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https://en.wikipedia.org/wiki/SIAM%20Journal%20on%20Computing
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The SIAM Journal on Computing is a scientific journal focusing on the mathematical and formal aspects of computer science. It is published by the Society for Industrial and Applied Mathematics (SIAM).
Although its official ISO abbreviation is SIAM J. Comput., its publisher and contributors frequently use the shorter abbreviation SICOMP.
SICOMP typically hosts the special issues of the IEEE Annual Symposium on Foundations of Computer Science (FOCS) and the Annual ACM Symposium on Theory of Computing (STOC), where about 15% of papers published in FOCS and STOC each year are invited to these special issues. For example, Volume 48 contains 11 out of 85 papers published in FOCS 2016.
References
External links
SIAM Journal on Computing
bibliographic information on DBLP
Computer science journals
Academic journals established in 1972
Computing
Bimonthly journals
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https://en.wikipedia.org/wiki/Theodore%20William%20Richards
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Theodore William Richards (January 31, 1868 – April 2, 1928) was the first American scientist to receive the Nobel Prize in Chemistry, earning the award "in recognition of his exact determinations of the atomic weights of a large number of the chemical elements."
Biography
Theodore Richards was born in Germantown, Pennsylvania, to William Trost Richards, a land- and seascape painter, and Anna Matlack Richards, a poet. Richards received most of his pre-college education from his mother. During one summer's stay at Newport, Rhode Island, Richards met Professor Josiah Parsons Cooke of Harvard, who showed the young boy Saturn's rings through a small telescope. Years later Cooke and Richards would work together in Cooke's laboratory.
Beginning in 1878, the Richards family spent two years in Europe, largely in England, where Theodore Richards' scientific interests grew stronger. After the family's return to the United States, he entered Haverford College, Pennsylvania in 1883 at the age of 14, earning a Bachelor of Science degree in 1885. He then enrolled at Harvard University and received a Bachelor of Arts degree in 1886, as further preparation for graduate studies.
Richards continued on at Harvard, taking as his dissertation topic the determination of the atomic weight of oxygen relative to hydrogen. His doctoral advisor was Josiah Parsons Cooke. Following a year of post-doctoral work in Germany, where he studied under Victor Meyer at the University of Göttingen and o
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https://en.wikipedia.org/wiki/Constructive%20quantum%20field%20theory
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In mathematical physics, constructive quantum field theory is the field devoted to showing that quantum field theory can be defined in terms of precise mathematical structures. This demonstration requires new mathematics, in a sense analogous to classical real analysis, putting calculus on a mathematically rigorous foundation. Weak, strong, and electromagnetic forces of nature are believed to have their natural description in terms of quantum fields.
Attempts to put quantum field theory on a basis of completely defined concepts have involved most branches of mathematics, including functional analysis, differential equations, probability theory, representation theory, geometry, and topology. It is known that a quantum field is inherently hard to handle using conventional mathematical techniques like explicit estimates. This is because a quantum field has the general nature of an operator-valued distribution, a type of object from mathematical analysis. The existence theorems for quantum fields can be expected to be very difficult to find, if indeed they are possible at all.
One discovery of the theory that can be related in non-technical terms, is that the dimension d of the spacetime involved is crucial. Notable work in the field by James Glimm and Arthur Jaffe showed that with d < 4 many examples can be found. Along with work of their students, coworkers, and others, constructive field theory resulted in a mathematical foundation and exact interpretation to what previo
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https://en.wikipedia.org/wiki/Physics%20and%20Astronomy%20Classification%20Scheme
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The Physics and Astronomy Classification Scheme (PACS) is a scheme developed in 1970 by the American Institute of Physics (AIP) for classifying scientific literature using a hierarchical set of codes. PACS has been used by over 160 international journals, including the Physical Review series since 1975. Since 2016, American Physical Society introduced the PhySH (Physics Subject Headings) system instead of PACS.
Discontinuation
AIP has announced that PACS 2010 will be the final version, but it will continue to be available through their website. The decision was made to discontinue PACS, owing to the administrative complexity of the revision process and its future viability in light of changing technological and research trends. However, PACS is still in use by scientific journals.
In association with Access Innovations, Inc., the AIP has developed a new "AIP Thesaurus", which it states will enable faster, more accurate and more efficient searches.
See also
Mathematics Subject Classification (MSC)
Computing Classification System (CCS)
PhySH (Physics Subject Headings)
References
External links
https://journals.aps.org/PACS PACS
https://web.archive.org/web/20070826124822/http://www.aip.org/pacs/Information on PACS
https://web.archive.org/web/20171201041118/https://publishing.aip.org/publishing/pacs/pacs-2010-regular-editionPACS 2010
Scientific classification
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https://en.wikipedia.org/wiki/XORP
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XORP is an open-source Internet Protocol routing software suite originally designed at the International Computer Science Institute in Berkeley, California. The name is derived from eXtensible Open Router Platform. It supports OSPF, BGP, RIP, PIM, IGMP, OLSR.
The product is designed from principles of software modularity and extensibility and aims at exhibiting stability and providing feature requirements for production use while also supporting networking research. The development project was founded by Mark Handley in 2000. Receiving funding from Intel, Microsoft, and the National Science Foundation, it released its first production software in July 2004. The project was then run by Atanu Ghosh of the International Computer Science Institute, in Berkeley, California.
In July 2008, the International Computer Science Institute transferred the XORP technology to a new entity, XORP Inc., a commercial startup founded by the leaders of the opensource project team and backed by Onset Ventures and Highland Capital Partners. In February 2010, XORP Inc. was wound up, a victim of the recession. However the open source project continued, with the servers based at University College London. In March 2011, Ben Greear became the project maintainer and the www.xorp.org server is now hosted by Candela Technologies.
The XORP codebase consists of around 670,000 lines of C++ and is developed primarily on Linux, but supported on FreeBSD, OpenBSD, DragonFlyBSD, NetBSD. Support for XORP on
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https://en.wikipedia.org/wiki/Cannabidivarin
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Cannabidivarin (CBDV, GWP42006) is a non-intoxicating psychoactive cannabinoid found in Cannabis. It is a homolog (chemistry) of cannabidiol (CBD), with the side-chain shortened by two methylene bridges (CH2 units).
Although cannabidivarin (CBDV) is usually a minor constituent of the cannabinoid profile, enhanced levels of CBDV have been reported in feral populations of C. indica ( = C. sativa ssp. indica var. kafiristanica) from northwest India, and in hashish from Nepal.=
CBDV demonstrated anticonvulsant in rodent models in a single published study. It was identified for the first time in 1969 by Vollner et al.
Similarly to CBD, it has seven double bond isomers and 30 stereoisomers (see: Cannabidiol#Isomerism). It is not scheduled by Convention on Psychotropic Substances. It is being actively developed by GW Pharmaceuticals (as GWP42006) because of a demonstrated neurochemical pathway for previously observed anti-epileptic and anti-convulsive action. GW has begun several Phase-2 trials for adult epilepsy, for childhood epilepsy and for Prader-Willi Syndrome.
See also
List of investigational analgesics
References
External links
Erowid Compounds found in Cannabis sativa
CBDV (in German)
Cannabidivarin
Phytocannabinoids
Natural phenols
2,6-Dihydroxybiphenyls
Cyclohexenes
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https://en.wikipedia.org/wiki/Syed%20Muhammad%20Naquib%20al-Attas
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Syed Muhammad al Naquib bin Ali al-Attas ( ; born 5 September 1931) is a Malaysian Muslim philosopher. He is one of the few contemporary scholars who is thoroughly rooted in the traditional Islamic sciences and studies theology, philosophy, metaphysics, history, and literature. He pioneered the concept of Islamisation of knowledge. Al-Attas' philosophy and methodology of education have one goal: Islamisation of the mind, body and soul and its effects on the personal and collective life on Muslims as well as others, including the spiritual and physical non-human environment.
He is the author of 27 works on various aspects of Islamic thought and civilisation, particularly on Sufism, cosmology, metaphysics, philosophy and Malay language and literature.
Early life and education
Syed Muhammad Naquib al-Attas was born in Bogor, Java, Dutch East Indies into a family with a history of illustrious ancestors, saints. Some sources states his genealogical tree can be traced over a thousand years through the Ba' Alawi sayyids of Hadramaut. He was the second of three sons; his older brother, Syed Hussein Alatas later became an academian and politician. He is the cousin of the academic Ungku Abdul Aziz.
After World War II, in 1946 he returned to Johor to complete his secondary education. He was exposed to Malay literature, history, religion, and western classics in English.
After al-Attas finished secondary school in 1951, he entered the Malay Regiment as a cadet officer. There he was s
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https://en.wikipedia.org/wiki/Universal%20science
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Universal science (; ) is a branch of metaphysics. In the work of Gottfried Wilhelm Leibniz, the universal science is the true logic. The idea of establishing a universal science originated in the seventeenth century with philosophers Francis Bacon and Rene Descartes. Bacon and Descartes conceptualized universal science as a unified approach to collect scientific information similar to encyclopedias of universal knowledge but were unsuccessful. Leibniz extended their ideas to use logic as an "index" to order universal scientific and mathematical information as an operational system with a universal language. Plato's system of idealism, formulated using the teachings of Socrates, is a predecessor to the concept of universal science and influenced Leibniz' s views against materialism in favor of logic. It emphasizes on the first principles which appear to be the reasoning behind everything, emerging and being in state with everything. This mode of reasoning had a supporting influence on great scientists such as Boole, Frege, Cantor, Hilbert, Gödel, and Turing. All of these great minds shared a similar dream, vision or belief in a future where universal computing would eventually change everything.
See also
Architectonics
Unified Science
References
External links
Stephen Palmquist, Heading 6, Philosophy as the Theological Science
Philosophy of science
Gottfried Wilhelm Leibniz
Intellectual history
History of science
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https://en.wikipedia.org/wiki/Micellar%20electrokinetic%20chromatography
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Micellar electrokinetic chromatography (MEKC) is a chromatography technique used in analytical chemistry. It is a modification of capillary electrophoresis (CE), extending its functionality to neutral analytes, where the samples are separated by differential partitioning between micelles (pseudo-stationary phase) and a surrounding aqueous buffer solution (mobile phase).
The basic set-up and detection methods used for MEKC are the same as those used in CE. The difference is that the solution contains a surfactant at a concentration that is greater than the critical micelle concentration (CMC). Above this concentration, surfactant monomers are in equilibrium with micelles.
In most applications, MEKC is performed in open capillaries under alkaline conditions to generate a strong electroosmotic flow. Sodium dodecyl sulfate (SDS) is the most commonly used surfactant in MEKC applications. The anionic character of the sulfate groups of SDS causes the surfactant and micelles to have electrophoretic mobility that is counter to the direction of the strong electroosmotic flow. As a result, the surfactant monomers and micelles migrate quite slowly, though their net movement is still toward the cathode. During a MEKC separation, analytes distribute themselves between the hydrophobic interior of the micelle and hydrophilic buffer solution as shown in figure 1.
Analytes that are insoluble in the interior of micelles should migrate at the electroosmotic flow velocity, , and be detect
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https://en.wikipedia.org/wiki/Augmented%20truncated%20cube
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In geometry, the augmented truncated cube is one of the Johnson solids (). As its name suggests, it is created by attaching a square cupola () onto one octagonal face of a truncated cube.
References
Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
The first proof that there are only 92 Johnson solids.
External links
Johnson solids
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https://en.wikipedia.org/wiki/Hans%20Fischer
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Hans Fischer (; 27 July 1881 – 31 March 1945) was a German organic chemist and the recipient of the 1930 Nobel Prize for Chemistry "for his researches into the constitution of haemin and chlorophyll and especially for his synthesis of haemin."
Biography
Early years
Fischer was born on July 27, 1881, in Höchst on river Main, now a city district of Frankfurt located in Germany. His parents were Dr. Eugen Fischer, Director of the firm of Kalle & Co, Wiesbaden, and Privatdozent at the Technical High School, Stuttgart, and Anna Herdegen was his mother. He went to a primary school in Stuttgart, and later to the "Humanistisches Gymnasium" in Wiesbaden, matriculating in 1899. He read chemistry and medicine, first at the University of Lausanne and then at Marburg. He graduated in 1904 obtaining his chemistry degree, 2 years later in 1906 he licensed for medicine and in 1908 he qualified for his M.D. which he applied to the University of Munich.
Career
He worked first at a Medical Clinic in Munich and then at the First Berlin Chemical Institute under Emil Fischer. He returned to Munich in 1911 and qualified as lecturer on internal medicine one year later. In 1913, he became a lecturer in physiology at the Physiological Institute in Munich. In 1916, he became Professor of Medical Chemistry at the University of Innsbruck and from there he went to the University of Vienna in 1918.
From 1921 until his death, he held the position of Professor of Organic Chemistry at the Technical Univer
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https://en.wikipedia.org/wiki/Arthur%20Harden
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Sir Arthur Harden, FRS (12 October 1865 – 17 June 1940) was a British biochemist. He shared the Nobel Prize in Chemistry in 1929 with Hans Karl August Simon von Euler-Chelpin for their investigations into the fermentation of sugar and fermentative enzymes. He was a founding member of the Biochemical Society and editor of its journal for 25 years.
Biography
Early years
Arthur was born to Scottish Presbyterian businessman Albert Tyas Harden and Eliza Macalister. His early education was at a private school in Victoria Park run by Dr Ernest Adam. He went to study in 1877 at a Tettenhall College, Staffordshire, and entered Owens College in 1882, now the University of Manchester, in 1882, graduating in 1885. He studied chemistry under Professor Roscoe at Owens College and was influenced by J.B. Cohen.
Research
In 1886 Harden was awarded the Dalton Scholarship in Chemistry and spent a year working with Otto Fischer at Erlangen where he worked on the synthesis of β-nitroso-α-naphthylamine and studied its properties. After receiving a Ph.D. he returned to Manchester as a lecturer and demonstrator and taught along with Sir Philip Hartog. He researched the life and work of John Dalton during these years. In 1895 he wrote a textbook on Practical Organic Chemistry along with F.C. Garrett. Harden continued to work at Manchester until 1897 when he was appointed chemist to the newly founded British Institute of Preventive Medicine, which later became the Lister Institute. He earned the d
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https://en.wikipedia.org/wiki/Paul%20Karrer
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Professor Paul Karrer FRS FRSE FCS (21 April 1889 – 18 June 1971) was a Swiss organic chemist best known for his research on vitamins. He and Norman Haworth won the Nobel Prize for Chemistry in 1937.
