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https://en.wikipedia.org/wiki/Feynman%20parametrization
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Feynman parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. However, it is sometimes useful in integration in areas of pure mathematics as well.
Formulas
Richard Feynman observed that:
which is valid for any complex numbers A and B as long as 0 is not contained in the line segment connecting A and B. The formula helps to evaluate integrals like:
If A(p) and B(p) are linear functions of p, then the last integral can be evaluated using substitution.
More generally, using the Dirac delta function :
This formula is valid for any complex numbers A1,...,An as long as 0 is not contained in their convex hull.
Even more generally, provided that for all :
where the Gamma function was used.
Derivation
By using the substitution ,
we have , and ,
from which we get the desired result
In more general cases, derivations can be done very efficiently using the Schwinger parametrization. For example, in order to derive the Feynman parametrized form of , we first reexpress all the factors in the denominator in their Schwinger parametrized form:
and rewrite,
Then we perform the following change of integration variables,
to obtain,
where denotes integration over the region with .
The next step is to perform the integration.
where we have defined
Substituting this result, we get to the penultimate form,
and, after introducing an extra integral, we arrive at the final form of the Feynman parametrizati
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https://en.wikipedia.org/wiki/MINOS
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Main injector neutrino oscillation search (MINOS) was a particle physics experiment designed to study the phenomena of neutrino oscillations, first discovered by a Super-Kamiokande (Super-K) experiment in 1998. Neutrinos produced by the NuMI ("Neutrinos at Main Injector") beamline at Fermilab near Chicago are observed at two detectors, one very close to where the beam is produced (the near detector), and another much larger detector 735 km away in northern Minnesota (the far detector).
The MINOS experiment started detecting neutrinos from the NuMI beam in February 2005. On 30 March 2006, the MINOS collaboration announced that the analysis of the initial data, collected in 2005, is consistent with neutrino oscillations, with the oscillation parameters which are consistent with Super-K measurements.
MINOS received the last neutrinos from the NUMI beam line at midnight on 30 April 2012. It was upgraded to MINOS+ which started taking data in 2013. The experiment was shut down on June 29, 2016, and the far detector has been dismantled and removed.
Detectors
There are two detectors in the experiment.
The near detector is similar to the far detector in design, but smaller in size with a mass of (t). It is located at Fermilab, a few hundred meters away from the graphite target which the protons interact with, and approximately 100 meters underground. The commissioning of the near detector was completed in December 2004, and it is now fully operational.
The far detector has a mas
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https://en.wikipedia.org/wiki/William%20Brydone%20Jack
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William Brydone Jack, (23 November 1817 – 23 November 1886), was the University of New Brunswick's first surveying professor and its second president (1861-1885). He was educated at the University of St Andrews, Scotland. In 1840, he was appointed Professor of Mathematics and Natural Philosophy at what was then King's College (founded in 1785) and gave lectures in surveying as part of the mathematics curriculum. William Brydone Jack also designed a small wooden observatory which became operational in 1851.
In 1855, William Brydone Jack, together with Dr. J.B. Toldervy, determined the longitude of Fredericton using the exchange of telegraph signals with Harvard College Observatory. This was the first precisely determined longitude in Canada.
In 1859, the same year that the University of New Brunswick was created, a special three-term undergraduate course in civil engineering and surveying was initiated. The first diploma in this special course was awarded to Henry George Clopper Ketchum in June 1862. William Brydone Jack was appointed to the Board of Examiners in 1874 for the examination of candidates for admission to practice land surveying in New Brunswick.
J.E. Kennedy, professor of physics at UNB from 1945 to 1956, wrote extensively on William Brydone Jack's accomplishments in astronomy and land surveying including his efforts to build the observatory and the determination of longitude by electric telegraph.
Minor planet 79117 Brydonejack is named in his honor.
Re
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https://en.wikipedia.org/wiki/WeBWorK
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WeBWorK is an online homework delivery system primarily used for mathematics and science. It allows students to complete their homework over the web, and receive instantaneous feedback as to the correctness of their responses. WeBWorK uses a Perl-based language called PG to specify exercises, which allows instructors a great deal of flexibility in how exercises are presented.
WeBWorK was originally developed at the University of Rochester by professors Michael Gage and Arnold Pizer. It is now a free software project maintained by many contributors at several colleges and universities. It is made available under the Artistic License (the same license as Perl) and the GNU General Public License. WeBWorK is currently maintained by The WeBWorK Project.
WeBWorK is currently used by many universities and high-schools around the world.
WeBWorK is supported by the National Science Foundation and the Mathematical Association of America.
References
External links
WeBWorK Site
Original WeBWorK Site
Learning management systems
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https://en.wikipedia.org/wiki/Two-graph
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In mathematics, a two-graph is a set of (unordered) triples chosen from a finite vertex set X, such that every (unordered) quadruple from X contains an even number of triples of the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have been studied because of their connection with equiangular lines and, for regular two-graphs, strongly regular graphs, and also finite groups because many regular two-graphs have interesting automorphism groups.
