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https://en.wikipedia.org/wiki/Rydberg
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Rydberg may refer to:
People
Gerda Rydberg (1858–1928), Swedish artist better known as Gerda Tirén
Jan Rydberg, (1923-2015), Swedish chemist who worked on nuclear chemistry and recycling at Chalmers University of Technology
Johannes Rydberg (1854–1919), Swedish physicist and deviser of the Rydberg formula
Kaisu-Mirjami Rydberg (1905–1959), Finnish journalist and politician
Per Axel Rydberg (1860–1931), Swedish-American botanist
Sam Rydberg (1885–1956), Swedish composer
Viktor Rydberg (1828–1895), Swedish author, poet, and mythographer
Viktor Crus Rydberg (1995—), Swedish ice hockey player
Physics
Rydberg constant, a constant related to atomic spectra
Rydberg formula, a formula describing wavelengths
Rydberg atom, an excited atomic state
Rydberg molecule, an electronically excited chemical substance
Rydberg unit of energy (symbol Ry), derived from the Rydberg constant
Places
Rydberg (crater), a lunar crater named after Johannes Rydberg
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https://en.wikipedia.org/wiki/Derived%20category
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In mathematics, the derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the objects of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes. Derived functors can then be defined for chain complexes, refining the concept of hypercohomology. The definitions lead to a significant simplification of formulas otherwise described (not completely faithfully) by complicated spectral sequences.
The development of the derived category, by Alexander Grothendieck and his student Jean-Louis Verdier shortly after 1960, now appears as one terminal point in the explosive development of homological algebra in the 1950s, a decade in which it had made remarkable strides. The basic theory of Verdier was written down in his dissertation, published finally in 1996 in Astérisque (a summary had earlier appeared in SGA 4½). The axiomatics required an innovation, the concept of triangulated category, and the construction is based on localization of a category, a generalization of localization of a ring. The original impulse to develop the "derived" formalism came from the need to find a suitable formulation of Grothendieck's coherent duality theory. Derived categories have since become i
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https://en.wikipedia.org/wiki/BOC%20Group
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BOC Group may refer to:
Bank of China Group (BOCG),
Boc group, a protecting group used in organic chemistry
BOC (company), a British-based chemical company
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https://en.wikipedia.org/wiki/Strong%20CP%20problem
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The strong CP problem is a question in particle physics, which brings up the following quandary: why does quantum chromodynamics (QCD) seem to preserve CP-symmetry?
In particle physics, CP stands for the combination of charge conjugation symmetry (C) and parity symmetry (P). According to the current mathematical formulation of quantum chromodynamics, a violation of CP-symmetry in strong interactions could occur. However, no violation of the CP-symmetry has ever been seen in any experiment involving only the strong interaction. As there is no known reason in QCD for it to necessarily be conserved, this is a "fine tuning" problem known as the strong CP problem.
The strong CP problem is sometimes regarded as an unsolved problem in physics, and has been referred to as "the most underrated puzzle in all of physics." There are several proposed solutions to solve the strong CP problem. The most well-known is Peccei–Quinn theory, involving new pseudoscalar particles called axions.
Theory
CP-symmetry states that physics should be unchanged if particles were swapped with their antiparticles and then left-handed and right-handed particles were also interchanged. This corresponds to performing a charge conjugation transformation and then a parity transformation. The symmetry is known to be broken in the Standard Model through weak interactions, but it is also expected to be broken through strong interactions which govern quantum chromodynamics (QCD), something that has not yet been o
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https://en.wikipedia.org/wiki/Fine-tuning%20%28physics%29
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In theoretical physics, fine-tuning is the process in which parameters of a model must be adjusted very precisely in order to fit with certain observations. This had led to the discovery that the fundamental constants and quantities fall into such an extraordinarily precise range that if it did not, the origin and evolution of conscious agents in the universe would not be permitted.
Theories requiring fine-tuning are regarded as problematic in the absence of a known mechanism to explain why the parameters happen to have precisely the observed values that they return. The heuristic rule that parameters in a fundamental physical theory should not be too fine-tuned is called naturalness.
Background
The idea that naturalness will explain fine tuning was brought into question by Nima Arkani-Hamed, a theoretical physicist, in his talk "Why is there a Macroscopic Universe?", a lecture from the mini-series "Multiverse & Fine Tuning" from the "Philosophy of Cosmology" project, a University of Oxford and Cambridge Collaboration 2013. In it he describes how naturalness has usually provided a solution to problems in physics; and that it had usually done so earlier than expected. However, in addressing the problem of the cosmological constant, naturalness has failed to provide an explanation though it would have been expected to have done so a long time ago.
The necessity of fine-tuning leads to various problems that do not show that the theories are incorrect, in the sense of falsi
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https://en.wikipedia.org/wiki/Fermi%20surface
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In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic energy bands. The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle, which allows a maximum of one electron per quantum state. The study of the Fermi surfaces of materials is called fermiology.
Theory
Consider a spin-less ideal Fermi gas of particles. According to Fermi–Dirac statistics, the mean occupation number of a state with energy is given by
where,
is the mean occupation number of the state
is the kinetic energy of the state
is the chemical potential (at zero temperature, this is the maximum kinetic energy the particle can have, i.e. Fermi energy )
is the absolute temperature
is the Boltzmann constant
Suppose we consider the limit . Then we have,
By the Pauli exclusion principle, no two fermions can be in the same state. Therefore, in the state of lowest energy, the particles fill up all energy levels below the Fermi energy , which is equivalent to saying that is the energy level below which there are exactly states.
In momentum space, these particles fill up a ball of radius , the surface of which is called the Fermi surface.
The linear response of a metal to an electric, magnetic, or thermal gradient is determined by
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https://en.wikipedia.org/wiki/Geoffrey%20Marcy
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Geoffrey William Marcy (born September 29, 1954) is an American astronomer. He was an early influence in the field of exoplanet detection, discovery, and characterization. Marcy was a professor of astronomy at the University of California, Berkeley, and an adjunct professor of physics and astronomy at San Francisco State University. Marcy and his research teams discovered many extrasolar planets, including 70 out of the first 100 known exoplanets and also the first planetary system around a Sun-like star, Upsilon Andromedae. Marcy was a co-investigator on the NASA Kepler mission. His collaborators have included R. Paul Butler, Debra Fischer and Steven S. Vogt, Jason Wright, Andrew Howard, Katie Peek, John Johnson, Erik Petigura, Lauren Weiss, Lea Hirsch and the Kepler Science Team. Following an investigation for sexual harassment in 2015, Marcy resigned his position at the University of California, Berkeley.
Early life and education
Marcy graduated from Granada Hills High School in Granada Hills, California, in 1972. He graduated with a Bachelor of Arts summa cum laude with a double major in physics and astronomy from the University of California, Los Angeles, in 1976. He then completed a doctorate in astronomy in 1982 at the University of California, Santa Cruz, with much of his work done at Lick Observatory.
Academic career
Marcy has held teaching and research positions, first at the Carnegie Institution of Washington (then the Mt. Wilson and Las Campanas Observatories)
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https://en.wikipedia.org/wiki/Peccei%E2%80%93Quinn%20theory
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In particle physics, the Peccei–Quinn theory is a well-known, long-standing proposal for the resolution of the strong CP problem formulated by Roberto Peccei and Helen Quinn in 1977. The theory introduces a new anomalous symmetry to the Standard Model along with a new scalar field which spontaneously breaks the symmetry at low energies, giving rise to an axion that suppresses the problematic CP violation. This model has long since been ruled out by experiments and has instead been replaced by similar invisible axion models which utilize the same mechanism to solve the strong CP problem.
Overview
Quantum chromodynamics (QCD) has a complicated vacuum structure which gives rise to a CP violating θ-term in the Lagrangian. Such a term can have a number of non-perturbative effects, one of which is to give the neutron an electric dipole moment. The absence of this dipole moment in experiments requires the fine-tuning of the θ-term to be very small, something known as the strong CP problem. Motivated as a solution to this problem, Peccei–Quinn (PQ) theory introduces a new complex scalar field in addition to the standard Higgs doublet. This scalar field couples to d-type quarks through Yukawa terms, while the Higgs now only couples to the up-type quarks. Additionally, a new global chiral anomalous U(1) symmetry is introduced, the Peccei–Quinn symmetry, under which is charged, requiring some of the fermions also have a PQ charge. The scalar field also has a potential
where is a
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https://en.wikipedia.org/wiki/Dynamism
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Dynamism may refer to:
Dynamism (metaphysics), a cosmological explanation of the material world
Dynamicism, the application of dynamical systems theory to cognitive science
Economic dynamism, a term related to the rate of change of an economy
"Plastic dynamism", a term used by the Italian futurist art movement to describe an object's intrinsic and extrinsic motion
See also
Dunamis (disambiguation)
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https://en.wikipedia.org/wiki/Em%C5%91ke%20Szathm%C3%A1ry
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Emőke J.E. Szathmáry, (born January 25, 1944, in Hungary) is a physical anthropologist, specializing in the study of human genetics. Dr. Szathmáry served as the 10th President and Vice-Chancellor of The University of Manitoba, 1996–2008.
Dr. Szathmáry's first administrative post was as chairman of the department of anthropology at McMaster University, a position she left to become Dean of the Faculty of Social Science at the University of Western Ontario. She left this position to serve as provost and vice-president (academic) at McMaster University in Hamilton, Ontario, before going to her position at the University of Manitoba. Szathmáry was appointed a member of the Order of Canada in 2003. In 2004, she was named one of Canada's top 100 most powerful women by the Women's Executive Network and the Richard Ivey School of Business. In 2005, she was made a Fellow of the Royal Society of Canada. She was named also as a Distinguished Lecturer by the American Anthropological Association, which is the highest recognition given by the anthropological discipline for a lifetime of exemplary scholarship.
Publications (partial list)
Prehistoric Mongoloid Dispersals, Takeru Akazawa (Editor), Emoke J. E. Szathmáry (Editor)
Out of Asia: peopling the Americas and the Pacific, Journal of Pacific History, 1985, Robert Kirk, Emöke J. E. Szathmary, editors
(obituary)
contributor
Directorships (partial)
International Institute for Sustainable Development
Power Corporation of Canada, si
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https://en.wikipedia.org/wiki/Combinatorial%20class
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In mathematics, a combinatorial class is a countable set of mathematical objects, together with a size function mapping each object to a non-negative integer, such that there are finitely many objects of each size.
Counting sequences and isomorphism
The counting sequence of a combinatorial class is the sequence of the numbers of elements of size i for i = 0, 1, 2, ...; it may also be described as a generating function that has these numbers as its coefficients. The counting sequences of combinatorial classes are the main subject of study of enumerative combinatorics. Two combinatorial classes are said to be isomorphic if they have the same numbers of objects of each size, or equivalently, if their counting sequences are the same. Frequently, once two combinatorial classes are known to be isomorphic, a bijective proof of this equivalence is sought; such a proof may be interpreted as showing that the objects in the two isomorphic classes are cryptomorphic to each other.
For instance, the triangulations of regular polygons (with size given by the number of sides of the polygon, and a fixed choice of polygon to triangulate for each size) and the set of unrooted binary plane trees (up to graph isomorphism, with a fixed ordering of the leaves, and with size given by the number of leaves) are both counted by the Catalan numbers, so they form isomorphic combinatorial classes. A bijective isomorphism in this case is given by planar graph duality: a triangulation can be transformed b
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https://en.wikipedia.org/wiki/List%20of%20genetics%20research%20organizations
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This is a list of organizations involved in genetics research.
Africa
Kenya
International Livestock Research Institute (ILRI), Nairobi
Namibia
The Life Technologies Conservation Genetics Laboratory (Cheetah Conservation Fund), Otjiwarongo
Asia
Pakistan
IBGE
Institute of Biomedical and Genetic Engineering
China
BGI Group
Chinese National Human Genome Center
India
Institute of Genomics and Integrative Biology
DNA Labs India
Iran
Royan Institute
Philippines
Philippine Genome Center
International Rice Research Institute
Singapore
Genome Institute of Singapore
Institute of Molecular and Cell Biology
Taiwan
National Health Research Institutes
Japan
National Institute of Genetics
Okinawa Institute of Science and Technology
RIKEN
Europe
Germany
Max Planck Institute for Molecular Genetics
Italy
Bioversity International
Sweden
Science for Life Laboratory
United Kingdom
The Genome Analysis Centre
Wellcome Sanger Institute
Wellcome Centre for Human Genetics (University of Oxford)
Russia
Research Centre for Medical Genetics (RCMG), Moscow
North America
Canada
The Centre for Applied Genomics (University of Toronto)
United States
Arizona
Translational Genomics Research Institute
California
Clear Labs
Genetic Information Research Institute
Joint Genome Institute (U.S. Department of Energy)
Salk Institute for Biological Studies
Illinois
Carl R. Woese Institute for Genomic Biology (University of Illinois, Urbana-Champaign)
Maine
The Jackson Laboratory
Maryland
Howard Hugh
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https://en.wikipedia.org/wiki/Food%20browning
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Browning is the process of food turning brown due to the chemical reactions that take place within. The process of browning is one of the chemical reactions that take place in food chemistry and represents an interesting research topic regarding health, nutrition, and food technology. Though there are many different ways food chemically changes over time, browning in particular falls into two main categories: enzymatic versus non-enzymatic browning processes.
Browning has many important implications on the food industry relating to nutrition, technology, and economic cost. Researchers are especially interested in studying the control (inhibition) of browning and the different methods that can be employed to maximize this inhibition and ultimately prolong the shelf life of food.
