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Nikolay Bogolyubov

August 28, 2023

For the actor, see Nikolay Bogolyubov (actor).
In this name that follows Eastern Slavic naming conventions, the patronymic is Nikolayevich and the family name is Bogolyubov.

Nikolay Nikolayevich Bogolyubov (Russian: Никола́й Никола́евич Боголю́бов; 21 August 1909 – 13 February 1992), also transliterated as Bogoliubov and Bogolubov, was a Soviet and Russian mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and the theory of dynamical systems; he was the recipient of the 1992 Dirac Medal.

Nikolay Bogolyubov
Born
Nikolay Nikolayevich Bogolyubov

(1909-08-21)21 August 1909
Nizhny Novgorod, Russian Empire
Died13 February 1992(1992-02-13) (aged 82)
Moscow, Russian Federation
NationalitySoviet, Russian
Known for
AwardsStalin Prize (1947, 1953)
USSR State Prize (1984)
Lenin Prize (1958)
Heineman Prize (1966)
Hero of Socialist Labor (1969, 1979)
Max Planck Medal (1973)
Lomonosov Gold Medal (1985)
Dirac Prize (1992)
Scientific career
FieldsTheoretical physics, mathematical physics, mathematics
InstitutionsKyiv University
Steklov Institute of Mathematics
Lomonosov Moscow State University
Joint Institute for Nuclear Research
Doctoral advisorNikolay Krylov
Doctoral studentsDmitry Zubarev
Yurii Mitropolskiy
Sergei Tyablikov
Dmitry Shirkov

Biography Edit

Early life (1909–1921) Edit

Nikolay Bogolyubov was born on 21 August 1909 in Nizhny Novgorod, Russian Empire to Russian Orthodox Church priest and seminary teacher of theology, psychology and philosophy Nikolay Mikhaylovich Bogolyubov, and Olga Nikolayevna Bogolyubova, a teacher of music. The Bogolyubovs relocated to the village of Velikaya Krucha in the Poltava Governorate (now in Poltava Oblast, Ukraine) in 1919, where the young Nikolay Bogolyubov began to study physics and mathematics. The family soon moved to Kyiv in 1921, where they continued to live in poverty as the elder Nikolay Bogolyubov only found a position as a priest in 1923.[1]

He attended research seminars in Kyiv University and soon started to work under the supervision of the well-known contemporary mathematician Nikolay Krylov. In 1924, at the age of 15, Nikolay Bogolyubov wrote his first published scientific paper On the behavior of solutions of linear differential equations at infinity. In 1925 he entered Ph.D. program at the Academy of Sciences of the Ukrainian SSR and obtained the degree of Kandidat Nauk (Candidate of Sciences, equivalent to a Ph.D.) in 1928, at the age of 19, with the doctoral thesis titled On direct methods of variational calculus. In 1930, at the age of 21, he obtained the degree of Doktor nauk (Doctor of Sciences, equivalent to Habilitation), the highest degree in the Soviet Union, which requires the recipient to have made a significant independent contribution to his or her scientific field.

This early period of Bogolyubov's work in science was concerned with such mathematical problems as direct methods of the calculus of variations, the theory of almost periodic functions, methods of approximate solution of differential equations, and dynamical systems. This earlier research had already earned him recognition. One of his essays was awarded the Bologna Academy of Sciences Prize in 1930, and the author was awarded the erudite degree of doctor of mathematics. This was the period when the scientific career of the young Nikolay Bogolyubov began, later producing new scientific trends in modern mathematics, physics, and mechanics.

Since 1931, Krylov and Bogolyubov worked together on the problems of nonlinear mechanics and nonlinear oscillations. They were the key figures in the "Kyiv school of nonlinear oscillation research", where their cooperation resulted in the paper "On the quasiperiodic solutions of the equations of nonlinear mechanics" (1934) and the book Introduction to Nonlinear Mechanics (1937; translated to English in 1947) leading to a creation of a large field of non-linear mechanics.

And this can explain, as the authors believe, the need to shape the collection of problems of non-linear perturbation theory into a special science, which could be named NON-LINEAR MECHANICS.

— N. M. Krylov and N. N. Bogolyubov, New methods in non-linear mechanics, ONTI GTTI, Moscow-Leningrad, 1934

Distinctive features of the Kyiv School approach included an emphasis on the computation of solutions (not just a proof of its existence), approximations of periodic solutions, use of the invariant manifolds in the phase space, and applications of a single unified approach to many different problems. From a control engineering point of view, the key achievement of the Kyiv School was the development by Krylov and Bogolyubov of the describing function method for the analysis of nonlinear control problems.

In the period 1928–1973, Nikolay Bogolyubov worked in the Institute for Theoretical Physics of the Academy of Sciences of the Ukrainian SSR holding the position of the Director of the institute since 1965. He lectured at Kyiv University in the period 1936–1959.

In evacuation (1941–1943) Edit

After the German attack against the Soviet Union on 22 June 1941 (beginning of the Great Patriotic War), most institutes and universities from the western part of Russia were evacuated into the eastern regions, far from the battle lines. Nikolay Bogolyubov moved to Ufa, where he became Head of the Departments of Mathematical Analysis at Ufa State Aviation Technical University and at Ufa Pedagogical Institute, remaining on these positions during the period of July 1941 – August 1943.

Moscow (1943–?) Edit

In autumn 1943, Bogolyubov came from evacuation to Moscow and on 1 November 1943 he accepted a position in the Department of Theoretical Physics at the Moscow State University (MSU). At that time the Head of the Department was Anatoly Vlasov (for a short period in 1944 the Head of the Department was Vladimir Fock). Theoretical physicists working in the department in that period included Dmitri Ivanenko, Arseny Sokolov, and other physicists.

In the period 1943–1946, Bogolyubov's research was essentially concerned with the theory of stochastic processes and asymptotic methods. In his work[citation needed] a simple example of an anharmonic oscillator driven by a superposition of incoherent sinusoidal oscillations with continuous spectrum was used to show that depending on a specific approximation time scale the evolution of the system can be either deterministic, or a stochastic process satisfying Fokker–Planck equation, or even a process which is neither deterministic nor stochastic. In other words, he showed that depending on the choice of the time scale for the corresponding approximations the same stochastic process can be regarded as both dynamical and Markovian, and in the general case as a non-Markov process. This work was the first to introduce the notion of time hierarchy in non-equilibrium statistical physics which then became the key concept in all further development of the statistical theory of irreversible processes.

In 1945, Bogolyubov proved a fundamental theorem on the existence and basic properties of a one-parameter integral manifold for a system of non-linear differential equations. He investigated periodic and quasi-periodic solutions lying on a one-dimensional manifold, thus forming the foundation for a new method of non-linear mechanics, the method of integral manifolds.

In 1946, he published in JETP two works on equilibrium and non-equilibrium statistical mechanics which became the essence of his fundamental monograph Problems of dynamical theory in statistical physics (Moscow, 1946).