Biography
Early years
Karrer was born in Moscow, Russia to Paul Karrer and Julie Lerch, both Swiss nationals. In 1892 Karrer's family returned to Switzerland where he was educated at Wildegg and at the grammar school in Lenzburg, Aarau, where he matriculated in 1908. He studied chemistry at the University of Zurich under Alfred Werner and after gaining his Ph.D. in 1911, he spent a further year as assistant in the Chemical Institute. He then took a post as chemist with Paul Ehrlich at the Georg Speyer Haus, Frankfurt-am-Main. In 1919 he became Professor of Chemistry and Director of the Chemical Institute.
Research
Karrer's early research concerned complex metal compounds but his most important work has concerned plant pigments, particularly the yellow carotenoids. He elucidated their chemical structure and showed that some of these substances are transformed in the body into vitamin A. His work led to the establishment of the correct constitutional formula for beta-carotene, the chief precursor of vitamin A; the first time that the structure of a vitamin or provitamin had been established. George Wald worked briefly in Karrer's lab while studying the role of vitamin A in the retina. Later, Karrer confirmed the structure of ascorbic acid (vitamin C) and extended his researches
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https://en.wikipedia.org/wiki/Seifert%E2%80%93Weber%20space
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In mathematics, Seifert–Weber space (introduced by Herbert Seifert and Constantin Weber) is a closed hyperbolic 3-manifold. It is also known as Seifert–Weber dodecahedral space and hyperbolic dodecahedral space. It is one of the first discovered examples of closed hyperbolic 3-manifolds.
It is constructed by gluing each face of a dodecahedron to its opposite in a way that produces a closed 3-manifold. There are three ways to do this gluing consistently. Opposite faces are misaligned by 1/10 of a turn, so to match them they must be rotated by 1/10, 3/10 or 5/10 turn; a rotation of 3/10 gives the Seifert–Weber space. Rotation of 1/10 gives the Poincaré homology sphere, and rotation by 5/10 gives 3-dimensional real projective space.
With the 3/10-turn gluing pattern, the edges of the original dodecahedron are glued to each other in groups of five. Thus, in the Seifert–Weber space, each edge is surrounded by five pentagonal faces, and the dihedral angle between these pentagons is 72°. This does not match the 117° dihedral angle of a regular dodecahedron in Euclidean space, but in hyperbolic space there exist regular dodecahedra with any dihedral angle between 60° and 117°, and the hyperbolic dodecahedron with dihedral angle 72° may be used to give the Seifert–Weber space a geometric structure as a hyperbolic manifold.
It is a (finite volume) quotient space of the (non-finite volume) order-5 dodecahedral honeycomb, a regular tessellation of hyperbolic 3-space by dodecahedra
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https://en.wikipedia.org/wiki/Emil%20Fischer%20%28disambiguation%29
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Emil Fischer (1852–1919) was a German Nobel laureate in chemistry.
Emil Fischer may also refer to:
Emil Fischer (American football executive) (1887–1958), American football executive and businessman
Emil Fischer (bass) (1838–1914), German dramatic basso
Emil Fischer (cartographer) (1838/9–1898), German-born American cartographer
See also
Franz Joseph Emil Fischer (1877–1947), German chemist, worked with oil and coal
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https://en.wikipedia.org/wiki/MacTutor%20History%20of%20Mathematics%20Archive
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The MacTutor History of Mathematics Archive is a website maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews in Scotland. It contains detailed biographies on many historical and contemporary mathematicians, as well as information on famous curves and various topics in the history of mathematics.
The History of Mathematics archive was an outgrowth of Mathematical MacTutor system, a HyperCard database by the same authors, which won them the European Academic Software award in 1994. In the same year, they founded their web site. it has biographies on over 2800 mathematicians and scientists.
In 2015, O'Connor and Robertson won the Hirst Prize of the London Mathematical Society for their work. The citation for the Hirst Prize calls the archive "the most widely used and influential web-based resource in history of mathematics".
See also
Mathematics Genealogy Project
MathWorld
PlanetMath
References
External links
Mathematical MacTutor system
Works about the history of mathematics
Mathematics websites
University of St Andrews
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https://en.wikipedia.org/wiki/Pratiwi%20Sudarmono
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Pratiwi Pujilestari Sudarmono (born 31 July 1952) is an Indonesian scientist. She is currently a professor of microbiology at the University of Indonesia, Jakarta.
Early life and education
Pratiwi Sudarmono received a master's degree from the University of Indonesia in 1977, and the Ph.D. in Molecular Biology from the University of Osaka, Japan, in 1984.
Career
She then started her scientific career as WHO grantee researching the molecular biology of Salmonella typhi. From 1994 to 2000, she was head of the Department of Microbiology of the Medical Faculty of the University of Indonesia. From 2001 to 2002, she was a scholar in the Fulbright New Century Scholars Program.
Space Shuttle Mission STS-61-H
In October 1985, she was selected to take part in the NASA Space Shuttle mission STS-61-H as a Payload Specialist. Taufik Akbar was her backup on the mission. However, after the Challenger disaster the deployment of commercial satellites like the Indonesian Palapa B-3 planned for the STS-61-H mission was canceled, thus the mission never took place. The satellite was later launched with a Delta rocket.
Awards and honors
In 2019, Sudarmono was the recipient of the GE Indonesia Recognition for Inspiring Women in STEM award.
References
External links
Spacefacts biography of Pratiwi Sudarmono
1952 births
Living people
University of Indonesia alumni
Indonesian biologists
People from Bandung
Osaka University alumni
Academic staff of the University of Indonesia
Indonesian women
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https://en.wikipedia.org/wiki/BCH
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BCH or BCh may refer to:
Science and technology
BCH code (Bose–Chaudhuri–Hocquenghem code), a code in coding theory
Bachelor of Surgery, a component of some undergraduate medical degrees
Baker–Campbell–Hausdorff formula, in mathematics and Lie group theory
Biosafety Clearing-House, an international mechanism that exchanges information about the movement of genetically modified organisms
Birdsell Clover Huller, an agricultural machine
Bitcoin Cash, a fork of the cryptocurrency Bitcoin
Bean chitinase, a defensive enzyme
Organisations
Birmingham Children's Hospital, a hospital in England
Boston Children’s Hospital, a hospital in Boston, Massachusetts
Blue Castle Holdings, developer of nuclear power stations in the US
British and Commonwealth Holdings, a defunct UK financial services company
Briefmarken-Club_Hannover_von_1886, a German stamp collectors club founded 1886
Bataliony Chłopskie, a Polish resistance movement in World War II
Belfast City Hospital, a hospital in Northern Ireland
Central Bank of Honduras (Spanish: Banco Central de Honduras)
Transportation
Baucau Airport (IATA code), East Timor
Belarusian Railway (BCh), (Belarusian: Беларуская чыгунка), the state railway company of Belarus
Birchington-on-Sea railway station, England
British Columbia Hydro and Power Authority (railway reporting mark)
Bch, short for "Beach"; a Street suffix as used in the US
Other uses
Barclays Cycle Hire, former name of a public bicycle sharing scheme in London, E
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https://en.wikipedia.org/wiki/Wisp
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Wisp or WISP may refer to:
Acronyms
Wartime Information Security Program
WISP (particle physics), Weakly Interacting Sub-eV Particle or Weakly Interacting Slender Particle in hypothetical quantum mechanics
WISP1, WISP2, and WISP3, the human genes encoding the WNT1 Inducible Signaling Pathway proteins 1, 2, and 3
Wireless Internet service provider, is an Internet Service Provider (ISP) that provides connectivity via WLAN
Wireless identification and sensing platform (WISP) is a software-configurable passive UHF RFID tag
Mythology and fiction
Night wisp, a fictional creature in the Sword of Truth series by Terry Goodkind
Wisp, the birth name of a fictional young orphan girl who would later become known as Rainbow Brite
Wisp is a nature spirit associated with the Night Elf race in the MMORPG World of Warcraft
Wisp (Sonic), the alien race in the Sonic the Hedgehog games
Other uses
WISP (AM), a radio station (1570 AM) licensed to Doylestown, Pennsylvania, United States
Wisp (musician), an electronic artist signed to Rephlex Records
Wisp Ski Resort, in western Maryland
Colgate Wisp, a single-use toothbrush
Agriocnemis, a genus of damselfly commonly known as a wisp
See also
Will-o'-the-wisp (disambiguation)
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https://en.wikipedia.org/wiki/Dirichlet%20integral
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In mathematics, there are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of the sinc function over the positive real line:
This integral is not absolutely convergent, meaning is not Lebesgue-integrable, because the Dirichlet integral is infinite in the sense of Lebesgue integration. It is, however, finite in the sense of the improper Riemann integral or the generalized Riemann or Henstock–Kurzweil integral. This can be seen by using Dirichlet's test for improper integrals.
It is a good illustration of special techniques for evaluating definite integrals. The sine integral, an antiderivative of the sinc function, is not an elementary function. However the improper definite integral can be determined in several ways: the Laplace transform, double integration, differentiating under the integral sign, contour integration, and the Dirichlet kernel.
Evaluation
Laplace transform
Let be a function defined whenever Then its Laplace transform is given by
if the integral exists.
A property of the Laplace transform useful for evaluating improper integrals is
provided exists.
In what follows, one needs the result which is the Laplace transform of the function (see the section 'Differentiating under the integral sign' for a derivation) as well as a version of Abel's theorem (a consequence of the final value theorem for the Laplace transform).
Therefore,
Double inte
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https://en.wikipedia.org/wiki/Pointed%20space
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In mathematics, a pointed space or based space is a topological space with a distinguished point, the basepoint. The distinguished point is just simply one particular point, picked out from the space, and given a name, such as that remains unchanged during subsequent discussion, and is kept track of during all operations.
Maps of pointed spaces (based maps) are continuous maps preserving basepoints, i.e., a map between a pointed space with basepoint and a pointed space with basepoint is a based map if it is continuous with respect to the topologies of and and if This is usually denoted
Pointed spaces are important in algebraic topology, particularly in homotopy theory, where many constructions, such as the fundamental group, depend on a choice of basepoint.
The pointed set concept is less important; it is anyway the case of a pointed discrete space.
Pointed spaces are often taken as a special case of the relative topology, where the subset is a single point. Thus, much of homotopy theory is usually developed on pointed spaces, and then moved to relative topologies in algebraic topology.
Category of pointed spaces
The class of all pointed spaces forms a category Top with basepoint preserving continuous maps as morphisms. Another way to think about this category is as the comma category, ( Top) where is any one point space and Top is the category of topological spaces. (This is also called a coslice category denoted Top.) Objects in this category are continuou
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https://en.wikipedia.org/wiki/Basepoint
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Basepoint may refer to a point singled out in a:
Pointed set, or in a
Pointed space
See also
Origin (mathematics)
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https://en.wikipedia.org/wiki/Nikolaus%20Joseph%20von%20Jacquin
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Nikolaus Joseph Freiherr von Jacquin (16 February 172726 October 1817) was a scientist who studied medicine, chemistry and botany.
Biography
Born in Leiden in the Netherlands, he studied medicine at Leiden University, then moved first to Paris and afterward to Vienna. In 1752, he studied under Gerard van Swieten in Vienna.
Between 1755 and 1759, Jacquin was sent to the West Indies, Central America, Venezuela and New Granada by Francis I to collect plants for the Schönbrunn Palace, and amassed a large collection of animal, plant and mineral samples. In 1797, Alexander von Humboldt profited from studying these collections and conversing with Jacquin in preparation of his own journey to the Americas.
In 1763, Jacquin became professor of chemistry and mineralogy at the Bergakademie Schemnitz (now Banská Štiavnica in Slovakia). In 1768, he was appointed Professor of Botany and Chemistry and became director of the botanical gardens of the University of Vienna. For his work, he received the title Edler in 1774. In 1783, he was elected a foreign member of the Royal Swedish Academy of Sciences. In 1806, he was created a baron. In 1809, he became a correspondent of the Royal Institute, which later became the Royal Netherlands Academy of Arts and Sciences.
His younger son, Emil Gottfried (1767–1792), and his daughter, Franziska (1769–1850), were friends of Mozart; Mozart wrote two songs for Gottfried to publish under Gottfried's name ("Als Luise ...", K. 520, and "Das Traumbild", K
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https://en.wikipedia.org/wiki/Magneton
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Magneton may refer to:
Bohr magneton, a physical constant of magnetic moment named after Niels Bohr
Nuclear magneton, a physical constant of magnetic moment
Parson magneton, a hypothetical object in atomic physics suggested by Alfred Lauck Parson in 1915
Weiss magneton, an experimentally derived unit of magnetic moment suggested in 1911 by Pierre-Ernest Weiss
Magneton, a term that some physicists use for magnetic monopole
Magneton (Pokémon), a Pokémon species
Magneton, an album by The Octagon Man
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https://en.wikipedia.org/wiki/Morph
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Morph may refer to:
Biology
Morph (zoology), a visual or behavioral difference between organisms of distinct populations in a species
Muller's morphs, a classification scheme for genetic mutations
"-morph", a suffix commonly used in taxonomy
Computing
Morphing, in motion pictures and animations, a special effect that changes one image into another through a seamless transition
Gryphon Software Morph, morphing software
Morph target animation, a method of animating computer generated imagery
Fiction
Morph, a British claymation character, who has featured in:
Morph (TV series), animated television series
The Amazing Adventures of Morph, a British stop-motion clay animation television show
Morph (comics), an X-Men character of Marvel comics
In Animorphs, "morphing" is alien technology that allows one to transform into any animal or person that one touches
Music
Morph, a 2014 album by Hins Cheung
Morph, a 2018 album by Yentl en De Boer
"Morph" (song), a 2018 song by Twenty One Pilots
Other uses
Morphs collaboration, a collaboration that studied the evolution of spiral galaxies using the Magellan and the Hubble Space Telescope
Nokia Morph, a bendable concept mobile phone
See also
Morpheme, the smallest component of a word, or other linguistic unit, that has semantic meaning
Morpher (disambiguation)
Morphic (disambiguation)
Morphism, between two mathematical structures
Morphogram, the representation of a morpheme by a grapheme based solely on its mean
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https://en.wikipedia.org/wiki/Delta%20rule
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In machine learning, the delta rule is a gradient descent learning rule for updating the weights of the inputs to artificial neurons in a single-layer neural network. It can be derived as the backpropagation algorithm for a single-layer neural network with mean-square error loss function.
