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Ashraf Huseynov
Ashraf Iskandar oglu Huseynov ( az, Əşrəf İskəndər oğlu Hüseynov, September 20, 1907, Amirvarli, Jabrayil District — August 26, 1981, Baku) was an Azerbaijani mathematician (Professor from 1948, member of Azerbaijan National Academy of Sciences from 1962). His area of contributions embraced nonlinear singular integral equations, differential equations, potential theory and functional analysis. Huseynov was first to study the nonlinear Hilbert problem as applied to analytic functions.''Azerbaijan Soviet Encyclopedia'' (1987), vol. 10, p. 285 He also created the ''Hα, β, γ'' function space and proved some theorems for nonlinear singular integral equations with Cauchy kernel In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary o ... within that space. Huseynov held positions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jabrayil District
Jabrayil District ( az, Cəbrayıl rayonu) is one of the 66 districts of Azerbaijan. It is located in the south-west of the country and belongs to the East Zangezur Economic Region. The district borders the districts of Khojavend, Fuzuli, Qubadli, Zangilan, and the Islamic Republic of Iran. Its capital is Jabrayil, however since the city is completely ruined following its occupation by ethnic Armenian forces, the current ''de facto'' capital is Jojug Marjanly until Jabrayil is rebuilt. As of 2020, the district had a nominal population of 81,700. Etymology The name of Jabrayil was taken from the name of the village Jabrayil that was the centre of the region. Father Jabrayil, who was the founder of the village Jabrayil, was one of the closes of the ruler by name Sultan Ahmed who lived in VIII century and the territories between Zuyaret Mountain and the river Araz belonged to Father Jabrayil and his sons. History In pre-modern times, the current territory of Jabrayil Distri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Functions
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real analytic functions. A function is analytic if and only if its Taylor series about ''x''0 converges to the function in some neighborhood for every ''x''0 in its domain. Definitions Formally, a function f is ''real analytic'' on an open set D in the real line if for any x_0\in D one can write : f(x) = \sum_^\infty a_ \left( x-x_0 \right)^ = a_0 + a_1 (x-x_0) + a_2 (x-x_0)^2 + a_3 (x-x_0)^3 + \cdots in which the coefficients a_0, a_1, \dots are real numbers and the series is convergent to f(x) for x in a neighborhood of x_0. Alternatively, a real analytic function is an infinitely differentiable function such that the Taylor series at any point x_0 in its domai ... [...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] |
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 Farabundo Martí National Liberation Front, FMLN launches its first major offensive, gaining control of most of Morazán Department, Morazán and Chalatenango Department, Chalatenango departments. * January 15 – Pope John Paul II receives a delegation led by Polish Solidarity (Polish trade union), Solidarity leader Lech Wałęsa at the Vatican City, Vatican. * January 20 – Iran releases the 52 Americans held for 444 days, minutes after Ronald Reagan is First inauguration of Ronald Reagan, sworn in as the 40th President of the United States, ending the Iran hostage crisis. * January 21 – The first DMC DeLorean, DeLorean automobile, a stainless steel sports car with gull-wing doors, rolls off the production line in Dunmurry, Northern Ireland. * January 24 – An 1981 Dawu ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1907 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 Slipk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy Kernel
In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk, and it provides integral formulas for all derivatives of a holomorphic function. Cauchy's formula shows that, in complex analysis, "differentiation is equivalent to integration": complex differentiation, like integration, behaves well under uniform limits – a result that does not hold in real analysis. Theorem Let be an open subset of the complex plane , and suppose the closed disk defined as :D = \bigl\ is completely contained in . Let be a holomorphic function, and let be the circle, oriented counterclockwise, forming the boundary of . Then for every in the interior of , :f(a) = \frac \oint_\gamma \frac\,dz.\, The proof of this statement uses the Cauchy integral theorem and like that theorem, it only requires t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorem
In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In the mainstream of mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice, or of a less powerful theory, such as Peano arithmetic. A notable exception is Wiles's proof of Fermat's Last Theorem, which involves the Grothendieck universes whose existence requires the addition of a new axiom to the set theory. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Space
In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set into a vector space has a natural vector space structure given by pointwise addition and scalar multiplication. In other scenarios, the function space might inherit a topological or metric structure, hence the name function ''space''. In linear algebra Let be a vector space over a field and let be any set. The functions → can be given the structure of a vector space over where the operations are defined pointwise, that is, for any , : → , any in , and any in , define \begin (f+g)(x) &= f(x)+g(x) \\ (c\cdot f)(x) &= c\cdot f(x) \end When the domain has additional structure, one might consider instead the subset (or subspace) of all such functions which respect that structure. For example, if is also a vector space over , the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert Problem
Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several proved to be very influential for 20th-century mathematics. Hilbert presented ten of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21, and 22) at the Paris conference of the International Congress of Mathematicians, speaking on August 8 at the Sorbonne. The complete list of 23 problems was published later, in English translation in 1902 by Mary Frances Winston Newson in the ''Bulletin of the American Mathematical Society''. Earlier publications (in the original German) appeared in and Nature and influence of the problems Hilbert's problems ranged greatly in topic and precision. Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative answer. For other problems, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baku
Baku (, ; az, Bakı ) is the capital and largest city of Azerbaijan, as well as the largest city on the Caspian Sea and of the Caucasus region. Baku is located below sea level, which makes it the lowest lying national capital in the world and also the largest city in the world located below sea level. Baku lies on the southern shore of the Absheron Peninsula, alongside the Bay of Baku. Baku's urban population was estimated at two million people as of 2009. Baku is the primate city of Azerbaijan—it is the sole metropolis in the country, and about 25% of all inhabitants of the country live in Baku's metropolitan area. Baku is divided into twelve administrative raions and 48 townships. Among these are the townships on the islands of the Baku Archipelago, and the town of Oil Rocks built on stilts in the Caspian Sea, away from Baku. The Inner City of Baku, along with the Shirvanshah's Palace and Maiden Tower, were inscribed as a UNESCO World Heritage Site in 2000. The c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, Topological space#Definition, topology, etc.) and the linear transformation, linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous function, continuous, unitary operator, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of variati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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