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Carle David Tolmé Runge
Carl David Tolmé Runge (; 30 August 1856 – 3 January 1927) was a German Reich, German mathematician, physicist, and spectroscopist. He was co-developer and co-eponym of the Runge–Kutta method (), in the field of what is today known as numerical analysis. Life and work Runge spent the first few years of his life in Havana, where his father Julius Runge was the Danish consul. His mother was Fanny Schwartz Tolmé. The family later moved to Bremen (city), Bremen, where his father died early (in 1864). In 1880, he received his Ph.D. in mathematics at Berlin, where he studied under Karl Weierstrass. In 1886, he became a professor at the Leibniz University Hannover, Technische Hochschule Hannover in Hanover, Germany. His interests included mathematics, spectroscopy, geodesy, and astrophysics. In addition to pure mathematics, he did experimental work studying spectral lines of various elements (together with Heinrich Kayser), and was very interested in the application of this wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bremen (city)
Bremen (Low German also: ''Breem'' or ''Bräm''), officially the City Municipality of Bremen (, ), is the capital of the German state of the Free Hanseatic City of Bremen (), a two-city-state consisting of the cities of Bremen and Bremerhaven. With about 577,000 inhabitants, the Hanseatic city is the 11th-largest city of Germany and the second-largest city in Northern Germany after Hamburg. Bremen is the largest city on the River Weser, the longest river flowing entirely in Germany, lying some upstream from its mouth into the North Sea at Bremerhaven, and is completely surrounded by the state of Lower Saxony. Bremen is the centre of the Northwest Metropolitan Region, which also includes the cities of Oldenburg and Bremerhaven, and has a population of around 2.8 million people. Bremen is contiguous with the Lower Saxon towns of Delmenhorst, Stuhr, Achim, Weyhe, Schwanewede and Lilienthal. There is an exclave of Bremen in Bremerhaven, the "Citybremian Overseas Port Are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Groeneveld
Jan, JaN or JAN may refer to: Acronyms * Jackson, Mississippi (Amtrak station), US, Amtrak station code JAN * Jackson-Evers International Airport, Mississippi, US, IATA code * Jabhat al-Nusra (JaN), a Syrian militant group * Japanese Article Number, a barcode standard compatible with EAN * Japanese Accepted Name, a Japanese nonproprietary drug name * Job Accommodation Network, US, for people with disabilities * ''Joint Army-Navy'', US standards for electronic color codes, etc. * ''Journal of Advanced Nursing'' Personal name * Jan (name), male variant of ''John'', female shortened form of ''Janet'' and ''Janice'' * Jan (Persian name), Persian word meaning 'life', 'soul', 'dear'; also used as a name * Ran (surname), romanized from Mandarin as Jan in Wade–Giles * Ján, Slovak name Other uses * January, as an abbreviation for the first month of the year in the Gregorian calendar * Jan (cards), a term in some card games when a player loses without taking any tricks or scoring a mini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Runge's Theorem
In complex analysis, Runge's theorem (also known as Runge's approximation theorem) is named after the German mathematician Carl Runge who first proved it in the year 1885. It states the following: Denoting by C the set of complex numbers, let ''K'' be a compact subset of C and let ''f'' be a function which is holomorphic on an open set containing ''K''. If ''A'' is a set containing at least one complex number from every bounded connected component of C\''K'' then there exists a sequence (r_n)_ of rational functions which converges uniformly to ''f'' on ''K'' and such that all the poles of the functions (r_n)_ are in ''A.'' Note that not every complex number in ''A'' needs to be a pole of every rational function of the sequence (r_n)_. We merely know that for all members of (r_n)_ that do have poles, those poles lie in ''A''. One aspect that makes this theorem so powerful is that one can choose the set ''A'' arbitrarily. In other words, one can choose any complex numbers from t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Runge's Phenomenon
In the mathematical field of numerical analysis, Runge's phenomenon () is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points. It was discovered by Carl David Tolmé Runge (1901) when exploring the behavior of errors when using polynomial interpolation to approximate certain functions. The discovery shows that going to higher degrees does not always improve accuracy. The phenomenon is similar to the Gibbs phenomenon in Fourier series approximations. The Weierstrass approximation theorem states that for every continuous function f(x) defined on an interval , b/math>, there exists a set of polynomial functions P_n(x) for n=0, 1, 2, \ldots, each of degree at most n, that approximates f(x) with uniform convergence over , b/math> as n tends to infinity. This can be expressed as: :\lim_ \left( \sup_ \left, f(x) - P_n(x) \ \right) = 0. Consider the case w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horst Von Sanden
Horst may refer to: Science * Horst (geology) In physical geography and geology, a horst is a raised fault block bounded by Fault (geology), normal faults. Horsts are typically found together with grabens. While a horst is lifted or remains stationary, the grabens on either side Subsidence, ..., a raised fault block bounded by normal faults or graben People * Horst (given name) * Horst (surname) * ter Horst, Dutch surname * van der Horst, Dutch surname Places Settlements Germany * Horst, Steinburg, a municipality in the district of Steinburg in Schleswig-Holstein * Horst, Lauenburg, a municipality in the district of Lauenburg in Schleswig-Holstein * Horst, Mecklenburg-Vorpommern, a village and district in the municipality of Sundhagen, Mecklenburg-Vorpommern * , a district in the city of Gelsenkirchen, North Rhine-Westphalia * , a town in the municipality of Seevetal, Lower Saxony Netherlands * Horst aan de Maas, a municipality in the province of Limburg ** Horst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Willers
Friedrich may refer to: Names *Friedrich (given name), people with the given name ''Friedrich'' *Friedrich (surname), people with the surname ''Friedrich'' Other *Friedrich (board game), a board game about Frederick the Great and the Seven Years' War * ''Friedrich'' (novel), a novel about anti-semitism written by Hans Peter Richter *Friedrich Air Conditioning, a company manufacturing air conditioning and purifying products *, a German cargo ship in service 1941-45 See also *Friedrichs (other) *Frederick (other) *Nikolaus Friedreich Nikolaus Friedreich (1 July 1825 in Würzburg – 6 July 1882 in Heidelberg) was a German pathologist and neurologist, and a third generation physician in the Friedreich family. His father was psychiatrist Johann Baptist Friedreich (1796–18 ... {{disambig ja:フリードリヒ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
August Wiegrefe
August is the eighth month of the year in the Julian and Gregorian calendars. Its length is 31 days. In the Southern Hemisphere, August is the seasonal equivalent of February in the Northern Hemisphere. In the Northern Hemisphere, August falls in summer. In the Southern Hemisphere, the month falls during winter. In many European countries, August is the holiday month for most workers. Numerous religious holidays occurred during August in ancient Rome. Certain meteor showers take place in August. The Kappa Cygnids occur in August, with yearly dates varying. The Alpha Capricornids meteor shower occurs as early as July 10 and ends around August 10. The Southern Delta Aquariids occur from mid-July to mid-August, with the peak usually around July 28–29. The Perseids, a major meteor shower, typically takes place between July 17 and August 24, with the peak days varying yearly. The star cluster of Messier 30 is best observed around August. Among the aborigines of the Canary Is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