Enzymatic browning
Enzymatic browning is one of the most important reactions that takes place in most fruits and vegetables as well as in seafood. These processes affect the taste, color, and value of such foods. Generally, it is a chemical reaction involving polyphenol oxidase (PPO), catechol oxidase, and other enzymes that create melanins and benzoquinone from natural phenols. Enzymatic browning (also called oxidation of foods) requires exposure to oxygen. It begins with the oxidation of phenols by polyphenol oxidase into quinones, whose strong electrophilic state causes high susceptibility to a nucleophilic attack from other proteins. These quinones are then polymerized in a series of reactions,
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https://en.wikipedia.org/wiki/Concerted%20reaction
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In chemistry, a concerted reaction is a chemical reaction in which all bond breaking and bond making occurs in a single step. Reactive intermediates or other unstable high energy intermediates are not involved. Concerted reaction rates tend not to depend on solvent polarity ruling out large buildup of charge in the transition state. The reaction is said to progress through a concerted mechanism as all bonds are formed and broken in concert. Pericyclic reactions, the S2 reaction, and some rearrangements - such as the Claisen rearrangement - are concerted reactions.
The rate of the SN2 reaction is second order overall due to the reaction being bimolecular (i.e. there are two molecular species involved in the rate-determining step). The reaction does not have any intermediate steps, only a transition state. This means that all the bond making and bond breaking takes place in a single step. In order for the reaction to occur both molecules must be situated correctly.
References
Organic reactions
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https://en.wikipedia.org/wiki/Norm%20%28mathematics%29
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In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the Euclidean norm, the 2-norm, or, sometimes, the magnitude of the vector. This norm can be defined as the square root of the inner product of a vector with itself.
A seminorm satisfies the first two properties of a norm, but may be zero for vectors other than the origin. A vector space with a specified norm is called a normed vector space. In a similar manner, a vector space with a seminorm is called a seminormed vector space.
The term pseudonorm has been used for several related meanings. It may be a synonym of "seminorm".
A pseudonorm may satisfy the same axioms as a norm, with the equality replaced by an inequality "" in the homogeneity axiom.
It can also refer to a norm that can take infinite values, or to certain functions parametrised by a directed set.
Definition
Given a vector space over a subfield of the complex numbers a norm on is a real-valued function with the following properties, where denotes the usual absolute value of a scalar :
Subadditivity/Triangle inequality: for all
Absolute homogeneity: for all and all scalars
Positive definiteness/positive
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https://en.wikipedia.org/wiki/Dynamical%20systems%20theory
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Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations.
This theory deals with the long-term qualitative behavior of dynamical systems, and studies the nature of, and when possible the solutions of, the equations of motion of systems that are often primarily mechanical or otherwise physical in nature, such as planetary orbits and the behaviour of electronic circuits, as well as systems that arise in biology, economics, and elsewhere. Much of modern research is focused on the study of chaotic systems.
This field of study is also called just dynamical systems, mathematical dynamical systems theory or the mathematical theor
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https://en.wikipedia.org/wiki/Roger%20Balian
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Roger Balian (born 18 January 1933) is a French-Armenian physicist who has worked on quantum field theory, quantum thermodynamics, and theory of measurement.
Balian is a member of French Académie des sciences (Academy of Sciences). His important work includes the Balian-Low theorem. He teaches statistical physics at the École Polytechnique.
Works
A. Aspect, R. Balian, G. Bastard, J.P. Bouchaud, B. Cabane, F. Combes, T. Encrenaz, S. Fauve, A. Fert, M. Fink, A. Georges, J.F. Joanny, D. Kaplan, D. Le Bihan, P. Léna, H. Le Treut, J-P Poirier, J. Prost et J.L. Puget, Demain la physique, (Odile Jacob, 2009) ()
References
École Polytechnique alumni
Mines Paris - PSL alumni
Corps des mines
1933 births
Living people
French physicists
Armenian physicists
French people of Armenian descent
Members of the French Academy of Sciences
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https://en.wikipedia.org/wiki/Grenville%20Turner
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Grenville Turner (born 1 November 1936, in Todmorden) is a research professor at the University of Manchester. He is one of the pioneers of cosmochemistry.
Education
Todmorden Grammar School
St. John's College, Cambridge (MA)
Balliol College, Oxford
In 1962, he was awarded his D.Phil. (Oxford University's equivalent of a PhD) in nuclear physics.
Career
University of California, Berkeley: assistant professor, 1962–64
University of Sheffield: lecturer in physics, 1964–74, senior lecturer 1974–79, reader 1979–80, professor 1980–88
Caltech: research associate, 1970–71
University of Manchester: professor of isotope geochemistry, Department of Earth Sciences, 1988–
Member of committees for SERC, the British National Space Centre and PPARC
Scientific work
Professor Turner has been a leading figure in cosmochemistry since the 1960s. His pioneering work on rare gases in meteorites led him to develop the argon–argon dating technique that demonstrated the great age of meteorites and provided a precise chronology of rocks brought back by the Apollo missions. He was one of the few UK scientists to be a Principal Investigator of these Apollo samples.
His argon-dating technique involved stepped pyrolysis of the rocks to force out the argon, then determining the isotopic ratios in the gas by mass spectrometry. This was later refined by the use of lasers. These techniques have been invaluable to cosmochemists and geochemists, and have been applied (by Turner and others) to de
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https://en.wikipedia.org/wiki/Eddington%20Medal
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The Eddington Medal is awarded by the Royal Astronomical Society for investigations of outstanding merit in theoretical astrophysics. It is named after Sir Arthur Eddington. First awarded in 1953, the frequency of the prize has varied over the years, at times being every one, two or three years. Since 2013 it has been awarded annually.
Recipients
Source is unless otherwise noted.
See also
List of astronomy awards
List of physics awards
List of prizes named after people
References
External links
Winners
Physics awards
Awards established in 1953
Awards of the Royal Astronomical Society
1953 establishments in the United Kingdom
Astrophysics
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https://en.wikipedia.org/wiki/Anatol%20Rapoport
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Anatol Rapoport (; ; May 22, 1911January 20, 2007) was an American mathematical psychologist. He contributed to general systems theory, to mathematical biology and to the mathematical modeling of social interaction and stochastic models of contagion.
Biography
Rapoport was born in Lozova, Kharkov Governorate, Russia (in today's Kharkiv Oblast, Ukraine) into a secular Jewish family. In 1922, he came to the United States, and in 1928 he became a naturalized citizen. He started studying music in Chicago and continued with piano, conducting and composition at the Vienna Hochschule für Musik where he studied from 1929 to 1934. However, due to the rise of Nazism, he found it impossible to make a career as a pianist.
He shifted his career into mathematics, completing a Ph.D. in mathematics under Otto Schilling and Abraham Adrian Albert at the University of Chicago in 1941 on the thesis Construction of Non-Abelian Fields with Prescribed Arithmetic. According to The Globe and Mail, he was a member of the American Communist Party for three years, but quit before enlisting in the U.S. Army Air Forces in 1941, serving in Alaska and India during World War II.
After the war, he joined the Committee on Mathematical Biology at the University of Chicago (1947–54), publishing his first book, Science and the Goals of Man, co-authored with semanticist S. I. Hayakawa in 1950. He also received a one-year fellowship at the prestigious Center for Advanced Study in the Behavioral Sciences at Sta
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https://en.wikipedia.org/wiki/Earth%20%28historical%20chemistry%29
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Earths were defined by the Ancient Greeks as "materials that could not be changed further by the sources of heat then available". Several oxides were thought to be earths, such as aluminum oxide and magnesium oxide. It was not discovered until 1808 that these weren't elements but metallic oxides.
See also
Rare earth metals
Alkaline earth metals
References
Inorganic chemistry
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https://en.wikipedia.org/wiki/Gender%20symbol
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A gender symbol is a pictogram or glyph used to represent sex and gender, for example in biology and medicine, in genealogy, or in the sociological fields of gender politics, LGBT subculture and identity politics.
In his books (1767) and (1771), Carl Linnaeus regularly used the planetary symbols of Mars, Venus and Mercury, , for male, female and hermaphroditic (perfect) flowers, respectively. Botanists now use for the last.
In genealogy, including kinship in anthropology and pedigrees in animal husbandry, the geometric shapes or are used for male and for female. These are also used on public toilets in some countries.
The modern international pictograms used to indicate male and female public toilets, and , became widely used in the 1960s and 1970s. They are sometimes abstracted to for male and for female.
Biology and medicine
The three standard sex symbols in biology are male , female and hermaphroditic ; originally the symbol for Mercury, , was used for the last. These symbols were first used by Carl Linnaeus in 1751 to denote whether flowers were male (stamens only), female (pistil only) or perfect flowers with both pistils and stamens. (Most flowering and conifer plant species are hermaphroditic and either bear flowers/cones that themselves are hermaphroditic, or bear both male and female flowers/cones on the same plant.) These symbols are now ubiquitous in biology and medicine to indicate the sex of an individual, for example of a patient.
Genealogy
Kin
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https://en.wikipedia.org/wiki/Annalen%20der%20Physik
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Annalen der Physik (English: Annals of Physics) is one of the oldest scientific journals on physics; it has been published since 1799. The journal publishes original, peer-reviewed papers on experimental, theoretical, applied, and mathematical physics and related areas. The editor-in-chief is Stefan Hildebrandt. Prior to 2008, its ISO 4 abbreviation was Ann. Phys. (Leipzig), after 2008 it became Ann. Phys. (Berl.).
The journal is the successor to , published from 1790 until 1794, and , published from 1795 until 1797. The journal has been published under a variety of names (, , , Wiedemann's Annalen der Physik und Chemie) during its history.
History
Originally, was published in German, then a leading scientific language. From the 1950s to the 1980s, the journal published in both German and English. Initially, only foreign authors contributed articles in English but from the 1970s German-speaking authors increasingly wrote in English in order to reach an international audience. After the German reunification in 1990, English became the only language of the journal.
The importance of unquestionably peaked in 1905 with Albert Einstein's Annus Mirabilis papers. In the 1920s, the journal lost ground to the concurrent Zeitschrift für Physik. With the 1933 emigration wave, German-language journals lost many of their best authors. During Nazi Germany, it was considered to represent "the more conservative elements within the German physics community", alongside Physikalische Zeits
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https://en.wikipedia.org/wiki/EGF
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EGF may refer to:
E.G.F., a Gabonese company
East Grand Forks, Minnesota, a city
East Garforth railway station in England
Epidermal growth factor
Equity Group Foundation, a Kenyan charity
European Gendarmerie Force, a military unit of the European Union
European Genetics Foundation, a training organization
European Globalisation Adjustment Fund
European Go Federation
Exponential generating function
Xinxiang East railway station, China Railway telegraph code EGF
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https://en.wikipedia.org/wiki/M-set
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M-set may refer to
Sydney Trains M set, a class of electric train
Set of uniqueness or Menshov set of harmonic analysis
Mandelbrot set, a two-dimensional fractal shape
A monoid acting on a set; see Semigroup action
Mathematics disambiguation pages
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https://en.wikipedia.org/wiki/Katharine%20Burr%20Blodgett
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Katharine Burr Blodgett (January 10, 1898 – October 12, 1979) was an American physicist and chemist known for her work on surface chemistry, in particular her invention of "invisible" or nonreflective glass while working at General Electric. She was the first woman to be awarded a PhD in physics from the University of Cambridge, in 1926.
Early life
Blodgett was born on January 10, 1898, in Schenectady, New York. She was the second child of Katharine Buchanan (Burr) and George Reddington Blodgett. Her father was a patent attorney at General Electric where he headed that department. He was shot and killed in his home by a burglar just before she was born. GE offered a $5,000 reward for the arrest and conviction of the killer, but the suspected killer hanged himself in his jail cell in Salem, New York. Her mother was financially secure after her husband's death, and she moved to New York City with Katharine and her son George Jr. shortly after Katharine's birth.
In 1901, Katharine's mother moved the family to France so that the children would be bilingual. They lived there for several years, returned to New York for a year, during which time Katharine attended school in Saranac Lake, then spent time traveling through Germany. In 1912, Blodgett returned to New York City with her family and attended New York City's Rayson School.
Education
Blodgett's early childhood was split between New York and Europe, and she wasn't enrolled in school until she was eight years old. After att
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https://en.wikipedia.org/wiki/Erik%20Demaine
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Erik D. Demaine (born February 28, 1981) is a Canadian-American professor of computer science at the Massachusetts Institute of Technology and a former child prodigy.
Early life and education
Demaine was born in Halifax, Nova Scotia, to mathematician and sculptor Martin L. Demaine and Judy Anderson. From the age of 7, he was identified as a child prodigy and spent time traveling across North America with his father. He was home-schooled during that time span until entering university at the age of 12.
Demaine completed his bachelor's degree at 14 years of age at Dalhousie University in Canada, and completed his PhD at the University of Waterloo by the time he was 20 years old.
Demaine's PhD dissertation, a work in the field of computational origami, was completed at the University of Waterloo under the supervision of Anna Lubiw and Ian Munro. This work was awarded the Canadian Governor General's Gold Medal from the University of Waterloo and the NSERC Doctoral Prize (2003) for the best PhD thesis and research in Canada. Some of the work from this thesis was later incorporated into his book Geometric Folding Algorithms on the mathematics of paper folding published with Joseph O'Rourke in 2007.
Professional accomplishments
Demaine joined the faculty of the Massachusetts Institute of Technology (MIT) in 2001 at age 20, reportedly the youngest professor in the history of MIT, and was promoted to full professorship in 2011. Demaine is a member of the Theory of Computation gr
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https://en.wikipedia.org/wiki/Landau%20theory
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Landau theory in physics is a theory that Lev Landau introduced in an attempt to formulate a general theory of continuous (i.e., second-order) phase transitions. It can also be adapted to systems under externally-applied fields, and used as a quantitative model for discontinuous (i.e., first-order) transitions. Although the theory has now been superseded by the
renormalization group and scaling theory formulations, it remains an exceptionally broad and powerful framework for phase transitions, and the associated concept of the order parameter as a descriptor of the essential character of the transition has proven transformative.
Mean-field formulation (no long-range correlation)
Landau was motivated to suggest that the free energy of any system should obey two conditions:
Be analytic in the order parameter and its gradients.
