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Bochner–Martinelli Formula
In mathematics, the Bochner–Martinelli formula is a generalization of the Cauchy integral formula to functions of several complex variables, introduced by and . History Bochner–Martinelli kernel For , in \C^n the Bochner–Martinelli kernel is a differential form in of bidegree defined by :\omega(\zeta,z) = \frac\frac \sum_(\overline\zeta_j-\overline z_j) \, d\overline\zeta_1 \land d\zeta_1 \land \cdots \land d\zeta_j \land \cdots \land d\overline\zeta_n \land d\zeta_n (where the term is omitted). Suppose that is a continuously differentiable function on the closure of a domain in \mathbb''n'' with piecewise smooth boundary . Then the Bochner–Martinelli formula states that if is in the domain then :\displaystyle f(z) = \int_f(\zeta)\omega(\zeta, z) - \int_D\overline\partial f(\zeta)\land\omega(\zeta,z). In particular if is holomorphic the second term vanishes, so :\displaystyle f(z) = \int_f(\zeta)\omega(\zeta, z). See also *Bergman–Weil formula Not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy Integral Formula
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 to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Krasnoyarsk
Krasnoyarsk is the largest types of inhabited localities in Russia, city and administrative center of Krasnoyarsk Krai, Russia. It is situated along the Yenisey, Yenisey River, and is the second-largest city in Siberia after Novosibirsk, with a population of over 1.1 million. Krasnoyarsk is an important junction of the renowned Trans-Siberian Railway, and is one of the largest producers of aluminum in the country. The city is known for its natural landscape; author Anton Chekhov judged Krasnoyarsk to be the most beautiful city in Siberia. The Krasnoyarsk Pillars, Stolby Nature Sanctuary is located 10 km south of the city. Krasnoyarsk is a major educational centre in Siberia, and hosts the Siberian Federal University. In 2019, Krasnoyarsk was the host city of the 2019 Winter Universiade, the third hosted in Russia. Etymology The predecessor fort was named Krasny Yar () after the Yarin (a dialect of Khakas language, Khakas) name of the place where it was built, ''Kyzyl Char'' ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accademia Nazionale Dei Lincei
The (; literally the "Academy of the Lynx-Eyed"), anglicised as the Lincean Academy, is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy. Founded in the Papal States in 1603 by Federico Cesi, the academy was named after the lynx, an animal whose sharp vision symbolizes the observational prowess that science requires. Galileo Galilei was the intellectual centre of the academy and adopted "Galileo Galilei Linceo" as his signature. "The Lincei did not long survive the death in 1630 of Cesi, its founder and patron", and "disappeared in 1651." During the nineteenth century, it was revived, first in the Papal States and later in the nation of Italy. Thus the Pontifical Academy of Sciences, established in 1936, claims this heritage as the ''Accademia Pontificia dei Nuovi Lincei (''"Pontifical Academy of the New Lynxes"'')'', founded in 1847, descending from the first two incarnations of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hartogs' Extension Theorem
In the theory of functions of several complex variables, Hartogs's extension theorem is a statement about the singularities of holomorphic functions of several variables. Informally, it states that the support of the singularities of such functions cannot be compact, therefore the singular set of a function of several complex variables must (loosely speaking) 'go off to infinity' in some direction. More precisely, it shows that an isolated singularity is always a removable singularity for any analytic function of complex variables. A first version of this theorem was proved by Friedrich Hartogs,See the original paper of and its description in various historical surveys by , and . In particular, in this last reference on p. 132, the Author explicitly writes :-"''As it is pointed out in the title of , and as the reader shall soon see, the key tool in the proof is the Cauchy integral formula''". and as such it is known also as Hartogs's lemma and Hartogs's principle: in ear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commentarii Mathematici Helvetici
