|
G. H. Hardy
Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of population genetics. G. H. Hardy is usually known by those outside the field of mathematics for his 1940 essay ''A Mathematician's Apology'', often considered one of the best insights into the mind of a working mathematician written for the layperson. Starting in 1914, Hardy was the mentor of the Indian mathematician Srinivasa Ramanujan, a relationship that has become celebrated.THE MAN WHO KNEW INFINITY: A Life of the Genius Ramanujan . Retrieved 2 December 2010. Hardy almost immediately reco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cranleigh
Cranleigh is a village and civil parishes in England, civil parish in the Borough of Waverley, Surrey, England. It lies southeast of Guildford on a minor road east of the A281, which links Guildford with Horsham. It is in the north-west corner of the Weald, a large remnant forest, the main local remnant being Winterfold Forest directly north-west on the northern Greensand Ridge. In 2011 it had a population of just over 11,000. Etymology Until the mid-1860s, the place was usually spelt Cranley. The Post Office persuaded the vestry to use "''-leigh''" to avoid misdirections to nearby Crawley in West Sussex. The older spelling is publicly visible in the ''Cranley Hotel''. The name is recorded in the ''Pipe Rolls'' as ''Cranlea'' in 1166 and ''Cranelega'' in 1167. A little later in the ''Feet of Fines'' of 1198 the name is written as ''Cranele''. Etymologists consider all these versions to be the fusion of the Old English words "Cran", meaning "Crane (bird), crane", and "Lēoh" that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sydney Chapman (mathematician)
Sydney Chapman (29 January 1888 – 16 June 1970) was a British mathematician and Geophysics, geophysicist. His work on the kinetic theory of gases, solar-terrestrial physics, and the Earth's ozone layer has inspired a broad range of research over many decades. Education and early life Chapman was born in Eccles, Greater Manchester, Eccles, near Salford, Greater Manchester, Salford in England and began his advanced studies at a technical institute, now the University of Salford, in 1902. In 1904 at age 16, Chapman entered the Victoria University of Manchester, University of Manchester. He competed for a scholarship to the university offered by his home county, and was the last student selected. Chapman later reflected, "I sometimes wonder what would have happened if I'd hit one place lower." He initially studied engineering in the department headed by Osborne Reynolds. Chapman was taught mathematics by Horace Lamb, the Beyer professor of mathematics, and John Edensor Littl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardy Field
In mathematics, a Hardy field is a field consisting of germs of real-valued functions at infinity that are closed under differentiation. They are named after the English mathematician G. H. Hardy. Definition Initially at least, Hardy fields were defined in terms of germs of real functions at infinity. Specifically we consider a collection ''H'' of functions that are defined for all large real numbers, that is functions ''f'' that map (''u'',∞) to the real numbers R, for some real number ''u'' depending on ''f''. Here and in the rest of the article we say a function has a property " eventually" if it has the property for all sufficiently large ''x'', so for example we say a function ''f'' in ''H'' is ''eventually zero'' if there is some real number ''U'' such that ''f''(''x'') = 0 for all ''x'' ≥ ''U''. We can form an equivalence relation on ''H'' by saying ''f'' is equivalent to ''g'' if and only if ''f'' − ''g'' is eventually zero. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardy's Theorem
In mathematics, Hardy's theorem is a result in complex analysis describing the behavior of holomorphic functions. Let f be a holomorphic function on the open ball centered at zero and radius R in the complex plane, and assume that f is not a constant function. If one defines :I(r) = \frac \int_0^\! \left, f(r e^) \ \,d\theta for 0< r < R, then this function is strictly increasing and is a convex function of . See also * *Hadamard three-circle theorem In complex analysis, a branch of mathematics, the
Hadamar ...
[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardy's Inequality
Hardy's inequality is an inequality in mathematics, named after G. H. Hardy. Its discrete version states that if a_1, a_2, a_3, \dots is a sequence of non-negative real numbers, then for every real number ''p'' > 1 one has :\sum_^\infty \left (\frac\right )^p\leq\left (\frac\right )^p\sum_^\infty a_n^p. If the right-hand side is finite, equality holds if and only if a_n = 0 for all ''n''. An integral version of Hardy's inequality states the following: if ''f'' is a measurable function with non-negative values, then :\int_0^\infty \left (\frac\int_0^x f(t)\, dt\right)^p\, dx\le\left (\frac\right )^p\int_0^\infty f(x)^p\, dx. If the right-hand side is finite, equality holds if and only if ''f''(''x'') = 0 almost everywhere. Hardy's inequality was first published and proved (at least the discrete version with a worse constant) in 1920 in a note by Hardy. The original formulation was in an integral form slightly different from the above. Statements General discrete Hardy i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardy–Littlewood Inequality
In mathematical analysis, the Hardy–Littlewood inequality, named after G. H. Hardy and John Edensor Littlewood, states that if f and g are nonnegative measurable real functions vanishing at infinity that are defined on n-dimensional Euclidean space \mathbb R^n, then :\int_ f(x)g(x) \, dx \leq \int_ f^*(x)g^*(x) \, dx where f^* and g^* are the symmetric decreasing rearrangement In mathematics, the symmetric decreasing rearrangement of a function is a function which is symmetric and decreasing, and whose level sets are of the same size as those of the original function. Definition for sets Given a measurable set, A, in \R ...s of f and g, respectively. The decreasing rearrangement f^* of f is defined via the property that for all r >0 the two super-level sets :E_f(r)=\left\ \quad and \quad E_(r)=\left\ have the same volume (n-dimensional Lebesgue measure) and E_(r) is a ball in \mathbb R^n centered at x=0, i.e. it has maximal symmetry. Proof The layer cake represe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardy Notation
Hardy may refer to: People * Hardy (surname) * Hardy (given name) * Hardy (singer), American singer-songwriter Places Antarctica * Mount Hardy, Enderby Land * Hardy Cove, Greenwich Island * Hardy Rocks, Biscoe Islands Australia * Hardy, South Australia, a locality * Cape Hardy, a headland in South Australia * Hardy Inlet, Western Australia Canada * Hardy Township, Ontario, Canada, administered by the Loring, Port Loring and District, Ontario, services board * Port Hardy, British Columbia * Hardy, Saskatchewan, Canada, a hamlet United States * Hardy, Arkansas, a city * Hardy, California, an unincorporated community * Hardy, Iowa, a city * Hardy, Kentucky, an unincorporated community * Hardy, Mississippi, an unincorporated community * Hardy, Montana, an unincorporated community * Hardy, Nebraska, a village * Hardy, Virginia, an unincorporated community * Hardy County, West Virginia * Hardy Dam, Michigan * Hardy Lake, Indiana, a state reservoir * Hardy Pond, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardy Space
In complex analysis, the Hardy spaces (or Hardy classes) H^p are spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper . In real analysis Hardy spaces are spaces of distributions on the real -space \mathbb^n, defined (in the sense of distributions) as boundary values of the holomorphic functions. Hardy spaces are related to the ''Lp'' spaces. For 1 \leq p < \infty these Hardy spaces are s of spaces, while for |
Critical Line Theorem
In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by , after whom it is named. The Riemann hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's list of twenty-three unsolved problems; it is also one of the Millennium Prize Problems of the Clay Mathematics Institute, which offers US$1 million for a solution to any of them. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields. The Riemann zeta function ''ζ''(''s'') is a function whose argument ''s'' may be any complex number othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Function (number Theory)
In number theory, the partition function represents the number of possible partitions of a non-negative integer . For instance, because the integer 4 has the five partitions , , , , and . No closed-form expression for the partition function is known, but it has both asymptotic expansions that accurately approximate it and recurrence relations by which it can be calculated exactly. It grows as an exponential function of the square root of its argument. The multiplicative inverse of its generating function is the Euler function; by Euler's pentagonal number theorem this function is an alternating sum of pentagonal number powers of its argument. Srinivasa Ramanujan first discovered that the partition function has nontrivial patterns in modular arithmetic, now known as Ramanujan's congruences. For instance, whenever the decimal representation of ends in the digit 4 or 9, the number of partitions of will be divisible by 5. Definition and examples For a positive integer , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