For a neuron with activation function , the delta rule for neuron 's -th weight is given by
where
is a small constant called learning rate
is the neuron's activation function
is the derivative of
is the target output
is the weighted sum of the neuron's inputs
is the actual output
is the -th input.
It holds that and .
The delta rule is commonly stated in simplified form for a neuron with a linear activation function as
While the delta rule is similar to the perceptron's update rule, the derivation is different. The perceptron uses the Heaviside step function as the activation function , and that means that does not exist at zero, and is equal to zero elsewhere, which makes the direct application of the delta rule impossible.
Derivation of the delta rule
The delta rule is derived by attempting to minimize the error in the output of the neural network through gradient descent. The error for a neural network with outputs can be measured as
In this case, we wish to move through "weight space" of the neuron (the space of all possible values of all of the neuron's weights) in proportion to the gradient of the error function with respect to each weight. In order to do
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https://en.wikipedia.org/wiki/Hyperbolic%203-manifold
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In mathematics, more precisely in topology and differential geometry, a hyperbolic 3-manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to −1. It is generally required that this metric be also complete: in this case the manifold can be realised as a quotient of the 3-dimensional hyperbolic space by a discrete group of isometries (a Kleinian group).
Hyperbolic 3-manifolds of finite volume have a particular importance in 3-dimensional topology as follows from Thurston's geometrisation conjecture proved by Perelman. The study of Kleinian groups is also an important topic in geometric group theory.
Importance in topology
Hyperbolic geometry is the most rich and least understood of the eight geometries in dimension 3 (for example, for all other geometries it is not hard to give an explicit enumeration of the finite-volume manifolds with this geometry, while this is far from being the case for hyperbolic manifolds). After the proof of the Geometrisation conjecture, understanding the topological properties of hyperbolic 3-manifolds is thus a major goal of 3-dimensional topology. Recent breakthroughs of Kahn–Markovic, Wise, Agol and others have answered most long-standing open questions on the topic but there are still many less prominent ones which have not been solved.
In dimension 2 almost all closed surfaces are hyperbolic (all but the sphere, projective plane, torus and Klein bott
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https://en.wikipedia.org/wiki/David%20Hodgson
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David Hodgson may refer to:
David Hodgson (rugby league) (born 1981), English rugby league footballer
David Hodgson (judge) (1939–2012), Australian judge
David Hodgson (chemist), English chemistry professor
David Hodgson (footballer) (born 1960), English football player
David Hodgson (artist) (1798–1864), English painter
Dave Hodgson (born 1959), English mayor of Bedford
David Hodgson, convicted murderer, see murder of Jenny Nicholl
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https://en.wikipedia.org/wiki/Alexander%20Markovich%20Polyakov
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Alexander Markovich Polyakov (; born 27 September 1945) is a Russian theoretical physicist, formerly at the Landau Institute in Moscow and, since 1989, at Princeton University, where he is the Joseph Henry Professor of Physics Emeritus.
Important discoveries
Polyakov is known for a number of fundamental contributions to quantum field theory, including work on what is now called the 't Hooft–Polyakov monopole in non-Abelian gauge theory, independent from Gerard 't Hooft. Polyakov and coauthors discovered the so-called BPST instanton which, in turn, led to the discovery of the vacuum angle in QCD. His path integral formulation of string theory had profound and lasting impacts on the conceptual and mathematical understanding of the theory. His paper "Infinite conformal symmetry in two-dimensional quantum field theory" written with Alexander Belavin and Alexander Zamolodchikov laid down the foundations of two-dimensional conformal field theory and has classic status. Polyakov also played an important role in elucidating the conceptual framework behind renormalization independent of Kenneth G. Wilson's Nobel Prize–winning work. He formulated pioneering ideas in gauge/string duality long before the breakthrough of AdS/CFT using D-branes. Other insightful conjectures that came years or even decades before active work by others include integrability of gauge and string theories and certain ideas about turbulence.
Very early in his career, in a 1965 student work, Polyakov suggested
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https://en.wikipedia.org/wiki/Weyl%20transformation
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See also Wigner–Weyl transform, for another definition of the Weyl transform.
In theoretical physics, the Weyl transformation, named after Hermann Weyl, is a local rescaling of the metric tensor:
which produces another metric in the same conformal class. A theory or an expression invariant under this transformation is called conformally invariant, or is said to possess Weyl invariance or Weyl symmetry. The Weyl symmetry is an important symmetry in conformal field theory. It is, for example, a symmetry of the Polyakov action. When quantum mechanical effects break the conformal invariance of a theory, it is said to exhibit a conformal anomaly or Weyl anomaly.
The ordinary Levi-Civita connection and associated spin connections are not invariant under Weyl transformations. Weyl connections are a class of affine connections that is invariant, although no Weyl connection is individual invariant under Weyl transformations.
Conformal weight
A quantity has conformal weight if, under the Weyl transformation, it transforms via
Thus conformally weighted quantities belong to certain density bundles; see also conformal dimension. Let be the connection one-form associated to the Levi-Civita connection of . Introduce a connection that depends also on an initial one-form via
Then is covariant and has conformal weight .
Formulas
For the transformation
We can derive the following formulas
Note that the Weyl tensor is invariant under a Weyl rescaling.
References
Confor
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https://en.wikipedia.org/wiki/Enol
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In organic chemistry, alkenols (shortened to enols) are a type of reactive structure or intermediate in organic chemistry that is represented as an alkene (olefin) with a hydroxyl group attached to one end of the alkene double bond (). The terms enol and alkenol are portmanteaus deriving from "-ene"/"alkene" and the "-ol" suffix indicating the hydroxyl group of alcohols, dropping the terminal "-e" of the first term. Generation of enols often involves deprotonation at the α position to the carbonyl group—i.e., removal of the hydrogen atom there as a proton . When this proton is not returned at the end of the stepwise process, the result is an anion termed an enolate (see images at right). The enolate structures shown are schematic; a more modern representation considers the molecular orbitals that are formed and occupied by electrons in the enolate. Similarly, generation of the enol often is accompanied by "trapping" or masking of the hydroxy group as an ether, such as a silyl enol ether.
Keto–enol tautomerism refers to a chemical equilibrium between a "keto" form (a carbonyl, named for the common ketone case) and an enol. The interconversion of the two forms involves the transfer of an alpha hydrogen atom and the reorganisation of bonding electrons. The keto and enol forms are tautomers of each other.
Enolization
Organic esters, ketones, and aldehydes with an α-hydrogen ( bond adjacent to the carbonyl group) often form enols. The reaction involves migration of a proton from
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https://en.wikipedia.org/wiki/UGC
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UGC may refer to:
Science and technology
Universal gravitational constant G, in physics
Uppsala General Catalogue, an astronomical catalogue of galaxies
UGC, a codon for cysteine
Unique games conjecture, a conjecture in computational complexity
Organisations
UGC (cinema operator), a European cinema chain, formerly Union Générale Cinématographique
UGC Fox Distribution, a former French-American film production company formed in 1995
Union Graduate College, Schenectady, New York
United Grain Company, a Russian grain trading company based in Moscow
University Grants Commission (disambiguation)
University Grants Committee (disambiguation)
UnitedGlobalCom, former name of the cable TV operator Liberty Global
UnderGround Crips, an African American street gang mainly from Los Angeles, California
Other
User-generated content, media content made by the general public
Urine Good Company, a fictional corporation in the musical Urinetown
Urgench International Airport, by IATA code
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https://en.wikipedia.org/wiki/Eccentricity%20%28mathematics%29
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In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape.
One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular:
The eccentricity of a circle is 0.
The eccentricity of an ellipse which is not a circle is between 0 and 1.
The eccentricity of a parabola is 1.
The eccentricity of a hyperbola is greater than 1.
The eccentricity of a pair of lines is
Two conic sections with the same eccentricity are similar.
Definitions
Any conic section can be defined as the locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio. That ratio is called the eccentricity, commonly denoted as .
The eccentricity can also be defined in terms of the intersection of a plane and a double-napped cone associated with the conic section. If the cone is oriented with its axis vertical, the eccentricity is
where β is the angle between the plane and the horizontal and α is the angle between the cone's slant generator and the horizontal. For the plane section is a circle, for a parabola. (The plane must not meet the vertex of the cone.)
The linear eccentricity of an ellipse or hyperbola, denoted (or sometimes or ), is the distance between its center and either of its two foci. The eccentricity can be defined as the ratio of the linear eccentricity to the semimajor axis : that is, (lacking a center, the linear eccentr
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https://en.wikipedia.org/wiki/Ellipse%20%28disambiguation%29
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In mathematics, an ellipse is a geometrical figure.
Ellipse may also refer to:
MacAdam ellipse, an area in a chromaticity diagram
Elliptic leaf shape
Superellipse, a geometric figure
As a name, it may also be:
The Ellipse, an area in Washington, D.C., United States
Ellipse Programmé, a French animation studio
Elipse, a Yugoslav rock band
Ellipse, a 2009 album by Imogen Heap
"Ellipse", a song from the album In Silence We Yearn by Oh Hiroshima
Explorer Ellipse, an American homebuilt aircraft design
La société Ellipse, a French aircraft manufacturer
Similar terms
Ellipsis, a punctuation mark
Ellipsis, a rhetorical suppression of words to give an expression more liveliness
Eclipse, an astronomical event
Elliptical (trainer), a stationary exercise machine
See also
Ellipsis (disambiguation)
Oval (disambiguation)
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https://en.wikipedia.org/wiki/Pariser%E2%80%93Parr%E2%80%93Pople%20method
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In molecular physics, the Pariser–Parr–Pople method applies semi-empirical quantum mechanical methods to the quantitative prediction of electronic structures and spectra, in molecules of interest in the field of organic chemistry. Previous methods existed—such as the Hückel method which led to Hückel's rule—but were limited in their scope, application and complexity, as is the Extended Hückel method.
This approach was developed in the 1950s by Rudolph Pariser with Robert Parr and co-developed by John Pople.
It is essentially a more efficient method of finding reasonable approximations of molecular orbitals, useful in predicting physical and chemical nature of the molecule under study since molecular orbital characteristics have implications with regards to both the basic structure and reactivity of a molecule. This method used the zero-differential overlap (ZDO) approximation to reduce the problem to reasonable size and complexity but still required modern solid state computers (as opposed to punched card or vacuum tube systems) before becoming fully useful for molecules larger than benzene.
Originally, Pariser's goal of using this method was to predict the characteristics of complex organic dyes, but this was never realized. The method has wide applicability in precise prediction of electronic transitions, particularly lower singlet transitions, and found wide application in theoretical and applied quantum chemistry. The two basic papers on this subject were among the top
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https://en.wikipedia.org/wiki/Dirichlet%27s%20principle
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In mathematics, and particularly in potential theory, Dirichlet's principle is the assumption that the minimizer of a certain energy functional is a solution to Poisson's equation.
Formal statement
Dirichlet's principle states that, if the function is the solution to Poisson's equation
on a domain of with boundary condition
on the boundary ,
then u can be obtained as the minimizer of the Dirichlet energy
amongst all twice differentiable functions such that on (provided that there exists at least one function making the Dirichlet's integral finite). This concept is named after the German mathematician Peter Gustav Lejeune Dirichlet.
History
The name "Dirichlet's principle" is due to Riemann, who applied it in the study of complex analytic functions.
Riemann (and others such as Gauss and Dirichlet) knew that Dirichlet's integral is bounded below, which establishes the existence of an infimum; however, he took for granted the existence of a function that attains the minimum. Weierstrass published the first criticism of this assumption in 1870, giving an example of a functional that has a greatest lower bound which is not a minimum value. Weierstrass's example was the functional
where is continuous on , continuously differentiable on , and subject to boundary conditions , where and are constants and . Weierstrass showed that , but no admissible function can make equal 0. This example did not disprove Dirichlet's principle per se, since the example inte
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https://en.wikipedia.org/wiki/Retrograde%20signaling
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Retrograde signaling in biology is the process where a signal travels backwards from a target source to its original source. For example, the nucleus of a cell is the original source for creating signaling proteins. During retrograde signaling, instead of signals leaving the nucleus, they are sent to the nucleus. In cell biology, this type of signaling typically occurs between the mitochondria or chloroplast and the nucleus. Signaling molecules from the mitochondria or chloroplast act on the nucleus to affect nuclear gene expression. In this regard, the chloroplast or mitochondria act as a sensor for internal external stimuli which activate a signaling pathway.
In neuroscience, retrograde signaling (or retrograde neurotransmission) refers more specifically to the process by which a retrograde messenger, such as anandamide or nitric oxide, is released by a postsynaptic dendrite or cell body, and travels "backwards" across a chemical synapse to bind to the axon terminal of a presynaptic neuron.
In cell biology
Retrograde signals are transmitted from plastids to the nucleus in plants and eukaryotic algae, and from mitochondria to the nucleus in most eukaryotes. Retrograde signals are generally considered to convey intracellular signals related to stress and environmental sensing. Many of the molecules associated with retrograde signaling act on modifying the transcription or by directly binding and acting as a transcription factor. The outcomes of these signaling pathways vary
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https://en.wikipedia.org/wiki/Red%20Ring
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Red Ring may refer to:
A ring with a red gemstone
Biology
Red ring disease, caused by the nematode Bursaphelenchus cocophilus
Bicyclus anisops, red ring bush brown, a butterfly
Hestina assimilis, red ring skirt, a butterfly
Phellinus pini, red ring rot, a fungus
Literature and comics
Narya, the Red Ring, one of the Rings in J. R. R. Tolkien's Middle-earth universe
Red power ring of the Red Lantern Corps in the DC universe
Video games
A special type of collectible ring in a number of Sonic the Hedgehog games
A red ring that appears in some Mario games
Red Ring of Death, a common Xbox 360 problem
See also
Ring of Red, 2000 video game
Red Ring Rico, Phantasy Star Online character
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https://en.wikipedia.org/wiki/Symmetry%20breaking
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In physics, symmetry breaking is a phenomenon where a disordered but symmetric state collapses into an ordered, but less symmetric state. This collapse is often one of many possible bifurcations that a particle can take as it approaches a lower energy state. Due to the many possibilities, an observer may assume the result of the collapse to be arbitrary. This phenomenon is fundamental to quantum field theory (QFT), and further, contemporary understandings of physics. Specifically, it plays a central role in the Glashow–Weinberg–Salam model which forms part of the Standard model modelling the electroweak sector.In an infinite system (Minkowski spacetime) symmetry breaking occurs, however in a finite system (that is, any real super-condensed system), the system is less predictable, but in many cases quantum tunneling occurs. Symmetry breaking and tunneling relate through the collapse of a particle into non-symmetric state as it seeks a lower energy.
