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Paul Butzer
Paul Leo Butzer (born April 15, 1928 in Mülheim an der Ruhr) is a German mathematician who specializes in Analysis (Approximation theory, Harmonic analysis). Life and work Butzer is the son of an engineer, and his mother studied mathematics at RWTH Aachen University. As opponents of the National Socialists (Nazis), Butzer's parents left Germany with their children in 1937 and moved to England. During World War II, they relocated to Canada, where Butzer attended school in Montreal and studied mathematics at Loyola College (later Concordia University), completing his bachelor's degree in 1948. He then pursued further studies at the University of Toronto, including studying under Harold Scott MacDonald Coxeter and William Tutte, and obtained his Ph.D. in 1951 under the supervision of George G. Lorentz (On Bernstein polynomials). In 1952, he became a lecturer and then an assistant professor at McGill University. In 1955/56, he lived in Paris and then in Mainz. He decided to st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
April 15
Events Pre-1600 * 769 – The Lateran Council ends by condemning the Council of Hieria and anathematizing its iconoclastic rulings. *1071 – Bari, the last Byzantine possession in southern Italy, is surrendered to Robert Guiscard. *1450 – Battle of Formigny: Toward the end of the Hundred Years' War, the French attack and nearly annihilate English forces, ending English domination in Northern France. 1601–1900 *1632 – Battle of Rain: Swedes under Gustavus Adolphus defeat the Holy Roman Empire during the Thirty Years' War. *1642 – Irish Confederate Wars: A Confederate Irish militia is routed in the Battle of Kilrush when it attempts to halt the progress of a Royalist Army. *1715 – The Pocotaligo Massacre triggers the start of the Yamasee War in colonial South Carolina. *1736 – Foundation of the short-lived Kingdom of Corsica. *1738 – '' Serse'', an Italian opera by George Frideric Handel, receives its premiere performa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Freiburg
The University of Freiburg (colloquially german: Uni Freiburg), officially the Albert Ludwig University of Freiburg (german: Albert-Ludwigs-Universität Freiburg), is a public research university located in Freiburg im Breisgau, Baden-Württemberg, Germany. The university was founded in 1457 by the Habsburg dynasty as the second university in Austrian-Habsburg territory after the University of Vienna. Today, Freiburg is the fifth-oldest university in Germany, with a long tradition of teaching the humanities, social sciences and natural sciences and technology and enjoys a high academic reputation both nationally and internationally. The university is made up of 11 faculties and attracts students from across Germany as well as from over 120 other countries. Foreign students constitute about 18.2% of total student numbers. The University of Freiburg has been associated with figures such as Hannah Arendt, Rudolf Carnap, David Daube, Johann Eck, Hans-Georg Gadamer, Friedr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugène Catalan
Eugene is a common male given name that comes from the Greek εὐγενής (''eugenēs''), "noble", literally "well-born", from εὖ (''eu''), "well" and γένος (''genos''), "race, stock, kin". Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Gene is a common shortened form. The feminine variant is or Eugenie. , a common given name in parts of central and northern Europe, is also a variant of Eugene / Eugine. Other male foreign-language varia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eduard Helly
Eduard Helly (June 1, 1884 in Vienna – 28 November 1943 in Chicago) was a mathematician after whom Helly's theorem, Helly families, Helly's selection theorem, Helly metric, and the Helly–Bray theorem were named. Life Helly earned his doctorate from the University of Vienna in 1907, with two advisors, Wilhelm Wirtinger and Franz Mertens. He then continued his studies for another year at the University of Göttingen. Richard Courant, also studying there at the same time, tells a story of Helly disrupting one of Courant's talks, which fortunately did not prevent David Hilbert from eventually hiring Courant as an assistant. After returning to Vienna, Helly worked as a tutor, Gymnasium teacher, and textbook editor until World War I, when he enlisted in the Austrian army. He was shot in 1915, and spent the rest of the war as a prisoner of the Russians. In one prison camp in Berezovka, Siberia, he organized a mathematical seminar in which Tibor Radó, then an engineer, began hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Gustav Lejeune Dirichlet
Johann Peter Gustav Lejeune Dirichlet (; 13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis; he is credited with being one of the first mathematicians to give the modern formal definition of a function. Although his surname is Lejeune Dirichlet, he is commonly referred to by his mononym Dirichlet, in particular for results named after him. Biography Early life (1805–1822) Gustav Lejeune Dirichlet was born on 13 February 1805 in Düren, a town on the left bank of the Rhine which at the time was part of the First French Empire, reverting to Prussia after the Congress of Vienna in 1815. His father Johann Arnold Lejeune Dirichlet was the postmaster, merchant, and city councilor. His paternal grandfather had come to Düren from Richelette (or more likely Richelle), a small community north ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aachen
Aachen ( ; ; Aachen dialect: ''Oche'' ; French and traditional English: Aix-la-Chapelle; or ''Aquisgranum''; nl, Aken ; Polish: Akwizgran) is, with around 249,000 inhabitants, the 13th-largest city in North Rhine-Westphalia, and the 28th-largest city of Germany. It is the westernmost city in Germany, and borders Belgium and the Netherlands to the west, the triborder area. It is located between Maastricht (NL) and Liège (BE) in the west, and Bonn and Cologne in the east. The Wurm River flows through the city, and together with Mönchengladbach, Aachen is the only larger German city in the drainage basin of the Meuse. Aachen is the seat of the City Region Aachen (german: link=yes, Städteregion Aachen). Aachen developed from a Roman settlement and (bath complex), subsequently becoming the preferred medieval Imperial residence of Emperor Charlemagne of the Frankish Empire, and, from 936 to 1531, the place where 31 Holy Roman Emperors were crowned Kings of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Analysis
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information communication systems and the processing of signals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sampling Theory
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population in question. Sampling has lower costs and faster data collection than measuring the entire population and can provide insights in cases where it is infeasible to measure an entire population. Each observation measures one or more properties (such as weight, location, colour or mass) of independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is widely used for gathering information about a population. Acceptance sampling is used to determine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convergence Tests
In mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series \sum_^\infty a_n. List of tests Limit of the summand If the limit of the summand is undefined or nonzero, that is \lim_a_n \ne 0, then the series must diverge. In this sense, the partial sums are Cauchy only if this limit exists and is equal to zero. The test is inconclusive if the limit of the summand is zero. This is also known as the nth-term test, test for divergence, or the divergence test. Ratio test This is also known as d'Alembert's criterion. : Suppose that there exists r such that :: \lim_\left, \frac\ = r. : If ''r'' 1, then the series diverges. If ''r'' = 1, the ratio test is inconclusive, and the series may converge or diverge. Root test This is also known as the ''n''th root test or Cauchy's criterion. : Let :: r=\limsup_\sqrt : where \limsup denotes the limit superior (pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Limit Theorem
In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern general form, this fundamental result in probability theory was precisely stated as late as 1920, thereby serving as a bridge between classical and modern probability theory. If X_1, X_2, \dots, X_n, \dots are random samples drawn from a population with overall mean \mu and finite variance and if \bar_n is the sample mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Banach Space
In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space. Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly. Maurice René Fréchet was the first to use the term "Banach space" and Banach in turn then coined the term " Fréchet space." Banach spaces originally grew out of the study of function spaces by Hilbert, Fréchet, and Riesz earlier in the century. Banach spaces play a central role in functional analysis. In other areas of analysis, the spaces under study are often Banach spaces. Definition A Banach space is a com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Analysis
In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize the same sound by including the frequency components as revealed in the Fourier analysis. In mathematics, the term ''Fourier a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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