Six months after Mykola's birth, the family moved to Nizhyn, city of Chernihiv Oblast, Ukraine, where his father taught until 1913.
From 1913 to 1918, the family lived in Kyiv. Mykola received his initial education at home. His father taught him the basics of arithmetic, as well as German, French, and English. At the age of six, he attended the preparatory class of the Kyiv Gymnasium. However, he did not stay long in the gymnasium—during the years of the Ukrainian War of Independence from 1917 to 1921, the family moved to the village of Velyka Krucha (now in Poltava Oblast, Ukraine). From 1919 to 1921, he studied at the Velykokruchanska seven-year school – the only educational institution he graduated from.[3]
Kyiv period (1921-1940)
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.[4] After finishing the seven-year school, Bogolyubov independently studied physics and mathematics, and by the age of 14, he was already participating in the seminar of the Department of Mathematical Physics at Kyiv University under the supervision of Academician Dmitry Grave.
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 under the supervision of the well-known contemporary mathematician Nikolay Krylov 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 1936, M. M. Bogolyubov was awarded the title of professor, and from 1936 to 1940, he chaired the Department of Mathematical Physics at Kyiv University In 1939, he was elected a corresponding member of the Academy of Sciences of the Ukrainian SSR (since 1994 – National Academy of Sciences of Ukraine). In 1940, after the reunification of Northern Bukovyna with Ukraine, Nikolay Bogolyubov was sent to Chernivtsi to organize mathematical departments at the Faculty of Physics and Mathematics of Chernivtsi State University.
In evacuation (1941–1943)
After the German attack against the Soviet Union on 22 June 1941 (beginning of the Eastern front of World War II), most institutes and universities from the western part 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–?)
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-equilibriumstatistical 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–?)
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 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)
This section needs expansion. You can help by adding to it. (December 2009)
In the post-war years, M. M. Bogolyubov worked as the dean of the Faculty of Mechanics and Mathematics at Kyiv University and headed the Department of Probability Theory at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR (now – NASU Institute of Mathematics). His first students in nonlinear mechanics were Yurii Mitropolskyi and Yu. V. Blagoveshchensky, and in probability theory and mathematical statistics, I. I. Gikhman.
In the first half of the 1960s, Bogolyubov worked on organizing the Institute for Theoretical Physics of the Academy of Sciences of the Ukrainian SSR (now – Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine) and from 1966 to 1973, he served as its director.[5] When the institute was established in 1966, it consisted of three departments: Mathematical Methods in Theoretical Physics (Head: Academician Ostap Parasyuk), Theory of the Nucleus (Head: Oleksandr Davydov), and Theory of Elementary Particles (Albert Tavkhelidze). In 1968, the institute organized the Department of Nuclear Reaction Theory (Head: Oleksiy Sytenko).
Nikolay Bogolyubov was married (since 1937) to Evgenia Pirashkova.[6] They had two sons – Pavel and Nikolay (jr). Nikolay Boglyubov (jr) is a theoretical physicist working in the fields of mathematical physics and statistical mechanics. Pavel was a theoretical physicist, Doctor of Physical and Mathematical Sciences, senior researcher, and head of the sector at the Laboratory of Theoretical Physics of the Joint Institute for Nuclear Research.[7]
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
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 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
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.[10]
1946 Developed a general method for a microscopic derivation of kinetic equations for classical systems.[11][12] 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.[13]
1947—1948 Introduced kinetic equations in the theory of superfluidity,[14][15] 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[16] 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
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 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.[17][18]
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. ISBN2-88124-879-9.
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.[20] Reading, Mass.: W. A. Benjamin, Advanced Book Program. ISBN978-0-8053-0982-9. ISBN0-8053-0982-9.
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. ISBN0-7923-0540-X. ISBN978-0-7923-0540-8.
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 Self conformed 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.
^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)
^"About BITP". Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine. Retrieved May 29, 2024.
^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. JSTOR1968511. 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, O. S. Parasyuk (1955). "[A theory of multiplication of causal singular functions]". Doklady Akademii Nauk SSSR (in Russian). 100: 25–28.
