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https://en.wikipedia.org/wiki/Proceedings%20of%20the%20Physical%20Society
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The Proceedings of the Physical Society was a journal on the subject of physics, originally associated with the Physical Society of London, England. In 1968, it was replaced by the Journal of Physics.
Journal history
1874–1925: Proceedings of the Physical Society of London
1926–1948: Proceedings of the Physical Society
1949–1957: Proceedings of the Physical Society, Section A
1949–1957: Proceedings of the Physical Society, Section B
1958–1967: Proceedings of the Physical Society
External links
Electronic access from the Institute of Physics (IoP)
Physics journals
IOP Publishing academic journals
Academic journals associated with learned and professional societies of the United Kingdom
Defunct journals of the United Kingdom
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https://en.wikipedia.org/wiki/Hasse%20invariant
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In mathematics, Hasse invariant may refer to:
Hasse invariant of an algebra
Hasse invariant of an elliptic curve
Hasse invariant of a quadratic form
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https://en.wikipedia.org/wiki/Physical%20Society%20of%20London
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The Physical Society of London, England, was a scientific society which was founded in 1874. In 1921, it was renamed the Physical Society, and in 1960 it merged with the Institute of Physics (IOP), the combined organisation eventually adopting the name of the latter society.
The society was founded due to the efforts of Frederick Guthrie, Professor of Physics at the Royal College of Science, South Kensington, and his assistant, William Fletcher Barrett. They canvassed support for a 'Society for physical research' and on 14 February 1874, the Physical Society of London was formed with an initial membership of 29 people. The Society's first president was John Hall Gladstone.
Meetings were held every two weeks, mainly at Imperial College London. From its beginning, the society held open meetings and demonstrations and published Proceedings of the Physical Society of London. The first Guthrie lecture, now known as the Faraday Medal and Prize, was delivered in 1914. In 1921 the society became the Physical Society, and in 1932 absorbed the Optical Society (of London). The Optical Society published Transactions of the Optical Society from 1899 to 1932.
In 1960, the merger with the Institute of Physics took place, creating the Institute of Physics and the Physical Society, which combined the learned society tradition of the Physical Society with the professional body tradition of the Institute of Physics. Upon being granted a royal charter in 1970, the organisation renamed itself
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https://en.wikipedia.org/wiki/Hasse%20invariant%20of%20a%20quadratic%20form
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In mathematics, the Hasse invariant (or Hasse–Witt invariant) of a quadratic form Q over a field K takes values in the Brauer group Br(K). The name "Hasse–Witt" comes from Helmut Hasse and Ernst Witt.
The quadratic form Q may be taken as a diagonal form
Σ aixi2.
Its invariant is then defined as the product of the classes in the Brauer group of all the quaternion algebras
(ai, aj) for i < j.
This is independent of the diagonal form chosen to compute it.
It may also be viewed as the second Stiefel–Whitney class of Q.
Symbols
The invariant may be computed for a specific symbol φ taking values in the group C2 = {±1}.
In the context of quadratic forms over a local field, the Hasse invariant may be defined using the Hilbert symbol, the unique symbol taking values in C2. The invariants of a quadratic forms over a local field are precisely the dimension, discriminant and Hasse invariant.
For quadratic forms over a number field, there is a Hasse invariant ±1 for every finite place. The invariants of a form over a number field are precisely the dimension, discriminant, all local Hasse invariants and the signatures coming from real embeddings.
See also
Hasse–Minkowski theorem
References
Quadratic forms
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https://en.wikipedia.org/wiki/Diagonal%20form
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In mathematics, a diagonal form is an algebraic form (homogeneous polynomial) without cross-terms involving different indeterminates. That is, it is
for some given degree m.
Such forms F, and the hypersurfaces F = 0 they define in projective space, are very special in geometric terms, with many symmetries. They also include famous cases like the Fermat curves, and other examples well known in the theory of Diophantine equations.
A great deal has been worked out about their theory: algebraic geometry, local zeta-functions via Jacobi sums, Hardy-Littlewood circle method.
Examples
is the unit circle in P2
is the unit hyperbola in P2.
gives the Fermat cubic surface in P3 with 27 lines. The 27 lines in this example are easy to describe explicitly: they are the 9 lines of the form (x : ax : y : by) where a and b are fixed numbers with cube −1, and their 18 conjugates under permutations of coordinates.
gives a K3 surface in P3.
Homogeneous polynomials
Algebraic varieties
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https://en.wikipedia.org/wiki/Peyman%20Faratin
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Peyman Faratin (born September 16, 1965) is an Iranian/American computer scientist, and the founder of Robust Links, an Internet company building algorithms for creating and processing a knowledge graph.
Background
Peyman completed his PhD in computer science under the supervision of Prof. Nicholas R. Jennings and Prof. Carles Sierra. He made significant contributions in the area of artificial intelligence, particularly to automated negotiation in multi-agent systems. He was then a research scientist at MIT's Computer Science and Artificial Intelligence (CSAIL) laboratory, working with David D. Clark in the Advanced Network Architecture group.
Peyman has over eighteen years of experience in design and implementation of online marketplaces. He graduated from University of London (EECS department) in 2000 completing his doctoral thesis on algorithms for online bargaining and auction mechanisms, with application to business process management and supply chain management in telecommunication domains. Between 2000 and 2008 he was a researcher at MIT (Computer Science and AI Lab and Sloan School of Management) working with David Clark (the chief Internet protocol architect between 81 and 89) on design, analysis and implementation of various online market mechanisms for multi-scaled provisioning, control and access problems to IP networks. Work included design of various markets at both layer 3 and 7 applications. Dr. Faratin joined Strands Inc. as VP of innovation in 2008, where
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https://en.wikipedia.org/wiki/Enriques%E2%80%93Kodaira%20classification
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In mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes. For each of these classes, the surfaces in the class can be parametrized by a moduli space. For most of the classes the moduli spaces are well understood, but for the class of surfaces of general type the moduli spaces seem too complicated to describe explicitly, though some components are known.
Max Noether began the systematic study of algebraic surfaces, and Guido Castelnuovo proved important parts of the classification. described the classification of complex projective surfaces. later extended the classification to include non-algebraic compact surfaces. The analogous classification of surfaces in positive characteristic was begun by and completed by ; it is similar to the characteristic 0 projective case, except that one also gets singular and supersingular Enriques surfaces in characteristic 2, and quasi-hyperelliptic surfaces in characteristics 2 and 3.
Statement of the classification
The Enriques–Kodaira classification of compact complex surfaces states that every nonsingular minimal compact complex surface is of exactly one of the 10 types listed on this page; in other words, it is one of the rational, ruled (genus > 0), type VII, K3, Enriques, Kodaira, toric, hyperelliptic, properly quasi-elliptic, or general type surfaces.
For the 9 classes of surfaces other than general type, there is a fairly complete description of what all the surfaces l
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https://en.wikipedia.org/wiki/Dave%20Hill%20%28automotive%20engineer%29
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David C. Hill (born January 15, 1943) is a former automotive engineer for General Motors. He is best known as the Chief Engineer for the 5th (C5) and 6th (C6) generations of the Chevrolet Corvette.
He graduated from Michigan Tech and from the University of Michigan (M.A., Mechanical Engineering 1970), and began his career at GM in engine engineering for Cadillac in 1965, and moved into engineering management assignments for Cadillac in the mid-1970s, rising to the position of Engineering Program Manager in early 1992. He officially became the third Chief Engineer for the Corvette on November 18, 1992. He retired on January 1, 2006, and was succeeded as Corvette Chief Engineer by Tadge Juechter.
References
http://www.corvetteactioncenter.com/history/hill.html
American automotive engineers
1943 births
Living people
General Motors former executives
Michigan Technological University alumni
20th-century American businesspeople
University of Michigan College of Engineering alumni
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https://en.wikipedia.org/wiki/Kalb%E2%80%93Ramond%20field
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In theoretical physics in general and string theory in particular, the Kalb–Ramond field (named after Michael Kalb and Pierre Ramond), also known as the Kalb–Ramond B-field or Kalb–Ramond NS–NS B-field, is a quantum field that transforms as a two-form, i.e., an antisymmetric tensor field with two indices.
The adjective "NS" reflects the fact that in the RNS formalism, these fields appear in the NS–NS sector in which all vector fermions are anti-periodic. Both uses of the word "NS" refer to André Neveu and John Henry Schwarz, who studied such boundary conditions (the so-called Neveu–Schwarz boundary conditions) and the fields that satisfy them in 1971.
Details
The Kalb–Ramond field generalizes the electromagnetic potential but it has two indices instead of one. This difference is related to the fact that the electromagnetic potential is integrated over one-dimensional worldlines of particles to obtain one of its contributions to the action while the Kalb–Ramond field must be integrated over the two-dimensional worldsheet of the string. In particular, while the
action for a charged particle moving in an electromagnetic
potential is given by
that for a string coupled to the Kalb–Ramond field has the form
This term in the action implies that the fundamental string of string theory is a source of the NS–NS B-field, much like charged particles are sources of the electromagnetic field.
The Kalb–Ramond field appears, together with the metric tensor and dilaton, as a set of mass
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https://en.wikipedia.org/wiki/Rho%20meson
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In particle physics, a rho meson is a short-lived hadronic particle that is an isospin triplet whose three states are denoted as , and . Along with pions and omega mesons, the rho meson carries the nuclear force within the atomic nucleus. After the pions and kaons, the rho mesons are the lightest strongly interacting particle, with a mass of for all three states.
The rho mesons have a very short lifetime and their decay width is about with the peculiar feature that the decay widths are not described by a Breit–Wigner form. The principal decay route of the rho mesons is to a pair of pions with a branching rate of 99.9%.
History
After several false starts, the ρ meson and the ω meson were discovered at Lawrence Berkeley Laboratory in 1961.
Composition
The rho mesons can be interpreted as a bound state of a quark and an anti-quark and is an excited version of the pion. Unlike the pion, the rho meson has spin j = 1 (a vector meson) and a much higher value of the mass. This mass difference between the pions and rho mesons is attributed to a large hyperfine interaction between the quark and anti-quark. The main objection with the De Rujula–Georgi–Glashow description is that it attributes the lightness of the pions as an accident rather than a result of chiral symmetry breaking.
The rho mesons can be thought of as the gauge bosons of a spontaneously broken gauge symmetry whose local character is emergent (arising from QCD); Note that this broken gauge symmetry (sometimes cal
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https://en.wikipedia.org/wiki/Goldberger%E2%80%93Wise%20mechanism
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In particle physics, the Goldberger–Wise mechanism is a popular mechanism that determines the size of the fifth dimension in Randall–Sundrum models. The mechanism uses a scalar field that propagates throughout the five-dimensional bulk. On each of the branes that end the fifth dimension (frequently referred to as the Planck brane and TeV brane, respectively) there is a potential for this scalar field. The minima for the potentials on the Planck brane and TeV brane are different and causes the vacuum expectation value of the scalar field to change throughout the fifth dimension. This configuration generates a potential for the radion causing it to have a vacuum expectation value and a mass. With reasonable values for the scalar potential, the size of the extra dimension is large enough to solve the hierarchy problem.
References
Physics beyond the Standard Model
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https://en.wikipedia.org/wiki/Fuzzy%20sphere
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In mathematics, the fuzzy sphere is one of the simplest and most canonical examples of non-commutative geometry. Ordinarily, the functions defined on a sphere form a commuting algebra. A fuzzy sphere differs from an ordinary sphere because the algebra of functions on it is not commutative. It is generated by spherical harmonics whose spin l is at most equal to some j. The terms in the product of two spherical harmonics that involve spherical harmonics with spin exceeding j are simply omitted in the product. This truncation replaces an infinite-dimensional commutative algebra by a -dimensional non-commutative algebra.
The simplest way to see this sphere is to realize this truncated algebra of functions as a matrix algebra on some finite-dimensional vector space.
Take the three j-dimensional matrices that form a basis for the j dimensional irreducible representation of the Lie algebra su(2). They satisfy the relations , where is the totally antisymmetric symbol with , and generate via the matrix product the algebra of j dimensional matrices. The value of the su(2) Casimir operator in this representation is
where I is the j-dimensional identity matrix.
Thus, if we define the 'coordinates'
where r is the radius of the sphere and k is a parameter, related to r and j by , then the above equation concerning the Casimir operator can be rewritten as
,
which is the usual relation for the coordinates on a sphere of radius r embedded in three dimensional space.
One can defi
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https://en.wikipedia.org/wiki/Anatoly%20Babko
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Anatoly Babko (15 October 1905 in Sudzhenskoye, Tomsk Governorate – 7 January 1968) was a Soviet chemist, specializing in analytical chemistry and in the chemistry of complex compounds.
Babko was a student of Professor N. Tananaev, a Member of the Academy of Sciences of the Ukrainian Soviet Republic (since 1957), and an Honoured Science Worker of the Ukrainian SSR (after 1966). In 1939, he organized the research department at the Institute of General and Inorganic Chemistry of the Ukrainian SSR, and managed it until the end of his life. In 1943 he was appointed to a professorship, and in 1944 became the Head of the Department of Analytical Chemistry at the University of Kyiv.
Babko's main works are devoted to the physical chemistry of complex compounds and their use in analytical chemistry as well as photometric and fluorescence methods of analysis.
He published more than 450 scientific works and 9 books that have been translated into several languages.
References
1905 births
1968 deaths
People from Anzhero-Sudzhensk
People from Tomsk Governorate
Soviet chemists
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https://en.wikipedia.org/wiki/Josif%20Shtokalo
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Josif Zakharovich Shtokalo (; November 16, 1897 – January 5, 1987) was a famous Ukrainian mathematician. Shtokalo worked mainly in the areas of differential equations, operational calculus and the history of mathematics.
Investigation of the Stability of Lindstedt's Equation Using Shtokalo’s Method by Samuel Kohn contains a description of Shotkalo's method in English.
