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Analytic Polyhedron
In mathematics, especially several complex variables, an analytic polyhedron is a subset of the complex space of the form :P = \ where is a bounded connected open subset of , f_j are holomorphic on and is assumed to be relatively compact in .See and . If f_j above are polynomials, then the set is called a polynomial polyhedron. Every analytic polyhedron is a domain of holomorphy and it is thus pseudo-convex. The boundary of an analytic polyhedron is contained in the union of the set of hypersurfaces : \sigma_j = \, \; 1 \le j \le N. An analytic polyhedron is a ''Weil polyhedron'', or Weil domain if the intersection of any of the above hypersurfaces has dimension no greater than .. See also *Behnke–Stein theorem In mathematics, especially several complex variables, the Behnke–Stein theorem states that a union of an increasing sequence G_k \subset \mathbb^n (i.e., G_k \subset G_) of domains of holomorphy is again a domain of holomorphy. It was proved by ... * Be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
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 poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Istituto Nazionale Di Alta Matematica
The Istituto Nazionale di Alta Matematica Francesco Severi, abbreviated as INdAM, is a government created non-profit research institution whose main purpose is to promote research in the field of mathematics and its applications and the diffusion of higher mathematical education in Italy.See the Italian law and its later amendment . Its founder and first president, later nominated life president, was Francesco Severi, who exerted also a major influence on the creation of the institute. History The institute was established on 13 July 1939 as the ''Royal National Institute of High Mathematics'', with a law signed by Vittorio Emanuele III, Benito Mussolini, Paolo Thaon di Revel and Giuseppe Bottai. Its foundation is largely due to the action of Francesco Severi, possibly starting from an idea by Luigi Fantappié. The first Scientific Council was made up of Francesco Severi (president), Luigi Fantappiè, Giulio Krall, Enrico Bompiani and Mauro Picone. In 1946, following the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walter De Gruyter
Walter de Gruyter GmbH, known as De Gruyter (), is a German scholarly publishing house specializing in academic literature. History The roots of the company go back to 1749 when Frederick the Great granted the Königliche Realschule in Berlin the royal privilege to open a bookstore and "to publish good and useful books". In 1800, the store was taken over by Georg Reimer (1776–1842), operating as the ''Reimer'sche Buchhandlung'' from 1817, while the school’s press eventually became the ''Georg Reimer Verlag''. From 1816, Reimer used the representative Sacken'sche Palace on Berlin's Wilhelmstraße for his family and the publishing house, whereby the wings contained his print shop and press. The building became a meeting point for Berlin salon life and later served as the official residence of the president of Germany. Born in Ruhrort in 1862, Walter de Gruyter took a position with Reimer Verlag in 1894. By 1897, at the age of 35, he had become sole proprietor of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elsevier
Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as '' The Lancet'', '' Cell'', the ScienceDirect collection of electronic journals, '' Trends'', the '' Current Opinion'' series, the online citation database Scopus, the SciVal tool for measuring research performance, the ClinicalKey search engine for clinicians, and the ClinicalPath evidence-based cancer care service. Elsevier's products and services also include digital tools for data management, instruction, research analytics and assessment. Elsevier is part of the RELX Group (known until 2015 as Reed Elsevier), a publicly traded company. According to RELX reports, in 2021 Elsevier published more than 600,000 articles annually in over 2,700 journals; as of 2018 its archives contained over 17 million documents and 40,000 e-books, with over one billion annual downloads. Researchers have criticized Elsevier for its high profit ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belmont, California
