THE 70TH ANNIVERSARY OF PROFESSOR VALERY GEORGIEVICH DURNEV
https://doi.org/10.22405/2226-8383-2017-18-2-279-297
Abstract
This article considers activities of an outstanding expert in the field of algorithmic issues of algebra and mathematical logic Professor, Doctor of Physical and Mathematical Sciences, head of the Chair of Computer Security and Mathematical Methods of Information Processing of the P.G. Demidov Yaroslavl State University Valeriy Georgievich Durnev. It provides a brief overview of his main scientific results, touches upon achievements in pedagogical and organizational activities, and includes biographical information.
About the Authors
V. N. Bezverkhnii
Civil defence Academy EMERCOM of Russia
Russian Federation
doctor of physico-mathematical Sciences, Professor of the Department of mathematics
Russian Federation
doctor of physico-mathematical Sciences, Professor of the Department of mathematics
A. E. Ustyan
Tula State Lev Tolstoy University
Russian Federation
Russian Federation
candidate of physico-mathematical Sciences, Professor of the Department of algebra, mathematical analysis and geometry
I. V. Dobrynina
Tula State Lev Tolstoy University
Russian Federation
Russian Federation
doctor of physico-mathematical Sciences, associate professor, Professor of the Department of algebra, mathematical analysis and geometry
References
1. Durnev, V. G. 1970, "On positive formulas on groups" , Proc. of Math. Dept. of Tula State Pedagogical Inst., Ser. Geometry and Algebra. [Uchtnye Zapiski Matematicheskoy Kafedry Tul’skogo Pedogogicheskogo Instituta], no. 2. pp. 215–241. (Russian)
2. Durnev, V. G. 1972, "On positive theory of free semigroup" , Groups and semigropus, Tula, pp. 122–172 (Russian).
3. Durnev, V. G. 1973, "Positive theory of free semigroup" , Doklady Akademii Nauk SSSR, vol. 211, no. 4. pp. 772–774. (Russian)
4. Durnev, V. G. 1974, "Positive formulas in free semigroups" , Siberian Mathematical Journal, vol. 15, issue 5, pp. 796–800 (Translated from Sibirskii Matematicheskii Zhurnal, vol. 15, no. 5, pp. 1131–1137) [doi: 10.1007/BF00966439]
5. Durnev, V. G. 1973, "Positive theories of free semigroups" , Ph D. Thesis, Moscow State Pedagogical Institution. (Russian)
6. Durnev, V. G. 1995, "Undecidability of the positive ∀∃3 -theory of a free semigroup" , Siberian Mathematical Journal, vol. 36, no. 5. pp. 917–929 (Translated from: Sibirskii Matematicheskii Zhurnal, vol. 36, no. 5, pp. 1067–1080)
7. Durnev, V. G. 2000, "Undecidability of a simple fragment of a positive theory with a single constant for a free semigroup of rank two" , Mathematical Notes, vol. 67, no. 2, pp. 191–200. (Russian)
8. Durnev, V. G. 1974, "On equations in free semigroups and groups" , Mathematical Notes, vol. 16, no. 5. pp. 717–724. (Russian)
9. Durnev, V. G. 1977, "On some equations on free semigropus" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’. pp. 57–59. (Russian)
10. Durnev, V. G. & Zetkina, O. V. 2003, "On equations in free semigroups with certain constraints on their solutions" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’. (Russian)
11. Durnev, V. G. & Zetkina, O. V. 2008, "Equations with language constraints to their solutions in free monoids" , Mathematics, cybernetics, informatics — Prof. A. Yu. Levin Memorial Conference. Yaroslavl’ State University., pp. 93–99. (Russian)
12. Durnev, V. G. & Zetkina, O. V. 2008, "On equations in free semigroups with certain constraints on their solutions" , Zapiski Nauchnykh Seminarov POMI (Proc. of St.-Petersburg branch of V. A. Steklov Math. Inst.), St.-Petersburg., vol. 358, pp. 120–129. (Russian)
13. Durnev, V. G. & Zetkina, O. V. 2008, "On equations in free semigroups with certain constraints to their solutions" , Journal of Mathematical Sciences., vol. 158, no. 5, pp. 671–676. (Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 358, 2008, pp. 120-–129)
14. Durnev, V. G. & Zetkina, O. V. 2010, "Equations with subsemigroup constraints to their solutions in free semigroups " , Chebyshevskii Sb., vol. XI, issue 3(35), pp. 78–87. (Russian)