Obey the symmetry of the Hamiltonian.
Given these two conditions, one can write down (in the vicinity of the critical temperature, Tc) a phenomenological expression for the free energy as a Taylor expansion in the order parameter.
Second-order transitions
Consider a system that breaks some symmetry below a phase transition, which is characterized by an order parameter . This order parameter is a measure of the order before and after a phase transition; the order parameter is often zero above some critical temperature and non-zero below the critical temperature. In a simple ferromagnetic system like the Ising model, the order parameter is characteriz
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https://en.wikipedia.org/wiki/Characteristic%20curve
|
Characteristic curve may refer to:
In electronics, a current–voltage characteristic curve
Semiconductor curve tracer, a device for displaying the above curve
In photography, a plot of film density: see sensitometry
In mathematics, used in the method of characteristics for solving partial differential equations.
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https://en.wikipedia.org/wiki/BWR
|
BWR or bwr may refer to:
Benedict–Webb–Rubin equation, an equation of state used in fluid dynamics
Black Warrior Review, a non-profit American literary magazine based at the University of Alabama
Boiling water reactor, a type of light water nuclear reactor used for the generation of electrical power
BWR, the Toronto Stock Exchange code for Breakwater Resources, a defunct Canadian mining company
bwr, the ISO 639-3 code for Bura language, Nigeria
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https://en.wikipedia.org/wiki/Burton%20process
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The Burton process is a thermal cracking process invented by William Merriam Burton and Robert E. Humphreys, both of whom held a PhD in chemistry from Johns Hopkins University. The process they developed is commonly referred to as the Burton process. However, it should be recognized as the Burton-Humphreys process, as both individuals played pivotal roles in its development. The legal dispute surrounding this matter was eventually settled, although the decision primarily recognized Burton's contributions.
The process involves the destructive distillation of crude oil, which is heated under pressure in a still. The innovative design of this still allows various products to emerge from a bubble tower at different temperatures and pressures. One crucial aspect of the process is that it significantly increased gasoline production from various types of oil, more than doubling the output. The first large-scale implementation of these towers occurred when Standard Oil of Indiana made the decision to construct 120 stills using an authorized budget of $709,000 in 1911. Notably, this decision coincided with the US Supreme Court's ruling to dissolve the Standard Oil Trust.
This thermal cracking process was patented on January 7, 1913 (Patent No. 1,049,667). The first thermal cracking method, the Shukhov cracking process, was invented by Vladimir Shukhov (Patent of Russian Empire No. 12926 on November 27, 1891). While the Russians contended that the Burton process was essentially a sli
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https://en.wikipedia.org/wiki/Autonomous%20learning
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Autonomous learning may refer to:
Autonomous learning in homeschooling
Learner autonomy
Machine learning
Self-paced instruction
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https://en.wikipedia.org/wiki/Node%20%28physics%29
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A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an anti-node, a point where the amplitude of the standing wave is at maximum. These occur midway between the nodes.
Explanation
Standing waves result when two sinusoidal wave trains of the same frequency are moving in opposite directions in the same space and interfere with each other. They occur when waves are reflected at a boundary, such as sound waves reflected from a wall or electromagnetic waves reflected from the end of a transmission line, and particularly when waves are confined in a resonator at resonance, bouncing back and forth between two boundaries, such as in an organ pipe or guitar string.
In a standing wave the nodes are a series of locations at equally spaced intervals where the wave amplitude (motion) is zero (see animation above). At these points the two waves add with opposite phase and cancel each other out. They occur at intervals of half a wavelength (λ/2). Midway between each pair of nodes are locations where the amplitude is maximum. These are called the antinodes. At these points the two waves add with the same phase and reinforce each other.
In cases where the two opposite wave trains are not the same ampli
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https://en.wikipedia.org/wiki/Node%20%28computer%20science%29
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A node is a basic unit of a data structure, such as a linked list or tree data structure. Nodes contain data and also may link to other nodes. Links between nodes are often implemented by pointers.
Nodes and trees
Nodes are often arranged into tree structures. A node represents the information contained in a single data structure. These nodes may contain a value or condition, or possibly serve as another independent data structure. Nodes are represented by a single parent node. The highest point on a tree structure is called a root node, which does not have a parent node, but serves as the parent or 'grandparent' of all of the nodes below it in the tree. The height of a node is determined by the total number of edges on the path from that node to the furthest leaf node, and the height of the tree is equal to the height of the root node. Node depth is determined by the distance between that particular node and the root node. The root node is said to have a depth of zero. Data can be discovered along these network paths.
An IP address uses this kind of system of nodes to define its location in a network.
Definitions
Child: A child node is a node extending from another node. For example, a computer with internet access could be considered a child node of a node representing the internet. The inverse relationship is that of a parent node. If node C is a child of node A, then A is the parent node of C.
Degree: the degree of a node is the number of children of the node.
Depth:
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https://en.wikipedia.org/wiki/Alfred%20Hershey
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Alfred Day Hershey (December 4, 1908 – May 22, 1997) was an American Nobel Prize–winning bacteriologist and geneticist.
He was born in Owosso, Michigan and received his B.S. in chemistry at Michigan State University in 1930 and his Ph.D. in bacteriology in 1934, taking a position shortly thereafter at the Department of Bacteriology at Washington University in St. Louis.
Around 1943, Hershey met bacteriophage researchers Max Delbrück, then at Vanderbilt University, and Salvador Luria at Columbia University. Hershey became part of their informal network of biologists, known as the Phage group.
Hershey began performing experiments with bacteriophages with Italian-American Prima Luria, German Max Delbrück, and observed that when two different strains of bacteriophage have infected the same bacteria, the two viruses may exchange genetic information.
In 1950 Hershey married his research partner Martha Chase at Laurel Hollow, New York and joined the Carnegie Institution of Washington's Department of Genetics. There he and his wife Martha Chase performed the famous Hershey–Chase experiment in 1952. This experiment provided additional evidence that DNA, not protein, was the genetic material of life. Notable post-doctoral fellows in Hershey's lab include Anna Marie Skalka.
Hershey became director of the Carnegie Institution (which later became Cold Spring Harbor Laboratory) in 1962 and was awarded the Nobel Prize in Physiology or Medicine in 1969, shared with Salvador Luria and M
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https://en.wikipedia.org/wiki/Frobenius%20method
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In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a second-order ordinary differential equation of the form
with and .
in the vicinity of the regular singular point .
One can divide by to obtain a differential equation of the form
which will not be solvable with regular power series methods if either or are not analytic at . The Frobenius method enables one to create a power series solution to such a differential equation, provided that p(z) and q(z) are themselves analytic at 0 or, being analytic elsewhere, both their limits at 0 exist (and are finite).
History: Frobenius' Actual Contributions
Frobenius' contribution was not so much in all the possible forms of the series solutions involved (see below). These forms had all been established earlier, by Fuchs. The indicial polynomial (see below) and its role had also been established by Fuchs.
A first contribution by Frobenius to the theory was to show that - as regards a first, linearly independent solution, which then has the form of an analytical power series multiplied by an arbitrary power r of the independent variable (see below) - the coefficients of the generalized power series obey a recurrence relation, so that they can always be straightforwardly calculated.
A second contribution by Frobenius was to show that, in cases in which the roots of the indicial equation differ by an integer, the general form of the second linearly
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https://en.wikipedia.org/wiki/Clarendon%20Laboratory
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The Clarendon Laboratory, located on Parks Road within the Science Area in Oxford, England (not to be confused with the Clarendon Building, also in Oxford), is part of the Department of Physics at Oxford University. It houses the atomic and laser physics, condensed matter physics, and biophysics groups within the Department, although four other Oxford Physics groups are not based in the Clarendon Lab. The Oxford Centre for Quantum Computation is also housed in the laboratory.
Buildings
The Clarendon Laboratory consists of two adjoining buildings, the Lindemann Building (named after Frederick Lindemann, 1st Viscount Cherwell) and the Grade II listed Townsend Building (named after Sir John Sealy Townsend).
The Beecroft Building (named after Adrian Beecroft) is now immediately in front of the Lindemann Building, completed in 2018 and designed by Hawkins\Brown, with a budget of approximately £40 million.
History
The Clarendon is named after Edward Hyde, 1st Earl of Clarendon, whose trustees paid £10,000 for the building of the original laboratory, completed in 1872, making it the oldest purpose-built physics laboratory in England. The building was designed by Robert Bellamy Clifton.
The brothers Fritz and Heinz London developed the London equations when working there in 1935.
In 2007, the laboratory was granted chemical landmark status.
The award was bestowed due to the work carried out by Henry Gwyn Jeffreys Moseley in 1914.
Current use
The original building, substantial
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https://en.wikipedia.org/wiki/William%20George%20Horner
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William George Horner (9 June 1786 – 22 September 1837) was a British mathematician. Proficient in classics and mathematics, he was a schoolmaster, headmaster and schoolkeeper who wrote extensively on functional equations, number theory and approximation theory, but also on optics. His contribution to approximation theory is honoured in the designation Horner's method, in particular respect of a paper in Philosophical Transactions of the Royal Society of London for 1819. The modern invention of the zoetrope, under the name Daedaleum in 1834, has been attributed to him.
Horner died comparatively young, before the establishment of specialist, regular scientific periodicals. So, the way others have written about him has tended to diverge, sometimes markedly, from his own prolific, if dispersed, record of publications and the contemporary reception of them.
Family life
The eldest son of the Rev. William Horner, a Wesleyan minister, Horner was born in Bristol. He was educated at Kingswood School, a Wesleyan foundation near Bristol, and at the age of sixteen became an assistant master there. In four years he rose to be headmaster (1806), but left in 1809, setting up his own school, The Classical Seminary, at Grosvenor Place, Bath, which he kept until he died there 22 September 1837. He and his wife Sarah (1787?–1864) had six daughters and two sons.
Physical sciences, optics
Although Horner's article on the Dædalum (zoetrope) appeared in Philosophical Magazine only in January, 18
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https://en.wikipedia.org/wiki/Sethi%E2%80%93Ullman%20algorithm
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In computer science, the Sethi–Ullman algorithm is an algorithm named after Ravi Sethi and Jeffrey D. Ullman, its inventors, for translating abstract syntax trees into machine code that uses as few registers as possible.
Overview
When generating code for arithmetic expressions, the compiler has to decide which is the best way to translate the expression in terms of number of instructions used as well as number of registers needed to evaluate a certain subtree. Especially in the case that free registers are scarce, the order of evaluation can be important to the length of the generated code, because different orderings may lead to larger or smaller numbers of intermediate values being spilled to memory and then restored. The Sethi–Ullman algorithm (also known as Sethi–Ullman numbering) produces code which needs the fewest instructions possible as well as the fewest storage references (under the assumption that at the most commutativity and associativity apply to the operators used, but distributive laws i.e. do not hold). The algorithm succeeds as well if neither commutativity nor associativity hold for the expressions used, and therefore arithmetic transformations can not be applied. The algorithm also does not take advantage of common subexpressions or apply directly to expressions represented as general directed acyclic graphs rather than trees.
Simple Sethi–Ullman algorithm
The simple Sethi–Ullman algorithm works as follows (for a load/store architecture):
Traverse th
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https://en.wikipedia.org/wiki/Total%20Control
|
Total Control may refer to:
Total Control (Yo-Yo album), 1996
Total Control (John Norum album), 1987
Total Control (EP) by Missy Higgins]], 2022
"Total Control" (song), the second single by The Motels, 1979
Total Control (band), an Australian post-punk/garage rock band
Total Control, media gateway technology created by U.S. Robotics and used by CommWorks Corporation
Total Control, a MIDI controller for DJs produced by Numark Industries
Total Control (novel), by David Baldacci, 1997
Total Control (video game), a 1995 Russian game
Total Control (TV series), 2019
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https://en.wikipedia.org/wiki/Centre%20for%20Applied%20Cryptographic%20Research
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The Centre for Applied Cryptographic Research (CACR) is a group of industrial representatives, professors, and students at the University of Waterloo in Waterloo, Ontario, Canada who work and do research in the field of cryptography.
The CACR aims to facilitate leading-edge cryptographic research, to educate students at postgraduate levels, to host conferences and research visits, and to partner with various industries. It was officially opened on June 19, 1998.
The CACR involves students and professors from four departments at the school: Combinatorics & Optimization, Computer Science, Electrical and Computer Engineering, and Pure Math. It does not have a physical location, but utilizes resources from all the aforementioned departments.
The CACR plays a part in many conferences and workshops, including the following:
CACR Information Security Workshop
Privacy and Security Workshop
Workshop on Elliptic Curve Cryptography (ECC)
Workshop on Selected Areas in Cryptography (SAC)
The CACR includes the following notable faculty:
Scott Vanstone, professor, co-author of the Handbook of Applied Cryptography, founder of Certicom
Alfred Menezes, professor, co-author of the Handbook of Applied Cryptography
Neal Koblitz, adjunct professor, creator of elliptic curve cryptography and hyperelliptic curve cryptography
Doug Stinson, professor, author of Cryptography: Theory and Practice
Ian Goldberg, assistant professor, creator of Off-the-Record Messaging
External links
Centre for Appl
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https://en.wikipedia.org/wiki/Natural%20Sciences%20%28Cambridge%29
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The Natural Sciences Tripos (NST) is the framework within which most of the science at the University of Cambridge is taught. The tripos includes a wide range of Natural Sciences from physics, astronomy, and geoscience, to chemistry and biology, which are taught alongside the history and philosophy of science. The tripos covers several courses which form the University of Cambridge system of Tripos. It is known for its broad range of study in the first year, in which students cannot study just one discipline, but instead must choose three courses in different areas of the natural sciences and one in mathematics. As is traditional at Cambridge, the degree awarded after Part II (three years of study) is a Bachelor of Arts (BA). A Master of Natural Sciences degree (MSci) is available to those who take the optional Part III (one further year). It was started in the 19th century.