Belmont is a city in San Mateo County in the U.S. state of California. It is in the San Francisco Bay Area, on the San Francisco Peninsula about halfway between San Francisco and San Jose. Known for its wooded hills, views of the San Francisco Bay and stretches of open space, Belmont is a quiet residential community in the midst of the culturally and technologically rich Bay Area. It was originally part of Rancho de las Pulgas, for which one of its main roads, the Alameda de las Pulgas, is named. The city was incorporated in 1926. Its population was 28,335 at the 2020 census. Ralston Hall is a historic landmark built by Bank of California founder William Chapman Ralston on the campus of Notre Dame de Namur University, and is also home to Notre Dame High School. It was built around a villa formerly owned by Count , an Italian aristocrat. The locally famous "Waterdog Lake" is also located in the foothills and highlands of Belmont. A surviving structure from the Panama-Pac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prentice-Hall
Prentice Hall was an American major educational publisher owned by Savvas Learning Company. Prentice Hall publishes print and digital content for the 6–12 and higher-education market, and distributes its technical titles through the Safari Books Online e-reference service. History On October 13, 1913, law professor Charles Gerstenberg and his student Richard Ettinger founded Prentice Hall. Gerstenberg and Ettinger took their mothers' maiden names, Prentice and Hall, to name their new company. Prentice Hall became known as a publisher of trade books by authors such as Norman Vincent Peale; elementary, secondary, and college textbooks; loose-leaf information services; and professional books. Prentice Hall acquired the training provider Deltak in 1979. Prentice Hall was acquired by Gulf+Western in 1984, and became part of that company's publishing division Simon & Schuster. S&S sold several Prentice Hall subsidiaries: Deltak and Resource Systems were sold to National Education ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Englewood Cliffs
Englewood Cliffs is a borough in Bergen County, in the U.S. state of New Jersey, whose population at the 2010 United States census was 5,281.DP-1 - Profile of General Population and Housing Characteristics: 2010 for Englewood Cliffs borough, Bergen County, New Jersey . Accessed March 1, 2012. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oka–Weil Theorem
In mathematics, especially the theory of several complex variables, the Oka–Weil theorem is a result about the uniform convergence of holomorphic functions on Stein spaces due to Kiyoshi Oka and André Weil. Statement The Oka–Weil theorem states that if ''X'' is a Stein space and ''K'' is a compact \mathcal(X)-convex subset of ''X'', then every holomorphic function in an open neighborhood of ''K'' can be approximated uniformly on ''K'' by holomorphic functions on \mathcal(X) (i.e. by polynomials). Applications Since Runge's theorem may not hold for several complex variables, the Oka–Weil theorem is often used as an approximation theorem for several complex variables. The Behnke–Stein theorem was originally proved using the Oka–Weil theorem. See also * Oka coherence theorem References Bibliography * * * * * * Further reading * – An example where Runge's theorem In complex analysis, Runge's theorem (also known as Runge's approximation theorem) is named after th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Of Several Complex Variables
The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions. The name of the field dealing with the properties of function of several complex variables is called several complex variables (and analytic space), that has become a common name for that whole field of study and Mathematics Subject Classification has, as a top-level heading. A function f:(z_1,z_2, \ldots, z_n) \rightarrow f(z_1,z_2, \ldots, z_n) is -tuples of complex numbers, classically studied on the complex coordinate space \Complex^n. As in complex analysis of functions of one variable, which is the case , the functions studied are '' holomorphic'' or ''complex analytic'' so that, locally, they are power series in the variables . Equivalently, they are locally uniform limits of polynomials; or locally square-integrable solutions to the -dimensional Cauchy–Riemann equations. For one complex variable, every domainThat is an open connected subset. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bergman–Weil Formula
In mathematics, the Bergman–Weil formula is an integral representation for holomorphic functions of several variables generalizing the Cauchy integral formula. It was introduced by and . Weil domains A Weil domain is an analytic polyhedron with a domain ''U'' in C''n'' defined by inequalities ''f''''j''(''z'') < 1 for functions ''f''''j'' that are holomorphic on some neighborhood of the closure of ''U'', such that the faces of the Weil domain (where one of the functions is 1 and the others are less than 1) all have dimension 2''n'' − 1, and the intersections of ''k'' faces have at least ''k''. See also * |
