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Makarov Evgenii Konstantinovich

Statistics Math-Net.Ru
Total publications: 33
Scientific articles: 32
Cited articles: 10
Citations in Math-Net.Ru: 29

Number of views:
This page:560
Abstract pages:994
Full texts:400
References:88
Professor
Doctor of physico-mathematical sciences (2001)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 06.08.1963
E-mail:
Keywords: linear systems of ordinary differential equations; Lyapunov characteristic exponents; total differential equations; control problems for Lyapunov exponents; vector optimization.

Subject:

Properties of Lyapunov irregularity sets for linear ordinary differential systems with parameter under derivative are investigated. Sufficient conditions for discretizability of asymptotic invariants of linear differential systems are proved. Interrelations between characteristic exponents and characteristic functionals of linear total differential equations are established. By means of these interrelations the structure of characteristic sets of such equations is investigated including sufficient conditions for closedness and boundednes. Sufficient conditions for complete integrability of linear approximation to nonlinear completely integrable total differential equation are proved. These condition holds e.g. for each equation with $C^1$ right part. A number of papers (with S. N. Popova)are dedicated to control problems for Lyapunov exponent and other asymptotic invariants of uniformly completely controllable linear systems. These problems are the generalization of classical pole assignment problem to the settings of non-autonomous system. Sufficient conditions for local and global controllability of the invariants under consideration are obtained. A number of papers (with N. N. Rachkovski) are dedicated to vector optimization theory. Arcwise connectedness of the efficient point set of convex compactum in any Hausdorff topological vector space is proved; exhaustive comparison theorems for various kinds of proper efficiency in normed linear space are obtained; density results for generalized Henig proper efficiency under the weakest suppositions are proved.

Biography

Graduated from Faculty of Mathematics and Mechanics of Byelorussian State University (BSU) in 1985 (department of differential equations). Ph.D. thesis was defended in 1989. D.Sci. thesis was defended in 2001. A list of my works contains more than 70 titles.

   
Main publications:
  • Makarov E. K., Rachkovski N. N. Efficient sets of convex compacta are arcwise connected // J. Optimiz. Theory and Appl., 2001, 110(1), 159–172.

http://www.mathnet.ru/eng/person17583
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List of publications on ZentralBlatt
http://www.ams.org/mathscinet/search/author.html?return=viewitems&mrauthid=231860