Symmetry breaking can be distinguished into two types, explicit and spontaneous. They are characterized by whether the equations of motion fail to be invariant, or the ground state fails to be invariant.
Non-technical description
This section describes spontaneous symmetry breaking. In layman's terms, this is the idea that for a physical system, the lowest energy configuration (the vacuum state) is not the most symmetric configuration of the system. Roughly speaking there are three types of symmetry that can be broken: discrete,
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https://en.wikipedia.org/wiki/Lickorish%E2%80%93Wallace%20theorem
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In mathematics, the Lickorish–Wallace theorem in the theory of 3-manifolds states that any closed, orientable, connected 3-manifold may be obtained by performing Dehn surgery on a framed link in the 3-sphere with ±1 surgery coefficients. Furthermore, each component of the link can be assumed to be unknotted.
The theorem was proved in the early 1960s by W. B. R. Lickorish and Andrew H. Wallace, independently and by different methods. Lickorish's proof rested on the Lickorish twist theorem, which states that any orientable automorphism of a closed orientable surface is generated by Dehn twists along 3g − 1 specific simple closed curves in the surface, where g denotes the genus of the surface. Wallace's proof was more general and involved adding handles to the boundary of a higher-dimensional ball.
A corollary of the theorem is that every closed, orientable 3-manifold bounds a simply-connected compact 4-manifold.
By using his work on automorphisms of non-orientable surfaces, Lickorish also showed that every closed, non-orientable, connected 3-manifold is obtained by Dehn surgery on a link in the non-orientable 2-sphere bundle over the circle. Similar to the orientable case, the surgery can be done in a special way which allows the conclusion that every closed, non-orientable 3-manifold bounds a compact 4-manifold.
References
3-manifolds
Theorems in topology
Theorems in geometry
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https://en.wikipedia.org/wiki/Parity%20%28physics%29
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In physics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point reflection):
It can also be thought of as a test for chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image.
All fundamental interactions of elementary particles, with the exception of the weak interaction, are symmetric under parity. As established by the Wu experiment conducted at the US National Bureau of Standards by Chinese-American scientist Chien-Shiung Wu, the weak interaction is chiral and thus provides a means for probing chirality in physics. In her experiment, Wu took advantage of the controlling role of weak interactions in radioactive decay of atomic isotopes to establish the chirality of the weak force.
By contrast, in interactions that are symmetric under parity, such as electromagnetism in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions.
A matrix representation of P (in any number of dimensions) has determinant equal to −1, and hence is distinct from a rotation, which has a determinant equal to 1. In a two-dimensional plane, a simultaneous flip of all coordinates in sign is not a parity transformation; it is the same as a 180° rotation.
In quantum mechanics, wave functions that are unchanged by a parity tra
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https://en.wikipedia.org/wiki/Dehn%20surgery
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In topology, a branch of mathematics, a Dehn surgery, named after Max Dehn, is a construction used to modify 3-manifolds. The process takes as input a 3-manifold together with a link. It is often conceptualized as two steps: drilling then filling.
Definitions
Given a 3-manifold and a link , the manifold drilled along is obtained by removing an open tubular neighborhood of from . If , the drilled manifold has torus boundary components . The manifold drilled along is also known as the link complement, since if one removed the corresponding closed tubular neighborhood from , one obtains a manifold diffeomorphic to .
Given a 3-manifold whose boundary is made of 2-tori , we may glue in one solid torus by a homeomorphism (resp. diffeomorphism) of its boundary to each of the torus boundary components of the original 3-manifold. There are many inequivalent ways of doing this, in general. This process is called Dehn filling.
Dehn surgery on a 3-manifold containing a link consists of drilling out a tubular neighbourhood of the link together with Dehn filling on all the components of the boundary corresponding to the link.
In order to describe a Dehn surgery (see ), one picks two oriented simple closed curves and on the corresponding boundary torus of the drilled 3-manifold, where is a meridian of (a curve staying in a small ball in and having linking number +1 with or, equivalently, a curve that bounds a disc that intersects once the component ) and is a longi
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https://en.wikipedia.org/wiki/Terahertz%20time-domain%20spectroscopy
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In physics, terahertz time-domain spectroscopy (THz-TDS) is a spectroscopic technique in which the properties of matter are probed with short pulses of terahertz radiation. The generation and detection scheme is sensitive to the sample's effect on both the amplitude and the phase of the terahertz radiation.
Explanation
Typically, an ultrashort pulsed laser is used in the terahertz pulse generation process. In the use of low-temperature grown GaAs as an antenna, the ultrashort pulse creates charge carriers that are accelerated to create the terahertz pulse. In the use of non-linear crystals as a source, a high-intensity ultrashort pulse produces THz radiation from the crystal. A single terahertz pulse can contain frequency components covering much of the terahertz range, often from 0.05 to 4 THz, though the use of an air plasma can yield frequency components up to 40 THz. After THz pulse generation, the pulse is directed by optical techniques, focused through a sample, then measured.
THz-TDS requires generation of an ultrafast (thus, large bandwidth) terahertz pulse from an even faster femtosecond optical pulse, typically from a Ti-sapphire laser. That optical pulse is first split to provide a probe pulse whose path length is adjusted using an optical delay line. The probe pulse strobes the detector that is sensitive to the electric field of the resulting terahertz signal at the time of the optical probe pulse sent to it. By varying the path length traversed by the probe pu
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https://en.wikipedia.org/wiki/Adjunction%20space
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In mathematics, an adjunction space (or attaching space) is a common construction in topology where one topological space is attached or "glued" onto another. Specifically, let X and Y be topological spaces, and let A be a subspace of Y. Let f : A → X be a continuous map (called the attaching map). One forms the adjunction space X ∪f Y (sometimes also written as X +f Y) by taking the disjoint union of X and Y and identifying a with f(a) for all a in A. Formally,
where the equivalence relation ~ is generated by a ~ f(a) for all a in A, and the quotient is given the quotient topology. As a set, X ∪f Y consists of the disjoint union of X and (Y − A). The topology, however, is specified by the quotient construction.
Intuitively, one may think of Y as being glued onto X via the map f.
Examples
A common example of an adjunction space is given when Y is a closed n-ball (or cell) and A is the boundary of the ball, the (n−1)-sphere. Inductively attaching cells along their spherical boundaries to this space results in an example of a CW complex.
Adjunction spaces are also used to define connected sums of manifolds. Here, one first removes open balls from X and Y before attaching the boundaries of the removed balls along an attaching map.
If A is a space with one point then the adjunction is the wedge sum of X and Y.
If X is a space with one point then the adjunction is the quotient Y/A.
Properties
The continuous maps h : X ∪f Y → Z are in 1-1 correspondence with the pairs of conti
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https://en.wikipedia.org/wiki/Retort
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In a chemistry laboratory, a retort is a device used for distillation or dry distillation of substances. It consists of a spherical vessel with a long downward-pointing neck. The liquid to be distilled is placed in the vessel and heated. The neck acts as a condenser, allowing the vapors to condense and flow along the neck to a collection vessel placed underneath.
In the chemical industry, a retort is an airtight vessel in which substances are heated for a chemical reaction producing gaseous products to be collected in a collection vessel or for further processing. Such industrial-scale retorts are used in shale oil extraction, the production of charcoal and in the recovery of mercury in gold mining processes and hazardous waste. A process of heating oil shale to produce shale oil, oil shale gas, and spent shale is commonly called retorting. Airtight vessels to apply pressure as well as heat are called autoclaves.
In the food industry, pressure cookers are often referred to as retorts, meaning "canning retorts", for sterilization under high temperature (116–130 °C).
History
Retorts were widely used by alchemists, and images of retorts appear in many drawings and sketches of their laboratories. Before the advent of modern condensers, retorts were used by many prominent chemists, such as Antoine Lavoisier and Jöns Berzelius.
An early method for producing phosphorus starts by roasting bones, and uses clay retorts encased in a very hot brick furnace to distill out the highly
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https://en.wikipedia.org/wiki/Percy%20Pennybacker
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Percy V. Pennybacker Jr. (1895–1963) was a Texas civil engineer who pioneered the technology of welded structures, particularly for bridges.
Professional success
Pennybacker worked for the Texas Highway Department in the early 1900s designing bridges. He earned his civil engineering degree from the University of Texas at Austin. He served as a captain in the Army Air Service during World War I. After the war, he worked in Kansas and Texas. During World War II, he became interested in welded construction as an alternative to rivets. By promoting the use of welding for heavy stress bridge design, he is credited with saving the state of Texas millions of dollars.
When he retired from the Texas Highway Department, he worked another three years for the city of Austin as a civil engineer.
He was honored as "Outstanding Engineer" by the Texas Society of Professional Engineers, was a member of the American Society of Civil Engineers, and brought the American Welding Society to Austin.
Childhood
His father, also Percy V. Pennybacker, and mother Anna (née Hardwicke) Pennybacker married in Tyler, Texas in 1884. Percy junior was born in Palestine, Texas and was one of four children. His father, a school superintendent, suffered from diabetes and died of the disease in 1899 while Percy was young. Like his father, Percy too suffered from diabetes. After spending a year in the hospital as a young civil engineer, he became one of the first patients treated with insulin. His mother Anna
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https://en.wikipedia.org/wiki/Pi%20backbonding
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In chemistry, π backbonding, also called π backdonation, is when electrons move from an atomic orbital on one atom to an appropriate symmetry antibonding orbital on a π-acceptor ligand. It is especially common in the organometallic chemistry of transition metals with multi-atomic ligands such as carbon monoxide, ethylene or the nitrosonium cation. Electrons from the metal are used to bond to the ligand, in the process relieving the metal of excess negative charge. Compounds where π backbonding occurs include Ni(CO)4 and Zeise's salt.
IUPAC offers the following definition for backbonding:
A description of the bonding of π-conjugated ligands to a transition metal which involves a synergic process with donation of electrons from the filled π-orbital or lone electron pair orbital of the ligand into an empty orbital of the metal (donor–acceptor bond), together with release (back donation) of electrons from an nd orbital of the metal (which is of π-symmetry with respect to the metal–ligand axis) into the empty π*-antibonding orbital of the ligand.
Metal carbonyls, nitrosyls, and isocyanides
The electrons are partially transferred from a d-orbital of the metal to anti-bonding molecular orbitals of CO (and its analogues). This electron-transfer (i) strengthens the metal–C bond and (ii) weakens the C–O bond. The strengthening of the M–CO bond is reflected in increases of the vibrational frequencies for the M–C bond (often outside of the range for the usual IR spectrophotometers).
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https://en.wikipedia.org/wiki/Kate%20Maki
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Kate Maki (born Katherine Ellen Maki) is a Canadian singer-songwriter.
Biography
Maki is of Finnish descent. Born and raised in Sudbury, Ontario, she studied neuroscience at Dalhousie University in Halifax, Nova Scotia and education at Nipissing University in North Bay, Ontario. She taught special education, French and science in Ottawa, Toronto and Sudbury for several years before deciding to pursue a full-time musical career.
In 2003, Maki recorded her debut album, Confusion Unlimited, with Dave Draves at Little Bullhorn Studios in Ottawa, Ontario. The album's blend of folk rock and alternative country earned her favourable reviews and quickly sold out its initial printing. In 2004, she returned to Little Bullhorn Studios to record her second album, The Sun Will Find Us. Both albums received Album of the Year awards at the Northern Ontario Music and Film Awards in 2004 and 2005.
In 2005, Maki, Nathan Lawr, Ryan Bishops, Ruth Minnikin and Dale Murray participated in two national concert tours, A Midautumn Night's Dream and A Midwinter Night's Dream, which were reportedly inspired by Bob Dylan's Rolling Thunder Revue. The five musicians also recorded limited edition tour compilations for each tour.
Maki took a break from touring between 2006 and 2008 and returned home to Sudbury, Ontario to teach high school science.
During March Break 2007, Maki recorded her third album, On High, at Little Bullhorn Studios with Howe Gelb as producer and Dave Draves as engineer. It was r
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https://en.wikipedia.org/wiki/Atoroidal
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In mathematics, an atoroidal 3-manifold is one that does not contain an essential torus.
There are two major variations in this terminology: an essential torus may be defined geometrically, as an embedded, non-boundary parallel, incompressible torus, or it may be defined algebraically, as a subgroup of its fundamental group that is not conjugate to a peripheral subgroup (i.e., the image of the map on fundamental group induced by an inclusion of a boundary component). The terminology is not standardized, and different authors require atoroidal 3-manifolds to satisfy certain additional restrictions. For instance:
gives a definition of atoroidality that combines both geometric and algebraic aspects, in terms of maps from a torus to the manifold and the induced maps on the fundamental group. He then notes that for irreducible boundary-incompressible 3-manifolds this gives the algebraic definition.
uses the algebraic definition without additional restrictions.
uses the geometric definition, restricted to irreducible manifolds.
requires the algebraic variant of atoroidal manifolds (which he calls simply atoroidal) to avoid being one of three kinds of fiber bundle. He makes the same restriction on geometrically atoroidal manifolds (which he calls topologically atoroidal) and in addition requires them to avoid incompressible boundary-parallel embedded Klein bottles. With these definitions, the two kinds of atoroidality are equivalent except on certain Seifert manifolds.
A 3-ma
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https://en.wikipedia.org/wiki/Boundary%20parallel
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In mathematics, a closed n-manifold N embedded in an (n + 1)-manifold M is boundary parallel (or ∂-parallel, or peripheral) if there is an isotopy of N onto a boundary component of M.
An example
Consider the annulus . Let π denote the projection map
If a circle S is embedded into the annulus so that π restricted to S is a bijection, then S is boundary parallel. (The converse is not true.)
If, on the other hand, a circle S is embedded into the annulus so that π restricted to S is not surjective, then S is not boundary parallel. (Again, the converse is not true.)
Geometric topology
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https://en.wikipedia.org/wiki/Actinism
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Actinism () is the property of solar radiation that leads to the production of photochemical and photobiological effects. Actinism is derived from the Ancient Greek ἀκτίς, ἀκτῖνος ("ray, beam"). The word actinism is found, for example, in the terminology of imaging technology (esp. photography), medicine (concerning sunburn), and chemistry (concerning containers that protect from photo-degradation), and the concept of actinism is applied, for example, in chemical photography and X-ray imaging.
