Hadamard Finite Part Integral

	Hadamard Finite Part Integral In mathematics, Hadamard regularization (also called Hadamard finite part or Hadamard's partie finie) is a method of regularizing divergent integrals by dropping some divergent terms and keeping the finite part, introduced by . showed that this can be interpreted as taking the meromorphic continuation of a convergent integral. If the Cauchy principal value integral \mathcal\int_a^b \frac \, dt \quad (\text a exists, then it may be differentiated with respect to to obtain the Hadamard finite part integral as follows: $\frac \left(\mathcal\int_^ \frac \,dt\right)=\mathcal\int_a^b \frac\, dt \quad (\text a Note that the symbols \mathcal and \mathcal are used here to denote Cauchy principal value and Hadamard finite-part integrals respectively. The Hadamard finite part integral above (for ) may also be given by the following equivalent definitions: \mathcal\int_a^b \frac\, dt = \lim_ \le ... [...More Info...] [...Related Items...]$ OR: [Wikipedia] [Google] [Baidu]
	Meromorphic Continuation In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where an infinite series representation in terms of which it is initially defined becomes divergent. The step-wise continuation technique may, however, come up against difficulties. These may have an essentially topological nature, leading to inconsistencies (defining more than one value). They may alternatively have to do with the presence of singularities. The case of several complex variables is rather different, since singularities then need not be isolated points, and its investigation was a major reason for the development of sheaf cohomology. Initial discussion Suppose ''f'' is an analytic function defined on a non-empty open subset ''U'' of the complex plane If ''V'' is a larger open subset of containing ''U'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Cauchy Principal Value In mathematics, the Cauchy principal value, named after Augustin Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined. Formulation Depending on the type of singularity in the integrand , the Cauchy principal value is defined according to the following rules: In some cases it is necessary to deal simultaneously with singularities both at a finite number and at infinity. This is usually done by a limit of the form \lim_\, \lim_ \,\left ,\int_^ f(x)\,\mathrmx \,~ + ~ \int_^ f(x)\,\mathrmx \,\right In those cases where the integral may be split into two independent, finite limits, \lim_ \, \left, \,\int_a^ f(x)\,\mathrmx \,\\; < \;\infty and $\lim_\;\left, \,\int_^c f(x)\,\mathrmx \,\ \; < \; \infty ,$ then the function is integrable in the ordinary sense. The result of the procedure for principal value is the same as the ordinary integral; since it no longer matches the definition, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Woodhead Publishing Woodhead Publishing Limited was established in 1989 as an independent international publishing company of science and technical books. The company publishes books in association with The Textile Institute, Cambridge International Science Publishing. They have previously published books in association with The Institute of Materials, Minerals and Mining (IOM3) and the European Federation of Corrosion. History In December 2008 Woodhead Publishing acquired the backlist, future titles and imprint of Chandos Publishing in Witney, Oxford, UK, comprising over 250 books in the fields of library and information management, knowledge management and Asian Studies. In 2011 they launched Woodhead Publishing Online, a resource of scientific, technical and information trends, comprising over 800 e-books, containing 12,000 chapters. This resource was hosted by MetaPress, a division of EBSCO Industries Inc. Woodhead (and its imprint Chandos) was acquired by Elsevier in August 2013. Its current ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Journal Of Mathematical Physics The ''Journal of Mathematical Physics'' is a peer-reviewed journal published monthly by the American Institute of Physics devoted to the publication of papers in mathematical physics. The journal was first published bimonthly beginning in January 1960; it became a monthly publication in 1963. The current editor is Jan Philip Solovej from University of Copenhagen The University of Copenhagen ( da, Københavns Universitet, KU) is a prestigious public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in .... Its 2018 Impact Factor is 1.355 Abstracting and indexing This journal is indexed by the following services:Wellesley College Library 2013. References External links [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Acta Scientiarum Mathematicarum ''Acta Scientiarum Mathematicarum'' is a Hungarian mathematical journal published by the János Bolyai Mathematical Institute (University of Szeged). It was established by Alfréd Haar and Frigyes Riesz in 1922. The current editor-in-chief is Lajos Molnár. The journal is abstracted and indexed in Scopus and 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 Infrastructur .... References External links * * {{ISSN, 0001-6969 Mathematics journals Publications established in 1922 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Szeged Szeged ( , ; see also #Etymology, other alternative names) is List of cities and towns of Hungary#Largest cities in Hungary, the third largest city of Hungary, the largest city and regional centre of the Southern Great Plain and the county seat of Csongrád-Csanád County, Csongrád-Csanád county. The University of Szeged is one of the most distinguished universities in Hungary. The Szeged Open Air (Theatre) Festival (first held in 1931) is one of the main attractions, held every summer and celebrated as the Day of the City on 21 May. Etymology The name ''Szeged'' might come from an old Hungarian language, Hungarian word for 'corner' (), pointing to the turn of the river Tisza that flows through the city. Others say it derives from the Hungarian word which means 'island'. Others still contend that means 'dark blond' () – a reference to the color of the water where the rivers Tisza and Mureș (river), Maros merge. The city has its own name in a number of foreign language ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Acta Mathematica ''Acta Mathematica'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics. According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research journals".. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 4.273, ranking it 5th out of 330 journals in the category "Mathematics". Publication history The journal was established by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences. The journal was printed and distributed by Springer from 2006 to 2016. Since 2017, Acta Mathematica has been published electronically and in print by International Press. Its electronic version is open access without publishing fees. Poincaré episode The journal's "most famous episode" (according to Villani) concerns Henri Poincaré, who won a prize offered ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Integrals In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]

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