source
stringlengths 31
207
| text
stringlengths 12
1.5k
|
|---|---|
https://en.wikipedia.org/wiki/Maurer%E2%80%93Cartan%20form
|
In mathematics, the Maurer–Cartan form for a Lie group is a distinguished differential one-form on that carries the basic infinitesimal information about the structure of . It was much used by Élie Cartan as a basic ingredient of his method of moving frames, and bears his name together with that of Ludwig Maurer.
As a one-form, the Maurer–Cartan form is peculiar in that it takes its values in the Lie algebra associated to the Lie group . The Lie algebra is identified with the tangent space of at the identity, denoted . The Maurer–Cartan form is thus a one-form defined globally on which is a linear mapping of the tangent space at each into . It is given as the pushforward of a vector in along the left-translation in the group:
Motivation and interpretation
A Lie group acts on itself by multiplication under the mapping
A question of importance to Cartan and his contemporaries was how to identify a principal homogeneous space of . That is, a manifold identical to the group , but without a fixed choice of unit element. This motivation came, in part, from Felix Klein's Erlangen programme where one was interested in a notion of symmetry on a space, where the symmetries of the space were transformations forming a Lie group. The geometries of interest were homogeneous spaces , but usually without a fixed choice of origin corresponding to the coset .
A principal homogeneous space of is a manifold abstractly characterized by having a free and transitive action of
|
https://en.wikipedia.org/wiki/Ramachandran%20plot
|
In biochemistry, a Ramachandran plot (also known as a Rama plot, a Ramachandran diagram or a [φ,ψ] plot), originally developed in 1963 by G. N. Ramachandran, C. Ramakrishnan, and V. Sasisekharan, is a way to visualize energetically allowed regions for backbone dihedral angles ψ against φ of amino acid residues in protein structure. The figure on the left illustrates the definition of the φ and ψ backbone dihedral angles (called φ and φ' by Ramachandran). The ω angle at the peptide bond is normally 180°, since the partial-double-bond character keeps the peptide bond planar. The figure in the top right shows the allowed φ,ψ backbone conformational regions from the Ramachandran et al. 1963 and 1968 hard-sphere calculations: full radius in solid outline, reduced radius in dashed, and relaxed tau (N-Cα-C) angle in dotted lines. Because dihedral angle values are circular and 0° is the same as 360°, the edges of the Ramachandran plot "wrap" right-to-left and bottom-to-top. For instance, the small strip of allowed values along the lower-left edge of the plot are a continuation of the large, extended-chain region at upper left.
Uses
A Ramachandran plot can be used in two somewhat different ways. One is to show in theory which values, or conformations, of the ψ and φ angles are possible for an amino-acid residue in a protein (as at top right). A second is to show the empirical distribution of datapoints observed in a single structure (as at right, here) in usage for structure validati
|
https://en.wikipedia.org/wiki/Indecomposability
|
Indecomposability or indecomposable may refer to any of several subjects in mathematics:
Indecomposable module, in algebra
Indecomposable distribution, in probability
Indecomposable continuum, in topology
Indecomposability (intuitionistic logic), a principle in constructive analysis and in computable analysis
Indecomposability of a polynomial in polynomial decomposition
A property of certain ordinals; see additively indecomposable ordinal
|
https://en.wikipedia.org/wiki/Functional%20calculus
|
In mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators. It is now a branch (more accurately, several related areas) of the field of functional analysis, connected with spectral theory. (Historically, the term was also used synonymously with calculus of variations; this usage is obsolete, except for functional derivative. Sometimes it is used in relation to types of functional equations, or in logic for systems of predicate calculus.)
If is a function, say a numerical function of a real number, and is an operator, there is no particular reason why the expression should make sense. If it does, then we are no longer using on its original function domain. In the tradition of operational calculus, algebraic expressions in operators are handled irrespective of their meaning. This passes nearly unnoticed if we talk about 'squaring a matrix', though, which is the case of and an matrix. The idea of a functional calculus is to create a principled approach to this kind of overloading of the notation.
The most immediate case is to apply polynomial functions to a square matrix, extending what has just been discussed. In the finite-dimensional case, the polynomial functional calculus yields quite a bit of information about the operator. For example, consider the family of polynomials which annihilates an operator . This family is an ideal in the ring of polynomials. Furthermore, it is a nontrivial ideal: let be th
|
https://en.wikipedia.org/wiki/Minimal%20counterexample
|
In mathematics, a minimal counterexample is the smallest example which falsifies a claim, and a proof by minimal counterexample is a method of proof which combines the use of a minimal counterexample with the ideas of proof by induction and proof by contradiction. More specifically, in trying to prove a proposition P, one first assumes by contradiction that it is false, and that therefore there must be at least one counterexample. With respect to some idea of size (which may need to be chosen carefully), one then concludes that there is such a counterexample C that is minimal. In regard to the argument, C is generally something quite hypothetical (since the truth of P excludes the possibility of C), but it may be possible to argue that if C existed, then it would have some definite properties which, after applying some reasoning similar to that in an inductive proof, would lead to a contradiction, thereby showing that the proposition P is indeed true.
If the form of the contradiction is that we can derive a further counterexample D, that is smaller than C in the sense of the working hypothesis of minimality, then this technique is traditionally called proof by infinite descent. In which case, there may be multiple and more complex ways to structure the argument of the proof.
The assumption that if there is a counterexample, there is a minimal counterexample, is based on a well-ordering of some kind. The usual ordering on the natural numbers is clearly possible, by the mo
|
https://en.wikipedia.org/wiki/ZL
|
ZL may refer to:
Aviation
Hazelton Airlines (1953–2001; IATA: ZL)
Rex Airlines (founded 2002; IATA: ZL)
ZL, an unused aircraft registration prefix for New Zealand
Science, technology and mathematics
ZL, ITU prefix for New Zealand, in radio and television
Zorn's lemma, a proposition in set theory
ZL, a Mazda Z5 engine variant
Other uses
Polish zloty (sign: zł), the currency of Poland
z"l, an honorific for the dead in Judaism
ZL, assistant (with ZR and ZY) of Golden Age superhero Masked Marvel (Centaur Publications)
|
https://en.wikipedia.org/wiki/Fluidics
|
Fluidics, or fluidic logic, is the use of a fluid to perform analog or digital operations similar to those performed with electronics.
The physical basis of fluidics is pneumatics and hydraulics, based on the theoretical foundation of fluid dynamics. The term fluidics is normally used when devices have no moving parts, so ordinary hydraulic components such as hydraulic cylinders and spool valves are not considered or referred to as fluidic devices.
A jet of fluid can be deflected by a weaker jet striking it at the side. This provides nonlinear amplification, similar to the transistor used in electronic digital logic. It is used mostly in environments where electronic digital logic would be unreliable, as in systems exposed to high levels of electromagnetic interference or ionizing radiation.
Nanotechnology considers fluidics as one of its instruments. In this domain, effects such as fluid–solid and fluid–fluid interface forces are often highly significant. Fluidics have also been used for military applications.
History
In 1920, Nikola Tesla patented a valvular conduit or Tesla valve that works as a fluidic diode. It's a leaky diode, i.e. the reverse flow is non-zero for any applied pressure difference. Tesla valve also has non-linear response, as it diodicity has frequency dependence. It could be used in fluid circuits, such as a full-wave rectifier, to convert AC to DC.
In 1957, Billy M. Horton of the Harry Diamond Laboratories (which later became a part of the Army R
|
https://en.wikipedia.org/wiki/Out%20of%20Control%20%28Kelly%20book%29
|
Out of Control: The New Biology of Machines, Social Systems, and the Economic World () is a 1992 book by Kevin Kelly. Major themes in Out of Control are cybernetics, emergence, self-organization, complex systems, negentropy and chaos theory and it can be seen as a work of techno-utopianism.
Summary
The central theme of the book is that several fields of contemporary science and philosophy point in the same direction: intelligence is not organized in a centralized structure but much more like a bee-hive of small simple components. Kelly applies this view to bureaucratic organizations, intelligent computers as well as to the human brain.
Reception
The book was not widely reviewed when first released in 1992, but got visibly reviewed and extensively cited during the next several years. Reviews often discussed Kelly's hive-mind analogy as a metaphor for the New Economy.
Reviewers have called this book a "mind-expanding exploration" (Publishers Weekly) and "the best of an important new genre" (Forbes ASAP).
Critics of the book have contended that its position leaves us without a critical approach to politics and social power.
References
Further reading
The book's homepage (includes the complete book online)
1992 non-fiction books
1992 in the environment
Systems theory books
Works about technology
Futurology books
Collective intelligence
|
https://en.wikipedia.org/wiki/Archerite
|
Archerite (IMA symbol: Aht) is a phosphate mineral with chemical formula (K,NH4)H2PO4. It's named after Michael Archer (born 25 March 1945), professor of Biology, University of New South Wales. Its type locality is Petrogale Cave, Madura Roadhouse, Dundas Shire, Western Australia. It occurs in guano containing caves as wall encrustations and stalactites.
References
Phosphate minerals
Tetragonal minerals
Minerals in space group 122
|
https://en.wikipedia.org/wiki/William%20Stallings
|
William Stallings is an American author. He has written computer science textbooks on operating systems, computer networks, computer organization, and cryptography.
Early life
Stallings earned his B.S. in electrical engineering from University of Notre Dame and his PhD in computer science from Massachusetts Institute of Technology.
Career
He maintains a website titled Computer Science Student Resource. He has authored 17 titles, and counting revised editions, a total of over 40 books on these subjects. He has been a technical contributor, technical manager, and an executive with several high-technology firms. He works as an independent consultant whose clients have included computer and networking manufacturers and customers, software development firms, and leading-edge government research institutions.
Recognition
He was awarded Computer Science textbook of the year from the Text and Academic Authors Association three times.
Books
Computer Organization and Architecture
Cryptography and Network Security: Principles and Practice
Data and Computer Communications
Operating Systems - Internals and Design Principles
Wireless Communications & Networks
Computer Security: Principles and Practice
Local and Metropolitan Area Networks
Network Security Essentials: Applications and Standards
Business Data Communications - Infrastructure, Networking and Security
References
External links
Williamstallings.com - Website for the books of William Stallings
Computer Science S
|
https://en.wikipedia.org/wiki/Algebraic
|
Algebraic may refer to any subject related to algebra in mathematics and related branches like algebraic number theory and algebraic topology. The word algebra itself has several meanings.
Algebraic may also refer to:
Algebraic data type, a datatype in computer programming each of whose values is data from other datatypes wrapped in one of the constructors of the datatype
Algebraic numbers, a complex number that is a root of a non-zero polynomial in one variable with integer coefficients
Algebraic functions, functions satisfying certain polynomials
Algebraic element, an element of a field extension which is a root of some polynomial over the base field
Algebraic extension, a field extension such that every element is an algebraic element over the base field
Algebraic definition, a definition in mathematical logic which is given using only equalities between terms
Algebraic structure, a set with one or more finitary operations defined on it
Algebraic, the order of entering operations when using a calculator (contrast reverse Polish notation)
Algebraic sum, a summation of quantities that takes into account their signs; e.g. the algebraic sum of 4, 3, and -8 is -1.
See also
Algebra (disambiguation)
Algebraic notation (disambiguation)
|
https://en.wikipedia.org/wiki/Biological%20patents%20in%20the%20United%20States
|
As with all utility patents in the United States, a biological patent provides the patent holder with the right to exclude others from making, using, selling, or importing the claimed invention or discovery in biology for a limited period of time - for patents filed after 1998, 20 years from the filing date.
Until recently, natural biological substances themselves could be patented (apart from any associated process or usage) in the United States if they were sufficiently "isolated" from their naturally occurring states. Prominent historical examples of such patents on isolated products of nature include adrenaline, insulin, vitamin B12, and gene patents. However, the US Supreme Court ruled in 2013 that mere isolation by itself is not sufficient for something to be deemed inventive subject matter.
History
The United States has been patenting chemical compositions based upon human products for over 100 years.
The first patent for a human product was granted on March 20, 1906, for a purified form of adrenaline. It was challenged and upheld in Parke-Davis v. Mulford. Judge Hand argued that natural substances when they are purified are more useful than the original natural substances.
The 1970s marked the first time when scientists patented methods on their biotechnological inventions with recombinant DNA. It wasn’t until 1980 that patents for whole-scale living organisms were permitted. In 1980, the U.S. Supreme Court, in Diamond v. Chakrabarty, upheld the first patent on a
|
https://en.wikipedia.org/wiki/Temporal%20paradox
|
A temporal paradox, time paradox, or time travel paradox, is a paradox, an apparent contradiction, or logical contradiction associated with the idea of time travel or other foreknowledge of the future. While the notion of time travel to the future complies with the current understanding of physics via relativistic time dilation, temporal paradoxes arise from circumstances involving hypothetical time travel to the past – and are often used to demonstrate its impossibility. Temporal paradoxes fall into three broad groups: bootstrap paradoxes, consistency paradoxes, and Newcomb's paradox.
Types
Temporal paradoxes fall into three broad groups: bootstrap paradoxes, consistency paradoxes, and Newcomb's paradox. Bootstrap paradoxes violate causality by allowing future events to influence the past and cause themselves, or "bootstrapping", which derives from the idiom "." Consistency paradoxes, on the other hand, are those where future events influence the past to cause an apparent contradiction, exemplified by the grandfather paradox, where a person travels to the past to kill their grandfather. Newcomb's paradox stems from the apparent contradictions that stem from the assumptions of both free will and foreknowledge of future events. All of these are sometimes referred to individually as "causal loops." The term "time loop" is sometimes referred to as a causal loop, but although they appear similar, causal loops are unchanging and self-originating, whereas time loops are constantl
|
https://en.wikipedia.org/wiki/Riesz%E2%80%93Thorin%20theorem
|
In mathematics, the Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem, is a result about interpolation of operators. It is named after Marcel Riesz and his student G. Olof Thorin.
