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Makarov, Evgenii Konstantinovich

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Total publications: 37
Scientific articles: 36

Number of views:
This page:928
Abstract pages:3904
Full texts:1632
References:218
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
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/231860

Publications in Math-Net.Ru
2019
1. E. K. Makarov, S. N. Popova, “On the definition of uniform complete observability”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:3 (2019),  129–140  mathnet  elib
2. I. N. Banshchikova, E. K. Makarov, S. N. Popova, “On the conditions of proportional local assignability of the Lyapunov spectrum of a linear discrete-time system”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:3 (2019),  301–311  mathnet
2017
3. E. K. Makarov, I. V. Marchenko, “On upward mobility of the highest exponent of a linear differential system under perturbations of the coefficients from the simplest classes with degeneracies”, Tr. Inst. Mat., 25:2 (2017),  50–59  mathnet
4. E. K. Makarov, S. N. Popova, “On the definition of uniform complete controllability”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:3 (2017),  326–343  mathnet  elib
2014
5. S. Ya. Kilin, E. K. Makarov, “On stationary solutions for Lindblad-type equations”, Tr. Inst. Mat., 22:2 (2014),  53–62  mathnet
6. E. K. Makarov, “Axiomatic representation for smallness classes of coefficient perturbations to linear differential systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, 1,  46–57  mathnet
2010
7. A. K. Demenchuk, E. K. Makarov, “Asymptotics of the solution of the main problem of the integral fire theory”, Differ. Uravn., 46:1 (2010),  23–28  mathnet  mathscinet  zmath  elib; Differ. Equ., 46:1 (2010), 24–29  scopus
2009
8. E. K. Makarov, A. A. Afanas'ev, A. N. Rubinov, “Forced oscillations of relativistic oscillator with periodic external exitation”, Tr. Inst. Mat., 17:1 (2009),  103–109  mathnet  zmath
2008
9. E. K. Makarov, A. A. Afanas'ev, A. N. Rubinov, “A solution for the problem on oscillations of quasi-relativistic oscillator with periodic external exitation”, Tr. Inst. Mat., 16:2 (2008),  76–84  mathnet  zmath
2006
10. E. K. Makarov, “On radial solutions of completely integrable total differential equations”, Differ. Uravn., 42:10 (2006),  1318–1323  mathnet  mathscinet; Differ. Equ., 42:10 (2006), 1385–1390
11. E. K. Makarov, “On the critical parameter value for the higher sigma-exponent of linear differential systems”, Differ. Uravn., 42:6 (2006),  844–846  mathnet  mathscinet; Differ. Equ., 42:6 (2006), 901–904
12. E. K. Makarov, “On the properties of bogdanov perturbations of linear differential systems”, Differ. Uravn., 42:2 (2006),  275–277  mathnet  mathscinet; Differ. Equ., 42:2 (2006), 294–296
13. V. A. Zaitsev, E. K. Makarov, S. N. Popova, E. L. Tonkov, “Problems of control over Lyapunov invariants”, Izv. IMI UdGU, 2006, 3(37),  43–48  mathnet
2005
14. E. K. Makarov, I. V. Marchenko, “On an Algorithm for Constructing an Attainable Upper Boundary for the Higher Exponent of Perturbed Systems”, Differ. Uravn., 41:12 (2005),  1621–1634  mathnet  mathscinet; Differ. Equ., 41:12 (2005), 1694–1709
15. E. K. Makarov, I. V. Marchenko, N. V. Semerikova, “On an Upper Bound for the Higher Exponent of a Linear Differential System with Integrable Perturbations on the Half-Line”, Differ. Uravn., 41:2 (2005),  215–224  mathnet  mathscinet; Differ. Equ., 41:2 (2005), 227–237
2003
16. E. K. Makarov, “The Characteristic Sets of Multidimensional Equations with Respect to a Polyhedral Cone Can Be Nonclosed”, Differ. Uravn., 39:4 (2003),  560–562  mathnet  mathscinet; Differ. Equ., 39:4 (2003), 599–601
17. E. K. Makarov, S. N. Popova, “Sufficient Conditions for the Local Proportional Controllability of Lyapunov Exponents of Linear Systems”, Differ. Uravn., 39:2 (2003),  217–226  mathnet  mathscinet; Differ. Equ., 39:2 (2003), 234–245
2000
18. E. K. Makarov, “The Complete Integrability of the Linear Approximation Equations for Completely Integrable Quasilinear Total Differential Equations”, Differ. Uravn., 36:12 (2000),  1631–1635  mathnet  mathscinet; Differ. Equ., 36:12 (2000), 1789–1793
19. E. K. Makarov, “On the higher exponent of a linear many-dimensional completely integrable equation”, Differ. Uravn., 36:1 (2000),  54–61  mathnet  mathscinet; Differ. Equ., 36:1 (2000), 64–70
