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https://en.wikipedia.org/wiki/Denny%27s%20paradox
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In biology, Denny's paradox refers to the apparent impossibility of surface-dwelling animals such as the water strider generating enough propulsive force to move. It is named after biologist Mark Denny, and relates to animal locomotion on the surface layer of water.
If capillary waves are assumed to generate the momentum transfer to the water, the animal's legs must move faster than the phase speed of the waves, given by
where is the acceleration due to gravity, is the strength of surface tension, and the density of water. For standard conditions, this works out to be about 0.23 m/s. In fact, water striders' legs move at speeds much less than this and, according to this physical picture, cannot move.
Writing in the Journal of Fluid Mechanics, David Hu and John Bush state that Denny's paradox "rested on two flawed assumptions. First, water striders' motion was assumed to rely on the generation of capillary waves, since the propulsive force was thought to be that associated with wave drag on the driving leg. Second, in order to generate capillary waves, it was assumed that the strider leg speed must exceed the minimum wave speed, . We note that this second assumption is strictly true only for steady motions".
References
Physical paradoxes
Animal locomotion
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https://en.wikipedia.org/wiki/MPRI
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MPRI may refer to:
Military Professional Resources Inc., a private military contractor.
Midwest Proton Radiotherapy Institute, a proton therapy treatment center in Bloomington, Indiana.
Master Parisien de Recherche en Informatique, a French master course in theoretical computer science
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https://en.wikipedia.org/wiki/Elastic%20scattering
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Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modified (by interaction with other particles and/or potentials) meaning the two particles in the collision do not lose energy. Furthermore, while the particle's kinetic energy in the center-of-mass frame is constant, its energy in the lab frame is not. Generally, elastic scattering describes a process in which the total kinetic energy of the system is conserved. During elastic scattering of high-energy subatomic particles, linear energy transfer (LET) takes place until the incident particle's energy and speed has been reduced to the same as its surroundings, at which point the particle is "stopped".
Rutherford scattering
When the incident particle, such as an alpha particle or electron, is diffracted in the Coulomb potential of atoms and molecules, the elastic scattering process is called Rutherford scattering. In many electron diffraction techniques like reflection high energy electron diffraction (RHEED), transmission electron diffraction (TED), and gas electron diffraction (GED), where the incident electrons have sufficiently high energy (>10 keV), the elastic electron scattering becomes the main component of the scattering process and the scattering intensity is expressed as a function of the momentum transfer defined as the differe
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https://en.wikipedia.org/wiki/Geoff%20Jenkins%20%28climatologist%29
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Geoffrey (Geoff) Jenkins is a climatologist and former head of climate change prediction at the Hadley Centre for Climate Prediction and Research, part of the Met Office.
Career
Jenkins is a physics graduate from Southampton university; PhD in atmospheric physics. Thirty years at the Met Office.
In response to why he believes that human activity has caused the recent rise in temperatures he responded:
Feeding in the different agents that cause climate change into our models – like greenhouse gases, output from the Sun, volcanoes - we’ve looked at the patterns of change they cause across the surface of the Earth and through the atmosphere. We compare them to what’s actually been observed and find the best match between computer simulations and the observations. This has indicated to us that over the past 30 or 40 years that most of the warming has been due to human activities.
See also
Global warming
Attribution of recent climate change
References
External links
The Guardian: Answers to burning questions
BBC: Climate: What science can tell us
British climatologists
Living people
Alumni of the University of Southampton
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Danny%20Kopec
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Daniel Kopec (February 28, 1954 – June 12, 2016) was an American chess International Master, author, and computer science professor at Brooklyn College.
Education
He graduated from Dartmouth College in the class of 1975. Kopec later received a PhD in Machine Intelligence from the University of Edinburgh in 1982 studying under Donald Michie.
Chess
Kopec was Greater NY High School Champion at 14, and reached master at 17. Kopec won the Scottish Chess Championship in 1980 while pursuing his doctorate in Edinburgh. He lived in Canada for two years during the 1980s, and competed there with success, including second-equal in the 1984 Canadian Chess Championship. Kopec achieved the FIDE International Master title in 1985 and had several top three finishes (including second place ties) in the US Open.
He wrote numerous books on the subject of chess, produced eight chess instructional DVDs, and ran chess camps starting in 1994. Kopec also worked to promote his chess opening, the Kopec System (1.e4 c5 2.Nf3 d6 3.Bd3!?). With Ivan Bratko, he was the creator of the Bratko–Kopec Test, which was one of the de facto standard testing systems for chess-playing computer programs in the 1980s.
Computer science
Kopec published notable academic pieces in the areas of artificial intelligence, machine error reduction, intelligent tutoring systems, and computer education.
Death
Kopec died on June 12, 2016, from pancreatic cancer.
Partial chess bibliography
(1980) Best Games Of The Young Grand
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https://en.wikipedia.org/wiki/Education%20in%20Taiwan
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The educational system in Taiwan is the responsibility of the Ministry of Education. The system produces pupils with some of the highest test scores in the world, especially in mathematics and science. Former president Ma Ying-jeou announced in January 2011 that the government would begin the phased implementation of a twelve-year compulsory education program by 2014.
In 2015, Taiwanese students achieved one of the world's best results in mathematics, science and literacy, as tested by the Programme for International Student Assessment (PISA), a worldwide evaluation of 15-year-old school pupils' scholastic performance. Taiwan is one of the top-performing OECD countries in reading literacy, mathematics and sciences with the average student scoring 523.7, compared with the OECD average of 493, placing it seventh in the world and has one of the world's most highly educated labor forces among OECD countries. Although current law mandates only nine years of schooling, 95 percent junior high school students go on to a senior vocational high school, trade school, junior college, or university.
In Taiwan, adhering to the Confucian paradigm for education where parents believe that receiving a good education is a very high priority for Taiwanese families and an important goal in their children's life. Many parents in Taiwan believe that effort and persistence matters more than innate ability if their children want to receive better grades in school. These beliefs are shared by the t
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https://en.wikipedia.org/wiki/Royal%20Institute%20of%20Chemistry
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The Royal Institute of Chemistry was a British scientific organisation. Founded in 1877 as the Institute of Chemistry of Great Britain and Ireland (ICGBI), its role was to focus on qualifications and the professional status of chemists, and its aim was to ensure that consulting and analytical chemists were properly trained and qualified.
The society received its first Royal Charter on 13 June 1885, and King George VI awarded the society royal patronage with effect from 14 May 1943, from which date it became the Royal Institute of Chemistry of Great Britain and Ireland (RICGBI). This re-designation was formally confirmed by the grant of a Supplemental Charter on 29 March 1944.
As well as insisting on thorough professional qualifications, it also laid down strict ethical standards. Its main qualifications were Licentiate (LRIC) (professional training following a course of practical study to a standard lower than an honours degree), Graduate (GRIC) (completion of study equivalent to at least second class honours degree), Associate (ARIC) (LRIC plus professional experience), Member (MRIC) (GRIC plus professional experience) and Fellow (FRIC) (more experience and standing than MRIC) of the Royal Institute of Chemistry. Following a supplemental Charter in 1975, Members and Fellows were permitted to use the letters CChem (Chartered Chemist). It published Royal Institute of Chemistry Reviews from 1968 to 1971, when it combined to form Chemical Society Reviews, and the Journal of
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https://en.wikipedia.org/wiki/Society%20for%20Analytical%20Chemistry
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The Society of Public Analysts was formed in the United Kingdom in 1874 and subsequently became the Society for Analytical Chemistry. It was incorporated in 1907.
The chemical industry had grown rapidly in the 19th century, and developments in the alkali, explosive and agricultural chemical fields produced a growing need for analytical chemists. Many of these chemists had little or no training in chemistry, and their lack of expertise was a danger to the public. Shortly after the Adulteration of Food and Drink Act 1860 the Society was formed. It established adulteration and food standards, and educated analysts in legal work.
It published The Analyst, Analytical Abstracts and the Proceedings of the Society for Analytical Chemistry (from 1964 to 1974).
In April 1966 it presented its first Gold Medal to Herbert Newton Wilson (author of An Approach To Chemical Analysis)* in recognition of his contribution to chemical analysis.*
On 15 May 1980, it amalgamated with the Chemical Society, the Royal Institute of Chemistry, and the Faraday Society to become the Royal Society of Chemistry.
Presidents
Theophilus Redwood: 1875–1876
August Dupré: 1877–1878
John Muter: 1879–1880
Charles Heisch: 1881–1882
George William Wigner: 1883–1884
Dr Alfred Hill: 1885–1886
Alfred Henry Allen: 1887–1888
Matthew Adams: 1889–1890
Otto Hehner: 1891–1892
Sir Charles Alexander Cameron: 1893–1894
Sir Thomas Stevenson: 1895–1896
Bernard Dyer: 1897–1898
Walter Fisher: 1899–1900
Edward V
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https://en.wikipedia.org/wiki/Creation%20and%20evolution%20in%20public%20education
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The status of creation and evolution in public education has been the subject of substantial debate and conflict in legal, political, and religious circles. Globally, there are a wide variety of views on the topic. Most western countries have legislation that mandates only evolutionary biology is to be taught in the appropriate scientific syllabuses.
Overview
While many Christian denominations do not raise theological objections to the modern evolutionary synthesis as an explanation for the present forms of life on planet Earth, various socially conservative, traditionalist, and fundamentalist religious sects and political groups within Christianity and Islam have objected vehemently to the study and teaching of biological evolution. Some adherents of these Christian and Islamic religious sects or political groups are passionately opposed to the consensus view of the scientific community. Literal interpretations of religious texts are the greatest cause of conflict with evolutionary and cosmological investigations and conclusions.
Internationally, biological evolution is taught in science courses with limited controversy, with the exception of a few areas of the United States and several Muslim-majority countries, primarily Turkey. In the United States, the Supreme Court has ruled the teaching of creationism as science in public schools to be unconstitutional, irrespective of how it may be purveyed in theological or religious instruction. In the United States, intelligent
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https://en.wikipedia.org/wiki/Matched%20filter
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In signal processing, a matched filter is obtained by correlating a known delayed signal, or template, with an unknown signal to detect the presence of the template in the unknown signal. This is equivalent to convolving the unknown signal with a conjugated time-reversed version of the template. The matched filter is the optimal linear filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise.
Matched filters are commonly used in radar, in which a known signal is sent out, and the reflected signal is examined for common elements of the out-going signal. Pulse compression is an example of matched filtering. It is so called because the impulse response is matched to input pulse signals. Two-dimensional matched filters are commonly used in image processing, e.g., to improve the SNR of X-ray observations.
Matched filtering is a demodulation technique with LTI (linear time invariant) filters to maximize SNR.
It was originally also known as a North filter.
Derivation
Derivation via matrix algebra
The following section derives the matched filter for a discrete-time system. The derivation for a continuous-time system is similar, with summations replaced with integrals.
The matched filter is the linear filter, , that maximizes the output signal-to-noise ratio.
where is the input as a function of the independent variable , and is the filtered output. Though we most often express filters as the impulse response of convolution systems
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https://en.wikipedia.org/wiki/Conjugate%20variables
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Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle—between them. In mathematical terms, conjugate variables are part of a symplectic basis, and the uncertainty relation corresponds to the symplectic form. Also, conjugate variables are related by Noether's theorem, which states that if the laws of physics are invariant with respect to a change in one of the conjugate variables, then the other conjugate variable will not change with time (i.e. it will be conserved).
Examples
There are many types of conjugate variables, depending on the type of work a certain system is doing (or is being subjected to). Examples of canonically conjugate variables include the following:
Time and frequency: the longer a musical note is sustained, the more precisely we know its frequency, but it spans a longer duration and is thus a more-distributed event or 'instant' in time. Conversely, a very short musical note becomes just a click, and so is more temporally-localized, but one can't determine its frequency very accurately.
Doppler and range: the more we know about how far away a radar target is, the less we can know about the exact velocity of approach or retreat, and vice versa. In this case, the two dimensional function of doppler and range is k
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https://en.wikipedia.org/wiki/Ambiguity%20function
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In pulsed radar and sonar signal processing, an ambiguity function is a two-dimensional function of propagation delay and Doppler frequency , . It represents the distortion of a returned pulse due to the receiver matched filter (commonly, but not exclusively, used in pulse compression radar) of the return from a moving target. The ambiguity function is defined by the properties of the pulse and of the filter, and not any particular target scenario.
Many definitions of the ambiguity function exist; some are restricted to narrowband signals and others are suitable to describe the delay and Doppler relationship of wideband signals. Often the definition of the ambiguity function is given as the magnitude squared of other definitions (Weiss).
For a given complex baseband pulse , the narrowband ambiguity function is given by
where denotes the complex conjugate and is the imaginary unit. Note that for zero Doppler shift (), this reduces to the autocorrelation of . A more concise way of representing the
ambiguity function consists of examining the one-dimensional
zero-delay and zero-Doppler "cuts"; that is, and
, respectively. The matched filter output as a function of time (the signal one would observe in a radar system) is a Doppler cut, with the constant frequency given by the target's Doppler shift: .
Background and motivation
Pulse-Doppler radar equipment sends out a series of radio frequency pulses. Each pulse has a certain shape (waveform)—how long the pulse is, what
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https://en.wikipedia.org/wiki/167%20%28number%29
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167 (one hundred [and] sixty-seven) is the natural number following 166 and preceding 168.
In mathematics
167 is an emirp, an isolated prime, a Chen prime, a Gaussian prime, a safe prime, and an Eisenstein prime with no imaginary part and a real part of the form .
167 is the smallest number which requires six terms when expressed using the greedy algorithm as a sum of squares, 167 = 144 + 16 + 4 + 1 + 1 + 1,
although by Lagrange's four-square theorem its non-greedy expression as a sum of squares can be shorter, e.g. 167 = 121 + 36 + 9 + 1.
167 is a full reptend prime in base 10, since the decimal expansion of 1/167 repeats the following 166 digits: 0.00598802395209580838323353293413173652694610778443113772455089820359281437125748502994 0119760479041916167664670658682634730538922155688622754491017964071856287425149700...
167 is a highly cototient number, as it is the smallest number k with exactly 15 solutions to the equation x - φ(x) = k. It is also a strictly non-palindromic number.
167 is the smallest multi-digit prime such that the product of digits is equal to the number of digits times the sum of the digits, i. e., 1×6×7 = 3×(1+6+7)
167 is the smallest positive integer d such that the imaginary quadratic field Q() has class number = 11.