This theorem bounds the norms of linear maps acting between spaces. Its usefulness stems from the fact that some of these spaces have rather simpler structure than others. Usually that refers to which is a Hilbert space, or to and . Therefore one may prove theorems about the more complicated cases by proving them in two simple cases and then using the Riesz–Thorin theorem to pass from the simple cases to the complicated cases. The Marcinkiewicz theorem is similar but applies also to a class of non-linear maps.
Motivation
First we need the following definition:
Definition. Let be two numbers such that . Then for define by: .
By splitting up the function in as the product and applying Hölder's inequality to its power, we obtain the following result, foundational in the study of -spaces:
This result, whose name derives from the convexity of the map on , implies that .
On the other hand, if we take the layer-cake decomposition , then we see that and , whence we obtain the following result:
In particular, the above result implies that is included in , the sumset of and in the space of all measurable functions. Therefore, we have the following chain of inclusions:
In practice, we often encounter operators defined
|
https://en.wikipedia.org/wiki/Richard%20Kuhn
|
Richard Johann Kuhn (; 3 December 1900 – 1 August 1967) was an Austrian-German biochemist who was awarded the Nobel Prize in Chemistry in 1938 "for his work on carotenoids and vitamins".
Biography
Early life
Kuhn was born in Vienna, Austria, where he attended grammar school and high school. His interest in chemistry surfaced early; however he had many interests and decided late to study chemistry. Between 1910 and 1918 he was a schoolmate of Wolfgang Pauli, who was awarded the Nobel Prize in Physics for 1945. Beginning in 1918, Kuhn attended lectures at the University of Vienna in chemistry. He finished his chemistry studies at University of Munich and received his doctoral degree in 1922 with Richard Willstätter for a scientific work on enzymes.
After graduating, Kuhn continued his scientific career, first in Munich, then at the ETH Zurich and from 1929 onwards at the University of Heidelberg, where he was head of the chemistry department beginning in 1937. In 1928 he married Daisy Hartmann and the couple subsequently had two sons and four daughters.
Research
Kuhn's areas of study included: investigations of theoretical problems of organic chemistry (stereochemistry of aliphatic and aromatic compounds; syntheses of polyenes and cumulenes; constitution and colour; the acidity of hydrocarbons), as well as extensive fields in biochemistry (carotenoids; flavins; vitamins and enzymes). Specifically, he carried out important work on vitamin B2 and the antidermatitis vitamin
|
https://en.wikipedia.org/wiki/Westminster%20%28disambiguation%29
|
Westminster is an area within the City of Westminster, London, UK.
Westminster may also refer to:
Education
University of Westminster, London, U.D.
Westminster College of Chemistry and Pharmacy, a defunct College of Chemistry and Pharmacy in London, founded in 1841
Westminster Seminary California, a Reformed seminary in Escondido, California, U.S.
Westminster Theological Seminary, a Reformed seminary headquartered in Philadelphia, Pennsylvania, U.S.
Westminster Academy
Westminster Academy (Florida), Fort Lauderdale, Florida, U.S.
Westminster Academy, London, London, UK
Westminster Academy (Tennessee), Memphis, Tennessee, U.S.
Westminster Christian Academy
Westminster Christian Academy (Georgia), Watkinsville, Georgia, U.S.
Westminster Christian Academy (Louisiana), Opelousas, Louisiana, U.S.
Westminster Christian Academy (Missouri), St. Louis, Missouri, U.S.
Westminster College
City of Westminster College, London, U.K.
Westminster Choir College, in Princeton, New Jersey, U.S.
Westminster College (Utah), Salt Lake City, Utah, U.S.
Westminster College, Cambridge, U.K.
Westminster College, Oxford
former name of Wesley College (Mississippi), U.S.
Westminster College (Missouri), Fulton, Missouri, U.S.
Westminster College (Pennsylvania), U.S.
Westminster College, Texas, U.S.
Westminster Kingsway College, London, U.K.
Other schools
Westminster High School (disambiguation)
Westminster School (disambiguation)
Entertainment
"Westminster", a song written by James Montgomery and r
|
https://en.wikipedia.org/wiki/Nobuo%20Yoneda
|
was a Japanese mathematician and computer scientist.
In 1952, he graduated the Department of Mathematics, the Faculty of Science, the University of Tokyo, and obtained his Bachelor of Science. That same year, he was appointed Assistant Professor in the Department of Mathematics of the University of Tokyo. He obtained his Doctor of Science (DSc) degree from the University of Tokyo in 1961, under the direction of Shokichi Iyanaga. In 1962, he was appointed Associate Professor in the Faculty of Science at Gakushuin University, and was promoted in 1966 to the rank of Professor. He became a professor of Theoretical Foundation of Information Science in 1972. After retiring from the University of Tokyo in 1990, he moved to Tokyo Denki University.
The Yoneda lemma in category theory and the Yoneda product in homological algebra are named after him.
In computer science, he is known for his work on dialects of the programming language ALGOL. He became involved with developing international standards in programming and informatics, as a Japanese representative on the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, supports, and maintains the languages ALGOL 60 and ALGOL 68.
References
External links
1930 births
1996 deaths
Japanese computer scientists
20th-century Japanese mathematicians
University of Tokyo alumni
Academic staff of the University of Tokyo
Academic staff of Gakushuin Universi
|
https://en.wikipedia.org/wiki/Max%20Planck%20Institute%20for%20Evolutionary%20Anthropology
|
The Max Planck Institute for Evolutionary Anthropology (, shortened to MPI EVA) is a research institute based in Leipzig, Germany, that was founded in 1997. It is part of the Max Planck Society network.
Well-known scientists currently based at the institute include founding director Svante Pääbo and Johannes Krause (genetics), Christophe Boesch (primatology), Jean-Jacques Hublin (human evolution), Richard McElreath (evolutionary ecology), and Russell Gray (linguistic and cultural evolution).
Departments
The institute comprises six departments, several Research Groups, and The Leipzig School of Human Origins. Currently, approximately 375 people are employed at the institute. The former department of Linguistics, which existed from 1998 to 2015, was closed in May 2015, upon the retirement of its director, Bernard Comrie. The former department of Developmental and Comparative Psychology operated from 1998 to 2018 under director Michael Tomasello.
Department of Archeogenetics (Johannes Krause)
Department of Comparative Cultural Psychology (Daniel Haun)
Department of Evolutionary Genetics (Svante Pääbo)
Neandertals and More (Svante Pääbo)
Human Population History (Mark Stoneking)
The Minerva Research Group for Bioinformatics (Janet Kelso)
Advanced DNA sequencing techniques (Matthias Meyer)
Max Planck Research Group on Single Cell Genomics (Barbara Treutlein)
Genetic Diversity through Space and Time (Ben Peter)
Department of Human Behavior, Ecology and Culture (Richard McE
|
https://en.wikipedia.org/wiki/Integrability%20conditions%20for%20differential%20systems
|
In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of the way a differential form restricts to a submanifold, and the fact that this restriction is compatible with the exterior derivative. This is one possible approach to certain over-determined systems, for example, including Lax pairs of integrable systems. A Pfaffian system is specified by 1-forms alone, but the theory includes other types of example of differential system. To elaborate, a Pfaffian system is a set of 1-forms on a smooth manifold (which one sets equal to 0 to find solutions to the system).
Given a collection of differential 1-forms on an -dimensional manifold , an integral manifold is an immersed (not necessarily embedded) submanifold whose tangent space at every point is annihilated by (the pullback of) each .
A maximal integral manifold is an immersed (not necessarily embedded) submanifold
such that the kernel of the restriction map on forms
is spanned by the at every point of . If in addition the are linearly independent, then is ()-dimensional.
A Pfaffian system is said to be completely integrable if admits a foliation by maximal integral manifolds. (Note that the foliation need not be regular; i.e. the leaves of the foliation might not be embedded submanifolds.)
An integrability condition is a condi
|
https://en.wikipedia.org/wiki/European%20Mathematical%20Society
|
The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The current president is Jan Philip Solovej, professor at the Department of Mathematics at the University of Copenhagen.
Goals
The Society seeks to serve all kinds of mathematicians in universities, research institutes and other forms of higher education. Its aims are to
Promote mathematical research, both pure and applied,
Assist and advise on problems of mathematical education,
Concern itself with the broader relations of mathematics to society,
Foster interaction between mathematicians of different countries,
Establish a sense of identity amongst European mathematicians,
Represent the mathematical community in supra-national institutions.
The EMS is itself an Affiliate Member of the International Mathematical Union and an Associate Member of the International Council for Industrial and Applied Mathematics.
History
The precursor to the EMS, the European Mathematical Council was founded in 1978 at the International Congress of Mathematicians in Helsinki. This informal federation of mathematical societies was chaired by Sir Michael Atiyah. The European Mathematical Society was founded on 28 October 1990 in Mądralin near Warsaw, Poland, with Friedrich Hirzebruch as founding President. Initially, the EMS had 27 member societies. The first Eur
|
https://en.wikipedia.org/wiki/Preimage%20attack
|
In cryptography, a preimage attack on cryptographic hash functions tries to find a message that has a specific hash value. A cryptographic hash function should resist attacks on its preimage (set of possible inputs).
In the context of attack, there are two types of preimage resistance:
preimage resistance: for essentially all pre-specified outputs, it is computationally infeasible to find any input that hashes to that output; i.e., given , it is difficult to find an such that .
second-preimage resistance: for a specified input, it is computationally infeasible to find another input which produces the same output; i.e., given , it is difficult to find a second input such that .
These can be compared with a collision resistance, in which it is computationally infeasible to find any two distinct inputs , that hash to the same output; i.e., such that .
Collision resistance implies second-preimage resistance, but does not guarantee preimage resistance. Conversely, a second-preimage attack implies a collision attack (trivially, since, in addition to , is already known right from the start).
Applied preimage attacks
By definition, an ideal hash function is such that the fastest way to compute a first or second preimage is through a brute-force attack. For an -bit hash, this attack has a time complexity , which is considered too high for a typical output size of = 128 bits. If such complexity is the best that can be achieved by an adversary, then the hash function is co
|
https://en.wikipedia.org/wiki/Collision%20attack
|
In cryptography, a collision attack on a cryptographic hash tries to find two inputs producing the same hash value, i.e. a hash collision. This is in contrast to a preimage attack where a specific target hash value is specified.
There are roughly two types of collision attacks:
Classical collision attack Find two different messages m1 and m2 such that hash(m1) = hash(m2).
More generally:
Chosen-prefix collision attack Given two different prefixes p1 and p2, find two suffixes s1 and s2 such that hash(p1 ∥ s1) = hash(p2 ∥ s2), where ∥ denotes the concatenation operation.
Classical collision attack
Much like symmetric-key ciphers are vulnerable to brute force attacks, every cryptographic hash function is inherently vulnerable to collisions using a birthday attack. Due to the birthday problem, these attacks are much faster than a brute force would be. A hash of n bits can be broken in 2n/2 time steps (evaluations of the hash function).
Mathematically stated, a collision attack finds two different messages m1 and m2, such that hash(m1) = hash(m2). In a classical collision attack, the attacker has no control over the content of either message, but they are arbitrarily chosen by the algorithm.
More efficient attacks are possible by employing cryptanalysis to specific hash functions. When a collision attack is discovered and is found to be faster than a birthday attack, a hash function is often denounced as "broken". The NIST hash function competition was largely induced by publi
|
https://en.wikipedia.org/wiki/Assortment
|
Assortment may refer to:
Assortment (assortiment, the parts of a clockwork movement other than the ébauche
Assortment (album), by Atomic Rooster, 1973
See also
Law of independent assortment in genetics
Retail assortment strategies
|
https://en.wikipedia.org/wiki/Vijay%20S.%20Pande
|
Vijay Satyanand Pande is a Trinidadian–American scientist and venture capitalist. Pande is the former director of the biophysics program and is best known for orchestrating the distributed computing disease research project known as Folding@home. His research is focused on distributed computing and computer-modelling of microbiology and on improving computer simulations regarding drug-binding, protein design, and synthetic bio-mimetic polymers. Pande became the ninth general partner at venture capital firm Andreessen Horowitz in November 2015. He is the founding investor of their Bio + Health Fund.
Career
Pande is an adjunct professor of bioengineering at Stanford University. Previously, he was the Henry Dreyfus Professor of Chemistry and professor of structural biology and of computer science. He was also director of the biophysics program.
Pande serves on the boards of Apeel Sciences, Bayesian Health, BioAge Labs, Citizen, Devoted Health, Freenome, Insitro, Nautilus Biotechnology, Nobell, Omada Health, Q.bio, and Scribe Therapeutics, a CRISPR company co-founded by 2020 Nobel Laureate Jennifer Doudna. He has also been a founder and advisor to startups in Silicon Valley.
Pande has written for TIME, STAT News, Fortune, and the New York Times, among others.
Globavir Biosciences, Inc.
In 2014, Pande co-founded Globavir Biosciences, an infectious disease startup addressing antibiotic resistance threats in developed countries as well as needs in viral infections around the
|
https://en.wikipedia.org/wiki/Space%20Combat
|
Space Combat is a game produced by Laminar Research to provide a simulation of space combat with accurate physics, unlike most other games of the same genre. Although originally a shareware game, the latest version of Space Combat—1.40—was released as freeware.
In the game, the laws of physics are modeled fully, so ships do not behave like aircraft: they behave like spaceships in a frictionless vacuum. This means that any velocity picked up will be maintained unless an opposite force is applied by the engines.
The game is a free-form simulation, with no plot or mission system. The spaceships have things such as biodomes and customizable engines. The ships can be equipped with weapons (such as lasers and torpedoes).
External links
(archived)
2004 video games
Freeware games
Linux games
MacOS games
Space flight simulator games
Video games developed in the United States
Windows games
|
https://en.wikipedia.org/wiki/Laminar%20Research
|
Laminar Research is a small software company based in Columbia, South Carolina, and dedicated to providing software that accurately reflects the laws of physics. Laminar's flagship product is the flight simulator X-Plane. The game works with Macintosh, Microsoft Windows, and Linux. They also have mobile versions for iPhone, iPad, and Android.
In 2004, Laminar Research released the software Space Combat.
Laminar also produced a Mecha simulator titled Young's Modulus.