Teaching
Teaching is carried out by 16 different departments. Subjects offered in Part IA in 2019 are Biology of Cells, Chemistry, Computer Science, Evolution and Behaviour, Earth Sciences, Materials Science, Mathematics, Physics, Physiology of Organisms and Mathematical Biology; students must take three experimental subjects and one mathematics course. There are three options for the compulsory mathematics element in IA: "Mathematics A", "Mathematics B" and "Mathematical Biology". From 2020 Computer Science will no longer be an option in the natural sciences course.
Students specialize further in th
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https://en.wikipedia.org/wiki/NPU
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NPU may mean:
Science and technology
Natural Product Updates, a journal in chemistry
Net protein utilization, the ratio of amino acid mass converted to proteins to the mass of amino acids supplied
NPU terminology, a medical terminology for the clinical laboratory sciences.
Computing
Network Processing Unit, for packet processing of network packets
Neural Processing Unit, for artificial intelligence processing
Numeric (floating point) Processing Unit
Organisations
Na Píobairí Uilleann, a non-profit organization dedicated to the promotion of the Irish Uilleann pipes and its music.
Neighborhood Planning Units in Atlanta, Georgia, USA
Nineveh Plain Protection Units, an Assyrian regional militia in Iraq
National Police of Ukraine, government agency
National Power Unity, nationalist political party in Latvia.
Universities
National Penghu University of Science and Technology, Penghu, Taiwan
Nilamber Pitamber University, Medininagar, Jharkhand, India.
Northwestern Polytechnical University, Xi'an, Shaanxi, China
Northwestern Polytechnic University, Fremont, California, USA
North Park University, Chicago, Illinois, USA
See also
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https://en.wikipedia.org/wiki/Artificial%20chemistry
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An artificial chemistry is a chemical-like system that usually consists of objects, called molecules, that interact according to rules resembling chemical reaction rules. Artificial chemistries are created and studied in order to understand fundamental properties of chemical systems, including prebiotic evolution, as well as for developing chemical computing systems. Artificial chemistry is a field within computer science wherein chemical reactions—often biochemical ones—are computer-simulated, yielding insights on evolution, self-assembly, and other biochemical phenomena. The field does not use actual chemicals, and should not be confused with either synthetic chemistry or computational chemistry. Rather, bits of information are used to represent the starting molecules, and the end products are examined along with the processes that led to them. The field originated in artificial life but has shown to be a versatile method with applications in many fields such as chemistry, economics, sociology and linguistics.
Formal definition
An artificial chemistry is defined in general as a triple (S,R,A). In some cases it is sufficient to define it as a tuple (S,I).
S is the set of possible molecules S={s1...,sn}, where n is the number of elements in the set, possibly infinite.
R is a set of n-ary operations on the molecules in S, the reaction rules R={r1...,rn}. Each rule ri is written like a chemical reaction a+b+c->a*+b*+c*. Note here that ri are operators, as opposed to +.
A is a
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https://en.wikipedia.org/wiki/Irreducibility%20%28mathematics%29
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In mathematics, the concept of irreducibility is used in several ways.
A polynomial over a field may be an irreducible polynomial if it cannot be factored over that field.
In abstract algebra, irreducible can be an abbreviation for irreducible element of an integral domain; for example an irreducible polynomial.
In representation theory, an irreducible representation is a nontrivial representation with no nontrivial proper subrepresentations. Similarly, an irreducible module is another name for a simple module.
Absolutely irreducible is a term applied to mean irreducible, even after any finite extension of the field of coefficients. It applies in various situations, for example to irreducibility of a linear representation, or of an algebraic variety; where it means just the same as irreducible over an algebraic closure.
In commutative algebra, a commutative ring R is irreducible if its prime spectrum, that is, the topological space Spec R, is an irreducible topological space.
A matrix is irreducible if it is not similar via a permutation to a block upper triangular matrix (that has more than one block of positive size). (Replacing non-zero entries in the matrix by one, and viewing the matrix as the adjacency matrix of a directed graph, the matrix is irreducible if and only if such directed graph is strongly connected.) A detailed definition is given here.
Also, a Markov chain is irreducible if there is a non-zero probability of transitioning (even if in more than o
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https://en.wikipedia.org/wiki/Class%20function
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In mathematics, especially in the fields of group theory and representation theory of groups, a class function is a function on a group G that is constant on the conjugacy classes of G. In other words, it is invariant under the conjugation map on G. Such functions play a basic role in representation theory.
Characters
The character of a linear representation of G over a field K is always a class function with values in K. The class functions form the center of the group ring K[G]. Here a class function f is identified with the element .
Inner products
The set of class functions of a group G with values in a field K form a K-vector space. If G is finite and the characteristic of the field does not divide the order of G, then there is an inner product defined on this space defined by where |G| denotes the order of G and bar is conjugation in the field K. The set of irreducible characters of G forms an orthogonal basis, and if K is a splitting field for G, for instance if K is algebraically closed, then the irreducible characters form an orthonormal basis.
In the case of a compact group and K = C the field of complex numbers, the notion of Haar measure allows one to replace the finite sum above with an integral:
When K is the real numbers or the complex numbers, the inner product is a non-degenerate Hermitian bilinear form.
See also
Brauer's theorem on induced characters
References
Jean-Pierre Serre, Linear representations of finite groups, Graduate Texts in Mathem
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https://en.wikipedia.org/wiki/Semisimple%20module
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In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring that is a semisimple module over itself is known as an Artinian semisimple ring. Some important rings, such as group rings of finite groups over fields of characteristic zero, are semisimple rings. An Artinian ring is initially understood via its largest semisimple quotient. The structure of Artinian semisimple rings is well understood by the Artin–Wedderburn theorem, which exhibits these rings as finite direct products of matrix rings.
For a group-theory analog of the same notion, see Semisimple representation.
Definition
A module over a (not necessarily commutative) ring is said to be semisimple (or completely reducible) if it is the direct sum of simple (irreducible) submodules.
For a module M, the following are equivalent:
M is semisimple; i.e., a direct sum of irreducible modules.
M is the sum of its irreducible submodules.
Every submodule of M is a direct summand: for every submodule N of M, there is a complement P such that .
For the proof of the equivalences, see .
The most basic example of a semisimple module is a module over a field, i.e., a vector space. On the other hand, the ring of integers is not a semisimple module over itself, since the submodule is not a direct summand.
Semisimple is stronger than completely decomposable,
which is a direct
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https://en.wikipedia.org/wiki/Convex%20conjugate
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In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known as Legendre–Fenchel transformation, Fenchel transformation, or Fenchel conjugate (after Adrien-Marie Legendre and Werner Fenchel). It allows in particular for a far reaching generalization of Lagrangian duality.
Definition
Let be a real topological vector space and let be the dual space to . Denote by
the canonical dual pairing, which is defined by
For a function taking values on the extended real number line, its is the function
whose value at is defined to be the supremum:
or, equivalently, in terms of the infimum:
This definition can be interpreted as an encoding of the convex hull of the function's epigraph in terms of its supporting hyperplanes.
Examples
For more examples, see .
The convex conjugate of an affine function is
The convex conjugate of a power function is
The convex conjugate of the absolute value function is
The convex conjugate of the exponential function is
The convex conjugate and Legendre transform of the exponential function agree except that the domain of the convex conjugate is strictly larger as the Legendre transform is only defined for positive real numbers.
Connection with expected shortfall (average value at risk)
See this article for example.
Let F denote a cumulative distribution function of a random variable X. Then (integra
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https://en.wikipedia.org/wiki/Watterson
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Watterson may refer to:
Places
Watterson Corners, Ontario, Canada
Watterson Park, Kentucky, United States
Other
Watterson estimator, in population genetics
Bishop Watterson High School, Columbus, Ohio, US
The Henry Watterson Expressway (I-264), a highway in Louisville, Kentucky, US
Watterson Towers, a student residence hall complex at Illinois State University, US
The Watterson family from the animated show The Amazing World of Gumball
Watterson (surname), a surname
See also
Waterson (disambiguation)
English-language surnames
Patronymic surnames
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https://en.wikipedia.org/wiki/Giant%20magnetoresistance
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Giant magnetoresistance (GMR) is a quantum mechanical magnetoresistance effect observed in multilayers composed of alternating ferromagnetic and non-magnetic conductive layers. The 2007 Nobel Prize in Physics was awarded to Albert Fert and Peter Grünberg for the discovery of GMR.
The effect is observed as a significant change in the electrical resistance depending on whether the magnetization of adjacent ferromagnetic layers are in a parallel or an antiparallel alignment. The overall resistance is relatively low for parallel alignment and relatively high for antiparallel alignment. The magnetization direction can be controlled, for example, by applying an external magnetic field. The effect is based on the dependence of electron scattering on spin orientation.
The main application of GMR is in magnetic field sensors, which are used to read data in hard disk drives, biosensors, microelectromechanical systems (MEMS) and other devices. GMR multilayer structures are also used in magnetoresistive random-access memory (MRAM) as cells that store one bit of information.
In literature, the term giant magnetoresistance is sometimes confused with colossal magnetoresistance of ferromagnetic and antiferromagnetic semiconductors, which is not related to a multilayer structure.
Formulation
Magnetoresistance is the dependence of the electrical resistance of a sample on the strength of an external magnetic field. Numerically, it is characterized by the value
where R(H) is the resistan
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https://en.wikipedia.org/wiki/N-hash
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In cryptography, N-hash is a cryptographic hash function based on the FEAL round function, and is now considered insecure. It was proposed in 1990 in an article by Miyaguchi, Ohta, and Iwata; weaknesses were published the following year.
N-hash has a 128-bit hash size. A message is divided into 128-bit blocks, and each block is combined with the hash value computed so far using the g compression function. g contains eight rounds, each of which uses an F function, similar to the one used by FEAL.
Eli Biham and Adi Shamir (1991) applied the technique of differential cryptanalysis to N-hash, and showed that collisions could be generated faster than by a birthday attack for N-hash variants with even up to 12 rounds.
References
Cryptographic hash functions
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https://en.wikipedia.org/wiki/Axiom%20of%20determinacy
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In mathematics, the axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962. It refers to certain two-person topological games of length ω. AD states that every game of a certain type is determined; that is, one of the two players has a winning strategy.
Steinhaus and Mycielski's motivation for AD was its interesting consequences, and suggested that AD could be true in the smallest natural model L(R) of a set theory, which accepts only a weak form of the axiom of choice (AC) but contains all real and all ordinal numbers. Some consequences of AD followed from theorems proved earlier by Stefan Banach and Stanisław Mazur, and Morton Davis. Mycielski and Stanisław Świerczkowski contributed another one: AD implies that all sets of real numbers are Lebesgue measurable. Later Donald A. Martin and others proved more important consequences, especially in descriptive set theory. In 1988, John R. Steel and W. Hugh Woodin concluded a long line of research. Assuming the existence of some uncountable cardinal numbers analogous to , they proved the original conjecture of Mycielski and Steinhaus that AD is true in L(R).
Types of game that are determined
The axiom of determinacy refers to games of the following specific form:
Consider a subset A of the Baire space ωω of all infinite sequences of natural numbers. Two players, I and II, alternately pick natural numbers
n0, n1, n2, n3, ...
After infinitely many moves,
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https://en.wikipedia.org/wiki/Gabor%20Herman
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Gabor Tamas Herman is a Hungarian-American professor of computer science. He is Emiritas Professor of Computer Science at The Graduate Center, City University of New York (CUNY) where he was Distinguished Professor until 2017. He is known for his work on computerized tomography. He is a fellow of the Institute of Electrical and Electronics Engineers (IEEE).
Early life and education
Herman studied mathematics at the University of London, receiving his B.Sc. in 1963 and M.Sc. in 1964. In 1966, he received his M.S. in electrical engineering from the University of California, Berkeley, and in 1968 his Ph.D. in mathematics from the University of London.
Career
In 1969, Herman joined the department of computer science at Buffalo State College as an assistant professor. He became an associate professor in 1970 and a full professor in 1974. In 1976, he formed the Medical Image Processing Group. In 1980, he published the first edition of Reconstruction from Projections, his textbook on computerized tomography.
Herman moved the Medical Image Processing Group to the University of Pennsylvania in 1981. He was a professor in the radiology department from 1981 to 2000. In 1991, he was elected fellow of the IEEE. The citation reads: "For contributions to medical imagine, particularly in the theory and development of techniques for the reconstruction and display of computed tomographic images". In 1997, he was elected fellow of the American Institute for Medical and Biological Engineering
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https://en.wikipedia.org/wiki/Azeotropic%20distillation
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In chemistry, azeotropic distillation is any of a range of techniques used to break an azeotrope in distillation. In chemical engineering, azeotropic distillation usually refers to the specific technique of adding another component to generate a new, lower-boiling azeotrope that is heterogeneous (e.g. producing two, immiscible liquid phases), such as the example below with the addition of benzene to water and ethanol.
This practice of adding an entrainer which forms a separate phase is a specific sub-set of (industrial) azeotropic distillation methods, or combination thereof. In some senses, adding an entrainer is similar to extractive distillation.
Material separation agent
The addition of a material separation agent, such as benzene to an ethanol/water mixture, changes the molecular interactions and eliminates the azeotrope. Added in the liquid phase, the new component can alter the activity coefficient of various compounds in different ways thus altering a mixture's relative volatility. Greater deviations from Raoult's law make it easier to achieve significant changes in relative volatility with the addition of another component. In azeotropic distillation the volatility of the added component is the same as the mixture, and a new azeotrope is formed with one or more of the components based on differences in polarity. If the material separation agent is selected to form azeotropes with more than one component in the feed then it is referred to as an entrainer. The ad
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https://en.wikipedia.org/wiki/Silvanus%20P.%20Thompson
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Silvanus Phillips Thompson (19 June 1851 – 12 June 1916) was an English professor of physics at the City and Guilds Technical College in Finsbury, England. He was elected to the Royal Society in 1891 and was known for his work as an electrical engineer and as an author. Thompson's most enduring publication is his 1910 text Calculus Made Easy, which teaches the fundamentals of infinitesimal calculus, and is still in print. Thompson also wrote a popular physics text, Elementary Lessons in Electricity and Magnetism, as well as biographies of Lord Kelvin and Michael Faraday.