A two-graph is not a graph and should not be confused with other objects called 2-graphs in graph theory, such as 2-regular graphs.
Examples
On the set of vertices {1,...,6} the following collection of unordered triples is a two-graph:
123 124 135 146 156 236 245 256 345 346
This two-graph is a regular two-graph since each pair of distinct vertices appears together in exactly two triples.
Given a simple graph G = (V,E), the set of triples of the vertex set V whose induced subgraph has an odd number of edges forms a two-graph on the set V. Every two-graph can be represented in this way. This example is referred to as the standard construction of a two-graph from a simple graph.
As a more complex example, let T be a tree with edge set E. The set of all triples of E that are not contained in a path of T form a two-graph on the set E.
Switching and graphs
A two-graph is equivalent to a switching class of graphs and also to a (signed) s
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https://en.wikipedia.org/wiki/Jim%20Horning
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James Jay Horning (24 August 1942 – 18 January 2013) was an American computer scientist and ACM Fellow.
Overview
Jim Horning received a PhD in computer science from Stanford University in 1969 for a thesis entitled A Study of Grammatical Inference. He was a founding member, and later chairman, of the Computer Systems Research Group at the University of Toronto, Canada, from 1969 until 1977. He was then a Research Fellow at the Xerox Palo Alto Research Center (PARC) from 1977 until 1984 and a founding member and senior consultant at DEC Systems Research Center (DEC/SRC) from 1984 until 1996. He was founder and director of STAR Lab from 1997 until 2001 at InterTrust Technologies Corp.
Peter G. Neumann reported on 22 January 2013 in the RISKS Digest, Volume 27, Issue 14, that Horning had died on 18 January 2013.
Horning's interests included programming languages, programming methodology, specification, formal methods, digital rights management and computer/network security. A major contribution was his involvement with the Larch approach to formal specification with John Guttag (MIT) et al.
Selected publications
A Compiler Generator (with William M. McKeeman and D. B. Wortman), Prentice Hall (1970). .
References
External links
Home page
Curriculum Vitae
1942 births
2013 deaths
Stanford University alumni
American computer scientists
Academic staff of the University of Toronto
Xerox people
Digital Equipment Corporation people
Fellows of the Association for Computing Mach
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https://en.wikipedia.org/wiki/Proximity%20effect
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Proximity effect may refer to:
Proximity effect (atomic physics)
Proximity effect (audio), an increase in bass or low frequency response when a sound source is close to a microphone
Proximity Effect (comics), a comic book series written by Scott Tucker and Aron Coleite
Proximity effect (electromagnetism), magnetically induced current distortions resulting in increased effective resistance of a conductor
Proximity effect (electron beam lithography), a phenomenon in electron beam lithography (EBL)
Proximity effect (superconductivity), a term used in the field of superconductivity
The Proximity Effect (Nada Surf album), 1998
The Proximity Effect (Laki Mera album), 2011
See also
Pressure sensitive (disambiguation)
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https://en.wikipedia.org/wiki/Fuzzy%20agent
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In computer science a fuzzy agent is a software agent that implements fuzzy logic. This software entity interacts with its environment through an adaptive rule-base and can therefore be considered a type of intelligent agent.
References
Artificial intelligence
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https://en.wikipedia.org/wiki/Physics%20education
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Physics education or physics teaching refers to the education methods currently used to teach physics. The occupation is called physics educator or physics teacher. Physics education research refers to an area of pedagogical research that seeks to improve those methods. Historically, physics has been taught at the high school and college level primarily by the lecture method together with laboratory exercises aimed at verifying concepts taught in the lectures. These concepts are better understood when lectures are accompanied with demonstration, hand-on experiments, and questions that require students to ponder what will happen in an experiment and why. Students who participate in active learning for example with hands-on experiments learn through self-discovery. By trial and error they learn to change their preconceptions about phenomena in physics and discover the underlying concepts. Physics education is part of the broader area of science education.
Ancient Greece
Aristotle wrote what is considered now as the first textbook of physics. Aristotle's ideas were taught unchanged until the Late Middle Ages, when scientists started making discoveries that didn't fit them. For example, Copernicus' discovery contradicted Aristotle's idea of an Earth-centric universe. Aristotle's ideas about motion weren't displaced until the end of the 17th century, when Newton published his ideas.
Today's physics students often think of physics concepts in Aristotelian terms, despite being tau
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https://en.wikipedia.org/wiki/Nonlinearity%20%28disambiguation%29
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Nonlinearity is a property of mathematical functions or data that cannot be graphed on straight lines, systems whose output(s) are not directly proportional to their input(s), objects that do not lie along straight lines, shapes that are not composed of straight lines, or events that are shown or told out-of-sequence.
Science and mathematics
Nonlinear acoustics is a branch of physics and acoustics dealing with sound waves of sufficiently large amplitudes.
