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Edwin Hewitt
Edwin Hewitt (January 20, 1920, Everett, Washington – June 21, 1999) was an American mathematician known for his work in abstract harmonic analysis and for his discovery, in collaboration with Leonard Jimmie Savage, of the Hewitt–Savage zero–one law. He received his Ph.D. in 1942 from Harvard University, and served on the faculty of mathematics at the University of Washington from 1954. Hewitt pioneered the construction of the hyperreal number, hyperreals by means of an ultrapower construction (Hewitt, 1948). Hewitt wrote the 1975 English translation of Alexandre Kirillov, A. A. Kirillov's 1972 Russian monograph ''Elements of the Theory of Representations'' (Элементы Теории Представлений), and co-authored ''Abstract Harmonic Analysis'' with Kenneth A. Ross (1st edn., 1st vol. in 1963; 1st edn., 2nd vol. in 1970), an extensive work in two volumes. See also *Cohen–Hewitt factorization theorem Publications * * * * References Edwin Hewitt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Everett, Washington
Everett is the county seat and largest city of Snohomish County, Washington, United States. It is north of Seattle and is one of the main cities in the metropolitan area and the Puget Sound region. Everett is the seventh-largest city in the state by population, with 110,629 residents as of the 2020 census. The city is primarily situated on a peninsula at the mouth of the Snohomish River along Port Gardner Bay, an inlet of Possession Sound (itself part of Puget Sound), and extends to the south and west. The Port Gardner Peninsula was historically inhabited by the Snohomish people, who had a winter village named Hibulb near the mouth of the river. Modern settlement in the area began with loggers and homesteaders arriving in the 1860s, but plans to build a city were not conceived until 1890. A consortium of East Coast investors seeking to build a major industrial city acquired land in the area and filed a plat for "Everett", which they named in honor of Everett Colby, the son o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperreal Number
In mathematics, the system of hyperreal numbers is a way of treating infinite and infinitesimal (infinitely small but non-zero) quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers greater than anything of the form :1 + 1 + \cdots + 1 (for any finite number of terms). Such numbers are infinite, and their reciprocals are infinitesimals. The term "hyper-real" was introduced by Edwin Hewitt in 1948. The hyperreal numbers satisfy the transfer principle, a rigorous version of Leibniz's heuristic law of continuity. The transfer principle states that true first-order statements about R are also valid in *R. For example, the commutative law of addition, , holds for the hyperreals just as it does for the reals; since R is a real closed field, so is *R. Since \sin()=0 for all integers ''n'', one also has \sin()=0 for all hyperintegers H. The transfer principle for ultrapowers is a consequence of Łoś' theorem of 1955. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University Alumni
The list of Harvard University people includes notable graduates, professors, and administrators affiliated with Harvard University. For a list of notable non-graduates of Harvard, see notable non-graduate alumni of Harvard. For a list of Harvard's presidents, see President of Harvard University. Eight President of the United States, Presidents of the United States have graduated from Harvard University: John Adams, John Quincy Adams, Rutherford B. Hayes, John F. Kennedy, Franklin Delano Roosevelt, Theodore Roosevelt, George W. Bush, and Barack Obama. Bush graduated from Harvard Business School, Hayes and Obama from Harvard Law School, and the others from Harvard College. Over 150 Nobel Prize winners have been associated with the university as alumni, researchers or faculty. Nobel laureates Pulitzer Prize winners ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysts
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1999 Deaths
File:1999 Events Collage.png, From left, clockwise: The funeral procession of King Hussein of Jordan in Amman; the 1999 İzmit earthquake kills over 17,000 people in Turkey; the Columbine High School massacre, one of the first major school shootings in the United States; the Year 2000 problem ("Y2K"), perceived as a major concern in the lead-up to the year 2000; the Millennium Dome opens in London; online music downloading platform Napster is launched, soon a source of online piracy; NASA loses both the Mars Climate Orbiter and the Mars Polar Lander; a destroyed T-55 tank near Prizren during the Kosovo War., 300x300px, thumb rect 0 0 200 200 Death and state funeral of King Hussein rect 200 0 400 200 1999 İzmit earthquake rect 400 0 600 200 Columbine High School massacre rect 0 200 300 400 Kosovo War rect 300 200 600 400 Year 2000 problem rect 0 400 200 600 Mars Climate Orbiter rect 200 400 400 600 Napster rect 400 400 600 600 Millennium Dome 1999 was designated as the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1920 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 Slip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theorists
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These conce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cohen–Hewitt Factorization Theorem
In mathematics, the Cohen–Hewitt factorization theorem states that if V is a left module In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of ''module'' generalizes also the notion of abelian group, since the abelian groups are exactly the mo ... over a Banach algebra B with a left approximate unit (u_)_ , then an element v of V can be factorized as a product v = b w (for some b \in B and w \in V ) whenever \displaystyle \lim_ u_ v = v . The theorem was introduced by and . References * * Banach algebras Theorems in functional analysis {{analysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monograph
A monograph is a specialist work of writing (in contrast to reference works) or exhibition on a single subject or an aspect of a subject, often by a single author or artist, and usually on a scholarly subject. In library cataloging, ''monograph'' has a broader meaning—that of a nonserial publication complete in one volume (book) or a definite number of volumes. Thus it differs from a serial or periodical publication such as a magazine, academic journal, or newspaper. In this context only, books such as novels are considered monographs.__FORCETOC__ Academia The English term "monograph" is derived from modern Latin "monographia", which has its root in Greek. In the English word, "mono-" means "single" and "-graph" means "something written". Unlike a textbook, which surveys the state of knowledge in a field, the main purpose of a monograph is to present primary research and original scholarship ascertaining reliable credibility to the required recipient. This research is prese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexandre Kirillov
Alexandre Aleksandrovich Kirillov (russian: Алекса́ндр Алекса́ндрович Кири́ллов, born 1936) is a Soviet and Russian mathematician, known for his works in the fields of representation theory, topological groups and Lie groups. In particular he introduced the orbit method into representation theory. He is an emeritus professor at the University of Pennsylvania. Career Kirillov studied at Moscow State University where he was a student of Israel Gelfand. His Ph.D. (kandidat) dissertation ''Unitary representations of nilpotent Lie groups'' was published in 1962. He was awarded the degree of Doctor of Science. At the time he was the youngest Doctor of Science in the Soviet Union. He worked at the Moscow State University until 1994 when he became the Francis J. Carey Professor of Mathematics at the University of Pennsylvania. During his school years, Kirillov was a winner of many mathematics competitions, and he is still an active organizer of Russia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ultrapower
The ultraproduct is a mathematical construction that appears mainly in abstract algebra and mathematical logic, in particular in model theory and set theory. An ultraproduct is a quotient of the direct product of a family of structures. All factors need to have the same signature. The ultrapower is the special case of this construction in which all factors are equal. For example, ultrapowers can be used to construct new fields from given ones. The hyperreal numbers, an ultrapower of the real numbers, are a special case of this. Some striking applications of ultraproducts include very elegant proofs of the compactness theorem and the completeness theorem, Keisler's ultrapower theorem, which gives an algebraic characterization of the semantic notion of elementary equivalence, and the Robinson–Zakon presentation of the use of superstructures and their monomorphisms to construct nonstandard models of analysis, leading to the growth of the area of nonstandard analysis, which was pion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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