Nikolay Mitrofanovich Krylov (, ; – May 11, 1955) was a Russian and

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

mathematician known for works on

interpolation In the mathematics, 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 ...

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

mathematical physics Mathematical physics is 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 the de ...

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 ( ) is a peninsula in Eastern Europe, on the northern coast of the Black Sea, almost entirely surrounded by the Black Sea and the smaller Sea of Azov. The Isthmus of Perekop connects the peninsula to Kherson Oblast in mainland Ukrain ...

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

Kyiv Kyiv, also Kiev, is the capital and most populous List of cities in Ukraine, city of Ukraine. Located in the north-central part of the country, it straddles both sides of the Dnieper, Dnieper River. As of 1 January 2022, its population was 2, ...

to become chairman of the mathematical physics department at the

Ukrainian Academy of Sciences The National Academy of Sciences of Ukraine (NASU; , ; ''NAN Ukrainy'') is a self-governing state-funded organization in Ukraine that is the main center of development of Science and technology in Ukraine, science and technology by coordinatin ...

. Nikolay Krylov was a member of the

Société mathématique de France Groupe Lactalis S.A. (doing business as 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 S.A. Lactalis is the largest dairy pr ...

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 Bogolyubov Nikolay Nikolayevich (Mykola Mykolayovych) Bogolyubov (; ; 21 August 1909 – 13 February 1992) was a Soviet, Ukrainian and Russian mathematician and theoretical physicist known for a significant contribution to quantum field theory, classi ...

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, such as in a parametric curve. Examples include the mathematical models ...

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 The Krylov–Bogolyubov averaging method (Krylov–Bogolyubov method of averaging) is a mathematical method for approximate analysis of oscillating processes in non-linear mechanics. The method is based on the averaging principle when the exact diff ...

and, together with

Yurii Mitropolskiy Yurii Oleksiiovych Mitropolskyi (; 3 January 1917 – 14 June 2008) was a renowned Soviet Union, Soviet and Ukraine, Ukrainian mathematician known for his contributions to the fields of dynamical systems and Nonlinear system, nonlinear oscillati ...

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

Doctoral students

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 of 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 20th-century Russian mathematicians 20th-century Russian physicists 20th-century Ukrainian mathematicians 20th-century Ukrainian physicists Mathematicians from Saint Petersburg Full Members of the USSR Academy of Sciences Saint Petersburg Mining University alumni Academic staff of the Taras Shevchenko National University of Kyiv Academic staff of Tavrida National V.I. Vernadsky University Recipients of the Order of Lenin Recipients of the Order of the Red Banner of Labour Control theorists Mathematicians from the Russian Empire Physicists from the Russian Empire Soviet mathematicians Soviet physicists Ukrainian people of Russian descent Burials at Novodevichy Cemetery Full Members of the All-Ukrainian Academy of Sciences

Biography

Research

Doctoral students

Publications

See also

References