On 26 January 1953, Nikolay Bogolyubov became the Head of the Department of Theoretical Physics at MSU, after Anatoly Vlasov decided to leave the position on January 2, 1953.

Steklov Institute (1947–?) Edit

 
N.Bogolyubov

In 1947, Nikolay Bogolyubov organized and became the Head of the Department of Theoretical Physics at the Steklov Institute of Mathematics. In 1969, the Department of Theoretical Physics was separated into the Departments of Mathematical Physics (Head Vasily Vladimirov), of Statistical Mechanics, and of Quantum Field Theory (Head Mikhail Polivanov). While working in the Steklov Institute, Nikolay Bogolyubov and his school contributed to science with many important works including works on renormalization theory, renormalization group, axiomatic S-matrix theory, and works on the theory of dispersion relations.

In the late 1940s and 1950s, Bogolyubov worked on the theory of superfluidity and superconductivity, where he developed the method of BBGKY hierarchy for a derivation of kinetic equations, formulated microscopic theory of superfluidity, and made other essential contributions. Later he worked on quantum field theory, where introduced the Bogoliubov transformation, formulated and proved the Bogoliubov's edge-of-the-wedge theorem and Bogoliubov–Parasyuk theorem (with Ostap Parasyuk), and obtained other significant results. In the 1960s his attention turned to the quark model of hadrons; in 1965 he was among the first scientists to study the new quantum number color charge.

In 1946, Nikolay Bogolyubov was elected as a Corresponding Member of the Academy of Sciences of the Soviet Union. He was elected a full member (academician) of the Academy of Sciences of the Ukrainian SSR and in full member of the Academy of Sciences of the USSR in 1953.

Dubna (1956–1992) Edit

Since 1956, he worked in the Joint Institute for Nuclear Research (JINR), Dubna, Russia, where he was a founder (together with Dmitry Blokhintsev) and the first director of the Laboratory of Theoretical Physics. This laboratory, where Nikolay Bogolyubov worked for a long time, has traditionally been the home of the prominent Russian schools in quantum field theory, theoretical nuclear physics, statistical physics, and nonlinear mechanics. Nikolay Bogolyubov was Director of the JINR in the period 1966–1988.

Family Edit

He had two sons - Pavel and Nikolay (jr). Nikolay Boglyubov (jr) is a theoretical physicist working in the fields of mathematical physics and statistical mechanics.

Students Edit

Nikolay Bogolyubov was a scientific supervisor[2] of Yurii Mitropolskiy, Dmitry Shirkov, Selim Krein, Iosif Gihman, Tofik Mamedov, Kirill Gurov, Mikhail Polivanov, Naftul Polsky, Galina Biryuk, Sergei Tyablikov, Dmitry Zubarev, Vladimir Kadyshevsky, and many other students. His method of teaching, based on creation of a warm atmosphere, politeness and kindness, is famous in Russia and is known as the "Bogolyubov approach".

Awards Edit

Nikolay Bogolyubov received various high USSR honors and international awards.

Soviet
Foreign awards
Academic awards
Academic recognition
Memory

Institutions, awards and locations have been named in Bogolyubov's memory:

In 2009, the centenary of Nikolay Bogolyubov's birth was celebrated with two conferences in Russia and Ukraine:

  • International Bogolyubov Conference: Problems of Theoretical and Mathematical Physics 21–27 August, Moscow-Dubna, Russia.
  • Bogolyubov Kyiv Conference: Modern Problems of Theoretical and Mathematical Physics 2009-06-05 at the Wayback Machine 15–18 September, Kyiv, Ukraine.

Research Edit

Fundamental works of Nikolay Bogolyubov were devoted to asymptotic methods of nonlinear mechanics, quantum field theory, statistical field theory, variational calculus, approximation methods in mathematical analysis, equations of mathematical physics, theory of stability, theory of dynamical systems, and to many other areas.

He built a new theory of scattering matrices, formulated the concept of microscopical causality, obtained important results in quantum electrodynamics, and investigated on the basis of the edge-of-the-wedge theorem the dispersion relations in elementary particle physics. He suggested a new synthesis of the Bohr theory of quasiperiodic functions and developed methods for asymptotic integration of nonlinear differential equations which describe oscillating processes.

Mathematics and non-linear mechanics Edit

  • In 1932–1943, in the early stage of his career, he worked in collaboration with Nikolay Krylov on mathematical problems of nonlinear mechanics and developed mathematical methods for asymptotic integration of non-linear differential equations. He also applied these methods to problems of statistical mechanics.
  • In 1937, jointly with Nikolay Krylov he proved the Krylov–Bogolyubov theorems.[3]
  • In 1956, at the International Conference on Theoretical Physics in Seattle, USA (September, 1956), he presented the formulation and the first proof of the edge-of-the-wedge theorem. This theorem in the theory of functions of several complex variables has important implications to the dispersion relations in elementary particle physics.

Statistical mechanics Edit

  • 1939 Jointly with Nikolay Krylov gave the first consistent microscopic derivation of the Fokker–Planck equation in the single scheme of classical and quantum mechanics.[4]
  • 1945 Suggested the idea of hierarchy of relaxation times, which is significant for statistical theory of irreversible processes.
  • 1946 Developed a general method for a microscopic derivation of kinetic equations for classical systems.[5][6] The method was based on the hierarchy of equations for multi-particle distribution functions known now as Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy.
  • 1947 Jointly with K. P. Gurov extended this method to the derivation of kinetic equations for quantum systems on the basis of the quantum BBGKY hierarchy.[7]
  • 1947—1948 Introduced kinetic equations in the theory of superfluidity,[8][9] computed the excitation spectrum for a weakly imperfect Bose gas, showed that this spectrum has the same properties as spectrum of Helium II, and used this analogy for a theoretical description of superfluidity of Helium II.
  • 1958 Formulated a microscopic theory of superconductivity[10] and established an analogy between superconductivity and superfluidity phenomena; this contribution was discussed in details in the book A New Method in the Theory of Superconductivity (co-authors V. V. Tolmachev and D. V. Shirkov, Moscow, Academy of Sciences Press, 1958).

Quantum theory Edit

Publications Edit

Main article: List of works by Nikolay Bogolyubov

Books Edit

Mathematics and Non-linear Mechanics:

  1. N. M. Krylov and N. N. Bogoliubov (1934): On various formal expansions of non-linear mechanics. Kyiv, Izdat. Zagal'noukr. Akad. Nauk. (in Ukrainian)
  2. N. M. Krylov and N. N. Bogoliubov (1947): Introduction to Nonlinear Mechanics. Princeton, Princeton University Press.
  3. N. N. Bogoliubov, Y. A. Mitropolsky (1961): Asymptotic Methods in the Theory of Non-Linear Oscillations. New York, Gordon and Breach.

