|
Dmitrii Menshov
Dmitrii Evgenevich Menshov (also spelled ''Men'shov'', ''Menchoff'', ''Menšov'', ''Menchov''; russian: Дми́трий Евгéньевич Меньшóв; 18 April 1892 – 25 November 1988) was a Russian mathematician known for his contributions to the theory of trigonometric series. Biography Dmitrii Menshov studied languages as a schoolboy, but from the age of 13 he began to show great interest in mathematics and physics. In 1911, he completed high school with a gold medal. After a semester at the Moscow Engineering School, he enrolled at Moscow State University in 1912 and became a student of Nikolai Luzin. In 1916, Menshov completed his dissertation on the topic of trigonometric series. He became a docent of Moscow State University in 1918. Soon after, he moved to Nizhny Novgorod where he was appointed a professor of the Ivanovsky Pedagogical Institute. After a few years, he returned to Moscow in 1922 and began to teach at Moscow State University. In 1935, Menshov became ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow
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] |
Russian Academy Of Sciences
The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such as libraries, publishing units, and hospitals. Peter the Great established the Academy (then the St. Petersburg Academy of Sciences) in 1724 with guidance from Gottfried Leibniz. From its establishment, the Academy benefitted from a slate of foreign scholars as professors; the Academy then gained its first clear set of goals from the 1747 Charter. The Academy functioned as a university and research center throughout the mid-18th century until the university was dissolved, leaving research as the main pillar of the institution. The rest of the 18th century continuing on through the 19th century consisted of many published academic works from Academy scholars and a few Ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysts
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...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 Government tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1988 Deaths
File:1988 Events Collage.png, From left, clockwise: The oil platform Piper Alpha explodes and collapses in the North Sea, killing 165 workers; The USS Vincennes (CG-49) mistakenly shoots down Iran Air Flight 655; Australia celebrates its Bicentennial on January 26; The 1988 Summer Olympics are held in Seoul, South Korea; Soviet troops begin their withdrawal from Afghanistan, which is completed the next year; The 1988 Armenian earthquake kills between 25,000-50,000 people; The 8888 Uprising in Myanmar, led by students, protests the Burma Socialist Programme Party; A bomb explodes on Pan Am Flight 103, causing the plane to crash down on the town of Lockerbie, Scotland- the event kills 270 people., 300x300px, thumb rect 0 0 200 200 Piper Alpha rect 200 0 400 200 Iran Air Flight 655 rect 400 0 600 200 Australian Bicentenary rect 0 200 300 400 Pan Am Flight 103 rect 300 200 600 400 1988 Summer Olympics rect 0 400 200 600 8888 Uprising rect 200 400 400 600 1988 Armenian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1892 Births
Year 189 ( CLXXXIX) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Silanus and Silanus (or, less frequently, year 942 ''Ab urbe condita''). The denomination 189 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Plague (possibly smallpox) kills as many as 2,000 people per day in Rome. Farmers are unable to harvest their crops, and food shortages bring riots in the city. China * Liu Bian succeeds Emperor Ling, as Chinese emperor of the Han Dynasty. * Dong Zhuo has Liu Bian deposed, and installs Emperor Xian as emperor. * Two thousand eunuchs in the palace are slaughtered in a violent purge in Luoyang, the capital of Han. By topic Arts and sciences * Galen publishes his ''"Treatise on the various temperaments"'' (aka ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lusin–Menchoff Theorem
In the mathematical field of real analysis, Lusin's theorem (or Luzin's theorem, named for Nikolai Luzin) or Lusin's criterion states that an almost-everywhere finite function is measurable if and only if it is a continuous function on nearly all its domain. In the informal formulation of J. E. Littlewood, "every measurable function is nearly continuous". Classical statement For an interval 'a'', ''b'' let :f: ,brightarrow \mathbb be a measurable function. Then, for every ''ε'' > 0, there exists a compact ''E'' ⊆ 'a'', ''b''such that ''f'' restricted to ''E'' is continuous and :\mu ( E ) > b - a - \varepsilon. Note that ''E'' inherits the subspace topology from 'a'', ''b'' continuity of ''f'' restricted to ''E'' is defined using this topology. Also for any function ''f'', defined on the interval 'a, b''and almost-everywhere finite, if for any ''ε > 0'' there is a function ''ϕ'', continuous on 'a, b'' such that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Looman–Menchoff Theorem
In the mathematical field of complex analysis, the Looman–Menchoff theorem states that a continuous complex-valued function defined in an open set of the complex plane is holomorphic if and only if it satisfies the Cauchy–Riemann equations. It is thus a generalization of a theorem by Édouard Goursat Édouard Jean-Baptiste Goursat (21 May 1858 – 25 November 1936) was a French mathematician, now remembered principally as an expositor for his ''Cours d'analyse mathématique'', which appeared in the first decade of the twentieth century. It se ..., which instead of assuming the continuity of ''f'', assumes its Fréchet differentiability when regarded as a function from a subset of R2 to R2. A complete statement of the theorem is as follows: * Let Ω be an open set in C and ''f'' : Ω → C be a continuous function. Suppose that the partial derivatives \partial f/\partial x and \partial f/\partial y exist everywhere but a countable set in Ω. Then ''f'' is holomorph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rademacher–Menchov Theorem
In mathematical analysis, the Rademacher–Menchov theorem, introduced by and , gives a sufficient condition for a series of orthogonal functions on an interval to converge almost everywhere In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities. The notion of "almost everywhere" is a companion notion to .... Statement If the coefficients ''c''ν of a series of bounded orthogonal functions on an interval satisfy :\sum , c_\nu, ^2\log(\nu)^2<\infty then the series converges almost everywhere. References * * * {{DEFAULTSORT:Rademacher-Menchov theorem Theorems in analysis ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Menshov Set
In mathematics, a set of uniqueness is a concept relevant to trigonometric expansions which are not necessarily Fourier series. Their study is a relatively pure branch of harmonic analysis. Definition A subset ''E'' of the circle is called a set of uniqueness, or a ''U''-set, if any trigonometric expansion :\sum_^c(n)e^ which converges to zero for t\notin E is identically zero; that is, such that :''c''(''n'') = 0 for all ''n''. Otherwise ''E'' is a set of multiplicity (sometimes called an ''M''-set or a Menshov set). Analogous definitions apply on the real line, and in higher dimensions. In the latter case one needs to specify the order of summation, e.g. "a set of uniqueness with respect to summing over balls". To understand the importance of the definition it is important to get out of the Fourier mind-set. In Fourier analysis there is no question of uniqueness, since the coefficients ''c''(''n'') are derived by integrating the function. Hence in Fourier analysis the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
