation of separatrices of the Lorenz system”, Differ. Uravn., 22:3 (1986),  411–415  mathnet  mathscinet
1985
52. G. A. Leonov, Al. A. Pervozvanskii, “Frequency bounds on the dissipative region of nonlinear control systems”, Dokl. Akad. Nauk SSSR, 283:4 (1985),  826–830  mathnet  mathscinet  zmath
53. G. A. Leonov, “Global stability of differential equations of phase synchronization systems”, Differ. Uravn., 21:2 (1985),  213–223  mathnet  mathscinet  zmath
1984
54. G. A. Leonov, “On one hypothesis of A.A. Voronov”, Avtomat. i Telemekh., 1984, 5,  17–20  mathnet  zmath; Autom. Remote Control, 45:5 (1984), 559–562
55. G. A. Leonov, “The nonlocal reduction method in the theory of absolute stability of nonlinear systems. II.”, Avtomat. i Telemekh., 1984, 3,  48–56  mathnet  mathscinet  zmath; Autom. Remote Control, 45:3 (1984), 315–323
56. G. A. Leonov, “The nonlocal reduction method in the theory of absolute stability of nonlinear systems. I.”, Avtomat. i Telemekh., 1984, 2,  45–53  mathnet  mathscinet  zmath; Autom. Remote Control, 45:2 (1984), 178–187
57. I. M. Burkin, G. A. Leonov, “Existence of periodic solutions to a third-order nonlinear system”, Differ. Uravn., 20:12 (1984),  2036–2042  mathnet  mathscinet  zmath
1983
58. O. B. Ershova, G. A. Leonov, “Frequency estimates of the number of cycle slidings in phase control systems”, Avtomat. i Telemekh., 1983, 5,  65–72  mathnet  zmath; Autom. Remote Control, 44:5 (1983), 600–607
59. G. A. Leonov, M. Yu. Filina, “Instability and oscillations of systems with hysteresis”, Avtomat. i Telemekh., 1983, 1,  44–49  mathnet  mathscinet  zmath; Autom. Remote Control, 44:1 (1983), 33–38
1982
60. L. I. Burkina, G. A. Leonov, “The limit cycles of the second kind in dynamical systems with cylindrical phase space”, Differ. Uravn., 18:10 (1982),  1819  mathnet  mathscinet
1981
61. G. A. Leonov, “The necessary frequency conditions of arsolute starility for nonstationary systems”, Avtomat. i Telemekh., 1981, 1,  15–19  mathnet  zmath; Autom. Remote Control, 42:1 (1981), 9–13
62. I. M. Burkin, L. I. Burkina, G. A. Leonov, “Barbashin's problem in the theory of phase systems”, Differ. Uravn., 17:11 (1981),  1932–1944  mathnet  mathscinet
1980
63. G. A. Leonov, “On one extension of Popov's frequency criterion to nonstationary nonlinearities”, Avtomat. i Telemekh., 1980, 11,  21–26  mathnet  zmath; Autom. Remote Control, 41:11 (1981), 1494–1499
64. S. M. Abramovich, G. A. Leonov, “A type of stability of phase systems”, Differ. Uravn., 16:5 (1980),  928–930  mathnet  mathscinet  zmath
65. L. I. Burkina, G. A. Leonov, “Frequency conditions for the existence of circular motions and second-order limit cycles in phase systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1980, 2,  15–21  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 24:2 (1980), 14–20
1978
66. Yu. A. Koryakin, G. A. Leonov, A. R. Liss, “A frequency criterion for stability of sampled-data system for control of the generator oscillation phase”, Avtomat. i Telemekh., 1978, 12,  64–69  mathnet  zmath; Autom. Remote Control, 39:12 (1979), 1787–1792
67. Z. U. Blyagoz, G. A. Leonov, “Stability of a dynamical system with a cylindrical phase space”, Differ. Uravn., 14:8 (1978),  1502–1503  mathnet  mathscinet  zmath
1977
68. G. A. Leonov, “An analogue of the Bendixson criterion for a third order equation”, Differ. Uravn., 13:2 (1977),  367–368  mathnet  mathscinet  zmath
1976
69. I. V. Ioffe, G. A. Leonov, “A generalization of the Brockett-Lee theorem”, Differ. Uravn., 12:11 (1976),  2095–2096  mathnet  mathscinet  zmath
1974
70. S. M. Abramovich, G. A. Leonov, “The global stability of a certain dissipative system”, Differ. Uravn., 10:11 (1974),  2056  mathnet  mathscinet  zmath
1970
71. G. A. Leonov, “The necessity of a frequency condition for the absolute stability of stationary systems in the critical case of a pair of pure imaginary roots”, Dokl. Akad. Nauk SSSR, 193:4 (1970),  756–759  mathnet  mathscinet  zmath
72. G. A. Leonov, “The asymptotic behavior of the solutions of nonlinear systems of differential equations”, Differ. Uravn., 6:6 (1970),  1131–1132  mathnet  mathscinet  zmath
1969
73. G. A. Leonov, “A certain hypothesis in the theory of the stability of nonlinear systems”, Differ. Uravn., 5:4 (1969),  753–756  mathnet  mathscinet  zmath

