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Lusternik
Lazar Aronovich Lyusternik (also Lusternik, Lusternick, Ljusternik; ; 31 December 1899 – 22 July 1981) was a Soviet mathematician. He is famous for his work in topology and differential geometry, to which he applied the variational principle. Using the theory he introduced, together with Lev Schnirelmann, he proved the theorem of the three geodesics, a conjecture by Henri Poincaré that every convex body in 3-dimensions has at least three simple closed geodesics. The ellipsoid with distinct but nearly equal axis is the critical case with exactly three closed geodesics. The ''Lusternik–Schnirelmann theory'', as it is called now, is based on the previous work by Poincaré, David Birkhoff, and Marston Morse. It has led to numerous advances in differential geometry and topology. For this work Lyusternik received the Stalin Prize in 1946. In addition to serving as a professor of mathematics at Moscow State University, Lyusternik also worked at the Steklov Mathematical Institute ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lusternik–Schnirelmann Category
In mathematics, the Lyusternik–Schnirelmann category (or, Lusternik–Schnirelmann category, LS-category) of a topological space X is the homotopy invariant defined to be the smallest integer number k such that there is an open covering \_ of X with the property that each inclusion map U_i\hookrightarrow X is nullhomotopic. For example, if X is a sphere, this takes the value two. Sometimes a different normalization of the invariant is adopted, which is one less than the definition above. Such a normalization has been adopted in the definitive monograph by Cornea, Lupton, Oprea, and Tanré (see below). In general it is not easy to compute this invariant, which was initially introduced by Lazar Lyusternik and Lev Schnirelmann in connection with variational problems. It has a close connection with algebraic topology, in particular cup-length. In the modern normalization, the cup-length is a lower bound for the LS-category. It was, as originally defined for the case of X a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lev Schnirelmann
Lev Genrikhovich Schnirelmann (also Shnirelman, Shnirel'man; ; 2 January 1905 – 24 September 1938) was a Soviet mathematician who worked on number theory, topology and differential geometry. Work Schnirelmann sought to prove Goldbach's conjecture. In 1930, using the Brun sieve, he proved that any natural number greater than 1 can be written as the sum of not more than ''C'' prime numbers, where ''C'' is an effectively computable constant. His other fundamental work is joint with Lazar Lyusternik. Together, they developed the ''Lusternik–Schnirelmann category'', as it is called now, based on the previous work by Henri Poincaré, George David Birkhoff, and Marston Morse. The theory gives a global invariant of spaces, and has led to advances in differential geometry and topology. They also proved the theorem of the three geodesics, that a Riemannian manifold topologically equivalent to a sphere has at least three simple closed geodesics. Biography Schnirelmann graduated from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abram Ilyich Fet
Abram Fet (, ) (5 December 1924 — 30 July 2009) was a Russian mathematician, Soviet dissident, philosopher, Samizdat translator and writer. He used various pseudonyms for Samizdat, like N. A. Klenov, A.B. Nazyvayev, D.A. Rassudin, S.T. Karneyev, etc. If published, his translations were usually issued under the name of A.I. Fedorov, which reproduced Fet's own initials and sometimes under the names of real people who agreed to publish Fet's translations under their names. Biography Abram Fet was born on 5 December 1924 in Odesa into a family of Ilya Fet and Revekka Nikolayevskaya. Ilya Fet was a medical doctor; he was born and grew in Rivne and studied medicine in Paris. Revekka was a housewife; she grew in Odesa. Fet's father often changed jobs, moving with his family over Ukraine looking for places where to escape starvation, and the children had to change schools. In 1936, the family settled in Odesa. There Abram Fet finished high school at the age of 15 and entered the Od ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mark Vishik
Mark Vishik (also Marko Vishik, ; 19 October 1921, Lwów, II Rzeczpospolita – 23 June 2012) was a Soviet mathematician who worked in the field of partial differential equations. Life and work Lwów In Lwów, Mark Vishik visited the fifth gymnasium (high school), which specialized in physics and mathematics. His mathematical talent was encouraged by a method of teaching, which left it up to the students to find mathematical proofs. He began studying mathematics at the University of Lviv in December 1939, at the time when the Lwów school mathematics was still active. Among his teachers were Juliusz Schauder, Stanisław Mazur, Bronislaw Knaster, and Edward Szpilrajn, who organized a student conference in 1940 in Lviv, also attended by Stefan Banach. From Lwów to Tbilisi In June 1941, during the occupation of Lwów the Germans, Vishik left the city with a Komsomol group. Vishik then joined the retreating army and on foot reached Ternopil and then Zhmerynka (in Vinnytsia) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zduńska Wola
Zduńska Wola is a city in central Poland with 40,730 inhabitants (2021). It is the seat of Zduńska Wola County in the Łódź Voivodeship. The city was once one of the largest cloth, linen and cotton weaving centres in Poland and is the birthplace of Saint Maximilian Kolbe as well as Maksymilian Faktorowicz, the founder of Max Factor cosmetics company. History Early history The city was first mentioned and documented in 1394. Zduńska Wola was then part of an important trade route which crossed through Poland and connected Eastern Europe, Eastern and Western Europe. Administratively, it was located in the Sieradz Voivodeship (1339–1793), Sieradz Voivodeship in the Greater Poland Province, Crown of the Kingdom of Poland, Greater Poland Province of the Kingdom of Poland. Over the course of its history, the town was owned by nobles or industrialists. At the beginning of the 18th century, Zduńska Wola was purchased by the aristocratic Złotnicki family. The development of the vi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marston Morse
