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Vladimir Iosifovich Kondrashov
Vladimir Iosifovich Kondrashov (; 2 February 1909 – 26 February 1971) was a Soviet mathematician most well known for proving the Rellich–Kondrachov theorem that shows that the embedding of certain Sobolev spaces into L''p'' spaces is compact. His name has also been transliterated as V.I. Kondrachoff, W. Kondrachov, or V.I. Kondrašov. Life Kondrashov was born on in Moscow. He graduated with a PhD from Moscow State University under the supervision of Sergei Sobolev in 1941. As a postdoc at Steklov Institute, where he obtained a DSc in 1950, he organised the Moscow Seminar on the Theory of Functions of Several Variables. For the final 20 years of his life until his death on 26 February 1971, he worked at the Moscow Engineering and Physics Institute National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) (russian: Национальный исследовательский ядерный университет "МИФИ" / НИЯУ МИФИ or ) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rellich–Kondrachov Theorem
In mathematics, the Rellich–Kondrachov theorem is a compact embedding theorem concerning Sobolev spaces. It is named after the Austrian-German mathematician Franz Rellich and the Russian mathematician Vladimir Iosifovich Kondrashov. Rellich proved the ''L''2 theorem and Kondrashov the ''L''''p'' theorem. Statement of the theorem Let Ω ⊆ R''n'' be an open, bounded Lipschitz domain, and let 1 ≤ ''p'' < ''n''. Set :p^ := \frac. Then the Sobolev space ''W''1,''p''(Ω; R) is continuously embedded in the ''L''''p'' space ''L''''p''∗(Ω; R) and is compactly embedded in ''L''''q''(Ω; R) for every 1 ≤ ''q'' < ''p''∗. In symbols, :W^ (\Omega) \hookrightarrow L^ (\Omega) and :W^ (\Omega) \subset \subset L^ (\Omega) \text 1 \leq q 2527916 Zblbr>1180.46001* {{DEFAULTSORT:Rellich-Kondrachov theorem Theorems in analysis Sobolev spaces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sobolev Space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, i.e. a Banach space. Intuitively, a Sobolev space is a space of functions possessing sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and regularity of a function. Sobolev spaces are named after the Russian mathematician Sergei Sobolev. Their importance comes from the fact that weak solutions of some important partial differential equations exist in appropriate Sobolev spaces, even when there are no strong solutions in spaces of continuous functions with the derivatives understood in the classical sense. Motivation In this section and throughout the article \Omega is an open subset of \R^n. There are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lp Space
In mathematics, the spaces are function spaces defined using a natural generalization of the -norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue , although according to the Bourbaki group they were first introduced by Frigyes Riesz . spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of their key role in the mathematical analysis of measure and probability spaces, Lebesgue spaces are used also in the theoretical discussion of problems in physics, statistics, economics, finance, engineering, and other disciplines. Applications Statistics In statistics, measures of central tendency and statistical dispersion, such as the mean, median, and standard deviation, are defined in terms of metrics, and measures of central tendency can be characterized as solutions to variational problems. In penalized regression, "L1 penalty" and "L2 penalty" refer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Embedding
In mathematics, the notion of being compactly embedded expresses the idea that one set or space is "well contained" inside another. There are versions of this concept appropriate to general topology and functional analysis. Definition (topological spaces) Let (''X'', ''T'') be a topological space, and let ''V'' and ''W'' be subsets of ''X''. We say that ''V'' is compactly embedded in ''W'', and write ''V'' ⊂⊂ ''W'', if * ''V'' ⊆ Cl(''V'') ⊆ Int(''W''), where Cl(''V'') denotes the closure of ''V'', and Int(''W'') denotes the interior of ''W''; and * Cl(''V'') is compact. Definition (normed spaces) Let ''X'' and ''Y'' be two normed vector spaces with norms , , •, , ''X'' and , , •, , ''Y'' respectively, and suppose that ''X'' ⊆ ''Y''. We say that ''X'' is compactly embedded in ''Y'', and write ''X'' ⊂⊂ ''Y'', if * ''X'' is continuously embedded in ''Y''; i.e., there is a constant ''C'' such that , , ''x'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow State University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious university in the country. The university includes 15 research institutes, 43 faculties, more than 300 departments, and six branches (including five foreign ones in the Commonwealth of Independent States countries). Alumni of the university include past leaders of the Soviet Union and other governments. As of 2019, 13 List of Nobel laureates, Nobel laureates, six Fields Medal winners, and one Turing Award winner had been affiliated with the university. The university was ranked 18th by ''The Three University Missions Ranking'' in 2022, and 76th by the ''QS World University Rankings'' in 2022, #293 in the world by the global ''Times Higher World University Rankings'', and #326 by ''U.S. News & World Report'' in 2022. It was the highest-ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergei Sobolev
Prof Sergei Lvovich Sobolev (russian: Серге́й Льво́вич Со́болев) H FRSE (6 October 1908 – 3 January 1989) was a 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 distributions) were first introduced by Sobolev in 1935 for weak solutions, and further developed by Laurent Schwartz. Sobolev abstracted the classical notion of differentiation, so expanding the range of application of the technique of Newton and Leibniz. The theory of distributions is considered now as the calculus of the modern epoch. Life He was born in St. Petersburg as the son of Lev Alexandrovich Sobolev, a lawyer, and his wife, Natalya Georgievna. His city was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steklov Institute
Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Steklov, who in 1919 founded the Institute of Physics and Mathematics in Leningrad. In 1934, this institute was split into separate parts for physics and mathematics, and the mathematical part became the Steklov Institute. At the same time, it was moved to Moscow. The first director of the Steklov Institute was Ivan Matveyevich Vinogradov. From 19611964, the institute's director was the notable mathematician Sergei Chernikov. The old building of the Institute in Leningrad became its Department in Leningrad. Today, that department has become a separate institute, called the '' St. Petersburg Department of Steklov Institute of Mathematics of Russian Aca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow Engineering And Physics Institute
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) (russian: Национальный исследовательский ядерный университет "МИФИ" / НИЯУ МИФИ or ) is a technical university in Russia. It was founded in 1942 as the Moscow Mechanical Institute of Munitions (), but was soon renamed the Moscow Mechanical Institute. Its original mission was to train skilled personnel for the Soviet military and Soviet atomic bomb project. It was renamed the Moscow Engineering Physics Institute () in 1953, which was its name until 2009. By the Order of the Government of Russia on April 8, 2009 (#480-r) on behalf of Russian President's Decree of October 7, 2008 (#1448) "On the pilot project launching on creating National Research Universities" MEPhI was granted this new status. The university was reorganized. The aim of the university existence is now preparing the specialists by giving them higher professional, post-grad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1909 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * '' Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album ''Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Sl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1971 Deaths
* The year 1971 had three partial solar eclipses ( February 25, July 22 and August 20) and two total lunar eclipses (February 10, and August 6). The world population increased by 2.1% this year, the highest increase in history. Events January * January 2 – 66 people are killed and over 200 injured during a crush in Glasgow, Scotland. * January 5 – The first ever One Day International cricket match is played between Australia and England at the Melbourne Cricket Ground. * January 8 – Tupamaros kidnap Geoffrey Jackson, British ambassador to Uruguay, in Montevideo, keeping him captive until September. * January 9 – Uruguayan president Jorge Pacheco Areco demands emergency powers for 90 days due to kidnappings, and receives them the next day. * January 12 – The landmark United States television sitcom '' All in the Family'', starring Carroll O'Connor as Archie Bunker, debuts on CBS. * January 14 – Seventy Brazilian political pri ... [...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] |
Mathematicians From Moscow
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