Statistical Mechanics:

  1. N. N. Bogoliubov (1945): On Some Statistical Methods in Mathematical Physics. Kyiv (in Russian).
  2. N. N. Bogoliubov, V. V. Tolmachev, D. V. Shirkov (1959): A New Method in the Theory of Superconductivity. New York, Consultants Bureau.
  3. N. N. Bogoliubov (1960): Problems of Dynamic Theory in Statistical Physics. Oak Ridge, Tenn., Technical Information Service.
  4. N. N. Bogoliubov (1967—1970): Lectures on Quantum Statistics. Problems of Statistical Mechanics of Quantum Systems. New York, Gordon and Breach.
  5. N. N. Bogolubov and N. N. Bogolubov, Jnr. (1992): Introduction to Quantum Statistical Mechanics. Gordon and Breach. ISBN 2-88124-879-9.

Quantum Field Theory:

  1. N. N. Bogoliubov, B. V. Medvedev, M. K. Polivanov (1958): Problems in the Theory of Dispersion Relations. Institute for Advanced Study, Princeton.
  2. N. N. Bogoliubov, D. V. Shirkov (1959): The Theory of Quantized Fields. New York, Interscience. The first text-book on the renormalization group theory.
  3. N. N. Bogoliubov, A. A. Logunov and I. T. Todorov (1975): Introduction to Axiomatic Quantum Field Theory.[14] Reading, Mass.: W. A. Benjamin, Advanced Book Program. ISBN 978-0-8053-0982-9. ISBN 0-8053-0982-9.
  4. N. N. Bogoliubov, D. V. Shirkov (1980): Introduction to the Theory of Quantized Field. John Wiley & Sons Inc; 3rd edition. ISBN 0-471-04223-4. ISBN 978-0-471-04223-5.
  5. N. N. Bogoliubov, D. V. Shirkov (1982): Quantum Fields. Benjamin-Cummings Pub. Co., ISBN 0-8053-0983-7.
  6. N. N. Bogoliubov, A. A. Logunov, A. I. Oksak, I. T. Todorov (1990): General Principles of Quantum Field Theory. Dordrecht [Holland]; Boston, Kluwer Academic Publishers. ISBN 0-7923-0540-X. ISBN 978-0-7923-0540-8.
Selected works
  1. N. N. Bogoliubov, Selected Works. Part I. Dynamical Theory. Gordon and Breach, New York, 1990. ISBN 2-88124-752-0, ISBN 978-2-88124-752-1.
  2. N. N. Bogoliubov, Selected Works. Part II. Quantum and Classical Statistical Mechanics. Gordon and Breach, New York, 1991. ISBN 2-88124-768-7.
  3. N. N. Bogoliubov, Selected Works. Part III. Nonlinear Mechanics and Pure Mathematics. Gordon and Breach, Amsterdam, 1995. ISBN 2-88124-918-3.
  4. N. N. Bogoliubov, Selected Works. Part IV. Quantum Field Theory. Gordon and Breach, Amsterdam, 1995. ISBN 2-88124-926-4, ISBN 978-2-88124-926-6.

Selected papers Edit

  • Bogoliubov, N. N. (1948). "Equations of Hydrodynamics in Statistical Mechanics" (in Ukrainian)". Sbornik Trudov Instituta Matematiki AN USSR. 10: 41–59.
  • "On Question about Superfluidity Condition in the Nuclear Matter Theory" (in Russian), Doklady Akademii Nauk USSR, 119, 52, 1958.
  • "On One Variational Principle in Many Body Problem" (in Russian), Doklady Akademii Nauk USSR, 119, N2, 244, 1959.
  • "On Compensation Principle in the Method of Selfconformed Field" (in Russian), Uspekhi Fizicheskhih Nauk, 67, N4, 549, 1959.
  • "The Quasi-averages in Problems of Statistical Mechanics" (in Russian), Preprint D-781, JINR, Dubna, 1961.
  • "On the Hydrodynamics of a Superfluiding" (in Russian), Preprint P-1395, JINR, Dubna, 1963.

See also Edit

References Edit

  1. ^ Bogolyubov, A. N. (2009). "Nikolay Nikolayevich Bogolyubov". N. N. Bogolyubov: K 100-letiyu so dnya rozhdeniya (Joint Institute for Nuclear Research). Retrieved 8 January 2012. (in Russian)
  2. ^ Nikolay Bogolyubov at the Mathematics Genealogy Project
  3. ^ N. N. Bogoliubov and N. M. Krylov (1937). "La theorie generalie de la mesure dans son application a l'etude de systemes dynamiques de la mecanique non-lineaire". Annals of Mathematics. Second Series (in French). 38 (1): 65–113. doi:10.2307/1968511. JSTOR 1968511. Zbl. 16.86.
  4. ^ N. N. Bogoliubov and N. M. Krylov (1939). Fokker–Planck equations generated in perturbation theory by a method based on the spectral properties of a perturbed Hamiltonian. Zapiski Kafedry Fiziki Akademii Nauk Ukrainian SSR 4: 81–157 (in Ukrainian).
  5. ^ N. N. Bogoliubov (1946). "Kinetic Equations". Journal of Experimental and Theoretical Physics (in Russian). 16 (8): 691–702.
  6. ^ N. N. Bogoliubov (1946). "Kinetic Equations". Journal of Physics. 10 (3): 265–274.
  7. ^ N. N. Bogoliubov, K. P. Gurov (1947). "Kinetic Equations in Quantum Mechanics". Journal of Experimental and Theoretical Physics (in Russian). 17 (7): 614–628.
  8. ^ N. N. Bogoliubov (1947). "On the Theory of Superfluidity". Izv. Academii Nauk USSR (in Russian). 11 (1): 77.
  9. ^ N. N. Bogoliubov (1947). "On the Theory of Superfluidity". Journal of Physics. 11 (1): 23–32.
  10. ^ N. N. Bogoliubov (1958). "On a New Method in the Theory of Superconductivity". Journal of Experimental and Theoretical Physics. 34 (1): 58.
  11. ^ N. N. Bogoliubov, O. S. Parasyuk (1955). "[A theory of multiplication of causal singular functions]". Doklady Akademii Nauk SSSR (in Russian). 100: 25–28.
  12. ^ N. N. Bogoliubov, O. S. Parasyuk (1957). "Uber die Multiplikation der Kausalfunktionen in der Quantentheorie der Felder". Acta Mathematica (in German). 97: 227–266. doi:10.1007/BF02392399.
  13. ^ N. Bogolubov, B. Struminsky, A. Tavkhelidze. On composite models in the theory of elementary particles. JINR Preprint D-1968, Dubna 1965.
  14. ^ Jaffee, Arthur (1977). "Review: N. N. Bogolubov, A. A. Logunov and I. T. Todorov, Introduction to axiomatic quantum field theory". Bull. Amer. Math. Soc. 83 (3): 349–351. doi:10.1090/s0002-9904-1977-14261-4.