Harold Calvin Marston Morse (March 24, 1892 – June 22, 1977) was an American mathematician best known for his work on the ''calculus of variations in the large'', a subject where he introduced the technique of differential topology now known as Morse theory. The Morse–Palais lemma, one of the key results in Morse theory, is named after him, as is the Thue–Morse sequence, an infinite binary sequence with many applications. He was elected to the American Academy of Arts and Sciences in 1929, the United States National Academy of Sciences in 1932, and the American Philosophical Society in 1936. In 1933 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis. J. Robert Oppenheimer described Morse as "almost a statesman of mathematics." Biography Morse was born in Waterville, Maine to Ella Phoebe Marston and Howard Calvin Morse in 1892. He received his bachelor's degree from Colby College (also in Waterville) in 1914. At Harvard University, he received b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
USSR State Prize
The USSR State Prize () was one of the Soviet Union’s highest civilian honours, awarded from its establishment in September 1966 until the dissolution of the USSR in 1991. It recognised outstanding contributions in the fields of science, mathematics, literature, the arts, and architecture. History State Stalin Prize (1941–1956) The award traces its origins to the State Stalin Prize (), commonly known as the Stalin Prize, which was established in 1941. It honoured achievements in science, technology, literature, and the arts deemed vital to the Soviet war effort and postwar reconstruction.Volkov, Solomon; Bouis, Antonina W., trans. 2004. ''Shostakovich and Stalin: The Extraordinary Relationship Between the Great Composer and the Brutal Dictator''. New York: Alfred A. Knopf. ISBN 0-375-41082-1. Ceremonies were suspended during 1944–45 and then held twice in 1946 (January for works from 1943–44; June for 1945 works). USSR State Prize (1966–1991) By 1966, the Stalin Prize h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dmitri Egorov
Dmitri Fyodorovich Egorov (; December 22, 1869 – September 10, 1931) was a Russian and Soviet mathematician known for contributions to the areas of differential geometry and mathematical analysis. He was President of the Moscow Mathematical Society (1923–1930). Life Egorov held spiritual beliefs to be of great importance, and openly defended the Church against Marxist supporters after the Russian Revolution. He was elected president of the Moscow Mathematical Society in 1921, and became director of the Institute for Mechanics and Mathematics at Moscow State University in 1923. He also edited the journal ''Matematicheskii Sbornik'' of the Moscow Mathematical Society. However, because of Egorov's stance against the repression of the Russian Orthodox Church, he was dismissed from the Institute in 1929 and publicly rebuked. In 1930 he was arrested and imprisoned as a "religious sectarian", and soon after was expelled from the Moscow Mathematical Society. Upon imprisonment, Egoro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brunn–Minkowski Theorem
In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. The original version of the Brunn–Minkowski theorem (Hermann Brunn 1887; Hermann Minkowski 1896) applied to convex sets; the generalization to compact nonconvex sets stated here is due to Lazar Lyusternik (1935). Statement Let ''n'' ≥ 1 and let ''μ'' denote the Lebesgue measure on R''n''. Let ''A'' and ''B'' be two nonempty compact subsets of R''n''. Then the following inequality holds: : \mu (A + B) \geq mu (A) + mu (B), where ''A'' + ''B'' denotes the Minkowski sum: :A + B := \. The theorem is also true in the setting where A, B, A + B are only assumed to be measurable and non-empty. Multiplicative version The multiplicative form of Brunn–Minkowski inequality states that \mu(\lambda A + (1 - \lambda) B) \geq \mu(A)^ \mu(B)^ for all \lambda \in ,1. The Brunn–Minkowsk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellipsoid
An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a Surface (mathematics), surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by either of the two following properties. Every planar Cross section (geometry), cross section is either an ellipse, or is empty, or is reduced to a single point (this explains the name, meaning "ellipse-like"). It is Bounded set, bounded, which means that it may be enclosed in a sufficiently large sphere. An ellipsoid has three pairwise perpendicular Rotational symmetry, axes of symmetry which intersect at a Central symmetry, center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the ''principal ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pavel Alexandrov
Pavel Sergeyevich Alexandrov (), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote roughly three hundred papers, making important contributions to set theory and topology. In topology, the Alexandroff compactification and the Alexandrov topology are named after him. Biography Alexandrov attended Moscow State University where he was a student of Dmitri Egorov and Nikolai Luzin. Together with Pavel Urysohn, he visited the University of Göttingen in 1923 and 1924. After getting his Ph.D. in 1927, he continued to work at Moscow State University and also joined the Steklov Institute of Mathematics. He was made a member of the Russian Academy of Sciences in 1953. Personal life Luzin challenged Alexandrov to determine if the continuum hypothesis is true. This still unsolved problem was too much for Alexandrov and he had a creative crisis at the end of 1917. The failure was a heavy blow for Alexandrov: "It became ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1899 Births
Events January * January 1 ** Spanish rule formally ends in Cuba with the cession of Spanish sovereignty to the U.S., concluding 400 years of the Spanish Empire in the Americas.''The American Monthly Review of Reviews'' (February 1899), pp. 153-157 ** In Samoa, followers of Mataafa, claimant to the rule of the island's subjects, burn the town of Upolu in an ambush of followers of other claimants, Malietoa Tanus and Tamasese, who are evacuated by the British warship HMS ''Porpoise''. ** Queens and Staten Island become administratively part of New York City. * January 2 – Theodore Roosevelt is inaugurated as Governor of New York at the age of 39. * January 3 – A treaty of alliance is signed between Russia and Afghanistan. * January 5 – **A fierce battle is fought between American troops and Filipino defenders at the town of Pililla on the island of Luzon. *The collision of a British steamer and a French steamer kills 12 people on the English Channel. * Jan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