Actinic () chemicals include silver salts used in photography and other light sensitive chemicals.
In chemistry
In chemical terms, actinism is the property of radiation that lets it be absorbed by a molecule and cause a photochemical reaction as a result. Albert Einstein was the first to correctly theorize that each photon would be able to cause only one molecular reaction. This distinction separates photochemical reactions from exothermic reduction reactions triggered by radiation.
For general purposes, photochemistry is the commonly used vernacular rather than actinic or actino-chemistry, which are again more commonly seen used for photography or imaging.
In medicine
In medicine, actinic effects are generally described in terms of the dermis or outer layers of the body, such as eyes (see: Actinic conjunctivitis) and upper tissues that the sun would normally affect, rather than deeper tissues that higher-energy shorter-wavelength radiation such as x-ray and gamma might affect. Act
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https://en.wikipedia.org/wiki/Repolarization
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In neuroscience, repolarization refers to the change in membrane potential that returns it to a negative value just after the depolarization phase of an action potential which has changed the membrane potential to a positive value. The repolarization phase usually returns the membrane potential back to the resting membrane potential. The efflux of potassium (K+) ions results in the falling phase of an action potential. The ions pass through the selectivity filter of the K+ channel pore.
Repolarization typically results from the movement of positively charged K+ ions out of the cell. The repolarization phase of an action potential initially results in hyperpolarization, attainment of a membrane potential, termed the afterhyperpolarization, that is more negative than the resting potential. Repolarization usually takes several milliseconds.
Repolarization is a stage of an action potential in which the cell experiences a decrease of voltage due to the efflux of potassium (K+) ions along its electrochemical gradient. This phase occurs after the cell reaches its highest voltage from depolarization. After repolarization, the cell hyperpolarizes as it reaches resting membrane potential (−70 mV in neuron). Sodium (Na+) and potassium ions inside and outside the cell are moved by a sodium potassium pump, ensuring that electrochemical equilibrium remains unreached to allow the cell to maintain a state of resting membrane potential. In the graph of an action potential, the hyper-polari
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https://en.wikipedia.org/wiki/Comenius%20University%20Faculty%20of%20Mathematics%2C%20Physics%20and%20Informatics
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The Faculty of Mathematics, Physics and Informatics (FMPH; ; ; colloquial: Matfyz) is one of 13 faculties of the Comenius University in Bratislava, the capital of Slovakia. The faculty provides higher education in mathematics, physics and informatics, as well as teacher training in subjects related to these branches of study. It was established in 1980 by separating from the Faculty of Natural Sciences under the name of Faculty of Mathematics and Physics (). Its name was changed to the contemporary name in 2000.
In 2015, Faculty of Mathematics, Physics and Informatics was ranked first in the group of natural sciences in the ranking of faculties in Slovakia by the Academic Ranking and Rating Agency (ARRA).
The campus is located in Mlynská dolina in Bratislava, along with the Faculty of Natural Sciences of the Comenius University, the Faculty of Informatics and Information Technologies and the Faculty of Electrical Engineering and Information Technology of the Slovak University of Technology.
Endowment of the faculty in 2015 was €11.7 million.
Departments
Mathematics
Department of Algebra, Geometry and Didactics of Mathematics
Department of Applied Mathematics and Statistics
Department of Mathematical Analysis and Numerical Mathematics
Physics
Department of Astronomy, Physics of the Earth and Meteorology
Department of Experimental Physics
Department of Nuclear Physics and Biophysics
Department of Theoretical Physics and Didactics of Physics
Informatics
Depa
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https://en.wikipedia.org/wiki/Department%20of%20Computer%20Science%2C%20FMPI%2C%20Comenius%20University
|
The Department of Computer Science is a department of the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, the capital of Slovakia. It is headed by Prof. RNDr. Branislav Rovan, Phd.
Educational and scientific achievements
The first comprehensive computer science curriculum in Czechoslovakia (now Slovakia) was introduced at the Faculty in 1973. The department, established in 1974, continues to be responsible for organizing the major part of the undergraduate and graduate computer science education to this date. The distinguishing feature of the curriculum has been a balanced coverage of the mathematical foundations, theoretical computer science, and practical computer science. The part of the curriculum covered by the department at present includes courses on computer architecture, system software, networks, databases, software design, design and analysis of algorithms, formal languages, computational complexity, discrete mathematics, cryptology, data security and others.
The department succeeded several times in project applications within the TEMPUS Programme of the EU. The projects CIPRO and „Neumann Network“ helped to build the departmental hardware infrastructure and to establish the expertise in Unix workstation technology, networking, and structured document processing. The CUSTU PARLAB parallel computing laboratory run jointly with the Department of Informatics of the Faculty of Electrical Engineering and Informatics of the
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https://en.wikipedia.org/wiki/Arne%20Tiselius
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Arne Wilhelm Kaurin Tiselius (10 August 1902 – 29 October 1971) was a Swedish biochemist who won the Nobel Prize in Chemistry in 1948 "for his research on electrophoresis and adsorption analysis, especially for his discoveries concerning the complex nature of the serum proteins."
Education
Tiselius was born in Stockholm. Following the death of his father, the family moved to Gothenburg where he went to school, and after graduation at the local "Realgymnasium" in 1921, he studied at the Uppsala University, specializing in chemistry.
Career and research
Tiselius became a research assistant at Theodor Svedberg's laboratory in 1925 and obtained his doctoral degree in 1930 on the moving-boundary method of studying the electrophoresis of proteins. From then to 1935 he published a number of papers on diffusion and adsorption in naturally occurring base-exchanging zeolites, and these studies continued during a year's visit to Hugh Stott Taylor's laboratory in Princeton University with support of a Rockefeller Foundation fellowship. On his return to Uppsala he resumed his interest in proteins, and the application of physical methods to biochemical problems. This led to a much-improved method of electrophoretic analysis which he refined in subsequent years.
Tiselius took an active part in the reorganization of scientific research in Sweden in the years following World War II, and was President of the International Union of Pure and Applied Chemistry 1951–1955. He was chairman of the
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https://en.wikipedia.org/wiki/Pointed%20set
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In mathematics, a pointed set (also based set or rooted set) is an ordered pair where is a set and is an element of called the base point, also spelled basepoint.
Maps between pointed sets and —called based maps, pointed maps, or point-preserving maps—are functions from to that map one basepoint to another, i.e. maps such that . Based maps are usually denoted .
Pointed sets are very simple algebraic structures. In the sense of universal algebra, a pointed set is a set together with a single nullary operation which picks out the basepoint. Pointed maps are the homomorphisms of these algebraic structures.
The class of all pointed sets together with the class of all based maps forms a category. Every pointed set can be converted to an ordinary set by forgetting the basepoint (the forgetful functor is faithful), but the reverse is not true. In particular, the empty set cannot be pointed, because it has no element that can be chosen as the basepoint.
Categorical properties
The category of pointed sets and based maps is equivalent to the category of sets and partial functions. The base point serves as a "default value" for those arguments for which the partial function is not defined. One textbook notes that "This formal completion of sets and partial maps by adding 'improper', 'infinite' elements was reinvented many times, in particular, in topology (one-point compactification) and in theoretical computer science." This category is also isomorphic to the coslice
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https://en.wikipedia.org/wiki/Projective%20differential%20geometry
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In mathematics, projective differential geometry is the study of differential geometry, from the point of view of properties of mathematical objects such as functions, diffeomorphisms, and submanifolds, that are invariant under transformations of the projective group. This is a mixture of the approaches from Riemannian geometry of studying invariances, and of the Erlangen program of characterizing geometries according to their group symmetries.
The area was much studied by mathematicians from around 1890 for a generation (by J. G. Darboux, George Henri Halphen, Ernest Julius Wilczynski, E. Bompiani, G. Fubini, Eduard Čech, amongst others), without a comprehensive theory of differential invariants emerging. Élie Cartan formulated the idea of a general projective connection, as part of his method of moving frames; abstractly speaking, this is the level of generality at which the Erlangen program can be reconciled with differential geometry, while it also develops the oldest part of the theory (for the projective line), namely the Schwarzian derivative, the simplest projective differential invariant.
Further work from the 1930s onwards was carried out by J. Kanitani, Shiing-Shen Chern, A. P. Norden, G. Bol, S. P. Finikov and G. F. Laptev. Even the basic results on osculation of curves, a manifestly projective-invariant topic, lack any comprehensive theory. The ideas of projective differential geometry recur in mathematics and its applications, but the formulations given are s
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https://en.wikipedia.org/wiki/Modification
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Modification may refer to:
Modifications of school work for students with special educational needs
Modifications (genetics), changes in appearance arising from changes in the environment
Posttranslational modifications, changes to proteins arising from protein biosynthesis
Modding, modifying hardware or software
Mod (video gaming)
Modified car
Body modification
Grammatical modifier
Home modifications
Chemical modification, processes involving the alteration of the chemical constitution or structure of molecules
See also
Modified (disambiguation)
Modifier (disambiguation)
Mod (disambiguation)
Edit (disambiguation)
Manipulation (disambiguation)
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https://en.wikipedia.org/wiki/Hodge%20index%20theorem
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In mathematics, the Hodge index theorem for an algebraic surface V determines the signature of the intersection pairing on the algebraic curves C on V. It says, roughly speaking, that the space spanned by such curves (up to linear equivalence) has a one-dimensional subspace on which it is positive definite (not uniquely determined), and decomposes as a direct sum of some such one-dimensional subspace, and a complementary subspace on which it is negative definite.
In a more formal statement, specify that V is a non-singular projective surface, and let H be the divisor class on V of a hyperplane section of V in a given projective embedding. Then the intersection
where d is the degree of V (in that embedding). Let D be the vector space of rational divisor classes on V, up to algebraic equivalence. The dimension of D is finite and is usually denoted by ρ(V). The Hodge index theorem says that the subspace spanned by H in D has a complementary subspace on which the intersection pairing is negative definite. Therefore, the signature (often also called index) is (1,ρ(V)-1).
The abelian group of divisor classes up to algebraic equivalence is now called the Néron-Severi group; it is known to be a finitely-generated abelian group, and the result is about its tensor product with the rational number field. Therefore, ρ(V) is equally the rank of the Néron-Severi group (which can have a non-trivial torsion subgroup, on occasion).
This result was proved in the 1930s by W. V. D. Hodge, f
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https://en.wikipedia.org/wiki/A%20Mathematician%27s%20Apology
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A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy, which offers a defence of the pursuit of mathematics. Central to Hardy's "apology" – in the sense of a formal justification or defence (as in Plato's Apology of Socrates) – is an argument that mathematics has value independent of possible applications. Hardy located this value in the beauty of mathematics, and gave some examples of and criteria for mathematical beauty. The book also includes a brief autobiography, and gives the layman an insight into the mind of a working mathematician.
Background
Hardy felt the need to justify his life's work in mathematics at this time mainly for two reasons. Firstly, at age 62, Hardy felt the approach of old age (he had survived a heart attack in 1939) and the decline of his mathematical creativity and skills.
By devoting time to writing the Apology, Hardy was admitting that his own time as a creative mathematician was finished. In his foreword to the 1967 edition of the book, C. P. Snow describes the Apology as
"a passionate lament for creative powers that used to be and that will never come again".
In Hardy's words, "Exposition, criticism, appreciation, is work for second-rate minds. [...] It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done."
S
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https://en.wikipedia.org/wiki/Flocculation
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In colloidal chemistry, flocculation is a process by which colloidal particles come out of suspension to sediment in the form of floc or flake, either spontaneously or due to the addition of a clarifying agent. The action differs from precipitation in that, prior to flocculation, colloids are merely suspended, under the form of a stable dispersion (where the internal phase (solid) is dispersed throughout the external phase (fluid) through mechanical agitation) and are not truly dissolved in solution.
Coagulation and flocculation are important processes in water treatment with coagulation aimed to destabilize and aggregate particles through chemical interactions between the coagulant and colloids, and flocculation to sediment the destabilized particles by causing their aggregation into floc.
Term definition
According to the IUPAC definition, flocculation is "a process of contact and adhesion whereby the particles of a dispersion form larger-size clusters". Flocculation
is synonymous with agglomeration and coagulation / coalescence.
Basically, coagulation is a process of addition of coagulant to destabilize a stabilized charged particle. Meanwhile, flocculation is a mixing technique that promotes agglomeration and assists in the settling of particles. The most common used coagulant is alum, Al2(SO4)3·14H2O.
The chemical reaction involved:
Al2(SO4)3 · 14 H2O → 2 Al(OH)3 + 6 H+ + 3 + 8 H2O
During flocculation, gentle mixing accelerates the rate of particle collision, and
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https://en.wikipedia.org/wiki/Thom%20space
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In mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space.
Construction of the Thom space
One way to construct this space is as follows. Let
be a rank n real vector bundle over the paracompact space B. Then for each point b in B, the fiber is an -dimensional real vector space. Choose an orthogonal structure on E, a smoothly varying inner product on the fibers; we can do this using partitions of unity. Let be the unit ball bundle with respect to our orthogonal structure, and let be the unit sphere bundle, then the Thom space is the quotient of topological spaces. is a pointed space with the image of in the quotient as basepoint. If B is compact, then is the one-point compactification of E.
For example, if E is the trivial bundle , then and . Writing for B with a disjoint basepoint, is the smash product of and ; that is, the n-th reduced suspension of .
The Thom isomorphism
The significance of this construction begins with the following result, which belongs to the subject of cohomology of fiber bundles. (We have stated the result in terms of coefficients to avoid complications arising from orientability; see also Orientation of a vector bundle#Thom space.)
Let be a real vector bundle of rank n. Then there is an isomorphism, now called a Thom isomorphism
for all k gr
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https://en.wikipedia.org/wiki/Exact%20sciences
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The exact sciences or quantitative sciences, sometimes called the exact mathematical sciences, are those sciences "which admit of absolute precision in their results"; especially the mathematical sciences. Examples of the exact sciences are mathematics, optics, astronomy, and physics, which many philosophers from Descartes, Leibniz, and Kant to the logical positivists took as paradigms of rational and objective knowledge. These sciences have been practiced in many cultures from antiquity to modern times. Given their ties to mathematics, the exact sciences are characterized by accurate quantitative expression, precise predictions and/or rigorous methods of testing hypotheses involving quantifiable predictions and measurements.