In astronomy
167 Urda is a main belt asteroid
167P/CINEOS is a periodic comet in the Solar System
IC 167 is interacting galaxies
In the military
Marine Light Attack Helicopter Squadron 167 is a United States Marine Corps helic
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https://en.wikipedia.org/wiki/Western%20College%20Program
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The Western College Program was created in 1974 when the Western College for Women merged with Miami University. The program consisted of an interdisciplinary living/learning community with small class sizes and student-designed focuses. Majors included Interdisciplinary Studies, Environmental Science, and Environmental Studies. Academics were divided into three core areas: Creativity and Culture, Social Systems, and Natural Systems.
Western, also known as the School of Interdisciplinary Studies, was cited as a primary reason for Miami University making the list of "Public Ivies" in Richard Moll's book, The Public Ivies: A Guide to America's Best Public Undergraduate Colleges and Universities. In the mid-1960s, when it was the Western College for Women, the campus served as the staging ground for Freedom Summer, a voter registration drive in Mississippi.
The Western campus
Located directly east of the main campus of Miami University, Western College is characterized by winding pathways through forest and stone bridges over creeks. Peabody Hall, currently a coed dormitory, is said to be haunted by its namesake Helen Peabody. Other buildings on Western Campus include McKee Hall, Mary Lyon Hall, Kumler Chapel, Western Lodge, Ernst Theater, Western Tower, Ice House, Summer House, Sawyer Hall (former gymnasium, heating plant, pool and dining hall), Boyd Hall, Hoyt Hall, the Art Museum, and non-WCP buildings, Clawson Hall, Alexander Dining Hall, Presser Hall, Langstroth Cottage,
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https://en.wikipedia.org/wiki/Noam%20Elkies
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Noam David Elkies (born August 25, 1966) is a professor of mathematics at Harvard University. At the age of 26, he became the youngest professor to receive tenure at Harvard. He is also a pianist, chess national master and a chess composer.
Early life
Elkies was born to an engineer father and a piano teacher mother. He attended Stuyvesant High School in New York City for three years before graduating in 1982 at age 15. A child prodigy, in 1981, at age 14, Elkies was awarded a gold medal at the 22nd International Mathematical Olympiad, receiving a perfect score of 42, one of the youngest to ever do so. He went on to Columbia University, where he won the Putnam competition at the age of sixteen years and four months, making him one of the youngest Putnam Fellows in history. Elkies was a Putnam Fellow twice more during his undergraduate years. He graduated valedictorian of his class in 1985. He then earned his PhD in 1987 under the supervision of Benedict Gross and Barry Mazur at Harvard University.
From 1987 to 1990, Elkies was a junior fellow of the Harvard Society of Fellows.
Work in mathematics
In 1987, Elkies proved that an elliptic curve over the rational numbers is supersingular at infinitely many primes. In 1988, he found a counterexample to Euler's sum of powers conjecture for fourth powers. His work on these and other problems won him recognition and a position as an associate professor at Harvard in 1990. In 1993, Elkies was made a full, tenured professor at the a
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https://en.wikipedia.org/wiki/Abstract%20semantic%20graph
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In computer science, an abstract semantic graph (ASG) or term graph is a form of abstract syntax in which an expression of a formal or programming language is represented by a graph whose vertices are the expression's subterms. An ASG is at a higher level of abstraction than an abstract syntax tree (or AST), which is used to express the syntactic structure of an expression or program.
ASGs are more complex and concise than ASTs because they may contain shared subterms (also known as "common subexpressions"). Abstract semantic graphs are often used as an intermediate representation by compilers to store the results of performing common subexpression elimination upon abstract syntax trees. ASTs are trees and are thus incapable of representing shared terms. ASGs are usually directed acyclic graphs (DAG), although in some applications graphs containing cycles may be permitted. For example, a graph containing a cycle might be used to represent the recursive expressions that are commonly used in functional programming languages as non-looping iteration constructs. The mutability of these types of graphs, is studied in the field of graph rewriting.
The nomenclature term graph is associated with the field of term graph rewriting, which involves the transformation and processing of expressions by the specification of rewriting rules, whereas abstract semantic graph is used when discussing linguistics, programming languages, type systems and compilation.
Abstract syntax trees are no
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https://en.wikipedia.org/wiki/Cambia%20%28non-profit%20organization%29
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Cambia is an Australian-based global non-profit social enterprise focusing on open science, biology, innovation system reform and intellectual property. Its projects include The Lens, formerly known as Patent Lens, and the Biological Innovation for Open Society Initiative.
Cambia derives its name from the Spanish verb cambiar, to change.
History
Cambia was established in 1992 by Richard Anthony Jefferson, a leading molecular biologist responsible for the invention of the GUS reporter system, with substantial early participation by Steven G Hughes, Kate J. Wilson, Andrzej Kilian, Chris A. Fields and Sujata Lakhani. Jefferson describes his vision to found a non-profit organisation in Innovations, to provide more efficient and effective tools to solve the problems of agriculture and society.
In 1992, Cambia relocated to Canberra, Australia from The Netherlands, to oversee and troubleshoot the Rockefeller Foundation's rice biotechnology network in Asia. During this time, Jefferson, Wilson and the growing Cambia team visited hundreds of laboratories to help develop, improve, and apply biotechnology capabilities, particularly pertaining to rice. Cambia offered scientific courses and workshops, and increasing assistance in Intellectual Property management. Cambia's ethic was influenced by Jefferson's early years in enabling technology invention and distribution, but greatly refined through increasing awareness of socially and scientifically complex systems and using new think
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https://en.wikipedia.org/wiki/Yusuf%20Hamied%201702%20Professor%20of%20Chemistry
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The Yusuf Hamied 1702 Chair of Chemistry is one of the senior professorships at the University of Cambridge, based in the Yusuf Hamied Department of Chemistry.
History
Founded in 1702 by the university as simply 'Professor of Chemistry', it was retitled as the Professorship of Organic Chemistry in 1943, and in 1991 was renamed after a benefaction from the oil company British Petroleum. In recognition of a donation from Yusuf Hamied, in 2018 the professorship was renamed the Yusuf Hamied 1702 Chair of Chemistry.
Professors of Chemistry
Giovanni Francisco Vigani (1703–1713)
John Waller (1713–1718)
John Mickleburgh (1718–1756)
John Hadley (1756–1764)
Richard Watson (1764–1771)
Isaac Pennington (1773–1793)
William Farish (1794–1813)
Smithson Tennant (1813–1815)
James Cumming (1815–1861)
George Downing Liveing (1861–1908)
William Jackson Pope (1908–1939)
Professors of Organic Chemistry
Alexander Robertus Todd (1944–1971)
Ralph Alexander Raphael (1972–1988)
Alan Rushton Battersby (1988–1992)
BP 1702 Professor of Organic Chemistry
Steven V. Ley (1992–2019)
Yusuf Hamied 1702 Professors of Chemistry
Matthew J. Gaunt (2019–)
References
Chemistry, Hamied, Yusuf
Faculty of Physics and Chemistry, University of Cambridge
1702 establishments in England
Chemistry, Hamied, Yusuf, Cambridge
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https://en.wikipedia.org/wiki/Bachelor%20of%20Mathematics
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A Bachelor of Mathematics (abbreviated B.Math or BMath) is an undergraduate academic degree awarded for successfully completing a program of study in mathematics or related disciplines, such as applied mathematics, actuarial science, computational science, data analytics, financial mathematics, mathematical physics, pure mathematics, operations research or statistics. The Bachelor of Mathematics caters to high-achieving students seeking to develop a comprehensive specialised knowledge in a field of mathematics or a high level of sophistication in the applications of mathematics.
In practice, this is essentially equivalent to a Bachelor of Science or Bachelor of Arts degree with a speciality in mathematics. Relatively few institutions award Bachelor of Mathematics degrees, and the distinction between those that do and those that award B.Sc or B.A. degrees for mathematics is usually bureaucratic, rather than curriculum related.
List of institutions awarding Bachelor of Mathematics degrees
Australia
Flinders University, Adelaide, South Australia
Queensland University of Technology, Brisbane, Queensland
The Australian National University, Canberra, Australian Capital Territory (a Bachelor of Mathematical Sciences BMASC)
University of Adelaide, Adelaide, South Australia (a Bachelor of Mathematical Sciences BMathSc or Bachelor of Mathematical and Computer Sciences BMath&CompSc)
University of Newcastle, Newcastle, New South Wales
University of Western Sydney - Penrith,
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https://en.wikipedia.org/wiki/Complex%20multiplication%20of%20abelian%20varieties
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In mathematics, an abelian variety A defined over a field K is said to have CM-type if it has a large enough commutative subring in its endomorphism ring End(A). The terminology here is from complex multiplication theory, which was developed for elliptic curves in the nineteenth century. One of the major achievements in algebraic number theory and algebraic geometry of the twentieth century was to find the correct formulations of the corresponding theory for abelian varieties of dimension d > 1. The problem is at a deeper level of abstraction, because it is much harder to manipulate analytic functions of several complex variables.
The formal definition is that
the tensor product of End(A) with the rational number field Q, should contain a commutative subring of dimension 2d over Q. When d = 1 this can only be a quadratic field, and one recovers the cases where End(A) is an order in an imaginary quadratic field. For d > 1 there are comparable cases for CM-fields, the complex quadratic extensions of totally real fields. There are other cases that reflect that A may not be a simple abelian variety (it might be a cartesian product of elliptic curves, for example). Another name for abelian varieties of CM-type is abelian varieties with sufficiently many complex multiplications.
It is known that if K is the complex numbers, then any such A has a field of definition which is in fact a number field. The possible types of endomorphism ring have been classified, as rings with invol
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https://en.wikipedia.org/wiki/John%20Cornforth
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Sir John Warcup Cornforth Jr., (7 September 1917 – 8 December 2013) was an AustralianBritish chemist who won the Nobel Prize in Chemistry in 1975 for his work on the stereochemistry of enzyme-catalysed reactions, becoming the only Nobel laureate born in New South Wales.
Cornforth investigated enzymes that catalyse changes in organic compounds, the substrates, by taking the place of hydrogen atoms in a substrate's chains and rings. In his syntheses and descriptions of the structure of various terpenes, olefins, and steroids, Cornforth determined specifically which cluster of hydrogen atoms in a substrate were replaced by an enzyme to effect a given change in the substrate, allowing him to detail the biosynthesis of cholesterol. For this work, he won a share of the Nobel Prize in Chemistry in 1975, alongside co-recipient Vladimir Prelog, and was knighted in 1977.
Early life and family
Born in Sydney, Cornforth was the son and the second of four children of English-born, Oxford-educated schoolmaster and teacher John Warcup Cornforth and Hilda Eipper (1887–1969), a granddaughter of pioneering missionary and Presbyterian minister Christopher Eipper. Before her marriage, Eipper had been a maternity nurse.
Cornforth was raised in Sydney as well as Armidale, in the north of New South Wales, where he undertook primary school education.
At about 10 years old, Cornforth had noted signs of deafness, which led to a diagnosis of otosclerosis, a disease of the middle ear which causes p
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https://en.wikipedia.org/wiki/Crystal%20field%20theory
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In molecular physics, crystal field theory (CFT) describes the breaking of degeneracies of electron orbital states, usually d or f orbitals, due to a static electric field produced by a surrounding charge distribution (anion neighbors). This theory has been used to describe various spectroscopies of transition metal coordination complexes, in particular optical spectra (colors). CFT successfully accounts for some magnetic properties, colors, hydration enthalpies, and spinel structures of transition metal complexes, but it does not attempt to describe bonding. CFT was developed by physicists Hans Bethe and John Hasbrouck van Vleck in the 1930s. CFT was subsequently combined with molecular orbital theory to form the more realistic and complex ligand field theory (LFT), which delivers insight into the process of chemical bonding in transition metal complexes. CFT can be complicated further by breaking assumptions made of relative metal and ligand orbital energies, requiring the use of inverted ligand field theory (ILFT) to better describe bonding.
Overview
According to crystal field theory, the interaction between a transition metal and ligands arises from the attraction between the positively charged metal cation and the negative charge on the non-bonding electrons of the ligand. The theory is developed by considering energy changes of the five degenerate d-orbitals upon being surrounded by an array of point charges consisting of the ligands. As a ligand approaches the metal i
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https://en.wikipedia.org/wiki/WCET
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WCET may refer to:
Worst-case execution time, a computer science term
WCET (TV), a PBS station serving the Cincinnati area
Wireless Communication Engineering Technologies Certification, an IEEE certification regarding wireless technologies
Western Cooperative for Educational Telecommunications
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https://en.wikipedia.org/wiki/512%20%28number%29
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512 (five hundred [and] twelve) is the natural number following 511 and preceding 513.
In mathematics
512 is a power of two: 29 (2 to the 9th power) and the cube of 8: 83.
It is the eleventh Leyland number.
It is also the third Dudeney number.
It is a self number in base 12.
It is a harshad number in decimal.
It is the cube of the sum of its digits in base 10.
It is the number of directed graphs on 3 labeled nodes.
In computing
512 bytes is a common disk sector size, and exactly a half of kibibyte.
Internet Relay Chat restricts the size of a message to 510 bytes, which fits to 512-bytes buffers when coupled with the message-separating CRLF sequence.
512 = 2·256 is the highest number of glyphs that the VGA character generator can use simultaneously.
In music
Selena Quintanilla released a song titled El Chico del Apartamento 512 (the title referring to area code 512, which serves Austin, Texas), in 1995.
Lamb of God recorded a song titled "512" for their 2015 album VII: Sturm und Drang.
Mora and Jhay Cortez recorded a song titled "512" (The number 512 in this song refers to the Percocet 512 pill, a white, round pill whose active substances are acetaminophen and oxycodone hydrochloride) in February of 2021.
References
Integers
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https://en.wikipedia.org/wiki/Abelian%20integral
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In mathematics, an abelian integral, named after the Norwegian mathematician Niels Henrik Abel, is an integral in the complex plane of the form
where is an arbitrary rational function of the two variables and , which are related by the equation
where is an irreducible polynomial in ,
whose coefficients , are rational functions of . The value of an abelian integral depends not only on the integration limits, but also on the path along which the integral is taken; it is thus a multivalued function of .
Abelian integrals are natural generalizations of elliptic integrals, which arise when
where is a polynomial of degree 3 or 4. Another special case of an abelian integral is a hyperelliptic integral, where , in the formula above, is a polynomial of degree greater than 4.
