Background
Mishchenko, Alexandr Sergei was born on August 18, 1941 in Rostov-Don, Rostov, Russia. Son of Sergei Timophey and Varvara Petr Mishchenko.
(In the last few years the use of geometrie methods has pe...)
In the last few years the use of geometrie methods has permeated many more branehes of mathematies and the seiences. Briefly its role may be eharaeterized as folIows. Whereas methods of mathematieal analysis deseribe phenomena 'in the sm all " geometrie methods eontribute to giving the picture 'in the large'. A seeond no less important property of geometrie methods is the eonvenienee of using its language to deseribe and give qualitative explanations for diverse mathematieal phenomena and patterns. From this point of view, the theory of veetor bundles together with mathematieal analysis on manifolds (global anal- ysis and differential geometry) has provided a major stimulus. Its language turned out to be extremely fruitful: connections on prineipal veetor bundles (in terms of whieh various field theories are deseribed), transformation groups including the various symmetry groups that arise in eonneetion with physieal problems, in asymptotie methods of partial differential equations with small parameter, in elliptie operator theory, in mathematieal methods of classieal meehanies and in mathematieal methods in eeonomies. There are other eur- rently less signifieant applieations in other fields. Over a similar period, uni- versity edueation has ehanged eonsiderably with the appearanee of new courses on differential geometry and topology. New textbooks have been published but 'geometry and topology' has not, in our opinion, been wen eovered from a prae- tieal applieations point of view.
http://www.amazon.com/gp/product/1441948023/?tag=2022091-20
(This book presents Maslov's canonical operator method for...)
This book presents Maslov's canonical operator method for finding asymptotic solutions of pseudo differential equations. The classical WKB method, so named in honor of its authors: Wentzel, Kramers and Brillouin, was created for finding quasi classical approximations in quantum mechanics. The simplicity, obviousness and "physicalness" of this method quickly made it popular: specialists in mathematical physics accepted it unequivocally as one of the weapons in their arsenal. The number of publications which are connected with the WKB method in one way or another can probably no longer be counted. The alternative name of the WKB method in diffraction problem- the ray method or the method of geometric optics - indicates that the approximations in the WKB method are constructed by means of rays. More precisely, the first approximation of the WKB method is constructed by means of rays (isolating the singular part), after which the usual methods of the (regular) theory of perturbations are applied. However, the ray method is not applicable at the points of space where the rays focus or form a caustic. Mathematically this fact expresses itself in the fact that the amplitude of the waves at such points become infinite.
http://www.amazon.com/gp/product/3642647650/?tag=2022091-20
Mishchenko, Alexandr Sergei was born on August 18, 1941 in Rostov-Don, Rostov, Russia. Son of Sergei Timophey and Varvara Petr Mishchenko.
Graduate, Moscow State University, 1965. Doctor of Philosophy, Moscow State University, 1968. DMath, Moscow State University, 1973.
Researcher Moscow State University, 1968-1979, professor department mathematics, since 1979. Researcher Steklov Mathematics Institute-Russian Academy of Sciences, Moscow, since 1979.
(This book presents Maslov's canonical operator method for...)
(In the last few years the use of geometrie methods has pe...)
Member Moscow Mathematics Society (prize 1971).
Married Tatiana Michail Vinogradova. Children: Michail, Varvara.