The distinction between the quantitative exact sciences and those sciences that deal with the causes of things is due to Aristotle, who distinguished mathematics from natural philosophy and considered the exact sciences to be the "more natural of the branches of mathematics." Thomas Aquinas employed this distinction when he said that astronomy explains the spherical shape of the Earth by mathematical reasoning while physics explains it by material causes. This distinction was widely, but not universally, accepted until the scientific revolution of the 17th century. Edward Grant has proposed that a fundamental change leading to the new sciences was the unification of the exact sciences and physics by Kepler, Newton, and others, which resulted in
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https://en.wikipedia.org/wiki/Constitutive
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Constitutive may refer to:
In physics, a constitutive equation is a relation between two physical quantities
In ecology, a constitutive defense is one that is always active, as opposed to an inducible defense
Constitutive theory of statehood
In genetics, a constitutive gene is always expressed – see constitutive expression
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https://en.wikipedia.org/wiki/Algebra%20bundle
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In mathematics, an algebra bundle is a fiber bundle whose fibers are algebras and local trivializations respect the algebra structure. It follows that the transition functions are algebra isomorphisms. Since algebras are also vector spaces, every algebra bundle is a vector bundle.
Examples include the tensor-algebra bundle, exterior bundle, and symmetric bundle associated to a given vector bundle, as well as the Clifford bundle associated to any Riemannian vector bundle.
See also
Lie algebra bundle
References
.
.
.
.
Vector bundles
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https://en.wikipedia.org/wiki/Moment%20problem
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In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ to the sequence of moments
More generally, one may consider
for an arbitrary sequence of functions Mn.
Introduction
In the classical setting, μ is a measure on the real line, and M is the sequence { xn : n = 0, 1, 2, ... }. In this form the question appears in probability theory, asking whether there is a probability measure having specified mean, variance and so on, and whether it is unique.
There are three named classical moment problems: the Hamburger moment problem in which the support of μ is allowed to be the whole real line; the Stieltjes moment problem, for [0, +∞); and the Hausdorff moment problem for a bounded interval, which without loss of generality may be taken as [0, 1].
Existence
A sequence of numbers mn is the sequence of moments of a measure μ if and only if a certain positivity condition is fulfilled; namely, the Hankel matrices Hn,
should be positive semi-definite. This is because a positive-semidefinite Hankel matrix corresponds to a linear functional such that and (non-negative for sum of squares of polynomials). Assume can be extended to . In the univariate case, a non-negative polynomial can always be written as a sum of squares. So the linear functional is positive for all the non-negative polynomials in the univariate case. By Haviland's theorem, the linear functional has a measure form, that is . A condition of similar form i
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https://en.wikipedia.org/wiki/John%20Earman
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John Earman (born 1942) is an American philosopher of physics. He is an emeritus professor in the History and Philosophy of Science department at the University of Pittsburgh. He has also taught at the University of California, Los Angeles, Rockefeller University, and the University of Minnesota, and was president of the Philosophy of Science Association.
Life and career
John Earman was born in Washington, D.C. in 1942. Earman received his PhD at Princeton University in 1968 with a dissertation on temporal asymmetry (titled Some Aspects of Temporal Asymmetry) and it was directed by Carl Gustav Hempel and Paul Benacerraf. After holding professorships at UCLA, the Rockefeller University, and the University of Minnesota, he joined the faculty of the History and Philosophy of Science department of the University of Pittsburgh in 1985. He remained at Pittsburgh for the rest of his career.
Earman is a former president of the Philosophy of Science Association and a fellow of the American Academy of Arts and Sciences, and of the American Association for the Advancement of Sciences. He is a member of the Archive Board of the Phil-Sci Archive.
The hole argument
Earman has notably contributed to debate about the "hole argument". The hole argument was invented for different purposes by Albert Einstein late in 1913 as part of his quest for the general theory of relativity (GTR). It was revived and reformulated in the modern context by John3 (a short form for the "three Johns": John E
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https://en.wikipedia.org/wiki/Analytic%20hierarchy%20process
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In the theory of decision making, the analytic hierarchy process (AHP), also analytical hierarchy process, is a structured technique for organizing and analyzing complex decisions, based on mathematics and psychology. It was developed by Thomas L. Saaty in the 1970s; Saaty partnered with Ernest Forman to develop Expert Choice software in 1983, and AHP has been extensively studied and refined since then. It represents an accurate approach to quantifying the weights of decision criteria. Individual experts’ experiences are utilized to estimate the relative magnitudes of factors through pair-wise comparisons. Each of the respondents compares the relative importance of each pair of items using a specially designed questionnaire.
Uses and applications
AHP is targeted at group decision making, and is used for decision situations, in fields such as government, business, industry, healthcare and education.
Rather than prescribing a "correct" decision, the AHP helps decision makers find the decision that best suits their goal and their understanding of the problem. It provides a comprehensive and rational framework for structuring a decision problem, for representing and quantifying its elements, for relating those elements to overall goals, and for evaluating alternative solutions.
Users of the AHP first decompose their decision problem into a hierarchy of more easily comprehended sub-problems, each of which can be analyzed independently. The elements of the hierarchy can relate t
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https://en.wikipedia.org/wiki/Tom%20Knight%20%28scientist%29
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Tom Knight is an American synthetic biologist and computer engineer, who was formerly a senior research scientist at the MIT Computer Science and Artificial Intelligence Laboratory, a part of the MIT School of Engineering. He now works at the synthetic biology company Ginkgo Bioworks, which he cofounded in 2008.
Work in electrical engineering and computer science
Tom Knight arrived at MIT when he was fourteen. Even though he only started his undergraduate studies at the regular age of 18, he took classes in computer programming and organic chemistry during high school because he lived close to the university. He built early hardware such as ARPANET interfaces for host #6 on the network, some of the first bitmapped displays, the ITS time sharing system, Lisp machines (he was also instrumental in releasing a version of the operating system for the Lisp machine under a BSD license), the Connection Machine, and parallel symbolic processing computer systems.
In 1967 Knight wrote the original kernel for the ITS operating system, as well as the combination of command processor and debugger that was used as its top-level user interface. ITS was the dominant operating system for first Project MAC and later the MIT Artificial Intelligence Laboratory and MIT Laboratory for Computer Science. ITS ran on PDP-6 and, later, PDP-10 computers.
In 1968, Knight designed and supervised the construction of the first PDP-10 ARPANET interfaces with Bob Metcalfe.
Knight developed a system to
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https://en.wikipedia.org/wiki/Homi%20J.%20Bhabha
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Homi Jehangir Bhabha, FNI, FASc, FRS, Hon.FRSE (30 October 1909 – 24 January 1966) was an Indian nuclear physicist who is widely credited as the "father of the Indian nuclear programme". He was the founding director and professor of physics at the Tata Institute of Fundamental Research (TIFR), as well as the founding director of the Atomic Energy Establishment, Trombay (AEET) which was renamed the Bhabha Atomic Research Centre in his honour. TIFR and AEET served as the cornerstone of the Indian nuclear energy and weapons programme. He was the first chairman of the Indian Atomic Energy Commission and secretary of the Department of Atomic Energy. By supporting space science projects which initially derived their funding from the AEC, he played an important role in the birth of the Indian space programme.
He was awarded the Adams Prize (1942) and Padma Bhushan (1954), and nominated for the Nobel Prize for Physics in 1951 and 1953–1956.
He died in the crash of Air India Flight 101 in 1966, at the age of 56.
Early life
Childhood
Homi Jehangir Bhabha was born on 30 October 1909 into a prominent wealthy Parsi family comprising Jehangir Hormusji Bhabha, a well-known lawyer, and Meherbai Framji Panday, granddaughter of Sir Dinshaw Maneckji Petit. He was named Hormusji after his paternal grandfather, Hormusji Bhabha, who was Inspector-General of Education in Mysore. He received his early studies at Mumbai's Cathedral and John Connon School.
Bhabha's upbringing instilled in him a
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https://en.wikipedia.org/wiki/Federated
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Federated may refer to:
Federated state, a constituent state within a federal state
Federated school, a model of administration in some educational institutions
Federated congregation, a type of religious congregation
Computing
Federated identity, a type of electronic identity
Federated learning, a machine learning technique
Federated protocol, in networking, the ability for users to send messages from one network to another
Federated architecture, a pattern in enterprise architecture
Federated search, a type of electronic search
Federated database system, a type of meta-database management system
Federated content, a type of digital media content
Other
Federated Tower, a skyscraper in Pittsburgh, Pennsylvania
Federated Department Stores, now known as the Macy's, Inc.
Federated Group, a 1980s era chain of home electronics retailers
Federated Investors, a financial services company in Pittsburgh, Pennsylvania
See also
Federal (disambiguation)
Federation (disambiguation)
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https://en.wikipedia.org/wiki/Mold%20%28disambiguation%29
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Mold (or mould) is a structure formed by fungi.
Mold or mould may also refer to:
Artifacts
Molding (process), in which a hollowed-out block is filled with pliable material
Mold (cooking implement), a container used to shape food
Biology
Leaf mold, composted soil or earth, particularly loose soil suitable for planting
Slime mold, a kind of protist
Water mold or oomycete, a kind of protist
Entertainment
Mold (album), Praxis' 1998 experimental music release
Master Mold, a fictional Marvel Comics villain
People
Mold (surname)
Mould (surname)
Places
Mold, Flintshire, a county town in Wales, UK
18240 Mould, a main-belt asteroid
Mold, an unincorporated community of Douglas County, Washington, US
Sports teams
Mold F.C., a defunct Welsh association football club
Mold Golf Club, an 18-hole course in Pantymwyn, Wales
Mold RFC, a rugby union team from Mold, Wales
See also
Molding (disambiguation)
Molde (disambiguation)
Mulling (disambiguation)
Mull (disambiguation)
Mulled wine, hot spiced alcoholic beverage
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https://en.wikipedia.org/wiki/Domo%20%28robot%29
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Domo is an experimental robot made by the Massachusetts Institute of Technology designed to interact with humans. The brainchild of Jeff Weber and Aaron Edsinger, cofounders of Meka Robotics, its name comes from the Japanese phrase for "thank you very much", domo arigato, as well as the Styx song, "Mr. Roboto". The Domo project was originally funded by NASA, and has now been joined by Toyota in funding robot's development.
Purpose
Domo was created to test many robotic circuits and commands that are very complex.
Origin
The home of the Domo Project is with the Humanoid Robotics Group at MIT Artificial Intelligence Labs. Its existence is inspired by the robot projects that came before it.
The Cardea Robot Project was a research project led by Professor Rodney Brooks in the Humanoid Robotics Group at MIT. The lab group worked to create a cable-drive brushless Series Elastic Actuator arm mounted to a Segway platform. Jeff Weber and Aaron Edsinger-Gonzales were a part of this research, specifically responsible for the design and implementation of the robotic arm. This collaboration allowed Edsinger-Gonzales and Weber to take some of the research and apply it to a new robot, Domo.
Edsinger and Weber collaborated on many other robots as well, and their experience working with the Kismet page and Cog projects influenced the design of Domo. Kismet was a robotic head developed by Cynthia Breazeal for experimenting with social expressions and cues. Edsinger's role in the project was
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https://en.wikipedia.org/wiki/Phytochemistry
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Phytochemistry is the study of phytochemicals, which are chemicals derived from plants. Phytochemists strive to describe the structures of the large number of secondary metabolites found in plants, the functions of these compounds in human and plant biology, and the biosynthesis of these compounds. Plants synthesize phytochemicals for many reasons, including to protect themselves against insect attacks and plant diseases. The compounds found in plants are of many kinds, but most can be grouped into four major biosynthetic classes: alkaloids, phenylpropanoids, polyketides, and terpenoids.
Phytochemistry can be considered a subfield of botany or chemistry. Activities can be led in botanical gardens or in the wild with the aid of ethnobotany. Phytochemical studies directed toward human (i.e. drug discovery) use may fall under the discipline of pharmacognosy, whereas phytochemical studies focused on the ecological functions and evolution of phytochemicals likely fall under the discipline of chemical ecology. Phytochemistry also has relevance to the field of plant physiology.
Techniques
Techniques commonly used in the field of phytochemistry are extraction, isolation, and structural elucidation (MS,1D and 2D NMR) of natural products, as well as various chromatography techniques (MPLC, HPLC, and LC-MS).
Phytochemicals
Many plants produce chemical compounds for defence against herbivores. The major classes of pharmacologically active phytochemicals are described below, with ex
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https://en.wikipedia.org/wiki/Mandelbrot%20Competition
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Named in honor of Benoit Mandelbrot, the Mandelbrot Competition was a mathematics competition founded by Sam Vandervelde, Richard Rusczyk and Sandor Lehoczky that operated from 1990 to 2019. It allowed high school students to compete individually and in four-person teams.
Competition
The Mandelbrot was a "correspondence competition," meaning that the competition was sent to a school's coach and students competed at their own school on a predetermined date. Individual results and team answers were then sent back to the contest coordinators. The most notable aspects of the Mandelbrot competition were the difficulty of the problems (much like the American Mathematics Competition and harder American Invitational Mathematics Examination problems) and the proof-based team round. Many past medalists at the International Mathematics Olympiad first tried their skills on the Mandelbrot Competition.
History
The Mandelbrot Competition was started by Sam Vandervelde, Richard Rusczyk, and Sandor Lehoczky while they were undergraduates in the early 1990s. Vandervelde ran the competition until its completion in 2019. Rusczyk now manages Art of Problem Solving Inc. and Lehoczky enjoys a successful career on Wall Street.
Contest format
The individual competition consisted of seven questions of varying value, worth a total of 14 points, that students had 40 minutes to answer. The team competition was a proof-based competition, where many questions were asked about a particular situatio
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https://en.wikipedia.org/wiki/Marcel%20Grossmann
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Marcel Grossmann (April 9, 1878 – September 7, 1936) was a Swiss mathematician and a friend and classmate of Albert Einstein. Grossmann was a member of an old Swiss family from Zurich. His father managed a textile factory. He became a Professor of Mathematics at the Federal Polytechnic School in Zurich, today the ETH Zurich, specializing in descriptive geometry.
