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Henstock
Ralph Henstock (2 June 1923 – 17 January 2007) was an English mathematician and author. As an Integration theorist, he is notable for Henstock–Kurzweil integral. Henstock brought the theory to a highly developed stage without ever having encountered Jaroslav Kurzweil's 1957 paper on the subject. Early life He was born in the coal-mining village of Newstead, Nottinghamshire, the only child of mineworker and former coalminer William Henstock and Mary Ellen Henstock (née Bancroft). On the Henstock side he was descended from 17th century Flemish immigrants called Hemstok. Because of his early academic promise it was expected that Henstock would attend the University of Nottingham where his father and uncle had received technical education, but as it turned out he won scholarships which enabled him to study mathematics at St John's College, Cambridge from October 1941 until November 1943, when he was sent for war service to the Ministry of Supply's department of Statistical M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henstock–Kurzweil Integral
In mathematics, the Henstock–Kurzweil integral or generalized Riemann integral or gauge integral – also known as the (narrow) Denjoy integral (pronounced ), Luzin integral or Perron integral, but not to be confused with the more general wide Denjoy integral – is one of a number of inequivalent definitions of the integral of a function. It is a generalization of the Riemann integral, and in some situations is more general than the Lebesgue integral. In particular, a function is Lebesgue integrable if and only if the function and its absolute value are Henstock–Kurzweil integrable. This integral was first defined by Arnaud Denjoy (1912). Denjoy was interested in a definition that would allow one to integrate functions like :f(x)=\frac\sin\left(\frac\right). This function has a singularity at 0, and is not Lebesgue integrable. However, it seems natural to calculate its integral except over the interval and then let . Trying to create a general theory, Denjoy used trans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jaroslav Kurzweil
Jaroslav Kurzweil (, 7 May 1926, Prague – 17 March 2022) was a Czech mathematician. Biography Born in Prague, Czechoslovakia, he was a specialist in ordinary differential equations and defined the Henstock–Kurzweil integral in terms of Riemann sums, first published in 1957 in the Czechoslovak Mathematical Journal. Kurzweil has been awarded the highest possible scientific prize of Czechia, the "Czech Brain" of the year 2006, as an acknowledgement of his life achievements. With limited opportunities of contact between mathematicians within the Iron Curtain and those from the West, Kurzweil and Ivo Babuška founded a series of international scientific conferences named EQUADIFF, being held every four years since 1962 alternately in Prague, Bratislava, and Brno. He was chief editor of Mathematica Bohemica (then called ''Časopis pro pěstovánà matematiky'') from 1956 to 1970 and was in its editorial board until 2007. In 2007, Kurzweil delivered a New Year's toast on Czech Televi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., an integral assigns numbers to functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with Derivative, 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 int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Dienes
Paul Dienes ( Hungarian: ''Dienes Pál''. November 24, 1882 Tokaj, Austria-Hungary – March 23, 1952) was a Hungarian mathematician, philosopher, linguist and poet. Born in to a wealthy and aristocratic Protestant family, he married Valéria Geiger (1879–1978) in December 1905. They had two sons, Gedeon Dienes (1914) and Zoltan Paul Dienes (1916). Following their divorce, he married Sari Dienes in 1922. He was an active member of the Galileo Circle. Dienes joined the Hungarian Communist Party during the establishment of the Hungarian Soviet Republic and in 1919 was appointed the political commissar of the University of Budapest. After the fall of the Soviet Republic he fled to Vienna and was later invited to the United Kingdom. From 1921 to 1923 he lectured at University College, Swansea, where his students included Evan Tom Davies. From 1923 to 1948 he was Professor of Mathematics at Birkbeck College, London, where his students included Ralph Henstock and Abraham Rob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New University Of Ulster
sco, Ulstèr Universitie , image = Ulster University coat of arms.png , caption = , motto_lang = , mottoeng = , latin_name = Universitas Ulidiae , established = 1865 – Magee College 1953 - Magee University 1982 – University of Ulster (remains official name) 2014 – Ulster University , type = Public research university , endowment = £14.365 million (2018) , budget = £185 million , chancellor = Colin Davidson , vice_chancellor = Paul Bartholomew , faculty = 1,665 , students = () , undergrad = () , postgrad = () , city = Belfast, Coleraine, Jordanstown, Derry, London, Birmingham , affiliations = * European University Association * Association of Commonwealth Universities * Universities UK * Universities Ireland , coordinates = , campus = Varied (urban/ rural) , colours = ''Logo'': Navy blue & bronze ''Seal' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Integral