Biography
Thompson was born on 19 June 1851 to a Quaker family in York, England. His father served as a master at the Quaker Bootham School in York and he also studied there. In 1873 Silvanus Thompson was made the science master at the school. He graduated and sat for Bachelor of Arts University of London external degree in 1869. After a teaching apprenticeship he was awarded a scholarship to the Royal School of Mines (RSM) in South Kensington, where he studied chemistry and physics. He graduated with honors with a Bachelor of Science degree and started working at RSM. He soon became a Fellow of the Royal Astronomical and Physical Society; he participated in meetings—lectures with demonstrations of experiments organized at the Royal Institution.
On 11 February 1876 he heard Sir William Crookes give an evening discourse at the Royal Institution on The Mechanical Action of Light when Crookes demonstrated his
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https://en.wikipedia.org/wiki/Reference%20%28C%2B%2B%29
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In the C++ programming language, a reference is a simple reference datatype that is less powerful but safer than the pointer type inherited from C. The name C++ reference may cause confusion, as in computer science a reference is a general concept datatype, with pointers and C++ references being specific reference datatype implementations. The definition of a reference in C++ is such that it does not need to exist. It can be implemented as a new name for an existing object (similar to rename keyword in Ada).
Syntax and terminology
The declaration of the form:
<Type>& <Name>
where <Type> is a type and <Name> is an identifier is said to define an identifier whose type is lvalue reference to <Type>.
Examples:
int a = 5;
int& r_a = a;
extern int& r_b;
Here, r_a and r_b are of type "lvalue reference to int"
int& Foo();
Foo is a function that returns an "lvalue reference to int"
void Bar(int& r_p);
Bar is a function with a reference parameter, which is an "lvalue reference to int"
class MyClass { int& m_b; /* ... */ };
MyClass is a class with a member which is lvalue reference to int
int FuncX() { return 42 ; };
int (&f_func)() = FuncX;
FuncX is a function that returns a (non-reference type) int and f_func is an alias for FuncX
const int& ref = 65;
const int& ref is an lvalue reference to const int pointing to a piece of storage having value 65.
The declaration of the form:
<Type>&& <Name>
where <Type> is a type and <Name> is an identifier is said to define an
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https://en.wikipedia.org/wiki/Rodrigues%27%20formula
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In mathematics, Rodrigues' formula (formerly called the Ivory–Jacobi formula) is a formula for the Legendre polynomials independently introduced by , and . The name "Rodrigues formula" was introduced by Heine in 1878, after Hermite pointed out in 1865 that Rodrigues was the first to discover it. The term is also used to describe similar formulas for other orthogonal polynomials. describes the history of the Rodrigues formula in detail.
Statement
Let be a sequence of orthogonal polynomials satisfying the orthogonality condition
where is a suitable weight function, is a constant depending on , and is the Kronecker delta. If the weight function satisfies the following differential equation (called Pearson's differential equation),
where is a polynomial with degree at most 1 and is a polynomial with degree at most 2 and, further, the limits
then it can be shown that satisfies a recurrence relation of the form,
for some constants . This relation is called Rodrigues' type formula, or just Rodrigues' formula.
The most known applications of Rodrigues' type formulas are the formulas for Legendre, Laguerre and Hermite polynomials:
Rodrigues stated his formula for Legendre polynomials :
Laguerre polynomials are usually denoted L0, L1, ..., and the Rodrigues formula can be written as
The Rodrigues formula for the Hermite polynomials can be written as
Similar formulae hold for many other sequences of orthogonal functions arising from Sturm–Liouville equations, and thes
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https://en.wikipedia.org/wiki/Olinde%20Rodrigues
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Benjamin Olinde Rodrigues (6 October 1795 – 17 December 1851), more commonly known as Olinde Rodrigues, was a French banker, mathematician, and social reformer. In mathematics Rodrigues is remembered for Rodrigues' rotation formula for vectors, the Rodrigues formula about series of orthogonal polynomials and the Euler–Rodrigues parameters.
Biography
Rodrigues was born into a well-to-do Sephardi Jewish family in Bordeaux. His family was of Portuguese-Jewish descent. He was awarded a doctorate in mathematics on 28 June 1815 by the University of Paris. His dissertation contains the result now called Rodrigues' formula.
After graduation, Rodrigues became a banker. A close associate of the Comte de Saint-Simon, Rodrigues continued, after Saint-Simon's death in 1825, to champion the older man's socialist ideals, a school of thought that came to be known as Saint-Simonianism. During this period, Rodrigues published writings on politics, social reform, and banking.
In 1840 he published a result on transformation groups, which applied Leonhard Euler's four squares formula, a precursor to the quaternions of William Rowan Hamilton, to the problem of representing rotations in space.
In 1846 Arthur Cayley acknowledged Euler's and Rodrigues' priority describing orthogonal transformations.
Rodrigues is credited as originating the idea of the artist as an avant-garde.
Publications
Mouvement de rotation d'un corps de révolution pesant, Paris, 1815
"Mémoire sur l'attraction des sphéro
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https://en.wikipedia.org/wiki/Steven%20Rose
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Steven Peter Russell Rose (born 4 July 1938) is an English neuroscientist, author, and social commentator. He is an emeritus professor of biology and neurobiology at the Open University and Gresham College, London.
Early life
Born in London, United Kingdom, he was brought up as an Orthodox Jew. Rose says that he decided to become an atheist when he was eight years old. He went to a direct grant school in northwest London which operated a numerus clausus restricting the numbers of Jewish students. He studied biochemistry at King's College, Cambridge, and neurochemistry at the Institute of Psychiatry, King's College London.
Academic career
Following a Fellowship at New College, Oxford, and a Medical Research Council research post, he was appointed to the professorship of biology at the newly instituted Open University in 1969. At the time he was Britain's youngest full professor and chair of the department. At the Open University he established the Brain Research Group, within which he and his colleagues investigated the biological processes involved in memory formation and treatments for Alzheimer's disease on which he has published some 300 research papers and reviews. He has written several popular science books and regularly writes for The Guardian newspaper and the London Review of Books. From 1999 to 2002, he gave public lectures as a Professor of Physick (Genetics and Society) with his wife, the feminist sociologist Hilary Rose at Gresham College, London. His work has
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https://en.wikipedia.org/wiki/S%20transform
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S transform as a time–frequency distribution was developed in 1994 for analyzing geophysics data. In this way, the S transform is a generalization of the short-time Fourier transform (STFT), extending the continuous wavelet transform and overcoming some of its disadvantages. For one, modulation sinusoids are fixed with respect to the time axis; this localizes the scalable Gaussian window dilations and translations in S transform. Moreover, the S transform doesn't have a cross-term problem and yields a better signal clarity than Gabor transform. However, the S transform has its own disadvantages: the clarity is worse than Wigner distribution function and Cohen's class distribution function.
A fast S transform algorithm was invented in 2010. It reduces the computational complexity from O[N2·log(N)] to O[N·log(N)] and makes the transform one-to-one, where the transform has the same number of points as the source signal or image, compared to storage complexity of N2 for the original formulation. An implementation is available to the research community under an open source license.
A general formulation of the S transform makes clear the relationship to other time frequency transforms such as the Fourier, short time Fourier, and wavelet transforms.
Definition
There are several ways to represent the idea of the S transform. In here, S transform is derived as the phase correction of the continuous wavelet transform with window being the Gaussian function.
S-Transform
Inverse S-T
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https://en.wikipedia.org/wiki/Orkin
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Orkin is an American pest control company that was founded in 1901 by Otto Orkin. Since 1964, the company has been owned by Rollins Inc. Orkin has held research collaborations with universities around the country and with organizations like the Centers for Disease Control and Prevention (CDC) dating back to 1990 for pest biology research and pest-related disease studies.
History
Otto the Rat Man
Orkin was founded in Walnutport, Pennsylvania in 1901 by Otto Orkin, who began selling rat poison door-to-door at age 14. One of six children of a Latvian immigrant family, Orkin was responsible since an early age for shooting and poisoning rats to keep them out of the family's food stores and away from their farm animals. At age 12, Orkin began experimenting with different methods to poison rats in order to discover the most effective ones. At the age of 14 Orkin borrowed 50 cents from his parents to buy arsenic in bulk, and he began consulting with apothecaries about the best proportions and mixtures to use. His initial rat poison formulas contained a combination of arsenic and phosphorus paste, mixed with fresh food scraps or red-dyed flour or sugar (so that it would not be mistaken as edible). He began offering his preparations to his neighbors for free.
Orkin carried in what would become his signature black satchel a number of measured amounts of poison in paper bags that bore the word POISON along with a drawing of a skull and crossbones. If the customer was satisfied with t
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https://en.wikipedia.org/wiki/Nasuella
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Mountain coatis are two species of procyonid mammals from the genus Nasuella. Unlike the larger coatis from the genus Nasua, mountain coatis only weigh and are endemic to the north Andean highlands in South America.
Genetics and taxonomy
Genetic evidence indicates that the genus Nasua is only monophyletic if it also includes the mountain coatis. Based on cytochrome b sequences, Nasua nasua is the sister taxon to a clade consisting of Nasua narica plus both species of Nasuella.
Until recently only a single species with three subspecies was recognized. In 2009 this species was split into two species, the eastern mountain coati (N. meridensis) from Venezuela, and the western mountain coati (N. olivacea, with subspecies quitensis) from Colombia and Ecuador.
After a genetic analysis in 2020, the American Society of Mammalogists currently considers N. meridensis a synonym of N. olivacea.
Range and description
Externally, the two species of mountain coatis are quite similar, but the eastern mountain coati is overall smaller, somewhat shorter-tailed on average, has markedly smaller teeth, a paler olive-brown pelage, and usually a dark mid-dorsal stripe on the back (versus more rufescent or blackish, and usually without a dark mid-dorsal stripe in the western mountain coati). Both are found in cloud forest and páramo; at altitudes of for the eastern mountain coati, and for the western mountain coati.
A population discovered in southern Peru (more than south of the previous dis
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https://en.wikipedia.org/wiki/Tus
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Tus or TUS may refer to:
Tus (biology), a protein that binds to terminator sequences
Thales Underwater Systems, an international defence contractor
Tuscarora language, an Iroquoian language, ISO 639-3 code
Education
Technological University of the Shannon, Ireland
Tokyo University of Science, Japan
People
Anton Tus (born 1931), retired Croatian general
Christos Tusis (born 1986), Greek rapper
Places
Tampa Union Station, a train station in Florida, United States
Tus, Iran, an ancient city in Razavi Khorasan
Tus-e Olya, a village in Razavi Khorasan Province, Iran
Tus-e Sofla, a village in Razavi Khorasan Province, Iran
Tus Rural District, in Razavi Khorasan Province, Iran
Tus citadel, a Sassanid-era citadel in Tus, Iran
Río Tus, a river of Spain
Tucson International Airport, Arizona, U.S.
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https://en.wikipedia.org/wiki/Paul%20Scherrer
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Paul Hermann Scherrer (3 February 1890 – 25 September 1969) was a Swiss physicist. Born in St. Gallen, Switzerland, he studied at Göttingen, Germany, before becoming a lecturer there. Later, Scherrer became head of the Department of Physics at ETH Zurich.
Early life and studies
Paul Scherrer was born in St. Gallen. In 1908, he enrolled at Swiss Federal Polytechnic (later known as ETH Zurich), changing course from Botany to Mathematics and Physics after two semesters. In 1912, Scherrer spent one semester at Königsberg University, then undertook further studies at the University of Göttingen, graduating from there with a doctorate on the Faraday Effect in the hydrogen molecule. In 1916, while still working on his dissertation, he and his tutor, Peter Debye, developed the “Debye–Scherrer powder method”, a procedure using X-rays for the structural analysis of crystals. This made an important contribution to the development of the scattering techniques that are still used in the large facilities at the Paul Scherrer Institute to this day. Debye received the Nobel Prize in Chemistry for this work in 1936.
He is perhaps best known for determining the inverse relationship between the width of an x-ray diffraction peak and the crystallite size. This work was published in 1918.
ETH Zurich appointed Scherrer to the post of Professor of Experimental Physics in 1920, at the early age of 30. In 1925, he organised the first international conference of physicists to take place after the
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https://en.wikipedia.org/wiki/Boost
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Boost, boosted or boosting may refer to:
Science, technology and mathematics
Boost, positive manifold pressure in turbocharged engines
Boost (C++ libraries), a set of free peer-reviewed portable C++ libraries
Boost (material), a material branded and used by Adidas in the midsoles of shoes.
Boost, a loose term for turbo or supercharger
Boost converter, an electrical circuit variation of a DC to DC converter, which increases (boosts) the voltage
Boosted fission weapon, a type of nuclear bomb that uses a small amount of fusion fuel to increase the rate, and thus yield, of a fission reaction
Boosting (machine learning), a supervised learning algorithm
Intel Turbo Boost, a technology that enables a processor to run above its base operating frequency
Jump start (vehicle), to start a vehicle
Lorentz boost, a type of Lorentz transformation
Arts, entertainment, and media
Fictional characters
Boost (Cars), a character from the Pixar franchise Cars
Boost (comics), a character from Marvel Comics
Films
Boost (film), a 2017 Canadian film directed by Darren Curtis
The Boost, a 1988 drama film directed by Harold Becker
Brands and enterprises
Boost (chocolate bar), a chocolate bar produced by Cadbury
Boost (drink), nutritional drinks brand made by Nestlé
Boost Energy, the Pay As You Go brand of OVO Energy
Boost!, American non-carbonated cola brand
Boost Drinks, British drinks company
Boost ETP, British independent boutique Exchange Traded Products provider
Boost J
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https://en.wikipedia.org/wiki/Supercritical%20flow
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A supercritical flow is a flow whose velocity is larger than the wave velocity. The analogous condition in gas dynamics is supersonic speed.
