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Singular Integrals
In mathematics, singular integrals are central to harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular integral is an integral operator : T(f)(x) = \int K(x,y)f(y) \, dy, whose kernel function ''K'' : R''n''×R''n'' → R is singular along the diagonal ''x'' = ''y''. Specifically, the singularity is such that , ''K''(''x'', ''y''), is of size , ''x'' − ''y'', −''n'' asymptotically as , ''x'' − ''y'', → 0. Since such integrals may not in general be absolutely integrable, a rigorous definition must define them as the limit of the integral over , ''y'' − ''x'', > ε as ε → 0, but in practice this is a technicality. Usually further assumptions are required to obtain results such as their boundedness on ''L''''p''(R''n''). The Hilbert transform The archetypal singular integral operator is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
American Journal Of Mathematics
The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press. History The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United States, established in 1878 at the Johns Hopkins University by James Joseph Sylvester, an English-born mathematician who also served as the journal's editor-in-chief from its inception through early 1884. Initially W. E. Story was associate editor in charge; he was replaced by Thomas Craig (mathematician), Thomas Craig in 1880. For volume 7 Simon Newcomb became chief editor with Craig managing until 1894. Then with volume 16 it was "Edited by Thomas Craig with the Co-operation of Simon Newcomb" until 1898. Other notable mathematicians who have served as editors or editorial associates of the journal include Frank Morley, Oscar Zariski, Lars Ahlfors, Hermann Weyl, Wei-Liang Chow, S. S. Chern, André Weil, Harish-Chandra, Jean Dieudonné, Hen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton, New Jersey
The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Princeton Township, New Jersey, Princeton Township, both of which are now defunct. As of the 2020 United States census, the borough's population was 30,681, an increase of 2,109 (+7.4%) from the 2010 United States census, 2010 census combined count of 28,572. In the 2000 United States census, 2000 census, the two communities had a total population of 30,230, with 14,203 residents in the borough and 16,027 in the township. Princeton was founded before the American Revolutionary War. The borough is the home of Princeton University, one of the world's most acclaimed research universities, which bears its name and moved to the community in 1756 from the educational institution's previous location in Newark, New Jersey, Newark. Although its associ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, '' The Daily Princetonian'', and later added book publishing ... [...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] |
Heidelberg
Heidelberg (; ; ) is the List of cities in Baden-Württemberg by population, fifth-largest city in the States of Germany, German state of Baden-Württemberg, and with a population of about 163,000, of which roughly a quarter consists of students, it is List of cities in Germany by population, Germany's 51st-largest city. Located about south of Frankfurt, Heidelberg is part of the densely populated Rhine-Neckar, Rhine-Neckar Metropolitan Region which has its centre in Mannheim. Heidelberg is located on the Neckar River, at the point where it leaves its narrow valley between the Oden Forest and the Kleiner Odenwald, Little Oden Forest, and enters the wide Upper Rhine Plain. The old town lies in the valley, the end of which is flanked by the Königstuhl (Odenwald), Königstuhl in the south and the Heiligenberg (Heidelberg), Heiligenberg in the north. The majority of the population lives in the districts west of the mountains in the Upper Rhine Plain, into which the city has expan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population within city limits, highest population within its city limits of any city in the European Union. The city is also one of the states of Germany, being the List of German states by area, third smallest state in the country by area. Berlin is surrounded by the state of Brandenburg, and Brandenburg's capital Potsdam is nearby. The urban area of Berlin has a population of over 4.6 million and is therefore the most populous urban area in Germany. The Berlin/Brandenburg Metropolitan Region, Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's second-largest metropolitan region after the Rhine-Ruhr region, as well as the List of EU metropolitan areas by GDP, fifth-biggest metropolitan region by GDP in the European Union. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pergamon Press
Pergamon Press was an Oxford-based publishing house, founded by Paul Rosbaud and Robert Maxwell, that published scientific and medical books and journals. Originally called Butterworth-Springer, it is now an imprint of Elsevier. History The core company, Butterworth-Springer, started in 1948 to bring the "Springer know-how and techniques of aggressive publishing in science"Joe Haines (1988) ''Maxwell'', Houghton Mifflin, p. 137. to Britain. Paul Rosbaud was the man with the knowledge. When Maxwell acquired the company in 1951, Rosbaud held a one-quarter share. They changed the house name to Pergamon Press, using a logo that was a reproduction of a Greek coin from Pergamon. Maxwell and Rosbaud worked together growing the company until May 1956, when, according to Joe Haines, Rosbaud was sacked. When Pergamon Press started it had only six serials and two books. Initially the company headquarters was in Fitzroy Square in West End of London. In 1959, the company moved into He ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frankfurt
Frankfurt am Main () is the most populous city in the States of Germany, German state of Hesse. Its 773,068 inhabitants as of 2022 make it the List of cities in Germany by population, fifth-most populous city in Germany. Located in the foreland of the Taunus on its namesake Main (river), Main, it forms a continuous conurbation with Offenbach am Main; Frankfurt Rhein-Main Regional Authority, its urban area has a population of over 2.7 million. The city is the heart of the larger Rhine-Main metropolitan region, which has a population of more than 5.8 million and is Germany's Metropolitan regions in Germany, second-largest metropolitan region after the Rhine-Ruhr metropolitan region, Rhine-Ruhr region and the List of EU metropolitan regions by GDP#2021 ranking of top four German metropolitan regions, fourth largest metropolitan region by GDP in the European Union (EU). Frankfurt is one of the ''de facto'' four main capitals of the European Union (alongside Brussels, Luxembourg Cit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of cities in the European Union by population within city limits, fourth-most populous city in the European Union and the List of cities proper by population density, 30th most densely populated city in the world in 2022. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, culture, Fashion capital, fashion, and gastronomy. Because of its leading role in the French art, arts and Science and technology in France, sciences and its early adoption of extensive street lighting, Paris became known as the City of Light in the 19th century. The City of Paris is the centre of the Île-de-France region, or Paris Region, with an official estimated population of 12,271,794 inhabitants in January 2023, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York City
New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive with a respective county. The city is the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area, the largest metropolitan area in the United States by both population and urban area. New York is a global center of finance and commerce, culture, technology, entertainment and media, academics, and scientific output, the arts and fashion, and, as home to the headquarters of the United Nations, international diplomacy. With an estimated population in 2024 of 8,478,072 distributed over , the city is the most densely populated major city in the United States. New York City has more than double the population of Los Angeles, the nation's second-most populous city. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edinburgh
Edinburgh is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. The city is located in southeast Scotland and is bounded to the north by the Firth of Forth and to the south by the Pentland Hills. Edinburgh had a population of in , making it the List of towns and cities in Scotland by population, second-most populous city in Scotland and the List of cities in the United Kingdom, seventh-most populous in the United Kingdom. The Functional urban area, wider metropolitan area had a population of 912,490 in the same year. Recognised as the capital of Scotland since at least the 15th century, Edinburgh is the seat of the Scottish Government, the Scottish Parliament, the Courts of Scotland, highest courts in Scotland, and the Palace of Holyroodhouse, the official residence of the Monarchy of the United Kingdom, British monarch in Scotland. It is also the annual venue of the General Assembly of the Church of Scotland. The city has long been a cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