In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. It was presented to the faculty at the University of Göttingen in 1854, but not published in a journal until 1868. For many functions and practical applications, the Riemann integral can be evaluated by the fundamental theorem of calculus or approximated by numerical integration. Overview Let be a non-negative real-valued function on the interval , and let be the region of the plane under the graph of the function and above the interval . See the figure on the top right. This region can be expressed in set-builder notation as S = \left \. We are interested in measuring the area of . Once we have measured it, we will denote the area in the usual way by \int_a^b f(x)\,dx. The basic idea of the Riemann integral is to use very simple approximations for the area of . By taking better and be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lebesgue Integral
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the -axis. The Lebesgue integral, named after French mathematician Henri Lebesgue, extends the integral to a larger class of functions. It also extends the domains on which these functions can be defined. Long before the 20th century, mathematicians already understood that for non-negative functions with a smooth enough graph—such as continuous functions on closed bounded intervals—the ''area under the curve'' could be defined as the integral, and computed using approximation techniques on the region by polygons. However, as the need to consider more irregular functions arose—e.g., as a result of the limiting processes of mathematical analysis and the mathematical theory of probability—it became clear that more careful approximation techniques were needed to define a suitable integral. Also, one might ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ministry Of Supply
The Ministry of Supply (MoS) was a department of the UK government formed in 1939 to co-ordinate the supply of equipment to all three British armed forces, headed by the Minister of Supply. A separate ministry, however, was responsible for aircraft production, and the Admiralty retained responsibilities for supplying the Royal Navy.Hornby (1958) During the war years the MoS was based at Shell Mex House in The Strand, London. The Ministry of Supply also took over all army research establishments in 1939. The Ministry of Aircraft Production was abolished in 1946, and the MoS took over its responsibilities for aircraft, including the associated research establishments. In the same year, it also took on increased responsibilities for atomic weapons, including the H-bomb development programme. The Ministry of Supply was abolished in late 1959 and its responsibilities passed to the Ministry of Aviation, the War Office, and the Air Ministry. The latter two ministries were subsequently ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathSciNet
MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal ''Mathematical Reviews'' (MR) since 1940 along with an extensive author database, links to other MR entries, citations, full journal entries, and links to original articles. It contains almost 3.6 million items and over 2.3 million links to original articles. Along with its parent publication ''Mathematical Reviews'', MathSciNet has become an essential tool for researchers in the mathematical sciences. Access to the database is by subscription only and is not generally available to individual researchers who are not affiliated with a larger subscribing institution. For the first 40 years of its existence, traditional typesetting was used to produce the Mathematical Reviews journal. Starting in 1980 bibliographic information and the reviews themselves were produced in both print and electronic form. This formed the basis of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical Society and the Operational Research Society (ORS). History The Society was established on 16 January 1865, the first president being Augustus De Morgan. The earliest meetings were held in University College, but the Society soon moved into Burlington House, Piccadilly. The initial activities of the Society included talks and publication of a journal. The LMS was used as a model for the establishment of the American Mathematical Society in 1888. Mary Cartwright was the first woman to be President of the LMS (in 1961–62). The Society was granted a royal charter in 1965, a century after its foundation. In 1998 the Society moved from rooms in Burlington House into De Morgan House (named after the society's first president), at 57–5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bounded Sequences
In mathematics, a function ''f'' defined on some set ''X'' with real or complex values is called bounded if the set of its values is bounded. In other words, there exists a real number ''M'' such that :, f(x), \le M for all ''x'' in ''X''. A function that is ''not'' bounded is said to be unbounded. If ''f'' is real-valued and ''f''(''x'') ≤ ''A'' for all ''x'' in ''X'', then the function is said to be bounded (from) above by ''A''. If ''f''(''x'') ≥ ''B'' for all ''x'' in ''X'', then the function is said to be bounded (from) below by ''B''. A real-valued function is bounded if and only if it is bounded from above and below. An important special case is a bounded sequence, where ''X'' is taken to be the set N of natural numbers. Thus a sequence ''f'' = (''a''0, ''a''1, ''a''2, ...) is bounded if there exists a real number ''M'' such that :, a_n, \le M for every natural number ''n''. The set of all bounded sequences forms the sequence space l^\infty. The definition of bound ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