History
The theory of abelian integrals originated with a paper by Abel published in 1841. This paper was written during his stay in Paris in 1826 and presented to Augustin-Louis Cauchy in October of the same year. This theory, later fully developed by others, was one of the crowning achievements of nineteenth century mathematics and has had a major impact on the development of modern mathematics. In more abstract and geometric language, it is contained in the concept of abelian variety, or more precisely in the way an algebraic curve can be mapped into abelian varieties. Abelian integrals were later connected to the prominent mathematician David Hilbert's 16th Problem, and they continue to be cons
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https://en.wikipedia.org/wiki/Differential%20of%20the%20first%20kind
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In mathematics, differential of the first kind is a traditional term used in the theories of Riemann surfaces (more generally, complex manifolds) and algebraic curves (more generally, algebraic varieties), for everywhere-regular differential 1-forms. Given a complex manifold M, a differential of the first kind ω is therefore the same thing as a 1-form that is everywhere holomorphic; on an algebraic variety V that is non-singular it would be a global section of the coherent sheaf Ω1 of Kähler differentials. In either case the definition has its origins in the theory of abelian integrals.
The dimension of the space of differentials of the first kind, by means of this identification, is the Hodge number
h1,0.
The differentials of the first kind, when integrated along paths, give rise to integrals that generalise the elliptic integrals to all curves over the complex numbers. They include for example the hyperelliptic integrals of type
where Q is a square-free polynomial of any given degree > 4. The allowable power k has to be determined by analysis of the possible pole at the point at infinity on the corresponding hyperelliptic curve. When this is done, one finds that the condition is
k ≤ g − 1,
or in other words, k at most 1 for degree of Q 5 or 6, at most 2 for degree 7 or 8, and so on (as g = [(1+ deg Q)/2]).
Quite generally, as this example illustrates, for a compact Riemann surface or algebraic curve, the Hodge number is the genus g. For the case of algebraic surf
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https://en.wikipedia.org/wiki/2%2C5-Dimethoxy-4-iodoamphetamine
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2,5-Dimethoxy-4-iodoamphetamine (DOI) is a psychedelic drug and a substituted amphetamine. Unlike many other substituted amphetamines, however, it is not primarily a stimulant. DOI has a stereocenter and R-(−)-DOI is the more active stereoisomer. In neuroscience research, [125I]-R-(−)-DOI is used as a radioligand and indicator of the presence of 5-HT2A serotonin receptors. DOI's effects have been compared to LSD, although there are differences that experienced users can distinguish. Besides the longer duration, the trip tends to be more energetic than an LSD trip, with more body load and a different subjective visual experience. The after effects include residual stimulation and difficulty sleeping, which, depending on the dose, may persist for days. While rare, it is sometimes sold as a substitute for LSD, or even sold falsely as LSD, which may be dangerous because DOI does not have the same established safety profile as LSD.
Research
Research suggests that administration of (R)-DOI blocks pulmonary inflammation, mucus hyper-production, airway hyper-responsiveness and turns off key genes in in-lung immune response. These effects block the development of allergic asthma in a mouse model.
Several 5-HT2A agonist hallucinogens including (R)-2,5-dimethoxy-4-iodoamphetamine DOI, TCB-2, LSD and LA-SS-Az have unexpectedly also been found to act as potent inhibitors of TNF, with DOI being the most active, showing TNF inhibition in the picomolar range, an order of magnitude more p
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https://en.wikipedia.org/wiki/Bruhat%20decomposition
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In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) G = BWB of certain algebraic groups G into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which generically writes a matrix as a product of an upper triangular and lower triangular matrices—but with exceptional cases. It is related to the Schubert cell decomposition of flag varieties: see Weyl group for this.
More generally, any group with a (B, N) pair has a Bruhat decomposition.
Definitions
G is a connected, reductive algebraic group over an algebraically closed field.
B is a Borel subgroup of G
W is a Weyl group of G corresponding to a maximal torus of B.
The Bruhat decomposition of G is the decomposition
of G as a disjoint union of double cosets of B parameterized by the elements of the Weyl group W. (Note that although W is not in general a subgroup of G, the coset wB is still well defined because the maximal torus is contained in B.)
Examples
Let G be the general linear group GLn of invertible matrices with entries in some algebraically closed field, which is a reductive group. Then the Weyl group W is isomorphic to the symmetric group Sn on n letters, with permutation matrices as representatives. In this case, we can take B to be the subgroup of upper triangular invertible matrices, so Bruhat decomposition says that one can write any invertible matrix A as a product U1PU2 where U1 and U2 ar
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https://en.wikipedia.org/wiki/Cartan%20decomposition
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In mathematics, the Cartan decomposition is a decomposition of a semisimple Lie group or Lie algebra, which plays an important role in their structure theory and representation theory. It generalizes the polar decomposition or singular value decomposition of matrices. Its history can be traced to the 1880s work of Élie Cartan and Wilhelm Killing.
Cartan involutions on Lie algebras
Let be a real semisimple Lie algebra and let be its Killing form. An involution on is a Lie algebra automorphism of whose square is equal to the identity. Such an involution is called a Cartan involution on if is a positive definite bilinear form.
Two involutions and are considered equivalent if they differ only by an inner automorphism.
Any real semisimple Lie algebra has a Cartan involution, and any two Cartan involutions are equivalent.
Examples
A Cartan involution on is defined by , where denotes the transpose matrix of .
The identity map on is an involution. It is the unique Cartan involution of if and only if the Killing form of is negative definite or, equivalently, if and only if is the Lie algebra of a compact semisimple Lie group.
Let be the complexification of a real semisimple Lie algebra , then complex conjugation on is an involution on . This is the Cartan involution on if and only if is the Lie algebra of a compact Lie group.
The following maps are involutions of the Lie algebra of the special unitary group SU(n):
The identity involution , which is
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https://en.wikipedia.org/wiki/Iwasawa%20decomposition
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In mathematics, the Iwasawa decomposition (aka KAN from its expression) of a semisimple Lie group generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix (QR decomposition, a consequence of Gram–Schmidt orthogonalization). It is named after Kenkichi Iwasawa, the Japanese mathematician who developed this method.
Definition
G is a connected semisimple real Lie group.
is the Lie algebra of G
is the complexification of .
θ is a Cartan involution of
is the corresponding Cartan decomposition
is a maximal abelian subalgebra of
Σ is the set of restricted roots of , corresponding to eigenvalues of acting on .
Σ+ is a choice of positive roots of Σ
is a nilpotent Lie algebra given as the sum of the root spaces of Σ+
K, A, N, are the Lie subgroups of G generated by and .
Then the Iwasawa decomposition of is
and the Iwasawa decomposition of G is
meaning there is an analytic diffeomorphism (but not a group homomorphism) from the manifold to the Lie group , sending .
The dimension of A (or equivalently of ) is equal to the real rank of G.
Iwasawa decompositions also hold for some disconnected semisimple groups G, where K becomes a (disconnected) maximal compact subgroup provided the center of G is finite.
The restricted root space decomposition is
where is the centralizer of in and is the root space. The number
is called the multiplicity of .
Examples
If G=SLn(R), then we can take K to be the ort
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https://en.wikipedia.org/wiki/Hyperbolic%20angle
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In geometry, hyperbolic angle is a real number determined by the area of the corresponding hyperbolic sector of xy = 1 in Quadrant I of the Cartesian plane. The hyperbolic angle parametrises the unit hyperbola, which has hyperbolic functions as coordinates. In mathematics, hyperbolic angle is an invariant measure as it is preserved under hyperbolic rotation.
The hyperbola xy = 1 is rectangular with a semi-major axis of , analogous to the magnitude of a circular angle corresponding to the area of a circular sector in a circle with radius .
Hyperbolic angle is used as the independent variable for the hyperbolic functions sinh, cosh, and tanh, because these functions may be premised on hyperbolic analogies to the corresponding circular trigonometric functions by regarding a hyperbolic angle as defining a hyperbolic triangle.
The parameter thus becomes one of the most useful in the calculus of real variables.
Definition
Consider the rectangular hyperbola , and (by convention) pay particular attention to the branch .
First define:
The hyperbolic angle in standard position is the angle at between the ray to and the ray to , where .
The magnitude of this angle is the area of the corresponding hyperbolic sector, which turns out to be .
Note that, because of the role played by the natural logarithm:
Unlike the circular angle, the hyperbolic angle is unbounded (because is unbounded); this is related to the fact that the harmonic series is unbounded.
The formula for the magn
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https://en.wikipedia.org/wiki/Tridilosa
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Tridilosa is a very light and resistant, materials-efficient 3-D structure, made from steel and concrete and widely used in civil engineering. Tridilosa was invented by the Mexican engineer Heberto Castillo.
Among the most remarkable features of this structure is that it can save up to 66% on concrete usage and up to 40% on steel, because filling with concrete is not required in the tension zone, only in the superior compression zone. It is so light that it can float on water, but is three times stronger than traditional construction flagstone. It was used, for example, to construct the 54-floor World Trade Center of Mexico City.
External links
Heberto Castillo Martinez
Science and technology in Mexico
Mexican inventions
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https://en.wikipedia.org/wiki/Member
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Member may refer to:
Military jury, referred to as "Members" in military jargon
Element (mathematics), an object that belongs to a mathematical set
In object-oriented programming, a member of a class
Field (computer science), entries in a database
Member variable, a variable that is associated with a specific object
Limb (anatomy), an appendage of the human or animal body
Euphemism for penis
Structural component of a truss, connected by nodes
User (computing), a person making use of a computing service, especially on the Internet
Member (geology), a component of a geological formation
Member of parliament
The Members, a British punk rock band
Meronymy, a semantic relationship in linguistics
Church membership, belonging to a local Christian congregation, a Christian denomination and the universal Church
Member, a participant in a club or learned society
See also
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https://en.wikipedia.org/wiki/Racks%20and%20quandles
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In mathematics, racks and quandles are sets with binary operations satisfying axioms analogous to the Reidemeister moves used to manipulate knot diagrams.
While mainly used to obtain invariants of knots, they can be viewed as algebraic constructions in their own right. In particular, the definition of a quandle axiomatizes the properties of conjugation in a group.
History
In 1943, Mituhisa Takasaki (高崎光久) introduced an algebraic structure which he called a Kei (圭), which would later come to be known as an involutive quandle. His motivation was to find a nonassociative algebraic structure to capture the notion of a reflection in the context of finite geometry. The idea was rediscovered and generalized in (unpublished) 1959 correspondence between John Conway and Gavin Wraith, who at the time were undergraduate students at the University of Cambridge. It is here that the modern definitions of quandles and of racks first appear. Wraith had become interested in these structures (which he initially dubbed sequentials) while at school. Conway renamed them wracks, partly as a pun on his colleague's name, and partly because they arise as the remnants (or 'wrack and ruin') of a group when one discards the multiplicative structure and considers only the conjugation structure. The spelling 'rack' has now become prevalent.
These constructs surfaced again in the 1980s: in a 1982 paper by David Joyce (where the term quandle, an arbitrary nonsense word, was coined), in a 1982 paper by
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https://en.wikipedia.org/wiki/Siegel%20upper%20half-space
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In mathematics, the Siegel upper half-space of degree g (or genus g) (also called the Siegel upper half-plane) is the set of g × g symmetric matrices over the complex numbers whose imaginary part is positive definite. It was introduced by . It is the symmetric space associated to the symplectic group .
The Siegel upper half-space has properties as a complex manifold that generalize the properties of the upper half-plane, which is the Siegel upper half-space in the special case g = 1. The group of automorphisms preserving the complex structure of the manifold is isomorphic to the symplectic group . Just as the two-dimensional hyperbolic metric is the unique (up to scaling) metric on the upper half-plane whose isometry group is the complex automorphism group = , the Siegel upper half-space has only one metric up to scaling whose isometry group is . Writing a generic matrix Z in the Siegel upper half-space in terms of its real and imaginary parts as Z = X + iY, all metrics with isometry group are proportional to
The Siegel upper half-plane can be identified with the set of tame almost complex structures compatible with a symplectic structure , on the underlying dimensional real vector space , that is, the set of such that and for all vectors .
See also
Moduli of abelian varieties
Paramodular group, a generalization of the Siegel modular group
Siegel domain, a generalization of the Siegel upper half space
Siegel modular form, a type of automorphic form defined on the S
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https://en.wikipedia.org/wiki/Arthur%20Farnsworth
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Arthur L. Farnsworth (born 1962) is an American politician and convicted tax protester. Evidence found by the government in Farnsworth's case helped the government indict actor Wesley Snipes on tax charges.
Farnsworth received his bachelor's degree in electrical engineering from Widener University and a master's degree in engineering science from Penn State. He ran for a number of offices as a member of the Libertarian Party of Pennsylvania, and served as township auditor for West Rockhill Township. Farnsworth also served as the treasurer of the Pennsylvania Libertarian Party. He ran as a candidate for the United States House of Representatives for Pennsylvania's 8th congressional district in 2004 and drew 3,710 votes.
Tax problems
In November 2004 Farnsworth was arrested on charges of tax evasion of approximately $87,000 in Federal income taxes under for years 1998, 1999, and 2000. On the campaign trail as well as on his personal website, Farnsworth argued that the federal law makes the payment of income taxes voluntary.
A federal grand jury charged the electrical engineer with failure to pay taxes for three years on more than $221,000 in income and with attempting to conceal his earnings by transferring assets to fraudulent trusts and overseas bank accounts.
During the case, investigators found that one of the trust funds belonged to actor Wesley Snipes. Snipes himself was indicted on tax charges in October 2006. Snipes was convicted of three misdemeanor counts of fai
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https://en.wikipedia.org/wiki/Human%20Genome%20Diversity%20Project
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The Human Genome Diversity Project (HGDP) was started by Stanford University's Morrison Institute in 1990s along with collaboration of scientists around the world. It is the result of many years of work by Luigi Cavalli-Sforza, one of the most cited scientists in the world, who has published extensively in the use of genetics to understand human migration and evolution. The HGDP data sets have often been cited in papers on such topics as population genetics, anthropology, and heritable disease research.
The project has noted the need to record the genetic profiles of indigenous populations, as isolated populations are the best way to understand the genetic frequencies that have clues into our distant past. Knowing about the relationship between such populations makes it possible to infer the journey of humankind from the humans who left Africa and populated the world to the humans of today. The HGDP-CEPH Human Genome Diversity Cell Line Panel is a resource of 1,063 cultured lymphoblastoid cell lines (LCLs) from 1,050 individuals in 52 world populations, banked at the Fondation Jean Dausset-CEPH in Paris.