In October 2012, Laminar Research announced that they were being sued by Uniloc over an alleged patent infringement. Austin Meyer produced a documentary film called The Patent Scam, about his experiences being sued by Uniloc.
In May 2017, X-Plane 11 was released, a major iteration in their flight simulator. X-Plane 11 is available in both a consumer version, as well as a Federal Aviation Administration certifiable professional version.
In January 2022, Laminar Research announced the release of their upcoming next-generation simulation game, X-Plane 12. It is slated to feature an overhaul of its weather engine, in addition to new aircraft.
In September 2022, Laminar Research has published the "early access" demo of X-Plane 12 and started selling it in their website. In December 2022, X-Plane 12 was released.
References
External links
Privately held companies based in South Carolina
Companies based in Columbia, South Carolina
Video game companies of the United States
Video game development companies
|
https://en.wikipedia.org/wiki/Chern%E2%80%93Weil%20homomorphism
|
In mathematics, the Chern–Weil homomorphism is a basic construction in Chern–Weil theory that computes topological invariants of vector bundles and principal bundles on a smooth manifold M in terms of connections and curvature representing classes in the de Rham cohomology rings of M. That is, the theory forms a bridge between the areas of algebraic topology and differential geometry. It was developed in the late 1940s by Shiing-Shen Chern and André Weil, in the wake of proofs of the generalized Gauss–Bonnet theorem. This theory was an important step in the theory of characteristic classes.
Let G be a real or complex Lie group with Lie algebra and let denote the algebra of -valued polynomials on (exactly the same argument works if we used instead of Let be the subalgebra of fixed points in under the adjoint action of G; that is, the subalgebra consisting of all polynomials f such that , for all g in G and x in ,
Given a principal G-bundle P on M, there is an associated homomorphism of -algebras,
,
called the Chern–Weil homomorphism, where on the right cohomology is de Rham cohomology. This homomorphism is obtained by taking invariant polynomials in the curvature of any connection on the given bundle. If G is either compact or semi-simple, then the cohomology ring of the classifying space for G-bundles, , is isomorphic to the algebra of invariant polynomials:
(The cohomology ring of BG can still be given in the de Rham sense:
when and are manifolds.)
Definit
|
https://en.wikipedia.org/wiki/Karl%20Wilhelm%20Gottlob%20Kastner
|
Karl Wilhelm Gottlob Kastner (31 October 1783 – 13 July 1857) was a German chemist, natural scientist and a professor of physics and chemistry.
Biography
Kastner received his doctorate in 1805 under the guidance of Johann Göttling and began lecturing at the University of Jena. He moved on to become professor at the University of Halle in 1812. In 1818 he relocated to the University of Bonn, where he would mentor famous chemist Justus Liebig. He then moved on to the University of Erlangen in the summer of 1821, where he would remain for the rest of his professional life.
Karl Wilhelm Gottlob Kastner was born in Greifenberg in Pommern as the son of Johann Friedrich Gottlob Kastner, who was teacher and headmaster at the school of Greifenberg and a Protestant pastor. After his father had been displaced to Swinemünde, Kastner started his vocational education at a pharmacy in 1798. Three years later, he travelled to Berlin, to work as assistant of a pharmacist and to visit lectures at the University of Berlin. In 1802 Kastner became an assistant of professor Bourgnet’s lectures of experimental physics and experimental chemistry. In 1804 he began studying natural sciences at the University of Jena. During his studies he already lectured chemistry. Kastner received his doctorate in 1805 under the guidance of Johann Göttling and began lecturing at the University of Jena. In the same year he moved on to the University of Heidelberg to lecture physics and chemistry. He became prof
|
https://en.wikipedia.org/wiki/Michael%20Drew
|
Michael Drew is a professor emeritus of chemistry at the University of Reading. He used to hold the position of head of physical chemistry. His main area of study centres on computational chemistry.
External links
British physical chemists
Academics of the University of Reading
Living people
Year of birth missing (living people)
Computational chemists
|
https://en.wikipedia.org/wiki/Mathematical%20Alphanumeric%20Symbols
|
Mathematical Alphanumeric Symbols is a Unicode block comprising styled forms of Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles. The letters in various fonts often have specific, fixed meanings in particular areas of mathematics. By providing uniformity over numerous mathematical articles and books, these conventions help to read mathematical formulas. These also may be used to differentiate between concepts that share a letter in a single problem.
Unicode now includes many such symbols (in the range U+1D400–U+1D7FF). The rationale behind this is that it enables design and usage of special mathematical characters (fonts) that include all necessary properties to differentiate from other alphanumerics, e.g. in mathematics an italic "𝐴" can have a different meaning from a roman letter "A". Unicode originally included a limited set of such letter forms in its Letterlike Symbols block before completing the set of Latin and Greek letter forms in this block beginning in version 3.1.
Unicode expressly recommends that these characters not be used in general text as a substitute for presentational markup; the letters are specifically designed to be semantically different from each other. Unicode does include a set of normal serif letters in the set. Still they have found some usage on social media, for example by people who want a stylized user name, and in email spam, in an attempt to bypass filters.
A
|
https://en.wikipedia.org/wiki/Reductive%20dechlorination
|
In organochlorine chemistry, reductive dechlorination describes any chemical reaction which cleaves the covalent bond between carbon and chlorine via reductants, to release chloride ions. Many modalities have been implemented, depending on the application. Reductive dechlorination is often applied to remediation of chlorinated pesticides or dry cleaning solvents. It is also used occasionally in the synthesis of organic compounds, e.g. as pharmaceuticals.
Chemical
Dechlorination is a well-researched reaction in organic synthesis, although it is not often used. Usually stoichiometric amounts of dechlorinating agent are required. In one classic application, the Ullmann reaction, chloroarenes are coupled to biphenyl]]s. For example, the activated substrate 2-chloronitrobenzene is converted into 2,2'-dinitrobiphenyl with a copper - bronze alloy.
Zerovalent iron effects similar reactions. Organophosphorus(III) compounds effect gentle dechlorinations. The products are alkenes and phosphorus(V).
Alkaline earth metals and zinc are used for more difficult dechlorinations. The side product is zinc chloride.
Biological
Vicinal reduction involves the removal of two halogen atoms that are adjacent on the same alkane or alkene, leading to the formation of an additional carbon-carbon bond.
Biological reductive dechlorination is often effected by certain species of bacteria. Sometimes the bacterial species are highly specialized for organochlorine respiration and even a particular
|
https://en.wikipedia.org/wiki/Johannes%20Acronius%20Frisius
|
Johannes Acronius Frisius (1520 – 18 October 1564) was a Dutch doctor and mathematician of the 16th century.
He was named after his city of birth, Akkrum in Friesland. From 1547 he worked as professor of mathematics in Basel, then after 1549 as professor of logic, and in 1564 of medicine. He died from the plague in the same year. Apart from mathematical and scientific works, he wrote Latin poetry and humanist tracts.
According to the Historical Dictionary of Switzerland, "nothing justifies the usual identification of A[cronius] with the philologist and botanist Johannes Atrocianus".
Publications
De motu terrae
De sphaera
De astrolabio et annuli astronomici confectione
Cronicon und Prognosticon astronomica, manuscript
biography and 45 aphorisms of the anabaptist David Joris.
References
1520 births
1564 deaths
16th-century deaths from plague (disease)
16th-century Dutch mathematicians
Frisius
Dutch Renaissance humanists
Frisian scientists
People from Boarnsterhim
Infectious disease deaths in Switzerland
|
https://en.wikipedia.org/wiki/Plane%20curve
|
In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves.
Plane curves also include the Jordan curves (curves that enclose a region of the plane but need not be smooth) and the graphs of continuous functions.
Symbolic representation
A plane curve can often be represented in Cartesian coordinates by an implicit equation of the form for some specific function f. If this equation can be solved explicitly for y or x – that is, rewritten as or for specific function g or h – then this provides an alternative, explicit, form of the representation. A plane curve can also often be represented in Cartesian coordinates by a parametric equation of the form for specific functions and
Plane curves can sometimes also be represented in alternative coordinate systems, such as polar coordinates that express the location of each point in terms of an angle and a distance from the origin.
Smooth plane curve
A smooth plane curve is a curve in a real Euclidean plane and is a one-dimensional smooth manifold. This means that a smooth plane curve is a plane curve which "locally looks like a line", in the sense that near every point, it may be mapped to a line by a smooth function.
Equivalently, a smooth plane curve can be given locally by an equation where is a smooth function, and the partia
|
https://en.wikipedia.org/wiki/Russell%20L.%20Rogers
|
Russell Lee Rogers (April 12, 1928 – September 13, 1967), (Lt Col, USAF), was an American electrical engineer, U.S. Air Force officer, test pilot, and astronaut in the X-20 Dyna-Soar program.
Early life and education
Rogers was born on April 12, 1928, in Lawrence, Kansas. He received a Bachelor of Science degree in electrical engineering from the University of Colorado in 1958. He was married with five children.
Test pilot
Rogers flew 142 missions as a fighter pilot during the Korean War. As a USAF Test Pilot School graduate, he was an experimental test pilot at Edwards AFB, California. During this assignment, Rogers served as a key member of the team that tested the Northrop T-38 Talon jet trainer. He was also a member of the Society of Experimental Test Pilots. In April 1960, he was selected for the X-20 program. After several years supporting the Boeing-led program as a pilot consultant, Rogers left the X-20 program on December 10, 1963, when it was cancelled.
After the X-20 program, he remained in the U.S. Air Force on active flight duty as a pilot and was commander of the 12th Tactical Fighter Squadron with the rank of Lt. Colonel at the time of his death.
Death
Rogers was killed when the engine of his F-105 fighter plane failed near Kadena AFB, Okinawa, Japan on September 13, 1967. He ejected from his aircraft, but his parachute failed to deploy properly. He was 39 years old.
References
External links
Spacefacts biography of Russell L. Rogers
1928 births
1967
|
https://en.wikipedia.org/wiki/Principal%20branch
|
In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function. Most often, this applies to functions defined on the complex plane.
Examples
Trigonometric inverses
Principal branches are used in the definition of many inverse trigonometric functions, such as the selection either to define that
or that
.
Exponentiation to fractional powers
A more familiar principal branch function, limited to real numbers, is that of a positive real number raised to the power of .
For example, take the relation , where is any positive real number.
This relation can be satisfied by any value of equal to a square root of (either positive or negative). By convention, is used to denote the positive square root of .
In this instance, the positive square root function is taken as the principal branch of the multi-valued relation .
Complex logarithms
One way to view a principal branch is to look specifically at the exponential function, and the logarithm, as it is defined in complex analysis.
The exponential function is single-valued, where is defined as:
where .
However, the periodic nature of the trigonometric functions involved makes it clear that the logarithm is not so uniquely determined. One way to see this is to look at the following:
and
where is any integer and continues the values of the -function from their principal value range , corresponding to into the principal value range of the -function , covering all fo
|
https://en.wikipedia.org/wiki/Progressive%20creationism
|
Progressive creationism (see for comparison intelligent design) is the religious belief that God created new forms of life gradually over a period of hundreds of millions of years. As a form of old Earth creationism, it accepts mainstream geological and cosmological estimates for the age of the Earth, some tenets of biology such as microevolution as well as archaeology to make its case. In this view creation occurred in rapid bursts in which all "kinds" of plants and animals appear in stages lasting millions of years. The bursts are followed by periods of stasis or equilibrium to accommodate new arrivals. These bursts represent instances of God creating new types of organisms by divine intervention. As viewed from the archaeological record, progressive creationism holds that "species do not gradually appear by the steady transformation of its ancestors; [but] appear all at once and "fully formed."
The view rejects macroevolution, claiming it is biologically untenable and not supported by the fossil record, as well as rejects the concept of universal descent from a last universal common ancestor. Thus the evidence for macroevolution is claimed to be false, but microevolution is accepted as a genetic parameter designed by the Creator into the fabric of genetics to allow for environmental adaptations and survival. Generally, it is viewed by proponents as a middle ground between literal creationism and theistic evolution.
Historical development
At the end of the 18th centur
|
https://en.wikipedia.org/wiki/CCMP%20%28cryptography%29
|
Counter Mode Cipher Block Chaining Message Authentication Code Protocol (Counter Mode CBC-MAC Protocol) or CCM mode Protocol (CCMP) is an encryption protocol designed for Wireless LAN products that implements the standards of the IEEE 802.11i amendment to the original IEEE 802.11 standard. CCMP is an enhanced data cryptographic encapsulation mechanism designed for data confidentiality and based upon the Counter Mode with CBC-MAC (CCM mode) of the Advanced Encryption Standard (AES) standard. It was created to address the vulnerabilities presented by Wired Equivalent Privacy (WEP), a dated, insecure protocol.
Technical details
CCMP uses CCM that combines CTR mode for data confidentiality and cipher block chaining message authentication code (CBC-MAC) for authentication and integrity. CCM protects the integrity of both the MPDU data field and selected portions of the IEEE 802.11 MPDU header. CCMP is based on AES processing and uses a 128-bit key and a 128-bit block size. CCMP uses CCM with the following two parameters:
M = 8; indicating that the MIC is 8 octets (eight bytes).
L = 2; indicating that the Length field is 2 octets.
A CCMP Medium Access Control Protocol Data Unit (MPDU) comprises five sections. The first is the MAC header which contains the destination and source address of the data packet. The second is the CCMP header which is composed of 8 octets and consists of the packet number (PN), the Ext IV, and the key ID. The packet number is a 48-bit number stored ac
|
https://en.wikipedia.org/wiki/Hyperfinite%20type%20II%20factor
|
In mathematics, there are up to isomorphism exactly two separably acting hyperfinite type II factors; one infinite and one finite. Murray and von Neumann proved that up to isomorphism there is a unique von Neumann algebra that is a factor of type II1 and also hyperfinite; it is called the hyperfinite type II1 factor.
There are an uncountable number of other factors of type II1. Connes proved that the infinite one is also unique.