Further reading Edit

  • Mitropolskiy, Yu. A.; Tyablikov, S. V. (1959). "Nikolai Nikolaevich Bogolyubov (on the occasion of his fiftieth birthday)". Soviet Physics Uspekhi. 2 (5): 765–770. Bibcode:1959SvPhU...2..765M. doi:10.1070/PU1959v002n05ABEH003172.
  • Zubarev, D. N.; et al. (1970). "Nikolai Nikolaevich Bogolyubov (On his 60th birthday)". Soviet Physics Uspekhi. 12 (4): 590–593. Bibcode:1970SvPhU..12..590Z. doi:10.1070/PU1970v012n04ABEH003911.
  • Vladimirov, V. S.; et al. (1969). "Nikolai Nikolaevich Bogolyubov (on the occasion of his sixtieth birthday)". Russian Math. Surveys. 24 (4): 167–175. Bibcode:1969RuMaS..24..167V. doi:10.1070/RM1969v024n04ABEH001356. S2CID 250852631.
  • Ambartsumyan, V. A.; et al. (1979). "Nikolai Nikolaevich Bogolyubov (on his seventieth birthday)". Soviet Physics Uspekhi. 22 (8): 672–676. Bibcode:1979SvPhU..22..672A. doi:10.1070/PU1979v022n08ABEH005604.
  • Aleksandrov, P. S.; et al. (1979). "Nikolai Nikolaevich Bogolyubov (on his seventieth birthday)". Russian Math. Surveys. 34 (5): 1–10. Bibcode:1979RuMaS..34R...1A. doi:10.1070/RM1979v034n05ABEH003905.
  • Logunov, A. A.; Novikov, S. P.; Vladimirov, V. S. (1989). "Nikolai Nikolaevich Bogolyubov (on his 80th birthday)". Russian Math. Surveys. 44 (5): 1–10. Bibcode:1989RuMaS..44....1L. doi:10.1070/RM1989v044n05ABEH002280. S2CID 250843264.
  • Abrikosov, A. A.; et al. (1989). "Nikolai Nikolaevich Bogolyubov (on his eightieth birthday)". Soviet Physics Uspekhi. 32 (12): 1111–1112. Bibcode:1989SvPhU..32.1111A. doi:10.1070/PU1989v032n12ABEH002785.
  • Faddeev, L. D.; et al. (1992). "Nikolai Nikolaevich Bogolyubov (obituary)". Russian Math. Surveys. 47 (3): 1–3. Bibcode:1992RuMaS..47....1F. doi:10.1070/RM1992v047n03ABEH000892. S2CID 250873759.
  • Anosov, D. V. (1994). "On the contribution of N.N. Bogolyubov to the theory of dynamical systems". Russian Math. Surveys. 49 (5): 1–18. Bibcode:1994RuMaS..49....1A. doi:10.1070/RM1994v049n05ABEH002417. S2CID 250861645.
  • Boglyubov, Nikolay (1994). "N. N. Bogolyubov and statistical mechanics". Russian Math. Surveys. 49 (5): 19–49. Bibcode:1994RuMaS..49...19B. doi:10.1070/RM1994v049n05ABEH002419. S2CID 250872382.
  • Vladimirov, V. S.; Zharinov, V. V.; Sergeev, A. G. (1994). "Bogolyubov's "edge of the wedge" theorem, its development and applications". Russian Math. Surveys. 49 (5): 51–65. Bibcode:1994RuMaS..49...51V. doi:10.1070/RM1994v049n05ABEH002421. S2CID 250899126.
  • Zav'yalov, O. I. (1994). "Bogolyubov's R-operation and the Bogolyubov-Parasyuk theorem". Russian Math. Surveys. 49 (5): 67–76. Bibcode:1994RuMaS..49...67Z. doi:10.1070/RM1994v049n05ABEH002426. S2CID 250829806.
  • Levitan, B. M. (1994). "On the work of Nikolai Nikolaevich Bogolyubov in the theory of almost periodic functions". Russian Math. Surveys. 49 (5): 77–88. Bibcode:1994RuMaS..49...77L. doi:10.1070/RM1994v049n05ABEH002428. S2CID 250883056.
  • Medvedev, B. V. (1994). "N.N. Bogolyubov and the scattering matrix". Russian Math. Surveys. 49 (5): 89–108. Bibcode:1994RuMaS..49...89M. doi:10.1070/RM1994v049n05ABEH002430. S2CID 250918073.
  • Samoilenko, A. M. (1994). "N.N. Bogolyubov and non-linear mechanics". Russian Math. Surveys. 49 (5): 109–154. Bibcode:1994RuMaS..49..109S. doi:10.1070/RM1994v049n05ABEH002432. S2CID 250911673.
  • Shirkov, D. V. (1994). "The Bogoliubov renormalization group". Russian Math. Surveys. 49 (5): 155–176. arXiv:hep-th/9602024. Bibcode:1994RuMaS..49..155S. doi:10.1070/rm1994v049n05abeh002434. S2CID 250886692.
  • Vladimirov, V. S. (2001). "N. N. Bogoliubov and mathematics". Russian Math. Surveys. 56 (3): 607–613. Bibcode:2001RuMaS..56..607V. doi:10.1070/RM2001v056n03ABEH000413.

External links Edit

  • Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine.
  • at the Lomonosov Moscow State University, Russia.
  • Bogolyubov Laboratory of Theoretical Physics at the Joint Institute for Nuclear Research, Dubna, Russia.
  • Department of Theoretical Physics in the Steklov Mathematical Institute, Moscow, Russia (created by Nikolay Bogolyubov).
  • The role of Nikolay Bogoliubov in Dubna's Russian Orthodox Christian church (in Russian).
  • Nikolay Bogolyubov at the Mathematics Genealogy Project
  • Author profile in the database zbMATH