The HGDP is not related to the Human Genome Project (HGP) and has attempted to maintain a distinct identity. The whole genome sequencing and analysis of the HGDP was published in 2020, creating a comprehensive resource of genetic variation from underrepresented human populations and illuminating patterns of genetic variation, demographic history and introgression of modern
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https://en.wikipedia.org/wiki/K1
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K1, K.I, K01, K 1 or K-1 can refer to:
Geography
K1, another name for Masherbrum, a mountain in the Karakoram range in Pakistan
K1, a small town to north of Kirkuk city, Iraq
K1 (building), a high-rise building in Kraków, Poland
Mathematics
denotes the first algebraic K-theory group of a ring .
Military
Denel K1, a South African mortar
Daewoo Precision Industries K1, a carbine of the South Korean army
EMER K-1, a Burmese assault rifle designated EMERK
Fokker K.I, a World War I German experimental aircraft
Kucher Model K1, a Hungarian submachine gun
, a World War I British submarine
HMS Acanthus (K01) / HNoMS Andenes (K01), a 1939 British, then Norwegian Flower-class corvette
K1 88-Tank, a modern main battle tank of the South Korean military
K-1 cart a United States Signal Corps cart for carrying signal equipment
K 1, a designation for a Swedish cavalry regiment
K1-class gunboat, planned World War II German gunboat
K1, a World War II Dutch sloop operated by the German Navy
Skoda K-1, of the Skoda K series, a World War II Czechoslovak howitzer
USS K-1 (SS-32), a 1913 United States Navy K class of submarine
K-1 Airfield, former name of the Gimhae Air Base
Soviet submarine K-1
IVL K.1 Kurki, a Finnish trainer aircraft
Names
An abbreviation of Keiichi Morisato, a character in the manga/anime Oh My Goddess!
First name of Keiichi Maebara, a character in Higurashi When They Cry franchise
K1, a nickname given to Kyler Murray (born 1997), American footbal
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https://en.wikipedia.org/wiki/The%20Age%20of%20Intelligent%20Machines
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The Age of Intelligent Machines is a non-fiction book about artificial intelligence by inventor and futurist Ray Kurzweil. This was his first book and the Association of American Publishers named it the Most Outstanding Computer Science Book of 1990. It was reviewed in The New York Times and The Christian Science Monitor. The format is a combination of monograph and anthology with contributed essays by artificial intelligence experts such as Daniel Dennett, Douglas Hofstadter, and Marvin Minsky.
Kurzweil surveys the philosophical, mathematical and technological roots of artificial intelligence, starting with the assumption that a sufficiently advanced computer program could exhibit human-level intelligence. Kurzweil argues the creation of humans through evolution suggests that humans should be able to build something more intelligent than themselves. He believes pattern recognition, as demonstrated by vision, and knowledge representation, as seen in language, are two key components of intelligence. Kurzweil details how quickly computers are advancing in each domain.
Driven by the exponential improvements in computer power, Kurzweil believes artificial intelligence will be possible and then commonplace. He explains how it will impact all areas of people's lives, including work, education, medicine, and warfare. As computers acquire human level faculties Kurzweil says people will be challenged to figure out what it really means to be human.
Background
Ray Kurzweil is an inv
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https://en.wikipedia.org/wiki/FROG
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In cryptography, FROG is a block cipher authored by
Georgoudis, Leroux and Chaves. The algorithm can work with any block size between 8 and 128 bytes, and supports key sizes between 5 and 125 bytes. The algorithm consists of 8 rounds and has a very complicated key schedule.
It was submitted in 1998 by TecApro, a Costa Rican software company, to the AES competition as a candidate to become the Advanced Encryption Standard. Wagner et al. (1999) found a number of weak key classes for FROG. Other problems included very slow key setup and relatively slow encryption. FROG was not selected as a finalist.
Design philosophy
Normally a block cipher applies a fixed sequence of primitive mathematical or logical operators (such as additions, XORs, etc.) on the plaintext and secret key in order to produce the ciphertext. An attacker uses this knowledge to search for weaknesses in the cipher which may allow the recovery of the plaintext.
FROG's design philosophy is to hide the exact sequence of primitive operations even though the cipher itself is known. While other ciphers use the secret key only as data (which are combined with the plain text to produce the cipher text), FROG uses the key both as data and as instructions on how to combine these data. In effect an expanded version of the key is used by FROG as a program. FROG itself operates as an interpreter that applies this key-dependent program on the plain text to produce the cipher text. Decryption works by applying the same p
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https://en.wikipedia.org/wiki/Overdetermined
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Overdetermined may refer to:
Overdetermined systems in various branches of mathematics
Overdetermination in various fields of psychology or analytical thought
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https://en.wikipedia.org/wiki/Radical%20initiator
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In chemistry, radical initiators are substances that can produce radical species under mild conditions and promote radical reactions. These substances generally possess weak bonds—bonds that have small bond dissociation energies. Radical initiators are utilized in industrial processes such as polymer synthesis. Typical examples are molecules with a nitrogen-halogen bond, azo compounds, and organic and inorganic peroxides.
Main types of initiation reaction
Halogens undergo homolytic fission relatively easily. Chlorine, for example, gives two chlorine radicals (Cl•) by irradiation with ultraviolet light. This process is used for chlorination of alkanes.
Azo compounds (R-N=N-R') can be the precursor of two carbon-centered radicals (R• and R'•) and nitrogen gas upon heating and/or by irradiation. For example, AIBN and ABCN yield isobutyronitrile and cyclohexanecarbonitrile radicals, respectively.
Organic peroxides each have a peroxide bond (-O-O-), which is readily cleaved to give two oxygen-centered radicals. The oxyl radicals are unstable and believed to be transformed into relatively stable carbon-centered radicals. For example, di-tert-butyl peroxide (t-BuOOt-Bu) gives two t-butoxy radicals (t-BuO•) and the radicals become methyl radicals (CH3•) with the loss of acetone. Benzoyl peroxide ((PhC)OO)2) generates benzoyloxyl radicals (PhCOO•), each of which loses carbon dioxide to be converted into a phenyl radical (Ph•). Methyl ethyl ketone peroxide is also common, and acetone
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https://en.wikipedia.org/wiki/Jonathan%20Borwein
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Jonathan Michael Borwein (20 May 1951 – 2 August 2016) was a Scottish mathematician who held an appointment as Laureate Professor of mathematics at the University of Newcastle, Australia. He was a close associate of David H. Bailey, and they have been prominent public advocates of experimental mathematics.
Borwein's interests spanned pure mathematics (analysis), applied mathematics (optimization), computational mathematics (numerical and computational analysis), and high performance computing. He authored ten books, including several on experimental mathematics, a monograph on convex functions, and over 400 refereed articles. He was a co-founder in 1995 of software company MathResources, consulting and producing interactive software primarily for school and university mathematics. He was not associated with MathResources at the time of his death.
Borwein was also an expert on the number pi and especially its computation.
Early life and education
Borwein was born in St. Andrews, Scotland in 1951 into a Jewish family. His father was mathematician David Borwein, with whom he collaborated. His brother Peter Borwein was also a mathematician.
Borwein was married to Judith, and had three daughters.
He received his B.A. (Honours Math) from University of Western Ontario in 1971, and his D.Phil. from Oxford University in 1974 as a Rhodes Scholar at Jesus College.
Career
Prior to joining Simon Fraser University in 1993, he worked at Dalhousie University (1974–91), Carnegie-Mello
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https://en.wikipedia.org/wiki/Moscow%20Engineering%20Physics%20Institute
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National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) () is a public technical university in Moscow, Russia. It was founded in 1942 as the Moscow Mechanical Institute of Munitions, but was soon renamed the Moscow Mechanical Institute. Its original mission was to train skilled personnel for the Soviet military and Soviet atomic bomb project. It was renamed the Moscow Engineering Physics Institute in 1953, which was its name until 2009.
By the Order of the Government of Russia on April 8, 2009 (#480-r) on behalf of Russian President's Decree of October 7, 2008 (#1448) "On the pilot project launching on creating National Research Universities" MEPhI was granted this new status. The university was reorganized. The aim of the university existence is now preparing the specialists by giving them higher professional, post-graduation professional, secondary professional and additional professional education, as well as educational and scientific activities.
In 2022, QS World University rankings rated the university #308 in the world, World University Rankings by Times Higher Education ranked the university #401 in the world, and in 2023 U.S. News & World Report rated the university #483 in the world.
Academics
Today, MEPhI has nine main departments (faculties or institutes):
Institute of Nuclear Physics and Engineering
Institute for Laser and Plasma Technologies
Institute of Engineering Physics for Biomedicine
Institute of Nanoengineering in Electro
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https://en.wikipedia.org/wiki/BIBO%20stability
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In signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded.
A signal is bounded if there is a finite value such that the signal magnitude never exceeds , that is
For discrete-time signals:
For continuous-time signals:
Time-domain condition for linear time-invariant systems
Continuous-time necessary and sufficient condition
For a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response, , be absolutely integrable, i.e., its L1 norm exists.
Discrete-time sufficient condition
For a discrete time LTI system, the condition for BIBO stability is that the impulse response be absolutely summable, i.e., its norm exists.
Proof of sufficiency
Given a discrete time LTI system with impulse response the relationship between the input and the output is
where denotes convolution. Then it follows by the definition of convolution
Let be the maximum value of , i.e., the -norm.
(by the triangle inequality)
If is absolutely summable, then and
So if is absolutely summable and is bounded, then is bounded as well because .
The proof for continuous-time follows the same arguments.
Frequency-domain condition for linear time-invariant systems
Continuous-time signals
For a rational and continuous-time system,
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https://en.wikipedia.org/wiki/Online%20codes
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In computer science, online codes are an example of rateless erasure codes. These codes can encode a message into a number of symbols such that knowledge of any fraction of them allows one to recover the original message (with high probability). Rateless codes produce an arbitrarily large number of symbols which can be broadcast until the receivers have enough symbols.
The online encoding algorithm consists of several phases. First the message is split into n fixed size message blocks. Then the outer encoding is an erasure code which produces auxiliary blocks that are appended to the message blocks to form a composite message.
From this the inner encoding generates check blocks. Upon receiving a certain number of check blocks some fraction of the composite message can be recovered. Once enough has been recovered the outer decoding can be used to recover the original message.
Detailed discussion
Online codes are parameterised by the block size and two scalars, q and ε. The authors suggest q=3 and ε=0.01. These parameters set the balance between the complexity and performance of the encoding. A message of n blocks can be recovered, with high probability, from (1+3ε)n check blocks. The probability of failure is (ε/2)q+1.
Outer encoding
Any erasure code may be used as the outer encoding, but the author of online codes suggest the following.
For each message block, pseudo-randomly choose q auxiliary blocks
(from a total of 0.55qεn auxiliary blocks) to attach it to. Each auxi
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https://en.wikipedia.org/wiki/Bruce%20Peebles%20%26%20Co.%20Ltd.
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Bruce Peebles & Co. Ltd. was an Edinburgh industrial electrical engineering company.
Early history
The company was founded as D. Bruce Peebles & Co. by Scottish engineer David Bruce Peebles (1826–1899) in Edinburgh in 1866. The company initially specialised in gas engineering but later expanded to include electrical engineering as well. It continued to trade after Peebles' death and, in 1902, the name was changed to Bruce Peebles & Co. Ltd. The company held the British manufacturing rights for the Cascade converter and a licence to manufacture three-phase electrical equipment designed by Ganz of Budapest.
Canadian Electric Traction Company
In 1903, Peebles expanded into Canada. Along with other investors, it formed the Canadian Electric Traction Company and supplied the three-phase equipment, car motors and generators for the South Western Traction Company of London, Ontario. The main line ran 28-miles between London and Port Stanley, a resort town on Lake Erie. It was the only three-phase traction line in Canada, and was closed in 1918.
New factory
In 1904 the company opened a new factory at a site in East Pilton, Edinburgh, employing 3,000 at its peak in the 1950s. The works had its own internal railway system, which was electrified and used electric shunting locomotives built by Peebles themselves. This was the first electric line in Edinburgh (main line electrification did not reach Edinburgh until the early 1990s). In 1905 the company was exhibiting at the Third Inter
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https://en.wikipedia.org/wiki/Pairing%20function
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In mathematics, a pairing function is a process to uniquely encode two natural numbers into a single natural number.
Any pairing function can be used in set theory to prove that integers and rational numbers have the same cardinality as natural numbers.
Definition
A pairing function is a bijection
More generally, a pairing function on a set A is a function that maps each pair of elements from A into an element of A, such that any two pairs of elements of A are associated with different elements of A, or a bijection from to A.
Hopcroft and Ullman pairing function
Hopcroft and Ullman (1979) define the following pairing function: , where . This is the same as the Cantor pairing function below, shifted to exclude 0 (i.e., , , and ).
Cantor pairing function
The Cantor pairing function is a primitive recursive pairing function
defined by
where .
It can also be expressed as .
It is also strictly monotonic w.r.t. each argument, that is, for all , if , then ; similarly, if , then .
The statement that this is the only quadratic pairing function is known as the Fueter–Pólya theorem. Whether this is the only polynomial pairing function is still an open question. When we apply the pairing function to and we often denote the resulting number as .
This definition can be inductively generalized to the
for as
with the base case defined above for a pair:
Inverting the Cantor pairing function
Let be an arbitrary natural number. We will show that there exist unique value
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https://en.wikipedia.org/wiki/Lucas%E2%80%93Carmichael%20number
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In mathematics, a Lucas–Carmichael number is a positive composite integer n such that
if p is a prime factor of n, then p + 1 is a factor of n + 1;
n is odd and square-free.
The first condition resembles the Korselt's criterion for Carmichael numbers, where -1 is replaced with +1. The second condition eliminates from consideration some trivial cases like cubes of prime numbers, such as 8 or 27, which otherwise would be Lucas–Carmichael numbers (since n3 + 1 = (n + 1)(n2 − n + 1) is always divisible by n + 1).
They are named after Édouard Lucas and Robert Carmichael.
Properties
The smallest Lucas–Carmichael number is 399 = 3 × 7 × 19. It is easy to verify that 3+1, 7+1, and 19+1 are all factors of 399+1 = 400.
The smallest Lucas–Carmichael number with 4 factors is 8855 = 5 × 7 × 11 × 23.
The smallest Lucas–Carmichael number with 5 factors is 588455 = 5 × 7 × 17 × 23 × 43.
It is not known whether any Lucas–Carmichael number is also a Carmichael number.