Romawi Kuno Artikel ini adalah bagian dari seri Politik dan KetatanegaraanRomawi Kuno Zaman Kerajaan Romawi753–509 SM Republik Romawi509–27 SM Kekaisaran Romawi27 SM – 395 M Principatus Dominatus Wilayah Barat395–476 M Wilayah Timur395–1453 M Lini Masa Konstitusi Romawi Konstitusi Zaman Kerajaan Konstitusi Zaman Republik Konstitusi Zaman Kekaisaran Konstitusi Akhir Zaman Kekaisaran Senatus Sidang Legislatif Magistratus Eksekutif Preseden dan Hukum Hukum Romawi Ius Imperium Mos Maior...
Questa voce sull'argomento calciatori italiani è solo un abbozzo. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Segui i suggerimenti del progetto di riferimento. Umberto Manzini Nazionalità Italia Calcio Ruolo Portiere Termine carriera 1936 Carriera Squadre di club1 1928-1933 Verona43 (-77)1935-1936 Trento? (-?) 1 I due numeri indicano le presenze e le reti segnate, per le sole partite di campionato.Il simbolo → indica un trasferimento in prestito. ...
Undisturbed natural environment This article is about wildland. For other uses, see The Wilderness and Wilderness (disambiguation). Not to be confused with Wildness or The bush. White Goat Wilderness Area in Canadian Rockies, Canada Stephen Mather Wilderness in the U.S. state of Washington Innoko Wilderness in the U.S. state of Alaska in the summer Wilderness or wildlands (usually in the plural) are natural environments on Earth that have not been significantly modified by human activity, or ...
Artikel ini membutuhkan rujukan tambahan agar kualitasnya dapat dipastikan. Mohon bantu kami mengembangkan artikel ini dengan cara menambahkan rujukan ke sumber tepercaya. Pernyataan tak bersumber bisa saja dipertentangkan dan dihapus.Cari sumber: Sinjai TV – berita · surat kabar · buku · cendekiawan · JSTOR (Januari 2023) Sinjai TVLPPL Sinjai TelevisiSinjai, Sulawesi SelatanIndonesiaSaluranDigital: 32 UHFVirtual: 5PemrogramanBahasaBahasa IndonesiaJari...
Centre-right political party in Lebanon 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: National Bloc Lebanon – news · newspapers · books · scholar · JSTOR (January 2021) (Learn how and when to remove this message) National Bloc الكتلة الوطنيةFrench nameBloc NationalAbbreviationNBPresidentS...
Keratocytes movement Corneal keratocytes (corneal fibroblasts) are specialized fibroblasts residing in the stroma. This corneal layer, representing about 85-90% of corneal thickness, is built up from highly regular collagenous lamellae and extracellular matrix components. Keratocytes play the major role in keeping it transparent, healing its wounds, and synthesizing its components. In the unperturbed cornea keratocytes stay dormant, coming into action after any kind of injury or inflammation....
Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Januari 2023. Yammoune Yammouneh, El YammoûnéDesaMata air Naba al-Arbain di YammouneNegara LebanonKegubernuranKegubernuran BeqaaDistrikDistik BaalbekKetinggian4.511 ft (1,375 m)Populasi (1955) • Total200YammouneLokasi di LebanonLoka...
Brazilian racing driver (born 1987) Carlos IaconelliIaconelli in 2009Nationality BrazilianBorn (1987-06-26) June 26, 1987 (age 36)FIA Formula Two Championship careerDebut season2009Current teamMotorSport VisionCar number17Starts14Wins0Poles0Fastest laps0Best finish11th in 2009Previous series20102008–092008200820082005–07200520052005–0620042003–04Auto GPGP2 Asia SeriesGP2 SeriesInternational Formula MasterFormula Master ItaliaFormula Renault 3.5 SeriesEurocup Formula Renault 2.0Fo...
Sport in which players attempt to throw a disc into a target This article is written like a manual or guide. Please help rewrite this article and remove advice or instruction. (November 2023) Disc golfHighest governing bodyProfessional Disc Golf AssociationRegistered players255048 (as of April 2023)[1]ClubsYesCharacteristicsContactNoTeam membersSingle competitors, doublesTypeOutdoor, passive recreationEquipmentFlying disc, target, tee off locationPresenceOlympicNoWorld Games2001 ...
Не следует путать с АЛиТ — учебным заведением, расположенным в Алма-Ате. Глутамат-пируват-трансаминаза Обозначения Символы GPT Entrez Gene 2875 HGNC 4552 OMIM 138200 RefSeq NM_005309 UniProt P24298 Другие данные Шифр КФ 2.6.1.2 Локус 8-я хр. , 8q24.2 -qter Информация в Викиданных ? Аланинаминотрансфераза (АЛТ...