August 28, 2023
nikolay, bogolyubov, actor, actor, this, article, needs, additional, citations, verification, please, help, improve, this, article, adding, citations, reliable, sources, unsourced, material, challenged, removed, find, sources, news, newspapers, books, scholar,. For the actor see Nikolay Bogolyubov actor This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Nikolay Bogolyubov news newspapers books scholar JSTOR July 2021 Learn how and when to remove this template message In this name that follows Eastern Slavic naming conventions the patronymic is Nikolayevich and the family name is Bogolyubov Nikolay Nikolayevich Bogolyubov Russian Nikola j Nikola evich Bogolyu bov 21 August 1909 13 February 1992 also transliterated as Bogoliubov and Bogolubov was a Soviet and Russian mathematician and theoretical physicist known for a significant contribution to quantum field theory classical and quantum statistical mechanics and the theory of dynamical systems he was the recipient of the 1992 Dirac Medal Nikolay BogolyubovBornNikolay Nikolayevich Bogolyubov 1909 08 21 21 August 1909Nizhny Novgorod Russian EmpireDied13 February 1992 1992 02 13 aged 82 Moscow Russian FederationNationalitySoviet RussianKnown forSignificant contributions to nonlinear mechanics quantum field theory statistical mechanics superconductivity superfluidity BBGKY hierarchy Bogoliubov edge of the wedge theorem Bogoliubov Parasyuk theorem Bogoliubov transformation Krylov Bogolyubov theoremAwardsStalin Prize 1947 1953 USSR State Prize 1984 Lenin Prize 1958 Heineman Prize 1966 Hero of Socialist Labor 1969 1979 Max Planck Medal 1973 Lomonosov Gold Medal 1985 Dirac Prize 1992 Scientific careerFieldsTheoretical physics mathematical physics mathematicsInstitutionsKyiv UniversitySteklov Institute of MathematicsLomonosov Moscow State UniversityJoint Institute for Nuclear ResearchDoctoral advisorNikolay KrylovDoctoral studentsDmitry ZubarevYurii MitropolskiySergei TyablikovDmitry Shirkov Contents 1 Biography 1 1 Early life 1909 1921 1 2 In evacuation 1941 1943 1 3 Moscow 1943 1 4 Steklov Institute 1947 1 5 Dubna 1956 1992 1 6 Family 1 7 Students 1 8 Awards 2 Research 2 1 Mathematics and non linear mechanics 2 2 Statistical mechanics 2 3 Quantum theory 3 Publications 3 1 Books 3 2 Selected papers 4 See also 5 References 6 Further reading 7 External linksBiography EditEarly life 1909 1921 Edit Nikolay Bogolyubov was born on 21 August 1909 in Nizhny Novgorod Russian Empire to Russian Orthodox Church priest and seminary teacher of theology psychology and philosophy Nikolay Mikhaylovich Bogolyubov and Olga Nikolayevna Bogolyubova a teacher of music The Bogolyubovs relocated to the village of Velikaya Krucha in the Poltava Governorate now in Poltava Oblast Ukraine in 1919 where the young Nikolay Bogolyubov began to study physics and mathematics The family soon moved to Kyiv in 1921 where they continued to live in poverty as the elder Nikolay Bogolyubov only found a position as a priest in 1923 1 He attended research seminars in Kyiv University and soon started to work under the supervision of the well known contemporary mathematician Nikolay Krylov In 1924 at the age of 15 Nikolay Bogolyubov wrote his first published scientific paper On the behavior of solutions of linear differential equations at infinity In 1925 he entered Ph D program at the Academy of Sciences of the Ukrainian SSR and obtained the degree of Kandidat Nauk Candidate of Sciences equivalent to a Ph D in 1928 at the age of 19 with the doctoral thesis titled On direct methods of variational calculus In 1930 at the age of 21 he obtained the degree of Doktor nauk Doctor of Sciences equivalent to Habilitation the highest degree in the Soviet Union which requires the recipient to have made a significant independent contribution to his or her scientific field This early period of Bogolyubov s work in science was concerned with such mathematical problems as direct methods of the calculus of variations the theory of almost periodic functions methods of approximate solution of differential equations and dynamical systems This earlier research had already earned him recognition One of his essays was awarded the Bologna Academy of Sciences Prize in 1930 and the author was awarded the erudite degree of doctor of mathematics This was the period when the scientific career of the young Nikolay Bogolyubov began later producing new scientific trends in modern mathematics physics and mechanics Since 1931 Krylov and Bogolyubov worked together on the problems of nonlinear mechanics and nonlinear oscillations They were the key figures in the Kyiv school of nonlinear oscillation research where their cooperation resulted in the paper On the quasiperiodic solutions of the equations of nonlinear mechanics 1934 and the book Introduction to Nonlinear Mechanics 1937 translated to English in 1947 leading to a creation of a large field of non linear mechanics And this can explain as the authors believe the need to shape the collection of problems of non linear perturbation theory into a special science which could be named NON LINEAR MECHANICS N M Krylov and N N Bogolyubov New methods in non linear mechanics ONTI GTTI Moscow Leningrad 1934 Distinctive features of the Kyiv School approach included an emphasis on the computation of solutions not just a proof of its existence approximations of periodic solutions use of the invariant manifolds in the phase space and applications of a single unified approach to many different problems From a control engineering point of view the key achievement of the Kyiv School was the development by Krylov and Bogolyubov of the describing function method for the analysis of nonlinear control problems In the period 1928 1973 Nikolay Bogolyubov worked in the Institute for Theoretical Physics of the Academy of Sciences of the Ukrainian SSR holding the position of the Director of the institute since 1965 He lectured at Kyiv University in the period 1936 1959 In evacuation 1941 1943 Edit After the German attack against the Soviet Union on 22 June 1941 beginning of the Great Patriotic War most institutes and universities from the western part of Russia were evacuated into the eastern regions far from the battle lines Nikolay Bogolyubov moved to Ufa where he became Head of the Departments of Mathematical Analysis at Ufa State Aviation Technical University and at Ufa Pedagogical Institute remaining on these positions during the period of July 1941 August 1943 Moscow 1943 Edit In autumn 1943 Bogolyubov came from evacuation to Moscow and on 1 November 1943 he accepted a position in the Department of Theoretical Physics at the Moscow State University MSU At that time the Head of the Department was Anatoly Vlasov for a short period in 1944 the Head of the Department was Vladimir Fock Theoretical physicists working in the department in that period included Dmitri Ivanenko Arseny Sokolov and other physicists In the period 1943 1946 Bogolyubov s research was essentially concerned with the theory of stochastic processes and asymptotic methods In his work citation