A nonlinear complementarity problem is found in applied mathematics.
Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both.
Nonlinear dimensionality reduction is a simplification that assumes that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space.
Nonlinear element, or nonlinear device, is an electrical element which does not have a linear relationship between current and voltage, e.g. a diode.
Nonlinear functional analysis is a branch of Mathematical Analysis that deals with nonlinear mappings.
Nonlinear optics, in physics, examines the properties of light in media in which the polarization responds nonlinearly to the electric field.
Nonlinear photonic crystals are periodic structures whose optical response depends on the intensity of the optical field that propagates into the crystal.
Nonlinear programming is the process of solving an optimization problem, where some of the parameters are nonlinear.
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https://en.wikipedia.org/wiki/Classical%20superconductor
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Classical superconductor may refer to:
In the context of classical electrodynamics or general physics: a perfect conductor with no special quantum mechanical properties. No such substances are known to exist, but they are useful simplifications of certain systems such as magnetohydrodynamics and electrical circuits.
In the context of high-temperature superconductivity: a conventional superconductor.
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https://en.wikipedia.org/wiki/Vector%20group
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In electrical engineering, a vector group, officially called a connection symbol, is the International Electrotechnical Commission (IEC) method of categorizing the high voltage (HV) windings and low voltage (LV) winding configurations of three-phase transformers. The vector group designation indicates the windings configurations and the difference in phase angle between them. For example, a star HV winding and delta LV winding with a 30-degree lead is denoted as Yd11.
The phase windings of a polyphase transformer can be connected internally in different configurations, depending on what characteristics are needed from the transformer. In a three-phase power system, it may be necessary to connect a three-wire system to a four-wire system, or vice versa. Because of this, transformers are manufactured with a variety of winding configurations to meet these requirements.
Different combinations of winding connections will result in different phase angles between the voltages on the windings. Transformers connected in parallel must have the same vector group; mismatching phase angles will result in circulating current and other system disturbances.
Symbol designation
The vector group provides a simple way of indicating how the connections of a transformer are arranged. In the system adopted by the IEC, the vector group is indicated by a code consisting of two or three letters, followed by one or two numeric digits. The letters indicate the winding configuration as follows:
D or
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https://en.wikipedia.org/wiki/Lehmer%E2%80%93Schur%20algorithm
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In mathematics, the Lehmer–Schur algorithm (named after Derrick Henry Lehmer and Issai Schur) is a root-finding algorithm for complex polynomials, extending the idea of enclosing roots like in the one-dimensional bisection method to the complex plane. It uses the Schur-Cohn test to test increasingly smaller disks for the presence or absence of roots.
Schur-Cohn algorithm
This algorithm allows one to find the distribution of the roots of a complex polynomial with respect to the unit circle in the complex plane. It is based on two auxiliary polynomials, introduced by Schur.
For a complex polynomial of degree its reciprocal adjoint polynomial is defined by and its Schur Transform by
where a bar denotes complex conjugation.
So, if with , then
,
with leading zero-terms, if any, removed. The coefficients of can therefore be directly expressed in those of and, since one or more leading coefficients cancel, has lower degree than . The roots of , , and are related as follows.
Lemma
Let be a complex polynomial and .
The roots of , including their multiplicities, are the images under inversion in the unit circle of the non-zero roots of .
If , then , and share roots on the unit circle, including their multiplicities.
If , then and have the same number of roots inside the unit circle.
If , then and have the same number of roots inside the unit circle.
Proof
For we have and, in particular,
for .
Also implies . From this and the definitions above the first t
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https://en.wikipedia.org/wiki/Cryptologic
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Cryptologic can refer to:
Cryptography, the study of message secrecy
CryptoLogic, a provider of online gambling software
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https://en.wikipedia.org/wiki/Fourth%20dimension
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Fourth dimension may refer to:
Science
Time in physics, the continued progress of existence and events
Four-dimensional space, the concept of a fourth spatial dimension
Spacetime, the unification of time and space as a four-dimensional continuum
Minkowski space, the mathematical setting for special relativity
Arts and media
Fourth dimension in art
Film
The Fourth Dimension, a 1988 experimental film by Zbigniew Rybczyński
The 4th Dimension (film), a 2008 film
The Fourth Dimension (film), a 2012 film made up of three segments, each with a different director
Literature
Fourth dimension in literature
The Fourth Dimension (book), a 1984 non-fiction book by Rudy Rucker
The Fourth Dimension, a book by David Yonggi Cho
Music
The Fourth Dimension (Hypocrisy album), 1994
The Fourth Dimension (Jack McDuff album), 1974
Fourth Dimension (Stratovarius album), 1995
Fourth Dimension (Radiophonic album), by Paddy Kingsland
Fourth Dimension Records, a UK record label
"The 4th Dimension", a song by Devo on their album Shout
"Fourth Dimension", a song by Lights on her album Siberia
4th Dimension, a jazz fusion quartet founded in 2007 by John McLaughlin
"4th Dimension" (song), a song by Kids See Ghosts on their 2018 album Kids See Ghosts
Computing
The Fourth Dimension (company), a publisher of computer games
4th Dimension (software), a relational database management system
Other
Four-dimensionalism, a philosophical view
4th Dimension roller coaster, a type of roller
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https://en.wikipedia.org/wiki/Sprengel
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Sprengel is a surname. Notable people with the surname include:
Hermann Sprengel (1834–1906), chemist
Karl or Carl Sprengel (1787–1859), botanist
Kurt Sprengel (1766–1833), botanist
Christian Konrad Sprengel (1750–1816), teacher and theologist who studied flower biology
Bernhard Sprengel (1899–1985), chocolate manufacturer and art collector
See also
Sprengel Museum, a museum of modern art in Hanover, Germany
Sprengel pump, a vacuum pump invented by Hermann Sprengel
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https://en.wikipedia.org/wiki/Symmetry%20in%20mathematics
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Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations.
Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. This can occur in many ways; for example, if X is a set with no additional structure, a symmetry is a bijective map from the set to itself, giving rise to permutation groups. If the object X is a set of points in the plane with its metric structure or any other metric space, a symmetry is a bijection of the set to itself which preserves the distance between each pair of points (i.e., an isometry).
In general, every kind of structure in mathematics will have its own kind of symmetry, many of which are listed in the given points mentioned above.
Symmetry in geometry
The types of symmetry considered in basic geometry include reflectional symmetry, rotation symmetry, translational symmetry and glide reflection symmetry, which are described more fully in the main article Symmetry (geometry).
Symmetry in calculus
Even and odd functions
Even functions
Let f(x) be a real-valued function of a real variable, then f is even if the following equation holds for all x and -x in the domain of f:
Geometrically speaking, the graph face of an even function is symmetric with respect to the y-axis, meaning that its graph remains unchanged after reflect
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https://en.wikipedia.org/wiki/Applications%20of%20randomness
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Randomness has many uses in science, art, statistics, cryptography, gaming, gambling, and other fields. For example, random assignment in randomized controlled trials helps scientists to test hypotheses, and random numbers or pseudorandom numbers help video games such as video poker.
These uses have different levels of requirements, which leads to the use of different methods. Mathematically, there are distinctions between randomization, pseudorandomization, and quasirandomization, as well as between random number generators and pseudorandom number generators. For example, applications in cryptography usually have strict requirements, whereas other uses (such as generating a "quote of the day") can use a looser standard of pseudorandomness.
Early uses
Games
Unpredictable (by the humans involved) numbers (usually taken to be random numbers) were first investigated in the context of gambling developing, sometimes, pathological forms like apophenia. Many randomizing devices such as dice, shuffling playing cards, and roulette wheels, seem to have been developed for use in games of chance. Electronic gambling equipment cannot use these and so theoretical problems are less easy to avoid; methods of creating them are sometimes regulated by governmental gaming commissions.
Modern electronic casino games contain often one or more random number generators which decide the outcome of a trial in the game. Even in modern slot machines, where mechanical reels seem to spin on the scree
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https://en.wikipedia.org/wiki/Eric%20Hehner
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Eric "Rick" C. R. Hehner (born 16 September 1947) is a Canadian computer scientist. He was born in Ottawa. He studied mathematics and physics at Carleton University, graduating with a Bachelor of Science (B.Sc.) in 1969. He studied computer science at the University of Toronto, graduating with a Master of Science (M.Sc.) in 1970, and a Doctor of Philosophy (Ph.D.) in 1974. He then joined the faculty there, becoming a full professor in 1983. He became the Bell University Chair in software engineering in 2001, and retired in 2012.
Hehner's main research area is formal methods of software design. His method, initially called predicative programming, later called Practical Theory of Programming, is to consider each specification to be a binary (boolean) expression, and each programming construct to be a binary expression specifying the effect of executing the programming construct. Refinement is just implication. This is the simplest formal method, and the most general, applying to sequential, parallel, stand-alone, communicating, terminating, nonterminating, natural-time, real-time, deterministic, and probabilistic programs, and includes time and space bounds. This idea has influenced other computer science researchers, including Tony Hoare.
Hehner's other research areas include probabilistic programming, unified algebra, and high-level circuit design. In 1979, Hehner invented a generalization of radix complement called quote notation, which is a representation of the rational
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https://en.wikipedia.org/wiki/Prime%20signature
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In mathematics, the prime signature of a number is the multiset of (nonzero) exponents of its prime factorization. The prime signature of a number having prime factorization is the multiset .
For example, all prime numbers have a prime signature of {1}, the squares of primes have a prime signature of {2}, the products of 2 distinct primes have a prime signature of } and the products of a square of a prime and a different prime (e.g. 12, 18, 20, ...) have a prime signature of }.
