|
Asymptotology
Asymptotology has been defined as “the art of dealing with applied mathematical systems in limiting cases” as well as “the science about the synthesis of simplicity and exactness by means of localization". Principles The field of asymptotics is normally first encountered in school geometry with the introduction of the asymptote, a line to which a curve tends at infinity. The word Ασύμπτωτος (asymptotos) in Greek means non-coincident and puts strong emphasis on the point that approximation does not turn into coincidence. It is a salient feature of asymptotics, but this property alone does not entirely cover the idea of asymptotics and, etymologically, the term seems to be quite insufficient. Perturbation theory, small and large parameters In physics and other fields of science, one frequently comes across problems of an asymptotic nature, such as damping, orbiting, stabilization of a perturbed motion, etc. Their solutions lend themselves to asymptotic analy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Kruskal
Martin David Kruskal (; September 28, 1925 – December 26, 2006) was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and from nonlinear analysis to asymptotic analysis. His most celebrated contribution was in the theory of solitons. He was a student at the University of Chicago and at New York University, where he completed his Ph.D. under Richard Courant in 1952. He spent much of his career at Princeton University, as a research scientist at the Plasma Physics Laboratory starting in 1951, and then as a professor of astronomy (1961), founder and chair of the Program in Applied and Computational Mathematics (1968), and professor of mathematics (1979). He retired from Princeton University in 1989 and joined the mathematics department of Rutgers University, holding the David Hilbert Chair of Mathematics. Apart from serious mathematical work, Kruskal was kno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonid Manevitch
Leonid Isakovich Manevitch (Russian: Леонид Исакович Маневич; 2 April 1938 – 20 August 2020) was a Soviet and Russian physicist, mechanical engineer, and mathematician. He made fundamental contributions to areas of nonlinear dynamics, composite and polymer physics, and asymptotology. Biography Manevitch was born on 2 April 1938 in Mogilev (USSR, now Belarus). He received his M.S. with great distinction in mechanics (1959) and his Candidate of Sciences (PhD, 1961) and Doctor of Sciences (1970) from Dnipro National University. From 1959 to 1964, Manevitch worked on missile design as an aerospace engineer and head of the Stress Analysis Team under Mikhail Yangel at the Yuzhnoye Design Office. In 1964, he became an Associate Professor at Dnipro National University. His doctoral thesis was devoted to asymptotic and group-theory methods in the mechanics of deformable solids. He was promoted in 1973 to Full Professor in the Department of Applied Theory of Ela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Analysis
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as becomes very large, the term becomes insignificant compared to . The function is said to be "''asymptotically equivalent'' to , as ". This is often written symbolically as , which is read as " is asymptotic to ". An example of an important asymptotic result is the prime number theorem. Let denote the prime-counting function (which is not directly related to the constant pi), i.e. is the number of prime numbers that are less than or equal to . Then the theorem states that \pi(x)\sim\frac. Asymptotic analysis is commonly used in computer science as part of the analysis of algorithms and is often expressed there in terms of big O notation. Definition Formally, given functions and , we define a binary relation f(x) \sim g(x) \qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotics
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as becomes very large, the term becomes insignificant compared to . The function is said to be "''asymptotically equivalent'' to , as ". This is often written symbolically as , which is read as " is asymptotic to ". An example of an important asymptotic result is the prime number theorem. Let denote the prime-counting function (which is not directly related to the constant pi), i.e. is the number of prime numbers that are less than or equal to . Then the theorem states that \pi(x)\sim\frac. Asymptotic analysis is commonly used in computer science as part of the analysis of algorithms and is often expressed there in terms of big O notation. Definition Formally, given functions and , we define a binary relation f(x) \sim g(x) \quad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limiting Case (mathematics)
In mathematics, a limiting case of a mathematical object is a special case that arises when one or more components of the object take on their most extreme possible values. For example: * In statistics, the limiting case of the binomial distribution is the Poisson distribution. As the number of events tends to infinity in the binomial distribution, the random variable changes from the binomial to the Poisson distribution. *A circle is a limiting case of various other figures, including the Cartesian oval, the ellipse, the superellipse, and the Cassini oval. Each type of figure is a circle for certain values of the defining parameters, and the generic figure appears more like a circle as the limiting values are approached. *Archimedes calculated an approximate value of π by treating the circle as the limiting case of a regular polygon with 3 × 2''n'' sides, as ''n'' gets large. *In electricity and magnetism, the long wavelength limit is the limiting case when the wavelength is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Expansion