needed a simple example of an anharmonic oscillator driven by a superposition of incoherent sinusoidal oscillations with continuous spectrum was used to show that depending on a specific approximation time scale the evolution of the system can be either deterministic or a stochastic process satisfying Fokker Planck equation or even a process which is neither deterministic nor stochastic In other words he showed that depending on the choice of the time scale for the corresponding approximations the same stochastic process can be regarded as both dynamical and Markovian and in the general case as a non Markov process This work was the first to introduce the notion of time hierarchy in non equilibrium statistical physics which then became the key concept in all further development of the statistical theory of irreversible processes In 1945 Bogolyubov proved a fundamental theorem on the existence and basic properties of a one parameter integral manifold for a system of non linear differential equations He investigated periodic and quasi periodic solutions lying on a one dimensional manifold thus forming the foundation for a new method of non linear mechanics the method of integral manifolds In 1946 he published in JETP two works on equilibrium and non equilibrium statistical mechanics which became the essence of his fundamental monograph Problems of dynamical theory in statistical physics Moscow 1946 On 26 January 1953 Nikolay Bogolyubov became the Head of the Department of Theoretical Physics at MSU after Anatoly Vlasov decided to leave the position on January 2 1953 Steklov Institute 1947 Edit N BogolyubovIn 1947 Nikolay Bogolyubov organized and became the Head of the Department of Theoretical Physics at the Steklov Institute of Mathematics In 1969 the Department of Theoretical Physics was separated into the Departments of Mathematical Physics Head Vasily Vladimirov of Statistical Mechanics and of Quantum Field Theory Head Mikhail Polivanov While working in the Steklov Institute Nikolay Bogolyubov and his school contributed to science with many important works including works on renormalization theory renormalization group axiomatic S matrix theory and works on the theory of dispersion relations In the late 1940s and 1950s Bogolyubov worked on the theory of superfluidity and superconductivity where he developed the method of BBGKY hierarchy for a derivation of kinetic equations formulated microscopic theory of superfluidity and made other essential contributions Later he worked on quantum field theory where introduced the Bogoliubov transformation formulated and proved the Bogoliubov s edge of the wedge theorem and Bogoliubov Parasyuk theorem with Ostap Parasyuk and obtained other significant results In the 1960s his attention turned to the quark model of hadrons in 1965 he was among the first scientists to study the new quantum number color charge In 1946 Nikolay Bogolyubov was elected as a Corresponding Member of the Academy of Sciences of the Soviet Union He was elected a full member academician of the Academy of Sciences of the Ukrainian SSR and in full member of the Academy of Sciences of the USSR in 1953 Dubna 1956 1992 Edit This section needs expansion You can help by adding to it December 2009 Since 1956 he worked in the Joint Institute for Nuclear Research JINR Dubna Russia where he was a founder together with Dmitry Blokhintsev and the first director of the Laboratory of Theoretical Physics This laboratory where Nikolay Bogolyubov worked for a long time has traditionally been the home of the prominent Russian schools in quantum field theory theoretical nuclear physics statistical physics and nonlinear mechanics Nikolay Bogolyubov was Director of the JINR in the period 1966 1988 Family Edit This section does not cite any sources Please help improve this section by adding citations to reliable sources Unsourced material may be challenged and removed June 2021 Learn how and when to remove this template message He had two sons Pavel and Nikolay jr Nikolay Boglyubov jr is a theoretical physicist working in the fields of mathematical physics and statistical mechanics Students Edit Nikolay Bogolyubov was a scientific supervisor 2 of Yurii Mitropolskiy Dmitry Shirkov Selim Krein Iosif Gihman Tofik Mamedov Kirill Gurov Mikhail Polivanov Naftul Polsky Galina Biryuk Sergei Tyablikov Dmitry Zubarev Vladimir Kadyshevsky and many other students His method of teaching based on creation of a warm atmosphere politeness and kindness is famous in Russia and is known as the Bogolyubov approach Awards Edit Nikolay Bogolyubov received various high USSR honors and international awards SovietTwo Stalin Prizes 1947 1953 USSR State Prize 1984 Lenin Prize 1958 Hero of Socialist Labour twice 1969 1979 Six Orders of Lenin 1953 1959 1967 1969 1975 1979 Order of the October Revolution 1984 Order of the Red Banner of Labour twice 1948 1954 Order of the Badge of Honour twice 1944 1944 Foreign awardsOrder of Cyril and Methodius 1st class Bulgaria 1969 Order For merits 2nd class Poland 1977 Academic awardsAward of the Bologna Academy of Sciences 1930 Heineman Prize for Mathematical Physics American Physical Society 1966 Gold Medal Helmholtz Academy of Sciences of the German Democratic Republic 1969 Max Planck Medal 1973 Franklin Medal 1974 Gold Medal For service to science and humanity Slovak Academy of Sciences 1975 Karpinski Prize Germany 1981 Gold Medal Lavrent ev 1983 for his work On stochastic processes in dynamical systems Lomonosov Gold Medal 1985 for outstanding achievement in mathematics and theoretical physics Gold Medal of Lyapunov 1989 for his work on sustainability critical phenomena and phase transitions in the theory of many interacting particles Dirac Medal 1992 posthumously Academic recognitionForeign Honorary Member of the National Academy of Sciences United States 1959 American Academy of Arts and Sciences 1960 Bulgarian Academy of Sciences 1961 a foreign member of the Polish Academy of Sciences 1962 GDR Academy of Sciences 1966 Hungarian Academy of Sciences 1970 Academy of Sciences in Heidelberg 1968 Czechoslovak Academy of Sciences 1980 Indian Academy of Sciences 1983 Mongolian Academy of Sciences 1983 Honorary Doctor of the University of Allahabad India 1958 Berlin East Germany 1960 Chicago USA 1967 Turin Italy 1969 Wroclaw Poland 1970 Bucharest Romania 1971 Helsinki Finland 1973 Ulan Bator Mongolia 1977 Warsaw Poland 1977 MemoryInstitutions awards and locations have been named in Bogolyubov s memory N N Bogolyubov Institute for Theoretical Problems of Microphysics Moscow State University Bogoliubov Institute of Theoretical Physics National Academy of Sciences of Ukraine Kyiv Ukraine Bogoliubov Laboratory of Theoretical Physics Joint Institute for Nuclear Research Dubna Bogolyubov Prize Joint Institute for Nuclear Research for scientists with outstanding contribution to theoretical physics and applied mathematics Bogolyubov Prize for young scientists Joint Institute for Nuclear Research Bogolyubov Prize National Academy of Sciences of Ukraine for scientists with outstanding