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Register a new userGeorg Cantor from St. Petersburg. Childhood and history of the family. Archival research
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G.I. Sinkevich
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Georg Cantor (1845-1918) was born, and spent the first 11 years of his life in St. Petersburg. The present lecture is devoted to his childhood and his family. Most of these documents were not available before and are now published for the first time.
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The Programme and Abstracts booklet of the sixth Conference on Physics of Neutron Stars held at the Ioffe Physical Technical Institute, St. Petersburg, Russia, on June 6 -- 8, 2001 is presented. The abstracts contain references to the web pages, LANL archive and published articles. More information on the Conference can be found at http://www.ioffe.rssi.ru/astro/NS2001/index.html
Throughout more than two millennia many formulas have been obtained, some of them beautiful, to calculate the number pi. Among them, we can find series, infinite products, expansions as continued fractions and expansions using radicals. Some expressions which are (amazingly) related to pi have been evaluated. In addition, a continual battle has been waged just to break the records computing digits of this number; records have been set using rapidly converging series, ultra fast algorithms and really surprising ones, calculating isolated digits. The development of powerful computers has played a fundamental role in these achievements of calculus.
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.
New understandings of the functioning of human brains engaged in mathematics raise interesting questions for mathematics educators. Novel lines of research are suggested by neuroscientific findings, and new light is shed on some longstanding issues in mathematics education.
In this survey paper we give an historical and at the same time thematical overview of the development of ring geometry from its origin to the current state of the art. A comprehensive up-to-date list of literature is added with articles that treat ring geometry within the scope of incidence geometry.
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