In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point. Investigations by revealed that the divergent part of an asymptotic expansion is latently meaningful, i.e. contains information about the exact value of the expanded function. The most common type of asymptotic expansion is a power series in either positive or negative powers. Methods of generating such expansions include the Euler–Maclaurin summation formula and integral transforms such as the Laplace and Mellin transforms. Repeated integration by parts will often lead to an asymptotic expansion. Since a '' convergent'' Taylor series fits the definition of asymptotic expansion as well, the phrase "asymptotic series" usually implies a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imperial College Press
Imperial College Press (ICP) was formed in 1995 as a partnership between Imperial College of Science, Technology and Medicine in London and World Scientific publishing. This publishing house was awarded the rights, by The Nobel Foundation, Sweden, to publish ''The Nobel Prize: The First 100 years'', edited by Agneta Wallin Levinovitz and Nils Ringertz. They publish areas of teaching and research at Imperial College: Chemistry, Computer Science, Economics, Finance & Management Management (or managing) is the administration of an organization, whether it is a business, a nonprofit organization, or a government body. It is the art and science of managing resources of the business. Management includes the activities o ..., Engineering, Environmental Science, Life Sciences, Mathematics, Medicine & Healthcare, and Physics. As of August 2016, ICP has been fully incorporated into World Scientific under the new imprint, ''World Scientific Europe''. Selected journals * ''Jour ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of The American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. It also publishes, by invitation only, book reviews and short ''Mathematical Perspectives'' articles. History It began as the ''Bulletin of the New York Mathematical Society'' and underwent a name change when the society became national. The Bulletin's function has changed over the years; its original function was to serve as a research journal for its members. Indexing The Bulletin is indexed in Mathematical Reviews, Science Citation Index, ISI Alerting Services, CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. See also *'' Journal of the American Mathematical Society'' *''Memoirs of the American Mathematical Society'' *''Notices of the American Mathematical Society'' *'' Proceedings of the American M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ANZIAM Journal
The Australian Mathematical Society (AustMS) was founded in 1956 and is the national society of the mathematics profession in Australia. One of the Society's listed purposes is to promote the cause of mathematics in the community by representing the interests of the profession to government. The Society also publishes three mathematical journals. In December 2020, Ole Warnaar moved from President-Elect to President, succeeding Jacqui Ramagge, who was elected in 2018. Society awards * The Australian Mathematical Society Medal * The George Szekeres Medal * The Gavin Brown Prize * The Mahler Lectureship * The B.H. Neumann Prize Society journals The society publishes three journals through Cambridge University Press: * ''Journal of the Australian Mathematical Society'' * ''ANZIAM Journal'' (formerly ''Series B, Applied Mathematics'') * ''Bulletin of the Australian Mathematical Society'' ANZIAM ANZIAM (Australia and New Zealand Industrial and Applied Mathematics) is a division of The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kluwer Academic Publishers
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, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Crighton
David George Crighton, FRS (15 November 1942 – 12 April 2000) was a British mathematician and physicist. Life Crighton was born in Llandudno, North Wales, where his mother, Violet Grace Garrison, had been sent because of the bombing of London during the Second World War. He did not become interested in mathematics until his last two years at Watford Grammar School for Boys. He entered St John's College, Cambridge, in 1961 and started lecturing at Woolwich Polytechnic (today University of Greenwich) in 1964, having completed only his bachelor's degree. A few years later he met John Ffowcs Williams and started to work for him at Imperial College London, while simultaneously studying for his doctorate (awarded in 1969) at the same place. In 1974, he was appointed as a research fellow in the Department of Engineering at the University of Cambridge. However, he never took up this post, but instead accepted the chair in applied mathematics at the University of Leeds, which he held ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