References
1897 births
1987 deaths
Soviet mathematicians
20th-century Ukrainian mathematicians
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https://en.wikipedia.org/wiki/Alfonso%20G%C3%B3mez-Lobo
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Alfonso Gómez-Lobo (January 1, 1940 – December 31, 2011) was a professor of metaphysics and moral philosophy at Georgetown University known for his critical evaluations of modern-day ethics. He was a member of The President's Council on Bioethics of the United States.
Born in Viña del Mar, Chile in 1940, Gomez-Lobo studied at the Pontifical Catholic University of Valparaiso, the University of Athens in Greece and three German universities: the University of Tübingen, the University of Munich and the University of Heidelberg. He completed his PhD in Munich in Philosophy, Classic and Ancient History in 1966, graduating magna cum laude. He then went on to teach at universities in Valparaiso, Puerto Rico, and finally at Penn State before joining with Georgetown University in 1977.
He has received a number of awards and several research fellowships, including one from the Guggenheim Foundation. His work translating Ancient Greek texts into Spanish has also received considerable attention.
References
External links
His profile at Georgetown University
Speech by Dr. Gomez-Lobo at the Greek Letters Celebration, January 28, 2000
American philosophy academics
Chilean philosophers
Pontifical Catholic University of Valparaíso alumni
Georgetown University faculty
1940 births
2011 deaths
Bioethicists
Chilean translators
20th-century translators
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https://en.wikipedia.org/wiki/Zero%20point
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Zero point may refer to:
The hypocenter of a nuclear explosion
Origin (mathematics), a fixed point of reference for a coordinate system
Zero Point (film), an Estonian film
Zero point (photometry), a calibration mechanism for magnitude in astronomy
Zero Point (South Georgia), a point in Possession Bay, South Georgia
Zero Point Interchange, a cloverleaf interchange in Islamabad, Pakistan, at the intersection of Islamabad Highway, Kashmir Highway and Khayaban-e-Suharwardy
Zero Point railway station, a railway station on the Pakistan–India border
Lingdian (band) (), sometimes translated in English as Zero Point, a Chinese band
"Zero Point", a song by Tori Amos, released on A Piano: The Collection
Zero Point, a fictional orb of energy in Fortnite Battle Royale
See also
Zero-point energy, the minimum energy a quantum mechanical system may have
Zero-point field, a synonym for the vacuum state in quantum field theory
Hofstadter zero-point, a special point associated with every plane triangle
Point of origin (disambiguation)
Triple zero (disambiguation)
Point Zero (disambiguation)
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https://en.wikipedia.org/wiki/Vladimir%20Potapov
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Vladimir Petrovich Potapov (24 January 1914 – 21 December 1980) was a Soviet mathematician. He was born in Odesa and died in Kharkiv.
External links
Vladimir Petrovich Potapov at the MacTutor History of Mathematics archive
Soviet mathematicians
1914 births
1980 deaths
People from Odesa
Academic staff of K. D. Ushinsky South Ukrainian National Pedagogical University
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https://en.wikipedia.org/wiki/Edward%20Ginzton
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Edward Leonard Ginzton (December 27, 1915 – August 13, 1998) was a Ukrainian-American engineer.
Education
Ginzton completed his B.S. (1936) and M.S. (1937) in Electrical Engineering at the University of California, Berkeley, and his Ph.D. in electrical engineering from Stanford University in 1941.
Career
As a student at Stanford University, Ginzton worked with William Hansen and brothers Russell and Sigurd Varian. In 1941 he became a member of the Varian–Hansen group at the Sperry Gyroscope Company.
Ginzton was appointed assistant professor in physics at Stanford University in 1945 and remained on the faculty until 1961.
In 1949, Ginzton and Marvin Chodorow developed the 1 BeV 220-foot accelerator at Stanford University. After completion of the 1 BeV accelerator, Ginzton became director of the Microwave Laboratory, which was later renamed the Ginzton Laboratory.
Ginzton, along with Russell and Sigurd Varian, was one of the original board members of Varian Associates, founded in 1948. The nine initial directors of the company were Ginzton, Russell, Sigurd, and Dorothy Varian, H. Myrl Stearns, Stanford University faculty members William Webster Hansen, and Leonard I. Schiff, legal counsel Richard M. Leonard, and patent attorney Paul B. Hunter.
Ginzton became CEO and chairman of Varian Associates after Russell Varian died of a heart attack and Sigurd Varian died in a plane crash.
Ginzton was awarded the IEEE Medal of Honor in 1969 for "his outstanding contributions in ad
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https://en.wikipedia.org/wiki/Anatoly%20Samoilenko
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Anatoly Mykhailovych Samoilenko () (2 January 1938 – 4 December 2020) was a Ukrainian mathematician, an Academician of the National Academy of Sciences of Ukraine (since 1995), the Director of the Institute of Mathematics of the National Academy of Sciences of Ukraine (since 1988).
Biography
Anatoly Samoilenko was born in 1938 in the village of Potiivka, Radomyshl district, Zhytomyr region. In 1955, he entered the Geologic Department at the Shevchenko Kyiv State University. In 1960, Samoilenko graduated from the Department of Mechanics and Mathematics at the Shevchenko Kyiv State University with mathematics specialization. At the same time, his first scientific works were published.
In 1963, after the graduation from the postgraduate courses at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR, Samoilenko defended his candidate-degree thesis "Application of Asymptotic Methods to the Investigation of Nonlinear Differential Equations with Irregular Right-Hand Side" and began his work at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR under the supervision of Academician Yu. A. Mitropolskiy. In few years of diligent research work, Samoilenko became one of the leading experts in the qualitative theory of differential equations. In 1967, based on the results of his research in the theory of multifrequency oscillations, he defended his doctoral-degree thesis "Some Problems of the Theory of Periodic and Quasiperiodic Systems
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https://en.wikipedia.org/wiki/Volodymyr%20Marchenko
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Volodymyr Oleksandrovych Marchenko (; born 7 July 1922) is a Soviet and Ukrainian mathematician who specializes in mathematical physics.
Biography
He was born in Kharkiv in 1922. He defended his PhD thesis in 1948 under the supervision of Naum Landkof, and in 1951, he defended his DSc thesis. He worked in Kharkiv University until 1961. For 4 decades, he headed the Mathematical Physics Department at the Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine.
He was awarded the Lenin Prize in 1962, the N. N. Krylov Prize in 1980, the State Prize of Ukraine in Science and Technology in 1989, and the N. N. Bogolyubov prize in 1996. Since 1969 he is a member of the National Academy of Sciences of Ukraine, since 1987 of the Russian Academy of Sciences and since 2001 of the Royal Norwegian Society of Sciences and Letters.
Marchenko turned 100 on July 7, 2022.
Work
Differential operators
Marchenko made fundamental contributions to the analysis of the Sturm–Liouville operators. He introduced one of the approaches to the inverse scattering problem for Sturm–Liouville operators, and derived what is now called the Marchenko equation.
Random matrices
Together with Leonid Pastur, Volodymyr Marchenko discovered the Marchenko–Pastur law in random matrix theory.
Homogenization
Together with E. Ya. Khruslov, Marchenko authored one of the first mathematical books on homogenization.
Integrable systems
Notes
Selected publications
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https://en.wikipedia.org/wiki/Mikhail%20Kravchuk
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Mykhailo Pylypovych Kravchuk, also Krawtchouk () (September 27, 1892 – March 9, 1942), was a Soviet Ukrainian mathematician and the author of around 180 articles on mathematics.
He primarily wrote papers on differential equations and integral equations, studying both their theory and applications. His two-volume monograph on the solution of linear differential and integral equations by the method of moments was translated 1938–1942 by John Vincent Atanasoff who found this work useful in his computer-project (Atanasoff–Berry computer). His student Klavdiya Latysheva was the first Ukrainian woman to obtain a doctorate in the mathematical and physical sciences (1936).
Kravchuk held a mathematics chair at the Kyiv Polytechnic Institute. His course listeners included Sergey Korolev, Arkhip Lyulka, and Vladimir Chelomei, future leading rocket and jet engine designers. Kravchuk was arrested by the Soviet secret police on February 23, 1938 on political and spying charges. He was sentenced to 20 years of prison in September 1938. Kravchuk died in a Gulag camp in the Kolyma region on March 9, 1942. In September 1956 Kravchuk was posthumously acquitted of all charges.
He was restored as a member of the National Academy of Sciences of Ukraine posthumously in 1992. He is the eponym of the Kravchuk polynomials and Kravchuk matrix.
References
External links
MacTutor biography
Biography page(this uses the transliteration Mikhail Krawtchouk, which is phonetic for Francophones, and un
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https://en.wikipedia.org/wiki/David%20Awschalom
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David D. Awschalom (born 1956 in Baton Rouge, Louisiana, United States) is an American condensed matter experimental physicist. He is best known for his work in spintronics in semiconductors.
Awschalom graduated from the University of Illinois at Urbana–Champaign with a B.Sc. in physics. He received a Ph.D. in experimental physics from Cornell University. He is the director of the Chicago Quantum Exchange and a Liew Family Professor in Molecular Engineering at the University of Chicago's Pritzker School of Molecular Engineering (PME). He previously served as the director of the California Nanosystems Institute and was a professor in the physics department at the University of California, Santa Barbara as well as an associated faculty member in the department of electrical and computer engineering. He has a Hirsch number of 96.
Awards and honors
elected Fellow of the American Physical Society (1992)
Oliver E. Buckley Prize by the American Physical Society (2005)
Agilent Europhysics Prize by the European Physical Society (2005)
elected fellow of the American Academy of Arts and Sciences (2006)
elected member of National Academy of Sciences (2007)
Turnbull Lectureship Award from the Materials Research Society (2010)
elected member of National Academy of Engineering (2011)
References
External links
Official Biographical Info
Buckley Prize press release
Europhysics Prize
1956 births
Living people
Grainger College of Engineering alumni
Cornell University alumni
21st-c
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https://en.wikipedia.org/wiki/Ciprian%20Manolescu
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Ciprian Manolescu (born December 24, 1978) is a Romanian-American mathematician, working in gauge theory, symplectic geometry, and low-dimensional topology. He is currently a professor of mathematics at Stanford University.
Biography
Manolescu completed his first eight classes at School no. 11 Mihai Eminescu and his secondary education at Ion Brătianu High School in Piteşti. He completed his undergraduate studies and PhD at Harvard University under the direction of Peter B. Kronheimer. He was the winner of the Morgan Prize, awarded jointly by AMS-MAA-SIAM, in 2002. His undergraduate thesis was on Finite dimensional approximation in Seiberg–Witten theory, and his PhD thesis topic was A spectrum valued TQFT from the Seiberg–Witten equations.
In early 2013, he released a paper detailing a disproof of the triangulation conjecture for manifolds of dimension 5 and higher. For this paper, he received the E. H. Moore Prize from the American Mathematical Society.
Awards and honors
He was among the recipients of the Clay Research Fellowship (2004–2008).
In 2012, he was awarded one of the ten prizes of the European Mathematical Society for his work on low-dimensional topology, and particularly for his role in the development of combinatorial Heegaard Floer homology.
He was elected as a member of the 2017 class of Fellows of the American Mathematical Society "for contributions to Floer homology and the topology of manifolds".
In 2018, he was an invited speaker at the International
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https://en.wikipedia.org/wiki/Roboteer
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The word roboteer refers to those with interests or careers in robotics. It dates back to the 1930s and is also used in 'Future Shock' (1970).
The term roboteer was used by Barbara Krasnov for a story on Deb Huglin, owner of the Robotorium, Inc., in New York City in the early 1980s. Huglin was a lightweight-robotics applications consultant, sculptor, and repatriation archeologist. Huglin worked with Jim Henson on the design and uses of the robotic mit controller for his experimental television series "Fraggle Rock". Huglin died in a fall in the wilderness near Hemet, California in 2008.
See also
Roboticist
References
External links
Debbie the Roboteer on IMDB.
Robotics
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https://en.wikipedia.org/wiki/Mykhailo%20Maksymovych
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Mykhailo Oleksandrovych Maksymovych (; 3 September 1804 – 10 November 1873) was a famous professor in plant biology, Ukrainian historian and writer in the Russian Empire of a Cossack background.
He contributed to the life sciences, especially botany and zoology, and to linguistics, folklore, ethnography, history, literary studies, and archaeology.
In 1871, he was elected as a corresponding member of the Russian Academy of Sciences, Russian language and literature department. Maksymovych also was a member of the Nestor the Chronicler Historical Association that existed in Kyiv in 1872-1931.
Life
Maksymovych was born into an old Zaporozhian Cossack family which owned a small estate on Mykhailova Hora near Prokhorivka, Zolotonosha county in Poltava Governorate (now in Cherkasy Oblast) in Left-bank Ukraine. After receiving his high school education at Novhorod-Siverskyi Gymnasium, he studied natural science and philology at philosophy faculty of Moscow University and later the medical faculty, graduating with his first degree in 1823, his second in 1827; thereafter, he remained at the university in Moscow for further academic work in botany. In 1833 he received his doctorate and was appointed as a professor for the chair of botany in the Moscow University.
He taught biology and was director of the botanical garden at the university. During this period, he published extensively on botany and also on folklore and literature, and got to know many of the leading lights of Russi
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https://en.wikipedia.org/wiki/Nikolay%20Krylov%20%28mathematician%2C%20born%201879%29
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Nikolay Mitrofanovich Krylov (, ; – May 11, 1955) was a Russian and Soviet mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.
Biography
Nikolay Krylov graduated from St. Petersburg State Mining Institute in 1902. In the period from 1912 until 1917, he held the Professor position in this institute. In 1917, he went to the Crimea to become Professor at the Crimea University. He worked there until 1922 and then moved to Kyiv to become chairman of the mathematical physics department at the Ukrainian Academy of Sciences.
Nikolay Krylov was a member of the Société mathématique de France and the American Mathematical Society.