According to the website Civil Engineering Terms, supercritical flow is defined as follows:
The flow at which depth of the channel is less than critical depth, velocity of flow is greater than critical velocity and slope of the channel is also greater than the critical slope is known as supercritical flow.
Information travels at the wave velocity. This is the velocity at which waves travel outwards from a pebble thrown into a lake. The flow velocity is the velocity at which a leaf in the flow travels. If a pebble is thrown into a supercritical flow then the ripples will all move down stream whereas in a subcritical flow some would travel up stream and some would travel down stream. It is only in supercritical flows that hydraulic jumps (bores) can occur. In fluid dynamics, the change from one behaviour to the other is often described by a dimensionless quantity, where the transition occurs whenever this number becomes less or more than one. One of these numbers is the Froude number:
where
U = velocity of the flow
g = acceleration due to gravity (9.81 m/s² or 32.2 ft/s²)
h = depth of flow relative to the channel bottom
If , we call the flow subcritical; if , we call the flow supercritical. If , it is critical.
See also
Supercritical fluid
Supercritical vs. subcritical flow
Supersonic
Hypersonic
Sonic black hole
Referen
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https://en.wikipedia.org/wiki/Artronix
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Artronix Incorporated began in 1970 and has roots in a project in a computer science class at Washington University School of Medicine in St Louis. The class designed, built and tested a 12-bit minicomputer, which later evolved to become the PC12 minicomputer. The new company entered the bio-medical computing market with a set of peripherals and software for use in Radiation Treatment Planning (see full article and abstract) and ultrasound scanning. Software for the PC12 was written in assembly language and FORTRAN; later software was written in MUMPS. The company was located in two buildings in the Hanley Industrial Park off South Hanley Road in Maplewood, Missouri.
The company later developed another product line of brain-scanning or computed tomography equipment based on the Lockheed SUE 16-bit minicomputer (see also Pluribus); later designs included an optional vector processor using AMD Am2900 bipolar bit-slices to speed tomographic reconstruction calculations. In contrast to earlier designs, the Artronix scanner used a fan-shaped beam with 128 detectors on a rotating gantry. The system would take 540 degrees of data (1½ rotations) to average out noise in the samples. The beam allowed 3mm slices, but several slices would routinely be mathematically combined into one image for display purposes. The first generation of scanners was a head scanner while a later generation was a torso (whole-body) scanner. The CAT-3 (computerized axial tomography) system was a suc
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https://en.wikipedia.org/wiki/List%20of%20theorems%20called%20fundamental
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In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus. The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory. Some of these are classification theorems of objects which are mainly dealt with in the field. For instance, the fundamental theorem of curves describe classification of regular curves in space up to translation and rotation.
Likewise, the mathematical literature sometimes refers to the fundamental lemma of a field. The term lemma is conventionally used to denote a proven proposition which is used as a stepping stone to a larger result, rather than as a useful statement in-and-of itself.
Fundamental theorems of mathematical topics
Fundamental theorem of algebra
Fundamental theorem of algebraic K-theory
Fundamental theorem of arithmetic
Fundamental theorem of Boolean algebra
Fundamental theorem of calculus
Fundamental theorem of calculus for line integrals
Fundamental theorem of curves
Fundamental theorem of cyclic groups
Fundamental theorem of dynamical systems
Fundamental theorem of equivalence relations
Fundamental theorem of exterior calculus
Fundamental theorem of finitely generated abelian groups
Fundamental theorem of finitely generated modules over a principal idea
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https://en.wikipedia.org/wiki/Apomorphy%20and%20synapomorphy
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In phylogenetics, an apomorphy (or derived trait) is a novel character or character state that has evolved from its ancestral form (or plesiomorphy). A synapomorphy is an apomorphy shared by two or more taxa and is therefore hypothesized to have evolved in their most recent common ancestor. In cladistics, synapomorphy implies homology.
Examples of apomorphy are the presence of erect gait, fur, the evolution of three middle ear bones, and mammary glands in mammals but not in other vertebrate animals such as amphibians or reptiles, which have retained their ancestral traits of a sprawling gait and lack of fur. Thus, these derived traits are also synapomorphies of mammals in general as they are not shared by other vertebrate animals.
Etymology
The word —coined by German entomologist Willi Hennig—is derived from the Ancient Greek words (sún), meaning "with, together"; (apó), meaning "away from"; and (morphḗ), meaning "shape, form".
Clade analysis
The concept of synapomorphy depends on a given clade in the tree of life. Cladograms are diagrams that depict evolutionary relationships within groups of taxa. These illustrations are accurate predictive device in modern genetics. They are usually depicted in either tree or ladder form. Synapomorphies then create evidence for historical relationships and their associated hierarchical structure. Evolutionarily, a synapomorphy is the marker for the most recent common ancestor of the monophyletic group consisting of a set of taxa i
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https://en.wikipedia.org/wiki/Biorobotics
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Biorobotics is an interdisciplinary science that combines the fields of biomedical engineering, cybernetics, and robotics to develop new technologies that integrate biology with mechanical systems to develop more efficient communication, alter genetic information, and create machines that imitate biological systems.
Cybernetics
Cybernetics focuses on the communication and system of living organisms and machines that can be applied and combined with multiple fields of study such as biology, mathematics, computer science, engineering, and much more.
This discipline falls under the branch of biorobotics because of its combined field of study between biological bodies and mechanical systems. Studying these two systems allow for advanced analysis on the functions and processes of each system as well as the interactions between them.
History
Cybernetic theory is a concept that has existed for centuries, dating back to the era of Plato where he applied the term to refer to the "governance of people". The term cybernetique is seen in the mid 1800s used by physicist André-Marie Ampère. The term cybernetics was popularized in the late 1940s to refer to a discipline that touched on, but was separate, from established disciplines, such as electrical engineering, mathematics, and biology.
Science
Cybernetics is often misunderstood because of the breadth of disciplines it covers. In the early 20th century, it was coined as an interdisciplinary field of study that combines biology, s
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https://en.wikipedia.org/wiki/Nanorobotics
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Nanoid robotics, or for short, nanorobotics or nanobotics, is an emerging technology field creating machines or robots whose components are at or near the scale of a nanometer (10−9 meters). More specifically, nanorobotics (as opposed to microrobotics) refers to the nanotechnology engineering discipline of designing and building nanorobots with devices ranging in size from 0.1 to 10 micrometres and constructed of nanoscale or molecular components. The terms nanobot, nanoid, nanite, nanomachine and nanomite have also been used to describe such devices currently under research and development.
Nanomachines are largely in the research and development phase, but some primitive molecular machines and nanomotors have been tested. An example is a sensor having a switch approximately 1.5 nanometers across, able to count specific molecules in the chemical sample. The first useful applications of nanomachines may be in nanomedicine. For example, biological machines could be used to identify and destroy cancer cells. Another potential application is the detection of toxic chemicals, and the measurement of their concentrations, in the environment. Rice University has demonstrated a single-molecule car developed by a chemical process and including Buckminsterfullerenes (buckyballs) for wheels. It is actuated by controlling the environmental temperature and by positioning a scanning tunneling microscope tip.
Another definition is a robot that allows precise interactions with nanoscale o
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https://en.wikipedia.org/wiki/Analytic%20proof
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In mathematics, an analytic proof is a proof of a theorem in analysis that only makes use of methods from analysis, and which does not predominantly make use of algebraic or geometrical methods. The term was first used by Bernard Bolzano, who first provided a non-analytic proof of his intermediate value theorem and then, several years later provided a proof of the theorem that was free from intuitions concerning lines crossing each other at a point, and so he felt happy calling it analytic (Bolzano 1817).
Bolzano's philosophical work encouraged a more abstract reading of when a demonstration could be regarded as analytic, where a proof is analytic if it does not go beyond its subject matter (Sebastik 2007). In proof theory, an analytic proof has come to mean a proof whose structure is simple in a special way, due to conditions on the kind of inferences that ensure none of them go beyond what is contained in the assumptions and what is demonstrated.
Structural proof theory
In proof theory, the notion of analytic proof provides the fundamental concept that brings out the similarities between a number of essentially distinct proof calculi, so defining the subfield of structural proof theory. There is no uncontroversial general definition of analytic proof, but for several proof calculi there is an accepted notion. For example:
In Gerhard Gentzen's natural deduction calculus the analytic proofs are those in normal form; that is, no formula occurrence is both the principa
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https://en.wikipedia.org/wiki/Karen%20Holbrook
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Karen Ann Holbrook (born November 6, 1942, in Des Moines, Iowa) is the regional chancellor of University of South Florida Sarasota-Manatee since January 2, 2018.
Career
Holbrook earned her B.S. and M.S. from the University of Wisconsin–Madison, in zoology. After teaching biology at Ripon College, she earned a Ph.D. in biological structure from the University of Washington School of Medicine in 1972, where she served as a postdoctoral fellow in dermatology, faculty member and research administrator. She then pursued further training in dermatology. She is an alumna of Gamma Phi Beta sorority.
Holbrook was a professor of biological structure and medicine at University of Washington School of Medicine, where she became the first woman to be named associate dean at the UW School of Medicine, vice president for research and dean of the graduate school at the University of Florida, and senior vice president for academic affairs and provost at the University of Georgia.
President of Ohio State
From 2002 to 2007, she was the 13th presiding president of Ohio State University. During Holbrook's tenure, she worked with Columbus Mayor Michael B. Coleman to improve safety both on- and off-campus. This was in reaction to riots following a Michigan–Ohio State football game in 2002. Holbrook announced in June 2006 that she would depart Ohio State when her five-year contract was up in 2007 to spend more time with her husband, Jim. Joseph A. Alutto, dean of the Max M. Fisher College of Bus
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https://en.wikipedia.org/wiki/Peter%20G.%20Schultz
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Peter G. Schultz (born June 23, 1956) is an American chemist. He is the CEO and Professor of Chemistry at The Scripps Research Institute, the founder and former director of GNF, and the founding director of the California Institute for Biomedical Research (Calibr), established in 2012. In August 2014, Nature Biotechnology ranked Schultz the #1 top translational researcher in 2013.
Academic career
Schultz completed his undergraduate degree at Caltech in 1979 and continued there for his doctoral degree (in 1984) with Peter Dervan. His thesis work focused on the generation and characterization of 1,1-diazenes and the generation of sequence-selective polypyrrole DNA binding/cleaving molecules. He then spent a year at the Massachusetts Institute of Technology with Christopher Walsh before joining the chemistry faculty at the University of California, Berkeley. He became a Principal Investigator of Lawrence Berkeley National Laboratory in 1985 and an investigator of the Howard Hughes Medical Institute in 1994. In 1999 Schultz moved to The Scripps Research Institute and also became founding Director of the Genomics Institute of the Novartis Research Foundation (GNF), which was initiated purely as a genomic research outlet of Novartis, but which grew during Schultz's tenure to include a significant drug discovery effort and more than triple the number of intended employees (currently over 500 people). In March 2010, he left GNF to return to the non-profit sector and founded th
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https://en.wikipedia.org/wiki/Consistency%20%28disambiguation%29
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Consistency, in logic, is a quality of no contradiction.
Consistency may also refer to:
Computer science
Consistency (database systems)
Consistency (knowledge bases)
Consistency (user interfaces)
Consistent hashing
Consistent heuristic
Consistency model
Data consistency
Statistics
Consistency (statistics), a property of an estimation technique giving the right answer with an infinite amount of data
Consistent estimator
Fisher consistency
Consistent test: see Statistical hypothesis testing
Physics
The viscosity of a thick fluid
Consistency (suspension) of a suspension
Consistent histories, in quantum mechanics
Other uses
Consistency (negotiation), the psychological need to be consistent with prior acts and statements
"Consistency", an 1887 speech by Mark Twain
"Consistency", a song by Megan Thee Stallion and Jhené Aiko from the album Traumazine, 2022
The consistency criterion, a measure of a voting system requiring that where one is elected by all segments of the voters, one must win the election
Consistency Theory, an album by 1200 Techniques
Consistent and inconsistent equations, in mathematics
Consistent life ethic, an ideology stating that life is sacred
Equiconsistency, in logic
Mr. Consistency (foaled 1958), American Thoroughbred racehorse
See also
Constancy (disambiguation)
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https://en.wikipedia.org/wiki/Chemistry%20%28band%29
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Chemistry (styled as CHEMISTRY) is a Japanese pop duo, consisting of and .
History
They were the winners of the Asayan audition (similar to the American Idol series) in 2000 organized by Sony Music Entertainment Japan.
Their first single "Pieces of a Dream" was released on March 3, 2001, and was the best selling single that year (over 2 million). Most of their singles have reached #1 on the Oricon charts; all five albums have reached #1 the day they were released. Their #1 streak was broken by the KinKi Kids' album H Album: Hand, scoring them a #2 rank for Fo(u)r.
Chemistry is also known in Korea for the popular collaboration song "Let's Get Together Now," featuring talents from both Korea and Japan and for collaborating with Korean singer Lena Park who appears in the B-side "Dance with Me" on the "Kimi ga Iru" single.
On March 6, 2008, Kaname Kawabata married model Miki Takahashi. They met after she appeared in the PV for "This Night."
Their single "Period" was selected as the fourth opening for the anime series Fullmetal Alchemist: Brotherhood.
In 2010, Chemistry worked together with the 4-person dance group Synergy to release "Shawty". Another joint work of the two groups was released November 3, 2010, titled "Keep Your Love".
