Nikolay Mitrofanovich Krylov (russian: Никола́й Митрофа́нович Крыло́в, uk, Микола Митрофанович Крилов) ( – May 11, 1955) was a Russian and

Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

mathematician known for works on

interpolation In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a n ...

, non-linear mechanics, and numerical methods for solving equations of

mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

Biography

Nikolay Krylov graduated from St. Petersburg State Mining Institute in 1902. In the period from 1912 until 1917, he held the Professor position in this institute. In 1917, he went to the

Crimea Crimea, crh, Къырым, Qırım, grc, Κιμμερία / Ταυρική, translit=Kimmería / Taurikḗ ( ) is a peninsula in Ukraine, on the northern coast of the Black Sea, that has been occupied by Russia since 2014. It has a pop ...

to become Professor at the Crimea University. He worked there until 1922 and then moved to

Kyiv Kyiv, also spelled Kiev, is the capital and most populous city of Ukraine. It is in north-central Ukraine along the Dnieper, Dnieper River. As of 1 January 2021, its population was 2,962,180, making Kyiv the List of European cities by populat ...

to become chairman of the mathematical physics department at the

Ukrainian Academy of Sciences The National Academy of Sciences of Ukraine (NASU; uk, Національна академія наук України, ''Natsional’na akademiya nauk Ukrayiny'', abbr: NAN Ukraine) is a self-governing state-funded organization in Ukraine th ...

. Nikolay Krylov was a member of the

Société Mathématique de France Lactalis is a French multinational dairy products corporation, owned by the Besnier family and based in Laval, Mayenne, France. The company's former name was Besnier SA. Lactalis is the largest dairy products group in the world, and is the sec ...

and the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Research

Nikolay Krylov developed new methods for analysis of equations of mathematical physics, which can be used not only for proving the existence of solutions but also for their construction. Since 1932, he worked together with his student

Nikolay Bogoliubov 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 theoretic ...

on mathematical problems of non-linear mechanics. In this period, they invented certain asymptotic methods for integration of non-linear differential equations, studied

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...

s, and made significant contributions to the foundations of non-linear mechanics. They proved the first theorems on existence of invariant measures known as

Krylov–Bogolyubov theorem In mathematics, the Krylov–Bogolyubov theorem (also known as the existence of invariant measures theorem) may refer to either of the two related fundamental theorems within the theory of dynamical systems. The theorems guarantee the existence of i ...

s, introduced the Krylov-Bogoliubov averaging method and, together with

Yurii Mitropolskiy Yurii Alekseevich Mitropolskiy ( uk, Юрій Олексійович Митропольський; 3 January 1917 – 14 June 2008) was a renowned Soviet and Ukrainian mathematician known for his contributions to the fields of dynamical systems a ...

, developed the Krylov–Bogoliubov–Mitropolskiy asymptotic method for approximate solving equations of non-linear mechanics.

Doctoral students

Nikolay 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 theoretica ...

Publications

Nikolay Krylov published over 200 papers on analysis and mathematical physics and two monographs: *Nicolas Kryloff (1931): ''Les Méthodes de Solution Approchée des Problèmes de la Physique Mathématique''. Paris: Gauthier-Villars

n French N, or n, is the fourteenth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''en'' (pronounced ), plural ''ens''. History ...

*N. M. Krylov, N. N. Bogoliubov (1947): ''Introduction to Nonlinear Mechanics''. Princeton: Princeton University Press. .

References

* {{DEFAULTSORT:Krylov, Nikolay Mitrofanovich 1879 births 1955 deaths Burials at Novodevichy Cemetery Control theorists Full Members of the USSR Academy of Sciences Mathematicians from Saint Petersburg 20th-century Russian mathematicians Soviet mathematicians Soviet scientists Saint Petersburg Mining University alumni Taras Shevchenko National University of Kyiv faculty Ukrainian mathematicians Ukrainian people of Russian descent

Biography

Research

Doctoral students

Publications

See also

References