Thomas Wright proved in 2016 that there are infinitely many Lucas–Carmichael numbers. If we let denote the number of Lucas–Carmichael numbers up to , Wright showed that there exists a positive constant such that
.
List of Lucas–Carmichael numbers
The first few Lucas–Carmichael numbers and their prime factors are listed below.
References
External links
Eponymous numbers in mathematics
Integer sequences
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https://en.wikipedia.org/wiki/Geometric%20quantization
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In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization, for which there is in general no exact recipe, in such a way that certain analogies between the classical theory and the quantum theory remain manifest. For example, the similarity between the Heisenberg equation in the Heisenberg picture of quantum mechanics and the Hamilton equation in classical physics should be built in.
Origins
One of the earliest attempts at a natural quantization was Weyl quantization, proposed by Hermann Weyl in 1927. Here, an attempt is made to associate a quantum-mechanical observable (a self-adjoint operator on a Hilbert space) with a real-valued function on classical phase space. The position and momentum in this phase space are mapped to the generators of the Heisenberg group, and the Hilbert space appears as a group representation of the Heisenberg group. In 1946, H. J. Groenewold considered the product of a pair of such observables and asked what the corresponding function would be on the classical phase space. This led him to discover the phase-space star-product of a pair of functions.
The modern theory of geometric quantization was developed by Bertram Kostant and Jean-Marie Souriau in the 1970s. One of the motivations of the theory was to understand and generalize Kirillov's orbit method in representation theory.
Types
The geometric quantization procedur
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https://en.wikipedia.org/wiki/Kac%E2%80%93Moody%20algebra
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In mathematics, a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently and simultaneously discovered them in 1968) is a Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix. These algebras form a generalization of finite-dimensional semisimple Lie algebras, and many properties related to the structure of a Lie algebra such as its root system, irreducible representations, and connection to flag manifolds have natural analogues in the Kac–Moody setting.
A class of Kac–Moody algebras called affine Lie algebras is of particular importance in mathematics and theoretical physics, especially two-dimensional conformal field theory and the theory of exactly solvable models. Kac discovered an elegant proof of certain combinatorial identities, the Macdonald identities, which is based on the representation theory of affine Kac–Moody algebras. Howard Garland and James Lepowsky demonstrated that Rogers–Ramanujan identities can be derived in a similar fashion.
History of Kac–Moody algebras
The initial construction by Élie Cartan and Wilhelm Killing of finite dimensional simple Lie algebras from the Cartan integers was type dependent. In 1966 Jean-Pierre Serre showed that relations of Claude Chevalley and Harish-Chandra, with simplifications by Nathan Jacobson, give a defining presentation for the Lie algebra. One could thus describe a simple Lie algebra in terms of generators and relations u
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https://en.wikipedia.org/wiki/Bogoliubov%20transformation
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In theoretical physics, the Bogoliubov transformation, also known as the Bogoliubov–Valatin transformation, was independently developed in 1958 by Nikolay Bogolyubov and John George Valatin for finding solutions of BCS theory in a homogeneous system. The Bogoliubov transformation is an isomorphism of either the canonical commutation relation algebra or canonical anticommutation relation algebra. This induces an autoequivalence on the respective representations. The Bogoliubov transformation is often used to diagonalize Hamiltonians, which yields the stationary solutions of the corresponding Schrödinger equation. The Bogoliubov transformation is also important for understanding the Unruh effect, Hawking radiation, pairing effects in nuclear physics, and many other topics.
The Bogoliubov transformation is often used to diagonalize Hamiltonians, with a corresponding transformation of the state function. Operator eigenvalues calculated with the diagonalized Hamiltonian on the transformed state function thus are the same as before.
Single bosonic mode example
Consider the canonical commutation relation for bosonic creation and annihilation operators in the harmonic basis
Define a new pair of operators
for complex numbers u and v, where the latter is the Hermitian conjugate of the first.
The Bogoliubov transformation is the canonical transformation mapping the operators and to and . To find the conditions on the constants u and v such that the transformation is canonical,
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https://en.wikipedia.org/wiki/Cartan%20matrix
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In mathematics, the term Cartan matrix has three meanings. All of these are named after the French mathematician Élie Cartan. Amusingly, the Cartan matrices in the context of Lie algebras were first investigated by Wilhelm Killing, whereas the Killing form is due to Cartan.
Lie algebras
A (symmetrizable) generalized Cartan matrix is a square matrix with integer entries such that
For diagonal entries, .
For non-diagonal entries, .
if and only if
can be written as , where is a diagonal matrix, and is a symmetric matrix.
For example, the Cartan matrix for G2 can be decomposed as such:
The third condition is not independent but is really a consequence of the first and fourth conditions.
We can always choose a D with positive diagonal entries. In that case, if S in the above decomposition is positive definite, then A is said to be a Cartan matrix.
The Cartan matrix of a simple Lie algebra is the matrix whose elements are the scalar products
(sometimes called the Cartan integers) where ri are the simple roots of the algebra. The entries are integral from one of the properties of roots. The first condition follows from the definition, the second from the fact that for is a root which is a linear combination of the simple roots ri and rj with a positive coefficient for rj and so, the coefficient for ri has to be nonnegative. The third is true because orthogonality is a symmetric relation. And lastly, let and . Because the simple roots span a Euclidean space,
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https://en.wikipedia.org/wiki/Ternary%20compound
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In inorganic chemistry and materials chemistry, a ternary compound or ternary phase is a chemical compound containing three different elements.
While some ternary compounds are molecular, e.g. chloroform (), more typically ternary phases refer to extended solids. Famous example are the perovskites.
Binary phases, with only two elements, have lower degrees of complexity than ternary phases. With four elements, quaternary phases are more complex.
The number of isomers of a ternary compound provide a distinction between inorganic and organic chemistry: "In inorganic chemistry one or, at most, only a few compounds composed of any two or three elements were known, whereas in organic chemistry the situation was very different."
Ternary crystalline compounds
An example is sodium phosphate, . The sodium ion has a charge of 1+ and the phosphate ion has a charge of 3–. Therefore, three sodium ions are needed to balance the charge of one phosphate ion. Another example of a ternary compound is calcium carbonate, . In naming and writing the formulae for ternary compounds, rules are similar to binary compounds.
Classifications of ternary crystals
According to Rustum Roy and Olaf Müller, "the chemistry of the entire mineral world informs us that chemical complexity can easily be accommodated within structural simplicity." The example of zircon is cited, where various metal atoms are replaced in the same crystal structure. "The structural entity ... remains ternary in character and
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https://en.wikipedia.org/wiki/Chris%20Wallace%20%28computer%20scientist%29
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Christopher Stewart Wallace (26 October 1933 – 7 August 2004) was an Australian computer scientist and physicist.
Wallace is notable for having devised:
The minimum message length principle — an information-theoretic principle in statistics, econometrics, machine learning, inductive inference and knowledge discovery which can be seen both as a mathematical formalisation of Occam's Razor and as an invariant Bayesian method of model selection and point estimation,
The Wallace tree form of binary multiplier (1964),
a variety of random number generators,
a theory in physics and philosophy that entropy is not the arrow of time,
a refrigeration system (from the 1950s, whose design is still in use in 2010),
hardware for detecting and counting cosmic rays,
design of computer operating systems,
the notion of universality probability in mathematical logic,
and a vast range of other works - see, e.g., and its Foreword re C. S. Wallace , pp 523-560.
He was appointed Foundation Chair of Information Science at Monash University in 1968 at the age of 34 (before the Department was re-named Computer Science), and Professor Emeritus in 1996. Wallace was a fellow of the Australian Computer Society and in 1995 he was appointed a fellow of the ACM "For research in a number of areas in Computer Science including fast multiplication algorithm, minimum message length principle and its applications, random number generation, computer architecture, numerical solution of ODE's, and contrib
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https://en.wikipedia.org/wiki/CWP
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CWP may refer to:
Cable & Wireless plc (stock symbol on the New York Stock Exchange)
Cakewalk Project, a Cakewalk Sonar sequencing software project file
Camp White Pine
Causeway Point
Centralized Warning Panel (see Annunciator panel)
Chinese Wikipedia
Chronic Widespread Pain (see Fibromyalgia#Genetics)
Coalition of Women for a Just Peace
Coalworker's pneumoconiosis
Commonwealth Writers' Prize
Communist Workers' Party (United States)
Computing with words and perceptions
Concealed Weapons Permit, see Concealed carry in the United States
Coordinating Working Party on Fishery Statistics
Cotswold Water Park
Cotswold Wildlife Park, a zoo in Oxfordshire, England
Crown Wheel and Pinion, see Differential (mechanical device)
Current Warming Period, see Global warming
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https://en.wikipedia.org/wiki/Genny%20Smith
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Genny Smith (1922 - March 4, 2018) was a publisher and editor of guidebooks about the Eastern Sierra Nevada and the Owens Valley of California, United States. Her writings about the history, geology and biology of the region had caused her to be dubbed "the Naturalist Queen of the Eastern Sierra".
Starting in 1958, Smith lobbied against a Trans-Sierra Highway starting at Minaret Summit near Mammoth Lakes, California. Smith and other residents of Mammoth worked with Norman Livermore to convince Governor Ronald Reagan to cancel the road in 1972.
She received a B.A. degree from Reed College in 1943. She a resident of Cupertino, California, while spending her summers in Mammoth Lakes, California. She was formerly on the board of directors of the Mono Lake Committee.
Smith received the Andrea Lawrence Award from the Mono Lake Committee in 2017, for her guidebook writing and work in preventing the trans-Sierra road.
References
2018 deaths
Reed College alumni
American book publishers (people)
People from Cupertino, California
People from Mammoth Lakes, California
1922 births
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https://en.wikipedia.org/wiki/BOOMERanG%20experiment
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In astronomy and observational cosmology, the BOOMERanG experiment (Balloon Observations Of Millimetric Extragalactic Radiation And Geophysics) was an experiment which measured the cosmic microwave background radiation of a part of the sky during three sub-orbital (high-altitude) balloon flights. It was the first experiment to make large, high-fidelity images of the CMB temperature anisotropies, and is best known for the discovery in 2000 that the geometry of the universe is close to flat, with similar results from the competing MAXIMA experiment.
By using a telescope which flew at over 42,000 meters high, it was possible to reduce the atmospheric absorption of microwaves to a minimum. This allowed massive cost reduction compared to a satellite probe, though only a tiny part of the sky could be scanned.
The first was a test flight over North America in 1997. In the two subsequent flights in 1998 and 2003 the balloon was launched from McMurdo Station in the Antarctic. It was carried by the Polar vortex winds in a circle around the South Pole, returning after two weeks. From this phenomenon the telescope took its name.
The BOOMERanG team was led by Andrew E. Lange of Caltech and Paolo de Bernardis of the University of Rome La Sapienza.
Instrumentation
The experiment uses bolometers for radiation detection. These bolometers are kept at a temperature of 0.27 kelvin. At this temperature the material has a very low heat capacity according to the Debye law, thus incoming microw
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https://en.wikipedia.org/wiki/Lami%27s%20theorem
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In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding vectors. According to the theorem,
where A, B and C are the magnitudes of the three coplanar, concurrent and non-collinear vectors, , which keep the object in static equilibrium, and α, β and γ are the angles directly opposite to the vectors.
Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named after Bernard Lamy.
Proof
As the vectors must balance , hence by making all the vectors touch its tip and tail the result is a triangle with sides A, B, C and angles By the law of sines then
Then by applying that for any angle , , and the result is
See also
Mechanical equilibrium
Parallelogram of force
Tutte embedding
References
Further reading
R.K. Bansal (2005). "A Textbook of Engineering Mechanics". Laxmi Publications. p. 4. .
I.S. Gujral (2008). "Engineering Mechanics". Firewall Media. p. 10.
Eponymous theorems of physics
Statics
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https://en.wikipedia.org/wiki/Grouping
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Grouping generally refers to the creation of one or more groups, or to the groups themselves.
More specifically, grouping may refer to:
Shot grouping in shooting sports and other uses of firearms
the use of symbols of grouping in mathematics (parentheses, etc.)
the creation of social groups
See also
Categorization
Classification
Segregation (disambiguation)
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https://en.wikipedia.org/wiki/Symmetry%20in%20biology
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Symmetry in biology refers to the symmetry observed in organisms, including plants, animals, fungi, and bacteria. External symmetry can be easily seen by just looking at an organism. For example, the face of a human being has a plane of symmetry down its centre, or a pine cone displays a clear symmetrical spiral pattern. Internal features can also show symmetry, for example the tubes in the human body (responsible for transporting gases, nutrients, and waste products) which are cylindrical and have several planes of symmetry.
Biological symmetry can be thought of as a balanced distribution of duplicate body parts or shapes within the body of an organism. Importantly, unlike in mathematics, symmetry in biology is always approximate. For example, plant leaves – while considered symmetrical – rarely match up exactly when folded in half. Symmetry is one class of patterns in nature whereby there is near-repetition of the pattern element, either by reflection or rotation.
While sponges and placozoans represent two groups of animals which do not show any symmetry (i.e. are asymmetrical), the body plans of most multicellular organisms exhibit, and are defined by, some form of symmetry. There are only a few types of symmetry which are possible in body plans. These are radial (cylindrical), bilateral, biradial and spherical symmetry. While the classification of viruses as an "organism" remains controversial, viruses also contain icosahedral symmetry.
The importance of symmetry is il
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https://en.wikipedia.org/wiki/Endonuclease
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In molecular biology, endonucleases are enzymes that cleave the phosphodiester bond within a polynucleotide chain (namely DNA or RNA). Some, such as deoxyribonuclease I, cut DNA relatively nonspecifically (without regard to sequence), while many, typically called restriction endonucleases or restriction enzymes, cleave only at very specific nucleotide sequences. Endonucleases differ from exonucleases, which cleave the ends of recognition sequences instead of the middle (endo) portion. Some enzymes known as "exo-endonucleases", however, are not limited to either nuclease function, displaying qualities that are both endo- and exo-like. Evidence suggests that endonuclease activity experiences a lag compared to exonuclease activity.