Research
Nikolay Krylov developed new methods for analysis of equations of mathematical physics, which can be used not only for proving the existence of solutions but also for their construction. Since 1932, he worked together with his student Nikolay Bogolyubov on mathematical problems of non-linear mechanics. In this period, they invented certain asymptotic methods for integration of non-linear differential equations, studied dynamical systems, and made significant contributions to the foundations of non-linear mechanics. They proved the first theorems on existence of invariant measures known as Krylov–Bogolyubov theorems, introduced the Krylov–Bogoliubov averaging method and, together with Yurii Mitropolskiy, developed the Krylov–Bogoliubov–Mitropolskiy asymptotic met
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https://en.wikipedia.org/wiki/Vafa%E2%80%93Witten%20theorem
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In theoretical physics, the Vafa–Witten theorem, named after Cumrun Vafa and Edward Witten, is a theorem that shows that vector-like global symmetries (those that transform as expected under reflections) such as isospin and baryon number in vector-like gauge theories like quantum chromodynamics cannot be spontaneously broken as long as the theta angle is zero. This theorem can be proved by showing the exponential fall off of the propagator of fermions.
See also
F-theory
References
Gauge theories
Theorems in quantum mechanics
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https://en.wikipedia.org/wiki/Solution
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Solution may refer to:
Solution (chemistry), a mixture where one substance is dissolved in another
Solution (equation), in mathematics
Numerical solution, in numerical analysis, approximate solutions within specified error bounds
Solution, in problem solving
Solution, in solution selling
Other uses
V-STOL Solution, an ultralight aircraft
Solution (band), a Dutch rock band
Solution (Solution album), 1971
Solution A.D., an American rock band
Solution (Cui Jian album), 1991
Solutions (album), a 2019 album by K.Flay
See also
The Solution (disambiguation)
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https://en.wikipedia.org/wiki/Weil%27s%20conjecture%20on%20Tamagawa%20numbers
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In mathematics, the Weil conjecture on Tamagawa numbers is the statement that the Tamagawa number of a simply connected simple algebraic group defined over a number field is 1. In this case, simply connected means "not having a proper algebraic covering" in the algebraic group theory sense, which is not always the topologists' meaning.
History
calculated the Tamagawa number in many cases of classical groups and observed that it is an integer in all considered cases and that it was equal to 1 in the cases when the group is simply connected. The first observation does not hold for all groups: found examples where the Tamagawa numbers are not integers. The second observation, that the Tamagawa numbers of simply connected semisimple groups seem to be 1, became known as the Weil conjecture.
Robert Langlands (1966) introduced harmonic analysis methods to show it for Chevalley groups. K. F. Lai (1980) extended the class of known cases to quasisplit reductive groups. proved it for all groups satisfying the Hasse principle, which at the time was known for all groups without E8 factors. V. I. Chernousov (1989) removed this restriction, by proving the Hasse principle for the resistant E8 case (see strong approximation in algebraic groups), thus completing the proof of Weil's conjecture. In 2011, Jacob Lurie and Dennis Gaitsgory announced a proof of the conjecture for algebraic groups over function fields over finite fields.
Applications
used the Weil conjecture to calculate th
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https://en.wikipedia.org/wiki/Quirico%20Filopanti
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Giuseppe Barilli (20 April 1812 – 18 December 1894), also known under his pseudonym Quirico Filopanti, was an Italian mathematician and politician.
Biography
Barilli was born in Budrio, near Bologna, Italy, on 20 April 1812. He graduated in 1834 in mathematics and became professor of mechanics and hydraulics in 1848.
He was actively committed in the political affairs of the Italian unification movement and in 1849 took part in the establishment of the Roman Republic. He was appointed secretary of the Assemblea Costituente (constituent assembly) and was the author of the Decreto Fondamentale ("Fundamental Decree") which on 9 February 1849 declared the temporal government of the Pope as forfeited and proclaimed the Republic.
After the fall of the Republic he found shelter in the United States and afterwards in London, United Kingdom. Even after the formation of the Kingdom of Italy and his return to Italy, he had to leave his appointment as teacher of mechanics at the University of Bologna since he repeatedly refused to take his oath of allegiance to the monarchy. In 1876 he was elected as a member of the Parliament for the Republican Party. He died poor in Bologna in 1894.
In his work Miranda in 1858 he develops the idea of time zones. Filopanti's hypothesis was to ideally split up the earth into 24 areas (zones) along the lines of the meridians, each of which should have its own time. Each time zone should differ from the next by one hour, whereas minutes and seconds shou
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https://en.wikipedia.org/wiki/List%20of%20eponyms%20of%20special%20functions
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This is a list of special function eponyms in mathematics, to cover the theory of special functions, the differential equations they satisfy, named differential operators of the theory (but not intended to include every mathematical eponym). Named symmetric functions, and other special polynomials, are included.
A
Niels Abel: Abel polynomials - Abelian function - Abel–Gontscharoff interpolating polynomial
Sir George Biddell Airy: Airy function
Waleed Al-Salam (1926–1996): Al-Salam polynomial - Al Salam–Carlitz polynomial - Al Salam–Chihara polynomial
C. T. Anger: Anger–Weber function
Kazuhiko Aomoto: Aomoto–Gel'fand hypergeometric function - Aomoto integral
Paul Émile Appell (1855–1930): Appell hypergeometric series, Appell polynomial, Generalized Appell polynomials
Richard Askey: Askey–Wilson polynomial, Askey–Wilson function (with James A. Wilson)
B
Ernest William Barnes: Barnes G-function
E. T. Bell: Bell polynomials
Bender–Dunne polynomial
Jacob Bernoulli: Bernoulli polynomial
Friedrich Bessel: Bessel function, Bessel–Clifford function
H. Blasius: Blasius functions
R. P. Boas, R. C. Buck: Boas–Buck polynomial
Böhmer integral
Erland Samuel Bring: Bring radical
de Bruijn function
Buchstab function
Burchnall, Chaundy: Burchnall–Chaundy polynomial
C
Leonard Carlitz: Carlitz polynomial
Arthur Cayley, Capelli: Cayley–Capelli operator
Celine's polynomial
Charlier polynomial
Pafnuty Chebyshev: Chebyshev polynomials
Elwin Bruno Christoffel, Darboux: Christoffel–Darboux re
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https://en.wikipedia.org/wiki/Whittaker%20function
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In mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by to make the formulas involving the solutions more symmetric. More generally, introduced Whittaker functions of reductive groups over local fields, where the functions studied by Whittaker are essentially the case where the local field is the real numbers and the group is SL2(R).
Whittaker's equation is
It has a regular singular point at 0 and an irregular singular point at ∞.
Two solutions are given by the Whittaker functions Mκ,μ(z), Wκ,μ(z), defined in terms of Kummer's confluent hypergeometric functions M and U by
The Whittaker function is the same as those with opposite values of , in other words considered as a function of at fixed and it is even functions. When and are real, the functions give real values for real and imaginary values of . These functions of play a role in so-called Kummer spaces.
Whittaker functions appear as coefficients of certain representations of the group SL2(R), called Whittaker models.
References
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Further reading
Special hypergeometric functions
E. T. Whittaker
Special functions
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https://en.wikipedia.org/wiki/Heteropolymetalate
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In chemistry, the heteropolymetalates are a subset of the polyoxometalates, which consist of three or more transition metal oxyanions linked together by shared oxygen atoms to form a closed 3-dimensional molecular framework. In contrast to isopolymetalates, which contain only one kind of metal atom, the heteropolymetalates contain differing main group oxyanions. The metal atoms are usually group 6 (Mo, W) or less commonly group 5 (V, Nb, Ta) transition metals in their highest oxidation states. They are usually colorless to orange, diamagnetic anions. For most heteropolymetalates the W, Mo, or V, is complemented by main group oxyanions phosphate and silicate. Many exceptions to these general statements exist, and the class of compounds includes hundreds of examples.
Structure
Certain structural motifs recur. The Keggin ion for example is common to both molybdates and tungstates with diverse central heteroatoms. The Keggin and Dawson structures have tetrahedrally-coordinated heteroatoms, such as P or Si, and the Anderson structure has an octahedral central atom, such as aluminium.
Heteropolyacids
Generally, the heteropolymetalates are more thermally robust than homopolymetalates. This trend reflects the stabilizing influence of the tetrahedral oxyanion that "glues" together the transition metal oxo framework. One reflection of their ruggedness, heteropolymetalates can be isolated in their acid form, whereas homopolymetalates typically cannot. Examples include:
Silicotungstic
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https://en.wikipedia.org/wiki/Craig%20Kennedy
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Professor Craig Kennedy is a character created by Arthur B. Reeve.
Description
Kennedy is a scientist detective at Columbia University similar to Sherlock Holmes and Dr. Thorndyke. He uses his knowledge of chemistry and psychoanalysis to solve cases, and uses exotic (at the time) devices in his work such as lie detectors, gyroscopes, and portable seismographs. Like Holmes and Thorndyke, Kennedy also has a companion who narrates his adventures in the form of reporter Walter Jameson.
Kennedy first appeared in the December 1910 issue of Cosmopolitan, in "The Case of Helen Bond." He ultimately made 82 appearances in Cosmopolitan, the last coming in the August 1918 issue. Twelve stories were reprinted in the first collection, and this continued, but soon the stories were fixed up into a novel, and some were adaptations of movie serials.
He returned for many short stories in magazines as various as The Popular Magazine, Detective Story Magazine, Country Gentleman, Everybody's Magazine, and Flynn's, as well as in 26 novels. Through the 1920s, he became more of a typical detective. Craig Kennedy appeared in a number of 1930s pulp magazines, Complete Detective Novel Magazine, Dime Detective, Popular Detective, Weird Tales, and World Man Hunters, but many of these appear to be ghost-written as they lack the style and flavor of the teen-era Craig Kennedy stories. A series of six Craig Kennedy stories in early issues of Popular Detective are known to have been unsold novelettes rewrit
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https://en.wikipedia.org/wiki/Spatial%20frequency
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In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components (as determined by the Fourier transform) of the structure repeat per unit of distance.
The SI unit of spatial frequency is the reciprocal metre (m-1), although cycles per meter (c/m) is also common. In image-processing applications, spatial frequency is often expressed in units of cycles per millimeter (c/mm) or also line pairs per millimeter (LP/mm).
In wave propagation, the spatial frequency is also known as wavenumber. Ordinary wavenumber is defined as the reciprocal of wavelength and is commonly denoted by or sometimes :
Angular wavenumber , expressed in radian per metre (rad/m), is related to ordinary wavenumber and wavelength by
Visual perception
In the study of visual perception, sinusoidal gratings are frequently used to probe the capabilities of the visual system, such as contrast sensitivity. In these stimuli, spatial frequency is expressed as the number of cycles per degree of visual angle. Sine-wave gratings also differ from one another in amplitude (the magnitude of difference in intensity between light and dark stripes), orientation, and phase.
Spatial-frequency theory
The spatial-frequency theory refers to the theory that the visual cortex operates on a code of spatial frequency, not on the code of straight edges and lines hypothesised by Hubel
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https://en.wikipedia.org/wiki/Jos%C3%A9%20Antonio%20Balseiro
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José Antonio Balseiro (March 29, 1919 in Córdoba – March 26, 1962 in Bariloche) was an Argentine physicist.
Balseiro studied at the Universidad Nacional de Córdoba in his home city, before moving to La Plata to study and research, obtaining a doctorate in physics at the Universidad Nacional de La Plata. His doctoral dissertation was directed by Dr. Guido Beck, an Austrian physicist who arrived as a refugee in 1943. In 1950 he received a scholarship granted by the British Council. Due to the limited funds provided by the scholarship, his wife and daughter remained in Argentina. Balseiro did his post-doctoral research at the University of Manchester, in the group directed by Léon Rosenfeld. His father was Galician and his mother was French.
The Argentine government requested that he return to Argentina in 1952, a few months before the expiration of his scholarship, to serve in the scientific review panel of the Huemul Project, a study on nuclear fusion conducted by Ronald Richter. Balseiro's report and those of other members of the panel finally convinced the government that the Huemul Project had no scientific merit. Based on this, and reports from a second review panel (composed of physicists Richard Gans and Antonio Rodríguez), the Huemul Project was abandoned.
Afterwards, Balseiro remained in Argentina where he was appointed director of the physics department of the Facultad de Ciencias Exactas y Naturales of the Universidad de Buenos Aires in 1952.
In 1955, using pa
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https://en.wikipedia.org/wiki/Cascading%20gauge%20theory
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In theoretical physics, a cascading gauge theory is a gauge theory whose coupling rapidly changes with the scale in such a way that Seiberg duality must be applied many times.
Igor Klebanov and Matthew Strassler studied this kind of N=1 gauge theory in the context of the AdS-CFT correspondence, which is dual to the warped deformed conifold.
See also
Ultraviolet fixed point
References
Gauge theories
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https://en.wikipedia.org/wiki/Berezinian
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In mathematics and theoretical physics, the Berezinian or superdeterminant is a generalization of the determinant to the case of supermatrices. The name is for Felix Berezin. The Berezinian plays a role analogous to the determinant when considering coordinate changes for integration on a supermanifold.
Definition
The Berezinian is uniquely determined by two defining properties:
where str(X) denotes the supertrace of X. Unlike the classical determinant, the Berezinian is defined only for invertible supermatrices.
The simplest case to consider is the Berezinian of a supermatrix with entries in a field K. Such supermatrices represent linear transformations of a super vector space over K. A particular even supermatrix is a block matrix of the form
Such a matrix is invertible if and only if both A and D are invertible matrices over K. The Berezinian of X is given by
For a motivation of the negative exponent see the substitution formula in the odd case.
More generally, consider matrices with entries in a supercommutative algebra R. An even supermatrix is then of the form
where A and D have even entries and B and C have odd entries. Such a matrix is invertible if and only if both A and D are invertible in the commutative ring R0 (the even subalgebra of R). In this case the Berezinian is given by
or, equivalently, by
These formulas are well-defined since we are only taking determinants of matrices whose entries are in the commutative ring R0. The matrix
is known as the
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https://en.wikipedia.org/wiki/IR/UV%20mixing
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In theoretical physics, it is usually possible to organize physical phenomena according to the energy scale or distance scale. The theory of renormalization group is based on this paradigm. The short-distance, ultraviolet (UV) physics does not directly affect qualitative features of the long-distance, infrared (IR) physics, and vice versa.
