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Johannes Van Der Corput
Johannes Gaultherus van der Corput (4 September 1890 – 16 September 1975) was a Dutch mathematician, working in the field of analytic number theory. He was appointed professor at the University of Fribourg (Switzerland) in 1922, at the University of Groningen in 1923, and at the University of Amsterdam in 1946. He was one of the founders of the Mathematisch Centrum in Amsterdam, of which he also was the first director. From 1953 on he worked in the United States at the University of California, Berkeley, and the University of Wisconsin–Madison. He introduced the van der Corput lemma, a technique for creating an upper bound on the measure of a set drawn from harmonic analysis, and the van der Corput theorem on equidistribution modulo 1. He became member of the Royal Netherlands Academy of Arts and Sciences in 1929, and foreign member in 1953. He was a Plenary Speaker of the ICM in 1936 in Oslo. See also * van der Corput inequality * van der Corput lemma (harmonic analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotterdam
Rotterdam ( , , , lit. ''The Dam on the River Rotte'') is the second largest city and municipality in the Netherlands. It is in the province of South Holland, part of the North Sea mouth of the Rhine–Meuse–Scheldt delta, via the ''"New Meuse"'' inland shipping channel, dug to connect to the Meuse first, but now to the Rhine instead. Rotterdam's history goes back to 1270, when a dam was constructed in the Rotte. In 1340, Rotterdam was granted city rights by William IV, Count of Holland. The Rotterdam–The Hague metropolitan area, with a population of approximately 2.7 million, is the 10th-largest in the European Union and the most populous in the country. A major logistic and economic centre, Rotterdam is Europe's largest seaport. In 2020, it had a population of 651,446 and is home to over 180 nationalities. Rotterdam is known for its university, riverside setting, lively cultural life, maritime heritage and modern architecture. The near-complete destruction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Analysis
Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis). In the past two centuries, it has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis and neuroscience. The term "harmonics" originated as the Ancient Greek word ''harmonikos'', meaning "skilled in music". In physical eigenvalue problems, it began to mean waves whose frequencies are Multiple (mathematics), integer multiples of one another, as are the frequencies of the Harmonic series (music), harmonics of music notes, but the term has been generalized beyond its original meaning. The classical Fourier transform on R''n'' is still an area of ongoing research, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theorists
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Members Of The Royal Netherlands Academy Of Arts And Sciences
The Royal Netherlands Academy of Arts and Sciences (Dutch: ''Koninklijke Nederlandse Akademie van Wetenschappen'', abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed in the Trippenhuis in Amsterdam. Founded in 1808, members are appointed for life by co-optation. Lists of members sorted alphabetically * Members of the Royal Netherlands Academy of Arts and Sciences (A) * Members of the Royal Netherlands Academy of Arts and Sciences (B) * Members of the Royal Netherlands Academy of Arts and Sciences (C) * Members of the Royal Netherlands Academy of Arts and Sciences (D) * Members of the Royal Netherlands Academy of Arts and Sciences (E) * Members of the Royal Netherlands Academy of Arts and Sciences (F) * Members of the Royal Netherlands Academy of Arts and Sciences (G) * Members of the Royal Netherlands Academy of Arts and Sciences (H) * Members of the Royal Netherlands Academy of Arts and Scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientists From Rotterdam
A scientist is a person who conducts scientific research to advance knowledge in an area of the natural sciences. In classical antiquity, there was no real ancient analog of a modern scientist. Instead, philosophers engaged in the philosophical study of nature called natural philosophy, a precursor of natural science. Though Thales (circa 624-545 BC) was arguably the first scientist for describing how cosmic events may be seen as natural, not necessarily caused by gods,Frank N. Magill''The Ancient World: Dictionary of World Biography'', Volume 1 Routledge, 2003 it was not until the 19th century that the term ''scientist'' came into regular use after it was coined by the theologian, philosopher, and historian of science William Whewell in 1833. In modern times, many scientists have advanced degrees in an area of science and pursue careers in various sectors of the economy such as academia, industry, government, and nonprofit environments.'''' History The roles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1975 Deaths