Restriction enzymes are endonucleases from eubacteria and archaea that recognize a specific DNA sequence. The nucleotide sequence recognized for cleavage by a restriction enzyme is called the restriction site. Typically, a restriction site will be a palindromic sequence about four to six nucleotides long. Most restriction endonucleases cleave the DNA strand unevenly, leaving complementary single-stranded ends. These ends can reconnect through hybridization and are termed "sticky ends". Once paired, the phosphodiester bonds of the fragments can be joined by DNA ligase. There are hundreds of restriction endonucleases known, each attacking a different restriction site. The DNA fragments cleaved by the same endonuclease can be joined regardless of the or
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https://en.wikipedia.org/wiki/Range%20fractionation
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Range fractionation is a term used in biology to describe the way by which a group of sensory neurons are able to encode varying magnitudes of a stimulus. Sense organs are usually composed of many sensory receptors measuring the same property. These sensory receptors show a limited degree of precision due to an upper limit in firing rate. If the receptors are endowed with distinct transfer functions in such a way that the points of highest sensitivity are scattered along the axis of the quality being measured, the precision of the sense organ as a whole can be increased.
The basis of the idea of range fractionation is that each stimulus (for example, touch) has a range of intensities that can be sensed (light-touch to deep/hard-touch). For an organism to be able to sense a range of stimulus intensities, sensory neurons are tuned to fractions of the entire range. Collectively, the pattern of activity among the sensory neurons is how the organism can identify specific stimulus parameters. This was shown for proprioceptive neurons in the locust leg, proprioceptive neurons in the stick insect, Johnston's Organ neurons in Drosophila, and in auditory-sensing neurons in crickets.
Range fraction is similar to the labeled line theory in that they both describe a phenomenon by which sensory neurons divide the task of encoding a range of stimulus intensities. However the difference lies within the downstream synaptic partners. Labeled line theory describes fully segregated channels p
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https://en.wikipedia.org/wiki/Sociobiology%3A%20The%20New%20Synthesis
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Sociobiology: The New Synthesis (1975; 25th anniversary edition 2000) is a book by the biologist E. O. Wilson. It helped start the sociobiology debate, one of the great scientific controversies in biology of the 20th century and part of the wider debate about evolutionary psychology and the modern synthesis of evolutionary biology. Wilson popularized the term "sociobiology" as an attempt to explain the evolutionary mechanics behind social behaviour such as altruism, aggression, and the nurturing of the young. It formed a position within the long-running nature versus nurture debate. The fundamental principle guiding sociobiology is that an organism's evolutionary success is measured by the extent to which its genes are represented in the next generation.
The book was generally well-reviewed in biological journals. It received a much more mixed reaction among sociologists, mainly triggered by the brief coverage of the implications of sociobiology for human society in the first and last chapters of the book; the body of the text was largely welcomed. Such was the level of interest in the debate that a review reached the front page of the New York Times. The sociologist Gerhard Lenski, admitting that sociologists needed to look further into non-human societies, agreed that human society was founded on biology but denied both biological reductionism and determinism. Lenski observed that since the nature-nurture dichotomy was false, there was no reason for sociologists and biolog
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https://en.wikipedia.org/wiki/PKC
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PKC may refer to:
Paroxysmal kinesogenic choreoathetosis, a neurological disorder
Protein kinase C, a family of enzymes
Public-key cryptography, a cryptographic system using pairs of keys
PKC (conference)
Petropavlovsk-Kamchatsky Airport or Yelizovo Airport, Kamchatka Krai, Russia (IATA code PKC)
PKC Group, a Finnish company
Perth and Kinross Council, a local authority in Scotland
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https://en.wikipedia.org/wiki/1591%20in%20science
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The year 1591 in science and technology included many events, some of which are listed here.
Mathematics
François Viète publishes In Artem Analyticien Isagoge, introducing the new algebra with innovative use of letters as parameters in equations.
Giordano Bruno publishes and in Francfort.
Technology
The Rialto Bridge in Venice, designed by Antonio da Ponte, is completed.
Publications
Prospero Alpini publishes De Medicina Egyptiorum in Venice, including accounts of coffee, bananas and the baobab.
Publication of the first of the Conimbricenses commentaries on Aristotle by the Jesuits of the University of Coimbra, Commentarii Collegii Conimbricensis Societatis Jesu in octo libros physicorum Aristotelis Stagyritæ, on Aristotle's Physics.
Births
February 21 – Gérard Desargues, French geometer (died 1661)
Deaths
July 2 – Vincenzo Galilei, Italian scientist and musician (born 1520)
References
16th century in science
1590s in science
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https://en.wikipedia.org/wiki/Othenio%20Abel
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Othenio Lothar Franz Anton Louis Abel (June 20, 1875 – July 4, 1946) was an Austrian paleontologist and evolutionary biologist. Together with Louis Dollo, he was the founder of "paleobiology" and studied the life and environment of fossilized organisms.
Life
Abel was born in Vienna, the son of the architect Lothar Abel. Abel earned a PhD, after studying both law and science, from the University of Vienna. He remained there as an assistant to Alpine geologist Eduard Suess, before being appointed a professor of paleontology. Three years later, he finished his habilitation thesis as a paleontologist at the University of Vienna. From 1900 to 1907, he worked at the Geologische Reichsanstalt.
In 1907, Abel became an extraordinary professor in Vienna, and from 1917 to 1934 he was a regular professor of paleontology in Vienna. As such, he led several expeditions that gave him broad recognition, such as the Pikermi-expedition to Greece in 1912, an American expedition (1925) and one to South Africa (1929).
Abel became a member of the Leopoldina academy in 1935. From 1935 to 1940, he was a professor at Göttingen University, after which he was retired, age 61. In 1942, he was appointed an honorary member of the Paläontologische Gesellschaft.
Scientific activity
Abel mainly studied fossil vertebrates. He was a supporter of Neo-Lamarckist evolution. His main contribution to the field, however, was the formulation, together with Louis Dollo, of paleobiology, which combines the methods
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https://en.wikipedia.org/wiki/Antonio%20Abetti
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Antonio Abetti (19 June 1846 – 20 February 1928) was an Italian astronomer.
Born in San Pietro di Gorizia (Šempeter-Vrtojba), he earned a degree in mathematics and engineering at the University of Padua. He was married to Giovanna Colbachini in 1879 and they had two sons. He died in Arcetri.
Work
Abetti mainly worked in positional astronomy and made many observations of minor planets, comets, and star occultations. In 1874 he was part of an expedition led by Pietro Tacchini to observe a transit of Venus with a spectroscope. Later he became director of the Osservatorio Astrofisico di Arcetri and a professor at the University of Florence. He refurbished the observatory at Arcetri by installing a new telescope.
Honors
Member of the Accademia dei Lincei.
Member of the Royal Astronomical Society.
The crater Abetti on the Moon is named after both Antonio and his son Giorgio Abetti.
The minor planet 2646 Abetti is also named after Antonio and his son.
References
External links
Biography of Abetti
1846 births
1928 deaths
People from Šempeter pri Gorici
19th-century Italian astronomers
20th-century Italian astronomers
University of Padua alumni
Academic staff of the University of Florence
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https://en.wikipedia.org/wiki/Homology%20%28anthropology%29
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In sociocultural anthropology and archaeology, homology is a type of analogy whereby two human beliefs, practices, or artifacts are separated by time and/or place but share similarities due to some underlying factor, whether genetics, historical connection, psychological archetype, or otherwise. This type of homology is the counterpart of biologic homology in physical anthropology, whereby an anatomic structure is shared through descent from a common ancestor.
The concept was explored by the American archaeologist William Duncan Strong in his direct historical approach to archaeological theory. It is important in structural anthropology in particular but also in sociocultural anthropology in general.
See also
Jungian archetypes
Anthropology
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https://en.wikipedia.org/wiki/Denise%20Faustman
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Denise Louise Faustman (born 1958) is an American physician and medical researcher. An associate professor of medicine at Harvard University and director of the Immunobiology Laboratory at Massachusetts General Hospital, her work specializes in diabetes mellitus type 1 (formerly called juvenile diabetes) and other autoimmune diseases. She has worked at Massachusetts General Hospital in Boston since 1985.
Education and career
Faustman was born in Royal Oak, Michigan in 1958. In 1978, she received her BS in zoology and chemistry from the University of Michigan. She earned a PhD in transplantation immunology in 1982 and an MD in 1985 from the Washington University School of Medicine in St. Louis, Missouri. She did her internship and residency in medicine at Massachusetts General Hospital.
Research
Faustman's current research is based on the observation that autoreactive T cells (T cells that mistakenly attack the body's own cells and tissues) are more sensitive than normal T cells to the effects of TNF-alpha (TNF-α), a cytokine that influences the immune system. Under some conditions, TNF-α causes T cells to undergo apoptosis, or programmed cell death. Faustman's hypothesis is that certain autoimmune diseases can be treated by stimulating TNF-α to trigger apoptosis in autoimmune T cells.
Prior to entering human clinical trials, Faustman's approach was tested in non-obese diabetic mice (NOD mice), a strain of mice that spontaneously develops type 1 diabetes. Injecting the mi
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https://en.wikipedia.org/wiki/Geoarchaeology
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Geoarchaeology is a multi-disciplinary approach which uses the techniques and subject matter of geography, geology, geophysics and other Earth sciences to examine topics which inform archaeological knowledge and thought. Geoarchaeologists study the natural physical processes that affect archaeological sites such as geomorphology, the formation of sites through geological processes and the effects on buried sites and artifacts post-deposition. Geoarchaeologists' work frequently involves studying soil and sediments as well as other geographical concepts to contribute an archaeological study. Geoarchaeologists may also use computer cartography, geographic information systems (GIS) and digital elevation models (DEM) in combination with disciplines from human and social sciences and earth sciences. Geoarchaeology is important to society because it informs archaeologists about the geomorphology of the soil, sediment, and rocks on the buried sites and artifacts they are researching. By doing this, scientists are able to locate ancient cities and artifacts and estimate by the quality of soil how "prehistoric" they really are. Geoarchaeology is considered a sub-field of environmental archaeology because soil can be altered by human behavior, which archaeologists are then able to study and reconstruct past landscapes and conditions.
Techniques used
Column sampling
Column sampling is a technique of collecting samples from a section for analyzing and detecting the buried processes down
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https://en.wikipedia.org/wiki/Dorothy%20Edgington
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Dorothy Margaret Doig Edgington FBA (née Milne, born 29 April 1941) is a philosopher active in metaphysics and philosophical logic. She is particularly known for her work on the logic of conditionals and vagueness.
Life and education
Dorothy Edgington was born on 29 April 1941 to Edward Milne and his wife Rhoda née Blair. She attended St Leonards School before going to St Hilda's College, Oxford to read PPE. She obtained her BA in 1964, followed in 1967 by a BPhil at Nuffield College, Oxford.
Career
Most of Edgington's career was spent at Birkbeck College. Her first academic post in 1968, was as Lecturer in Philosophy at Birkbeck and she remained there until 1996. From 1996 until 2001 she was appointed Fellow of University College, Oxford. This was followed by a professorship at Birkbeck from 2001 to 2003. She was then Waynflete Professor of Metaphysical Philosophy at the University of Oxford from 2003 until 2006. She is now Emeritus Professor, and Fellow of Magdalen College, Oxford and teaches at Birkbeck again part-time.
Birkbeck College hosts a lecture series named after Edgington; in 2012, the lectures were given by John McDowell, in 2014 they were given by Rae Langton, and in 2016 the Edgington Lectures were given by Kit Fine.
From 2004 to 2005 she was President of the Mind Association 2004–5 and she was President of the Aristotelian Society for 2007–8. She is a Fellow of the British Academy.
Selected publications
'The Paradox of Knowability' (1985), Mind 94:55
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https://en.wikipedia.org/wiki/Memory%20space
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Memory space can refer to:
Memory space (computational resource), a computer science/information theory concept related to computational resources
Memory space (social science), a sociological concept related to collective memory
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https://en.wikipedia.org/wiki/Ernie%20Parsons
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Ernie Parsons (born June 5, 1946) is a former politician in Ontario, Canada. He was a member of the Legislative Assembly of Ontario, representing the riding of Prince Edward—Hastings for the Ontario Liberal Party from 1999 to 2007. In 2007 he was appointed as a Justice of the Peace.
Background
Parsons received a Civil Engineering degree from Carleton University in 1969, and was employed by the Ministry of Transportation from 1969 to 1974, and taught Technology courses at Loyalist College from 1974 to 1999. He also worked as a farmer, and was a board member of the Hastings County Children's Aid Society for twenty-five years and its chair for three. Parsons was a founding member of the Hastings County Museum of Agricultural Heritage, and sat on advisory committees to the Kingston Hotel Dieu, the Kingston General Hospital and the Queen's University Faculty of Medicine. Parsons served on the school board of the Hastings—Prince Edward district from 1982 to 1999.
Politics
In the 1999 provincial election he defeated Progressive Conservative incumbent Gary Fox by 56 votes in Prince Edward—Hastings. The Progressive Conservatives won the election, and Parsons spent the next four years in opposition.
The Liberals won the 2003 provincial election, and Parsons was re-elected in Prince Edward—Hastings by over 10,000 votes over Tory John Williams. He was named parliamentary assistant to Ontario Minister of Transportation Harinder Takhar on October 23, 2003, and parliamentary assistant
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https://en.wikipedia.org/wiki/Hauke%20Harder
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Hauke Harder (born 1963 in Heide (Holstein), Germany) is a German composer and experimental physicist.
Life
Harder received a PhD in chemistry, and works at the Institute for Physical Chemistry, Department of Chemistry and Physics, University of Kiel, Kiel, Germany.
In 1989, he studied with Wolfgang von Schweinitz, a New Simplicity composer.
He is the founder, (with Rainer Grodnick) of the "Gesellschaft für Akustische Lebenshilfe", (Society for Musical Living Assistance), Kiel, Germany. Since 1995, he has worked as an assistant to composer Alvin Lucier and is associated with the Material group of composers, along with Daniel James Wolf, and Markus Trunk. His compositional work is in an extreme minimal style, and is connected to the work of the composers Morton Feldman, Walter Zimmermann, and Alvin Lucier. His music has also been influenced by Monochrome Painting and the films of Robert Bresson.
His work in sound installation, exhibitions and concerts include: the International New Music Festival Rümlingen, Switzerland, Evenings of New Music Bratislava, Flanders Music Festival Antwerp, Nové Expozice hudby Brno.
Awards
In 2001 he received a "Kulturnetz-Preis", and 3,000 Mark, by Schleswig-Holstein's culture minister Ute Erdsiek-Rave.
Works
His works as a scientist in the field of molecular spectroscopy have been featured in:
,
Performances
Hildegard Kleeb has premiered his work. On 14 April 2009, his piece in honor of Walter Zimmermann was played in concert by
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https://en.wikipedia.org/wiki/Universalizability
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The concept of universalizability was set out by the 18th-century German philosopher Immanuel Kant as part of his work Groundwork of the Metaphysics of Morals. It is part of the first formulation of his categorical imperative, which states that the only morally acceptable maxims of our actions are those that could rationally be willed to be universal law.