Constructions
The von Neumann group algebra of a discrete group with the infinite conjugacy class property is a factor of type II1, and if the group is amenable and countable the factor is hyperfinite. There are many groups with these properties, as any locally finite group is amenable. For example, the von Neumann group algebra of the infinite symmetric group of all permutations of a countable infinite set that fix all but a finite number of elements gives the hyperfinite type II1 factor.
The hyperfinite type II1 factor also arises from the group-measure space construction for ergodic free measure-preserving actions of countable amenable groups on probability spaces.
The infinite tensor product of a countable number of factors of type In with respect to their tracial states is the hyperfinite type II1 factor. When n=2, this is also sometimes called the Clifford algebra of an infinite separable Hilbert space.
If p is any non-zero finite projection in a hyperfinite von Neumann algebra A of type II, then pAp is the hyperfinite type II1 factor. Equ
|
https://en.wikipedia.org/wiki/Auxology
|
Auxology (from Greek , auxō, or , auxanō 'grow'; and , -logia) is a meta-term covering the study of all aspects of human physical growth. (Although, it is also fundamental of biology.) Auxology is a multi-disciplinary science involving health sciences/medicine (pediatrics, general practice, endocrinology, neuroendocrinology, physiology, epidemiology), and to a lesser extent: nutrition science, genetics, anthropology, anthropometry, ergonomics, history, economic history, economics, socio-economics, sociology, public health, and psychology, among others.
History of auxology
""Ancient Babylonians and Egyptians left some writings on child growth and variation in height between ethnic groups. In the late 18th century, scattered documents of child growth started to appear in the scientific literature, the studies of Jamberts in 1754 and the annual measurements of the son of Montbeillard published by Buffon in 1777 being the most cited ones [1]. Louis René Villermé (1829) was the first to realize that growth and adult height of an individual depend on the country's socio-economic situation. In the 19th century, the number of growth studies rapidly increased, with increasing interest also in growth velocity [2]. Günther documented monthly height increments in a group of 33 boys of various ages [3]. Kotelmann [4] first noted the adolescent growth spurt. In fact, the adolescent growth spurt appears to be a novel achievement in the history of human growth and the amount and intensity
|
https://en.wikipedia.org/wiki/Systematics%20%28disambiguation%29
|
In biology, systematics studies the diversity of organismal characteristics.
Systematics may also refer to:
Other academic fields
Systematics (systems science), the study of inherent properties of systems based on their number of terms
Systematic theology, of Christian doctrine
Other uses
Systematic Paris-Region, a tech business cluster in Île-de-France
Systematics, Inc, an American data processing company
See also
System (disambiguation)
Systematic (disambiguation)
|
https://en.wikipedia.org/wiki/Tong%20Dizhou
|
Tong Dizhou (; May 28, 1902 – March 30, 1979) was a Chinese embryologist known for his contributions to the field of cloning. He was a vice president of Chinese Academy of Science.
Biography
Born in Yinxian, Zhejiang province, Tong graduated from Fudan University in 1924 with a degree in biology, and received a PhD in zoology in 1930 from Free University Brussels (ULB).
In 1963, Tong inserted DNA of a male carp into the egg of a female carp and became the first to successfully clone a fish. He is regarded as "the father of China's clone".
Tong was also an academician at the Chinese Academy of Sciences and the first director of its Institute of Oceanology from its founding in 1950 until 1978.
Tong died on 30 March 1979 at Beijing Hospital in Beijing.
References
1902 births
1979 deaths
20th-century biologists
20th-century Chinese scientists
Biologists from Zhejiang
Cloning
Educators from Ningbo
Free University of Brussels (1834–1969) alumni
Fudan University alumni
Academic staff of Fudan University
Members of Academia Sinica
Members of the Chinese Academy of Sciences
Academic staff of the National Central University
Scientists from Ningbo
Academic staff of Tongji University
Vice Chairpersons of the National Committee of the Chinese People's Political Consultative Conference
|
https://en.wikipedia.org/wiki/Crelle%27s%20Journal
|
Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).
History
The journal was founded by August Leopold Crelle (Berlin) in 1826 and edited by him until his death in 1855. It was one of the first major mathematical journals that was not a proceedings of an academy. It has published many notable papers, including works of Niels Henrik Abel, Georg Cantor, Gotthold Eisenstein, Carl Friedrich Gauss and Otto Hesse. It was edited by Carl Wilhelm Borchardt from 1856 to 1880, during which time it was known as Borchardt's Journal. The current editor-in-chief is Daniel Huybrechts (Rheinische Friedrich-Wilhelms-Universität Bonn).
Past editors
1826–1856 August Leopold Crelle
1856–1880 Carl Wilhelm Borchardt
1881–1888 Leopold Kronecker, Karl Weierstrass
1889–1892 Leopold Kronecker
1892–1902 Lazarus Fuchs
1903–1928 Kurt Hensel
1929–1933 Kurt Hensel, Helmut Hasse, Ludwig Schlesinger
1934–1936 Kurt Hensel, Helmut Hasse
1937–1952 Helmut Hasse
1952–1977 Helmut Hasse, Hans Rohrbach
1977–1980 Helmut Hasse
References
External links
Journal archive at the Göttinger Digitalisierungszentrum
Journal index at The European Digital Mathematics Library
Multilingual journals
English-language journals
French-language journals
German-language journals
Mathematics journals
Publications established in 1826
Monthly journals
De Gruyter academic journals
18
|
https://en.wikipedia.org/wiki/Charles%20Bassett
|
Charles Arthur Bassett II (December 30, 1931 – February 28, 1966), (Major, USAF), was an American electrical engineer and United States Air Force test pilot. He went to Ohio State University for two years and later graduated from Texas Tech University with a Bachelor of Science degree in Electrical Engineering. He joined the Air Force as a pilot and graduated from both the Air Force's Experimental Test Pilot School and the Aerospace Research Pilot School. Bassett was married and had two children.
He was selected as a NASA astronaut in 1963 and was assigned to Gemini 9. He died in an airplane crash during training for his first spaceflight. He is memorialized on the Space Mirror Memorial; The Astronaut Monument; and the Fallen Astronaut memorial plaque, which was placed on the Moon during the Apollo 15 mission.
Early life and education
Bassett was born on December 30, 1931, in Dayton, Ohio, to Charles Arthur "Pete" Bassett (1897–1958) and Fannie Belle Milby Bassett ( James; 1905–1993). Bassett was active in the Boy Scouts of America, where he achieved its second highest rank, Life Scout. During high school, Bassett was a model plane aficionado. He belonged to a club that built gasoline-powered models and flew them in the school gym. Bassett's interest in model airplanes translated to real aircraft; he made his first solo flight at age 16. He worked odd jobs at the airport to earn money for flying lessons and earned his private pilot license at age seventeen.
After graduati
|
https://en.wikipedia.org/wiki/Infinite%20conjugacy%20class%20property
|
In mathematics, a group is said to have the infinite conjugacy class property, or to be an ICC group, if the conjugacy class of every group element but the identity is infinite.
The von Neumann group algebra of a group is a factor if and only if the group has the infinite conjugacy class property. It will then be, provided the group is nontrivial, of type II1, i.e. it will possess a unique, faithful, tracial state.
Examples of ICC groups are the group of permutations of an infinite set that leave all but a finite subset of elements fixed, and free groups on two generators.
In abelian groups, every conjugacy class consists of only one element, so ICC groups are, in a way, as far from being abelian as possible.
References
Infinite group theory
Properties of groups
|
https://en.wikipedia.org/wiki/Relativistic%20Euler%20equations
|
In fluid mechanics and astrophysics, the relativistic Euler equations are a generalization of the Euler equations that account for the effects of general relativity. They have applications in high-energy astrophysics and numerical relativity, where they are commonly used for describing phenomena such as gamma-ray bursts, accretion phenomena, and neutron stars, often with the addition of a magnetic field. Note: for consistency with the literature, this article makes use of natural units, namely the speed of light and the Einstein summation convention.
Motivation
For most fluids observable on Earth, traditional fluid mechanics based on Newtonian mechanics is sufficient. However, as the fluid velocity approaches the speed of light or moves through strong gravitational fields, or the pressure approaches the energy density (), these equations are no longer valid. Such situations occur frequently in astrophysical applications. For example, gamma-ray bursts often feature speeds only less than the speed of light, and neutron stars feature gravitational fields that are more than times stronger than the Earth's. Under these extreme circumstances, only a relativistic treatment of fluids will suffice.
Introduction
The equations of motion are contained in the continuity equation of the stress–energy tensor :
where is the covariant derivative. For a perfect fluid,
Here is the total mass-energy density (including both rest mass and internal energy density) of the fluid, is the f
|
https://en.wikipedia.org/wiki/Addition%20theorem
|
In mathematics, an addition theorem is a formula such as that for the exponential function:
ex + y = ex · ey,
that expresses, for a particular function f, f(x + y) in terms of f(x) and f(y). Slightly more generally, as is the case with the trigonometric functions and , several functions may be involved; this is more apparent than real, in that case, since there is an algebraic function of (in other words, we usually take their functions both as defined on the unit circle).
The scope of the idea of an addition theorem was fully explored in the nineteenth century, prompted by the discovery of the addition theorem for elliptic functions. To "classify" addition theorems it is necessary to put some restriction on the type of function G admitted, such that
F(x + y) = G(F(x), F(y)).
In this identity one can assume that F and G are vector-valued (have several components). An algebraic addition theorem is one in which G can be taken to be a vector of polynomials, in some set of variables. The conclusion of the mathematicians of the time was that the theory of abelian functions essentially exhausted the interesting possibilities: considered as a functional equation to be solved with polynomials, or indeed rational functions or algebraic functions, there were no further types of solution.
In more contemporary language this appears as part of the theory of algebraic groups, dealing with commutative groups. The connected, projective variety examples are indeed exhausted by abelia
|
https://en.wikipedia.org/wiki/Grounding
|
Grounding or grounded may refer to:
Science and philosophy
Grounding (metaphysics), a topic of wide philosophical interest
Grounding (psychology), a strategy for coping with stress or other negative emotions
Grounding in communication, the collection of mutual knowledge, beliefs, and assumptions; "common ground"
Ground (electricity), a common return path for electric current
Symbol grounding, a problem in cognition and artificial intelligence
Arts and media
Grounded (comics), a comic book by Mark Sable for Image Comics
Grounded (opera), 2023 opera by Jeanine Tesori (music) and George Brant (libretto)
Grounded (video game), a multiplayer survival game by Obsidian Entertainment
"Superman: Grounded" a storyline in the Superman comic book, written by J. Michael Straczynski
Grounding (film), 2006 film about the collapse of the airline Swissair
Unaccompanied Minors, a 2006 Christmas film that was titled Grounded in the UK and Ireland
"Grounded", a song by Lower Than Atlantis from World Record
"Grounded", a song by My Vitriol
"Grounded", a song by Soul Asylum from the 1990 album And the Horse They Rode In On
"Grounded", a song by Ross Jennings from the 2021 album A Shadow of My Future Self
"Grounding", an interdisciplinary performance project by artist Gita Hashemi
Other uses
Grounding (discipline technique), restrictions placed on movement, privileges, or both as punishment
Grounding (nature therapy), a pseudoscientific practice that involves people grounding t
|
https://en.wikipedia.org/wiki/BIOS-3
|
BIOS-3 is an experimental closed ecosystem at the Institute of Biophysics in Krasnoyarsk, Russia.
Its construction began in 1965, and was completed in 1972. BIOS-3 consists of a underground steel structure suitable for up to three persons, and was initially used for developing closed ecological human life-support ecosystems. It was divided into 4 compartments, one of which is a crew area. The crew area consists of 3 single-cabins, a galley, lavatory and control room. Initially one other compartment was an algal cultivator, and the other two phytotrons for growing wheat or vegetables. The plants growing in the two phytotrons contributed approximately 25% of the air filtering in the compound. Later, the algal cultivator was converted into a third phytotron. A level of light comparable to sunlight was supplied in each of the 4 compartments by 20 kW xenon lamps, cooled by water jackets. The facility used 400 kW of electricity, supplied by a nearby hydroelectric power station.
Chlorella algae were used to recycle air breathed by humans, absorbing carbon dioxide and replenishing it with oxygen through photosynthesis. The algae were cultivated in stacked tanks under artificial light. To achieve a balance of oxygen and carbon dioxide, one human needed of exposed Chlorella. Air was purified of more complex organic compounds by heating to in the presence of a catalyst. Water and nutrients were stored in advance and were also recycled. By 1968, system efficiency had reached 85% by
|
https://en.wikipedia.org/wiki/Automorphic%20function
|
In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient space. Often the space is a complex manifold and the group is a discrete group.
Factor of automorphy
In mathematics, the notion of factor of automorphy arises for a group acting on a complex-analytic manifold. Suppose a group acts on a complex-analytic manifold . Then, also acts on the space of holomorphic functions from to the complex numbers. A function is termed an automorphic form if the following holds:
where is an everywhere nonzero holomorphic function. Equivalently, an automorphic form is a function whose divisor is invariant under the action of .
The factor of automorphy for the automorphic form is the function . An automorphic function is an automorphic form for which is the identity.
Some facts about factors of automorphy:
Every factor of automorphy is a cocycle for the action of on the multiplicative group of everywhere nonzero holomorphic functions.
The factor of automorphy is a coboundary if and only if it arises from an everywhere nonzero automorphic form.
For a given factor of automorphy, the space of automorphic forms is a vector space.
The pointwise product of two automorphic forms is an automorphic form corresponding to the product of the corresponding factors of automorphy.
Relation between factors of automorphy and other notions:
Let be a lattice in a Lie group . Then, a facto
|
https://en.wikipedia.org/wiki/Algebraic%20function
|
In mathematics, an algebraic function is a function that can be defined
as the root of an irreducible polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. Examples of such functions are:
Some algebraic functions, however, cannot be expressed by such finite expressions (this is the Abel–Ruffini theorem). This is the case, for example, for the Bring radical, which is the function implicitly defined by
.
