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Alexandre Mikhaĭlovich Vinogradov. (English. Russian original) Zbl 1445.01025

Russ. Math. Surv. 75, No. 2, 369-375 (2020); translation from Usp. Mat. Nauk 75, No. 2, 185-190 (2020).

MSC:

01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Vinogradov, Alexandre Mikhaĭlovich
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[1] А. М. Виноградов 1960 О спектральной последовательности Адамса Докл. АН СССР133 5 999-1002
[2] English transl. A. M. Vinogradov 1960 On Adams’ spectral sequence Soviet Math. Dokl.1 910-913 · Zbl 0097.16101
[3] А. М. Виноградов 1972 Алгебра логики линейных дифференциальных операторов Докл. АН СССР205 5 1025-1028
[4] English transl. A. M. Vinogradov 1960 The logic algebra for the theory of linear differential operators Soviet Math. Dokl.13 1058-1062 · Zbl 0267.58013
[5] А. М. Виноградов, И. С. Красильщик, В. В. Лычагин 1986 Введение в геометрию нелинейных дифференциальных уравнений Наука, М. 336 pp.
[6] English transl. I. S. Krasil’shchik, V. V. Lychagin, and A. M. Vinogradov 1986 Geometry of jet spaces and nonlinear partial differential equations Advanced Studies in Contemporary Mathematics 1 Gordon and Breach Science Publishers, New York xx+441 pp. · Zbl 0722.35001
[7] Дж. Неструев 2000 Гладкие многообразия и наблюдаемые МЦНМО, М. 300 pp.
[8] English transl. J. Nestruev 2003 Smooth manifolds and observables Grad. Texts in Math. 220 Springer-Verlag, New York xiv+222 pp. · Zbl 1021.58001 · doi:10.1007/b98871
[9] A. M. Vinogradov 2016 Logic of differential calculus and the zoo of geometric structures Geometry of jets and fields Banach Center Publ. 110 Polish Acad. Sci. Inst. Math., Warsaw 257-285 · Zbl 1380.58004 · doi:10.4064/bc110-0-17
[10] А. М. Виноградов, И. С. Красильщик 1975 Что такое гамильтонов формализм? УМН30 1(181) 173-198
[11] English transl. A. M. Vinogradov and I. S. Krasil’shchik 1975 What is the Hamiltonian formalism? Russian Math. Surveys30 1 177-202 · Zbl 0327.70006 · doi:10.1070/RM1975v030n01ABEH001403
[12] I. S. Krasil’shchik and A. M. Vinogradov 1989 Nonlocal trends in the geometry of differential equations: symmetries, conservation laws, and Bäcklund transformations Acta Appl. Math.15 1-2 161-209 · Zbl 0692.35003 · doi:10.1007/BF00131935
[13] А. М. Виноградов, Б. А. Купершмидт 1977 Структура гамильтоновой механики УМН32 4(196) 175-236 · Zbl 0365.70016
[14] English transl. A. M. Vinogradov and B. A. Kupershmidt 1977 The structures of Hamiltonian mechanics Russian Math. Surveys32 4 177-243 · Zbl 0383.70020 · doi:10.1070/RM1977v032n04ABEH001642
[15] Д. В. Алексеевский, А. М. Виноградов, В. В. Лычагин 1988 Основные идеи и понятия дифференциальной геометрии Геометрия - 1 Итоги науки и техн. Сер. Соврем. пробл. матем. Фундам. направления 28 ВИНИТИ, М. 5-289
[16] English transl. D. V. Alekseevskij, A. M. Vinogradov, and V. V. Lychagin 1991 Basic ideas and concepts of differential geometry Geometry I Encycl. Math. Sci. 28 1-264 · Zbl 0741.00027
[17] А. М. Виноградов, И. С. Красильщик (ред.) 2005 Симметрии и законы сохранения уравнений математической физики Факториал Пресс, М. 2-е изд., испр.380 pp.
[18] English transl. of 1st ed. I. S. Krasil’shchik and A. M. Vinogradov (eds.) 1999 Symmetries and conservation laws for differential equations of mathematical physics Transl. Math. Monogr. 182 Amer. Math. Soc., Providence, RI xiv+333 pp. · Zbl 0911.00032
[19] A. M. Vinogradov 1984 Local symmetries and conservation laws Acta Appl. Math.2 1 21-78 · Zbl 0534.58005 · doi:10.1007/BF01405491
[20] А. М. Виноградов 1980 Геометрия нелинейных дифференциальных уравнений Итоги науки и техн. Сер. Пробл. геом. 11 ВИНИТИ, М. 89-134
[21] English transl. A. M. Vinogradov 1981 The geometry of nonlinear differential equations J. Soviet Math.17 1 1624-1649 · Zbl 0475.58025 · doi:10.1007/BF01084594
[22] А. М. Виноградов 1982 Категория нелинейных дифференциальных уравнений Уравнения на многообразиях Новое в глобальном анализе Изд-во Воронеж. гос. ун-та, Воронеж 26-51
[23] English transl. A. M. Vinogradov 1984 Category of nonlinear differential equations Global analysis – studies and applications I Lecture Notes in Math. 1108 Amer. Math. Soc., Providence, RI 77-102 · Zbl 0547.58005 · doi:10.1007/BFb0099553
[24] A. Vinogradov 1998 Introduction to secondary calculus Secondary calculus and cohomological physicsMoscow 1997 Contemp. Math. 219 Amer. Math. Soc., Providence, RI 241-272 · Zbl 0931.58021 · doi:10.1090/conm/219/03079