The precise meaning of universalizability is contentious, but the most common interpretation is that the categorical imperative asks whether the maxim of your action could become one that everyone could act upon in similar circumstances. An action is socially acceptable if it can be universalized (i.e., everyone could do it).
For instance, one can determine whether a maxim of lying to secure a loan is moral by attempting to universalize it and applying reason to the results. If everyone lied to secure loans, the very practices of promising and lending would fall apart, and the maxim would then become impossible.
Kant calls such acts examples of a contradiction in conception, which is much like a performative contradiction, because they undermine the very basis for their existence.
Kant's notion of universalizability has a clear antecedent in Rousseau's idea of a general will. Both notions provide for a radical separation of will and nature, leading to the idea that true freedom lies substantially in self-legislation.
See also
Categorical imperative
Deontology
References
Concepts in ethics
Kantianism
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https://en.wikipedia.org/wiki/157%20%28number%29
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157 (one hundred [and] fifty-seven) is the number following 156 and preceding 158.
In mathematics
157 is:
the 37th prime number. The next prime is 163 and the previous prime is 151.
a balanced prime, because the arithmetic mean of those primes yields 157.
an emirp.
a Chen prime.
the largest known prime p which is also prime. (see ).
the least irregular prime with index 2.
a palindromic number in bases 7 (3137) and 12 (11112).
a repunit in base 12, so it is a unique prime in the same base.
a prime whose digits sum to a prime. (see ).
a prime index prime.
In base 10, 1572 is 24649, and 1582 is 24964, which uses the same digits. Numbers having this property are listed in . The previous entry is 13, and the next entry after 157 is 913.
The simplest right angle triangle with rational sides that has area 157 has the longest side with a denominator of 45 digits.
In the military
was a United States Coast Guard cutter built in 1926
was a United States Navy Type T2 tanker during World War II
was a United States Navy Alamosa-class cargo ship during World War II
was a United States Navy Admirable-class minesweeper during World War II
was a United States Navy Wickes-class destroyer during World War II
was a United States Navy Buckley-class destroyer escort during World War II
was a United States Navy General G. O. Squier-class transport ship during World War II
was a United States Navy LST-542-class tank landing ship during World War II
was a United State
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https://en.wikipedia.org/wiki/Mega%20Man%20Battle%20Network
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is a tactical role-playing video game series created by Masahiro Yasuma and developed and published by Capcom as a spin-off of the Mega Man series; it premiered in 2001 on the Game Boy Advance and takes place in an alternate continuity where computers and networking technology was the main focus on scientific advancement, rather than robotics. There are a total of six mainline games, alongside several spin-offs.
Created amidst the success of Nintendo's and Game Freak's Pokémon series, alongside the rise of collectable card games, Mega Man Battle Network has players control MegaMan.EXE, a NetNavi operated by Lan Hikari as they attempt to stop the schemes of a net-crime organization called WWW (called "World Three"), headed by the universe's interpretation of Dr. Wily. Players battle enemies on a 6x3 grid, selecting "Battle Chips" which allow for more powerful attacks.
The series has been met with positive reviews from critics, although later games, particularly 5 and 6, have been criticized for a perceived lack of innovation; the series was followed-up by a sequel series titled Mega Man Star Force, which is set 200 years after Battle Network and focuses on radio waves. A compilation of all six mainline entries, Mega Man Battle Network Legacy Collection, was released in April 2023 for PlayStation 4, Nintendo Switch and PC.
Plot
Mega Man Battle Network is set in an ambiguous year in the 21st century ("20XX AD") in an alternate reality to the original Mega Man series. Within
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https://en.wikipedia.org/wiki/Dyson%20Perrins%20Laboratory
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The Dyson Perrins Laboratory is in the science area of the University of Oxford and was the main centre for research into organic chemistry of the University from its foundation in 1916 until its closure as a research laboratory in 2003. Until 2018, parts of the building were used as teaching laboratories in which undergraduate students were trained in practical organic chemistry.
It was founded with an endowment from Charles Dyson Perrins, heir to the Lea & Perrins Worcestershire sauce company, and stands on the north side of South Parks Road in Oxford.
Notable chemists
The heads of the laboratory were the four consecutive Waynflete Professors of Chemistry:
William Henry Perkin, Jr., from 1912 to 1929;
Sir Robert Robinson, from 1930 to 1954. Nobel Prize winner, 1947;
Sir Ewart Jones, from 1954 to 1978;
Sir Jack Baldwin, from 1978 to 2003.
During its 87-year working life, the laboratory had an extremely distinguished career; it can claim a stake in shaping the scientific careers of two Nobel Laureates, namely Lord Todd (1957) and Sir John W. Cornforth (1975) who passed their formative years as young chemists in the laboratories.
History and present use
The building of the laboratory began in 1913 and was finished in 1916 to the designs of Paul Waterhouse, the contractors being Armitage and Hodgson of Leeds. Funding came in part from C. W. Dyson Perrins of Queen's College. In 1920–22 an eastern wing was added as contemplated in the original design, this was followed
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https://en.wikipedia.org/wiki/Power%20series%20solution%20of%20differential%20equations
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In mathematics, the power series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.
Method
Consider the second-order linear differential equation
Suppose is nonzero for all . Then we can divide throughout to obtain
Suppose further that and are analytic functions.
The power series method calls for the construction of a power series solution
If is zero for some , then the Frobenius method, a variation on this method, is suited to deal with so called "singular points". The method works analogously for higher order equations as well as for systems.
Example usage
Let us look at the Hermite differential equation,
We can try to construct a series solution
Substituting these in the differential equation
Making a shift on the first sum
If this series is a solution, then all these coefficients must be zero, so for both k=0 and k>0:
We can rearrange this to get a recurrence relation for .
Now, we have
We can determine A0 and A1 if there are initial conditions, i.e. if we have an initial value problem.
So we have
and the series solution is
which we can break up into the sum of two linearly independent series solutions:
which can be further simplified by the use of hypergeometric series.
A simpler way using Taylor series
A much simpler way of so
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https://en.wikipedia.org/wiki/Thue%20equation
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In mathematics, a Thue equation is a Diophantine equation of the form
ƒ(x,y) = r,
where ƒ is an irreducible bivariate form of degree at least 3 over the rational numbers, and r is a nonzero rational number. It is named after Axel Thue, who in 1909 proved that a Thue equation can have only finitely many solutions in integers x and y, a result known as Thue's theorem,
The Thue equation is solvable effectively: there is an explicit bound on the solutions x, y of the form where constants C1 and C2 depend only on the form ƒ. A stronger result holds: if K is the field generated by the roots of ƒ, then the equation has only finitely many solutions with x and y integers of K, and again these may be effectively determined.
Finiteness of solutions and diophantine approximation
Thue's original proof that the equation named in his honour has finitely many solutions is through the proof of what is now known as Thue's theorem: it asserts that for any algebraic number having degree and for any there exists only finitely many co-prime integers with such that . Applying this theorem allows one to almost immediately deduce the finiteness of solutions. However, Thue's proof, as well as subsequent improvements by Siegel, Dyson, and Roth were all ineffective.
Solution algorithm
Finding all solutions to a Thue equation can be achieved by a practical algorithm, which has been implemented in the following computer algebra systems:
in PARI/GP as functions thueinit() and thue().
in Magm
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https://en.wikipedia.org/wiki/Logic%20in%20computer%20science
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Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three main areas:
Theoretical foundations and analysis
Use of computer technology to aid logicians
Use of concepts from logic for computer applications
Theoretical foundations and analysis
Logic plays a fundamental role in computer science. Some of the key areas of logic that are particularly significant are computability theory (formerly called recursion theory), modal logic and category theory. The theory of computation is based on concepts defined by logicians and mathematicians such as Alonzo Church and Alan Turing. Church first showed the existence of algorithmically unsolvable problems using his notion of lambda-definability. Turing gave the first compelling analysis of what can be called a mechanical procedure and Kurt Gödel asserted that he found Turing's analysis "perfect."
In addition some other major areas of theoretical overlap between logic and computer science are:
Gödel's incompleteness theorem proves that any logical system powerful enough to characterize arithmetic will contain statements that can neither be proved nor disproved within that system. This has direct application to theoretical issues relating to the feasibility of proving the completeness and correctness of software.
The frame problem is a basic problem that must be overcome when using first-order logic to represent the goals and state of an a
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https://en.wikipedia.org/wiki/K-minimum%20spanning%20tree
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The -minimum spanning tree problem, studied in theoretical computer science, asks for a tree of minimum cost that has exactly vertices and forms a subgraph of a larger graph. It is also called the -MST or edge-weighted -cardinality tree. Finding this tree is NP-hard, but it can be approximated to within a constant approximation ratio in polynomial time.
Problem statement
The input to the problem consists of an undirected graph with weights on its edges, and a The output is a tree with vertices and edges, with all of the edges of the output tree belonging to the input graph. The cost of the output is the sum of the weights of its edges, and the goal is to find the tree that has minimum cost. The problem was formulated by and by .
Ravi et al. also considered a geometric version of the problem, which can be seen as a special case of the graph problem.
In the geometric -minimum spanning tree problem, the input is a set of points in the plane. Again, the output should be a tree with of the points as its vertices, minimizing the total Euclidean length of its edges. That is, it is a graph -minimum spanning tree on a complete graph with Euclidean distances as weights.
Computational complexity
When is a fixed constant, the -minimum spanning tree problem can be solved in polynomial time by a brute-force search algorithm that tries all -tuples of vertices.
However, for variable , the -minimum spanning tree problem has been shown to be NP-hard by a reduction from the Steiner t
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https://en.wikipedia.org/wiki/Mathematics%20Genealogy%20Project
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The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians. it contained information on 274,575 mathematical scientists who contributed to research-level mathematics. For a typical mathematician, the project entry includes graduation year, thesis title (in its Mathematics Subject Classification), alma mater, doctoral advisor, and doctoral students.
Origin of the database
The project grew out of founder Harry Coonce's desire to know the name of his advisor's advisor. Coonce was Professor of Mathematics at Minnesota State University, Mankato, at the time of the project's founding, and the project went online there in fall 1997. Coonce retired from Mankato in 1999, and in fall 2002 the university decided that it would no longer support the project. The project relocated at that time to North Dakota State University. Since 2003, the project has also operated under the auspices of the American Mathematical Society and in 2005 it received a grant from the Clay Mathematics Institute. Harry Coonce has been assisted by Mitchel T. Keller, Assistant Professor at Morningside College. Keller is currently the Managing Director of the project.
Mission and scope
The Mathematics Genealogy Mission statement: "Throughout this project when we use the word 'mathematics' or 'mathematician' we mean that word in a very inclusive sense. Thus, all relevant data from statistics, computer science, philosophy or operations research is welcome."
Scope
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https://en.wikipedia.org/wiki/William%20Smith%20%28teacher%29
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William Macdonald Smith (born 25 June 1939) is a South African science and mathematics teacher who is best known for his maths and science lessons on television. Born in Makhanda (Grahamstown), he is the son of the ichthyologist Margaret Mary Smith and Professor J. L. B. Smith, the renowned chemist and ichthyologist who identified the coelacanth.
Early life and education
He attended St. Andrew's Prep before matriculating at Union High School in Graaff-Reinet. He then went on to study at Rhodes University, where he obtained a Bachelor of Science degree in physics and chemistry, followed by an honours degree (cum laude) in chemistry at the same institution. Following that, he obtained a master's degree from the University of Natal (Pietermaritzburg campus) in only seven months.
During his time at school and university, Smith showed an interest in film and camerawork, scripting, shooting, and producing the 50-minute feature documentary, ‘The Garden Route,’ in 1960. The film was digitised and relaunched in 2010.
He started working at African Explosives and Chemical Industries (AECI). Deciding that he would rather pursue a teaching career, Smith left the industry and moved to the education sector, where he started 'Star Schools,' named for the mass-circulation Johannesburg newspaper, The Star, which published material that Smith prepared to support his lessons. The aim of these schools is to provide value-for-money supplementary education with top-class teachers to prepare lea
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https://en.wikipedia.org/wiki/Side%20chain
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In organic chemistry and biochemistry, a side chain is a chemical group that is attached to a core part of the molecule called the "main chain" or backbone. The side chain is a hydrocarbon branching element of a molecule that is attached to a larger hydrocarbon backbone. It is one factor in determining a molecule's properties and reactivity. A side chain is also known as a pendant chain, but a pendant group (side group) has a different definition.
Conventions
The placeholder R is often used as a generic placeholder for alkyl (saturated hydrocarbon) group side chains in chemical structure diagrams. To indicate other non-carbon groups in structure diagrams, X, Y, or Z are often used.
History
The R symbol was introduced by 19th-century French chemist Charles Frédéric Gerhardt, who advocated its adoption on the grounds that it would be widely recognizable and intelligible given its correspondence in multiple European languages to the initial letter of "root" or "residue": French ("root") and ("residue"), these terms' respective English translations along with radical (itself derived from Latin below), Latin ("root") and ("residue"), and German ("remnant" and, in the context of chemistry, both "residue" and "radical").
Usage
Organic chemistry
In polymer science, the side chain of an oligomeric or polymeric offshoot extends from the backbone chain of a polymer. Side chains have noteworthy influence on a polymer's properties, mainly its crystallinity and density. An oligo
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https://en.wikipedia.org/wiki/Subsumption
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Subsumption may refer to:
A minor premise in symbolic logic (see syllogism)
The Liskov substitution principle in object-oriented programming
Subtyping in programming language theory
Subsumption architecture in robotics
A subsumption relation in category theory, semantic networks and linguistics, also known as a "hyponym-hypernym relationship" (Is-a)
Formal and real capitalist subsumption describes different processes whereby capital comes to dominate an economic process. Coined in Karl Marx's Capital, Volume I
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https://en.wikipedia.org/wiki/UA1%20experiment
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The UA1 experiment (an abbreviation of Underground Area 1) was a high-energy physics experiment that ran at CERN's Proton-Antiproton Collider (SpS), a modification of the one-beam Super Proton Synchrotron (SPS). The data was recorded between 1981 and 1990. The joint discovery of the W and Z bosons by this experiment and the UA2 experiment in 1983 led to the Nobel Prize for physics being awarded to Carlo Rubbia and Simon van der Meer in 1984. Peter Kalmus and John Dowell, from the UK groups working on the project, were jointly awarded the 1988 Rutherford Medal and Prize from the Institute of Physics for their outstanding roles in the discovery of the W and Z particles.