15. Durnev, V. G. 1991, "On equations with endomorphisms in free semigroups and groups" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’., pp. 30–35. (Russian)
16. Durnev, V. G. 1992, "Equations with endomorphisms in free semigroups" , Diskret. Mat.. vol. 4, no. 2, pp. 136–141. (Russian)
17. Durnev, V. G. 1992, "On equations in words and lengths with endomorphisms" , Russian Mathematics (Izvestiya VUZ. Matematika). vol. 36, no. 8, pp. 26–30. (Russian)
18. Durnev, V. G. 2003, "NP-completeness of the problem of endomorphic reducibility for elements of a free semigroup of an countable rank" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’. (Russian)
19. Durnev, V. G. 1990, "On one generalization of the Problem 9.25 from the “Kourovka notebook”" , Mathematical Notes., vol. 47, no. 2, pp. 117–121. (Translated from Matematicheskie Zametki. 1990. Vol. 47, no. 2. P. 15–19.)
20. Durnev, V. G. 1993, "Equations with constraints on the solution in free groups" , Mathematical Notes., vol. 53, no. 1, pp. 26—29. (Translated from Matematicheskie Zametki. Vol. 53, no. 1. P. 36–40.)
21. Durnev, V. G. 1995, "On equations with subgroup constraints on solutions in free groups " , Discrete Math. Appl., vol. 5, no. 6, pp. 567—575. (Translated from: Diskret. Mat. 1995. Vol. 7. no. 4, 60–67.)
22. Durnev, V. G. & Zetkina, O. V. 2006, "On equations with subgroup constraints on solutions in free groups" , Mathematics in Yaroslavl’ University (30th aniversary of Math. Faculty). Yaroslavl’, pp. 181–200. (Russian)
23. Durnev, V. G. & Zetkina, O. V. 2010, "On some equations with with constraints to their solutions" , Chebyshevskii Sb., vol. XI, issue 3(35), pp. 88–97. (Russian)
24. Durnev, V. G. 1996, "On the solvability problem for equations with a single coefficient" , Mathematical Notes., vol. 59, no. 6, pp. 601–610. (Translated from Matematicheskie Zametki, 1996. Vol. 59. no. 6. P. 832–845).
25. Durnev, V. G. & Zetkina, O. V. 2012, "On the equations resolved with respect to variables in free groups with constraints to the solutions" , Chebyshevskii Sb., vol. XIII, issue 1(41), pp. 63– 80. (Russian)
26. Durnev V. G. & Zetkina, O. V. 2012, "NP-complexity of the decidability problem for the equations with right-hand-side in a free group" , Chebyshevskii Sb., vol. XIII, issue 1(41), pp. 46– 53. (Russian)
27. Durnev, V. G. 2012, "On equations in free groups" , Chebyshevskii Sb., vol. XIII, issue 1(41), pp. 59–62. (Russian)
28. Durnev, V. G. 2012, "On one A. I. Mal’cev’s question from the “Kourovka notebook”" , Chebyshevskii Sb., vol. XIII, issue 1(41), pp. 54–58. (Russian)
29. Durnev, V. G. 1981, "On systems of equations on free nilpotent groups" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’, pp. 66–69. (Russian)
30. Durnev, V. G. 1988, "Undecidability of endomorphic reducibility problem for sets of elements of a free nilpotent group" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’., pp. 56–63. (Russian)
31. Durnev, V. G. & Zetkina, O. V. 2003, "On fragments of elementary theories of free nilpotent groups" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’. (Russian)
32. Durnev, V. G. 1989, "The Mal’tsev-Nielsen equation in a free metabelian group of rank two" , Mathematical notes of the Academy of Sciences of the USSR., vol. 46, Issue 6, pp. 927–929. (Translated from Matematicheskie Zametki, vol. 46, No. 6, pp. 57–60, December, 1989)
33. Durnev, V. G. 1992, "Undecidability of a positive ∃-theory with one constant for a free solvable group" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’., pp. 30– 35. (Russian)
34. Durnev, V. G. 1990, "On Tarski problem for free groups of some manifolds" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’., pp. 25–35. (Russian)
35. Durnev, V. G. & Kazarin, L. S. 1994 , "On unversal theories of some groups" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’. (Russian)
36. Durnev, V. G. 1994, "Undecidability of some bounded theories of групп SL(n,Z) and GL(n,Z)
37. (n ≥ 3) groups", Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’. (Russian)
38. Durnev, V. G. 1995, "On elementary theories of integer linear groups" , Izvestiya: Mathematics, vol. 59, no. 5, pp. 919–934.