contribution to theoretical physics and applied mathematics Bogolyubov Gold Medal Russian Academy of Sciences Bust of Academician NN Bogolyubov Nizhny Novgorod Bust of Academician NN Bogolyubov Dubna Bogolyubov prospect Russian prospekt Bogolyubova Dubna s central street Commemorative plaque at the entrance of the Physics Department of Moscow State UniversityIn 2009 the centenary of Nikolay Bogolyubov s birth was celebrated with two conferences in Russia and Ukraine International Bogolyubov Conference Problems of Theoretical and Mathematical Physics 21 27 August Moscow Dubna Russia Bogolyubov Kyiv Conference Modern Problems of Theoretical and Mathematical Physics Archived 2009 06 05 at the Wayback Machine 15 18 September Kyiv Ukraine Research EditFundamental works of Nikolay Bogolyubov were devoted to asymptotic methods of nonlinear mechanics quantum field theory statistical field theory variational calculus approximation methods in mathematical analysis equations of mathematical physics theory of stability theory of dynamical systems and to many other areas He built a new theory of scattering matrices formulated the concept of microscopical causality obtained important results in quantum electrodynamics and investigated on the basis of the edge of the wedge theorem the dispersion relations in elementary particle physics He suggested a new synthesis of the Bohr theory of quasiperiodic functions and developed methods for asymptotic integration of nonlinear differential equations which describe oscillating processes Mathematics and non linear mechanics Edit In 1932 1943 in the early stage of his career he worked in collaboration with Nikolay Krylov on mathematical problems of nonlinear mechanics and developed mathematical methods for asymptotic integration of non linear differential equations He also applied these methods to problems of statistical mechanics In 1937 jointly with Nikolay Krylov he proved the Krylov Bogolyubov theorems 3 In 1956 at the International Conference on Theoretical Physics in Seattle USA September 1956 he presented the formulation and the first proof of the edge of the wedge theorem This theorem in the theory of functions of several complex variables has important implications to the dispersion relations in elementary particle physics Statistical mechanics Edit 1939 Jointly with Nikolay Krylov gave the first consistent microscopic derivation of the Fokker Planck equation in the single scheme of classical and quantum mechanics 4 1945 Suggested the idea of hierarchy of relaxation times which is significant for statistical theory of irreversible processes 1946 Developed a general method for a microscopic derivation of kinetic equations for classical systems 5 6 The method was based on the hierarchy of equations for multi particle distribution functions known now as Bogoliubov Born Green Kirkwood Yvon hierarchy 1947 Jointly with K P Gurov extended this method to the derivation of kinetic equations for quantum systems on the basis of the quantum BBGKY hierarchy 7 1947 1948 Introduced kinetic equations in the theory of superfluidity 8 9 computed the excitation spectrum for a weakly imperfect Bose gas showed that this spectrum has the same properties as spectrum of Helium II and used this analogy for a theoretical description of superfluidity of Helium II 1958 Formulated a microscopic theory of superconductivity 10 and established an analogy between superconductivity and superfluidity phenomena this contribution was discussed in details in the book A New Method in the Theory of Superconductivity co authors V V Tolmachev and D V Shirkov Moscow Academy of Sciences Press 1958 Quantum theory Edit 1955 Developed an axiomatic theory for the scattering matrix S matrix in quantum field theory and introduced the causality condition for S matrix in terms of variational derivatives 1955 Jointly with Dmitry Shirkov developed the renormalization group method 1955 Jointly with Ostap Parasyuk proved the theorem on the finiteness and uniqueness for renormalizable theories of the scattering matrix in any order of perturbation theory Bogoliubov Parasyuk theorem and developed a procedure R operation for a practical subtraction of singularities in quantum field theory 11 12 1965 Jointly with Boris Struminsky and Albert Tavkhelidze and independently of Moo Young Han Yoichiro Nambu and Oscar W Greenberg suggested a triplet quark model and introduced a new quantum degree of freedom later called as color charge for quarks 13 Suggested a first proof of dispersion relations in quantum field theory Publications EditMain article List of works by Nikolay Bogolyubov Books Edit Mathematics and Non linear Mechanics N M Krylov and N N Bogoliubov 1934 On various formal expansions of non linear mechanics Kyiv Izdat Zagal noukr Akad Nauk in Ukrainian N M Krylov and N N Bogoliubov 1947 Introduction to Nonlinear Mechanics Princeton Princeton University Press N N Bogoliubov Y A Mitropolsky 1961 Asymptotic Methods in the Theory of Non Linear Oscillations New York Gordon and Breach Statistical Mechanics N N Bogoliubov 1945 On Some Statistical Methods in Mathematical Physics Kyiv in Russian N N Bogoliubov V V Tolmachev D V Shirkov 1959 A New Method in the Theory of Superconductivity New York Consultants Bureau N N Bogoliubov 1960 Problems of Dynamic Theory in Statistical Physics Oak Ridge Tenn Technical Information Service N N Bogoliubov 1967 1970 Lectures on Quantum Statistics Problems of Statistical Mechanics of Quantum Systems New York Gordon and Breach N N Bogolubov and N N Bogolubov Jnr 1992 Introduction to Quantum Statistical Mechanics Gordon and Breach ISBN 2 88124 879 9 Quantum Field Theory N N Bogoliubov B V Medvedev M K Polivanov 1958 Problems in the Theory of Dispersion Relations Institute for Advanced Study Princeton N N Bogoliubov D V Shirkov 1959 The Theory of Quantized Fields New York Interscience The first text book on the renormalization group theory N N Bogoliubov A A Logunov and I T Todorov 1975 Introduction to Axiomatic Quantum Field Theory 14 Reading Mass W A Benjamin Advanced Book Program ISBN 978 0 8053 0982 9 ISBN 0 8053 0982 9 N N Bogoliubov D V Shirkov 1980 Introduction to the Theory of Quantized Field John Wiley amp Sons Inc 3rd edition ISBN 0 471 04223 4 ISBN 978 0 471 04223 5 N N Bogoliubov D V Shirkov 1982 Quantum Fields Benjamin Cummings Pub Co ISBN 0 8053 0983 7 N N Bogoliubov A A Logunov A I Oksak I T Todorov 1990 General Principles of Quantum Field Theory Dordrecht Holland Boston Kluwer Academic Publishers ISBN 0 7923 0540 X ISBN 978 0 7923 0540 8 Selected worksN N Bogoliubov Selected Works Part I Dynamical Theory Gordon and Breach New York 1990 ISBN 2 88124 752 0 ISBN 978 2 88124 752 1 N N Bogoliubov Selected Works Part II Quantum and Classical Statistical Mechanics Gordon and Breach New York 1991 ISBN 2 88124 768 7 N N Bogoliubov Selected Works Part III Nonlinear Mechanics and Pure Mathematics Gordon and Breach Amsterdam 1995 ISBN 2 88124 918 3 N N Bogoliubov Selected Works Part IV Quantum Field Theory Gordon and Breach Amsterdam 1995 ISBN 2 88124 926 4 ISBN 978 2 