It was named as the first experiment in a CERN "Underground Area" (UA), i.e. located underground, outside of the two main CERN sites, at an interaction point on the SPS accelerator, which had been modified to operate as a collider.
The UA1 central detector was crucial to understanding the complex topology of proton-antiproton collisions. It played a most important role in identifying a handful of W and Z particles among billions of collisions.
After the discovery of the W and Z boson, the UA1 collaboration went on to search for the top quark. Physicists had anticipated its existence since 1977, when its partner — the bottom quark — was discovered. It was felt that the discovery of the top quark was imminent. In June 1984, Carlo Rubbia at the UA1 experiment expressed to the New York Times that evidence of the t
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https://en.wikipedia.org/wiki/BMD
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BMD may refer to:
Organisations
Bangladesh Meteorological Department
BMD Group, an Australian civil engineering company
Botswana Movement for Democracy, a minor right-wing populist opposition party in Botswana
Civil registration or General Register Office (from Births, Marriages and Deaths)
FreeBMD, a website for searching births, deaths and marriages records
Blackmagic Design, an Australian digital cinema company
Military
Ballistic Missile Defense
Boyevaya Mashina Desanta (Russian "Боевая Машина Десанта", literally "Combat Vehicle of the Airborne"), a series of Soviet/Russian airborne infantry fighting vehicles
BMD-1
BMD-2
BMD-3
BMD-4
Medicine
Bacitracin methylene disalicylate, an antibiotic growth promoter
Becker muscular dystrophy
Berkeley Mortality Database, a precursor to the Human Mortality Database
Bone mineral density
Broth microdilution
Bipolar Mood Disorder (Bipolar disorder)
Other
Ballot marking device
Bermudian dollar by ISO 4217 code
Bending moment diagram, a type of shear and moment diagram used in mechanical engineering
Bernese Mountain Dog
Brimsdown railway station, London (National Rail station code BMD)
Bruce Mau Design
Binary moment diagram
See also
BDM (disambiguation)
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https://en.wikipedia.org/wiki/KEK
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, known as KEK, is a Japanese organization whose purpose is to operate the largest particle physics laboratory in Japan, situated in Tsukuba, Ibaraki prefecture. It was established in 1997. The term "KEK" is also used to refer to the laboratory itself, which employs approximately 695 employees. KEK's main function is to provide the particle accelerators and other infrastructure needed for high-energy physics, material science, structural biology, radiation science, computing science, nuclear transmutation and so on. Numerous experiments have been constructed at KEK by the internal and international collaborations that have made use of them. Makoto Kobayashi, emeritus professor at KEK, is known globally for his work on CP-violation, and was awarded the 2008 Nobel Prize in Physics.
History
KEK was established in 1997 in a reorganization of the Institute of Nuclear Study, the University of Tokyo (established in 1955), the National Laboratory for High Energy Physics (established in 1971), and the Meson Science Laboratory of the University of Tokyo (established in 1988). However, the reorganization was not a simple merge of the aforementioned laboratories. As such, KEK was not the only new institute created at that time, because not all of the work of the parent institutions fell under the umbrella of high energy physics; for example, the Center for Nuclear Study, the University of Tokyo, was concurrently established for low energy nuclear physics in a research partnership with
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https://en.wikipedia.org/wiki/Ahmad%20Motamedi
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Seyyed Ahmad Motamedi (; born 1953 in Tehran) is an Iranian politician & member of Amirkabir University of Technology (Tehran Polytechnic)'s Electrical Engineering faculty.
He was the chancellor of Amirkabir University of Technology from June 2014 to September 2021. He was the Iranian Minister of Communication and Information Technology until August 24, 2005, and was replaced by Mohammad Soleimani.Seyyed Ahmad Motamedi, Head of the Scientific and Industrial Research Organization of the Ministry of Science and Riyal of the Ministry of Science and Technology (RIA) Currency Quota for the Year 2000 He entered the country claiming to be used for endorsement plans. Despite the claim, he sold imported materials to the open market, but according to the official theory of the Law Office of the Scientific and Industrial Research Organization, there is no evidence that the product entered the warehouse or sold and opened. The Culture News report, in connection with the misconduct, led to the conviction of a trustee and his crime partner (deputy chief financial officer of the organization), both of whom were convicted last year after numerous bans on archery. They appealed, but the court of appeals ultimately upheld the judgment of the second panel of the Tribunal. In his performance record, Moamadi was in charge of the reform of the Ministry of Post and Telegraph and Telephone, which was impeached because of a weak performance on November 7, without the presence of the head of reform,
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https://en.wikipedia.org/wiki/Graded%20vector%20space
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In mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct sum of vector subspaces, generally indexed by the integers.
For "pure" vector spaces, the concept has been introduced in homological algebra, and it is widely used for graded algebras, which are graded vector spaces with additional structures.
Integer gradation
Let be the set of non-negative integers. An -graded vector space, often called simply a graded vector space without the prefix , is a vector space together with a decomposition into a direct sum of the form
where each is a vector space. For a given n the elements of are then called homogeneous elements of degree n.
Graded vector spaces are common. For example the set of all polynomials in one or several variables forms a graded vector space, where the homogeneous elements of degree n are exactly the linear combinations of monomials of degree n.
General gradation
The subspaces of a graded vector space need not be indexed by the set of natural numbers, and may be indexed by the elements of any set I. An I-graded vector space V is a vector space together with a decomposition into a direct sum of subspaces indexed by elements i of the set I:
Therefore, an -graded vector space, as defined above, is just an I-graded vector space where the set I is (the set of natural numbers).
The case where I is the ring (the elements 0 and 1) is parti
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https://en.wikipedia.org/wiki/Doubling
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Doubling may refer to:
Mathematics
Arithmetical doubling of a count or a measure, expressed as:
Multiplication by 2
Increase by 100%, i.e. one-hundred percent
Doubling the cube (i. e., hypothetical geometric construction of a cube with twice the volume of a given cube)
Doubling time, the length of time required for a quantity to double in size or value
Doubling map, a particular infinite two-dimensional geometrical construction
see also: Period-doubling bifurcation
Music
The composition or performance of a melody with itself or itself transposed at a constant interval such as the octave, third, or sixth, Voicing (music)#Doubling
The assignment of a melody to two instruments in an arrangement
The playing of two (or more) instruments alternately by a single player, e.g. Flute, doubling piccolo
Musicians who play more than one woodwind instrument are called woodwind doublers or reed players
Doubletracking, a recording technique in which a musical part (or vocal) is recorded twice and mixed together, to strengthen or "fatten" the tone.
Other
Doubling (psychodrama) is a technique of provoking a protagonist by a participant, for effect.
Doubling in the theatre is where one actor plays more than one part in the same performance.
Doubling (textiles) is the process where six slivers of cotton are fed into a draw frame, stretched and drawn together to improve the uniformity of the roving before it is spun
Doubling (naval tactic) was a means of focusing gunfire i
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https://en.wikipedia.org/wiki/Richard%20Brent
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Richard Brent may refer to:
Richard Brent (politician) (1757–1814), U.S. Congressman and senator from Virginia
Richard P. Brent (born 1946), Australian mathematician and computer science professor
See also
R. Brent Tully (born 1943), Canadian-born American astronomer based in Hawaii
|
https://en.wikipedia.org/wiki/Helmholtz%20equation
|
In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the linear partial differential equation
where is the Laplace operator, is the eigenvalue, and is the (eigen)function. When the equation is applied to waves, is known as the wave number. The Helmholtz equation has a variety of applications in physics and other sciences, including the wave equation, the diffusion equation, and the Schrödinger equation for a free particle.
Motivation and uses
The Helmholtz equation often arises in the study of physical problems involving partial differential equations (PDEs) in both space and time. The Helmholtz equation, which represents a time-independent form of the wave equation, results from applying the technique of separation of variables to reduce the complexity of the analysis.
For example, consider the wave equation
Separation of variables begins by assuming that the wave function is in fact separable:
Substituting this form into the wave equation and then simplifying, we obtain the following equation:
Notice that the expression on the left side depends only on , whereas the right expression depends only on . As a result, this equation is valid in the general case if and only if both sides of the equation are equal to the same constant value. This argument is key in the technique of solving linear partial differential equations by separation of variables. From this observation, we obtain two equations, one for ,
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https://en.wikipedia.org/wiki/Hans%20Berliner
|
Hans Jack Berliner (January 27, 1929 – January 13, 2017) was an American chess player, and was the World Correspondence Chess Champion, from 1965–1968. He was a Grandmaster of Correspondence Chess. Berliner was a Professor of Computer Science at Carnegie Mellon University. He directed the construction of the chess computer HiTech, and was also a published chess writer.
Early life
Berliner was born January 27, 1929, in Berlin to a Jewish family. One of his classmates at school was future Estonian President Lennart Meri, whose father was serving as Estonia's ambassador to Germany.
In 1937, Berliner's family moved to the United States to escape Nazi persecution, taking up residence in Washington, D.C. He learned chess at age 13, and "it quickly became his main preoccupation."
Berliner is mentioned in "How I Started To Write", an essay by Carlos Fuentes, where he is described as "an extremely brilliant boy", with "a brilliant mathematical mind". "I shall always remember his face, dark and trembling, his aquiline nose and deep-set, bright eyes with their great sadness, the sensitivity of his hands..."
Chess career
In 1949, he became a master, won the District of Columbia Championship (the first of five wins of that tournament) and the Southern States Championship, and tied for second place with Larry Evans at the New York State Championship. He also won the 1953 New York State Championship (the first win by a non-New Yorker), the 1956 Eastern States Open directed by Norman Twee
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https://en.wikipedia.org/wiki/American%20Council%20on%20Science%20and%20Health
|
The American Council on Science and Health (ACSH) is a pro-industry advocacy organization founded in 1978 by Elizabeth Whelan with support from the Scaife Foundation and John M. Olin Foundation. ACSH's publications focus on industry advocacy related to food, nutrition, health, chemicals, pharmaceuticals, biology, biotechnology, infectious disease, and the environment. Its critics have accused it of being a front group for anti-science denialism.
History
The American Council on Science and Health (ACSH) was founded in 1978 by Elizabeth Whelan. In the 1970s, ACSH scientists, saying they were concerned with what they described as the lack of sound scientific basis, common sense, reason, and balance in public forums and public policy regarding such issues as health and the environment, began to produce their own policy statements. In 1981, ACSH decided to start taking some corporate funding, but not for specific projects or programs, only for general support. Over the years, their articles have included such topics as the U.S. Food and Drug Administration (FDA), obesity, chemophobia, phthalates, DDT, fracking, e-cigarettes, GMOs, atrazine, and bisphenol A.
Whelan says she was motivated to found the American Council on Science and Health after doing research for the pharmaceutical company Pfizer about a section of the Food Additives Amendment of 1958 to ban certain chemicals from foods. With further research, she says she found that public discourse and public policy were chemo
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https://en.wikipedia.org/wiki/Nilakantha%20Somayaji
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Keļallur Nilakantha Somayaji (14 June 1444 – 1545), also referred to as Keļallur Comatiri, was a major mathematician and astronomer of the Kerala school of astronomy and mathematics. One of his most influential works was the comprehensive astronomical treatise Tantrasamgraha completed in 1501. He had also composed an elaborate commentary on Aryabhatiya called the Aryabhatiya Bhasya. In this Bhasya, Nilakantha had discussed infinite series expansions of trigonometric functions and problems of algebra and spherical geometry. Grahapariksakrama is a manual on making observations in astronomy based on instruments of the time. Known popularly as Kelallur Chomaathiri, he is considered an equal to Vatasseri Parameshwaran Nambudiri.
Early life
Nilakantha was born into a Brahmin family which came from South Malabar in Kerala.
Biographical details
Nilakantha Somayaji was one of the very few authors of the scholarly traditions of India who had cared to record details about his own life and times.
In one of his works titled Siddhanta-star and also in his own commentary on Siddhanta-darpana, Nilakantha Somayaji has stated that he was born on Kali-day 1,660,181 which works out to 14 June 1444 CE. A contemporary reference to Nilakantha Somayaji in a Malayalam work on astrology implies that Somayaji lived to a ripe old age even to become a centenarian. Sankara Variar, a pupil of Nilakantha Somayaji, in his commentary on Tantrasamgraha titled Tantrasamgraha-vyakhya, points out that the
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https://en.wikipedia.org/wiki/Narayana%20Pandita%20%28mathematician%29
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Nārāyaṇa Paṇḍita () (1340–1400) was an Indian mathematician. Plofker writes that his texts were the most significant Sanskrit mathematics treatises after those of Bhaskara II, other than the Kerala school. He wrote the Ganita Kaumudi (lit "Moonlight of mathematics") in 1356 about mathematical operations. The work anticipated many developments in combinatorics. About his life, the most that is known is that:
Narayana Pandit wrote two works, an arithmetical treatise called Ganita Kaumudi and an algebraic treatise called Bijaganita Vatamsa. Narayanan is also thought to be the author of an elaborate commentary of Bhaskara II's Lilavati, titled Karmapradipika (or Karma-Paddhati). Although the Karmapradipika contains little original work, it contains seven different methods for squaring numbers, a contribution that is wholly original to the author, as well as contributions to algebra and magic squares.
Narayana's other major works contain a variety of mathematical developments, including a rule to calculate approximate values of square roots, investigations into the second order indeterminate equation nq2 + 1 = p2 (Pell's equation), solutions of indeterminate higher-order equations, mathematical operations with zero, several geometrical rules, methods of integer factorization, and a discussion of magic squares and similar figures. Evidence also exists that Narayana made minor contributions to the ideas of differential calculus found in Bhaskara II's work. Narayana has also made c
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https://en.wikipedia.org/wiki/Tetanic%20stimulation
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In neurobiology, a tetanic stimulation consists of a high-frequency sequence of individual stimulations of a neuron. It is associated with potentiation.
High-frequency stimulation causes an increase in release called post-tetanic potentiation (Kandel 2003). This presynaptic event is caused by calcium influx. Calcium-protein interactions then produce a change in vesicle exocytosis. The result of these changes is to make the postsynaptic cell more likely to fire an action potential.
Tetanic stimulation is used in medicine to detect a non-depolarizing block or a depolarizing block on the neuromuscular junction. Lower elicitations of tetanic stimulation in aged muscles were shown to be caused by lower levels of anaerobic energy provision in skeletal muscles.
See also
Hebbian theory
References
Neurophysiologists
de:Tetanisierung
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