[25] M. Henneaux, I. S. Krasil’shchik, and A. M. Vinogradov (eds.) 1998 Secondary calculus and cohomological physicsMoscow 1997 Contemp. Math. 219 Amer. Math. Soc., Providence, RI xiv+287 pp. · doi:10.1090/conm/219/03079
[26] А. М. Виноградов 1978 Одна спектральная последовательность, связанная с нелинейным дифференциальным уравнением и алгебро-геометрические основания лагранжевой теории поля со связями Докл. АН СССР238 5 1028-1031
[27] English transl. A. M. Vinogradov 1978 A spectral sequence associated with a nonlinear differential equation, and algebro-geometric foundations of Lagrangian field theory with constraints Soviet Math. Dokl.19 144-148 · Zbl 0406.58015
[28] A. M. Vinogradov 1984 The \(\mathscr{C} \)-spectral sequence, Lagrangian formalism, and conservation laws. I. The linear theory J. Math. Anal. Appl.100 1 1-40 · Zbl 0548.58014 · doi:10.1016/0022-247X(84)90071-4
[29] A. M. Vinogradov II. The nonlinear theory J. Math. Anal. Appl. 41-129 · Zbl 0548.58015 · doi:10.1016/0022-247X(84)90072-6
[30] R. L. Bryant and P. A. Griffiths 1995 Characteristic cohomology of differential systems. I. General theory J. Amer. Math. Soc.8 3 507-596 · Zbl 0845.58004 · doi:10.2307/2152923
[31] A. Verbovetsky 1998 Notes on the horizontal cohomology Secondary calculus and cohomological physicsMoscow 1997 Contemp. Math. 219 Amer. Math. Soc., Providence, RI 211-231 · Zbl 0936.58002 · doi:10.1090/conm/219/03079
[32] T. Tsujishita 1982 On variation bicomplexes associated to differential equations Osaka Math. J.19 2 311-363 · Zbl 0524.58041 · doi:10.1090/conm/219/03079
[33] J. Stasheff 1998 The (secret?) homological algebra of the Batalin-Vilkovisky approach Secondary calculus and cohomological physicsMoscow 1997 Contemp. Math. 219 Amer. Math. Soc., Providence, RI 195-210 · Zbl 0969.17012 · doi:10.1090/conm/219/03079
[34] А. М. Виноградов 1990 Объединение скобок Схоутена и Нийенхейса, когомологии и супердифференциальные операторы Матем. заметки47 6 138-140
[35] A. M. Vinogradov 1990 The union of the Schouten and Nijenhuis brackets, cohomology, and superdifferential operators Mat. Zametki47 6 138-140 · Zbl 0712.58059
[36] A. Cabras and A. M Vinogradov 1992 Extensions of the Poisson bracket to differential forms and multi-vector fields J. Geom. Phys.9 1 75-100 · Zbl 0748.58008 · doi:10.1016/0393-0440(92)90026-W
[37] Y. Kosmann-Schwarzbach 1996 From Poisson algebras to Gerstenhaber algebras Ann. Inst. Fourier (Grenoble)46 5 1243-1274 · Zbl 0858.17027 · doi:10.5802/aif.1547
[38] P. W. Michor and A. M. Vinogradov \(1996 n\)-ary Lie and associative algebras. Geometrical structures for physical theories. II Rend. Sem. Mat. Univ. Politec. Torino54 4 373-392 · Zbl 0928.17029
[39] G. Marmo, G. Vilasi, and A. M. Vinogradov 1998 The local structure of \(n\)-Poisson and \(n\)-Jacobi manifolds J. Geom. Phys.25 1-2 141-182 · Zbl 0978.53126 · doi:10.1016/S0393-0440(97)00057-0
[40] A. M. Vinogradov and M. M. Vinogradov 2002 Graded multiple analogs of Lie algebras Acta Appl. Math.72 1-2 183-197 · Zbl 1020.17003 · doi:10.1023/A:1015281004171
[41] А. М. Виноградов, Е. М. Воробьев 1976 Применение симметрии для нахождения точных решений уравнения Заболотской-Хохлова Акустич. журн.22 1 23-27
[42] A. M. Vinogradov and E. M. Vorob’ev 1976 Application of symmetry for finding exact solutions of the Khokhlov-Zabolotskaya equation Akusticheskii Zh.22 1 23-27
[43] V. N. Gusyatnikova, A. V. Samokhin, V. S. Titov, A. M. Vinogradov, and V. A. Yumaguzhin 1989 Symmetries and conservation laws of Kadomtsev-Pogutse equations (their computation and first applications) Acta Appl. Math.15 1-2 23-64 · Zbl 0692.35087 · doi:10.1007/BF00131929
[44] G. Sparano, G. Vilasi, and A. M. Vinogradov 2002 Vacuum Einstein metrics with bidimensional Killing leaves. I. Local aspects Differential Geom. Appl.16 2 95-120 · Zbl 1033.53021 · doi:10.1016/S0926-2245(01)00062-6
[45] G. Sparano, G. Vilasi, and A. M. Vinogradov 2002 Vacuum Einstein metrics with bidimensional Killing leaves. II. Global aspects Differential Geom. Appl.17 1 15-35 · Zbl 1035.53099 · doi:10.1016/S0926-2245(02)00078-5
[46] G. Sparano, G. Vilasi, and A. M. Vinogradov 2001 Gravitational fields with a non-Abelian, bidimensional Lie algebra of symmetries Phys. Lett. B513 1-2 142-146 · Zbl 0969.83525 · doi:10.1016/S0370-2693(01)00722-5
[47] A. M. Vinogradov 2017 Particle-like structure of Lie algebras J. Math. Phys.58 7 071703 49 pp. · Zbl 1422.17008 · doi:10.1063/1.4991657
[48] A. M. Vinogradov 2018 Particle-like structure of coaxial Lie algebras J. Math. Phys.59 1 011703 42 pp. · Zbl 1422.17009 · doi:10.1063/1.5001787
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