1999
20. E. K. Makarov, S. N. Popova, “On the global controllability of a complete set of Lyapunov invariants of two-dimensional linear systems”, Differ. Uravn., 35:1 (1999),  97–106  mathnet  mathscinet; Differ. Equ., 35:1 (1999), 97–107
21. E. K. Makarov, S. N. Popova, “On the global controllability of central exponents of linear systems.”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, 2,  60–67  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 43:2 (1999), 56–63
1998
22. E. K. Makarov, “On the existence of weakly normal bases of solutions of linear multidimensional completely integrable equations”, Differ. Uravn., 34:12 (1998),  1703–1705  mathnet  mathscinet; Differ. Equ., 34:12 (1998), 1713–1715
23. E. K. Makarov, “On the discreteness of asymptotic invariants of linear differential systems”, Differ. Uravn., 34:10 (1998),  1322–1331  mathnet  mathscinet; Differ. Equ., 34:10 (1998), 1323–1331
1997
24. E. K. Makarov, “On boundedness conditions for characteristic sets of solutions of linear multidimensional equations”, Differ. Uravn., 33:5 (1997),  653–657  mathnet  mathscinet; Differ. Equ., 33:5 (1997), 656–660
25. E. K. Makarov, S. N. Popova, “Local controllability of characteristic Lyapunov exponents of systems with simple exponents”, Differ. Uravn., 33:4 (1997),  495–499  mathnet  mathscinet; Differ. Equ., 33:4 (1997), 496–500
26. E. K. Makarov, “On weakly regular linear completely solvable multidimensional equations”, Differ. Uravn., 33:2 (1997),  221–225  mathnet  mathscinet; Differ. Equ., 33:2 (1997), 221–225
1996
27. E. K. Makarov, “On the realization of partial exponents of solutions of linear differential systems on geometric progressions”, Differ. Uravn., 32:12 (1996),  1710–1711  mathnet  mathscinet; Differ. Equ., 32:12 (1996), 1705–1706
28. E. K. Makarov, “Malkin estimates for the norm of the Cauchy matrix of a linear differential system”, Differ. Uravn., 32:3 (1996),  328–334  mathnet  mathscinet; Differ. Equ., 32:3 (1996), 333–339
1995
29. E. K. Makarov, “On the structure of characteristic sets of solutions of linear completely solvable total differential equations”, Differ. Uravn., 31:2 (1995),  220–227  mathnet  mathscinet; Differ. Equ., 31:2 (1995), 203–208
1994
30. E. K. Makarov, “On the interrelation between characteristic functionals and weak characteristic exponents”, Differ. Uravn., 30:3 (1994),  393–399  mathnet  mathscinet  zmath; Differ. Equ., 30:3 (1994), 362–367
1992
31. E. K. Makarov, “The effect of Lyapunov transforms and different perturbations on the nonregularity sets of linear differential systems”, Differ. Uravn., 28:10 (1992),  1708–1715  mathnet  mathscinet; Differ. Equ., 28:10 (1992), 1392–1398
1991
32. E. K. Makarov, “On a criterion for joint behavior of higher sigma exponents of a triangular system and the system of its diagonal approximation”, Differ. Uravn., 27:5 (1991),  910–911  mathnet  mathscinet  zmath
33. E. K. Makarov, “A remark on sets of nonregularity of almost periodic linear differential systems”, Differ. Uravn., 27:3 (1991),  539–541  mathnet  mathscinet  zmath
1989
34. E. K. Makarov, “Linear systems with nonregularity sets of full measure”, Differ. Uravn., 25:2 (1989),  209–212  mathnet  mathscinet; Differ. Equ., 25:2 (1989), 151–153
1988
35. E. K. Makarov, “Sets of irregularity of linear systems with a parameter multiplying the derivative”, Differ. Uravn., 24:12 (1988),  2091–2098  mathnet  mathscinet; Differ. Equ., 24:12 (1988), 1413–1419
36. N. A. Izobov, E. K. Makarov, “Lyapunov irregular linear systems with a parameter multiplying the derivative”, Differ. Uravn., 24:11 (1988),  1870–1880  mathnet  mathscinet; Differ. Equ., 24:11 (1988), 1243–1250
1986
37. E. K. Makarov, “A case of time-optimality for a linear homogeneous system”, Differ. Uravn., 22:2 (1986),  203–208  mathnet  mathscinet

2014
38. 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, “In memory of Evgenii Leonidovich Tonkov (27.06.1940–28.09.2014)”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, 4,  146–154  mathnet
2010
39. 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, “Nikolai Alekseevich Izobov (A tribute in honor of his 70th birthday)”, Differ. Uravn., 46:1 (2010),  3–8  mathnet  mathscinet  zmath; Differ. Equ., 46:1 (2010), 1–7

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