Career
In 1900 Grossmann graduated from the Federal Polytechnic School (ETH) and became an assistant to the geometer Wilhelm Fiedler. He continued to do research on non-Euclidean geometry and taught in high schools for the next seven years. In 1902, he earned his doctorate from the University of Zurich with the thesis Ueber die metrischen Eigenschaften kollinearer Gebilde (translated On the Metrical Properties of Collinear Structures) with Fiedler as advisor. In 1907, he was appointed full professor of descriptive geometry at the Federal Polytechnic School.
As a professor of geometry, Grossmann organized summer courses for high school teachers. In 1910, he became one of the founders of the Swiss Mathematical Society. He was an Invited Speaker of the ICM in 1912 at Cambridge and in 1920 at Strasbourg.
Collaborations with Albert Einstein
Albert Einstein's friendship with Grossmann began with their school days in Zurich. Grossmann's careful and complete lecture notes at the Federal Polytechnic School proved to be a salvation for Einstein, who missed many lectures. Grossmann's father helped Einstein get his job at the
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https://en.wikipedia.org/wiki/Volume%20integral
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In mathematics (particularly multivariable calculus), a volume integral (∭) refers to an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculate flux densities, or to calculate mass from a corresponding density function.
In coordinates
It can also mean a triple integral within a region of a function and is usually written as:
A volume integral in cylindrical coordinates is
and a volume integral in spherical coordinates (using the ISO convention for angles with as the azimuth and measured from the polar axis (see more on conventions)) has the form
Example
Integrating the equation over a unit cube yields the following result:
So the volume of the unit cube is 1 as expected. This is rather trivial however, and a volume integral is far more powerful. For instance if we have a scalar density function on the unit cube then the volume integral will give the total mass of the cube. For example for density function:
the total mass of the cube is:
See also
Divergence theorem
Surface integral
Volume element
External links
Multivariable calculus
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https://en.wikipedia.org/wiki/The%20Fabric%20of%20the%20Cosmos
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The Fabric of the Cosmos: Space, Time, and the Texture of Reality (2004) is the second book on theoretical physics, cosmology, and string theory written by Brian Greene, professor and co-director of Columbia's Institute for Strings, Cosmology, and Astroparticle Physics (ISCAP).
Introduction
Greene begins with the key question: "what is reality?", or more specifically, "what is spacetime?" He sets out to describe the features he finds both exciting and essential to forming a full picture of the reality painted by modern science. In almost every chapter, Greene introduces basic concepts and then slowly builds to a climax, usually a scientific breakthrough. Greene then attempts to connect with his reader by posing simple analogies to help explain the meaning of a scientific concept without oversimplifying the theory behind it.
In the preface, Greene acknowledges that some parts of the book are controversial among scientists. He discusses the leading viewpoints in the main text and points of contention in the endnotes. The endnotes contain more complete explanations of points that are simplified in the main text.
Summary
Part I: Reality's Arena
The main focus of Part I is space and time.
Chapter 1, "Roads to Reality", Introduces what is to come later in the book, such as discussions revolving around classical physics, quantum mechanics, and cosmological physics.
Chapter 2, "The Universe and the Bucket", features space as its key point. The question posed by Greene is this:
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https://en.wikipedia.org/wiki/Barton%20Zwiebach
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Barton Zwiebach (born Barton Zwiebach Cantor, October 4, 1954) is a Peruvian string theorist and professor at the Massachusetts Institute of Technology.
Work
Zwiebach's undergraduate work was in Electrical Engineering at the Universidad Nacional de Ingeniería in Peru, from which he graduated in 1977.
His graduate work was in physics at the California Institute of Technology. Zwiebach obtained his Ph.D. in 1983, working under the supervision of Murray Gell-Mann. He has held postdoctoral positions at the University of California, Berkeley, and at the Massachusetts Institute of Technology, where he became an assistant professor of physics in 1987, and a permanent member of the faculty in 1994.
He is one of the world's leading experts in string field theory. He wrote the textbook A First Course in String Theory (2004, ), meant for undergraduates.
Selected publications
Professor Zwiebach's publications are available on the SPIRES HEP Literature Database.
References
External links
1954 births
Living people
Scientists from Lima
Peruvian emigrants to the United States
California Institute of Technology alumni
University of California, Berkeley staff
Peruvian physicists
Massachusetts Institute of Technology faculty
American string theorists
National University of Engineering alumni
MIT Center for Theoretical Physics faculty
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https://en.wikipedia.org/wiki/Into
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Into, entering or changing form, may also refer to:
INTO University Partnerships, a British business
Into (album), an album by the Rasmus
Into (magazine), a digital magazine owned by Grindr
Into, a male Finnish name
Irish National Teachers' Organisation
Mathematics
Into, referring to mathematical functions, taking distinct arguments to distinct values (injective)
Into, used as a multiplier in mathematical jargon in Indian English (3 into 3 = 9)
See also
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https://en.wikipedia.org/wiki/Greater%20Hartford%20Academy%20of%20Mathematics%20and%20Science
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The Academy of Aerospace and Engineering (also known as AAE, Aerospace, and Aerospace and Engineering) is a regional magnet high school located in Windsor, Connecticut. The school's half-day program operates as the Greater Hartford Academy of Mathematics And Science (also known as GHAMAS). The building houses a grade 6-12 program. It is run by the Capitol Region Education Council (CREC), one of 6 Regional Educational Service Centers (RESC) in Connecticut. Trinity College has been involved in some of the projects with GHAMAS, such as the Brain Bee, a neuroscience competition. Hartford Hospital is involved in school activities as well.
The Academy of Aerospace and Engineering was built as GHAMAS in 1999. Labs at the Academy include the Robotics, Physics, Earth Science, Biology, Cell Culture, Greenhouse & Potting, Biochemistry, Chemistry, Special Instrumentation, and Engineering Labs. There are also several smaller student laboratories which are used by students to conduct independent research through a senior design and research course called Capstone. Occasionally, speakers from industry or academia come to lecture full-day and morning half-day students (grades 9 and 10) about the field that they work in and educate them to possible careers in that field. Students partake in a variety of clubs at the high school level, including competitive FIRST Tech Challenge robotics and debate teams. Select students pursue scientific research and engineering projects throughout the year a
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https://en.wikipedia.org/wiki/Tunnel%20ionization
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In physics, tunnel ionization is a process in which electrons in an atom (or a molecule) tunnel through the potential barrier and escape from the atom (or molecule). In an intense electric field, the potential barrier of an atom (molecule) is distorted drastically. Therefore, as the length of the barrier that electrons have to pass decreases, the electrons can escape from the atom's potential more easily. Tunneling ionization is a quantum mechanical phenomenon, since in the classical picture an electron does not have sufficient energy to overcome the potential barrier of the atom.
When the atom is in a DC external field, the Coulomb potential barrier is lowered and the electron has an increased, non-zero probability of tunnelling through the potential barrier. In the case of an alternating electric field, the direction of the electric field reverses after the half period of the field. The ionized electron may come back to its parent ion. The electron may recombine with the nucleus (nuclei) and its kinetic energy is released as light (high harmonic generation). If the recombination does not occur, further ionization may proceed by collision between high-energy electrons and a parent atom (molecule). This process is known as non-sequential ionization.
DC tunneling ionization
Tunneling ionization from the ground state of a hydrogen atom in an electrostatic (DC) field was solved schematically by Lev Landau, using parabolic coordinates. This provides a simplified physical sys
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https://en.wikipedia.org/wiki/William%20Chauvenet
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William Chauvenet (24 May 1820 in Milford, Pennsylvania – 13 December 1870 in St. Paul, Minnesota) was a professor of mathematics, astronomy, navigation, and surveying who was instrumental in the establishment of the U.S. Naval Academy at Annapolis, Maryland, and later the second chancellor of Washington University in St. Louis.
Early life
William Chauvenet was born on a farm near Milford, Pennsylvania to Guillaume Marc Chauvenet, a former soldier of Napoleon's army reconverted in silk trade after the Emperor's fall, and Mary B. Kerr and was raised in Philadelphia. He entered Yale University at age 16, and graduated in 1840 with high honors. While at Yale, Chauvenet contributed to the school newspaper and was a pianist with the Beethoven Society. He was one of eight founding members of the Skull and Bones Society.
United States Navy
In 1841, he was appointed a professor of mathematics in the United States Navy, and for a while served on the USS Mississippi teaching math. His professorship led Chauvenet to see the necessity of a United States naval academy. While others had proposed the idea, no one had actually seen it through. In 1842, he was appointed head of the naval asylum in Philadelphia, Pennsylvania. At the Naval Asylum, prospective officers took an eight-month course before sailing. Chauvenet felt the course was lacking and drew up his own plan for a two-year course. Presenting to several secretaries of the navy, the course was finally accepted in 1845.
He was i
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https://en.wikipedia.org/wiki/Coulomb%20explosion
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A Coulombic explosion is a condensed-matter physics process in which a molecule or crystal lattice is destroyed by the Coulombic repulsion between its constituent atoms. Coulombic explosions are a prominent technique in laser-based machining, and appear naturally in certain high-energy reactions.
Mechanism
A Coulombic explosion begins when an intense electric field (often from a laser) excites the valence electrons in a solid, ejecting them from the system and leaving behind positively charged ions. The chemical bonds holding the solid together are weakened by the loss of the electrons, enabling the Coulombic repulsion between the ions to overcome them. The result is an explosion of ions and electrons – a plasma.
The laser must be very intense to produce a Coulomb explosion. If it is too weak, the energy given to the electrons will be transferred to the ions via electron-phonon coupling. This will cause the entire material to heat up, melt, and thermally ablate away as a plasma. The end result is similar to Coulomb explosion, except that any fine structure in the material will be damaged by thermal melting.
It may be shown that the Coulomb explosion occurs in the same parameter regime as the superradiant phase transition i.e. when the destabilizing interactions become overwhelming and dominate over the oscillatory phonon-solid binding motions.
Technological use
A Coulomb explosion is a "cold" alternative to the dominant laser etching technique of thermal ablation, which d
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https://en.wikipedia.org/wiki/Hyperbolic%20link
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In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry. A hyperbolic knot is a hyperbolic link with one component.
As a consequence of the work of William Thurston, it is known that every knot is precisely one of the following: hyperbolic, a torus knot, or a satellite knot. As a consequence, hyperbolic knots can be considered plentiful. A similar heuristic applies to hyperbolic links.
As a consequence of Thurston's hyperbolic Dehn surgery theorem, performing Dehn surgeries on a hyperbolic link enables one to obtain many more hyperbolic 3-manifolds.
Examples
Borromean rings are hyperbolic.
Every non-split, prime, alternating link that is not a torus link is hyperbolic by a result of William Menasco.
41 knot (the figure-eight knot)
52 knot (the three-twist knot)
61 knot (the stevedore knot)
62 knot
63 knot
74 knot
10 161 knot (the "Perko pair" knot)
12n242 knot
See also
SnapPea
Hyperbolic volume (knot)
Further reading
Colin Adams (1994, 2004) The Knot Book, American Mathematical Society, .
William Menasco (1984) "Closed incompressible surfaces in alternating knot and link complements", Topology 23(1):37–44.
William Thurston (1978-1981) The geometry and topology of three-manifolds, Princeton lecture notes.
External links
Colin Adams, Handbook of Knot Theory
3-manifolds
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https://en.wikipedia.org/wiki/Excision%20theorem
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In algebraic topology, a branch of mathematics, the excision theorem is a theorem about relative homology and one of the Eilenberg–Steenrod axioms. Given a topological space and subspaces and such that is also a subspace of , the theorem says that under certain circumstances, we can cut out (excise) from both spaces such that the relative homologies of the pairs into are isomorphic.
This assists in computation of singular homology groups, as sometimes after excising an appropriately chosen subspace we obtain something easier to compute.
Theorem
Statement
If are as above, we say that can be excised if the inclusion map of the pair into induces an isomorphism on the relative homologies:
The theorem states that if the closure of is contained in the interior of , then can be excised.
Often, subspaces that do not satisfy this containment criterion still can be excised—it suffices to be able to find a deformation retract of the subspaces onto subspaces that do satisfy it.
Proof Sketch
The proof of the excision theorem is quite intuitive, though the details are rather involved. The idea is to subdivide the simplices in a relative cycle in to get another chain consisting of "smaller" simplices, and continuing the process until each simplex in the chain lies entirely in the interior of or the interior of . Since these form an open cover for and simplices are compact, we can eventually do this in a finite number of steps. This process leaves the original ho
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https://en.wikipedia.org/wiki/Relative%20homology
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In algebraic topology, a branch of mathematics, the (singular) homology of a topological space relative to a subspace is a construction in singular homology, for pairs of spaces. The relative homology is useful and important in several ways. Intuitively, it helps determine what part of an absolute homology group comes from which subspace.
Definition
Given a subspace , one may form the short exact sequence
where denotes the singular chains on the space X. The boundary map on descends to and therefore induces a boundary map on the quotient. If we denote this quotient by , we then have a complex
By definition, the th relative homology group of the pair of spaces is
One says that relative homology is given by the relative cycles, chains whose boundaries are chains on A, modulo the relative boundaries (chains that are homologous to a chain on A, i.e., chains that would be boundaries, modulo A again).
Properties
The above short exact sequences specifying the relative chain groups gives rise to a chain complex of short exact sequences. An application of the snake lemma then yields a long exact sequence
The connecting map takes a relative cycle, representing a homology class in , to its boundary (which is a cycle in A).
It follows that , where is a point in X, is the n-th reduced homology group of X. In other words, for all . When , is the free module of one rank less than . The connected component containing becomes trivial in relative homology.
The excision the
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https://en.wikipedia.org/wiki/MSRI
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MSRI may refer to:
Malaysian Social Research Institute, Kuala Lumpur, assists refugees
Mathematical Sciences Research Institute, California, undertakes research in mathematics
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https://en.wikipedia.org/wiki/Ideal%20theory
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In mathematics, ideal theory is the theory of ideals in commutative rings. While the notion of an ideal exists also for non-commutative rings, a much more substantial theory exists only for commutative rings (and this article therefore only considers ideals in commutative rings.)
Throughout the articles, rings refer to commutative rings. See also the article ideal (ring theory) for basic operations such as sum or products of ideals.
Ideals in a finitely generated algebra over a field
Ideals in a finitely generated algebra over a field (that is, a quotient of a polynomial ring over a field) behave somehow nicer than those in a general commutative ring. First, in contrast to the general case, if is a finitely generated algebra over a field, then the radical of an ideal in is the intersection of all maximal ideals containing the ideal (because is a Jacobson ring). This may be thought of as an extension of Hilbert's Nullstellensatz, which concerns the case when is a polynomial ring.
