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H. Iwaniec
Henryk Iwaniec (born October 9, 1947) is a Polish-American mathematician, and since 1987 a professor at Rutgers University. He is a member of the American Academy of Arts and Sciences and Polish Academy of Sciences. He has made important contributions to analytic and algebraic number theory as well as harmonic analysis. He is the recipient of Cole Prize (2002), Steele Prize (2011), and Shaw Prize (2015). Background and education Iwaniec studied at the University of Warsaw, where he got his PhD in 1972 under Andrzej Schinzel. He then held positions at the Institute of Mathematics of the Polish Academy of Sciences until 1983 when he left Poland. He held visiting positions at the Institute for Advanced Study, University of Michigan, and University of Colorado Boulder before being appointed Professor of Mathematics at Rutgers University. He is a citizen of both Poland and the United States. He and mathematician Tadeusz Iwaniec are twin brothers. Work Iwaniec studies both sieve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elbląg
Elbląg (; ; ) is a city in the Warmian-Masurian Voivodeship, in northern Poland, located in the eastern edge of the Żuławy region with 127,390 inhabitants, as of December 2021. It is the capital of Elbląg County. Elbląg is one of the oldest cities in the province. Its history dates back to 1237, when the Teutonic Order constructed their fortified stronghold on the banks of a nearby river. The castle subsequently served as the official seat of the Teutonic Order Masters. Elbląg became part of the Hanseatic League, which contributed much to the city's wealth. Through the Hanseatic League, the city was linked to other major ports like Gdańsk, Lübeck and Amsterdam. Elbląg joined Poland in 1454 and after the defeat of the Teutonic Knights in the Thirteen Years’ War was recognized as part of Poland in 1466. It then flourished and turned into a significant trading point, but its growth was eventually hindered by the Second Northern War and the Swedish Deluge. The city ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shaw Prize
The Shaw Prize is a set of three annual awards presented by the Shaw Prize Foundation in the fields of astronomy, medicine and life sciences, and mathematical sciences. Established in 2002 in Hong Kong, by Hong Kong entertainment mogul and philanthropist Run Run Shaw (邵逸夫), the awards honour "individuals who are currently active in their respective fields and who have recently achieved distinguished and significant advances, who have made outstanding contributions in academic and scientific research or applications, or who in other domains have achieved excellence." The prize has been described as the "Nobel of the East". Award The prize consists of three awards in the fields of astronomy, life science and medicine, and mathematical sciences; it is not awarded posthumously. Nominations are submitted by invited individuals beginning each year in September. Winners are announced in the summer and receive the award at a ceremony in early autumn. Each award consists of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes, since they include two primes, or second numbers, by analogy with how "prime" means "first". Alternatively non-prime semiprimes are called almost-prime numbers, specifically the "2-almost-prime" biprime and "3-almost-prime" triprime Examples and variations The semiprimes less than 100 are: Semiprimes that are not square numbers are called discrete, distinct, or squarefree semiprimes: The semiprimes are the case k=2 of the k- almost primes, numbers with exactly k prime factors. However some sources use "semiprime" to refer to a larger set of numbers, the numbers with at most two prime factors (including unit (1), primes, and semiprimes). These are: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity Problem (sieve Theory)
In number theory, the parity problem refers to a limitation in sieve theory that prevents sieves from giving good estimates in many kinds of prime-counting problems. The problem was identified and named by Atle Selberg in 1949. Beginning around 1996, John Friedlander and Henryk Iwaniec developed some parity-sensitive sieves that make the parity problem less of an obstacle. Statement Terence Tao gave this "rough" statement of the problem: This problem is significant because it may explain why it is difficult for sieves to "detect primes," in other words to give a non-trivial lower bound for the number of primes with some property. For example, in a sense Chen's theorem is very close to a solution of the twin prime conjecture, since it says that there are infinitely many primes ''p'' such that ''p'' + 2 is either prime or the product of two primes (semiprime). The parity problem suggests that, because the case of interest has an odd number of prime factors (namely 1), it won't be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The National Academy Of Sciences
''Proceedings of the National Academy of Sciences of the United States of America'' (often abbreviated ''PNAS'' or ''PNAS USA'') is a peer-reviewed multidisciplinary scientific journal. It is the official journal of the National Academy of Sciences, published since 1915, and publishes original research, scientific reviews, commentaries, and letters. According to ''Journal Citation Reports'', the journal has a 2022 impact factor of 9.4. ''PNAS'' is the second most cited scientific journal, with more than 1.9 million cumulative citations from 2008 to 2018. In the past, ''PNAS'' has been described variously as "prestigious", "sedate", "renowned" and "high impact". ''PNAS'' is a delayed open-access journal, with an embargo period of six months that can be bypassed for an author fee ( hybrid open access). Since September 2017, open access articles are published under a Creative Commons license. Since January 2019, ''PNAS'' has been online-only, although print issues are available ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorization, factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow primality test, method of checking the primality of a given number , called trial division, tests whether is a multiple of any integer between 2 and . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Friedlander
John Friedlander is a Canadian mathematician specializing in analytic number theory. He received his B.Sc. from the University of Toronto in 1965, an M.A. from the University of Waterloo in 1966, and a Ph.D. from Pennsylvania State University in 1972. He was a lecturer at M.I.T. in 1974–76, and has been on the faculty of the University of Toronto since 1977, where he served as Chair during 1987–91. He has also spent several years at the Institute for Advanced Study. In addition to his individual work, he has been notable for his collaborations with other well-known number theorists, including Enrico Bombieri, William Duke, Andrew Granville, and especially Henryk Iwaniec. In 1997, in joint work with Henryk Iwaniec, Friedlander proved that infinitely many prime numbers can be obtained as the sum of a square and fourth power: . Friedlander and Iwaniec improved Enrico Bombieri's "asymptotic sieve" technique to construct their proof. Awards and honors * In 1999, Friedlander rece ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to the sum function given by its Taylor series (that is, it is analytic), complex analysis is particularly concerned with analytic functions of a complex variable, that is, '' holomorphic functions''. The concept can be extended to functions of several complex variables. Complex analysis is contrasted with real analysis, which dea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sieve Theory
Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers. The prototypical example of a sifted set is the set of prime numbers up to some prescribed limit ''X''. Correspondingly, the prototypical example of a sieve is the sieve of Eratosthenes, or the more general Legendre sieve. The direct attack on prime numbers using these methods soon reaches apparently insuperable obstacles, in the way of the accumulation of error terms. In one of the major strands of number theory in the twentieth century, ways were found of avoiding some of the difficulties of a frontal attack with a naive idea of what sieving should be. One successful approach is to approximate a specific sifted set of numbers (e.g. the set of prime numbers) by another, simpler set (e.g. the set of almost prime numbers), which is typically somewhat larger than the original set, and easier to analyze. More sophisticated sieves a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tadeusz Iwaniec
Tadeusz Iwaniec (born October 9, 1947 in Elbląg) is a Polish-American mathematician, and since 1996 John Raymond French Distinguished Professor of Mathematics at Syracuse University.Biography of Tadeusz Iwaniec Mathematics Department, Syracuse University. Retrieved 2010-01-22. He and mathematician are twin brothers. Awards and honors Iwaniec was given the Prize of the President of the Polish Academy of Sciences, 1980, the Alfred Jurzykowski Award in Mathematics in 1997, the Prix 2001 Institut Henri-Poincaré Gauthier-Villars, and the 2009 Sierpinski Medal of the Polish Mathematical Society and Warsaw University. In 1998 he was elected as a forei ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Colorado Boulder
The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a public research university in Boulder, Colorado, United States. Founded in 1876, five months before Colorado became a state, it is the flagship university of the University of Colorado system. CU Boulder is a member of the Association of American Universities, considered a Public Ivy and is classified among R1: Doctoral Universities – Very high research activity. The university consists of nine colleges and schools and offers over 150 academic programs, enrolling more than 35,000 students as of January 2022. In 2021, the university attracted the support of over $634 million for research and spent $536 million on research and development according to the National Science Foundation, ranking it 50th in the nation. It receives the most NASA astrophysics technology grants of all academic institutions and is the only university in the world that has sent instruments to all planets in the Solar System. The Col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Analysis
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals. Generalizing these transforms to other domains is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis. Harmonic analysis has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis, spectral analysis, and neuroscience. The term "harmonics" originated from the Ancient Greek word ''harmonikos'', meaning "skilled in music". In physical eigenvalue problems, it began to mean waves whose frequencies are integer multiples of one another, as are the freq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
