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Semën Samsonovich Kutateladze
Semyon Samsonovich Kutateladze (; October 2, 1945 – January 15, 2025) was a Russian mathematician. He was known for his contributions to functional analysis and its applications to vector lattices and optimization. In particular, he made contributions to the calculus of subdifferentials for vector-lattice valued functions, to whose study he introduced methods of Boolean-valued models and infinitesimals. He was professor of mathematics at Novosibirsk State University, where he continued and enriched the scientific tradition of Leonid Kantorovich. His father was the Soviet heat physicist Samson Kutateladze. Kutateladze died on January 15, 2025, aged 79. Selected publications *. *Gordon, E. I.; Kusraev, A. G.; Kutateladze, S. SInfinitesimal Analysis.Updated and revised translation of the 2001 Russian original. Translated by Kutateladze. Mathematics and its Applications, 544. Kluwer Academic Publishers, Dordrecht, 2002. *Kutateladze, S. SFundamentals of Functional Analysis.Trans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leningrad
Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland on the Baltic Sea. The city had a population of 5,601,911 residents as of 2021, with more than 6.4 million people living in the Saint Petersburg metropolitan area, metropolitan area. Saint Petersburg is the List of European cities by population within city limits, fourth-most populous city in Europe, the List of cities and towns around the Baltic Sea, most populous city on the Baltic Sea, and the world's List of northernmost items#Cities and settlements, northernmost city of more than 1 million residents. As the former capital of the Russian Empire, and a Ports of the Baltic Sea, historically strategic port, it is governed as a Federal cities of Russia, federal city. The city was founded by Tsar Peter the Great on 27 May 1703 on the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Lane Bell
John Lane Bell (born March 25, 1945) is an Anglo-Canadian philosopher, mathematician and logician. He is Professor Emeritus of Philosophy at the University of Western Ontario in Canada. His research includes such topics as set theory, model theory, lattice theory, modal logic, quantum logic, constructive mathematics, type theory, topos theory, infinitesimal analysis, spacetime theory, and the philosophy of mathematics. He is the author of more than 70 articles and of 13 books. In 2009, he was elected a Fellow of the Royal Society of Canada. Biography John Bell was awarded a scholarship to Oxford University at the age of 15, and graduated with a D.Phil. in Mathematics: his dissertation supervisor was John Crossley. During 1968–89 he was Lecturer in Mathematics and Reader in Mathematical Logic at the London School of Economics. Bell's students include Graham Priest Graham Priest (born 1948) is a philosopher and logician who is distinguished professor of philosophy at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1945 Births
1945 marked the end of World War II, the fall of Nazi Germany, and the Empire of Japan. It is also the year concentration camps were liberated and the only year in which atomic weapons have been used in combat. Events World War II will be abbreviated as “WWII” January * January 1 – WWII: ** Germany begins Operation Bodenplatte, an attempt by the ''Luftwaffe'' to cripple Allied air forces in the Low Countries. ** Chenogne massacre: German prisoners are allegedly killed by American forces near the village of Chenogne, Belgium. * January 6 – WWII: A German offensive recaptures Esztergom, Hungary from the Soviets. * January 9 – WWII: American and Australian troops land at Lingayen Gulf on western coast of the largest Philippine island of Luzon, occupied by Japan since 1942. * January 12 – WWII: The Soviet Union begins the Vistula–Oder Offensive in Eastern Europe, against the German Army. * January 13 – WWII: The Soviet Union begins the East Prussia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smooth Infinitesimal Analysis
Smooth infinitesimal analysis is a modern reformulation of the calculus in terms of infinitesimals. Based on the ideas of F. W. Lawvere and employing the methods of category theory, it views all functions as being continuous and incapable of being expressed in terms of discrete entities. As a theory, it is a subset of synthetic differential geometry. Terence Tao has referred to this concept under the name "cheap nonstandard analysis." The ''nilsquare'' or ''nilpotent'' infinitesimals are numbers ''ε'' where ''ε''² = 0 is true, but ''ε'' = 0 need not be true at the same time. ''Calculus Made Easy'' notably uses nilpotent infinitesimals. Overview This approach departs from the classical logic used in conventional mathematics by denying the law of the excluded middle, e.g., ''NOT'' (''a'' ≠ ''b'') does not imply ''a'' = ''b''. In particular, in a theory of smooth infinitesimal analysis one can prove for all infinitesimals ''ε'', ''NOT'' (''ε'' ≠ 0); yet it is provably f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dana Scott
Dana Stewart Scott (born October 11, 1932) is an American logician who is the emeritus Hillman University Professor of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University; he is now retired and lives in Berkeley, California. His work on automata theory earned him the Turing Award in 1976, while his collaborative work with Christopher Strachey in the 1970s laid the foundations of modern approaches to the semantics of programming languages. He has also worked on modal logic, topology, and category theory. Early career He received his B.A. in Mathematics from the University of California, Berkeley, in 1954. He wrote his Ph.D. thesis on ''Convergent Sequences of Complete Theories'' under the supervision of Alonzo Church while at Princeton, and defended his thesis in 1958. Solomon Feferman (2005) writes of this period: After completing his Ph.D. studies, he moved to the University of Chicago, working as an instructor there until 1960. In 1959, h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abraham Robinson
Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics. Nearly half of Robinson's papers were in applied mathematics rather than in pure mathematics. Biography He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Wałbrzych, in Poland. In 1933, he immigrated to British Mandate of Palestine, where he earned a first degree from the Hebrew University. Robinson was in France when the Nazis invaded during World War II, and escaped by train and on foot, being alternately questioned by French soldiers suspicious of his German passport and asked by them to share his map, which was more detailed than theirs. While in London, he joined the Free French Air Force and contributed to the war effort by teaching himself aerodynam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonstandard Analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using (ε, δ)-definition of limit, limits rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Nonstandard analysis originated in the early 1960s by the mathematician Abraham Robinson. He wrote: ... the idea of infinitely small or ''infinitesimal'' quantities seems to appeal naturally to our intuition. At any rate, the use of infinitesimals was widespread during the formative stages of the Differential and Integral Calculus. As for the objection ... that the distance between two distinct real numbers cannot be infinitely small, Gottfried Wilhelm Leibniz argued that the theory of infinitesimals implies the introduction of ideal numbers which might be infinitely small or inf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aleksandr Danilovich Aleksandrov
Aleksandr Danilovich Aleksandrov (; 4 August 1912 – 27 July 1999) was a Soviet and Russian mathematician, physicist, philosopher and mountaineer. Personal life Aleksandr Aleksandrov was born in 1912 in Volyn, Ryazan Oblast. His father was a headmaster of a secondary school in St Petersburg and his mother a teacher at said school, thus the young Alekandrov spent a majority of his childhood in the city. His family was old Russian nobility—students noted ancestral portraits which hung in his office. His sisters were Soviet botanist Vera Danilovna Aleksandrov (RU) and Maria Danilovna Aleksandrova, author of the first monograph on gerontopsychology in the USSR. In 1937, he married a student of the Faculty of Physics, Marianna Leonidovna Georg. Together they had two children: Daria (b. 1948) and Daniil (RU) (b. 1957). In 1980, he married Svetlana Mikhailovna Vladimirova (nee Bogacheva). In 1951 he became a member of the Communist Party. Alekandrov had a personal love for po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergei Sobolev
Prof Sergei Lvovich Sobolev, FRSE (; 6 October 1908 – 3 January 1989) was a Soviet Union, Soviet mathematician working in mathematical analysis and partial differential equations. Sobolev introduced notions that are now fundamental for several areas of mathematics. Sobolev spaces can be defined by some growth conditions on the Fourier transform. They and their embedding theorems are an important subject in functional analysis. Generalized functions (later known as distribution (mathematics), distributions) were first introduced by Sobolev in 1935 for weak solutions, and further developed by Laurent Schwartz. Sobolev abstracted the classical notion of derivative, differentiation, so expanding the range of application of the technique of Newton and Leibniz. The theory of Distribution (mathematics), distributions is considered now as the calculus of the modern epoch. Life He was born in Saint Petersburg, St. Petersburg as the son of Lev Aleksandrovich Sobolev, a lawyer, and his w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikolai Luzin
Nikolai Nikolayevich Luzin (also spelled Lusin; rus, Никола́й Никола́евич Лу́зин, p=nʲɪkɐˈlaj nʲɪkɐˈlajɪvʲɪtɕ ˈluzʲɪn, a=Ru-Nikilai Nikilayevich Luzin.ogg; 9 December 1883 – 28 February 1950) was a Soviet and Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the eponym of Luzitania, a loose group of young Moscow mathematicians of the first half of the 1920s. They adopted his set-theoretic orientation, and went on to apply it in other areas of mathematics. Life He started studying mathematics in 1901 at Moscow State University, where his advisor was Dmitri Egorov. He graduated in 1905. Luzin underwent great personal turmoil in the years 1905 and 1906, when his materialistic worldview had collapsed and he found himself close to suicide. In 1906 he wrote to Pavel Florensky, a former fellow mathematics student who was now studying ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Influence Of Non-standard Analysis
Abraham Robinson's theory of nonstandard analysis has been applied in a number of fields. Probability theory "Radically elementary probability theory" of Edward Nelson combines the discrete and the continuous theory through the infinitesimal approach. The model-theoretical approach of nonstandard analysis together with Loeb measure theory allows one to define Brownian motion as a hyperfinite random walk, obviating the need for cumbersome measure-theoretic developments. Jerome Keisler used this classical approach of nonstandard analysis to characterize general stochastic processes as hyperfinite ones. Economics Economists have used nonstandard analysis to model markets with large numbers of agents (see Robert M. Anderson (economist)). Education An article by Michèle Artigue concerns the teaching of analysis. Artigue devotes a section, "The non standard analysis and its weak impact on education" on page 172, to non-standard analysis. She writes: :The non-standard analysis rev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mathematical logic), mathematical structure), and their Structure (mathematical logic), models (those Structure (mathematical logic), structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be definable set, defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