This separation of scales holds in quantum field theory. However, in its generalizations such as noncommutative field theory and quantum gravity—string theory in particular—it is expected that interrelations between UV and IR physics start to emerge. In many cases, these interrelations, UV/IR mixing, may be demonstrated explicitly.
Longer, technical description can be found here
See also
Hierarchy problem
Cutoff
Quantum gravity
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https://en.wikipedia.org/wiki/Harvey%20Friedman
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Harvey Friedman (born 23 September 1948) is an American mathematical logician at Ohio State University in Columbus, Ohio. He has worked on reverse mathematics, a project intended to derive the axioms of mathematics from the theorems considered to be necessary. In recent years, this has advanced to a study of Boolean relation theory, which attempts to justify large cardinal axioms by demonstrating their necessity for deriving certain propositions considered "concrete".
Friedman earned his Ph.D. from the Massachusetts Institute of Technology in 1967, with a dissertation on Subsystems of Analysis. His advisor was Gerald Sacks. Friedman received the Alan T. Waterman Award in 1984. He also assumed the title of Visiting Scientist at IBM.<ref>Barwise et al., Harvey Friedman's Research on the Foundations of Mathematics p.xiii. Studies in Logic and the Foundations of Mathematics, vol. 117, North-Holland Amsterdam</ref> He delivered the Tarski Lectures in 2007.
In 1967, Friedman was listed in the Guinness Book of World Records for being the world's youngest professor when he taught at Stanford University at age 18 as an assistant professor of philosophy.Dr. Harvey Martin Friedman - Distinctions He has also been a professor of mathematics and a professor of music. He officially retired in July 2012. In September 2013, he received an honorary doctorate from Ghent University.
Jordana Cepelewicz (2017) profiled Friedman in Nautilus as "The Man Who Wants to Rescue Infinity".
Friedman
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https://en.wikipedia.org/wiki/Massive%20gravity
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In theoretical physics, massive gravity is a theory of gravity that modifies general relativity by endowing the graviton with a nonzero mass. In the classical theory, this means that gravitational waves obey a massive wave equation and hence travel at speeds below the speed of light.
Background
Massive gravity has a long and winding history, dating back to the 1930s when Wolfgang Pauli and Markus Fierz first developed a theory of a massive spin-2 field propagating on a flat spacetime background. It was later realized in the 1970s that theories of a massive graviton suffered from dangerous pathologies, including a ghost mode and a discontinuity with general relativity in the limit where the graviton mass goes to zero. While solutions to these problems had existed for some time in three spacetime dimensions, they were not solved in four dimensions and higher until the work of Claudia de Rham, Gregory Gabadadze, and Andrew Tolley (dRGT model) in 2010.
One of the very early massive gravity theories was constructed in 1965 by Ogievetsky and Polubarinov (OP). Despite the fact that the OP model coincides with the ghost-free massive gravity models rediscovered in dRGT, the OP model has been almost unknown among contemporary physicists who work on massive gravity, perhaps because the strategy followed in that model was quite different from what is generally adopted at present. Massive dual gravity to the OP model can be obtained by coupling the dual graviton field to the curl of it
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https://en.wikipedia.org/wiki/Ernesto%20Bustamante
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Ernesto Bustamante (born May 19, 1950) is a scientist known for his expertise and contributions to the field of molecular biology. He is currently also a politician and member of the Peruvian Parliament.
Academia
He has served as professor of biochemistry at Universidad Cayetano Heredia (Lima, Peru) during eight years (1977–1984). He also was visiting professor, researcher, visiting researcher, or research scholar at the following institutions: Johns Hopkins University School of Medicine (Baltimore, Maryland, USA) [1979, 1980, 1981, 1984], Universidad de Chile Facultad de Ciencias (Santiago, Chile) [1980, 1981], and recently at the School of Medicine of the University of North Carolina at Chapel Hill (Chapel Hill, North Carolina, USA) [2002–2005].
Bustamante was a fellow from the Ford Foundation, The Commonwealth Fund of New York, Eli Lilly and Company's Pre-doctoral Fellowship in Biology, E.I. DuPont de Nemours & Co., and The Rockefeller Foundation. In 2002 he was awarded competitively a Breast Cancer Concept Award by the U.S. Department of Defense as recommended by the Congressionally-directed Medical Research Programs.
He has published over thirty peer-reviewed original research articles (Google Scholar) in the specialty of mitochondrial bioenergetics and molecular biology.
His largest contribution to biochemistry and cell biology was to demonstrate that the mitochondrial hexokinase is the enzyme responsible for driving the high rates of glycolysis that occur under ae
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https://en.wikipedia.org/wiki/Composite%20gravity
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In theoretical physics, composite gravity refers to models that attempted to derive general relativity in a framework where the graviton is constructed as a composite bound state of more elementary particles, usually fermions. A theorem by Steven Weinberg and Edward Witten shows that this is not possible in Lorentz covariant theories: massless particles with spin greater than one are forbidden. The AdS/CFT correspondence may be viewed as a loophole in their argument. However, in this case not only the graviton is emergent; a whole spacetime dimension is emergent, too.
See also
Weinberg–Witten theorem
References
Theories of gravity
Quantum gravity
Emergence
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https://en.wikipedia.org/wiki/Poole%20Grammar%20School
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Poole Grammar School (commonly abbreviated to PGS) is a selective, all‐boys grammar school and academy in the coastal town of Poole in Dorset, on the south coast of England. It is a member of the South West Academic Trust (SWAT). The school was a mathematics and computing school, with an additional specialism, cognition, added in 2006.
It is situated in the north of Poole, on the A349 (known locally as Gravel Hill), in a campus built in 1966, with various additions made since.
Admissions
The school has 1,200 male students from the surrounding area aged 11 to 18. To gain acceptance to the school, pupils must sit and pass the Eleven-plus exams, testing mathematics, English, and verbal reasoning.
Excellence in the fields of sport or arts is not grounds for special admission; however, many of its pupils compete at county, national and international level, or go on to study at film schools, conservatories and art houses.
History
An early Poole Grammar School was built in 1628 by Thomas Robarts, Mayor of Poole. This school taught "Latin grammar and kindred subjects" and saw moderate success in the 18th century, before a decline against "competition from nonconformist academies and the general economic decline of the town," and eventual closure in 1835.
In 1902 the Board of Education approved funding for the construction of Poole Technical and Commercial School, offering "an education of a practical character for boys and girls of twelve years of age and upwards."
On 19 Septem
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https://en.wikipedia.org/wiki/Four-tensor
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In physics, specifically for special relativity and general relativity, a four-tensor is an abbreviation for a tensor in a four-dimensional spacetime.
Generalities
General four-tensors are usually written in tensor index notation as
with the indices taking integer values from 0 to 3, with 0 for the timelike components and 1, 2, 3 for spacelike components. There are n contravariant indices and m covariant indices.
In special and general relativity, many four-tensors of interest are first order (four-vectors) or second order, but higher-order tensors occur. Examples are listed next.
In special relativity, the vector basis can be restricted to being orthonormal, in which case all four-tensors transform under Lorentz transformations. In general relativity, more general coordinate transformations are necessary since such a restriction is not in general possible.
Examples
First-order tensors
In special relativity, one of the simplest non-trivial examples of a four-tensor is the four-displacement
a four-tensor with contravariant rank 1 and covariant rank 0. Four-tensors of this kind are usually known as four-vectors. Here the component x0 = ct gives the displacement of a body in time (coordinate time t is multiplied by the speed of light c so that x0 has dimensions of length). The remaining components of the four-displacement form the spatial displacement vector x = (x1, x2, x3).
The four-momentum for massive or massless particles is
combining its energy (divided by c) p0
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https://en.wikipedia.org/wiki/Torsion%20%28algebra%29
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In mathematics, specifically in ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion submodule of a module is the submodule formed by the torsion elements. A torsion module is a module that equals its torsion submodule. A module is torsion-free if its torsion submodule comprises only the zero element.
This terminology is more commonly used for modules over a domain, that is, when the regular elements of the ring are all its nonzero elements.
This terminology applies to abelian groups (with "module" and "submodule" replaced by "group" and "subgroup"). This is allowed by the fact that the abelian groups are the modules over the ring of integers (in fact, this is the origin of the terminology, that has been introduced for abelian groups before being generalized to modules).
In the case of groups that are noncommutative, a torsion element is an element of finite order. Contrary to the commutative case, the torsion elements do not form a subgroup, in general.
Definition
An element m of a module M over a ring R is called a torsion element of the module if there exists a regular element r of the ring (an element that is neither a left nor a right zero divisor) that annihilates m, i.e.,
In an integral domain (a commutative ring without zero divisors), every non-zero element is regular, so a torsion element of a module over an integral domain is one annihilated by a non-zero element of the int
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https://en.wikipedia.org/wiki/List%20of%20topology%20topics
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In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing.
A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connectedness, which allows distinguishing a circle from two non-intersecting circles.
The ideas underlying topology go back to Gottfried Leibniz, who in the 17th century envisioned the and . Leonhard Euler's Seven Bridges of Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed.
This is a list of topology topics. See also:
Topology glossary
List of topologies
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https://en.wikipedia.org/wiki/Douglas%20Wiens
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Douglas Paul Wiens is a Canadian statistician; he is a professor in the Department of Mathematical and Statistical Sciences at the University of Alberta.
Wiens earned a B.Sc. in mathematics (1972), two master's degrees in mathematical logic (1974) and statistics (1979), and a Ph.D. in statistics (1982), all from the University of Calgary. As part of his work on mathematical logic, in connection with Hilbert's tenth problem, Wiens helped find a diophantine formula for the primes: that is, multivariate polynomial with the property that the positive values of this polynomial, over integer arguments, are exactly the prime numbers. Wiens and his co-authors won the Lester R. Ford award of the Mathematical Association of America in 1977 for their paper describing this result. His Ph.D. dissertation was entitled Robust Estimation for Multivariate Location and Scale in the Presence of Asymmetry and was supervised by John R. Collins. After receiving his Ph.D. in 1982, Wiens took a faculty position at Dalhousie University, and moved in 1987 to Alberta.
Wiens was editor-in-chief of The Canadian Journal of Statistics from 2004 to 2006 and program chair of the 2003 annual meeting of the Statistical Society of Canada. Along with the Ford award, Wiens received The Canadian Journal of Statistics Award in 1990 for his paper "Minimax-variance L- and R-estimators of location". In 2005 he was elected as a Fellow of the American Statistical Association.
References
External links
Home page at t
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https://en.wikipedia.org/wiki/Central%20field%20approximation
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In atomic physics, the central field approximation for many-electron atoms takes the combined electric fields of the nucleus and all the electrons acting on any of the electrons to be radial and to be the same for all the electrons in the atom. That is, every electron sees an identical potential that is only a function of its distance from the nucleus.
This facilitates an approximate analytical solution to the eigenvalue problem for the Hamiltonian operator.
References
Atomic physics
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https://en.wikipedia.org/wiki/Michael%20Sacks
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Michael Sacks (born September 11, 1948 in New York City) is an American actor and technology industry executive who played the role of Billy Pilgrim in George Roy Hill's Slaughterhouse Five (1972).
Biography
Sacks has a Bachelor of Arts in Social Relations from Harvard College and a Master of Science in Computer Science from Columbia University.
Sacks played the role of Billy Pilgrim in George Roy Hill's Slaughterhouse Five (1972), an adaptation from the novel by Kurt Vonnegut.
Sacks also appeared in Steven Spielberg's Sugarland Express (1974), as the kidnapped highway patrolman; The Private Files of J. Edgar Hoover (1977), as Melvin Purvis; The Amityville Horror (1979), as Jeff; Hanover Street (1979), with Harrison Ford; the thriller Split Image (1982); and the television disaster film Starflight: The Plane That Couldn't Land (1983). On Broadway, he was the bewildered Vietnam vet "Mark" in Kennedy's Children by Robert Patrick. He retired from the entertainment industry in 1984; his last role was in the black comedy film The House of God, with Tim Matheson.
After spending time working in technology positions on Wall Street, Sacks in 2004 joined the online bond trading company, MarketAxess, as head of global applications development. He was employed by Morgan Stanley from 1994 to 2004, as executive director, global head of bond technology for the fixed income division. Other assignments at Morgan Stanley included chief operating officer for fixed income technology and glob
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https://en.wikipedia.org/wiki/Christopher%20Glaser
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Christopher Glaser (1615 – between 1670 and 1678), a pharmaceutical chemist of the 17th century.
Life
He was born in Basel. He became demonstrator of chemistry, as successor of Lefebvre, at the Jardin du Roi in Paris, and apothecary to Louis XIV and to the Duke of Orléans.
He is best known through his Traité de la chymie (Paris, 1663), which went through some ten editions in about twenty-five years, and was translated into both German and English.
It has been alleged that he was an accomplice in the notorious poisonings carried out by Madame de Brinvilliers, but the extent of his complicity in providing Godin de Sainte-Croix poison in the Affair of the Poisons is doubtful. He appears to have died before 1676. The sal polychrestum Glaseri is normal potassium sulfate which Glaser prepared and used medicinally.
The mineral K3Na(SO4) 2 (Glaserite) is named after him.
Further reading
Mi Gyung Kim - Affinity, that Elusive Dream: A Genealogy of the Chemical Revolution (Cambridge, Mass.: MIT Press (2003) )
Martyn Paine - Materia medica and therapeutics (3 ed) (New York (1859))
Anne Somerset - The Affair of the Poisons: Murder, Infanticide, and Satanism at the Court of Louis XIV (St. Martin's Press (October 12, 2003) )
References
Attribution
External links
Long table of chemists with short note of Glaser
1615 births
1670s deaths
Swiss chemists
Swiss science writers
17th-century Swiss writers
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https://en.wikipedia.org/wiki/Gbenga%20Daniel
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Gbenga Daniel (born 6 April 1956) is a Nigerian politician who served as Senator for Ogun East since 2023. He previously served as governor of Ogun State from 2003 to 2011.
