Alexandre Mikhailovich Vinogradov (obituary)
- 作者: Astashov A.M., Astashova I.V., Bocharov A.V., Buchstaber V.M., Vassiliev V.A., Verbovetsky A.M., Vershik A.M., Veselov A.P., Vinogradov M.M., Vitagliano L., Vitolo R.F., Voronov T.T., Kac V.G., Kosmann-Schwarzbach Y., Krasil'shchik I.S., Krichever I.M., Krishchenko A.P., Lando S.K., Lychagin V.V., Marvan M., Maslov V.P., Mishchenko A.S., Novikov S.P., Rubtsov V.N., Samokhin A.V., Sosinskii A.B., Stasheff J., Fuchs D.B., Helemskii A.Y., Khor'kova N.G., Chetverikov V.N., Schwarz A.S.
- 期: 卷 75, 编号 2 (2020)
- 页面: 185-190
- 栏目: Articles
- URL: https://journal-vniispk.ru/0042-1316/article/view/133605
- DOI: https://doi.org/10.4213/rm9931
- ID: 133605
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作者简介
A. Astashov
Irina Astashova
Doctor of physico-mathematical sciences, Professor
Aleksei Bocharov
Candidate of physico-mathematical sciences
Victor Buchstaber
Email: buchstab@mi-ras.ru
Doctor of physico-mathematical sciences, Professor
Victor Vassiliev
Email: vva@mi-ras.ru
Doctor of physico-mathematical sciences, no status
Alexander Verbovetsky
Email: alik@ejik.org
Candidate of physico-mathematical sciences, no status
Anatolii Vershik
Email: avershik@gmail.com
Doctor of physico-mathematical sciences, Professor
Aleksandr Veselov
Email: A.P.Veselov@lboro.ac.uk
Doctor of physico-mathematical sciences, Professor
Michael Vinogradov
Candidate of physico-mathematical sciences
L. Vitagliano
Email: lvitagliano@unisa.it
R. Vitolo
Email: raffaele.vitolo@unile.it
Theodore Voronov
Email: theodore.voronov@manchester.ac.uk
Candidate of physico-mathematical sciences, no status
Victor Kac
Email: kac@math.mit.edu
Yvette Kosmann-Schwarzbach
Email: Yvette.Kosmann-Schwarzbach@math.cnrs.fr
Iosif Krasil'shchik
Email: josephkra@gmail.com
Doctor of physico-mathematical sciences, Professor
Igor Krichever
Email: krichev@math.columbia.edu
Doctor of physico-mathematical sciences, Professor
Alexander Krishchenko
Email: apkri@bmstu.ru
Doctor of physico-mathematical sciences, Professor
Sergei Lando
Email: lando@mccme.ru
Doctor of physico-mathematical sciences
Valentin Lychagin
Email: lychagin@math.uit.no
Doctor of physico-mathematical sciences, Professor
Michal Marvan
Email: M.Marvan@math.slu.cz
Victor Maslov
Email: v.p.maslov@mail.ru
Doctor of physico-mathematical sciences, Professor
Alexandr Mishchenko
Email: asmish@mech.math.msu.su
Doctor of physico-mathematical sciences, Professor
Sergei Novikov
Email: snovikov@mi-ras.ru
Doctor of physico-mathematical sciences, Professor
Vladimir Rubtsov
Email: volodya@univ-angers.fr
Candidate of physico-mathematical sciences, Professor
Alexey Samokhin
Email: samohinalexey@gmail.com
Doctor of technical sciences, Associate professor
Aleksei Sosinskii
Candidate of physico-mathematical sciences
J. Stasheff
Email: jds@math.upenn.edu
Dmitrii Fuchs
Email: fuchs@math.ucdavis.edu
Alexander Helemskii
Nina Khor'kova
Candidate of physico-mathematical sciences, Associate professor
Vladimir Chetverikov
Email: chetveri@diffiety.ac.ru
Candidate of physico-mathematical sciences, Associate professor
Albert Schwarz
Doctor of physico-mathematical sciences, Professor
参考
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- А. М. Виноградов, “Алгебра логики линейных дифференциальных операторов”, Докл. АН СССР, 205:5 (1972), 1025–1028
- А. М. Виноградов, И. С. Красильщик, В. В. Лычагин, Введение в геометрию нелинейных дифференциальных уравнений, Наука, М., 1986, 336 с.
- Дж. Неструев, Гладкие многообразия и наблюдаемые, МЦНМО, М., 2000, 300 с.
- A. M. Vinogradov, “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, 2016, 257–285
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- I. S. Krasil'shchik, A. M. Vinogradov, “Nonlocal trends in the geometry of differential equations: symmetries, conservation laws, and Bäcklund transformations”, Acta Appl. Math., 15:1-2 (1989), 161–209
- А. М. Виноградов, Б. А. Купершмидт, “Структура гамильтоновой механики”, УМН, 32:4(196) (1977), 175–236
- Д. В. Алексеевский, А. М. Виноградов, В. В. Лычагин, “Основные идеи и понятия дифференциальной геометрии”, Геометрия – 1, Итоги науки и техн. Сер. Соврем. пробл. матем. Фундам. направления, 28, ВИНИТИ, М., 1988, 5–289
- А. М. Виноградов, И. С. Красильщик (ред.), Симметрии и законы сохранения уравнений математической физики, 2-е изд., испр., Факториал Пресс, М., 2005, 380 с.