Properties
The divisor function τ(n), the Möbius function μ(n), the number of distinct prime divisors ω(n) of n, the number of prime divisors Ω(n) of n, the indicator function of the squarefree integers, and many other important functions in number theory, are functions of the prime signature of n.
In particular, τ(n) equals the product of the incremented by 1 exponents from the prime signature of n.
For example, 20 has prime signature {2,1} and so the number of divisors is (2+1) × (1+1) = 6. Indeed, there are six divisors: 1, 2, 4, 5, 10 and 20.
The smallest number of each prime signature is a product of primorials. The first few are:
1, 2, 4, 6, 8, 12, 16, 24, 30, 32, 36, 48, 60, 64, 72, 96, 120, 128, 144, 180, 192, 210, 216, ... .
A number cannot divide another unless its prime signature is included in the other numbers prime signature in the Young's lattice.
Numbers with same prime signature
Sequences defined by their prime signature
Given a number with prime signature S, it is
A prime
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https://en.wikipedia.org/wiki/Robin%20Wilson%20%28mathematician%29
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Robin James Wilson (born 5 December 1943) is an emeritus professor in the Department of Mathematics at the Open University, having previously been Head of the Pure Mathematics Department and Dean of the Faculty. He was a stipendiary lecturer at Pembroke College, Oxford and, , Gresham Professor of Geometry at Gresham College, London, where he has also been a visiting professor. On occasion, he teaches at Colorado College in the United States. He is also a long standing fellow of Keble College, Oxford.
Professor Wilson is a son of former British Prime Minister Harold Wilson and his wife, Mary.
Early life and education
Wilson was born in 1943 to the politician Harold Wilson, who later became Prime Minister, and his wife the poet Mary Wilson (née Baldwin). He has a younger brother, Giles, who in his 50s gave up a career as a teacher to be a train driver. Wilson attended University College School in Hampstead, North London. He achieved a BA First Class Honours in Mathematics from Balliol College, Oxford, an MA from the University of Pennsylvania, a PhD from the University of Pennsylvania (1965–1968) and a BA First Class Honours in Humanities with Music from the Open University. In a Guardian interview in 2008, Wilson spoke of the fact he grew up known to everyone primarily as a son of the Labour Party leader and Prime Minister Harold Wilson: "I hated the attention and I still dislike being introduced as Harold Wilson's son. I feel uncomfortable talking about it to strangers eve
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https://en.wikipedia.org/wiki/Symmetry%20%28physics%29
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In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation.
A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see Symmetry group).
These two concepts, Lie and finite groups, are the foundation for the fundamental theories of modern physics. Symmetries are frequently amenable to mathematical formulations such as group representations and can, in addition, be exploited to simplify many problems.
Arguably the most important example of a symmetry in physics is that the speed of light has the same value in all frames of reference, which is described in special relativity by a group of transformations of the spacetime known as the Poincaré group. Another important example is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations, which is an important idea in general relativity.
As a kind of invariance
Invariance is specified mathematically by transformations that leave some property (e.g. quantity) unchanged. This idea can apply to basic real-world observations. For example,
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https://en.wikipedia.org/wiki/John%20C.%20Reynolds
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John Charles Reynolds (June 1, 1935 – April 28, 2013) was an American computer scientist.
Education and affiliations
John Reynolds studied at Purdue University and then earned a Doctor of Philosophy (Ph.D.) in theoretical physics from Harvard University in 1961. He was a professor of information science at Syracuse University from 1970 to 1986. From then until his death, he was a professor of computer science at Carnegie Mellon University. He also held visiting positions at Aarhus University (Denmark), The University of Edinburgh, Imperial College London, Microsoft Research (Cambridge, UK) and Queen Mary University of London.
Academic work
Reynolds's main research interest was in the area of programming language design and associated specification languages, especially concerning formal semantics. He invented the polymorphic lambda calculus (System F) and formulated the property of semantic parametricity; the same calculus was independently discovered by Jean-Yves Girard. He wrote a seminal paper on definitional interpreters, which clarified early work on continuations and introduced the technique of defunctionalization. He applied category theory to programming language semantics. He defined the programming languages Gedanken and Forsythe, known for their use of intersection types. He worked on a separation logic to describe and reason about shared mutable data structures.
Reynolds created an elegant, idealized formulation of the programming language ALGOL, which exhibits
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https://en.wikipedia.org/wiki/Primefree%20sequence
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In mathematics, a primefree sequence is a sequence of integers that does not contain any prime numbers. More specifically, it usually means a sequence defined by the same recurrence relation as the Fibonacci numbers, but with different initial conditions causing all members of the sequence to be composite numbers that do not all have a common divisor. To put it algebraically, a sequence of this type is defined by an appropriate choice of two composite numbers a1 and a2, such that the greatest common divisor is equal to 1, and such that for there are no primes in the sequence of numbers calculated from the formula
.
The first primefree sequence of this type was published by Ronald Graham in 1964.
