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Laplace Transforms
In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t, in the ''time domain'') to a function of a complex variable s (in the complex frequency domain, also known as ''s''-domain, or s-plane). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms ordinary differential equations into algebraic equations and convolution into multiplication. For suitable functions ''f'', the Laplace transform is the integral \mathcal\(s) = \int_0^\infty f(t)e^ \, dt. History The Laplace transform is named after mathematician and astronomer Pierre-Simon, marquis de Laplace, who used a similar transform in his work on probability theory. Laplace wrote extensively about the use of generating functions in ''Essai philosophique sur les probabilités'' (1814), and the integral form of the Lapla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great powers—forming two opposing military alliances: the Allies of World War II, Allies and the Axis powers. World War II was a total war that directly involved more than 100 million Military personnel, personnel from more than 30 countries. The major participants in the war threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. Air warfare of World War II, Aircraft played a major role in the conflict, enabling the strategic bombing of population centres and deploying the Atomic bombings of Hiroshima and Nagasaki, only two nuclear weapons ever used in war. World War II was by far the List of wars by death toll, deadliest conflict in hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Proceedings Of The 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Thomas John I'Anson Bromwich
Thomas John I'Anson Bromwich (8 February 1875 – 24 August 1929) was an English mathematician, and a Fellow of the Royal Society. Life Thomas John I'Anson Bromwich was born on 8 February 1875, in Wolverhampton, England. He was descended from Bryan I'Anson, of Ashby St Ledgers, Sheriff of London and father of the 17th century 1st Baronet Sir Bryan I'Anson of Bassetsbury. His parents emigrated to South Africa, where in 1892 he graduated from high school. He attended St John's College, Cambridge, where in 1895 he became Senior Wrangler. In 1897, he became a lecturer at St. John’s. From 1902 to 1907, he was a professor of mathematics at Queen’s College, Galway. In 1906, he was elected a Fellow of the Royal Society. In 1907, he returned to Cambridge and again became a Fellow and lecturer at St. John’s. He was a vice president of the Royal Society in 1919 and 1920. He died in Northampton on 24 August 1929, a suicide. Work Bromwich worked in both algebra and analysis. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Oliver Heaviside
Oliver Heaviside FRS (; 18 May 1850 – 3 February 1925) was an English self-taught mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vector calculus, and rewrote Maxwell's equations in the form commonly used today. He significantly shaped the way Maxwell's equations are understood and applied in the decades following Maxwell's death. His formulation of the telegrapher's equations became commercially important during his own lifetime, after their significance went unremarked for a long while, as few others were versed at the time in his novel methodology. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science. Biography Early life Heaviside was born in Camden Town, London, at 55 Kings Street (now Plender Street), the youngest of three children of Thomas, a draughtsman and wood ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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] |
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Mathias Lerch
Mathias Lerch (''Matyáš Lerch'', ) (20 February 1860, Milínov – 3 August 1922, Sušice) was a Czech mathematician who published about 250 papers, largely on mathematical analysis and number theory. He studied in Prague and Berlin, and held teaching positions at the Czech Technical Institute in Prague, the University of Fribourg in Switzerland, the Czech Technical Institute in Brno, and Masaryk University in Brno; he was the first mathematics professor at Masaryk University when it was founded in 1920. In 1900, he was awarded the Grand Prize of the French Academy of Sciences for his number-theoretic work. The Lerch zeta function is named after him, as is the Appell–Lerch sum. His doctoral students include Michel Plancherel Michel Plancherel (16 January 1885, Bussy, Fribourg4 March 1967, Zurich) was a Swiss mathematician. He was born in Bussy (Fribourg, Switzerland) and obtained his Diplom in mathematics from the University of Fribourg and then his doctoral degree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Niels Henrik Abel
Niels Henrik Abel ( , ; 5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for over 250 years. He was also an innovator in the field of elliptic functions, discoverer of Abelian functions. He made his discoveries while living in poverty and died at the age of 26 from tuberculosis. Most of his work was done in six or seven years of his working life. Regarding Abel, the French mathematician Charles Hermite said: "Abel has left mathematicians enough to keep them busy for five hundred years." Another French mathematician, Adrien-Marie Legendre, said: "What a head the young Norwegian has!" The Abel Prize in mathematics, originally proposed in 1899 to complement the Nobel Prizes (but f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Continuous Variable
In mathematics and statistics, a quantitative variable may be continuous or discrete if they are typically obtained by ''measuring'' or ''counting'', respectively. If it can take on two particular real values such that it can also take on all real values between them (even values that are arbitrarily close together), the variable is continuous in that interval. If it can take on a value such that there is a non- infinitesimal gap on each side of it containing no values that the variable can take on, then it is discrete around that value. In some contexts a variable can be discrete in some ranges of the number line and continuous in others. Continuous variable A continuous variable is a variable whose value is obtained by measuring, i.e., one which can take on an uncountable set of values. For example, a variable over a non-empty range of the real numbers is continuous, if it can take on any value in that range. The reason is that any range of real numbers between a and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Z-transform
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain (z-domain or z-plane) representation. It can be considered as a discrete-time equivalent of the Laplace transform (s-domain). This similarity is explored in the theory of time-scale calculus. Whereas the continuous-time Fourier transform is evaluated on the Laplace s-domain's imaginary line, the discrete-time Fourier transform is evaluated over the unit circle of the z-domain. What is roughly the s-domain's left half-plane, is now the inside of the complex unit circle; what is the z-domain's outside of the unit circle, roughly corresponds to the right half-plane of the s-domain. One of the means of designing digital filters is to take analog designs, subject them to a bilinear transform which maps them from the s-domain to the z-domain, and then produce the digital filter by inspection, manipulation, or nume ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Generating Function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers () by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary series, the ''formal'' power series is not required to converge: in fact, the generating function is not actually regarded as a function, and the "variable" remains an indeterminate. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem. One can generalize to formal power series in more than one indeterminate, to encode information about infinite multi-dimensional arrays of numbers. There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series; definitions and examples are given below. Every sequence in principle has a generating function of each type (exc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |