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Shikao Ikehara
was a Japanese mathematician. He was a student of Norbert Wiener at MIT (PhD 1930). Following Wiener in 1928, in 1931 Ikehara used Wiener's Tauberian theory to derive another proof of the prime number theorem, demonstrated solely via the non-vanishing of the zeta function on the line Re s = 1. An improved version of Ikehara's 1931 result by Wiener in 1932 is now known as the Wiener–Ikehara theorem. Proofs of the prime number theorem before 1928 and only using the behaviour of the zeta function on the line Re s = 1 (as the 1908 proof of Edmund Landau), also appealed to some bound on the order of growth of the zeta function on this line. Returning to Japan after studying with Dr Wiener, he taught at Osaka University , abbreviated as , is a public research university located in Osaka Prefecture, Japan. It is one of Japan's former Imperial Universities and a Designated National University listed as a "Top Type" university in the Top Global University Project. ... and the T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norbert Wiener
Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher in stochastic and mathematical noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems. Wiener is considered the originator of cybernetics, the science of communication as it relates to living things and machines, with implications for engineering, systems control, computer science, biology, neuroscience, philosophy, and the organization of society. Norbert Wiener is credited as being one of the first to theorize that all intelligent behavior was the result of feedback mechanisms, that could possibly be simulated by machines and was an important early step towards the development of modern artificial intelligence. Biography Youth Wiener was born in Columbia, Missouri, the first ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massachusetts Institute Of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the most prestigious and highly ranked academic institutions in the world. Founded in response to the increasing industrialization of the United States, MIT adopted a European polytechnic university model and stressed laboratory instruction in applied science and engineering. MIT is one of three private land grant universities in the United States, the others being Cornell University and Tuskegee University. The institute has an urban campus that extends more than a mile (1.6 km) alongside the Charles River, and encompasses a number of major off-campus facilities such as the MIT Lincoln Laboratory, the Bates Center, and the Haystack Observatory, as well as affiliated laboratories such as the Broad and Whitehead Institutes. , 98 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common Academic degree, degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a Thesis, dissertation, and defend their work before a panel of other experts in the field. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy degree may, in many jurisdictions, use the title ''Doctor (title), Doctor'' (often abbreviated "Dr" or "Dr.") with their name, although the proper etiquette associated with this usage may also be subject to the professional ethics of their own scholarly field, culture, or society. Those who teach at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number Theorem
In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function). The first such distribution found is , where is the prime-counting function (the number of primes less than or equal to ''N'') and is the natural logarithm of . This means that for large enough , the probability that a random integer not greater than is prime is very close to . Consequently, a random integer with at most digits (for large enough ) is about half as likely to be prime as a random integer with at most digits. For example, among the positive integers of at most 1000 digits, about one in 2300 is prime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiener–Ikehara Theorem
The Wiener–Ikehara theorem is a Tauberian theorem introduced by . It follows from Wiener's Tauberian theorem, and can be used to prove the prime number theorem (Chandrasekharan, 1969). Statement Let ''A''(''x'') be a non-negative, monotonic nondecreasing function of ''x'', defined for 0 ≤ ''x'' 1 to the function ''ƒ''(''s'') and that, for some non-negative number ''c'', :f(s) - \frac has an extension as a continuous function for ℜ(''s'') ≥ 1. Then the limit as ''x'' goes to infinity of ''e''−''x'' ''A''(''x'') is equal to c. One Particular Application An important number-theoretic application of the theorem is to Dirichlet series of the form :\sum_^\infty a(n) n^ where ''a''(''n'') is non-negative. If the series converges to an analytic function in :\Re(s) \ge b with a simple pole of residue ''c'' at ''s'' = ''b'', then :\sum_a(n) \sim \frac X^b. Applying this to the logarithmic derivative of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edmund Landau
Edmund Georg Hermann Landau (14 February 1877 – 19 February 1938) was a German mathematician who worked in the fields of number theory and complex analysis. Biography Edmund Landau was born to a Jewish family in Berlin. His father was Leopold Landau, a gynecologist and his mother was Johanna Jacoby. Landau studied mathematics at the University of Berlin, receiving his doctorate in 1899 and his habilitation (the post-doctoral qualification required to teach in German universities) in 1901. His doctoral thesis was 14 pages long. In 1895, his paper on scoring chess tournaments is the earliest use of eigenvector centrality. Landau taught at the University of Berlin from 1899 to 1909, after which he held a chair at the University of Göttingen. He married Marianne Ehrlich, the daughter of the Nobel Prize-winning biologist Paul Ehrlich, in 1905. At the 1912 International Congress of Mathematicians Landau listed four problems in number theory about primes that he said were parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Osaka University
, abbreviated as , is a public research university located in Osaka Prefecture, Japan. It is one of Japan's former Imperial Universities and a Designated National University listed as a "Top Type" university in the Top Global University Project. The university is often ranked among the top three public universities in Japan, along with the University of Tokyo and Kyoto University. It is ranked third overall among Japanese universities and 75th worldwide in the 2022 QS World University Rankings. Osaka University was one of the earliest modern universities in Japan at its founding in 1931. The history of the institution includes much older predecessors in Osaka such as the Kaitokudō founded in 1724 and the Tekijuku founded in 1838. In 2007, it merged with Osaka University of Foreign Studies and became the largest national university in Japan. Osaka University is one of the most productive research institutions in Japan. Numerous prominent scholars and scientists have attended or w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Or Control And Communication In The Animal And The Machine
Or or OR may refer to: Arts and entertainment Film and television * "O.R.", a 1974 episode of M*A*S*H * Or (My Treasure), a 2004 movie from Israel (''Or'' means "light" in Hebrew) Music * ''Or'' (album), a 2002 album by Golden Boy with Miss Kittin * ''O*R'', the original title of Olivia Rodrigo's album '' Sour'', 2021 * "Or", a song by Israeli singer Chen Aharoni in Kdam Eurovision 2011 * Or Records, a record label * Organized Rhyme, a Canadian hip-hop group featuring Tom Green Businesses and organizations * Or (political party) (), Israel * OR Books, an American publisher * Owasco River Railway, Auburn, New York, U.S. (by reporting mark) * TUI fly Netherlands, formerly ''Arke'', a Dutch charter airline (by IATA designator) Language and linguistics * Or (digraph), in the Uzbek alphabet * Or (letter) (or ''forfeda''), in Ogham, the Celtic tree alphabet * Odia language, an ancient Indo-Aryan tongue spoken in East India (ISO 639) * Or, an English grammatical conjuncti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1904 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1984 Deaths
Events January * January 1 – The Bornean Sultanate of Brunei gains full independence from the United Kingdom, having become a British protectorate in 1888. * January 7 – Brunei becomes the sixth member of the Association of Southeast Asian Nations (ASEAN). * January 10 ** The United States and the Vatican (Holy See) restore full diplomatic relations. ** The Victoria Agreement is signed, institutionalising the Indian Ocean Commission. *January 24 – Steve Jobs launches the Macintosh personal computer in the United States. February * February 3 ** Dr. John Buster and the research team at Harbor–UCLA Medical Center announce history's first embryo transfer from one woman to another, resulting in a live birth. ** STS-41-B: Space Shuttle ''Challenger'' is launched on the 10th Space Shuttle mission. * February 7 – Astronauts Bruce McCandless II and Robert L. Stewart make the first untethered space walk. * February 8– 19 – The 1984 Winter Olympics are held i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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