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Lazar Lyusternik
Lazar Aronovich Lyusternik (also Lusternik, Lusternick, Ljusternik; ; 31 December 1899, in Zduńska Wola, Congress Poland, Russian Empire – 23 July 1981, in Moscow, Soviet Union) 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 Mosc ... [...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 and 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 and Western Europe. Administratively it was located in the Sieradz Voivodeship in the Greater Poland Province of the Kingdom of Poland. Over the course of its history, the town was owned by nobles or industrialists and eventually transformed into a shtetl. At the beginning of the 18th century, Zduńska Wola was purchased by the aristocratic Złotnicki family. The development of the village is closely linked with the rapid influx of Silesian weavers and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed Geodesic
In differential geometry and dynamical systems, a closed geodesic on a Riemannian manifold is a geodesic that returns to its starting point with the same tangent direction. It may be formalized as the projection of a closed orbit of the geodesic flow on the tangent space of the manifold. Definition In a Riemannian manifold (''M'',''g''), a closed geodesic is a curve \gamma:\mathbb R\rightarrow M that is a geodesic for the metric ''g'' and is periodic. Closed geodesics can be characterized by means of a variational principle. Denoting by \Lambda M the space of smooth 1-periodic curves on ''M'', closed geodesics of period 1 are precisely the critical points of the energy function E:\Lambda M\rightarrow\mathbb R, defined by : E(\gamma)=\int_0^1 g_(\dot\gamma(t),\dot\gamma(t))\,\mathrmt. If \gamma is a closed geodesic of period ''p'', the reparametrized curve t\mapsto\gamma(pt) is a closed geodesic of period 1, and therefore it is a critical point of ''E''. If \gamma is a critical po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow State University Alumni
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. When th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soviet Mathematicians
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national republics; in practice, both its government and its economy were highly centralized until its final years. It was a one-party state governed by the Communist Party of the Soviet Union, with the city of Moscow serving as its capital as well as that of its largest and most populous republic: the Russian SFSR. Other major cities included Leningrad (Russian SFSR), Kiev (Ukrainian SSR), Minsk ( Byelorussian SSR), Tashkent (Uzbek SSR), Alma-Ata (Kazakh SSR), and Novosibirsk (Russian SFSR). It was the largest country in the world, covering over and spanning eleven time zones. The country's roots lay in the October Revolution of 1917, when the Bolsheviks, under the leadership of Vladimir Lenin, overthrew the Russian Provisional Governmen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1981 Deaths
Events January * January 1 ** Greece enters the European Economic Community, predecessor of the European Union. ** Palau becomes a self-governing territory. * January 10 – Salvadoran Civil War: The FMLN launches its first major offensive, gaining control of most of Morazán and Chalatenango departments. * January 15 – Pope John Paul II receives a delegation led by Polish Solidarity leader Lech Wałęsa at the Vatican. * January 20 – Iran releases the 52 Americans held for 444 days, minutes after Ronald Reagan is sworn in as the 40th President of the United States, ending the Iran hostage crisis. * January 21 – The first DeLorean automobile, a stainless steel sports car with gull-wing doors, rolls off the production line in Dunmurry, Northern Ireland. * January 24 – An earthquake of magnitude in Sichuan, China, kills 150 people. Japan suffers a less serious earthquake on the same day. * January 25 – In South Africa the largest part of the town La ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1899 Births
Events January 1899 * January 1 ** Spanish rule ends in Cuba, concluding 400 years of the Spanish Empire in the Americas. ** Queens and Staten Island become administratively part of New York City. * January 2 – ** Bolivia sets up a customs office in Puerto Alonso, leading to the Brazilian settlers there to declare the Republic of Acre in a revolt against Bolivian authorities. **The first part of the Jakarta Kota–Anyer Kidul railway on the island of Java is opened between Batavia Zuid ( Jakarta Kota) and Tangerang. * January 3 – Hungarian Prime Minister Dezső Bánffy fights an inconclusive duel with his bitter enemy in parliament, Horánszky Nándor. * January 4 – **U.S. President William McKinley's declaration of December 21, 1898, proclaiming a policy of benevolent assimilation of the Philippines as a United States territory, is announced in Manila by the U.S. commander, General Elwell Otis, and angers independence activists who had fought ag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pavel Aleksandrov
Pavel Sergeyevich Alexandrov (russian: Па́вел Серге́евич Алекса́ндров), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote about 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 ... [...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.Gardner, Richard J. (2002). "The Brunn–Minkowski inequality". Bull. Amer. Math. Soc. (N.S.) 39 (3): pp. 355–405 (electronic). doi:10.1090/S0273-0979-02-00941-2. . Multiplicative version T ... [...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 man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dmitri Egorov
Dmitri Fyodorovich Egorov (russian: Дми́трий Фёдорович Его́ров; 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
USSR State Prize
The USSR State Prize (russian: links=no, Государственная премия СССР, Gosudarstvennaya premiya SSSR) was the Soviet Union's state honor. It was established on 9 September 1966. After the dissolution of the Soviet Union, the prize was followed up by the State Prize of the Russian Federation. The State Stalin Prize ( Государственная Сталинская премия, ''Gosudarstvennaya Stalinskaya premiya''), usually called the Stalin Prize, existed from 1941 to 1954, although some sources give a termination date of 1952. It essentially played the same role; therefore upon the establishment of the USSR State Prize, the diplomas and badges of the recipients of Stalin Prize were changed to that of USSR State Prize. In 1944 and 1945, the last two years of the Second World War World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