In more precise terms, an algebraic function of degree in one variable is a function that is continuous in its domain and satisfies a polynomial equation
where the coefficients are polynomial functions of , with integer coefficients. It can be shown that the same class of functions is obtained if algebraic numbers are accepted for the coefficients of the 's. If transcendental numbers occur in the coefficients the function is, in general, not algebraic, but it is algebraic over the field generated by these coefficients.
The value of an algebraic function at a rational number, and more generally, at an algebraic number is always an algebraic number.
Sometimes, coefficients that are polynomial over a ring are considered, and one then talks about "functions algebraic over ".
A function which is not algebraic is called a transcendental function, as it is for example the case of . A
|
https://en.wikipedia.org/wiki/Subfield
|
Subfield may refer to:
an area of research and study within an academic discipline
Field extension, used in field theory (mathematics)
a Division (heraldry)
a division in MARC standards
|
https://en.wikipedia.org/wiki/Abelian%20surface
|
In mathematics, an abelian surface is a 2-dimensional abelian variety.
One-dimensional complex tori are just elliptic curves and are all algebraic, but Riemann discovered that most complex tori of dimension 2 are not algebraic via the Riemann bilinear relations. Essentially, these are conditions on the parameter space of period matrices for complex tori which define an algebraic subvariety. This subvariety contains all of the points whose period matrices correspond to a period matrix of an abelian variety.
The algebraic ones are called abelian surfaces and are exactly the 2-dimensional abelian varieties. Most of their theory is a special case of the theory of higher-dimensional tori or abelian varieties. Finding criteria for a complex torus of dimension 2 to be a product of two elliptic curves (up to isogeny) was a popular subject of study in the nineteenth century.
Invariants: The plurigenera are all 1. The surface is diffeomorphic to S1×S1×S1×S1 so the fundamental group is Z4.
Hodge diamond:
Examples: A product of two elliptic curves. The Jacobian variety of a genus 2 curve.
See also
Hodge theory
Complex torus
References
Algebraic surfaces
Complex surfaces
|
https://en.wikipedia.org/wiki/Vincenzo%20Antinori
|
Vincenzo Antinori (1792–1865) was a science administrator in Italy.
From 1829 to 1859, Antinori was director of the Regal Museum of Physics and Natural History in Florence where he worked with Leopoldo Nobili on electromagnetic induction. He had originally attracted Nobili to Florence to teach physics, as he had Giovanni Battista Amici to teach astronomy.
He was one of the promoters of the Congress of Italian Scientists in Pisa in 1839 and in Florence in 1841 and was responsible for bringing permanence, order and security to the Italian legacy of meteorological data by founding the Italian Meteorological Archive.
Antinori was a member of the Accademia della Crusca and wrote many entries for the Crusca dictionary on scientific topics. He had a particular interest in preserving and interpreting documents and artefacts from the work of Galileo Galilei and his followers.
Bibliografía: "Antonio Meucci e la città di Firenze. Tra scienza, tecnica e ingegneria". Editado por Angotti, Franco, Giuseppe Pelosi
Honours and positions
Honours
Knight of Grace of the Order of Saint Stephen. (Grand Duchy of Tuscany)
Knight commander of the Order of Saint Joseph. (Grand Duchy of Tuscany)
Positions
Chamberlain of His Imperial and Royal Highness the Grand Duke of Tuscany.
Director of the Museo di Fisica e di Storia Naturale di Firenze.
Scientific Member of the Academia Toscana d'Arte e Manifatture.
References
19th-century Italian scientists
1792 births
1865 deaths
Chamberlains of
|
https://en.wikipedia.org/wiki/Jerry%20Saltzer
|
Jerome Howard "Jerry" Saltzer (born October 9, 1939) is an American computer scientist.
Career
Jerry Saltzer received an ScD in Electrical Engineering from MIT in 1966. His dissertation 'Traffic Control in a Multiplexed System' was advised by Fernando Corbató. In 1966, he joined the faculty of the Department of Electrical Engineering and Computer Science at MIT.
One of Saltzer's earliest involvements with computers was with MIT's Compatible Time-Sharing System in the early 1960s. In the later 1960s and early 1970s, he was one of the team leaders of the Multics operating system project. Multics, though not particularly commercially successful in itself, has had a major impact on all subsequent operating systems; in particular, it was an inspiration for Ken Thompson to develop Unix. Saltzer's contributions to Multics included the now-standard kernel stack switching method of process switching, as well as oft-cited work on the security architecture for shared information systems.
Saltzer led the Computer Systems Research group of MIT's Laboratory for Computer Science. In the late 1970s and early 1980s, the Computer Systems Research group was one of the key players in the development of the Internet and ring network technology for local area networks. During this time, Saltzer patented the Proteon ProNet ring network. Another contribution in that area was the end-to-end principle in systems design (Saltzer and Schroeder's design principles), which is one of the important und
|
https://en.wikipedia.org/wiki/Jack%20Dennis
|
Jack Bonnell Dennis (born October 13, 1931) is a computer scientist and Emeritus Professor of Computer Science and Engineering at Massachusetts Institute of Technology.
The work of Dennis in computer systems and computer languages is recognized to have played a key role in hacker culture. As a Massachusetts Institute of Technology faculty member he sponsored easier access to computer facilities at MIT during the early development of the subculture. Much of what would later become Unix came from his early collaboration with Dennis Ritchie and Ken Thompson. This collaborative and open philosophy lives on today.
Dennis was also a member of the historic Tech Model Railroad Club, which incubated much of the early slang and traditions of hacking.
Early life and education
Dennis graduated from the Massachusetts Institute of Technology (MIT) as Bachelor of Science (1953), Master of Science (1954), and Doctor of Science (1958). His doctoral thesis analyzed the relation between mathematical programming problems and electrical networks. After completing his doctorate, Dennis became part of the MIT's Department of Electrical Engineering and Computer Science's faculty, being promoted to full professor in 1969.
Career
As a professor at MIT, Dennis was influential in the work of student Alan Kotok and fellow professors Marvin Minsky and John McCarthy. He gave young programmers access to multi-million dollar computers and allowed them to see where their abilities could take them, inspi
|
https://en.wikipedia.org/wiki/Robert%20M.%20Graham%20%28computer%20scientist%29
|
Robert M. Graham (1929 in Michigan, US – January 2, 2020) was a cybersecurity researcher computer scientist and Professor Emeritus of Computer Science at the University of Massachusetts Amherst. He was born to a Scottish emigrant.
He received his undergraduate and graduate degrees from the University of Michigan. While working at the UofM's Computing Center he co-authored two compilers, GAT for the IBM 650 and MAD for the IBM 704/709/7090.
In 1963 he moved to MIT to participate in the development of Multics, one of the first virtual memory time-sharing computer operating systems. He had responsibility for protection, dynamic linking, and other key system kernel areas.
Later worked at University of California, Berkeley, City College of New York, and the University of Massachusetts Amherst. Officially retired in 1996, but continued to teach until the end of 2003.
In 1996 he was inducted as a Fellow of the Association for Computing Machinery.
He is the author of numerous books and professional articles.
References
External links
Robert M. Graham Home Page
1929 births
2020 deaths
American computer scientists
Fellows of the Association for Computing Machinery
Multics people
University of Michigan alumni
|
https://en.wikipedia.org/wiki/Monadic
|
Monadic may refer to:
Monadic, a relation or function having an arity of one in logic, mathematics, and computer science
Monadic, an adjunction if and only if it is equivalent to the adjunction given by the Eilenberg–Moore algebras of its associated monad, in category theory
Monadic, in computer programming, a feature, type, or function related to a monad (functional programming)
Monadic or univalent, a chemical valence
Monadic, in theology, a religion or philosophy possessing a concept of a divine Monad
See also
Monadic predicate calculus, in logic
Monad (disambiguation)
|
https://en.wikipedia.org/wiki/Michael%20Heath%20%28computer%20scientist%29
|
Michael Thomas Heath (born December 11, 1946) is a retired computer scientist who specializes in scientific computing. He is the director of the Center for the Simulation of Advanced Rockets, a Department of Energy-sponsored computing center at the University of Illinois at Urbana–Champaign, and the former Fulton Watson Copp Professor of Computer Science at UIUC. Heath was inducted as member of the European Academy of Sciences in 2002, a Fellow of the Association for Computing Machinery in 2000, and a Fellow of the Society for Industrial and Applied Mathematics in 2010. He also received the 2009 Taylor L. Booth Education Award from IEEE. He became an emeritus professor in 2012.
Heath is the author of Scientific Computing: An Introductory Survey, an introductory text on numerical analysis.
Education
Michael Heath earned his BA in mathematics from the University of Kentucky in 1968. In 1974, Heath earned his MS in mathematics from the University of Tennessee. Heath earned his PhD in computer science from Stanford University in 1978; his PhD dissertation was entitled Numerical Algorithms for Nonlinearly Constrained Optimization and was completed under the direction of Gene Golub.
Early work
Prior to his work with the University of Illinois, Michael Heath spent a number of years at Oak Ridge National Laboratory. Heath joined Oak Ridge in 1968 as a Scientific Applications Programmer, and he became a Eugene P. Wigner Postdoctoral Fellow in 1978.
Michael Heath served as an ad
|
https://en.wikipedia.org/wiki/Simon%20Donaldson
|
Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London.
Biography
Donaldson's father was an electrical engineer in the physiology department at the University of Cambridge, and his mother earned a science degree there. Donaldson gained a BA degree in mathematics from Pembroke College, Cambridge, in 1979, and in 1980 began postgraduate work at Worcester College, Oxford, at first under Nigel Hitchin and later under Michael Atiyah's supervision. Still a postgraduate student, Donaldson proved in 1982 a result that would establish his fame. He published the result in a paper "Self-dual connections and the topology of smooth 4-manifolds" which appeared in 1983. In the words of Atiyah, the paper "stunned the mathematical world."
Whereas Michael Freedman classified topological four-manifolds, Donaldson's work focused on four-manifolds admitting a differentiable structure, using instantons, a particular solution to the equations of Yang–Mills gauge theory which has its origin in quantum field theory. One of Donaldson's first results gave severe restrictions on the intersection form of a smooth four-manifold. As a consequence,
|
https://en.wikipedia.org/wiki/Divided%20differences
|
In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. Charles Babbage's difference engine, an early mechanical calculator, was designed to use this algorithm in its operation.
Divided differences is a recursive division process. Given a sequence of data points , the method calculates the coefficients of the interpolation polynomial of these points in the Newton form.
Definition
Given n + 1 data points
where the are assumed to be pairwise distinct, the forward divided differences are defined as:
To make the recursive process of computation clearer, the divided differences can be put in tabular form, where the columns correspond to the value of j above, and each entry in the table is computed from the difference of the entries to its immediate lower left and to its immediate upper left, divided by a difference of corresponding x-values:
Notation
Note that the divided difference depends on the values and , but the notation hides the dependency on the x-values. If the data points are given by a function f,
one sometimes writes the divided difference in the notation
Other notations for the divided difference of the function ƒ on the nodes x0, ..., xn are:
Example
Divided differences for and the first few values of :
Properties
Linearity
Leibniz rule
Divided differences are symmetric: If is a permutation then
Polynomial interpolation in the Newton form: if is a polynomial functio
|
https://en.wikipedia.org/wiki/Monomial%20basis
|
In mathematics the monomial basis of a polynomial ring is its basis (as a vector space or free module over the field or ring of coefficients) that consists of all monomials. The monomials form a basis because every polynomial may be uniquely written as a finite linear combination of monomials (this is an immediate consequence of the definition of a polynomial).
One indeterminate
The polynomial ring of univariate polynomials over a field is a -vector space, which has
as an (infinite) basis. More generally, if is a ring then is a free module which has the same basis.
The polynomials of degree at most form also a vector space (or a free module in the case of a ring of coefficients), which has as a basis.
The canonical form of a polynomial is its expression on this basis:
or, using the shorter sigma notation:
The monomial basis is naturally totally ordered, either by increasing degrees
or by decreasing degrees
Several indeterminates
In the case of several indeterminates a monomial is a product
where the are non-negative integers. As an exponent equal to zero means that the corresponding indeterminate does not appear in the monomial; in particular is a monomial.
Similar to the case of univariate polynomials, the polynomials in form a vector space (if the coefficients belong to a field) or a free module (if the coefficients belong to a ring), which has the set of all monomials as a basis, called the monomial basis.
The homogeneous polynomials of degree for
|
https://en.wikipedia.org/wiki/Hilbert%E2%80%93Schmidt%20operator
|
In mathematics, a Hilbert–Schmidt operator, named after David Hilbert and Erhard Schmidt, is a bounded operator that acts on a Hilbert space and has finite Hilbert–Schmidt norm
where is an orthonormal basis. The index set need not be countable. However, the sum on the right must contain at most countably many non-zero terms, to have meaning. This definition is independent of the choice of the orthonormal basis.
In finite-dimensional Euclidean space, the Hilbert–Schmidt norm is identical to the Frobenius norm.
||·|| is well defined
The Hilbert–Schmidt norm does not depend on the choice of orthonormal basis. Indeed, if and are such bases, then
If then As for any bounded operator, Replacing with in the first formula, obtain The independence follows.
Examples
An important class of examples is provided by Hilbert–Schmidt integral operators.
Every bounded operator with a finite-dimensional range (these are called operators of finite rank) is a Hilbert–Schmidt operator.
The identity operator on a Hilbert space is a Hilbert–Schmidt operator if and only if the Hilbert space is finite-dimensional.
Given any and in , define by , which is a continuous linear operator of rank 1 and thus a Hilbert–Schmidt operator;
moreover, for any bounded linear operator on (and into ), .
If is a bounded compact operator with eigenvalues of , where each eigenvalue is repeated as often as its multiplicity, then is Hilbert–Schmidt if and only if , in which case the Hilbert
|
https://en.wikipedia.org/wiki/Whitehead%20theorem
|
In homotopy theory (a branch of mathematics), the Whitehead theorem states that if a continuous mapping f between CW complexes X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence. This result was proved by J. H. C. Whitehead in two landmark papers from 1949, and provides a justification for working with the concept of a CW complex that he introduced there. It is a model result of algebraic topology, in which the behavior of certain algebraic invariants (in this case, homotopy groups) determines a topological property of a mapping.