Topology determined by an ideal
If I is an ideal in a ring A, then it determines the topology on A where a subset U of A is open if, for each x in U,
for some integer . This topology is called the I-adic topology. It is also called an a-adic topology if is generated by an element .
For example, take , the ring of integers and an ideal generated by a prime number p. For each integer , define when , prime to . Then, clearly,
where denotes an open ball of radius with center . Hence, t
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https://en.wikipedia.org/wiki/Ernst%20Otto%20Fischer
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Ernst Otto Fischer (; 10 November 1918 – 23 July 2007) was a German chemist who won the Nobel Prize for pioneering work in the area of organometallic chemistry.
Early life
He was born in Solln, a borough of Munich. His parents were Karl T. Fischer, Professor of Physics at the Technical University of Munich (TU), and Valentine née Danzer. He graduated in 1937 with Abitur. Before the completion of two years' compulsory military service, the Second World War broke out, and he served in Poland, France, and Russia. During a period of study leave, towards the end of 1941 he began to study chemistry at the Technical University of Munich. Following the end of the War, he was released by the Americans in the autumn of 1945 and resumed his studies.
Training
Fischer graduated from TUM in 1949. He then started his doctoral thesis as an assistant to Professor Walter Hieber in the Inorganic Chemistry Institute, His thesis was entitled "The Mechanisms of Carbon Monoxide Reactions of Nickel(II) Salts in the Presence of Dithionites and Sulfoxylates".
Research career
After receiving his doctorate in 1952, he remained at TU. He continued his research on the organometallic chemistry of the transition metal. He almost immediately challenged the structure for ferrocene as postulated by Pauson and Keally. Shortly thereafter, he published the structural data of ferrocene and the new complexes nickelocene and cobaltocene. Near the same time, he focused also on the then baffling chemistry resu
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https://en.wikipedia.org/wiki/Computational%20topology
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Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory.
A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for solving problems that arise naturally in fields such as computational geometry, graphics, robotics, structural biology and chemistry, using methods from computable topology.
Major algorithms by subject area
Algorithmic 3-manifold theory
A large family of algorithms concerning 3-manifolds revolve around normal surface theory, which is a phrase that encompasses several techniques to turn problems in 3-manifold theory into integer linear programming problems.
Rubinstein and Thompson's 3-sphere recognition algorithm. This is an algorithm that takes as input a triangulated 3-manifold and determines whether or not the manifold is homeomorphic to the 3-sphere. It has exponential run-time in the number of tetrahedral simplexes in the initial 3-manifold, and also an exponential memory profile. Moreover, it is implemented in the software package Regina. Saul Schleimer went on to show the problem lies in the complexity class NP. Furthermore, Raphael Zentner showed that the problem lies in the complexity class coNP, provided that the generalized Riemann hypothesis holds. He uses instanton gauge theory, the geometrization theorem of 3-manifolds, and subsequent work of Greg Kuperber
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https://en.wikipedia.org/wiki/Geoffrey%20Wilkinson
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Sir Geoffrey Wilkinson FRS (14 July 1921 – 26 September 1996) was a Nobel laureate English chemist who pioneered inorganic chemistry and homogeneous transition metal catalysis.
Education and early life
Wilkinson was born at Springside, Todmorden, in the West Riding of Yorkshire. His father, Henry Wilkinson, was a master house painter and decorator; his mother, Ruth, worked in a local cotton mill. One of his uncles, an organist and choirmaster, had married into a family that owned a small chemical company making Epsom and Glauber's salts for the pharmaceutical industry; this is where he first developed an interest in chemistry.
He was educated at the local council primary school and, after winning a County Scholarship in 1932, went to Todmorden Grammar School. His physics teacher there, Luke Sutcliffe, had also taught Sir John Cockcroft, who received a Nobel Prize for "splitting the atom". In 1939 he obtained a Royal Scholarship for study at Imperial College London, from where he graduated in 1941, with his PhD awarded in 1946 entitled "Some physico-chemical observations of hydrolysis in the homogeneous vapour phase".
Career and research
In 1942 Professor Friedrich Paneth was recruiting young chemists for the nuclear energy project. Wilkinson joined and was sent out to Canada, where he stayed in Montreal and later Chalk River Laboratories until he could leave in 1946. For the next four years he worked with Professor Glenn T. Seaborg at University of California, Berkeley, mo
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https://en.wikipedia.org/wiki/Nothing-up-my-sleeve%20number
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In cryptography, nothing-up-my-sleeve numbers are any numbers which, by their construction, are above suspicion of hidden properties. They are used in creating cryptographic functions such as hashes and ciphers. These algorithms often need randomized constants for mixing or initialization purposes. The cryptographer may wish to pick these values in a way that demonstrates the constants were not selected for a nefarious purpose, for example, to create a backdoor to the algorithm. These fears can be allayed by using numbers created in a way that leaves little room for adjustment. An example would be the use of initial digits from the number as the constants. Using digits of millions of places after the decimal point would not be considered trustworthy because the algorithm designer might have selected that starting point because it created a secret weakness the designer could later exploit.
Digits in the positional representations of real numbers such as , e, and irrational roots are believed to appear with equal frequency (see normal number). Such numbers can be viewed as the opposite extreme of Chaitin–Kolmogorov random numbers in that they appear random but have very low information entropy. Their use is motivated by early controversy over the U.S. Government's 1975 Data Encryption Standard, which came under criticism because no explanation was supplied for the constants used in its S-box (though they were later found to have been carefully selected to protect against t
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https://en.wikipedia.org/wiki/Water%20of%20crystallization
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In chemistry, water(s) of crystallization or water(s) of hydration are water molecules that are present inside crystals. Water is often incorporated in the formation of crystals from aqueous solutions. In some contexts, water of crystallization is the total mass of water in a substance at a given temperature and is mostly present in a definite (stoichiometric) ratio. Classically, "water of crystallization" refers to water that is found in the crystalline framework of a metal complex or a salt, which is not directly bonded to the metal cation.
Upon crystallization from water, or water-containing solvents, many compounds incorporate water molecules in their crystalline frameworks. Water of crystallization can generally be removed by heating a sample but the crystalline properties are often lost.
Compared to inorganic salts, proteins crystallize with large amounts of water in the crystal lattice. A water content of 50% is not uncommon for proteins.
Applications
Knowledge of hydration is essential for calculating the masses for many compounds. The reactivity of many salt-like solids is sensitive to the presence of water.
The hydration and dehydration of salts is central to the use of phase-change materials for energy storage.
Position in the crystal structure
A salt with associated water of crystallization is known as a hydrate. The structure of hydrates can be quite elaborate, because of the existence of hydrogen bonds that define polymeric structures.
Historically, the
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https://en.wikipedia.org/wiki/Igor%20Gamow
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Rustem Igor Gamow (November 4, 1935, in Georgetown, D.C. – April 15, 2021) was a microbiology professor at the University of Colorado and inventor. His best known inventions included the Gamow bag and the Shallow Underwater Breathing Apparatus. He was fired from CU in 2004 following sexual harassment and assault charges.
Early life and education
Rustem Igor Gamow was the son of Soviet émigré physicists George Gamow and Lyubov Vokhmintseva "Rho" Gamow. Finishing high school at age 17, he joined the National Ballet Company. He worked breaking horses, delivering packages by motorcycle, and teaching karate before enrolling at the University of Colorado in 1958, where his father taught. Igor Gamow received a B.A. and M.S. in biology, and a Ph.D. in biophysics, all at University of Colorado.
Research
Gamow worked on Phycomyces blakesleeanus during postdoctoral research under Max Delbrück at Caltech. At CU-Boulder, he did Phycomyces research for over twenty years, mainly on the avoidance and anemotropic responses, helical growth, and cell-wall mechanical properties. He also studied the infrared-detectors of the Boa constrictor.
An avid outdoorsman, Gamow developed a number of inventions for safety in outdoor activities. His first important one, patented in 1990, was the Gamow bag enabling mountain climbers to avoid altitude sickness by raising the surrounding pressure. Sir Edmund Hillary, the first expedition leader to summit Mount Everest, wrote him in congratulation. Ano
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https://en.wikipedia.org/wiki/Electronic%20Systems%20Center
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The Electronic Systems Center was a product center of Air Force Materiel Command (AFMC) headquartered at Hanscom Air Force Base, Massachusetts. Its mission was to develop and acquire command and control, communications, computer, and intelligence systems. ESC consisted of professional teams specializing in engineering, computer science, and business management. The teams supervised the design, development, testing, production, and deployment of command and control systems. Two of ESC's most well-known developments were the Boeing E-3 Sentry Airborne Warning and Control System (AWACS), developed in the 1970s, and the Joint Surveillance Target Attack Radar System (Joint STARS), developed in the 1980s.
The Electronic Systems Center served into five decades as the Air Force's organization for developing and acquiring Command and Control (C2) systems. As of December 2004, ESC managed approximately two hundred programs ranging from secure communications systems to mission planning systems. ESC had an annual budget of over $3 billion and more than eighty-seven hundred personnel. In addition to the Air Force, ESC works with other branches of the United States Department of Defense, the North American Aerospace Defense Command (NORAD), the National Aeronautics and Space Administration (NASA), the Federal Aviation Administration (FAA), the North Atlantic Treaty Organization (NATO), and foreign governments.
Due to AFMC restructuring ESC was inactivated on 1 October 2012.
History
ES
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https://en.wikipedia.org/wiki/Joachim%20Lambek
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Joachim "Jim" Lambek (5 December 1922 – 23 June 2014) was a Canadian mathematician. He was Peter Redpath Emeritus Professor of Pure Mathematics at McGill University, where he earned his PhD degree in 1950 with Hans Zassenhaus as advisor.
Biography
Lambek was born in Leipzig, Germany, where he attended a Gymnasium. He came to England in 1938 as a refugee on the Kindertransport. From there he was interned as an enemy alien and deported to a prison work camp in New Brunswick, Canada. There, he began in his spare time a mathematical apprenticeship with Fritz Rothberger, also
interned, and wrote the McGill Junior Matriculation in fall of 1941. In the spring of 1942, he was released and settled in Montreal, where he entered studies at McGill University, graduating with an honours mathematics degree in 1945 and an MSc a year later. In 1950, he completed his doctorate under Hans Zassenhaus becoming McGill's first PhD in mathematics.
Lambek became assistant professor at McGill; he was made a full professor in 1963. He spent his sabbatical year 1965–66 in at the Institute for Mathematical Research at ETH Zurich, where Beno Eckmann had gathered together a group of researchers interested in algebraic topology and category theory, including Bill Lawvere. There Lambek reoriented his research into category theory.
Lambek retired in 1992 but continued his involvement at McGill's mathematics department. In 2000 a festschrift celebrating Lambek's contributions to mathematical structures i
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https://en.wikipedia.org/wiki/Walter%20Sutton
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Walter Stanborough Sutton (April 5, 1877 – November 10, 1916) was an American geneticist and biologist whose most significant contribution to present-day biology was his theory that the Mendelian laws of inheritance could be applied to chromosomes at the cellular level of living organisms. This is now known as the Boveri–Sutton chromosome theory.
Early life
Sutton was born in Utica, New York, and was raised on a farm as the fifth of seven sons to Judge William B. Sutton and his wife, Agnes Black Sutton, in Russell, Kansas. On the farm, he developed a mechanical aptitude by maintaining and repairing farm equipment, an aptitude that proved helpful later as he worked on oil drilling rigs and with medical instrumentation.
University of Kansas
After graduating high school in Russell, he enrolled at the University of Kansas in engineering in 1896. Following the death of his younger brother (John) from typhus in 1897, Sutton switched his major to biology with an interest in medicine. While at the University of Kansas, both he and his older brother, William Sutton, played basketball for Dr. James Naismith. Sutton distinguished himself as a student by being elected to both Phi Beta Kappa and Sigma Xi and receiving both bachelor's and master's degrees by 1901. For his Masters thesis, he studied the spermatogenesis of Brachystola magna, a large grasshopper indigenous to the farmlands upon which Sutton was raised.
Columbia University
Considering the advice of his mentor at KU, Dr
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https://en.wikipedia.org/wiki/Solid%20torus
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In mathematics, a solid torus is the topological space formed by sweeping a disk around a circle. It is homeomorphic to the Cartesian product of the disk and the circle, endowed with the product topology.
A standard way to visualize a solid torus is as a toroid, embedded in 3-space. However, it should be distinguished from a torus, which has the same visual appearance: the torus is the two-dimensional space on the boundary of a toroid, while the solid torus includes also the compact interior space enclosed by the torus.
A solid torus is a torus plus the volume inside the torus. Real-world objects that approximate a solid torus include O-rings, non-inflatable lifebuoys, ring doughnuts, and bagels.
Topological properties
The solid torus is a connected, compact, orientable 3-dimensional manifold with boundary. The boundary is homeomorphic to , the ordinary torus.
Since the disk is contractible, the solid torus has the homotopy type of a circle, . Therefore the fundamental group and homology groups are isomorphic to those of the circle:
See also
Cheerios
Hyperbolic Dehn surgery
Reeb foliation
Whitehead manifold
Donut
References
3-manifolds
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https://en.wikipedia.org/wiki/Club%20set
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In mathematics, particularly in mathematical logic and set theory, a club set is a subset of a limit ordinal that is closed under the order topology, and is unbounded (see below) relative to the limit ordinal. The name club is a contraction of "closed and unbounded".
Formal definition
Formally, if is a limit ordinal, then a set is closed in if and only if for every if then Thus, if the limit of some sequence from is less than then the limit is also in
If is a limit ordinal and then is unbounded in if for any there is some such that
If a set is both closed and unbounded, then it is a club set. Closed proper classes are also of interest (every proper class of ordinals is unbounded in the class of all ordinals).
For example, the set of all countable limit ordinals is a club set with respect to the first uncountable ordinal; but it is not a club set with respect to any higher limit ordinal, since it is neither closed nor unbounded.
If is an uncountable initial ordinal, then the set of all limit ordinals is closed unbounded in In fact a club set is nothing else but the range of a normal function (i.e. increasing and continuous).
More generally, if is a nonempty set and is a cardinal, then (the set of subsets of of cardinality ) is club if every union of a subset of is in and every subset of of cardinality less than is contained in some element of (see stationary set).
The closed unbounded filter
Let be a limit ordinal of uncountable cofina
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