88124 926 6 Selected papers Edit Bogoliubov N N 1948 Equations of Hydrodynamics in Statistical Mechanics in Ukrainian Sbornik Trudov Instituta Matematiki AN USSR 10 41 59 On Question about Superfluidity Condition in the Nuclear Matter Theory in Russian Doklady Akademii Nauk USSR 119 52 1958 On One Variational Principle in Many Body Problem in Russian Doklady Akademii Nauk USSR 119 N2 244 1959 On Compensation Principle in the Method of Selfconformed Field in Russian Uspekhi Fizicheskhih Nauk 67 N4 549 1959 The Quasi averages in Problems of Statistical Mechanics in Russian Preprint D 781 JINR Dubna 1961 On the Hydrodynamics of a Superfluiding in Russian Preprint P 1395 JINR Dubna 1963 See also EditBogoliubov approximation Bogolyubov Born Green Kirkwood Yvon hierarchy Bogoliubov causality condition Bogolyubov s edge of the wedge theorem Bogolyubov inequality Bogoliubov inner product Bogolyubov s lemma Bogoliubov Parasyuk theorem Bogoliubov quasiparticle Bogoliubov transformation Describing function method Goldstone boson Krylov Bogoliubov averaging method Krylov Bogolyubov theorem Landau pole Peierls Bogoliubov inequality Quantum trivialityReferences Edit Bogolyubov A N 2009 Nikolay Nikolayevich Bogolyubov N N Bogolyubov K 100 letiyu so dnya rozhdeniya Joint Institute for Nuclear Research Retrieved 8 January 2012 in Russian Nikolay Bogolyubov at the Mathematics Genealogy Project N N Bogoliubov and N M Krylov 1937 La theorie generalie de la mesure dans son application a l etude de systemes dynamiques de la mecanique non lineaire Annals of Mathematics Second Series in French 38 1 65 113 doi 10 2307 1968511 JSTOR 1968511 Zbl 16 86 N N Bogoliubov and N M Krylov 1939 Fokker Planck equations generated in perturbation theory by a method based on the spectral properties of a perturbed Hamiltonian Zapiski Kafedry Fiziki Akademii Nauk Ukrainian SSR 4 81 157 in Ukrainian N N Bogoliubov 1946 Kinetic Equations Journal of Experimental and Theoretical Physics in Russian 16 8 691 702 N N Bogoliubov 1946 Kinetic Equations Journal of Physics 10 3 265 274 N N Bogoliubov K P Gurov 1947 Kinetic Equations in Quantum Mechanics Journal of Experimental and Theoretical Physics in Russian 17 7 614 628 N N Bogoliubov 1947 On the Theory of Superfluidity Izv Academii Nauk USSR in Russian 11 1 77 N N Bogoliubov 1947 On the Theory of Superfluidity Journal of Physics 11 1 23 32 N N Bogoliubov 1958 On a New Method in the Theory of Superconductivity Journal of Experimental and Theoretical Physics 34 1 58 N N Bogoliubov O S Parasyuk 1955 A theory of multiplication of causal singular functions Doklady Akademii Nauk SSSR in Russian 100 25 28 N N Bogoliubov O S Parasyuk 1957 Uber die Multiplikation der Kausalfunktionen in der Quantentheorie der Felder Acta Mathematica in German 97 227 266 doi 10 1007 BF02392399 N Bogolubov B Struminsky A Tavkhelidze On composite models in the theory of elementary particles JINR Preprint D 1968 Dubna 1965 Jaffee Arthur 1977 Review N N Bogolubov A A Logunov and I T Todorov Introduction to axiomatic quantum field theory Bull Amer Math Soc 83 3 349 351 doi 10 1090 s0002 9904 1977 14261 4 Further reading EditMitropolskiy Yu A Tyablikov S V 1959 Nikolai Nikolaevich Bogolyubov on the occasion of his fiftieth birthday Soviet Physics Uspekhi 2 5 765 770 Bibcode 1959SvPhU 2 765M doi 10 1070 PU1959v002n05ABEH003172 Zubarev D N et al 1970 Nikolai Nikolaevich Bogolyubov On his 60th birthday Soviet Physics Uspekhi 12 4 590 593 Bibcode 1970SvPhU 12 590Z doi 10 1070 PU1970v012n04ABEH003911 Vladimirov V S et al 1969 Nikolai Nikolaevich Bogolyubov on the occasion of his sixtieth birthday Russian Math Surveys 24 4 167 175 Bibcode 1969RuMaS 24 167V doi 10 1070 RM1969v024n04ABEH001356 S2CID 250852631 Ambartsumyan V A et al 1979 Nikolai Nikolaevich Bogolyubov on his seventieth birthday Soviet Physics Uspekhi 22 8 672 676 Bibcode 1979SvPhU 22 672A doi 10 1070 PU1979v022n08ABEH005604 Aleksandrov P S et al 1979 Nikolai Nikolaevich Bogolyubov on his seventieth birthday Russian Math Surveys 34 5 1 10 Bibcode 1979RuMaS 34R 1A doi 10 1070 RM1979v034n05ABEH003905 Logunov A A Novikov S P Vladimirov V S 1989 Nikolai Nikolaevich Bogolyubov on his 80th birthday Russian Math Surveys 44 5 1 10 Bibcode 1989RuMaS 44 1L doi 10 1070 RM1989v044n05ABEH002280 S2CID 250843264 Abrikosov A A et al 1989 Nikolai Nikolaevich Bogolyubov on his eightieth birthday Soviet Physics Uspekhi 32 12 1111 1112 Bibcode 1989SvPhU 32 1111A doi 10 1070 PU1989v032n12ABEH002785 Faddeev L D et al 1992 Nikolai Nikolaevich Bogolyubov obituary Russian Math Surveys 47 3 1 3 Bibcode 1992RuMaS 47 1F doi 10 1070 RM1992v047n03ABEH000892 S2CID 250873759 Anosov D V 1994 On the contribution of N N Bogolyubov to the theory of dynamical systems Russian Math Surveys 49 5 1 18 Bibcode 1994RuMaS 49 1A doi 10 1070 RM1994v049n05ABEH002417 S2CID 250861645 Boglyubov Nikolay 1994 N N Bogolyubov and statistical mechanics Russian Math Surveys 49 5 19 49 Bibcode 1994RuMaS 49 19B doi 10 1070 RM1994v049n05ABEH002419 S2CID 250872382 Vladimirov V S Zharinov V V Sergeev A G 1994 Bogolyubov s edge of the wedge theorem its development and applications Russian Math Surveys 49 5 51 65 Bibcode 1994RuMaS 49 51V doi 10 1070 RM1994v049n05ABEH002421 S2CID 250899126 Zav yalov O I 1994 Bogolyubov s R operation and the Bogolyubov Parasyuk theorem Russian Math Surveys 49 5 67 76 Bibcode 1994RuMaS 49 67Z doi 10 1070 RM1994v049n05ABEH002426 S2CID 250829806 Levitan B M 1994 On the work of Nikolai Nikolaevich Bogolyubov in the theory of almost periodic functions Russian Math Surveys 49 5 77 88 Bibcode 1994RuMaS 49 77L doi 10 1070 RM1994v049n05ABEH002428 S2CID 250883056 Medvedev B V 1994 N N Bogolyubov and the scattering matrix Russian Math Surveys 49 5 89 108 Bibcode 1994RuMaS 49 89M doi 10 1070 RM1994v049n05ABEH002430 S2CID 250918073 Samoilenko A M 1994 N N Bogolyubov and non linear mechanics Russian Math Surveys 49 5 109 154 Bibcode 1994RuMaS 49 109S doi 10 1070 RM1994v049n05ABEH002432 S2CID 250911673 Shirkov D V 1994 The Bogoliubov renormalization group Russian Math Surveys 49 5 155 176 arXiv hep th 9602024 Bibcode 1994RuMaS 49 155S doi 10 1070 rm1994v049n05abeh002434 S2CID 250886692 Vladimirov V S 2001 N N Bogoliubov and mathematics Russian Math Surveys 56 3 607 613 Bibcode 2001RuMaS 56 607V doi 10 1070 RM2001v056n03ABEH000413 External links EditBogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine Bogolyubov Institute for Theoretical Problems of Microphysics at the Lomonosov Moscow State University Russia Bogolyubov Laboratory of Theoretical Physics at the Joint Institute for Nuclear Research Dubna Russia Department of Theoretical Physics in the Steklov Mathematical Institute Moscow Russia created by Nikolay Bogolyubov The role of Nikolay Bogoliubov in Dubna s Russian Orthodox Christian church in Russian Nikolay Bogolyubov at the Mathematics Genealogy Project Author profile in the database zbMATH Retrieved from https en wikipedia org w index php title Nikolay Bogolyubov amp oldid 1169035699, wikipedia, wiki, book, books, library,

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