It was also declared the ''International Women's Year'' by the United Nations and the European Architectural Heritage Year by the Council of Europe. Events January * January 1 - Watergate scandal (United States): John N. Mitchell, H. R. Haldeman and John Ehrlichman are found guilty of the Watergate cover-up. * January 2 ** The Federal Rules of Evidence are approved by the United States Congress. ** Bangladesh revolutionary leader Siraj Sikder is killed by police while in custody. ** A bomb blast at Samastipur, Bihar, India, fatally wounds Lalit Narayan Mishra, Minister of Railways. * January 5 – Tasman Bridge disaster: The Tasman Bridge in Hobart, Tasmania, Australia, is struck by the bulk ore carrier , killing 12 people. * January 7 – OPEC agrees to raise crude oil prices by 10%. * January 10–February 9 – The flight of ''Soyuz 17'' with the crew of Georgy Grechko and Aleksei Gubarev aboard the ''Salyut 4'' space station. * January 15 – Alvor Agreement: Portuga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1890 Births
Year 189 ( CLXXXIX) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Silanus and Silanus (or, less frequently, year 942 ''Ab urbe condita''). The denomination 189 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Plague (possibly smallpox) kills as many as 2,000 people per day in Rome. Farmers are unable to harvest their crops, and food shortages bring riots in the city. China * Liu Bian succeeds Emperor Ling, as Chinese emperor of the Han Dynasty. * Dong Zhuo has Liu Bian deposed, and installs Emperor Xian as emperor. * Two thousand eunuchs in the palace are slaughtered in a violent purge in Luoyang, the capital of Han. By topic Arts and sciences * Galen publishes his ''"Treatise on the various temperaments"'' (aka ''O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acta Arithmetica
''Acta Arithmetica'' is a scientific journal of mathematics publishing papers on number theory. It was established in 1935 by Salomon Lubelski and Arnold Walfisz. The journal is published by the Institute of Mathematics of the Polish Academy of Sciences The Institute of Mathematics of the Polish Academy of Sciences is a research institute of the Polish Academy of Sciences.Online archives (Library of Science, Issues: 1935–2000) 1935 establishments in Poland [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Corput's Theorem
In mathematics, a sequence (''s''1, ''s''2, ''s''3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling in a subinterval is proportional to the length of that subinterval. Such sequences are studied in Diophantine approximation theory and have applications to Monte Carlo integration. Definition A sequence (''s''1, ''s''2, ''s''3, ...) of real numbers is said to be ''equidistributed'' on a non-degenerate interval 'a'', ''b''if for every subinterval 'c'', ''d''of 'a'', ''b''we have :\lim_= . (Here, the notation , ∩ 'c'', ''d'' denotes the number of elements, out of the first ''n'' elements of the sequence, that are between ''c'' and ''d''.) For example, if a sequence is equidistributed in , 2 since the interval .5, 0.9occupies 1/5 of the length of the interval , 2 as ''n'' becomes large, the proportion of the first ''n'' members of the sequence which fall between 0.5 and 0.9 must approach 1/5. L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Corput's Method
In mathematics, van der Corput's method generates estimates for exponential sums. The method applies two processes, the van der Corput processes A and B which relate the sums into simpler sums which are easier to estimate. The processes apply to exponential sums of the form : \sum_^b e(f(n)) \ where ''f'' is a sufficiently smooth function and ''e''(''x'') denotes exp(2Ï€i''x''). Process A To apply process A, write the first difference ''f''''h''(''x'') for ''f''(''x''+''h'')−''f''(''x''). Assume there is ''H'' ≤ ''b''−''a'' such that : \sum_^H \left\vert\right\vert \le b-a \ . Then : \left\vert\right\vert \ll \frac \ . Process B Process B transforms the sum involving ''f'' into one involving a function ''g'' defined in terms of the derivative of f. Suppose that ''f is monotone increasing with ''f'''(''a'') = α, ''f'''(''b'') = β. Then ''f''' is invertible on ±,βwith inverse ''u'' say. Further suppose ''f'''' ≥ λ > 0. Write : g(y) = f(u(y)) - y u(y) \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Corput Inequality
In mathematics, the van der Corput inequality is a corollary of the Cauchy–Schwarz inequality that is useful in the study of correlations among vectors, and hence random variables. It is also useful in the study of equidistributed sequences, for example in the Weyl equidistribution estimate. Loosely stated, the van der Corput inequality asserts that if a unit vector v in an inner product space V is strongly correlated with many unit vectors u_, \dots, u_ \in V, then many of the pairs u_, u_ must be strongly correlated with each other. Here, the notion of correlation is made precise by the inner product of the space V: when the absolute value of \langle u, v \rangle is close to 1, then u and v are considered to be strongly correlated. (More generally, if the vectors involved are not unit vectors, then strong correlation means that , \langle u, v \rangle , \approx \, u \, \, v \, .) Statement of the inequality Let V be a real or complex inner product space with inne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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