Wilf's sequence
A primefree sequence found by Herbert Wilf has initial terms
The proof that every term of this sequence is composite relies on the periodicity of Fibonacci-like number sequences modulo the members of a finite set of primes. For each prime , the positions in the sequence where the numbers are divisible by repeat in a periodic pattern, and different primes in the set have overlapping patterns that result in a covering set for the whole sequence.
Nontriviality
The requirement that the initial terms of a primefree sequence be coprime is necessary for the question to be non-trivial. If the initial terms share a prime factor (e.g., set and for some and both greater than 1), due to the distributive property of multiplication and more generally all subsequent va
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https://en.wikipedia.org/wiki/Rolf%20Pfeifer
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Rolf Pfeifer (born 1947) is a former professor of computer science at the Department of Informatics University of Zurich, and director of the Artificial Intelligence Laboratory, where he retired from in 2014. Currently he is a specially appointed professor at Osaka University, and a visiting professor at Shanghai Jiao Tong University.
He has a master's degree in physics and mathematics and a Ph.D. in computer science from the Swiss Federal Institute of Technology (ETH) in Zurich, Switzerland. He spent three years as a post-doctoral fellow at Carnegie Mellon University and at Yale University in the U.S.
Having worked as a visiting professor and research fellow at Free University of Brussels, the MIT Artificial Intelligence Laboratory, the Neurosciences Institute (NSI) in San Diego, and the Sony Computer Science Laboratory in Paris, he was elected "21st Century COE Professor, Information Science and Technology" at the University of Tokyo for 2003/2004, from where he held the first global, fully interactive, videoconferencing-based lecture series "The AI Lectures from Tokyo" (including Tokyo, Beijing, Jeddah, Warsaw, Munich, and Zurich). This lectures were renamed the ShanghAI Lectures and since 2009 they have been broadcast all over the world.
He is the author of the books Understanding Intelligence (co-author: C. Scheier), How the Body Shapes the Way We Think: A New View of Intelligence MIT Press, 2006 (with Josh Bongard), and "Designing Intelligence" (with Josh Bongard an
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https://en.wikipedia.org/wiki/Channel%20use
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Channel use is a quantity used in signal processing or telecommunication related to symbol rate and channel capacity. Capacity is measured in bits per input symbol into the channel (bits per channel use). If a symbol enters the channel every Ts seconds (for every symbol period a symbol is transmitted) the channel capacity in bits per second is C/Ts. The phrase "1 bit per channel use" denotes the transmission of 1 symbol (of duration Ts) containing 1 data bit.
See also
Adaptive communications
End instrument
Spectral efficiency and modulation efficiency in (bit/s)/Hz
Data transmission
Information theory
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https://en.wikipedia.org/wiki/Computational%20epidemiology
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Computational epidemiology is a multidisciplinary field that uses techniques from computer science, mathematics, geographic information science and public health to better understand issues central to epidemiology such as the spread of diseases or the effectiveness of a public health intervention. Computational epidemiology traces its origins to mathematical epidemiology, but began to experience significant growth with the rise of big data and the democratization of high-performance computing through cloud computing.
Introduction
In contrast with traditional epidemiology, computational epidemiology looks for patterns in unstructured sources of data, such as social media. It can be thought of as the hypothesis-generating antecedent to hypothesis-testing methods such as national surveys and randomized controlled trials.
A mathematical model is developed which describes the observed behavior of the viruses, based on the available data. Then simulations of the model are performed to understand the possible outcomes given the model used. These simulations produce as results projections which can then be used to make predictions or verify the facts and then be used to plan interventions and meters towards the control of the disease's spread.
References
External links
Sax Institute - Decision Analytics
Computational science
Epidemiology
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https://en.wikipedia.org/wiki/Strictness%20analysis
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In computer science, strictness analysis refers to any algorithm used to prove that a function in a non-strict functional programming language is strict in one or more of its arguments. This information is useful to compilers because strict functions can be compiled more efficiently. Thus, if a function is proven to be strict (using strictness analysis) at compile time, it can be compiled to use a more efficient calling convention without changing the meaning of the enclosing program.
Note that a function f is said to diverge if it returns : operationally, that would mean that f either causes abnormal termination of the enclosing program (e.g., failure with an error message) or that it loops infinitely. The notion of "divergence" is significant because a strict function is one that always diverges when given an argument that diverges, whereas a lazy (or non-strict) function is one that may or may not diverge when given such an argument. Strictness analysis attempts to determine the "divergence properties" of functions, which thus identifies some functions that are strict.
Approaches to strictness analysis
Forward abstract interpretation
Strictness analysis can be characterized as a forward abstract interpretation which approximates each function in the program by a function that maps divergence properties of the arguments onto divergence properties of the results. In the classical approach pioneered by Alan Mycroft, the abstract interpretation used a two-point domain wit
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https://en.wikipedia.org/wiki/Jane%20English
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Jane English (born 1942 in Boston, Massachusetts) is a philosopher, physicist, photographer, journalist, and translator.