39. D38. Durnev, V. G. 1998, "Semigroups with identities of some F-groups", Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’. (Russian)
40. Durnev, V. G., Zetkina, O. V. & Zetkina, A. I. 2014, "On the Tits’ alternative for subgroups of F-groups" , Chebyshevskii Sb., vol. 15, issue 1(49), pp. 110—120. (Russian)
41. Durnev, V. G. 1987, "On width of the commutant of B3 и B4 braid groups", XIX USSR algebraic conference. Book of abstracts. L’vov. (Russian)
42. Durnev, V. G. & Zetkina, O. V. 1994, "On factor-groups of B(n) braids and linear SL(n,Z) and GL(n,Z) groups", Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’. (Russian)
43. Durnev, V. G. 1988, "On formulae with a length function on a free group" , 10th USSR Conference on math. logics. Book of abstracts. Leningrad., pp. 56 (Russian)
44. Durnev, V. G. & Zetkina, O. V. 1991, "On a positive theory of a free group in a signature extended by a length function" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’., pp. 25–29. (Russian)
45. Durnev, V. G. & Zetkina, O. V. 1994, "Algoritmically undecidable problems for Diophantine sets in Π2" , Group Theory & Homological Algebra, Yaroslavl’ State University. Yaroslavl’. (Russian)
46. Durnev, V. 1997, "Studying Algorithmic Problems for Free Semigroups and Groups" , Lecture Notes in Computer Science., vol. 1234, pp. 88–101. (Russian)
47. Durnev, V. G. 1997, "Studying Algorithmic Problems for Free Semigroups and Groups": Dr. Sci. Thesis, Moscow State University. (Russian)
48. Adian, S. I. & Durnev, V. G. 2000, "Decision problems for groups and semigroups" , Russian Mathematical Surveys., vol. 55, no. 2, pp. 207. [doi: 10.1070/ RM2000v055n02ABEH000267]
49. Durnev, V. G., Zetkina, O. V. & Zetkina, A. I. 2016, "On equations and inequalities in words and word lengths" , Chebyshevskii Sb., vol. XVII, issue 2(58), pp. 137–145. (Russian)
50. Durnev, V. G., Zetkina, O. V. & Zetkina, A. I. 2016, "On amenable subgroups of F -groups" , Chebyshevskii Sb., vol. XVII, issue 2(58), pp. 128–136. (Russian)
51. Durnev, V. G., Zetkina, O. V., Zetkina, A. I. & Murin, D. M. 2016, "About the coNP-complete "Injective knapsack" problem" , Prikl. Diskr. Mat., no. 3(33), pp. 85–92. (Russian)
52. Durnev, V. G. & Zetkina, O. V. 2014, "Some of the results obtained in the Yaroslavl branch algebraic school of M. D. Grindlinger" , Chebyshevskii Sb., vol. XV, issue 4(50), pp. 5–31. (Russian)
Review
For citations:
Bezverkhnii V.N., Ustyan A.E., Dobrynina I.V. THE 70TH ANNIVERSARY OF PROFESSOR VALERY GEORGIEVICH DURNEV. Chebyshevskii Sbornik. 2017;18(2):279-297. (In Russ.) https://doi.org/10.22405/2226-8383-2017-18-2-279-297
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