In 2011, Chemistry was tapped by Bandai Visual to record a song for the OVA series, Mobile Suit Gundam Unicorn, due to be the title song for the 3rd episode, "The Ghost of Laplace". "Merry-go-round" is due for release on March 2, 2011, as a
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https://en.wikipedia.org/wiki/Wigner%E2%80%93Eckart%20theorem
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The Wigner–Eckart theorem is a theorem of representation theory and quantum mechanics. It states that matrix elements of spherical tensor operators in the basis of angular momentum eigenstates can be expressed as the product of two factors, one of which is independent of angular momentum orientation, and the other a Clebsch–Gordan coefficient. The name derives from physicists Eugene Wigner and Carl Eckart, who developed the formalism as a link between the symmetry transformation groups of space (applied to the Schrödinger equations) and the laws of conservation of energy, momentum, and angular momentum.
Mathematically, the Wigner–Eckart theorem is generally stated in the following way. Given a tensor operator and two states of angular momenta and , there exists a constant such that for all , , and , the following equation is satisfied:
where
is the -th component of the spherical tensor operator of rank ,
denotes an eigenstate of total angular momentum and its z component ,
is the Clebsch–Gordan coefficient for coupling with to get ,
denotes some value that does not depend on , , nor and is referred to as the reduced matrix element.
The Wigner–Eckart theorem states indeed that operating with a spherical tensor operator of rank on an angular momentum eigenstate is like adding a state with angular momentum k to the state. The matrix element one finds for the spherical tensor operator is proportional to a Clebsch–Gordan coefficient, which arises when consider
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https://en.wikipedia.org/wiki/Starquake
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Starquake may refer to:
Starquake (astrophysics), a phenomenon when the crust of a neutron star undergoes a sudden adjustment
Starquake (novel), a 1989 novel by Robert L. Forward
Starquake (video game), a 1985 computer game
See also
Asteroseismology, the study of oscillations in stars
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https://en.wikipedia.org/wiki/Pendulum%20%28disambiguation%29
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A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity.
Pendulum may also refer to:
Devices
Pendulum (mathematics), the mathematical principles of a pendulum
Pendulum clock, a kind of clock that uses a pendulum to keep time
Pendulum car, an experimental tilting train
Foucault pendulum, a pendulum that demonstrates the Earth's rotation
Spherical pendulum
Spring pendulum
Conical pendulum
Centrifugal pendulum absorber, torsional vibration reduction by using a pendulum principle
For other types and uses of pendulums, see: :Category:Pendulums
Mackerras Pendulum, a model devised by Malcolm Mackerras to predict election outcomes
Pendulum (torture device), a device allegedly used by the Spanish Inquisition
Pendulum Instruments, a Swedish manufacturer of scientific instruments
Music
Pendulum (Australian band), an Australian electronic rock group formed in 2002
Pendulum (ambient band), an Australian house music group formed in 1994
Albums
Pendulum (Broadcast EP), and its title track
Pendulum (Creedence Clearwater Revival album)
Pendulum (Dave Liebman album), and its title track
Pendulum (Eberhard Weber album), and its title track
Pendulum (Lowen & Navarro album), and its title track
Pendulum (Tara Simmons EP), and its title track
The Pendulum, a comic book miniseries based on Insane Clown Posse's Dark Carnival universe, and associated songs and album
Songs
"Pendulum" (song), by FKA Twigs
"Pe
|
https://en.wikipedia.org/wiki/Weak%20equivalence
|
In mathematics, weak equivalence may refer to:
Weak equivalence of categories
Weak equivalence (homotopy theory)
Weak equivalence (formal languages)
|
https://en.wikipedia.org/wiki/Callus%20%28cell%20biology%29
|
Plant callus (plural calluses or calli) is a growing mass of unorganized plant parenchyma cells. In living plants, callus cells are those cells that cover a plant wound. In biological research and biotechnology callus formation is induced from plant tissue samples (explants) after surface sterilization and plating onto tissue culture medium in vitro (in a closed culture vessel such as a Petri dish). The culture medium is supplemented with plant growth regulators, such as auxin, cytokinin, and gibberellin, to initiate callus formation or somatic embryogenesis. Callus initiation has been described for all major groups of land plants.
Callus induction and tissue culture
Plant species representing all major land plant groups have been shown to be capable of producing callus in tissue culture. A callus cell culture is usually sustained on gel medium. Callus induction medium consists of agar and a mixture of macronutrients and micronutrients for the given cell type. There are several types of basal salt mixtures used in plant tissue culture, but most notably modified Murashige and Skoog medium, White's medium, and woody plant medium. Vitamins are also provided to enhance growth such as Gamborg B5 vitamins. For plant cells, enrichment with nitrogen, phosphorus, and potassium is especially important. Plant callus is usually derived from somatic tissues. The tissues used to initiate callus formation depends on plant species and which tissues are available for explant cultur
|
https://en.wikipedia.org/wiki/Cruciform
|
Cruciform is a term for physical manifestations resembling a common cross or Christian cross. The label can be extended to architectural shapes, biology, art, and design.
Cruciform architectural plan
Christian churches are commonly described as having a cruciform architecture. In Early Christian, Byzantine and other Eastern Orthodox forms of church architecture this is likely to mean a tetraconch plan, a Greek cross, with arms of equal length or, later, a cross-in-square plan.
In the Western churches, a cruciform architecture usually, though not exclusively, means a church built with the layout developed in Gothic architecture. This layout comprises the following:
An east end, containing an altar and often with an elaborate, decorated window, through which light will shine in the early part of the day.
A west end, which sometimes contains a baptismal font, being a large decorated bowl, in which water can be firstly, blessed (dedicated to the use and purposes of God) and then used for baptism.
North and south transepts, being "arms" of the cross and often containing rooms for gathering, small side chapels, or in many cases other necessities such as an organ and toilets.
The crossing, which in later designs often was under a tower or dome.
In churches that are not oriented with the altar at the geographical east end, it is usual to refer to the altar end as "liturgical east" and so forth.
Methodist tabernacles also have a cruciform shape.
Another example of ancient cruc
|
https://en.wikipedia.org/wiki/GSD
|
GSD may refer to:
Places
Garsdale railway station, England (GB CRS code)
Georgia School for the Deaf, Cave Spring, Georgia, United States
Harvard Graduate School of Design, Gund Hall, Cambridge, Massachusetts, US
Science and technology
Biology and medicine
Genetic significant dose
German shepherd dog
Global Species Database
Glutathione synthetase deficiency
Glycogen storage disease
Other uses in science and technology
GSD microscopy
GSD chemical file format
Geometric standard deviation
Graphical system design
Ground sample distance
Other uses
Gender and sexual diversity
Gibraltar Social Democrats, a political party in Gibraltar
Go Skateboarding Day
General sewing data or garment sewing data, in a predetermined motion time system
Great Sun of Discovery, in the dating system used by the Improved Order of Red Men
Government shutdown
See also
General Security Directorate (disambiguation)
General Staff Department (disambiguation)
GSD&M, an American advertising agency
GSDP or gross domestic product
GSDS (disambiguation)
|
https://en.wikipedia.org/wiki/Firewalking
|
Firewalking is the act of walking barefoot over a bed of hot embers or stones. It has been practiced by many people and cultures in many parts of the world, with the earliest known reference dating from Iron Age India . It is often used as a rite of passage, as a test of strength and courage, and in religion as a test of faith.
Modern physics has explained the phenomenon, concluding that the foot does not touch the hot surface long enough to burn and that embers are poor conductors of heat.
History
Walking on fire has existed for several thousand years, with records dating back to 1200 BCE. Cultures across the globe use firewalking for rites of healing, initiation, and faith.
Firewalking is also practiced by:
The Sawau clan on the island of Beqa, to the south of Viti Levu in the Fijian Islands. The phenomenon was examined in 1902 when it was already a tourist attraction, with a "Probable Explanation of the Mystery" arrived at.
San Pedro Manrique, a village of Soria, Central Spain
Eastern Orthodox Christians in parts of Greece (see Anastenaria) and Bulgaria (see nestinarstvo), during some popular religious feasts.
Tribes throughout Polynesia, documented in scientific journals (with pictures and chants) between 1893 and 1953.
Persistence and functions
Social theorists have long argued that the performance of intensely arousing collective events such as firewalking persists because it serves some basic socialising function, such as social cohesion, team building, and so
|
https://en.wikipedia.org/wiki/Julio%20Garavito%20Armero
|
Julio Garavito Armero (January 5, 1865 – March 11, 1920) was a Colombian astronomer.
Life
Born in Bogotá, he was a child prodigy in science and mathematics. He obtained his degrees as mathematician and civil engineer in the Universidad Nacional de Colombia (National university of Colombia). In 1892, he worked as the director of the Observatorio Astronómico Nacional (National Astronomical Observatory). His investigative works had been published in Los Anales de Ingeniería (The Annals of Engineering) since 1890, seven years before he took over editing the publication.
In his youth he studied at San Bartolomé high school, but in 1885 he had to interrupt his studies temporarily because of the civil wars which were affecting his home country. During the Thousand Days War, Garavito was part of a secret scientific society called El Círculo de los Nueve Puntos (the nine-point circle), where the condition for admission was to solve a problem about Euler's theorem. This group was active until Garavito's death. As an astronomer of the observatory, he did many useful scientific investigations such as calculating the latitude of Bogotá, studies about the comets which passed by the Earth between 1901 and 1910 (such as Comet Halley), and the 1916 solar eclipse (seen in the majority of Colombia).
But perhaps the most important were his studies about celestial mechanics, which finally turned into studies about lunar fluctuations and their influence on weather, floods, polar ice, and the E
|
https://en.wikipedia.org/wiki/Closed%20convex%20function
|
In mathematics, a function is said to be closed if for each , the sublevel set
is a closed set.
Equivalently, if the epigraph defined by
is closed, then the function is closed.
This definition is valid for any function, but most used for convex functions. A proper convex function is closed if and only if it is lower semi-continuous. For a convex function that is not proper, there is disagreement as to the definition of the closure of the function.
Properties
If is a continuous function and is closed, then is closed.
If is a continuous function and is open, then is closed if and only if it converges to along every sequence converging to a boundary point of .
A closed proper convex function f is the pointwise supremum of the collection of all affine functions h such that h ≤ f (called the affine minorants of f).
References
Convex analysis
Types of functions
|
https://en.wikipedia.org/wiki/Bartonella%20henselae
|
Bartonella henselae, formerly Rochalimæa henselae, is a bacterium that is the causative agent of cat-scratch disease (bartonellosis).
Bartonella henselae is a member of the genus Bartonella, one of the most common types of bacteria in the world. The specific name henselae honors Diane Marie Hensel (b. 1953), a clinical microbiology technologist at University of Oklahoma Health Sciences Center, who collected numerous strains and samples of the infective agent during an outbreak in Oklahoma in 1985. It is a facultative intracellular microbe that targets red blood cells. One study showed it invaded the mature blood cells of humans. It infects the host cell by sticking to it using trimeric autotransporter adhesins. In the United States, about 20,000 cases are diagnosed each year, most under 15 years old. Most often, it is transmitted by scratches or bites from kittens.
Diagnosis
Bartonella henselae is a Gram-negative rod. It can be cultured in a lysis-centrifugation blood culture. The presence of bacteria can be detected by Warthin-Starry stain, or by a similar silver stain technique performed on infected tissue. A pan-Bartonella PCR detection is non-invasive and uses blood or biopsies to diagnose.
Symptoms
Bartonella henselae infection can appear up to 10 days after exposure to the microbe. Symptoms start with a papule at the site the microbe entered, followed by lymphadenopathy, usually in the axillary node. Half of patients also get aches, nausea, abdominal pain, and mala
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https://en.wikipedia.org/wiki/Giemsa%20stain
|
Giemsa stain (), named after German chemist and bacteriologist Gustav Giemsa, is a nucleic acid stain used in cytogenetics and for the histopathological diagnosis of malaria and other parasites.
Uses
It is specific for the phosphate groups of DNA and attaches itself to regions of DNA where there are high amounts of adenine-thymine bonding. Giemsa stain is used in Giemsa banding, commonly called G-banding, to stain chromosomes and often used to create a karyogram (chromosome map). It can identify chromosomal aberrations such as translocations and rearrangements.
It stains the trophozoite Trichomonas vaginalis, which presents with greenish discharge and motile cells on wet prep.
Giemsa stain is also a differential stain, such as when it is combined with Wright stain to form Wright-Giemsa stain. It can be used to study the adherence of pathogenic bacteria to human cells. It differentially stains human and bacterial cells purple and pink respectively. It can be used for histopathological diagnosis of the Plasmodium species that cause malaria and some other spirochete and protozoan blood parasites. It is also used in Wolbachia cell stain in Drosophila melanogaster.
Giemsa stain is a classic blood film stain for peripheral blood smears and bone marrow specimens. Erythrocytes stain pink, platelets show a light pale pink, lymphocyte cytoplasm stains sky blue, monocyte cytoplasm stains pale blue, and leukocyte nuclear chromatin stains magenta. It is also used to visualize the cl
|
https://en.wikipedia.org/wiki/Bourbaki%E2%80%93Witt%20theorem
|
In mathematics, the Bourbaki–Witt theorem in order theory, named after Nicolas Bourbaki and Ernst Witt, is a basic fixed point theorem for partially ordered sets. It states that if X is a non-empty chain complete poset, and
such that
for all
then f has a fixed point. Such a function f is called inflationary or progressive.
Special case of a finite poset
If the poset X is finite then the statement of the theorem has a clear interpretation that leads to the proof. The sequence of successive iterates,
where x0 is any element of X, is monotone increasing. By the finiteness of X, it stabilizes:
for n sufficiently large.
It follows that x∞ is a fixed point of f.
Proof of the theorem
Pick some . Define a function K recursively on the ordinals as follows:
If is a limit ordinal, then by construction
is a chain in X. Define
This is now an increasing function from the ordinals into X. It cannot be strictly increasing, as if it were we would have an injective function from the ordinals into a set, violating Hartogs' lemma. Therefore the function must be eventually constant, so for some
that is,
So letting
we have our desired fixed point. Q.E.D.