Statement
In more detail, let X and Y be topological spaces. Given a continuous mapping
and a point x in X, consider for any n ≥ 1 the induced homomorphism
where πn(X,x) denotes the n-th homotopy group of X with base point x. (For n = 0, π0(X) just means the set of path components of X.) A map f is a weak homotopy equivalence if the function
is bijective, and the homomorphisms f* are bijective for all x in X and all n ≥ 1. (For X and Y path-connected, the first condition is automatic, and it suffices to state the second condition for a single point x in X.) The Whitehead theorem states that a weak homotopy equivalence from one CW complex to another is a homotopy equivalence. (That is, the map f: X → Y has a homotopy inverse g: Y → X, which is not at all clear from the assumptions.) This implies the same conclusion for spaces X and Y that are homotopy equivalent to CW complexes.
Combining this with the Hurewic
|
https://en.wikipedia.org/wiki/Gene%20Spafford
|
Eugene Howard Spafford (born 1956), known as Spaf, is an American professor of computer science at Purdue University and a computer security expert.
Spafford serves as an advisor to U.S. government agencies and corporations. In 1998, he founded and was the first director of the Center for Education and Research in Information Assurance and Security (CERIAS) at Purdue University.
Biography
Education and early career
Spafford attended the State University of New York at Brockport, graduating with a double major in mathematics and computer science in three years. He then attended the School of Information and Computer Sciences (now the College of Computing) at the Georgia Institute of Technology. He received his Master of Science (M.S.) in 1981, and Doctor of Philosophy (Ph.D.) in 1986, for his design and implementation of the kernel of the original Clouds distributed operating system.
During the formative years of the Internet, Spafford made significant contributions to establishing semi-formal processes to organize and manage Usenet, then the primary channel of communication between users, and to defining the standards of behavior governing its use. Spafford initiated the Phage List as a response to the Morris Worm, one of the earliest computer worms.
Computer science at Purdue
Spafford has served on the faculty at Purdue University in Indiana since 1987, and is a full professor of computer science. He is executive director emeritus of Purdue's Center for Education and Re
|
https://en.wikipedia.org/wiki/Cupola%20%28disambiguation%29
|
A cupola is a relatively small, most often dome-like, tall structure on top of a building.
Cupola may also refer to:
Science, mathematics, and technology
Cupola (cave formation), a recess in the ceiling of a lava tube
Cupola (geology), a type of igneous rock intrusion
Cupola (geometry), a geometric solid
Cupola (ISS module), an observation dome on the International Space Station
Cupola (military), a small gun turret mounted on a larger one
Cupola gecko, a species of gecko
Cupola sign, in medicine, a radiologic sign
Cupola furnace, a variety of small blast furnace
Reverberatory furnace, for smelting some non-ferrous metals
Cupola, an observation area on top of a railway caboose
Other uses
Sicilian Mafia Commission or Cupola, a body of Sicilian Mafia leaders
The Cupola (mountain), Tasmania, Australia
The Cupola, the yearbook of Western New England University, Springfield, Massachusetts, US
"Cupola", a 2001 song by Zeromancer from Eurotrash
See also
Cupola House (disambiguation)
Copala (disambiguation)
Coppola (disambiguation)
Copula (disambiguation)
Cupula (disambiguation)
|
https://en.wikipedia.org/wiki/Information%20loss
|
Information loss may refer to:
Data loss in information systems
lossy compression
Digital obsolescence
Black hole information paradox in theoretical physics
|
https://en.wikipedia.org/wiki/Max%20Planck%20Medal
|
The Max Planck medal is the highest award of the German Physical Society , the world's largest organization of physicists, for extraordinary achievements in theoretical physics. The prize has been awarded annually since 1929, with few exceptions, and usually to a single person. The winner is awarded with a gold medal and hand-written parchment.
In 1943 it was not possible to manufacture the gold medal because the Berlin foundry was hit by a bomb. The board of directors of the German Physical Society decided to manufacture the medals in a substitute metal and to deliver the gold medals later.
The highest award of the German Physical Society for outstanding results in experimental physics is the Stern–Gerlach Medal.
List of recipients
2023 Rashid A. Sunyaev
2022 Annette Zippelius
2021 Alexander Markovich Polyakov
2020 Andrzej Buras
2019 Detlef Lohse
2018 Juan Ignacio Cirac
2017 Herbert Spohn
2016 Herbert Wagner
2015 Viatcheslav Mukhanov
2014 David Ruelle
2013 Werner Nahm
2012 Martin Zirnbauer
2011 Giorgio Parisi
2010 Dieter Vollhardt
2009 Robert Graham
2008 Detlev Buchholz
2007 Joel Lebowitz
2006 Wolfgang Götze
2005 Peter Zoller
2004 Klaus Hepp
2003 Martin Gutzwiller
2002 Jürgen Ehlers
2001 Jürg Fröhlich
2000 Martin Lüscher
1999 Pierre Hohenberg
1998 Raymond Stora
1997 Gerald E. Brown
1996 Ludvig Faddeev
1995 Siegfried Grossmann
1994 Hans-Jürgen Borchers
1993 Kurt Binder
1992 Elliott H. Lieb
1991 Wolfhart Zimmermann
1990 Hermann Haken
1989 Bruno Zumino
1988 Valentine Bargma
|
https://en.wikipedia.org/wiki/Substituent
|
In organic chemistry, a substituent is one or a group of atoms that replaces (one or more) atoms, thereby becoming a moiety in the resultant (new) molecule. (In organic chemistry and biochemistry, the terms substituent and functional group, as well as side chain and pendant group, are used almost interchangeably to describe those branches from the parent structure, though certain distinctions are made in polymer chemistry. In polymers, side chains extend from the backbone structure. In proteins, side chains are attached to the alpha carbon atoms of the amino acid backbone.)
The suffix -yl is used when naming organic compounds that contain a single bond replacing one hydrogen; -ylidene and -ylidyne are used with double bonds and triple bonds, respectively. In addition, when naming hydrocarbons that contain a substituent, positional numbers are used to indicate which carbon atom the substituent attaches to when such information is needed to distinguish between isomers. Substituents can be a combination of the inductive effect and the mesomeric effect. Such effects are also described as electron-rich and electron withdrawing. Additional steric effects result from the volume occupied by a substituent.
The phrases most-substituted and least-substituted are frequently used to describe or compare molecules that are products of a chemical reaction. In this terminology, methane is used as a reference of comparison. Using methane as a reference, for each hydrogen atom that is repla
|
https://en.wikipedia.org/wiki/Leo%20Buss
|
Leo W. Buss (born 1953) is a retired Professor at Yale University's departments of geology, geophysics, and ecology and evolutionary biology.
Life
He graduated from Johns Hopkins University with a B.A., M.A., and Ph.D in 1979.
His evolutionary developmental biology book approaches the subject of the evolution of metazoan development from a cell lineage selection point of view.
He reevaluates August Weismann's model of the cell compartmentalization of somatic and germline cell lineages (see Weismann barrier), and argues that the vision of the individual taken by the modern synthesis is insufficient to explain the early evolution of development or ontogeny.
He collaborated with Walter Fontana in producing some of the first papers on artificial chemistries.
Works
The Evolution of Individuality, Princeton University Press, 1987,
"Beyond Digital Naturalism", Artificial life: an overview, Editor Christopher G. Langton, MIT Press, 1997,
"What would be conserved "If the tape were played twice?"", Complexity: metaphors, models, and reality, Editors George A. Cowan, David Pines, David Elliott Meltzer, Westview Press, 1999,
"Growth by Intussusception in Hyrdactiniid Hydroids", Evolutionary patterns: growth, form, and tempo in the fossil record in honor of Allan Cheetham, Editors Alan H. Cheetham, Jeremy B. C. Jackson, Scott Lidgard, Frank Kenneth McKinney, University of Chicago Press, 2001,
References
External links
"Leo W. Buss", Scientific Commons
1953 births
Living people
|
https://en.wikipedia.org/wiki/Truncated%20power%20function
|
In mathematics, the truncated power function with exponent is defined as
In particular,
and interpret the exponent as conventional power.
Relations
Truncated power functions can be used for construction of B-splines.
is the Heaviside function.
where is the indicator function.
Truncated power functions are refinable.
See also
Macaulay brackets
External links
Truncated Power Function on MathWorld
References
Numerical analysis
|
https://en.wikipedia.org/wiki/Semi-local%20ring
|
In mathematics, a semi-local ring is a ring for which R/J(R) is a semisimple ring, where J(R) is the Jacobson radical of R.
The above definition is satisfied if R has a finite number of maximal right ideals (and finite number of maximal left ideals). When R is a commutative ring, the converse implication is also true, and so the definition of semi-local for commutative rings is often taken to be "having finitely many maximal ideals".
Some literature refers to a commutative semi-local ring in general as a
quasi-semi-local ring, using semi-local ring to refer to a Noetherian ring with finitely many maximal ideals.
A semi-local ring is thus more general than a local ring, which has only one maximal (right/left/two-sided) ideal.
Examples
Any right or left Artinian ring, any serial ring, and any semiperfect ring is semi-local.
The quotient is a semi-local ring. In particular, if is a prime power, then is a local ring.
A finite direct sum of fields is a semi-local ring.
In the case of commutative rings with unity, this example is prototypical in the following sense: the Chinese remainder theorem shows that for a semi-local commutative ring R with unit and maximal ideals m1, ..., mn
.
(The map is the natural projection). The right hand side is a direct sum of fields. Here we note that ∩i mi=J(R), and we see that R/J(R) is indeed a semisimple ring.
The classical ring of quotients for any commutative Noetherian ring is a semilocal ring.
The endomorphism ring of an
|
https://en.wikipedia.org/wiki/Candace%20Pert
|
Candace Beebe Pert (June 26, 1946 – September 12, 2013) was an American neuroscientist and pharmacologist who discovered the opioid receptor, the cellular binding site for endorphins in the brain.
Early life and education
She was born on June 26, 1946, in Manhattan, New York City.
She completed her undergraduate studies in biology, cum laude in 1970 from Bryn Mawr College in Pennsylvania.
Academic career
In 1974, Candace Pert earned a Ph.D. in pharmacology from Johns Hopkins University School of Medicine, where she worked in the laboratory of Solomon Snyder and discovered the brain's opiate receptor. She also was the first person to isolate the T cell receptor. She tells the story of her discoveries in her book Molecules of Emotion.
Pert conducted a National Institutes of Health Postdoctoral Fellowship with the Department of Pharmacology at the Johns Hopkins University School of Medicine from 1974 to 1975. She conducted research at the National Institute of Mental Health from 1975 to 1987.
In 1983, she became the Chief of the Section on Brain Biochemistry of the Clinical Neuroscience Branch, the only female chief at NIMH.
She left to found and direct a private biotech laboratory in 1987.
Pert was a research professor in the department of physiology and biophysics at Georgetown University School of Medicine in Washington, D.C.
In her latter years, she was with RAPID Pharmaceuticals.Candace Pert candacepert.com
In 1997 she published her book Molecules of Emotion.She a
|
https://en.wikipedia.org/wiki/Qux
|
Qux or variation, may refer to:
Yauyos–Chincha Quechua (ISO 639 language code: qux), a South American language
Quadra FNX Mining (stock ticker: QUAixX), a Canadian mining company
Qüxü County (geocode QUX), Tibet, China; see List of administrative divisions of the Tibet Autonomous Region
qux (computer science), a commonly defined metasyntactic variable
Qux (programming), a common placeholder name
QUX (radiotelegraphy), a Q-code encoding the phrase Do you have any navigational warnings or gale warnings in force?
Unicode symbol U+A40D (qux), see Yi Syllables
See also
"qux", a word in the Chitimacha language
|
https://en.wikipedia.org/wiki/Clerke%20%28crater%29
|
Clerke is a tiny lunar impact crater named after Irish astronomer Agnes Mary Clerke, who played a role in bringing astronomy and astrophysics to the public in Victorian England. It is located near the eastern edge of Mare Serenitatis in the midst of a rille system named the Rimae Littrow after the crater Littrow to the east. It is roughly circular and cup-shaped, with a relatively high albedo. In a valley to the southeast is the landing site of the Apollo 17 mission. Clerke was previously designated Littrow B.
See also
Asteroid 9583 Clerke
References
External links
Closeup of Clerke by Lunar Orbiter 5
LTO-42C2 Clerke — L&PI topographic map.
Impact craters on the Moon
|
https://en.wikipedia.org/wiki/Concepts%20of%20Modern%20Mathematics
|
Concepts of Modern Mathematics is a book by mathematician and science popularizer Ian Stewart about then-recent developments in mathematics. It was originally published by Penguin Books in 1975, updated in 1981, and reprinted by Dover publications in 1995 and 2015.
Overview
The book arose out of an extramural class that Ian Stewart taught at the University of Warwick about "Modern mathematics". In the 1995 Dover edition Stewart wrote that the aim of the class was:
to explain why the underlying abstract point of view had gained currency among research mathematicians, and to examine how it opened up entirely new realms of mathematical thought.
The book is aimed at non-mathematicians. However, there are frequent equations and diagrams and the level of presentation is more technical than some of Stewart's other popular books such as Flatterland. Topics covered include analytic geometry, set theory, abstract algebra, group theory, topology, and probability.
References
Books by Ian Stewart (mathematician)
1975 non-fiction books
Mathematics books
|
https://en.wikipedia.org/wiki/Brittleness
|
A material is brittle if, when subjected to stress, it fractures with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength. Breaking is often accompanied by a sharp snapping sound.
When used in materials science, it is generally applied to materials that fail when there is little or no plastic deformation before failure. One proof is to match the broken halves, which should fit exactly since no plastic deformation has occurred.
Brittleness in different materials
Polymers
Mechanical characteristics of polymers can be sensitive to temperature changes near room temperatures. For example, poly(methyl methacrylate) is extremely brittle at temperature 4˚C, but experiences increased ductility with increased temperature.
