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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 * Bergman–Weil formula * Oka–Weil theorem Notes References *. * (also available as ). *. *. *. *. *. Notes from a course held by Francesco Severi at the Istituto Nazionale di Alta Matematica The Istituto Nazionale di Alta Matematica Francesco Seve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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 a representative palace at Wilhelmstraße 73 in Berlin for his family and the publishing house, whereby the wings contained his print shop and press. The building later served as the Palace of the Reich President. 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 the hundred-year-old company then known for publishing the works of German romantic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Elsevier
Elsevier ( ) is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell (journal), Cell'', the ScienceDirect collection of electronic journals, ''Trends (journals), Trends'', the ''Current Opinion (Elsevier), 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 include digital tools for Data management platform, 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 2022 Elsevier published more than 600,000 articles annually in over 2,800 journals. As of 2018, its archives contained over 17 million documents and 40,000 Ebook, e-books, with over one b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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. 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–Pacific International Exposition is on Belmont Avenue (another is the Palace of Fine Arts in San Francisco). The building was brought to Belmont by E.D. Swift shortly after the exposition cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Prentice-Hall
Prentice Hall was a major American educational publisher. It published print and digital content for the 6–12 and higher-education market. It was an independent company throughout the bulk of the twentieth century. In its last few years it was owned by, then absorbed into, Savvas Learning Company. In the Web era, it distributed its technical titles through the Safari Books Online e-reference service for some years. 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. At the time the name was usually styled as Prentice-Hall (as seen for example on many title pages), per an orthographic norm for coordinate elements within such compounds (compare also ''McGraw-Hill'' with later styling as ''McGraw Hill''). Prentice-Hall became known as a publisher of trade books by authors such as Norman Vincent Peale; ele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Englewood Cliffs
Englewood Cliffs is a borough in Bergen County, in the U.S. state of New Jersey. As of the 2020 United States census, the borough's population was 5,342, an increase of 61 (+1.2%) from the 2010 census count of 5,281, which in turn reflected a decline of 41 (-0.8%) from the 5,322 counted in the 2000 census. The borough houses the world headquarters of CNBC (NBCUniversal), the North American headquarters of South Korean conglomerate LG Corp,LG's Sustainable Flagship HOK, backed up by the as of October 17, 2012. Acces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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 internationally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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) (in particular, 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 In mathematics, the Oka coherence theorem, proved by , states that the sheaf \mathcal_ of holomorphic functions on \mathbb^n (and subsequently the sheaf \mathcal_ of holomorphic functio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Function Of Several Complex Variables
The theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space \mathbb C^n, that is, -tuples of complex numbers. The name of the field dealing with the properties of these functions is called several complex variables (and analytic space), which the Mathematics Subject Classification has as a top-level heading. 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. (D \subset \mathbb C), is the domain of holomorphy of some function, in other words every domain has a function for which it is the domain of holomorphy. For several complex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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 *Andreotti–Norguet for ...
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