The ''Commentarii Mathematici Helvetici'' is a quarterly peer-reviewed scientific journal in mathematics. The Swiss Mathematical Society (SMG) started the journal in 1929 after a meeting in May of the previous year. The Swiss Mathematical Society still owns and operates the journal; the publishing is currently handled on its behalf by the European Mathematical Society. The scope of the journal includes research articles in all aspects in mathematics. The editors-in-chief have been Rudolf Fueter (1929–1949), J.J. Burckhardt (1950–1981), P. Gabriel (1982–1989), H. Kraft (1990–2005), and Eva Bayer-Fluckiger (2006–present). Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2019 impact factor of 0.854. History The idea for a society-owned research journal emerged in June 1926, when the SMG petitioned the Swiss Confederation for a CHF 3,500 subsidy "to establish its own scientific jour ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atti Della Reale Accademia D'Italia , Italy, in the 13th-15th centuries
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Atti may refer to: *Atti, Jalandhar, a village in Punjab, India *Atti (film), a 2016 Tamil film *Atti Aboyni (1946), Hungarian-born Australian soccer player and manager *Isotta degli Atti (1433–1474), Italian noble and regent *Atti family, lords of Sassoferrato Sassoferrato is a town and ''comune'' of the province of Ancona in the Marche region of central-eastern Italy. It is one of I Borghi più belli d'Italia ("The most beautiful villages of Italy"). History Between Sassoferrato and Arcevia was t ... [...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 internationally, op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dordrecht
Dordrecht (), historically known in English as Dordt (still colloquially used in Dutch, ) or Dort, is a List of cities in the Netherlands by province, city and List of municipalities of the Netherlands, municipality in the Western Netherlands, located in the Provinces of the Netherlands, province of South Holland. It is the province's fifth-largest city after Rotterdam, The Hague, Leiden, and Zoetermeer, with a population of . The municipality covers the entire Dordrecht Island, also often called ''Het Eiland van Dordt'' ("the Island of Dordt"), bordered by the rivers Oude Maas, Beneden Merwede, Nieuwe Merwede, Hollands Diep, and Dordtsche Kil. Dordrecht is the largest and most important city in the Drechtsteden and is also part of the Randstad, the main conurbation in the Netherlands. Dordrecht is the oldest city in Holland and has a rich history and culture. Etymology The name Dordrecht comes from ''Thuredriht'' (circa 1120), ''Thuredrecht'' (circa 1200). The name seems to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Siberian Federal University
Siberian Federal University (, ''Sibirskiĭ federalʹnyĭ universitet'', often shortened to SibFU, СФУ) is a multidisciplinary university located in Krasnoyarsk in Siberia, that combines fundamental and applied research and teaching. The Siberian Federal University was ranked # 1,589 in the world in 2023 by ''US News & World Report''. The university was established in 2006 by merging four universities of Krasnoyarsk city that had been training professionals in the most competitive sectors of economy in Siberia and the Far East Russia: Krasnoyarsk State University, Krasnoyarsk State Technical University, Krasnoyarsk State Academy of Architecture and Construction and Krasnoyarsk State University of Non-Ferrous Metals and Gold. SibFU is a higher educational institution and consists of 19 institutes with more than 3,000 faculty staff teaching 41,000 students. The universities' fundamental and applied research is closely connected with Akademgorodok (Krasnoyarsk), Institutions o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birkhäuser Verlag
Birkhäuser was a Switzerland, Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint (trade name), imprint used by two companies in unrelated fields: * Springer continues to publish science (particularly: history of science, geosciences, computer science) and mathematics books and journals under the Birkhäuser imprint (with a leaf logo) sometimes called Birkhäuser Science. * Birkhäuser Verlag – an architecture and design publishing company was (re)created in 2010 when Springer sold its design and architecture segment to ACTAR. The resulting Spanish-Swiss company was then called ActarBirkhäuser. After a bankruptcy, in 2012 Birkhäuser Verlag was sold again, this time to De Gruyter. Additionally, the Reinach, Basel-Landschaft, Reinach-based Printer (publishing), printer Birkhäuser+GBC operates independently of the above, being now owned by ''Basler Zeitung''. History The original Swiss publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