He is the owner of Kresta Laurel, an Electro-mechanical Engineering company, he started in 1990. He is also the Founder of Conference Hotels with branches in Ijebu-Ode, Sagamu, Abeokuta and Isheri part of Lagos.
As governor, his programs on Public Private Partnership attracted several businesses into the State during his tenure.
Early life and education
Gbenga Daniel was born on 6 April 1956 in Ibadan, Oyo State, to Christian parents, Most Rev. Adebola Daniel of Makun, Sagamu and Madam Olaitan Daniel of Omu-Ijebu. His father was a notable missionary of the Church of the Lord (Aladura) while his mother was a trader.
Daniel attended the Baptist Boys' High School, Abeokuta from 1969 to 1973. While there, he represented the school in debates and quiz competitions – a factor that made him exceptionally popular among his contemporaries and stimulated his inclination towards intellectual pursuits. Having graduated from the Baptist Boys High School in flying colors, he proceeded first to the School of Basic Studies at The Polytechnic, Ibadan.
for his Advanced Level (A' Level) and thereafter moved to the School of Engineering of the University of Lagos. In his early years as an undergraduate, he won several scholarships and also became well acquainted with the renowned, Prof. Ayodele Awojobi as one of the b
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https://en.wikipedia.org/wiki/International%20Mathematics%20Competition
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The International Mathematics Competition (IMC) for University Students is an annual mathematics competition open to all undergraduate students of mathematics. Participating students are expected to be at most twenty three years of age at the time of the IMC. The IMC is primarily a competition for individuals, although most participating universities select and send one or more teams of students. The working language is English.
The IMC is a residential competition and all student participants are required to stay in the accommodation provided by the organisers. It aims to provide a friendly, comfortable and secure environment for university mathematics students to enjoy mathematics with their peers from all around the world, to broaden their world perspective and to be inspired to set mathematical goals for themselves that might not have been previously imaginable or thought possible. Notably, in 2018 Caucher Birkar (born Fereydoun Derakhshani), an Iranian Kurdish mathematician, who participated in the 7th IMC held at University College London in 2000, received mathematics' most prestigious award, the Fields Medal. He is now a professor at Tsinghua University and at the University of Cambridge. In 2022 a Kyiv-born mathematician, Maryna Viazovska, was also awarded the Fields Medal. She participated in the IMC as a student four times, in 2002, 2003, 2004 and 2005. She is now a Professor and the Chair of Number Theory at the Institute of Mathematics of the École Polytechnique
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https://en.wikipedia.org/wiki/Modern%20valence%20bond%20theory
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Modern valence bond theory is the application of valence bond theory (VBT) with computer programs that are competitive in accuracy and economy with programs for the Hartree–Fock or post-Hartree-Fock methods. The latter methods dominated quantum chemistry from the advent of digital computers because they were easier to program. The early popularity of valence bond methods thus declined. It is only recently that the programming of valence bond methods has improved. These developments are due to and described by Gerratt, Cooper, Karadakov and Raimondi (1997); Li and McWeeny (2002); Joop H. van Lenthe and co-workers (2002); Song, Mo, Zhang and Wu (2005); and Shaik and Hiberty (2004)
While molecular orbital theory (MOT) describes the electronic wavefunction as a linear combination of basis functions that are centered on the various atoms in a species (linear combination of atomic orbitals), VBT describes the electronic wavefunction as a linear combination of several valence bond structures. Each of these valence bond structures can be described using linear combinations of either atomic orbitals, delocalized atomic orbitals (Coulson-Fischer theory), or even molecular orbital fragments. Although this is often overlooked, MOT and VBT are equally valid ways of describing the electronic wavefunction, and are actually related by a unitary transformation. Assuming MOT and VBT are applied at the same level of theory, this relationship ensures that they will describe the same wavefunctio
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https://en.wikipedia.org/wiki/Nuclear%20binding%20energy
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Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other. Nucleons are attracted to each other by the strong nuclear force. In theoretical nuclear physics, the nuclear binding energy is considered a negative number. In this context it represents the energy of the nucleus relative to the energy of the constituent nucleons when they are infinitely far apart. Both the experimental and theoretical views are equivalent, with slightly different emphasis on what the binding energy means.
The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons. The difference in mass can be calculated by the Einstein equation, , where E is the nuclear binding energy, c is the speed of light, and m is the difference in mass. This 'missing mass' is known as the mass defect, and represents the energy that was released when the nucleus was formed.
The term "nuclear binding energy" may also refer to the energy balance in processes in which the nucleus splits into fragments composed of more than one nucleon. If new binding energy is available when light nuclei fuse (nuclear fusion), or when heavy nuclei split (nuclear fission), either process can result in re
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https://en.wikipedia.org/wiki/Moduli%20scheme
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In mathematics, a moduli scheme is a moduli space that exists in the category of schemes developed by Alexander Grothendieck. Some important moduli problems of algebraic geometry can be satisfactorily solved by means of scheme theory alone, while others require some extension of the 'geometric object' concept (algebraic spaces, algebraic stacks of Michael Artin).
History
Work of Grothendieck and David Mumford (see geometric invariant theory) opened up this area in the early 1960s. The more algebraic and abstract approach to moduli problems is to set them up as a representable functor question, then apply a criterion that singles out the representable functors for schemes. When this programmatic approach works, the result is a fine moduli scheme. Under the influence of more geometric ideas, it suffices to find a scheme that gives the correct geometric points. This is more like the classical idea that the moduli problem is to express the algebraic structure naturally coming with a set (say of isomorphism classes of elliptic curves).
The result is then a coarse moduli scheme. Its lack of refinement is, roughly speaking, that it doesn't guarantee for families of objects what is inherent in the fine moduli scheme. As Mumford pointed out in his book Geometric Invariant Theory, one might want to have the fine version, but there is a technical issue (level structure and other 'markings') that must be addressed to get a question with a chance of having such an answer.
Teruhisa Mat
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https://en.wikipedia.org/wiki/Mario%20Salvadori
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Mario G. Salvadori (March 19, 1907 – June 25, 1997) was an American structural engineer and professor of both civil engineering and architecture at Columbia University.
Early life
Salvadori was born in Rome, Italy in 1907. His father, Riccardo, an engineer who worked for the telephone company, became the chief engineer of the city of Genoa when the phone company merged with their French counterpart. Salvadori's father later became the head of the gas and electric company in Spain. His mother, Ermelinda Alatri, belonged to a rich Jewish family. Following his father's activities, Salvadori spent many years of his youth in Madrid and only returned to Italy in 1923. Two years later, when he was 18, he started what was the first student jazz band in Italy; one of his youthful dreams was to become a concert conductor, although his parents did not encourage this. He was also a skillful mountain climber; he found several new climbing routes on Dolomites.
He earned doctoral degrees in both civil engineering and mathematics from the University of Rome in 1930 and 1933, respectively. Then he served as an instructor at Engineering department of the University of Rome and as consultant for Istituto Nazionale per le Applicazioni del Calcolo (INAC), directed by Mauro Picone, his mathematics teacher. Thanks to a grant, he went to London and in the next two years he did graduate research in photoelasticity at University College London, where he was in contact with Jews escaping from Naz
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https://en.wikipedia.org/wiki/Half%20range%20Fourier%20series
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In mathematics, a half range Fourier series is a Fourier series defined on an interval instead of the more common , with the implication that the analyzed function should be extended to as either an even (f(-x)=f(x)) or odd function (f(-x)=-f(x)). This allows the expansion of the function in a series solely of sines (odd) or cosines (even). The choice between odd and even is typically motivated by boundary conditions associated with a differential equation satisfied by .
Example
Calculate the half range Fourier sine series for the function where .
Since we are calculating a sine series,
Now,
When n is odd,
When n is even,
thus
With the special case , hence the required Fourier sine series is
Fourier series
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https://en.wikipedia.org/wiki/Why%20We%20Nap
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Why We Nap: Evolution, Chronobiology, and Functions of Polyphasic and Ultrashort Sleep is a 1992 book edited by Claudio Stampi, sole proprietor of the Chronobiology Research Institute. It is frequently mentioned by "polyphasic sleepers", as it is one of the few published books about the subject of systematic short napping in extreme situations where consolidated sleep is not possible.
According to the book, in a sleep deprived condition, measurements of a polyphasic sleeper's memory retention and analytical ability show increases as compared with monophasic and biphasic sleep (but still a decrease of 12% as compared with free running sleep). According to Stampi, the improvement is due to an extraordinary evolutionary predisposition to adopt such a sleep schedule; he hypothesizes this is possibly because polyphasic sleep was the preferred schedule of ancestors of the human race for thousands of years prior to the adoption of the monophasic schedule.
According to EEG measurements collected by Dr. Stampi during a 50-day trial of polyphasic ultrashort sleep with a test subject and published in his book Why We Nap, the proportion of sleep stages remains roughly the same during both polyphasic and monophasic sleep schedules. The major differences are that the ratio of lighter sleep stages to deeper sleep stages is slightly reduced and that sleep stages are often taken out of order or not at all, that is, some naps may be composed primarily of slow wave sleep while rapid eye move
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https://en.wikipedia.org/wiki/Moishezon%20manifold
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In mathematics, a Moishezon manifold is a compact complex manifold such that the field of meromorphic functions on each component has transcendence degree equal the complex dimension of the component:
Complex algebraic varieties have this property, but the converse is not true: Hironaka's example gives a smooth 3-dimensional Moishezon manifold that is not an algebraic variety or scheme. showed that a Moishezon manifold is a projective algebraic variety if and only if it admits a Kähler metric. showed that any Moishezon manifold carries an algebraic space structure; more precisely, the category of Moishezon spaces (similar to Moishezon manifolds, but are allowed to have singularities) is equivalent with the category of algebraic spaces that are proper over .
References
Algebraic geometry
Analytic geometry
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https://en.wikipedia.org/wiki/David%20Hull%20%28philosopher%29
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David Lee Hull (15 June 1935 – 11 August 2010) was an American philosopher who was most notable for founding the field philosophy of biology. Additionally, Hull is recognized within evolutionary culture studies as contributing heavily in early discussions of the conceptualization of memetics. In addition to his academic prominence, he was well known as a gay man who fought for the rights of other gay and lesbian philosophers. Hull was partnered with Richard "Dick" Wellman, a Chicago school teacher, until Wellman's passing during the drafting of Science as Process.
Education and career
Hull initially got a bachelor's degree in Biology at Illinois Wesleyan University. He then became one of the first graduates of the History and Philosophy of Science department at Indiana University (IU). After earning his PhD from IU, he taught at the University of Wisconsin–Milwaukee for 20 years before moving to Northwestern, where he taught for another 20 years. Hull was a former president of the Philosophy of Science Association, the ISHPSSB, and the Society for Systematic Biology. He was particularly well known for his argument that species are not sets or collections but rather spatially and temporally extended individuals (also called the individuality thesis or "species-as-individuals" thesis).
He is considered to have founded and systematically developed the area of philosophy of biology as it is understood in contemporary philosophy. Hull proposed an elaborate discussion of scienc
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https://en.wikipedia.org/wiki/Reshef%20Tenne
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Reshef Tenne (; 1944) is an Israeli scientist.
Biography
Born in Kibbutz Usha, Tenne received his BSc in Chemistry and Physics from Hebrew University in Jerusalem in 1969, where he also received his MSc (1971) and PhD (1976).
Academic and scientific career
He then spent three years at the Battelle Institute in Geneva, Switzerland, before joining the Weizmann Institute on 1979. He was promoted to full professor in 1995.
Tenne is the Drake Family Professor and Head of the Department of Materials and Interfaces at the Weizmann Institute of Science, and Director of the Helen and Martin Kimmel Center for Nanoscale Sciences, director of the G.Schmidt Minerva Center for Supramolecular Architectures and holds the Drake Family Chair in Nanotechnology. Tenne recently joined the Advisory Board of the newly launched Veruscript Functional Nanomaterials.
In 1992, following the discovery of carbon nanotubes, he predicted that nanoparticles of inorganic compounds with layered structures, such as MoS2, would not be stable against folding and would also form non-carbon nanotubes and fullerene-like structures.
Awards and recognition
In 2005, Tenne received the Materials Research Society (MRS) Medal for his work on inorganic fullerenes.
In 2020, awarded the EMET Prize
References
External links
Reshef Tenne home page at the Weizmann Institute of Science.
1944 births
Living people
Israeli scientists
Israeli chemists
Israeli nanotechnologists
Academic staff of Weizmann Institute of Science
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https://en.wikipedia.org/wiki/M.%20M.%20Pattison%20Muir
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Matthew Moncrieff Pattison Muir, FRSE, FCS (1848–1931) was a British chemist and author. He taught chemistry at Gonville and Caius College, Cambridge and was head of the Caius Laboratory there. Although he published some research on bismuth compounds, he became known through his textbooks and history of science works.
Life
He was born on 1 April 1848 in Glasgow, the son of William Muir and his wealthy wife, Margaret Moncrieff Pattison.
Muir was educated at Glasgow High School then studied Sciences at the University of Glasgow and University of Tübingen. For a short period after his studies, he was a Demonstrator at Anderson's College, Glasgow in Sir Edward Thorpe's laboratory, and also at Owens College, Manchester under Sir Henry Roscoe.
In 1873 he married Florence Haslam. In the same year he was elected a Fellow of the Royal Society of Edinburgh. His proposers were William Thomson. Lord Kelvin, James Thomson Bottomley, Sir Thomas Edward Thorpe and James Young. He resigned from the Society in 1889.
In 1877 he was appointed Praelector at Gonville and Caius College, Cambridge, and in 1881 elected a Fellow of the college. He then became head of the Caius Laboratory here, a position he held until 1908, when he retired.