- A. M. Vinogradov, “Local symmetries and conservation laws”, Acta Appl. Math., 2:1 (1984), 21–78
- А. М. Виноградов, “Геометрия нелинейных дифференциальных уравнений”, Итоги науки и техн. Сер. Пробл. геом., 11, ВИНИТИ, М., 1980, 89–134
- А. М. Виноградов, “Категория нелинейных дифференциальных уравнений”, Уравнения на многообразиях, Новое в глобальном анализе, Изд-во Воронеж. гос. ун-та, Воронеж, 1982, 26–51
- A. Vinogradov, “Introduction to secondary calculus”, Secondary calculus and cohomological physics (Moscow, 1997), Contemp. Math., 219, Amer. Math. Soc., Providence, RI, 1998, 241–272
- M. Henneaux, I. S. Krasil'shchik, A. M. Vinogradov (eds.), Secondary calculus and cohomological physics (Moscow, 1997), Contemp. Math., 219, Amer. Math. Soc., Providence, RI, 1998, xiv+287 pp.
- А. М. Виноградов, “Одна спектральная последовательность, связанная с нелинейным дифференциальным уравнением и алгебро-геометрические основания лагранжевой теории поля со связями”, Докл. АН СССР, 238:5 (1978), 1028–1031
- A. M. Vinogradov, “The $mathscr{C}$-spectral sequence, Lagrangian formalism, and conservation laws. I. The linear theory”, J. Math. Anal. Appl., 100:1 (1984), 1–40
- R. L. Bryant, P. A. Griffiths, “Characteristic cohomology of differential systems. I. General theory”, J. Amer. Math. Soc., 8:3 (1995), 507–596
- A. Verbovetsky, “Notes on the horizontal cohomology”, Secondary calculus and cohomological physics (Moscow, 1997), Contemp. Math., 219, Amer. Math. Soc., Providence, RI, 1998, 211–231
- T. Tsujishita, “On variation bicomplexes associated to differential equations”, Osaka Math. J., 19:2 (1982), 311–363
- J. Stasheff, “The (secret?) homological algebra of the Batalin–Vilkovisky approach”, Secondary calculus and cohomological physics (Moscow, 1997), Contemp. Math., 219, Amer. Math. Soc., Providence, RI, 1998, 195–210
- А. М. Виноградов, “Объединение скобок Схоутена и Нийенхейса, когомологии и супердифференциальные операторы”, Матем. заметки, 47:6 (1990), 138–140
- A. Cabras, A. M Vinogradov, “Extensions of the Poisson bracket to differential forms and multi-vector fields”, J. Geom. Phys., 9:1 (1992), 75–100
- Y. Kosmann-Schwarzbach, “From Poisson algebras to Gerstenhaber algebras”, Ann. Inst. Fourier (Grenoble), 46:5 (1996), 1243–1274
- P. W. Michor, A. M. Vinogradov, “$n$-ary Lie and associative algebras”, Geometrical structures for physical theories. II (Vietri, 1996), Rend. Sem. Mat. Univ. Politec. Torino, 54:4 (1996), 373–392
- G. Marmo, G. Vilasi, A. M. Vinogradov, “The local structure of $n$-Poisson and $n$-Jacobi manifolds”, J. Geom. Phys., 25:1-2 (1998), 141–182
- A. M. Vinogradov, M. M. Vinogradov, “Graded multiple analogs of Lie algebras”, Acta Appl. Math., 72:1-2 (2002), 183–197
- А. М. Виноградов, Е. М. Воробьев, “Применение симметрии для нахождения точных решений уравнения Заболотской–Хохлова”, Акустич. журн., 22:1 (1976), 23–27
- V. N. Gusyatnikova, A. V. Samokhin, V. S. Titov, A. M. Vinogradov, V. A. Yumaguzhin, “Symmetries and conservation laws of Kadomtsev–Pogutse equations (their computation and first applications)”, Acta Appl. Math., 15:1-2 (1989), 23–64
- G. Sparano, G. Vilasi, A. M. Vinogradov, “Vacuum Einstein metrics with bidimensional Killing leaves. I. Local aspects”, Differential Geom. Appl., 16:2 (2002), 95–120
- G. Sparano, G. Vilasi, A. M. Vinogradov, “Vacuum Einstein metrics with bidimensional Killing leaves. II. Global aspects”, Differential Geom. Appl., 17:1 (2002), 15–35
- G. Sparano, G. Vilasi, A. M. Vinogradov, “Gravitational fields with a non-Abelian, bidimensional Lie algebra of symmetries”, Phys. Lett. B, 513:1-2 (2001), 142–146
- A. M. Vinogradov, “Particle-like structure of Lie algebras”, J. Math. Phys., 58:7 (2017), 071703, 49 pp.
- A. M. Vinogradov, “Particle-like structure of coaxial Lie algebras”, J. Math. Phys., 59:1 (2018), 011703, 42 pp.
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