Amorphous polymers are polymers that can behave differently at different temperatures. They may behave like a glass at low temperatures (the glassy region), a rubbery solid at intermediate temperatures (the leathery or glass transition region), and a viscous liquid at higher temperatures (the rubbery flow and viscous flow region). This behavior is known as viscoelastic behavior. In the glassy region, the amorphous polymer will be rigid and brittle. With increasing temperature, the polymer will become less brittle.
Metals
Some metals show brittle characteristics due to their slip systems. The more slip systems a metal has, the less brittle it is, b
|
https://en.wikipedia.org/wiki/Evolving%20the%20Alien
|
Evolving the Alien: The Science of Extraterrestrial Life (published in the US, and UK second edition as What Does a Martian Look Like?: The Science of Extraterrestrial Life) is a 2002 popular science book about xenobiology by biologist Jack Cohen and mathematician Ian Stewart.
The concept for the book originated with a lecture that Cohen had revised over many years, which he called POLOOP, for "Possibility of Life on Other Planets".
Synopsis
Cohen and Stewart argue against a conception of extraterrestrial life that assumes life can only evolve in environments similar to Earth (the so-called Rare Earth hypothesis), and that extraterrestrial lifeforms will converge toward characteristics similar to those of life on Earth, a common trope of certain science fiction styles. They suggest that any investigation of extraterrestrial life relying on these assumptions is overly restrictive, and it is possible to make a scientific and rational study of the possibility of life forms that are so different from life on Earth that we may not even recognise them as life in the first instance.
Cohen and Stewart return to two contrasts throughout the book. The first is between exobiology (which considers the possibilities for conventional, Earth-like biology on Earth-like planets) and xenoscience (which embraces a much broader and more speculative range for the forms that life may take). The second contrast drawn is between parochials (features of life that are likely to be unique to Earth)
|
https://en.wikipedia.org/wiki/Drone%20%28bee%29
|
A drone is a male honey bee. Unlike the female worker bee, a drone has no stinger. He does not gather nectar or pollen and cannot feed without assistance from worker bees. His only role is to mate with a maiden queen in nuptial flight.
Genetics
Drones carry only one type of allele at each chromosomal position, because they are haploid (containing only one set of chromosomes from the mother). During the development of eggs within a queen, a diploid cell with 32 chromosomes divides to generate haploid cells called gametes with 16 chromosomes. The result is a haploid egg, with chromosomes having a new combination of alleles at the various loci. This process is called arrhenotokous parthenogenesis or simply arrhenotoky.
Because the male bee technically has only a mother, and no father, its genealogical tree is unusual. The first generation has one member (the male). One generation back also has one member (the mother). Two generations back are two members (the mother and father of the mother). Three generations back are three members. Four back are five members. This sequence – 1, 1, 2, 3, 5, 8, and so on – is the Fibonacci sequence.
Much debate and controversy exists in scientific literature about the dynamics and apparent benefit of the combined forms of reproduction in honey bees and other social insects, known as the haplodiploid sex-determination system. The drones have two reproductive functions: each drone grows from the queen's unfertilized haploid egg and produces so
|
https://en.wikipedia.org/wiki/Working%20range
|
Each instrument used in analytical chemistry has a useful working range. This is the range of concentration (or mass) that can be adequately determined by the instrument, where the instrument provides a useful signal that can be related to the concentration of the analyte.
All instruments have an upper and a lower working limit. Concentrations below the working limit do not provide enough signal to be useful, and concentrations above the working limit provide too much signal to be useful. When calibrating an instrument for use, the experimenter must be familiar with both the lower and upper working range of the chosen instrument.
Analytical chemistry
|
https://en.wikipedia.org/wiki/Combinatorial%20group%20theory
|
In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It is much used in geometric topology, the fundamental group of a simplicial complex having in a natural and geometric way such a presentation.
A very closely related topic is geometric group theory, which today largely subsumes combinatorial group theory, using techniques from outside combinatorics besides.
It also comprises a number of algorithmically insoluble problems, most notably the word problem for groups; and the classical Burnside problem.
History
See for a detailed history of combinatorial group theory.
A proto-form is found in the 1856 icosian calculus of William Rowan Hamilton, where he studied the icosahedral symmetry group via the edge graph of the dodecahedron.
The foundations of combinatorial group theory were laid by Walther von Dyck, student of Felix Klein, in the early 1880s, who gave the first systematic study of groups by generators and relations.
References
|
https://en.wikipedia.org/wiki/Ring%20species
|
In biology, a ring species is a connected series of neighbouring populations, each of which interbreeds with closely sited related populations, but for which there exist at least two "end populations" in the series, which are too distantly related to interbreed, though there is a potential gene flow between each "linked" population and the next. Such non-breeding, though genetically connected, "end populations" may co-exist in the same region (sympatry) thus closing a "ring". The German term , meaning a circle of races, is also used.
Ring species represent speciation and have been cited as evidence of evolution. They illustrate what happens over time as populations genetically diverge, specifically because they represent, in living populations, what normally happens over time between long-deceased ancestor populations and living populations, in which the intermediates have become extinct. The evolutionary biologist Richard Dawkins remarks that ring species "are only showing us in the spatial dimension something that must always happen in the time dimension".
Formally, the issue is that interfertility (ability to interbreed) is not a transitive relation; if A breeds with B, and B breeds with C, it does not mean that A breeds with C, and therefore does not define an equivalence relation. A ring species is a species with a counterexample to the transitivity of interbreeding. However, it is unclear whether any of the examples of ring species cited by scientists actually permit
|
https://en.wikipedia.org/wiki/Barry%20Greenstein
|
Barry Greenstein (born December 30, 1954, in Chicago, Illinois) is an American professional poker player and former mathematics postgraduate student. He has won a number of major events, including three at the World Series of Poker and two on the World Poker Tour. Greenstein donates his profit from tournament winnings to charities, primarily Children Incorporated, earning him the nickname "the Robin Hood of poker". He was elected into the Poker Hall of Fame in 2011.
Personal life
After graduating from Bogan High School, he earned a bachelor's degree in computer science from the University of Illinois at Urbana-Champaign. He studied for a PhD in mathematics without ever defending his completed dissertation.
According to his book, Ace on the River, Greenstein was doing well playing poker, but figured a more conventional job would improve his chances of adopting his stepchildren, so he went to work for the new startup company Symantec, where he worked on their first product Q&A. He left the company in 1991 at age 36.
Greenstein has two children and four stepchildren, and he resides in Rancho Palos Verdes, California. His stepson, Joe Sebok, with whom he started PokerRoad—a poker strategy and entertainment website—also played professionally for a few years.
Poker career
Greenstein has appeared in each of the first three series of Poker Superstars Invitational Tournament and all seven seasons of the GSN series High Stakes Poker. He has also appeared in the first three seasons
|
https://en.wikipedia.org/wiki/Shockley
|
Shockley is a surname. Notable people with the surname include:
Dolores Cooper Shockley, American pharmacist
D. J. Shockley, American football player
William Shockley, winner of the Nobel Prize for physics
Fictional characters
Detective Ben Shockley, protagonist of the 1977 film The Gauntlet
See also
Shockley Semiconductor Laboratory
William Shockley (disambiguation)
|
https://en.wikipedia.org/wiki/Western%20corn%20rootworm
|
The Western corn rootworm, Diabrotica virgifera virgifera, is one of the most devastating corn rootworm species in North America, especially in the midwestern corn-growing areas such as Iowa. A related species, the Northern corn rootworm, D. barberi, co-inhabits in much of the range and is fairly similar in biology.
Two other subspecies of D. virgifera are described, including the Mexican corn rootworm (Diabrotica virgifera zeae), a significant pest in its own right, attacking corn in that country.
Corn rootworm larvae can destroy significant percentages of corn if left untreated. In the United States, current estimates show that of corn (out of 80 million grown) are infested with corn rootworm. The United States Department of Agriculture estimates that corn rootworms cause $1 billion in lost revenue each year, including $800 million in yield loss and $200 million in cost of treatment for corn growers.
Life cycle
There are many similarities in the life cycles of the northern and western corn rootworm. Both overwinter in the egg stage in the soil. Eggs, which are deposited in the soil during the summer, are American football-shaped, white, and less than long. Larvae hatch in late May or early June and begin to feed on corn roots. Newly hatched larvae are small, less than long, white worms. Corn rootworms go through three larval instars, pupate in the soil and emerge as adults in July and August. One generation emerges each year. Larvae have brown heads and a brown mark
|
https://en.wikipedia.org/wiki/Selberg%20trace%20formula
|
In mathematics, the Selberg trace formula, introduced by , is an expression for the character of the unitary representation of a Lie group on the space of square-integrable functions, where is a cofinite discrete group. The character is given by the trace of certain functions on .
The simplest case is when is cocompact, when the representation breaks up into discrete summands. Here the trace formula is an extension of the Frobenius formula for the character of an induced representation of finite groups. When is the cocompact subgroup of the real numbers , the Selberg trace formula is essentially the Poisson summation formula.
The case when is not compact is harder, because there is a continuous spectrum, described using Eisenstein series. Selberg worked out the non-compact case when is the group ; the extension to higher rank groups is the Arthur–Selberg trace formula.
When is the fundamental group of a Riemann surface, the Selberg trace formula describes the spectrum of differential operators such as the Laplacian in terms of geometric data involving the lengths of geodesics on the Riemann surface. In this case the Selberg trace formula is formally similar to the explicit formulas relating the zeros of the Riemann zeta function to prime numbers, with the zeta zeros corresponding to eigenvalues of the Laplacian, and the primes corresponding to geodesics. Motivated by the analogy, Selberg introduced the Selberg zeta function of a Riemann surface, whose analytic pr
|
https://en.wikipedia.org/wiki/Ehresmann%27s%20lemma
|
In mathematics, or specifically, in differential topology, Ehresmann's lemma or Ehresmann's fibration theorem states that if a smooth mapping , where and are smooth manifolds, is
a surjective submersion, and
a proper map (in particular, this condition is always satisfied if M is compact),
then it is a locally trivial fibration. This is a foundational result in differential topology due to Charles Ehresmann, and has many variants.
See also
Thom's first isotopy lemma
References
Theorems in differential topology
|
https://en.wikipedia.org/wiki/L1
|
L1, L01, L.1, L 1 or L-1 may refer to:
Mathematics, science and technology
Math
L1 distance in mathematics, used in taxicab geometry
L1, the space of Lebesgue integrable functions
ℓ1, the space of absolutely convergent sequences
Science
L1 family, a protein family of cell adhesion molecules
L1 (protein), a cell adhesion molecule
L1 or LINE1; transposable elements in the DNA
, Lagrangian point 1, the most intuitive position for an object to be gravitationally stationary relative to two larger objects (such as a satellite with respect to the Earth and Moon)
Anthranilic acid, also called vitamin L1
The first lumbar vertebra of the vertebral column in human anatomy
The first larval stage in the Caenorhabditis elegans worm development
Technology
L1, one of the frequencies used by GPS systems (see GPS frequencies)
L1, the common name for the Soviet space effort known formally as Soyuz 7K-L1, designed to launch men from the Earth to circle the Moon without going into lunar orbit
ISO/IEC 8859-1 (Latin-1), an 8-bit character encoding
An L-carrier cable system developed by AT&T
The level-1 CPU cache in a computer
Sony Xperia L1, an Android smartphone
A class of FM broadcast station in North America
Transportation and military
Lehrgeschwader 1, from its historic Geschwaderkennung code with the Luftwaffe in World War II
Lufthansa Systems' IATA code
Lawrance L-1, a predecessor of the 1920s American Lawrance J-1 aircraft engine
Inner West Light Rail, a light rail ser
|
https://en.wikipedia.org/wiki/Star%20refinement
|
In mathematics, specifically in the study of topology and open covers of a topological space X, a star refinement is a particular kind of refinement of an open cover of X. A related concept is the notion of barycentric refinement.
Star refinements are used in the definition of fully normal space and in one definition of uniform space. It is also useful for stating a characterization of paracompactness.
Definitions
The general definition makes sense for arbitrary coverings and does not require a topology. Let be a set and let be a covering of that is, Given a subset of the star of with respect to is the union of all the sets that intersect that is,
Given a point we write instead of
A covering of is a refinement of a covering of if every is contained in some The following are two special kinds of refinement. The covering is called a barycentric refinement of if for every the star is contained in some The covering is called a star refinement of if for every the star is contained in some
Properties and Examples
Every star refinement of a cover is a barycentric refinement of that cover. The converse is not true, but a barycentric refinement of a barycentric refinement is a star refinement.
Given a metric space let be the collection of all open balls of a fixed radius The collection is a barycentric refinement of and the collection is a star refinement of
See also
Notes
References
General topology
|
https://en.wikipedia.org/wiki/Killing%20form
|
In mathematics, the Killing form, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and Lie algebras. Cartan's criteria (criterion of solvability and criterion of semisimplicity) show that Killing form has a close relationship to the semisimplicity of the Lie algebras.
History and name
The Killing form was essentially introduced into Lie algebra theory by in his thesis. In a historical survey of Lie theory, has described how the term "Killing form" first occurred in 1951 during one of his own reports for the Séminaire Bourbaki; it arose as a misnomer, since the form had previously been used by Lie theorists, without a name attached. Some other authors now employ the term "Cartan-Killing form". At the end of the 19th century, Killing had noted that the coefficients of the characteristic equation of a regular semisimple element of a Lie algebra are invariant under the adjoint group, from which it follows that the Killing form (i.e. the degree 2 coefficient) is invariant, but he did not make much use of the fact. A basic result that Cartan made use of was Cartan's criterion, which states that the Killing form is non-degenerate if and only if the Lie algebra is a direct sum of simple Lie algebras.
Definition
Consider a Lie algebra over a field . Every element of defines the adjoint endomorphism (also written as ) of with the help of the Lie bracket, as
Now, supposing is of finite dimension, the trace of th
|
https://en.wikipedia.org/wiki/Taqi%20ad-Din%20Muhammad%20ibn%20Ma%27ruf
|
Taqi ad-Din Muhammad ibn Ma'ruf ash-Shami al-Asadi (; ; 1526–1585) was an Ottoman polymath active in Cairo and Istanbul. He was the author of more than ninety books on a wide variety of subjects, including astronomy, clocks, engineering, mathematics, mechanics, optics and natural philosophy.