At Cambridge, between 1876 and 1888, Muir lead the research on bismuth compounds, resulting in 18 papers published by him alone or together with his students in the Journal of the Chemical Society. His coauthors were all young graduates, because there were no
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https://en.wikipedia.org/wiki/Divergence%20%28disambiguation%29
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Divergence is a mathematical function that associates a scalar with every point of a vector field.
Divergence, divergent, or variants of the word, may also refer to:
Mathematics
Divergence (computer science), a computation which does not terminate (or terminates in an exceptional state)
Divergence, the defining property of divergent series; series that do not converge to a finite limit
Divergence, a result of instability of a dynamical system in stability theory
Statistics
Divergence (statistics), a measure of dissimilarity between probability measures
Bregman divergence
f-divergence
Jensen–Shannon divergence
Kullback–Leibler divergence, also known as the "information divergence" in probability theory and information theory
Rényi's divergence
Science
Divergence (eye), the simultaneous outward movement of both eyes away from each other
Divergence (optics), the angle formed between spreading rays of light
Beam divergence, the half-angle of the cone formed by a beam of light as it propagates and spreads out
Divergence problem, an anomaly between the instrumental record and temperatures calculated using some tree ring proxies
Divergent boundary, a linear feature that exists between tectonic plates that are moving away from each other
Evolutionary divergence, the accumulation of differences between populations of closely related species
Genetic divergence, the process in which two or more populations of an ancestral species accumulate independent genetic chang
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https://en.wikipedia.org/wiki/Leonardo%20Sinisgalli
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Leonardo Sinisgalli (1908–1981) was an Italian poet and art critic active from the 1930s to the 1970s.
Sinisgalli was born in Montemurro, Basilicata. His early education and careers led to him being called the "engineer poet".
In 1925, Sinisgalli moved to Rome where he studied engineering and mathematics. After completing his engineering degree in 1932, he moved to Milan where he worked as an architect and graphic artist. He was a close friend of the poet Giuseppe Ungaretti and painter Scipione. He worked at Milan for architecture and graphic design projects.
Sinisgalli's early collections such as Cuore (1927), 18 poesie (1936), Campi Elisi (1939) focused on themes from ancestral southern Italian myths. Later he explored a more relaxed style in I nuovi Campi Elisi (1947), La vigna vecchia (1952), L'età della luna (1962), Il passero e il lebbroso (1970), Mosche in bottiglia (1975) and Dimenticatoio (1978). He authored prose that analyzed the conflicts of existentialism and realism such as Fiori pari, fiori dispari (1945) and Belliboschi (1948). He also explored the scientific culture of the day in Furor mathematicus (1944) and Horror vacui (1945).
Sinisgalli founded and managed the magazine Civiltà delle Macchine (1953–1959), and was a member of the Scuola Romana. He also created two documentaries which consecutively won the Biennale di Venezia awards and edited radio broadcasting programs.
He died in Rome in 1981.
References
Luigi Beneduci, Bestiario sinisgalliano
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https://en.wikipedia.org/wiki/Christopher%20Kelk%20Ingold
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Sir Christopher Kelk Ingold (28 October 1893 – 8 December 1970) was a British chemist based in Leeds and London. His groundbreaking work in the 1920s and 1930s on reaction mechanisms and the electronic structure of organic compounds was responsible for the introduction into mainstream chemistry of concepts such as nucleophile, electrophile, inductive and resonance effects, and such descriptors as SN1, SN2, E1, and E2. He also was a co-author of the Cahn–Ingold–Prelog priority rules. Ingold is regarded as one of the chief pioneers of physical organic chemistry.
Early life and education
Born in London to a silk merchant who died of tuberculosis when Ingold was five years old, Ingold began his scientific studies at Hartley University College at Southampton (now Southampton University) taking an external BSc in 1913 with the University of London. He then joined the laboratory of Jocelyn Field Thorpe at Imperial College, London, with a brief hiatus from 1918-1920 during which he conducted research into chemical warfare and the manufacture of poison gas with Cassel Chemical at Glasgow. Ingold received an MSc from the University of London and returned to Imperial College in 1920 to work with Thorpe. He was awarded a PhD in 1918 and a DSc in 1921.
Academic career
In 1924 Ingold moved to the University of Leeds where he spent six years as Professor of Organic Chemistry. He returned to London in 1930, and served for 24 years as head of the chemistry department at University Colleg
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https://en.wikipedia.org/wiki/Grant%20O.%20Gale%20Observatory
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Grant O. Gale Observatory is an astronomical observatory owned and operated by Grinnell College Department of Physics. The observatory is located in Grinnell, Iowa (USA). Constructed in 1984, it is named after Grant O. Gale, a distinguished teacher and curator of the Grinnell Physics Historical Museum. Designed by Woodburn and O'Neil of Des Moines, the building is a 38-foot by 55-foot structure rising 26 feet to the top of the dome. It houses a 24-inch Cassegrain reflecting telescope built by DFM Engineering of Longmont, Colorado. The observatory houses two computer systems: the first controls the telescope and the second accommodates data acquisition and analysis and can be used to store television images. In addition to its primary function as an instructional and research tool, the observatory is also a facility for public viewing of astronomical phenomena under staff supervision.
See also
List of astronomical observatories
References
External links
Grant O. Gale Observatory Clear Sky Clock Forecasts of observing conditions.
Astronomical observatories in Iowa
Grinnell College
Buildings and structures in Poweshiek County, Iowa
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https://en.wikipedia.org/wiki/Royal%20Australian%20Chemical%20Institute
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The Royal Australian Chemical Institute (RACI) is both the qualifying body in Australia for professional chemists and a learned society promoting the science and practice of chemistry in all its branches. The RACI hosts conferences, seminars and workshops. It is the professional body for chemistry in Australia, with the ability to award the status of Chartered Chemist (CChem) to suitably qualified candidates.
History
The RACI was formed as the Australian Chemical Institute in Sydney in September 1917. The driving force was David Orme Masson, professor of chemistry at the University of Melbourne. It was incorporated under the Companies Act in New South Wales in 1923. It was given a royal charter in 1932, but it was not until a supplementary royal charter in 1953 that "Royal" was added to the title of the institute. It moved to Melbourne in 1934. It was incorporated in Victoria in 2000. Since 1993, the institute has had its office at 21 Vale Street, North Melbourne, VIC 3051, Australia.
Affiliations
The RACI is a member of the Federation of Australian Scientific and Technological Societies (FASTS), and the Federation of Asian Chemical Societies (FACS).
It has branches in all states and territories in Australia and divisions for the following areas of chemistry:
Analytical and Environmental chemistry
Carbon science
Chemical education
Interfaces, Colloids and Surface science
Electrochemistry
Industrial chemistry
Inorganic chemistry
Materials chemistry
Medicinal chemistry and C
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https://en.wikipedia.org/wiki/Ryotaro%20Azuma
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was a Japanese physician and bureaucrat who served as Governor of Tokyo from 1959 to 1967. In 1950, Azuma became a member of the international Olympic Committee (IOC).
Education
Born in Osaka, he attended Tokyo Imperial University and studied at the University of London, specializing in physical chemistry and physiology.
Career
He served in the Imperial Japanese Navy during World War II, took a position in the Health Ministry after the war, and later became head of Ibaraki University. In the 1950s he served as head of the Japanese Olympic Committee and played a role in bringing the 1964 Summer Olympics to Tokyo.
In 1959, he was nominated as the Liberal Democratic Party candidate for the Tokyo gubernatorial election. He defeated Socialist candidate Hachirō Arita and took office on April 27. Much of his legacy as governor surrounds the improvements to Tokyo before and during the 1964 Olympics, and accompanying pollution and administrative issues.
Personal life
In 1919, he married Teruko, a daughter of Yamakawa Kenjirō.
He is interred in the Tama Reien Cemetery in Fuchū, Tokyo, Japan.
References
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Governors of Tokyo
People from Osaka Prefecture
University of Tokyo alumni
Academic staff of the University of Tokyo
1893 births
1983 deaths
Japanese government officials
Japanese International Olympic Committee members
Recipients of the Order of the Rising Sun with Paulownia Flowers
Imperial Japanese Navy officers
Japanese military doctors
Japanese healthcare
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https://en.wikipedia.org/wiki/Rahul%20Sarpeshkar
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Rahul Sarpeshkar is the Thomas E. Kurtz Professor and a professor of engineering, professor of physics, professor of microbiology & immunology, and professor of molecular and systems biology at Dartmouth. Sarpeshkar, whose interdisciplinary work is in bioengineering, electrical engineering, quantum physics, and biophysics, is the inaugural chair of the William H. Neukom cluster of computational science, which focuses on analog, quantum, and biological computation. The clusters, designed by faculty from across the institution to address major global challenges, are part of President Philip Hanlon's vision for strengthening academic excellence at Dartmouth. Prior to Dartmouth, Sarpeshkar was a tenured professor at the Massachusetts Institute of Technology and led the Analog Circuits and Biological Systems Group. He is now also a visiting scientist at MIT's Research Laboratory of Electronics.
Research fields
His research has contributed to the fields of:
Analog circuits and analog computation
Molecular, systems, and synthetic biology
Ultra-low-power and ultra-energy-efficient systems
Energy-harvesting design
Glucose-powered medical implants
Bioelectronics
Bio-inspired and biomimetic systems
Cytomorphic (cell-inspired) systems
Analog supercomputing systems
Quantum and quantum-inspired analog computers
Medical devices
Cochlear implants
Brain-machine interfaces
Control theory
Research summary
Sarpeshkar's recent TEDx talk 'Analog Supercomputers: From Quantum Atom
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https://en.wikipedia.org/wiki/Fredholm%20alternative
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In mathematics, the Fredholm alternative, named after Ivar Fredholm, is one of Fredholm's theorems and is a result in Fredholm theory. It may be expressed in several ways, as a theorem of linear algebra, a theorem of integral equations, or as a theorem on Fredholm operators. Part of the result states that a non-zero complex number in the spectrum of a compact operator is an eigenvalue.
Linear algebra
If V is an n-dimensional vector space and is a linear transformation, then exactly one of the following holds:
For each vector v in V there is a vector u in V so that . In other words: T is surjective (and so also bijective, since V is finite-dimensional).
A more elementary formulation, in terms of matrices, is as follows. Given an m×n matrix A and a m×1 column vector b, exactly one of the following must hold:
Either: A x = b has a solution x
Or: AT y = 0 has a solution y with yTb ≠ 0.
In other words, A x = b has a solution if and only if for any y such that AT y = 0, it follows that yTb = 0 .
Integral equations
Let be an integral kernel, and consider the homogeneous equation, the Fredholm integral equation,
and the inhomogeneous equation
The Fredholm alternative is the statement that, for every non-zero fixed complex number , either the first equation has a non-trivial solution, or the second equation has a solution for all .
A sufficient condition for this statement to be true is for to be square integrable on the rectangle (where a and/or b may be minus or plus
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https://en.wikipedia.org/wiki/Kodaira%27s%20classification
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In mathematics, Kodaira's classification is either
The Enriques–Kodaira classification, a classification of complex surfaces, or
Kodaira's classification of singular fibers, which classifies the possible fibers of an elliptic fibration.
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https://en.wikipedia.org/wiki/Leo%20Palatnik
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Leo Samoylovich Palatnik (); (1909–1994) was an outstanding Ukrainian physicist known for his contributions in the field of thin film physics and film material.
External links
Leo Palatnik
20th-century Ukrainian physicists
National University of Kharkiv alumni
1909 births
1994 deaths
Laureates of the State Prize of Ukraine in Science and Technology
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https://en.wikipedia.org/wiki/Polyspermy
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In biology, polyspermy describes the fertilization of an egg by more than one sperm. Diploid organisms normally contain two copies of each chromosome, one from each parent. The cell resulting from polyspermy, on the other hand, contains three or more copies of each chromosome—one from the egg and one each from multiple sperm. Usually, the result is an unviable zygote. This may occur because sperm are too efficient at reaching and fertilizing eggs due to the selective pressures of sperm competition. Such a situation is often deleterious to the female: in other words, the male–male competition among sperm spills over to create sexual conflict.
Physiological polyspermy
Physiological polyspermy happens when the egg normally accepts more than one sperm but only one of the multiple sperm will fuse its nucleus with the nucleus of the egg. Physiological polyspermy is present in some species of vertebrates and invertebrates. Some species utilize physiological polyspermy as the proper mechanism for developing their offspring. Some of these animals include birds, ctenophora, reptiles and amphibians. Some vertebrates that are both amniote or anamniote, including urodele amphibians, cartilaginous fish, birds and reptiles, undergo physiological polyspermy because of the internal fertilization of their yolky eggs. Sperm triggers egg activation by the induction of free calcium ion concentration in the cytoplasm of the egg. This induction plays a very critical role in both physiological pol
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https://en.wikipedia.org/wiki/Cartan%27s%20criterion
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In mathematics, Cartan's criterion gives conditions for a Lie algebra in characteristic 0 to be solvable, which implies a related criterion for the Lie algebra to be semisimple. It is based on the notion of the Killing form, a symmetric bilinear form on defined by the formula
where tr denotes the trace of a linear operator. The criterion was introduced by .
Cartan's criterion for solvability
Cartan's criterion for solvability states:
A Lie subalgebra of endomorphisms of a finite-dimensional vector space over a field of characteristic zero is solvable if and only if whenever
The fact that in the solvable case follows from Lie's theorem that puts in the upper triangular form over the algebraic closure of the ground field (the trace can be computed after extending the ground field). The converse can be deduced from the nilpotency criterion based on the Jordan–Chevalley decomposition (for the proof, follow the link).
Applying Cartan's criterion to the adjoint representation gives:
A finite-dimensional Lie algebra over a field of characteristic zero is solvable if and only if (where K is the Killing form).
Cartan's criterion for semisimplicity
Cartan's criterion for semisimplicity states:
A finite-dimensional Lie algebra over a field of characteristic zero is semisimple if and only if the Killing form is non-degenerate.
gave a very short proof that if a finite-dimensional Lie algebra (in any characteristic) has a non-degenerate invariant bilinear form and
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https://en.wikipedia.org/wiki/Cyril%20Sinelnikov
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Kirill Dmitriyevich Sinelnikov (; 29 May 1901, Pavlohrad, Russian Empire — 16 October 1966, Kharkiv, Soviet Union) was a Soviet physicist of Ukrainian origin who was world renowned, considered as the greatest organizer of science the USSR has ever had. The Sinelnikov Prize for outstanding works in the field of physics is named after him.