Applications
The Bourbaki–Witt theorem has various important applications. One of the most common is in the proof that the axiom of choice implies Zorn's lemma. We first prove it for the case where X is chain complete and has no maximal element. Let g be a choice function on
Define a function
by
This is a
|
https://en.wikipedia.org/wiki/Fixed-point%20theorem
|
In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms.
In mathematical analysis
The Banach fixed-point theorem (1922) gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point.
By contrast, the Brouwer fixed-point theorem (1911) is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, but it doesn't describe how to find the fixed point (See also Sperner's lemma).
For example, the cosine function is continuous in [−1,1] and maps it into [−1, 1], and thus must have a fixed point. This is clear when examining a sketched graph of the cosine function; the fixed point occurs where the cosine curve y = cos(x) intersects the line y = x. Numerically, the fixed point (known as the Dottie number) is approximately x = 0.73908513321516 (thus x = cos(x) for this value of x).
The Lefschetz fixed-point theorem (and the Nielsen fixed-point theorem) from algebraic topology is notable because it gives, in some sense, a way to count fixed points.
There are a number of generalisations to Banach fixed-point theorem and further; these are applied in PDE theory. See fixed-point theorems in infinite-dimensional spaces.
The collage theorem in fractal compression proves that, fo
|
https://en.wikipedia.org/wiki/Chain-complete%20partial%20order
|
In mathematics, specifically order theory, a partially ordered set is chain-complete if every chain in it has a least upper bound. It is ω-complete when every increasing sequence of elements (a type of countable chain) has a least upper bound; the same notion can be extended to other cardinalities of chains.
Examples
Every complete lattice is chain-complete. Unlike complete lattices, chain-complete posets are relatively common. Examples include:
The set of all linearly independent subsets of a vector space V, ordered by inclusion.
The set of all partial functions on a set, ordered by restriction.
The set of all partial choice functions on a collection of non-empty sets, ordered by restriction.
The set of all prime ideals of a ring, ordered by inclusion.
The set of all consistent theories of a first-order language.
Properties
A poset is chain-complete if and only if it is a pointed dcpo. However, this equivalence requires the axiom of choice.
Zorn's lemma states that, if a poset has an upper bound for every chain, then it has a maximal element. Thus, it applies to chain-complete posets, but is more general in that it allows chains that have upper bounds but do not have least upper bounds.
Chain-complete posets also obey the Bourbaki–Witt theorem, a fixed point theorem stating that, if f is a function from a chain complete poset to itself with the property that f(x) ≥ x for all x, then f has a fixed point. This theorem, in turn, can be used to prove that Zorn's lemma
|
https://en.wikipedia.org/wiki/Branch%20%28computer%20science%29
|
A branch is an instruction in a computer program that can cause a computer to begin executing a different instruction sequence and thus deviate from its default behavior of executing instructions in order. Branch (or branching, branched) may also refer to the act of switching execution to a different instruction sequence as a result of executing a branch instruction. Branch instructions are used to implement control flow in program loops and conditionals (i.e., executing a particular sequence of instructions only if certain conditions are satisfied).
A branch instruction can be either an unconditional branch, which always results in branching, or a conditional branch, which may or may not cause branching depending on some condition. Also, depending on how it specifies the address of the new instruction sequence (the "target" address), a branch instruction is generally classified as direct, indirect or relative, meaning that the instruction contains the target address, or it specifies where the target address is to be found (e.g., a register or memory location), or it specifies the difference between the current and target addresses.
Implementation
Branch instructions can alter the contents of the CPU's Program Counter (or PC) (or Instruction Pointer on Intel microprocessors). The PC maintains the memory address of the next machine instruction to be fetched and executed. Therefore, a branch, if executed, causes the CPU to execute code from a new memory address, changing th
|
https://en.wikipedia.org/wiki/JCA
|
JCA may refer to:
Computing
Java Cryptography Architecture
Java EE Connector Architecture, for connecting application servers and enterprise information systems (EIS)
Military
Joint capability areas, US Department of Defense listing of military capabilities
Joint Cargo Aircraft, US Army and Air Force designation for the C-27 Spartan
Joint Combat Aircraft, Royal Navy and RAF designation for the F-35 Joint Strike Fighter
Organizations
Camp JCA Shalom, a sleep-away camp in Malibu, California
Jain Center of America, a Jain temple in New York, United States
Japan Cricket Association, the governing body for cricket in Japan
Japan Chess Association, the governing body for chess in Japan
Japanese Cancer Association, a cancer research association in Japan
Jewish Colonisation Association, founded 1891 to facilitate emigration of Jews
Joliet Catholic Academy, Illinois, US
Josephite Community Aid, Australian charity founded in 1986
Publications
Journal of Computational Acoustics
Other uses
Juvenile chronic arthritis
Jean-Claude Ades, German electronic music producer
Jackie Chan Adventures
|
https://en.wikipedia.org/wiki/Newmark-beta%20method
|
The Newmark-beta method is a method of numerical integration used to solve certain differential equations. It is widely used in numerical evaluation of the dynamic response of structures and solids such as in finite element analysis to model dynamic systems. The method is named after Nathan M. Newmark, former Professor of Civil Engineering at the University of Illinois at Urbana–Champaign, who developed it in 1959 for use in structural dynamics. The semi-discretized structural equation is a second order ordinary differential equation system,
here is the mass matrix, is the damping matrix, and are internal force per unit displacement and external forces, respectively.
Using the extended mean value theorem, the Newmark- method states that the first time derivative (velocity in the equation of motion) can be solved as,
where
therefore
Because acceleration also varies with time, however, the extended mean value theorem must also be extended to the second time derivative to obtain the correct displacement. Thus,
where again
The discretized structural equation becomes
Explicit central difference scheme is obtained by setting and
Average constant acceleration (Middle point rule) is obtained by setting and
Stability Analysis
A time-integration scheme is said to be stable if there exists an integration time-step so that for any , a finite variation of the state vector at time induces only a non-increasing variation of the state-vector calculated at a subseque
|
https://en.wikipedia.org/wiki/Mike%20Pinkerton
|
Mike "Pink" Pinkerton is an American software engineer who is known for his work on the Mozilla browsers. He lectures on Development of Open Source Software at George Washington University.
Pinkerton studied at University of California, San Diego where he graduated with a B.S. in Computer Science, then at Georgia Institute of Technology where he graduated with a Master's Degree in Computer Science.
Pinkerton started working at Netscape Communications in June 1997 where he worked on the Netscape Navigator and then Mozilla browsers. While at Netscape he started development of the Camino (then Chimera) web browser with Dave Hyatt. Hyatt, whom Pinkerton inexplicably refers to as "Jinglepants," was hired by Apple Inc. to work on the Safari browser and Pinkerton became the Camino project lead. In October 2002 he started working at AOL as Netscape Communications became a division within AOL.
In September 2005, he accepted a position at Google where he originally was part of their Firefox team. On January 9, 2006, Pinkerton announced on his blog that he had moved to Google's "Mac Client Team". On September 3, 2008, he announced on his blog that he was working on Mac port of Google's Chrome browser.
In 2018 Pink’s team launched version 69 of Chrome iOS as part of the Chrome 10th Anniversary.
Prior to his Chrome work, Mike was the Technical Lead for Google Desktop for Mac.
References
External links
Mike's Slice of Home - a personal website
Mike Pinkerton on Camino - "Open Sour
|
https://en.wikipedia.org/wiki/Volterra%20%28disambiguation%29
|
Volterra is a town in Italy.
Volterra may also refer:
People
Aaron Ḥai Volterra (), Italian poet and rabbi
Daniele da Volterra (1509–1566), Italian painter
Francesco da Volterra, Italian painter
Vito Volterra (1860–1940), Italian mathematician
Mathematics
Lotka–Volterra equations, also known as the predator–prey equations
Smith–Volterra–Cantor set, a Cantor set with measure greater than zero
Volterra's function, a differentiable function whose derivative is not Riemann integrable
Volterra integral equation, a generalization of the indefinite integral
Volterra operator, a bounded linear operator on the space of square integrable functions, the operator corresponding to an indefinite integral
Volterra series
Volterra space, a property of topological spaces
Othe
Volterra (crater), a lunar impact crater on the far side of the Moon
Volterra Semiconductor, an American semiconductor company
Project Volterra, a compact desktop PC intended to be used as developer kit from Microsoft
|
https://en.wikipedia.org/wiki/Ratio%20Club
|
The Ratio Club was a small British informal dining club from 1949 to 1958 of young psychiatrists, psychologists, physiologists, mathematicians and engineers who met to discuss issues in cybernetics.
History
The idea of the club arose from a symposium on animal behaviour held in July 1949 by the Society of Experimental Biology in Cambridge. The club was founded by the neurologist John Bates, with other notable members such as W. Ross Ashby.
The name Ratio was suggested by Albert Uttley, it being the Latin root meaning "computation or the faculty of mind which calculates, plans and reasons". He pointed out that it is also the root of rationarium, meaning a statistical account, and ratiocinatius, meaning argumentative. The use was probably inspired by an earlier suggestion by Donald Mackay of the 'MR club', from Machina ratiocinatrix, a term used by Norbert Wiener in the introduction to his then recently published book Cybernetics, or Control and Communication in the Animal and the Machine. Wiener used the term in reference to calculus ratiocinator, a calculating machine constructed by Leibniz.
The initial membership was W. Ross Ashby, Horace Barlow, John Bates, George Dawson, Thomas Gold, W. E. Hick, Victor Little, Donald MacKay, Turner McLardy, P. A. Merton, John Pringle, Harold Shipton, Donald Sholl, Eliot Slater, Albert Uttley, W. Grey Walter and John Hugh Westcott. Alan Turing joined after the first meeting with I. J. Good, Philip Woodward and William Rushton added soo
|
https://en.wikipedia.org/wiki/Michael%20Barnsley
|
Michael Fielding Barnsley (born 1946) is a British mathematician, researcher and an entrepreneur who has worked on fractal compression; he holds several patents on the technology. He received his Ph.D. in theoretical chemistry from University of Wisconsin–Madison in 1972 and BA in mathematics from Oxford in 1968. In 1987 he founded Iterated Systems Incorporated, and in 1988 he published a book entitled Fractals Everywhere and in 2006 SuperFractals.
He has also published these scientific papers: "Existence and Uniqueness of Orbital Measures", "Theory and Applications of Fractal Tops", "A Fractal Valued Random Iteration Algorithm and Fractal Hierarchy", "V-variable fractals and superfractals", "Fractal Transformations" and "Ergodic Theory, Fractal Tops and Colour Stealing".
He is also credited for discovering the collage theorem.
Iterated Systems was initially devoted to fractal image compression (epitomised by the Barnsley fern), and later focused on image archive management and was renamed to MediaBin. It was acquired in 2003 by Interwoven, by which time Barnsley was no longer affiliated with the company.
As of 2005, he is on the faculty of the Mathematical Sciences Institute of the Australian National University. Barnsley previously held a faculty position at Georgia Tech.
Michael Barnsley is the son of author Gabriel Fielding (Alan Fielding Barnsley) and a descendant of Henry Fielding.
References
External links
Michael Barnsley's Australian National University direct
|
https://en.wikipedia.org/wiki/Hartley%20Rogers%20Jr.
|
Hartley Rogers Jr. (July 6, 1926 – July 17, 2015) was an American mathematician who worked in computability theory, and was a professor in the Mathematics Department of the Massachusetts Institute of Technology.
Biography
Born in 1926 in Buffalo, New York, he studied under Alonzo Church at Princeton, and received his Ph.D. there in 1952. He served on the MIT faculty from 1956 until his death, July 17, 2015. He is survived by his wife, Dr. Adrianne E. Rogers, by his three children, Hartley R. Rogers, Campbell D.K. Rogers, and Caroline R. Broderick, and by his 10 grandchildren.
At MIT he had been involved in many scholarly extracurricular activities, including running SPUR (Summer Program in Undergraduate Research) for MIT undergraduates, overseeing the mathematics section of RSI (Research Science Institute) for advanced high school students, and coaching the MIT Putnam exam team for nearly two decades starting in 1990, including the years 2003 and 2004 when MIT won for the first time since 1979. He also ran a seminar called 18.S34: Mathematical Problem Solving for MIT freshmen.
Rogers is known within the MIT undergraduate community also for having developed a multivariable calculus course (18.022: Multivariable Calculus with Theory) with the explicit goal of providing a firm mathematical foundation for the study of physics. In 2005 he announced that he would no longer be teaching the course himself, but it is likely that it will continue to be taught in a similar manner in
|
https://en.wikipedia.org/wiki/William%20Brooke%20O%27Shaughnessy
|
Sir William Brooke O'Shaughnessy (from 1861 as William O'Shaughnessy Brooke) MD FRS (October 1809, in Limerick, Ireland – 8 January 1889, in Southsea, England) was an Irish physician famous for his wide-ranging scientific work in pharmacology, chemistry, and inventions related to telegraphy and its use in India. His medical research led to the development of intravenous therapy and introduced the therapeutic use of Cannabis sativa to Western medicine.
Early life
O'Shaughnessy was born at Limerick in 1809 to Daniel O'Shaughnessy and Sarah Boswell. His mother was a Protestant and many in the family were clergymen. An uncle of his was the Dean of Ennis and a great uncle the Roman Catholic Bishop of Killaloe. William studied briefly at Trinity College, Dublin matriculating in 1825 but moved to Scotland before graduating. O'Shaughnessy studied forensic toxicology and chemistry in Scotland, and graduated in 1829 with an MD from the University of Edinburgh Medical School. In 1829 he was a clinical assistant of William Alison. In 1831, at the age of 22, as a result of his analysis of the blood of cholera victims, O'Shaughnessy laid the foundation, along with Thomas Aitchison Latta, for what was to become intravenous fluid and electrolyte-replacement therapy in the treatment of cholera. O'Shaughnessy analyzed the urine and blood of cholera patients and came to the conclusion that oxygen in the blood could reverse the actions. He found the blood deficient in water, salt, and "free al
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