Jalal AlamgirBorn(1971-01-17)17 January 1971Bangladesh[1]Died3 December 2011(2011-12-03) (aged 40)Phuket, Thailand[2]EducationPh.D. (political science)Alma materBrown University St. Lawrence UniversityOccupationProfessorEmployerUniversity of Massachusetts Boston Jalal Alamgir (17 January 1971 – 3 December 2011), was a Bangladeshi-American academic and an associate professor of political science at the University of Massachusetts-Boston and the son of Awami League ...
Untuk seniman, lihat Charles Thomson (seniman). Charles Thomson (29 November 1729 - 16 Agustus 1824) lahir di Tobermore, sebuah desa tepat di luar Maghera, County Londonderry, Irlandia dari orang tua Skotlandia-Irlandia. Ayahnya beremigrasi dari Irlandia Utara ke Koloni Inggris di Amerika (lalu menjadi Amerika Serikat) saat Charles berusia 8 tahun. Saat tiba di Amerika, Charles menjadi yatim saat ayahnya meninggal. Ia menjadi pedagang dan politikus Philadelphia. Ia aktif melawan Britania sela...
عازفون في الفرقة السمفونية القومية العراقية خلال تقديم عرض في العراق عام 2007م. الفرقة السيمفونية العراقية هي فرقة الأوركسترا السيمفونية الوطنية في العراق ومقرها في العاصمة العراقية بغداد، بدأت مشوارها الموسيقي في أربعينيات القرن الماضي لكن تم الإعلان عن تأسيسها رسمياً ع�...
Martin TomczykKebangsaan JermanLahir07 Desember 1981 (umur 42)Rosenheim (Germany)Karier DTMMusim debut2001Tim saat iniTeam PhoenixNomor mobil2Start106Menang5Pole8Lap tercepat5Hasil terbaik1st di 2011Ajang sebelumnya200019991998German Formula 3Formula BMW ADACFormula BMW Junior Martin Tomczyk (lahir 7 Desember 1981) merupakan seorang pembalap mobil profesional asal Jerman yang saat ini turun di ajang DTM dengan Team Phoenix yang memakai mobil Audi. Ia merupakan juara umum DTM musim 2011. ...
1964 studio album by Herbie HancockInventions & DimensionsStudio album by Herbie HancockReleased1964RecordedAugust 30, 1963StudioVan Gelder Studio, Englewood Cliffs, NJGenreModal Jazz, Post-Bop, Latin JazzLength39:49LabelBlue NoteBST 84147ProducerAlfred LionHerbie Hancock chronology My Point of View(1963) Inventions & Dimensions(1964) Empyrean Isles(1964) Succotash cover Professional ratingsReview scoresSourceRatingAll About Jazz(favorable) [1]Allmusic[2]The Ro...
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: 1790 in Canada – news · newspapers · books · scholar · JSTOR (July 2023) (Learn how and when to remove this message) ← 1789 1788 1787 1790 in Canada → 1791 1792 1793 Decades: 1770s 1780s 1790s 1800s 1810s See also: History of Canada Timeline of Can...
American Nazi propagandist (1900–1988) Mildred GillarsGillars's prison photo, 1949BornMildred Elizabeth Sisk(1900-11-29)November 29, 1900Portland, Maine, U.S.DiedJune 25, 1988(1988-06-25) (aged 87)Columbus, Ohio, U.S.Resting placeSaint Joseph Cemetery, ColumbusOther namesMidge at the MikeAxis SallyOccupationRadio broadcasterYears active1940–1945Known forPresenting Nazi propaganda on German State Radio, directed to U.S. troops and audience, during World War IICriminal s...
Questa voce sull'argomento cestisti finlandesi è solo un abbozzo. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Segui i suggerimenti del progetto di riferimento. Veikko VainioNazionalità Finlandia Altezza205 cm Peso100 kg Pallacanestro RuoloCentro Termine carriera1974 CarrieraGiovanili 1967-1971 BYU Cougars Squadre di club 1964-1967 KTP-Basket1971-1974 Pantterit Nazionale 1965-1973 Finlandia68 (414) Il simbolo → indica un trasferimento in presti...