|
Naum Ilyich Akhiezer
Naum Ilyich Akhiezer ( uk, Нау́м Іллі́ч Ахіє́зер; russian: link=no, Нау́м Ильи́ч Ахие́зер; 6 March 1901 – 3 June 1980) was a Soviet and Ukrainian mathematician of Jewish origin, known for his works in approximation theory and the theory of differential and integral operators.NAUM IL’ICH AKHIEZER (ON THE 100TH ANNIVERSARY OF HIS BIRTH), by V. A. Marchenko, Yu. A. Mitropol’skii, A. V. Pogorelov, A. M. Samoilenko, I. V. Skrypnik, and E. Ya. Khruslov (restricted access) He is also known as the author of classical books on various subjects in [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cherykaw
Cherykaw ( be, Чэрыкаў; russian: Чериков; pl, Czeryków) is a town in the Mogilev Region, Eastern Belarus. It is located in the east of the Region, on the Sozh River, and serves as the administrative center of Cherykaw District. As of 2009, its population was 8,177. History Cherykaw was first mentioned in 1460. At the time, it was a part of Kingdom of Poland, and Casimir IV Jagiellon, the king, ordered to have an Orthodox church to be built in Cherykaw. In 1604, Cherykaw was granted the town status, and in 1641, it was granted a coat of arms. In 1772, as a result of the First Partition of Poland, it was transferred to Russia. In the 19th century it belonged to Mogilev Governorate. In 1919, Mogilev Governorate was abolished, and Cherykaw was transferred to Gomel Governorate. On July 17, 1924 the governorate was abolished, and Cherykaw became the administrative center of Cherykaw Raion, which belonged to Kalinin Okrug of Byelorussian Soviet Socialist Republic. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zentralblatt MATH
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH. Editors are the European Mathematical Society, FIZ Karlsruhe, and the Heidelberg Academy of Sciences. zbMATH is distributed by Springer Science+Business Media. It uses the Mathematics Subject Classification codes for organising reviews by topic. History Mathematicians Richard Courant, Otto Neugebauer, and Harald Bohr, together with the publisher Ferdinand Springer, took the initiative for a new mathematical reviewing journal. Harald Bohr worked in Copenhagen. Courant and Neugebauer were professors at the University of Göttingen. At that time, Göttingen was considered one of the central places for mathematical research, having appointed mathematicians like David Hilbert, Hermann Minkowski, Carl Runge, and Felix Klein, the great ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abelian Integral
In mathematics, an abelian integral, named after the Norwegian mathematician Niels Henrik Abel, is an integral in the complex plane of the form :\int_^z R(x,w) \, dx, where R(x,w) is an arbitrary rational function of the two variables x and w, which are related by the equation :F(x,w)=0, where F(x,w) is an irreducible polynomial in w, :F(x,w)\equiv\varphi_n(x)w^n+\cdots+\varphi_1(x)w +\varphi_0\left(x\right), whose coefficients \varphi_j(x), j=0,1,\ldots,n are rational functions of x. The value of an abelian integral depends not only on the integration limits, but also on the path along which the integral is taken; it is thus a multivalued function of z. Abelian integrals are natural generalizations of elliptic integrals, which arise when :F(x,w)=w^2-P(x), \, where P\left(x\right) is a polynomial of degree 3 or 4. Another special case of an abelian integral is a hyperelliptic integral, where P(x), in the formula above, is a polynomial of degree greater than 4. Histor ... [...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] |
Riemann Surface
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together. The main interest in Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are nowadays considered the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the logarithm. Every Riemann surface is a two-dimensional real analytic manifold (i.e., a surface), but it contains more structure (specifically a complex structure) which is needed for the unambiguous definitio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Map
In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U and V be open subsets of \mathbb^n. A function f:U\to V is called conformal (or angle-preserving) at a point u_0\in U if it preserves angles between directed curves through u_0, as well as preserving orientation. Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature. The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation. The transformation is conformal whenever the Jacobian at each point is a positive scalar times a rotation matrix (orthogonal with determinant one). Some authors define conformality to include orientation-reversing mappings whose Jacobians can be written as any scalar times any orthogonal matrix. For mappings in two dimensions, the (orientation-preserving) conformal mappings are precisely the locally i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics. By extension, use of complex analysis also has applications in engineering fields such as nuclear engineering, nuclear, aerospace engineering, aerospace, mechanical engineering, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to its Taylor series (that is, it is Analyticity of holomorphic functions, analytic), complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions). History Complex analysis is one of the classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Problem
In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure ''μ'' to the sequences of moments :m_n = \int_^\infty x^n \,d\mu(x)\,. More generally, one may consider :m_n = \int_^\infty M_n(x) \,d\mu(x)\,. for an arbitrary sequence of functions ''M''''n''. Introduction In the classical setting, μ is a measure on the real line, and ''M'' is the sequence . In this form the question appears in probability theory, asking whether there is a probability measure having specified mean, variance and so on, and whether it is unique. There are three named classical moment problems: the Hamburger moment problem in which the support of μ is allowed to be the whole real line; the Stieltjes moment problem, for , +∞); and the Hausdorff moment problem for a bounded interval, which without loss of generality may be taken as , 1 Existence A sequence of numbers ''m''''n'' is the sequence of moments of a measure ''μ'' if an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructive Function Theory
In mathematical analysis, constructive function theory is a field which studies the connection between the smoothness of a function and its degree of approximation. It is closely related to approximation theory. The term was coined by Sergei Bernstein. Example Let ''f'' be a 2''π''-periodic function. Then ''f'' is ''α''- Hölder for some 0 < ''α'' < 1 if and only if for every natural ''n'' there exists a ''Pn'' of degree ''n'' such that : where ''C''(''f'') is a positive number depending on ''f''. The "only if" is due to , see |
Kharkov Mathematical Society
The Kharkov Mathematical Society ( uk, Харківське математичне товариство, translit=Kharkivske matematychne tovarystvo, russian: Харьковское математическое общество) is an association of professional mathematicians in Kharkiv aimed at advancement of mathematical research and education, popularizing achievements of mathematics. The structure of the Society includes mathematicians of Verkin Institute for Low Temperature Physics and Engineering, V. N. Karazin Kharkiv National University and other higher educational institutions of Kharkov. History and members of the Kharkov Mathematical Society Kharkov Mathematical Society was established in 1879 at Kharkov University by the initiative of Vasilii Imshenetskii, who also later founded the St. Petersburg Mathematical Society. According to the statute of the society, "the aim of the Kharkov Mathematical Society was to support the development of mathematical science and edu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National University Of Kharkiv
The Kharkiv University or Karazin University ( uk, Каразінський університет), or officially V. N. Karazin Kharkiv National University ( uk, Харківський національний університет імені В. Н. Каразіна), is one of the major universities in Ukraine, and earlier in the Russian Empire and Soviet Union. It was founded in 1804 through the efforts of Vasily Karazin becoming the second oldest university in modern-day Ukraine. History Russian Empire On , the Decree on the Opening of the Imperial University in Kharkiv came into force. The university became the second university in the south of the Russian Empire. It was founded on the initiative of the local community with Vasily Karazin at the fore, whose idea was supported by the nobility and the local authorities. Count Seweryn Potocki was appointed the first supervisor of the university, the first rector being the philologist and philosopher Ivan Rizhsky. In 1811 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> National University Of Kharkiv")