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 on mathematical problems of non-linear mechanics. In this period, they invented certain asymptotic methods for integration of non-linear differential equations, studied dynamical systems, 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 theorems, introduced the Krylov-Bogoliubov averaging method and, together with Yurii Mitropolskiy, developed the Krylov-Bogoliubov-Mitropolskiy asymptotic method for approximate solving equations of non-linear mechanics.
Read more about this topic: Nikolay Mitrofanovich Krylov
Famous quotes containing the word research:
“Feeling that you have to be the perfect parent places a tremendous and completely unnecessary burden on you. If we’ve learned anything from the past half-century’s research on child development, it’s that children are remarkably resilient. You can make lots of mistakes and still wind up with great kids.”
—Lawrence Kutner (20th century)
“I did my research and decided I just had to live it.”
—Karina O’Malley, U.S. sociologist and educator. As quoted in the Chronicle of Higher Education, p. A5 (September 16, 1992)
“Our science has become terrible, our research dangerous, our findings deadly. We physicists have to make peace with reality. Reality is not as strong as we are. We will ruin reality.”
—Friedrich Dürrenmatt (1921–1990)