Biography
English received her B.A. in physics from Mount Holyoke College in 1964 and Ph.D. from the University of Wisconsin–Madison for her work in high energy particle physics. She taught courses in Oriental thought and modern physics at Colorado College.
English collaborated on a translation of the Tao Te Ching of Lao Tsu which she illustrated through photography, in collaboration with her spouse Gia-Fu Feng.
Bibliography
"The Ceremony Cards:A Living Introduction to the Traditional Teachings of the Far North from Greenland" (Earth Heart 2014'')
"Lao Tsu - Tao Te Ching" in collaboration with Gia-Fu Feng (Random House 1972 and 2011)
"Chuang Tsu - Inner Chapters" in collaboration with Gia-Fu Feng (Random House 1974, Earth Heart 1997, Amber Lotus 2000, Hay House 2014)
Co-editor with Ben English, Jr. of "Our Mountain Trips, Parts I & II" (Bondcliff Books 2005 & 2007)
"Different Doorway: Adventures of a Caesarean Born" (Earth Heart 1985)
Illustrated "Waterchild" (Hunter House, 1980). Jane's photographs of nature and Judith Bolinger's poems of pregnancy.
Photographic illustration of "Accept This Gift," "A Gift of Peace," and "A Gift of Healing" (Tarcher 1983, 1986, 1988), edited by Frances Vaughan and Roger Walsh
"Childlessness Transformed" (Earth Heart 1989)
"Mount Shasta: Where Heaven and Earth Meet," (Earth Heart 1995) with Jenny Coyle
"Finger
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https://en.wikipedia.org/wiki/Monitoring
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Monitoring may refer to:
Science and technology
Biology and healthcare
Monitoring (medicine), the observation of a disease, condition or one or several medical parameters over time
Baby monitoring
Biomonitoring, of toxic chemical compounds, elements, or their metabolites, in biological substances
Fetal monitoring in childbirth
Heart rate monitoring
Intraoperative neurophysiological monitoring
Monitoring in clinical trials, oversight and administrative efforts that monitor a participant's health during a clinical trial
Self-monitoring, a psychological term meaning awareness of what one knows
Computing
Application performance management, also called application performance monitoring, monitoring and management of performance and availability of software applications
Event monitoring, process of collecting, analyzing, and signaling event occurrences to subscribers such as operating system processes, active database rules as well as human operators
Business transaction management, also called business transaction monitoring, managing information technology from a business transaction perspective
Network monitoring, systems that constantly monitors a computer network for slow or failing components and that notifies the network administrator
System monitoring, a process within a distributed system for collecting and storing state data
User activity monitoring, the process of recording user input
Website monitoring, the process of testing and verifying that end-use
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https://en.wikipedia.org/wiki/Diane%20Pozefsky
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Diane P. Pozefsky is a research professor at the University of North Carolina in the department of Computer Science. Pozefsky was awarded the Women in Technology International (WITI) 2011 Hall of Fame Award for contributions to the fields of Science and Technology.
Education
Pozefsky earned a A.B in applied mathematics from Brown University in 1972 and her Ph.D. from the Department of Computer Science at UNC in 1979 under the tutelage of Doctor Mehdi Jazayeri.
Career
Pozefsky joined IBM Corporation, Raleigh, NC, in 1979 as a member of the Communication Systems Architecture Department working in the specification and application of the Systems Network Architecture (SNA), a large and complex feature-rich network architecture developed in the 1970s by IBM. Similar in some respects to the OSI reference model, but with a number of differences. SNA is essentially composed of seven layers. She worked for IBM for 25 years and was named an IBM Fellow in 1994 in recognition of her work on APPN and AnyNet architectures and development. She was tasked with the network and application design for the 1998 and 2000 Olympics. Her work life has largely been focused on networking and software engineering, including:
developing networking protocols
deploying the network at the Nagano Olympics
development processes
storage networking
application development
mobile computing
She has worked in development, design, and architecture and two areas that she has become particularly intereste
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https://en.wikipedia.org/wiki/Prizes%20%28novel%29
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Prizes is a 1995 novel written by Erich Segal. It tells stories of three principal characters: Adam Coopersmith (a genius immunologist), Sandy Raven (a cell biologist bitter from betrayal), and Isabel Da Costa (a child prodigy who goes on to win a Nobel Prize in Physics).
Plot
The novel deals with the relationships of three principal characters.