In 1574 the Ottoman Sultan Murad III invited Taqi ad-Din to build an observatory in the Ottoman capital, Istanbul. Taqi ad-Din constructed instruments such as an armillary sphere and mechanical clocks that he used to observe the Great Comet of 1577. He also used European celestial and terrestrial globes that were delivered to Istanbul in gift exchanges.
His major work from the use of his observatory is titled "The tree of ultimate knowledge [in the end of time or the world] in the Kingdom of the Revolving Spheres: The astronomical tables of the King of Kings [Murad III]" (Sidrat al-muntah al-afkar fi malkūt al-falak al-dawār– al-zij al-Shāhinshāhi). The work was prepared according to the results of the observations carried out in Egypt and Istanbul in order to correct and complete Ulugh Beg's 15th century work, the Zij-i Sultani. The first 40 pages of the work dealt with calculations, followed by discussions of astronomical clocks, heavenly circles, and information on three eclipses which he observed in Cairo and Istanbul.
As a polymath, Taqi al-Din wrote numerous books on astronomy, mathematics, mechanics, and theology. His method of finding coordinates of stars were reportedly so p
|
https://en.wikipedia.org/wiki/Double%20coset
|
In group theory, a field of mathematics, a double coset is a collection of group elements which are equivalent under the symmetries coming from two subgroups. More precisely, let be a group, and let and be subgroups. Let act on by left multiplication and let act on by right multiplication. For each in , the -double coset of is the set
When , this is called the -double coset of . Equivalently, is the equivalence class of under the equivalence relation
if and only if there exist in and in such that .
The set of all -double cosets is denoted by
Properties
Suppose that is a group with subgroups and acting by left and right multiplication, respectively. The -double cosets of may be equivalently described as orbits for the product group acting on by . Many of the basic properties of double cosets follow immediately from the fact that they are orbits. However, because is a group and and are subgroups acting by multiplication, double cosets are more structured than orbits of arbitrary group actions, and they have additional properties that are false for more general actions.
Two double cosets and are either disjoint or identical.
is the disjoint union of its double cosets.
There is a one-to-one correspondence between the two double coset spaces and given by identifying with .
If , then . If , then .
A double coset is a union of right cosets of and left cosets of ; specifically,
The set of -double cosets is in bijection with the orb
|
https://en.wikipedia.org/wiki/Society%20of%20Physics%20Students
|
The Society of Physics Students (SPS) is a professional association with international participation, granting membership through college chapters with the only requirement that the student member be interested in physics. All college majors are welcome to join SPS, but the highest representation tends to come from majors in the natural sciences, engineering, and medicine.
National organization
The SPS's national council and its executive committee decide the policies of SPS. The national council is made up of 36 members, elected by chapters from one of 18 geographic zones. Each zone represents a section of the country and is represented by a faculty zone councilor and a student associate councilor. Both councilors and associate councilors participate in zone activities and in the annual policy-making meeting of the council. The SPS's executive committee consists of the presidents of the Society of Physics Students and Sigma Pi Sigma, the SPS national office director, the SPS/Sigma Pi Sigma historian, an at-large member, a student representative, and the CEO of the American Institute of Physics. The director of the SPS national office is Brad R. Conrad, a salaried physicist designated by as the Executive Administrative Officer of the Society. The director is supported by additional National Office staff from the American Institute of Physics (AIP) Education Division.
Programs and activities
SPS strives to shape students into contributing members of the professional sc
|
https://en.wikipedia.org/wiki/Kevin%20E.%20Trenberth
|
Kevin Edward Trenberth (born 8 November 1944) was part of the Climate Analysis Section at the US NCAR National Center for Atmospheric Research. He was appointed Distinguished Scholar at NCAR in 2020. He is also an honorary faculty member in the Physics Department at the University of Auckland, New Zealand. He was a lead author of the 1995, 2001 and 2007 IPCC Scientific Assessment of Climate Change (see IPCC Fourth Assessment Report) and served on the Scientific Steering Group for the Climate Variability and Predictability (CLIVAR) program. He chaired the WCRP Observation and Assimilation Panel from 2004 to 2010 and chaired the Global Energy and Water Exchanges (GEWEX) scientific steering group from 2010 to 2013 (member 2007-14). In addition, he served on the Joint Scientific Committee of the World Climate Research Programme, and has made significant contributions to research into El Niño-Southern Oscillation.
Trenberth's work is highly cited and he had an h-index of 100 (100 papers have over 100 citations) in 2020.
Awards
Trenberth is a fellow of the American Meteorological Society (AMS), the American Association for Advancement of Science, and the American Geophysical Union; and an honorary fellow of the Royal Society of New Zealand. In 2000 he received the Jule G. Charney award from the American Meteorological Society; in 2003 he was given the NCAR Distinguished Achievement Award; and in 2013 he was awarded the Prince Sultan Bin Abdulaziz International Prize for Water,
|
https://en.wikipedia.org/wiki/List%20of%20people%20from%20Bangalore
|
This is a list of notable people from Bangalore.
Founder and Architect of Bengaluru
Nada Prabhu Kempe Gowda
Scientists
C V Raman – Nobel Prize in Physics (1930), Bharat Ratna (1954)
M. Visvesvarayya – Bharat Ratna, in 1955, Indian civil engineer, statesman, Diwan of Mysore
C. N. R. Rao – Bharat Ratna (2014) Indian Institute of Science (Material Sciences) Bharat Ratna (2014)
H Narasimhaiah – Indian physicist, educator, writer, freedom fighter and rationalist Padma Bhushan (1984)
Bangalore Puttaiya Radhakrishna – geologist
Politicians
H. D. Deve Gowda - former prime minister
H. D. Kumaraswamy - former chief minister of Karnataka
Gundu Rao - former Chief Minister
Siddaramaiah - former Chief Minister
B S Yediyurappa - former Chief Minister
Ramalinga Reddy - former State Home Minister and various ministry, seven time MLA from Bangalore
D. K. Shivakumar - former minister of medical education
B.Vaikunta Vaikunta Baliga - former Law Minister; former Speaker, Mysore State
S.Bangarappa - former Chief Minister
S. R. Bommai - former Chief Minister
George Fernandes - former Defence Minister
Kengal Hanumanthaiah - former Chief Minister
Ramakrishna Hegde - former Chief Minister
Qamar ul Islam - former Housing and Labour Minister
Basappa Danappa Jatti - former Vice-President
M.N. Jois - former M.L.C, Deputy Speaker of Legislative Council - Mysore State
Mallikarjun Kharge - former State Minister (various portfolios); former Union Labour Minister in the Manmohan S
|
https://en.wikipedia.org/wiki/What%20the%20Bleep%20Do%20We%20Know%21%3F
|
What the Bleep Do We Know!? (stylized as What tнē #$*! D̄ө ωΣ (k)πow!? and What the #$*! Do We Know!?) is a 2004 American pseudo-scientific film that posits a spiritual connection between quantum physics and consciousness. The plot follows the fictional story of a photographer, using documentary-style interviews and computer-animated graphics, as she encounters emotional and existential obstacles in her life and begins to consider the idea that individual and group consciousness can influence the material world. Her experiences are offered by the filmmakers to illustrate the film's scientifically unsupported thesis about quantum physics and consciousness.
Bleep was conceived and its production funded by William Arntz, who co-directed the film along with Betsy Chasse and Mark Vicente; all three were students of Ramtha's School of Enlightenment. A moderately low-budget independent film, it was promoted using viral marketing methods and opened in art-house theaters in the western United States, winning several independent film awards before being picked up by a major distributor and eventually grossing over $10 million. The 2004 theatrical release was succeeded by a substantially changed, extended home media version in 2006.
The film has been described as an example of quantum mysticism, and has been criticized for both misrepresenting science and containing pseudoscience. While many of its interviewees and subjects are professional scientists in the fields of physics, chemis
|
https://en.wikipedia.org/wiki/Fon
|
Fon or FON may refer to:
Terms
Fon (title), a traditional title for a ruler in Cameroon
Fiber-optic network
Freedom of navigation
The chemistry mnemonic "FON", used for determining which elements hydrogen forms hydrogen bonds with.
Fon language, spoken by the Fon people
Funding Opportunity Number, assigned by United States federal agencies to available grants
Organizations
Fon (company), a Wi-Fi provider
Federation of Ontario Naturalists, now Ontario Nature, a Canadian environmental organization
FON University, university in Macedonia
University of Belgrade Faculty of Organizational Sciences, faculty in Serbia
Fundusz Obrony Narodowej, or Fund for National Defense, a collection attempt in Poland prior to World War II
Sprint Corporation
People
Fon people, a major West African ethnic and linguistic group
Bryn Fôn (born 1954), Welsh actor and musician
Other
Fish On Next, a video game
Fon Fjord in Greenland
See also
Fun (disambiguation)
Fawn (disambiguation)
Faun (disambiguation)
Phon (disambiguation)
Language and nationality disambiguation pages
|
https://en.wikipedia.org/wiki/Sed%20%28disambiguation%29
|
sed is a Unix utility for processing text.
Sed or SED may also refer to:
Science and technology
Spectral energy distribution, of an astronomical source
Stochastic electrodynamics, in quantum mechanics
Sedirea (Sed.), a genus of orchids
Medicine
Selective eating disorder or avoidant/restrictive food intake disorder
Spondyloepiphyseal dysplasia congenita, an inherited genetic bone disorder
Erythrocyte sedimentation rate (sed rate), a haematology test
Technology, engineering and computing
Surface-conduction electron-emitter display, a flat-panel display technology
DEC SED (text editor), for some DEC operating systems
Self-encrypting device, an encrypting hard drive
Organisations
Socialist Unity Party of Germany (), East German communist party
Swiss Seismological Service ()
Education
Scottish Education Department
Companies
SED Systems, a Canadian satellite communications provider
Tata Power SED, Tata Power Strategic Electronics Division
Other uses
Survey of English Dialects
Strategic Economic Dialogue
Sed card, a "portfolio-on-a-card" used by models and actors
Sed festival, in Ancient Egypt
Shippers Export Declaration, a US form
See also
Students for the Exploration and Development of Space (SEDS)
|
https://en.wikipedia.org/wiki/Keldysh%20Institute%20of%20Applied%20Mathematics
|
The Keldysh Institute of Applied Mathematics () is a research institute specializing in computational mathematics. It was established to solve computational tasks related to government programs of nuclear and fusion energy, space research and missile technology. The Institute is a part of the Department of Mathematical Sciences of the Russian Academy of Sciences. The main direction of activity of the institute is the use of computer technology to solve complex scientific and technical issues of practical importance. Since 2016, the development of mathematical and computational methods for biological research, as well as a direct solution to the problems of computational biology with the use of such methods, has also been included in the circle of scientific activities of the institute.
Scientific activity
Nuclear physics
Theoretical physicist Yakov Borisovich Zel'dovich headed one of the departments placed in charge of the theoretical aspects of the work on the creation of nuclear and thermonuclear weapons. Alexander Andreevich Samarskii performed the first realistic calculations of macrokinetics of chain reaction of a nuclear explosion, which led to the practical importance estimated power of nuclear weapons. In relation to nuclear energy, the institute was also involved in modelling of processes of neutron transport and nuclear reactions. In particular, E. Kuznetsov is known for his work on the theory of nuclear reactors.
Currently, such work in KIAM is continuing in the
|
https://en.wikipedia.org/wiki/Steklov%20Institute%20of%20Mathematics
|
Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Steklov, who in 1919 founded the Institute of Physics and Mathematics in Leningrad. In 1934, this institute was split into separate parts for physics and mathematics, and the mathematical part became the Steklov Institute. At the same time, it was moved to Moscow. The first director of the Steklov Institute was Ivan Matveyevich Vinogradov. From 19611964, the institute's director was the notable mathematician Sergei Chernikov.
The old building of the Institute in Leningrad became its Department in Leningrad. Today, that department has become a separate institute, called the St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences or PDMI RAS, located in Saint Petersburg, Russia. The name St. Petersburg Department is misleading, however, because the St. Petersburg Department is now an independent institute. In 1966, the Moscow-based Keldysh Institute of Applied Mathematics (Russian: Институт прикладной математики им. М.В.Келдыша) split off from the Steklov Institute.
References
External links
Steklov Mathematical Institute
Petersburg Department of Steklov Institute of Mathematics
Mathematical institutes
Buildings and structures in Moscow
Education in Moscow
Research institutes in Russia
Universi
|
https://en.wikipedia.org/wiki/Viva%20Las%20Vegas
|
Viva Las Vegas is a 1964 American musical film directed by George Sidney, choreographed by David Winters, and starring Elvis Presley and Ann-Margret. The film is regarded by fans and film critics as one of Presley's best films, and it is noted for the on-screen chemistry between Presley and Ann-Margret.
Viva Las Vegas was a hit at film theaters, as it was #14 on the Variety year end box office list of the top-grossing films of 1964.
Plot
Lucky Jackson (Elvis) goes to Las Vegas, Nevada to participate in the city's first annual Grand Prix Race. However, his race car, an Elva Mark VI, is in need of a new engine in order to compete in the event.
Lucky raises the necessary money in Las Vegas, but he loses it when he is shoved into the pool by the hotel's young swimming instructor, Rusty Martin (Ann-Margret). Lucky then has to work as a waiter at the hotel to replace the lost money to pay his hotel bill, as well as enter the hotel's talent contest in hopes of winning a cash prize sizable enough to pay for his car's engine.
During all this time, Lucky attempts to win the affections of Rusty. His main competition arrives in the form of Count Elmo Mancini (Cesare Danova) and his Ferrari 250 GT Berlinetta. Mancini attempts to win both the Grand Prix and the affections of Rusty. Rusty soon falls in love with Lucky, and immediately tries to change him into what she wants.
Cast
Production
George Sidney later said "that was one of those cases where we had no script and we had a comm
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.