External links
Cyril Sinelnikov
1901 births
1966 deaths
Soviet nuclear physicists
20th-century Ukrainian physicists
Academic staff of the School of Physics and Technology of University of Kharkiv
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https://en.wikipedia.org/wiki/MINDO
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MINDO, or Modified Intermediate Neglect of Differential Overlap is a semi-empirical method for the quantum calculation of molecular electronic structure in computational chemistry. It is based on the Intermediate Neglect of Differential Overlap (INDO) method of John Pople. It was developed by the group of Michael Dewar and was the original method in the MOPAC program. The method should actually be referred to as MINDO/3. It was later replaced by the MNDO method, which in turn was replaced by the PM3 and AM1 methods.
References
Semiempirical quantum chemistry methods
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https://en.wikipedia.org/wiki/Brauer%27s%20theorem%20on%20induced%20characters
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Brauer's theorem on induced characters, often known as Brauer's induction theorem, and named after Richard Brauer, is a basic result in the branch of mathematics known as character theory, within representation theory of a finite group.
Background
A precursor to Brauer's induction theorem was Artin's induction theorem, which states that |G| times the trivial character of G is an integer combination of characters which are each induced from trivial characters of cyclic subgroups of G. Brauer's theorem removes the factor |G|,
but at the expense of expanding the collection of subgroups used. Some years after the proof of Brauer's theorem appeared, J.A. Green showed (in 1955) that no such induction theorem (with integer combinations of characters induced from linear characters) could be proved with a collection of subgroups smaller than the Brauer elementary subgroups.
Another result between Artin's induction theorem and Brauer's induction theorem, also due to Brauer and also known as Brauer's theorem or Brauer's lemma is the fact that the regular representation of G can be written as where the are positive rationals and the are induced from characters of cyclic subgroups of G. Note that in Artin's theorem the characters are induced from the trivial character of the cyclic group, while here they are induced from arbitrary characters (in applications to Artin's L functions it is important that the groups are cyclic and hence all characters are linear giving that the corresp
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https://en.wikipedia.org/wiki/Apodization
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In signal processing, apodization (from Greek "removing the foot") is the modification of the shape of a mathematical function. The function may represent an electrical signal, an optical transmission, or a mechanical structure. In optics, it is primarily used to remove Airy disks caused by diffraction around an intensity peak, improving the focus.
Apodization in electronics
Apodization in signal processing
The term apodization is used frequently in publications on Fourier-transform infrared (FTIR) signal processing. An example of apodization is the use of the Hann window in the fast Fourier transform analyzer to smooth the discontinuities at the beginning and end of the sampled time record.
Apodization in digital audio
An apodizing filter can be used in digital audio processing instead of the more common brick-wall filters, in order to reduce the pre- and post-ringing that the latter introduces.
Apodization in mass spectrometry
During oscillation within an Orbitrap, ion transient signal may not be stable until the ions settle into their oscillations. Toward the end, subtle ion collisions have added up to cause noticeable dephasing. This presents a problem for the Fourier transformation, as it averages the oscillatory signal across the length of the time-domain measurement. The software allows “apodization”, the removal of the front and back section of the transient signal from consideration in the FT calculation. Thus, apodization improves the resolution of the resul
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https://en.wikipedia.org/wiki/Complex%20torus
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In mathematics, a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian product of some number N circles). Here N must be the even number 2n, where n is the complex dimension of M.
All such complex structures can be obtained as follows: take a lattice Λ in a vector space V isomorphic to Cn considered as real vector space; then the quotient group
is a compact complex manifold. All complex tori, up to isomorphism, are obtained in this way. For n = 1 this is the classical period lattice construction of elliptic curves. For n > 1 Bernhard Riemann found necessary and sufficient conditions for a complex torus to be an algebraic variety; those that are varieties can be embedded into complex projective space, and are the abelian varieties.
The actual projective embeddings are complicated (see equations defining abelian varieties) when n > 1, and are really coextensive with the theory of theta-functions of several complex variables (with fixed modulus). There is nothing as simple as the cubic curve description for n = 1. Computer algebra can handle cases for small n reasonably well. By Chow's theorem, no complex torus other than the abelian varieties can 'fit' into projective space.
Definition
One way to define complex tori is as a compact connected complex Lie group . These are Lie groups where the structure maps are holomorphic maps of complex manifolds. It turns out that all such compact conn
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https://en.wikipedia.org/wiki/Timothy%20Williamson
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Timothy Williamson (born 6 August 1955) is a British philosopher whose main research interests are in philosophical logic, philosophy of language, epistemology and metaphysics. He is the Wykeham Professor of Logic at the University of Oxford, and fellow of New College, Oxford.
Education and career
Born on 6 August 1955, Williamson's education began at Leighton Park School and continued at Henley Grammar School (now the Henley College). He then went to Balliol College, Oxford University. He graduated in 1976 with a Bachelor of Arts degree with first-class honours in mathematics and philosophy, and in 1980 with a doctorate in philosophy (DPhil) for a thesis entitled The Concept of Approximation to the Truth.
Prior to taking up the Wykeham Professorship in 2000, Williamson was Professor of Logic and Metaphysics at the University of Edinburgh (1995–2000); fellow and lecturer in philosophy at University College, Oxford (1988–1994); and lecturer in philosophy at Trinity College, Dublin (1980–1988).
He has been visiting professor at Yale University, Princeton University, MIT, the University of Michigan, and the Chinese University of Hong Kong.
He was president of the Aristotelian Society from 2004 to 2005.
He is a Fellow of the British Academy (FBA), the Norwegian Academy of Science and Letters, Fellow of the Royal Society of Edinburgh (FRSE), and a Foreign Honorary Fellow of the American Academy of Arts & Sciences.
Since 2022 he is visiting professor at the Università dell
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https://en.wikipedia.org/wiki/Hilbert%20modular%20variety
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In mathematics, a Hilbert modular surface or Hilbert–Blumenthal surface is an algebraic surface obtained by taking a quotient of a product of two copies of the upper half-plane by a Hilbert modular group. More generally, a Hilbert modular variety is an algebraic variety obtained by taking a quotient of a product of multiple copies of the upper half-plane by a Hilbert modular group.
Hilbert modular surfaces were first described by using some unpublished notes written by David Hilbert about 10 years before.
Definitions
If R is the ring of integers of a real quadratic field, then
the Hilbert modular group SL2(R) acts on the product H×H of two copies of the upper half plane H.
There are several birationally equivalent surfaces related to this action, any of which may be called Hilbert modular surfaces:
The surface X is the quotient of H×H by SL2(R); it is not compact and usually has quotient singularities coming from points with non-trivial isotropy groups.
The surface X* is obtained from X by adding a finite number of points corresponding to the cusps of the action. It is compact, and has not only the quotient singularities of X, but also singularities at its cusps.
The surface Y is obtained from X* by resolving the singularities in a minimal way. It is a compact smooth algebraic surface, but is not in general minimal.
The surface Y0 is obtained from Y by blowing down certain exceptional −1-curves. It is smooth and compact, and is often (but not always) minimal.
There a
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https://en.wikipedia.org/wiki/Mike%20Fischer
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Mike David Fischer CBE is the co-founder of the computer company RM plc.
Fischer graduated with a physics degree from Oxford University. In 1973, with Mike O'Regan (who had an economics degree from Cambridge), Fischer co-founded Research Machines, a British microcomputer and then software company for the educational market. He was CEO for 24 years and became a non-executive director and lifetime president in 1997. He stood down as a non-executive director in 2004, but retains his position as lifetime president of the company.
Fischer is a founder of the Fischer Family Trust which runs projects in health and education. In education, the key project of the Fischer Family Trust has been to change the way school performance is measured in England.
Fischer is also Director of SBL, a (Community Interest) Company dedicated to improving patient treatment options through high quality, collaborative and clinically focused research, and co–founder of Alamy Ltd, a stock photography agency. Fisher is also co-founder and Chair of Videoloft Ltd, a cloud video surveillance software platform.
He and RM co-founder Mike O'Regan were awarded honorary degrees by the Open University in 2002.
Personal life and education
Fischer completed an undergraduate degree in physics at Oxford University in 1971 and a second undergraduate degree in physiological sciences at Oxford University in 1978. He has also been awarded an honorary doctorate from the Open University in 2002 with the other RM cofound
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https://en.wikipedia.org/wiki/Michael%20O%27Regan
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Michael Rowan Hamilton John O'Regan OBE (born c. 1947) is a British businessman and the co-founder of RM plc.
O'Regan graduated with an economics degree from Cambridge University.
In 1973, with Mike Fischer (who had a physics degree from Oxford), O'Regan co-founded Research Machines, a British microcomputer and then software company for the educational market. He was an executive director until 1992, when he became a non-executive director. He has been a non-executive director of a number of other companies as well, including the Oxford Technology Venture Capital Trusts.
O'Regan was awarded an honorary degree by Oxford Brookes University in 1999. With RM co-founder, Mike Fischer O'Regan was awarded an honorary degree by the Open University in 2002.
O'Regan was awarded an OBE in the Queen's Birthday Honours in 2000. He was a governor of Oxford Brookes University and of The Oxford Academy Trust, and a Deputy Lieutenant of Oxfordshire from 2003 until 2014 when he and his wife Jane moved to Wiltshire.
O'Regan is the founder and Chair of Hamilton Trust which ran Maths Year 2000 for the British government, and co-founded early years charity Peeple.
References
External links
RM Directors Biographies, 1999
Oxford Technology VCT information
British businesspeople
Alumni of the University of Cambridge
Officers of the Order of the British Empire
1940s births
Living people
Place of birth missing (living people)
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https://en.wikipedia.org/wiki/Conrad%20Allen
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Conrad Keene Allen (born 1968 in Marion, Illinois) is an American inventor and Exploration Geologist. While exploring for oil in the Middle East, Allen discovered and mapped one of the largest helium reserves in the world. He is the inventor of the Helium Junction, which utilizes nanotechnology to separate isotopic helium from an aqueous fluid.
A recognized expert in natural resource Exploration & Production, Allen served two terms on the National Petroleum Council in Washington D.C.; first appointed in 2000 by Secretary of Energy Bill Richardson and reappointed in 2003 by Secretary Spencer Abraham. A favorite of political moderates, Allen formed a Congressional Exploratory Committee (TX-02) to challenge incumbent Ted Poe in 2009. Allen's committee notably included Texas Gubernatorial Candidate Chris Bell and US Senate Candidate Barbara Radnofsky. Allen garnered broad support in Texas and Washington D.C. before announcing that district gerrymandering engineered by Tom Delay rendered the district out of reach for a near term challenge. Poe returned to Congress unopposed. Allen name is often mentioned on the short list of potential candidates for US Congress and Texas Railroad Commissioner.
Allen delivered a notable Commencement Address at Bowling Green State University in 2011 where he encouraged graduates to use their education as an intellectual compass to guide them towards practical discovery and innovation, recognizing fellow alum Shantanu Narayen, CEO of Adobe Sys
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https://en.wikipedia.org/wiki/Complex%20measure
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In mathematics, specifically measure theory, a complex measure generalizes the concept of measure by letting it have complex values. In other words, one allows for sets whose size (length, area, volume) is a complex number.
Definition
Formally, a complex measure on a measurable space is a complex-valued function
that is sigma-additive. In other words, for any sequence of disjoint sets belonging to , one has
As for any permutation (bijection) , it follows that converges unconditionally (hence absolutely).
Integration with respect to a complex measure
One can define the integral of a complex-valued measurable function with respect to a complex measure in the same way as the Lebesgue integral of a real-valued measurable function with respect to a non-negative measure, by approximating a measurable function with simple functions. Just as in the case of ordinary integration, this more general integral might fail to exist, or its value might be infinite (the complex infinity).
Another approach is to not develop a theory of integration from scratch, but rather use the already available concept of integral of a real-valued function with respect to a non-negative measure. To that end, it is a quick check that the real and imaginary parts μ1 and μ2 of a complex measure μ are finite-valued signed measures. One can apply the Hahn-Jordan decomposition to these measures to split them as
and
where μ1+, μ1−, μ2+, μ2− are finite-valued non-negative measures (which are unique i
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https://en.wikipedia.org/wiki/Anil%20Nerode
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Anil Nerode (born 1932) is an American mathematician, known for his work in mathematical logic and for his many-decades tenure as a professor at Cornell University.
He received his undergraduate education and a Ph.D. in mathematics from the University of Chicago, the latter under the directions of Saunders Mac Lane. He enrolled in the Hutchins College at the University of Chicago in 1947 at the age of 15, and received his Ph.D. in 1956. His Ph.D. thesis was on an algebraic abstract formulation of substitution in many-sorted free algebras and its relation to equational definitions of the partial recursive functions.
While in graduate school, beginning in 1954, he worked at Professor Walter Bartky's Institute for Air Weapons Research, which did classified work for the US Air Force. He continued to work there following the completion of his Ph.D., from 1956 to 1957. In the summer of 1957 he attended the Cornell NSF Summer 1957 Institute in Logic. In 1958 to 1959 he went to the Institute for Advanced Study in Princeton, New Jersey, where he worked with Kurt Gödel. He also did post-graduate work at University of California, Berkeley.
When in 1959 he got an unsolicited offer of a faculty position at Cornell University, he accepted, in part because on his previous visit to the campus he had thought "it was the prettiest place I'd ever seen". Nerode is Goldwin Smith Professor of Mathematics at Cornell, having been named to that chair in 1991. His interests are in mathemati
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https://en.wikipedia.org/wiki/P-form%20electrodynamics
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In theoretical physics, -form electrodynamics is a generalization of Maxwell's theory of electromagnetism.