2017
74. V. G. Peshekhonov, G. A. Leonov, R. M. Yusupov, “To the 85th anniversary of Rosenwasser E. N.”, Avtomat. i Telemekh., 2017, 10,  189–190  mathnet  elib
2015
75. D. G. Benua, M. V. Bondarko, N. A. Vavilov, M. A. Vsemirnov, A. I. Generalov, N. L. Gordeev, I. B. Zhukov, G. A. Leonov, B. B. Lur'e, I. A. Panin, A. L. Smirnov, I. B. Fesenko, A. V. Yakovlev, “To the anniversary of Sergei Vladimirovich Vostokov”, Algebra i Analiz, 27:6 (2015),  3–5  mathnet  mathscinet  elib; St. Petersburg Math. J., 27:6 (2016), 861–862  isi  scopus
2014
76. V. N. Igolkin, V. V. Karelin, S. K. Myshkov, L. N. Polyakova, G. Sh. Tamasyan, L. A. Petrosyan, E. I. Veremey, Yu. M. Dahl, O. I. Drivotin, V. Yu. Dobrynin, N. V. Egorov, A. P. Zhabko, A. M. Kamachkin, G. A. Leonov, V. S. Novoselov, D. A. Ovsyannikov, A. N. Terekhov, S. V. Chistyakov, V. L. Kharitonov, V. M. Bure, A. Yu. Aleksandrov, S. N. Andrianov, A. O. Bochkarev, V. V. Evstafieva, V. S. Ermolin, V. V. Zakharov, I. V. Olemskoy, Yu. G. Pronina, S. L. Sergeev, A. Yu. Uteshev, O. N. Chizhova, “V. F. Demianov”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2014, 2,  154–156  mathnet
2010
77. G. A. Leonov, O. A. Kuznetsova, “Lyapunov quantities and limit cycles of two-dimensional dynamical systems. Analytical methods and symbolic computation”, Regul. Chaotic Dyn., 15:2-3 (2010),  354–377  mathnet
78. A. M. Vershik, O. Ya. Viro, V. N. Isakov, G. A. Leonov, M. J. Pratussevitch, V. P. Havin, N. A. Shirokov, “Odinets Vladimir Petrovich (on his 65th birthday)”, Vladikavkaz. Mat. Zh., 12:4 (2010),  79–81  mathnet
2006
79. A. Kh. Gelig, G. A. Leonov, A. L. Fradkov, “Vladimir Andreevich Yakubovich”, Avtomat. i Telemekh., 2006, 10,  4–19  mathnet  mathscinet  zmath  elib; Autom. Remote Control, 67:10 (2006), 1530–1546
2002
80. Yu. N. Bibikov, N. A. Izobov, V. A. Il'in, V. A. Kondratiev, N. N. Krasovskii, L. D. Kudryavtsev, G. A. Leonov, V. M. Millionshchikov, Yu. S. Osipov, S. Yu. Pilyugin, N. Kh. Rozov, “Viktor Aleksandrovich Pliss (A tribute in honor of his seventieth birthday)”, Differ. Uravn., 38:2 (2002),  147–154  mathnet  mathscinet; Differ. Equ., 38:2 (2002), 155–163
2001
81. A. M. Vershik, V. I. Derguzov, I. A. Ibragimov, O. A. Ladyzhenskaya, G. A. Leonov, “Vladimir Andreevich Yakubovich (on the occasion of his 75th birthday)”, Algebra i Analiz, 13:4 (2001),  254–256  mathnet  mathscinet  zmath; St. Petersburg Math. J., 13:4 (2002), 703–704
82. Yu. D. Burago, A. M. Vershik, I. A. Ibragimov, G. A. Leonov, N. Yu. Netsvetaev, A. V. Pogorelov, Yu. G. Reshetnyak, “Viktor Abramovich Zalgaller. To the 80th anniversary”, Zap. Nauchn. Sem. POMI, 280 (2001),  7–13  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 119:2 (2004), 129–132
1996
83. A. M. Vershik, O. A. Ladyzhenskaya, G. A. Leonov, V. N. Fomin, “Vladimir Andreevich Yakubovich (on his seventieth birthday)”, Uspekhi Mat. Nauk, 51:6(312) (1996),  231–232  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:6 (1996), 1237–1239  isi
1994
84. V. I. Arnol'd, M. Sh. Birman, I. M. Gel'fand, I. A. Ibragimov, S. V. Kerov, A. A. Kirillov, O. A. Ladyzhenskaya, G. A. Leonov, A. A. Lodkin, S. P. Novikov, Ya. G. Sinai, M. Z. Solomyak, L. D. Faddeev, “Anatolii Moiseevich Vershik (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 49:3(297) (1994),  195–204  mathnet  mathscinet; Russian Math. Surveys, 49:3 (1994), 207–221  isi
1991
85. N. N. Krasovskii, L. D. Kudryavtsev, G. A. Leonov, Yu. S. Osipov, S. Yu. Pilyugin, “Viktor Aleksandrovich Pliss (on the occasion of his sixtieth birthday)”, Differ. Uravn., 27:12 (1991),  2186–2189  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. Analytical and numerical methods for the study of attractors in dynamical systems: bifurcations, localization and dimension characteristics
N. Kuznetsov, G. A. Leonov
Dynamics in Siberia - 2018
March 1, 2018 09:30
2. Скрытые колебания в нелинейных динамических системах
G. A. Leonov
All-Moscow regular scientific seminar "Control Theory and Optimization"
November 22, 2011 11:30

Organisations
 
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