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Register a new userMisha Shubin. 1944 -- 2020
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The article describes the biography and manifold contributions to research in mathematics of Mikhail Aleksandrovich Shubin.
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The article is dedicated to thye memory of a distinguished mathematician Professor Misha Shubin
Boris R. Vainberg was born on March 17, 1938, in Moscow. His father was a Lead Engineer in an aviation design institute. His mother was a homemaker. From early age, Boris was attracted to mathematics and spent much of his time at home and in school working through collections of practice problems for the Moscow Mathematical Olympiad. His first mathematical library consisted of the books he received as one of the prize-winners of these olympiads.
Appearing in 1921 as an equation for small-amplitude waves on the surface of an infinitely deep liquid, the Nekrasov equation quickly became a source of new results. This manifested itself both in the field of mathematics (theory of nonlinear integral equations of A.I. Nekrasov; 1922, later - of N.N. Nazarov; 1941), and in the field of mechanics (transition to a fluid of finite depth - A.I. Nekrasov; 1927 and refusal on the smallness of the wave amplitude - Yu.P. Krasovskii; 1960).The main task of the author is to find out the prehistory of the Nekrasov equation and to trace the change in approaches to its solution in the context of the nonlinear functional analysis development in the 1940s - 1960s. Close attention will be paid to the contribution of European and Russian mathematicians and mechanics: A.M. Lyapunov, E. Schmidt, T. Levi-Civita, A. Villat, L. Lichtenstein, M.A. Krasnoselskii, N.N. Moiseev, V.V. Pokornyi, etc. In the context of the development of qualitative methods for the Nekrasov equation investigating, the question of the interaction between Voronezh school of nonlinear functional analysis under the guidance of Professor M.A. Krasnoselskii and Rostov school of nonlinear mechanics under the guidance of Professor I.I. Vorovich.
In this Letter we comment on one particular aspect of Hypatias enigmatic biography by translating into English a short poem that appeared in a recent review of the third revised Polish edition of Maria Dzielskas book about Hypatia. It poses a simple and specifc question: did Hypatia know about the negative numbers?
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations of quantum mechanics had been established in around 1930, by von Neumann. The formulation uses functional analysis, linear algebra and probability theory. The knowledge of the mathematical formulation of QM is enough quantum mechanical knowledge for approaching to quantum algorithm and it might be efficient way for mathematicians that starting with mathematical formulations of QM. We explain the mathematical formulations of quantum mechanics briefly, quantum bits, quantum gates, quantum discrete Fourier transformation, Deutschs algorithm and Shors algorithm.
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