Ordinary (via. one-form) Abelian electrodynamics
We have a one-form , a gauge symmetry
where is any arbitrary fixed 0-form and is the exterior derivative, and a gauge-invariant vector current with density 1 satisfying the continuity equation
where is the Hodge star operator.
Alternatively, we may express as a closed -form, but we do not consider that case here.
is a gauge-invariant 2-form defined as the exterior derivative .
satisfies the equation of motion
(this equation obviously implies the continuity equation).
This can be derived from the action
where is the spacetime manifold.
p-form Abelian electrodynamics
We have a -form , a gauge symmetry
where is any arbitrary fixed -form and is the exterior derivative, and a gauge-invariant -vector with density 1 satisfying the continuity equation
where is the Hodge star operator.
Alternatively, we may express as a closed -form.
is a gauge-invariant -form defined as the exterior derivative .
satisfies the equation of motion
(this equation obviously implies the continuity equation).
This can be derived from the action
where is the spacetime manifold.
Other sign conventions do exist.
The Kalb–Ramond field is an example with in string theory; the Ramond–Ramond fields whose charged sources are D-branes are examples for all values of . In 11-dimensional supergravity or M-theory, we have a 3-form
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https://en.wikipedia.org/wiki/Free%20Boolean%20algebra
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In mathematics, a free Boolean algebra is a Boolean algebra with a distinguished set of elements, called generators, such that:
Each element of the Boolean algebra can be expressed as a finite combination of generators, using the Boolean operations, and
The generators are as independent as possible, in the sense that there are no relationships among them (again in terms of finite expressions using the Boolean operations) that do not hold in every Boolean algebra no matter which elements are chosen.
A simple example
The generators of a free Boolean algebra can represent independent propositions. Consider, for example, the propositions "John is tall" and "Mary is rich". These generate a Boolean algebra with four atoms, namely:
John is tall, and Mary is rich;
John is tall, and Mary is not rich;
John is not tall, and Mary is rich;
John is not tall, and Mary is not rich.
Other elements of the Boolean algebra are then logical disjunctions of the atoms, such as "John is tall and Mary is not rich, or John is not tall and Mary is rich". In addition there is one more element, FALSE, which can be thought of as the empty disjunction; that is, the disjunction of no atoms.
This example yields a Boolean algebra with 16 elements; in general, for finite n, the free Boolean algebra with n generators has 2n atoms, and therefore elements.
If there are infinitely many generators, a similar situation prevails except that now there are no atoms. Each element of the Boolean algebra is a combi
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https://en.wikipedia.org/wiki/Atom%20%28measure%20theory%29
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In mathematics, more precisely in measure theory, an atom is a measurable set which has positive measure and contains no set of smaller positive measure. A measure which has no atoms is called non-atomic or atomless.
Definition
Given a measurable space and a measure on that space, a set in is called an atom if
and for any measurable subset with
the set has measure zero, i.e. .
If is an atom, all the subsets in the -equivalence class of are atoms, and is called an atomic class. If is a -finite measure, there are countably many atomic classes.
Examples
Consider the set X = {1, 2, ..., 9, 10} and let the sigma-algebra be the power set of X. Define the measure of a set to be its cardinality, that is, the number of elements in the set. Then, each of the singletons {i}, for i = 1, 2, ..., 9, 10 is an atom.
Consider the Lebesgue measure on the real line. This measure has no atoms.
Atomic measures
A -finite measure on a measurable space is called atomic or purely atomic if every measurable set of positive measure contains an atom. This is equivalent to say that there is a countable partition of formed by atoms up to a null set. The assumption of -finitude is essential. Consider otherwise the space where denotes the counting measure. This space is atomic, with all atoms being the singletons, yet the space is not able to be partitioned into the disjoint union of countably many disjoint atoms, and a null set since the countable union of singletons is a count
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https://en.wikipedia.org/wiki/T8
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T8 or T-8 may refer to the following:
Measurement
T8, a Torx screwhead size
T8, a 1 inch fluorescent lamp size
A tornado intensity rating on the TORRO scale
Biology
The 8th thoracic vertebra
The T8 spinal nerve
Transportation
Trikke8, a scooter-like vehicle
An OS T1000 train class model, used on the Oslo Metro
Airport & South Line, a rail service in Sydney numbered T8
Île-de-France tramway Line 8, one of the Tramways in Île-de-France
Other
One of the Hong Kong Tropical Cyclone Warning Signals used by the Hong Kong Observatory
Tekken 8, an upcoming fighting game
The International Telecommunication Union prefix for Palau
YouTube Channel based on The Lion King
See also
8T (disambiguation)
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https://en.wikipedia.org/wiki/Schubert%20calculus
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In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry (part of enumerative geometry). It was a precursor of several more modern theories, for example characteristic classes, and in particular its algorithmic aspects are still of current interest. The term Schubert calculus is sometimes used to mean the enumerative geometry of linear subspaces of a vector space, which is roughly equivalent to describing the cohomology ring of Grassmannians. Sometimes it is used to mean the more general enumerative geometry of algebraic varieties that are homogenous spaces of simple Lie groups. Even more generally, Schubert calculus is often understood to encompass the study of analogous questions in generalized cohomology theories.
The objects introduced by Schubert are the Schubert cells, which are locally closed sets in a Grassmannian defined by conditions of incidence of a linear subspace in projective space with a given flag. For further details see Schubert variety.
The intersection theory of these cells, which can be seen as the product structure in the cohomology ring of the Grassmannian of associated cohomology classes, in principle allows the prediction of the cases where intersections of cells results in a finite set of points, which are potentially concrete answers to enumerative questions. A key result is that the Schubert cells (or rather, th
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https://en.wikipedia.org/wiki/Methane%20%28data%20page%29
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This page provides supplementary chemical data on methane.
Material Safety Data Sheet
The handling of this chemical may incur notable safety precautions.
Structure and properties
Thermodynamic properties
Vapor pressure of liquid
Table data obtained from CRC Handbook of Chemistry and Physics 44th ed. Annotation "(s)" indicates equilibrium temperature of vapor over solid. Otherwise temperature is equilibrium of vapor over liquid. Note that these are all negative temperature values.
Spectral data
References
Cited sources
Chemical data pages
Methane
Chemical data pages cleanup
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https://en.wikipedia.org/wiki/J-homomorphism
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In mathematics, the J-homomorphism is a mapping from the homotopy groups of the special orthogonal groups to the homotopy groups of spheres. It was defined by , extending a construction of .
Definition
Whitehead's original homomorphism is defined geometrically, and gives a homomorphism
of abelian groups for integers q, and . (Hopf defined this for the special case .)
The J-homomorphism can be defined as follows.
An element of the special orthogonal group SO(q) can be regarded as a map
and the homotopy group ) consists of homotopy classes of maps from the r-sphere to SO(q).
Thus an element of can be represented by a map
Applying the Hopf construction to this gives a map
in , which Whitehead defined as the image of the element of under the J-homomorphism.
Taking a limit as q tends to infinity gives the stable J-homomorphism in stable homotopy theory:
where is the infinite special orthogonal group, and the right-hand side is the r-th stable stem of the stable homotopy groups of spheres.
Image of the J-homomorphism
The image of the J-homomorphism was described by , assuming the Adams conjecture of which was proved by , as follows. The group is given by Bott periodicity. It is always cyclic; and if r is positive, it is of order 2 if r is 0 or 1 modulo 8, infinite if r is 3 or 7 modulo 8, and order 1 otherwise . In particular the image of the stable J-homomorphism is cyclic. The stable homotopy groups are the direct sum of the (cyclic) image of the J-homomorphism,
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https://en.wikipedia.org/wiki/The%20World%20of%20Chemistry
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The World of Chemistry is a television series on introductory chemistry hosted by Nobel prize-winning chemist Roald Hoffmann. The series consists of 26 half-hour video programs, along with coordinated books, which explore various topics in chemistry through experiments conducted by Stevens Point emeritus professor Don Showalter the "series demonstrator" and interviews with working chemists, it also includes physics and earth science related components. The series was produced by the University of Maryland, College Park and the Educational Film Center and was funded by the Annenberg/CPB Project (now the Annenberg Foundation), it was filmed in 1988 and first aired on PBS in 1990. This series supports science standards recognized nationally by the United States (NSTA and NCSESA) and is still widely used in high school and college chemistry courses. The entire series was previously available on learner.org for free in an online video streaming format, but streaming for this series was discontinued on June 25, 2019.
Awards
The awards won by The World of Chemistry are given below
American Film and Video Festival1990 Finalist Award for "On the Surface"
Columbus International Film and Video Festival1991 Honorable Mention Award for "Color"
Houston International Film Festival "Worldfest Houston"1991 Silver Award for "Color"
National Educational Film and Video Festival1990 Gold Apple Award for "The Periodic Table"
List of episodes
The World of Chemistry - The relationships of chemistr
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https://en.wikipedia.org/wiki/Anonymous%20recursion
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In computer science, anonymous recursion is recursion which does not explicitly call a function by name. This can be done either explicitly, by using a higher-order function – passing in a function as an argument and calling it – or implicitly, via reflection features which allow one to access certain functions depending on the current context, especially "the current function" or sometimes "the calling function of the current function".
In programming practice, anonymous recursion is notably used in JavaScript, which provides reflection facilities to support it. In general programming practice, however, this is considered poor style, and recursion with named functions is suggested instead. Anonymous recursion via explicitly passing functions as arguments is possible in any language that supports functions as arguments, though this is rarely used in practice, as it is longer and less clear than explicitly recursing by name.
In theoretical computer science, anonymous recursion is important, as it shows that one can implement recursion without requiring named functions. This is particularly important for the lambda calculus, which has anonymous unary functions, but is able to compute any recursive function. This anonymous recursion can be produced generically via fixed-point combinators.
Use
Anonymous recursion is primarily of use in allowing recursion for anonymous functions, particularly when they form closures or are used as callbacks, to avoid having to bind the name of
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https://en.wikipedia.org/wiki/Abdallat%E2%80%93Davis%E2%80%93Farrage%20syndrome
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Abdallat–Davis–Farrage syndrome is a form of phakomatosis, a disease of the central nervous system accompanied by skin abnormalities. It is characterized by the out of the ordinary pigment of the skin that is abnormal to one's genetics or the color perceived on a basis.
The condition is named after the team of medical professionals who first wrote it up, describing the appearance of the syndrome in a family from Jordan. It was characterized in 1980 by Adnan Abdallat, a Jordanian doctor.
Signs and symptoms
Clinical presentation is as follows:
Albinism (hair)
Irregular decreased skin pigmentation
Excessive freckling
Insensitivity to pain
Paraparesis/quadraparesis
Genetics
The syndrome is thought to be inherited as an autosomal recessive genetic trait, meaning that in order to manifest symptoms, a person must inherit a gene for Abdallat–Davis–Farrage syndrome from both parents. As it is also autosomal (not linked to either of the genes that determine gender), it can manifest in both men and women. Those with only one gene are carriers, and they typically manifest no symptoms; in the event that a person inherits both genes, symptoms usually appear before one year of age.
Treatment
References
External links
Autosomal recessive disorders
Syndromes affecting the skin
Genetic disorders with OMIM but no gene
Syndromes affecting the nervous system
Diseases named for discoverer
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https://en.wikipedia.org/wiki/Neuroinformatics
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Neuroinformatics is the field that combines informatics and neuroscience. Neuroinformatics is related with neuroscience data and information processing by artificial neural networks. There are three main directions where neuroinformatics has to be applied:
the development of computational models of the nervous system and neural processes.
the development of tools for analyzing and modeling neuroscience data,
the development of tools and databases for management and sharing of neuroscience data at all levels of analysis,
Neuroinformatics is related to philosophy (computational theory of mind), psychology (information processing theory), computer science (natural computing, bio-inspired computing), among others. Neuroinformatics doesn't deal with matter or energy, so it can be seen as a branch of neurobiology that studies various aspects of nervous systems. The term neuroinformatics seems to be used synonymously with cognitive informatics, described by Journal of Biomedical Informatics as interdisciplinary domain that focuses on human information processing, mechanisms and processes within the context of computing and computing applications. According to German National Library, neuroinformatics is synonymous with neurocomputing. At Proceedings of the 10th IEEE International Conference on Cognitive Informatics and Cognitive Computing was introduced the following description: Cognitive Informatics (CI) as a transdisciplinary enquiry of computer science, information sciences,
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https://en.wikipedia.org/wiki/Inertia%20%28disambiguation%29
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Inertia is the resistance of a physical object to change in its velocity.
Inertia may also refer to:
Science and engineering
Moment of inertia, the resistance to angular acceleration
In mechanical engineering, simply "inertia" is often used to refer to "inertial mass" or "moment of inertia"
Second moment of area, a geometrical property of a body that determines its resistance to bending
Thermal inertia or effusivity, the resistance of an object or body to temperature change in response to heat input
Sylvester's law of inertia, a theorem in matrix algebra
Sleep inertia, a psychological state
Climate inertia, a slowness of the Earth system to changes in significant factors such as greenhouse gas levels
Ecological inertia, the ability of a living system to resist external fluctuations
Social science
Cognitive inertia, resistance to change in an individual's beliefs
Psychological inertia, a tendency to favor omission over commission due to a lack of incentive to act
Psychical inertia, a term introduced by Carl Jung
Social inertia, description of a person's resistance to change in psychology and sociology
Corporate inertia or unwillingness to change, a diseconomy of scale in microeconomics
Arts and entertainment
Inertia (film), a 2001 Canadian drama
Inertia (Marvel Comics), a fictional hero
Inertia (DC Comics), a fictional antagonist
"Inertia" (short story), a story by Nancy Kress
Music
Inertia, an Irish DJ duo, the pairing of John O'Callaghan and Neal Scarb
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https://en.wikipedia.org/wiki/Reflection%20map
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Reflection map may refer to:
Reflection mapping in computer graphics
A reflection (mathematics), specifically
an element of a reflection group
an element of a Weyl group
Reflection map (logic optimization), a conventional Gray code Karnaugh map in logic optimization
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