Publications in Math-Net.Ru
1. On stationary solutions for Lindblad-type equations
S. Ya. Kilin, E. K. Makarov
Tr. Inst. Mat., 22:2 (2014),  53–62
2. Axiomatic representation for smallness classes of coefficient perturbations to linear differential systems
E. K. Makarov
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 1,  46–57
3. Asymptotics of the solution of the main problem of the integral fire theory
A. K. Demenchuk, E. K. Makarov
Differ. Uravn., 46:1 (2010),  23–28
4. Forced oscillations of relativistic oscillator with periodic external exitation
E. K. Makarov, A. A. Afanas'ev, A. N. Rubinov
Tr. Inst. Mat., 17:1 (2009),  103–109
5. A solution for the problem on oscillations of quasi-relativistic oscillator with periodic external exitation
E. K. Makarov, A. A. Afanas'ev, A. N. Rubinov
Tr. Inst. Mat., 16:2 (2008),  76–84
6. On radial solutions of completely integrable total differential equations
E. K. Makarov
Differ. Uravn., 42:10 (2006),  1318–1323
7. On the critical parameter value for the higher sigma-exponent of linear differential systems
E. K. Makarov
Differ. Uravn., 42:6 (2006),  844–846
8. On the properties of bogdanov perturbations of linear differential systems
E. K. Makarov
Differ. Uravn., 42:2 (2006),  275–277
9. Problems of control over Lyapunov invariants
V. A. Zaitsev, E. K. Makarov, S. N. Popova, E. L. Tonkov
Izv. IMI UdGU, 2006, no. 3(37),  43–48
10. On an Algorithm for Constructing an Attainable Upper Boundary for the Higher Exponent of Perturbed Systems
E. K. Makarov, I. V. Marchenko
Differ. Uravn., 41:12 (2005),  1621–1634
11. On an Upper Bound for the Higher Exponent of a Linear Differential System with Integrable Perturbations on the Half-Line
E. K. Makarov, I. V. Marchenko, N. V. Semerikova
Differ. Uravn., 41:2 (2005),  215–224
12. The Characteristic Sets of Multidimensional Equations with Respect to a Polyhedral Cone Can Be Nonclosed
E. K. Makarov
Differ. Uravn., 39:4 (2003),  560–562
13. Sufficient Conditions for the Local Proportional Controllability of Lyapunov Exponents of Linear Systems
E. K. Makarov, S. N. Popova
Differ. Uravn., 39:2 (2003),  217–226
14. The Complete Integrability of the Linear Approximation Equations for Completely Integrable Quasilinear Total Differential Equations
E. K. Makarov
Differ. Uravn., 36:12 (2000),  1631–1635
15. On the higher exponent of a linear many-dimensional completely integrable equation
E. K. Makarov
Differ. Uravn., 36:1 (2000),  54–61
16. On the global controllability of a complete set of Lyapunov invariants of two-dimensional linear systems
E. K. Makarov, S. N. Popova
Differ. Uravn., 35:1 (1999),  97–106
17. On the global controllability of central exponents of linear systems.
E. K. Makarov, S. N. Popova
Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 2,  60–67
18. On the existence of weakly normal bases of solutions of linear multidimensional completely integrable equations
E. K. Makarov
Differ. Uravn., 34:12 (1998),  1703–1705
19. On the discreteness of asymptotic invariants of linear differential systems
E. K. Makarov
Differ. Uravn., 34:10 (1998),  1322–1331
20. On boundedness conditions for characteristic sets of solutions of linear multidimensional equations
E. K. Makarov
Differ. Uravn., 33:5 (1997),  653–657
21. Local controllability of characteristic Lyapunov exponents of systems with simple exponents
E. K. Makarov, S. N. Popova
Differ. Uravn., 33:4 (1997),  495–499
22. On weakly regular linear completely solvable multidimensional equations
E. K. Makarov
Differ. Uravn., 33:2 (1997),  221–225
23. On the realization of partial exponents of solutions of linear differential systems on geometric progressions
E. K. Makarov
Differ. Uravn., 32:12 (1996),  1710–1711
24. Malkin estimates for the norm of the Cauchy matrix of a linear differential system
E. K. Makarov
Differ. Uravn., 32:3 (1996),  328–334
25. On the structure of characteristic sets of solutions of linear completely solvable total differential equations
E. K. Makarov
Differ. Uravn., 31:2 (1995),  220–227
26. On the interrelation between characteristic functionals and weak characteristic exponents
E. K. Makarov
Differ. Uravn., 30:3 (1994),  393–399
27. The effect of Lyapunov transforms and different perturbations on the nonregularity sets of linear differential systems
E. K. Makarov
Differ. Uravn., 28:10 (1992),  1708–1715
28. On a criterion for joint behavior of higher sigma exponents of a triangular system and the system of its diagonal approximation
E. K. Makarov
Differ. Uravn., 27:5 (1991),  910–911
29. A remark on sets of nonregularity of almost periodic linear differential systems
E. K. Makarov
Differ. Uravn., 27:3 (1991),  539–541
30. Linear systems with nonregularity sets of full measure
E. K. Makarov
Differ. Uravn., 25:2 (1989),  209–212
31. Sets of irregularity of linear systems with a parameter multiplying the derivative
E. K. Makarov
Differ. Uravn., 24:12 (1988),  2091–2098
32. Lyapunov irregular linear systems with a parameter multiplying the derivative
N. A. Izobov, E. K. Makarov
Differ. Uravn., 24:11 (1988),  1870–1880
33. A case of time-optimality for a linear homogeneous system
E. K. Makarov
Differ. Uravn., 22:2 (1986),  203–208

34. In memory of Evgenii Leonidovich Tonkov (27.06.1940–28.09.2014)
I. V. Gaishun, A. A. Gryzlov, V. Ya. Derr, N. A. Izobov, A. I. Karpov, E. K. Makarov, G. V. Merzlyakova, N. N. Petrov, S. N. Popova, L. I. Rodina, N. Kh. Rozov, I. N. Sergeev, A. A. Tolstonogov, V. N. Ushakov, A. G. Chentsov
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 4,  146–154
35. Nikolai Alekseevich Izobov (A tribute in honor of his 70th birthday)
A. V. Arutyunov, Yu. N. Bibikov, F. P. Vasil'ev, I. V. Gaishun, S. V. Emel'yanov, V. A. Il'in, I. T. Kiguradze, S. K. Korovin, L. D. Kudryavtsev, A. B. Kurzhanskii, S. A. Mazanik, E. K. Makarov, A. A. Martynyuk, E. F. Mishchenko, E. I. Moiseev, Yu. S. Osipov, V. A. Pliss, N. Kh. Rozov, V. A. Sadovnichy, A. M. Samoilenko, T. K. Shemjakina
Differ. Uravn., 46:1 (2010),  3–8

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