Adam Coopersmith, an obstetrician and immunologist, saves the life of his mentor, Dr. Max Rudolph. Although normally an ethical researcher, Coppersmith decides to test a life-saving cancer treatment on a man, against the wishes of the Food and Drug Administration. This man is Thomas Hartnell, an advisor to the President of the United States. While acting as the attending doctor, Adam meets Hartnell's daughter, Antonia, and falls in love. Antonia works as the Assistant Attorney General of the United States. Later, when Adam's mentor, Max, dies, he takes solace in Antonia's arms. They get married and have a daughter of their own, Heather. Though their relationship starts off well, things slowing begin to change. As both Adam and his daughter grow older, they realize that Antonia's top priority is her job. As Adam and Antonia slowly fall apart, he is drawn to another woman, Anya Avilov, the childless and abandoned wife of a Russian émigré. Her husband, Dr. Dmitri Avilov, abandoned her when he realized she was incapable of conceiving a child. Adam jumps at the chance to fill the void that is present in both he and Anya's hearts. Adam
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https://en.wikipedia.org/wiki/Machin-like%20formula
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In mathematics, Machin-like formulae are a popular technique for computing (the ratio of the circumference to the diameter of a circle) to a large number of digits. They are generalizations of John Machin's formula from 1706:
which he used to compute to 100 decimal places.
Machin-like formulas have the form
where is a positive integer, are signed non-zero integers, and and are positive integers such that .
These formulas are used in conjunction with Gregory's series, the Taylor series expansion for arctangent:
Derivation
The angle addition formula for arctangent asserts that
if
All of the Machin-like formulas can be derived by repeated application of equation . As an example, we show the derivation of Machin's original formula one has:
and consequently
Therefore also
and so finally
An insightful way to visualize equation is to picture what happens when two complex numbers are multiplied together:
The angle associated with a complex number is given by:
Thus, in equation , the angle associated with the product is:
Note that this is the same expression as occurs in equation . Thus equation can be interpreted as saying that multiplying two complex numbers means adding their associated angles (see multiplication of complex numbers).
The expression:
is the angle associated with:
Equation can be re-written as:
Here is an arbitrary constant that accounts for the difference in magnitude between the vectors on the two sides of the equation. The magnitud
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https://en.wikipedia.org/wiki/Carel%20van%20Schaik
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Carolus Philippus "Carel" van Schaik (born 15 June 1953, Rotterdam) is a Dutch primatologist who since 2004 is professor and director of the Anthropological Institute and Museum at the University of Zürich, Switzerland.
Van Schaik studied biology at the University of Utrecht, graduating in 1979. He was a researcher for the Netherlands Foundation for the Advancement of Tropical Research until 1984 and finished his doctoral dissertation for the Utrecht University in 1985. After positions at this university and at Princeton University, he became Associate Professor at the Department of Biological Anthropology and Anatomy at Duke University in Durham in 1989. In 2004 he moved to the University of Zurich. In 2007 Van Schaik became a correspondent of the Royal Netherlands Academy of Arts and Sciences.
The interest for the monkeys was born toward the seventies, during an expedition to Sumatra beside his wife.
Soon after, van Schaik become always more interested to the monkeys that to the plants, and when in the north-western part of Sumatra he comes upon in the marshy region of the Suaq, he finally meets his orangutans.
His book Among Orangutans: Red Apes and the Rise of Human Culture tells the story of his discovery of a group of orangutans in northern Sumatra and the challenge their tool use and sociality pose to theories of primatology and the insights they offer into key moments in human evolution.
Selected publications
van Schaik, C. P., M. Ancrenaz, G. Borgan, B. Galdika
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https://en.wikipedia.org/wiki/Walle%20Nauta
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Walle Jetze Harinx Nauta (June 8, 1916 – March 24, 1994) was a leading Dutch-American neuroanatomist, and one of the founders of the field of neuroscience. Nauta is best known for his silver staining, which helped to revolutionize neuroscience. He was an Institute Professor of neuroscience at MIT and also worked at the University of Utrecht, the University of Zurich, the Walter Reed Army Institute of Research, and the University of Maryland. In addition, he was a founder and president of the Society for Neuroscience.
Early life
Nauta was born on June 8, 1916, in Medan, Sumatra, Dutch East Indies. His father had traveled there from the Netherlands as a missionary of the Dutch Reformed Church, but his focus quickly evolved into improving the overall education, health, and governance of the Indonesians. Growing up in a household that emphasized ideas of social justice and empathy toward others contributed to Nauta's character and actions as he grew into a young man in the midst of World War II. He is remembered as a man intolerant of others' personal entitlement and having a strong passion for helping his fellow man.
Nauta and his family returned the Netherlands in the 1930s, and so escaped imprisonment during the Japanese occupation. It was there that Nauta finished his elementary schooling.
Education and career
Nauta attended medical school at the University of Leiden from 1934 to 1941. Under the German occupation, the University was closed, and Nauta continued his educati
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https://en.wikipedia.org/wiki/SNi
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In chemistry, Si (substitution nucleophilic internal) refers to a specific but not often encountered reaction mechanism for nucleophilic aliphatic substitution. The name was introduced by Cowdrey et al. in 1937 to label nucleophilic reactions which occur with retention of configuration, but later was employed to describe various reactions that proceed with a similar mechanism.
A typical representative organic reaction displaying this mechanism is the chlorination of alcohols with thionyl chloride, or the decomposition of alkyl chloroformates, the main feature is retention of stereochemical configuration. Some examples for this reaction were reported by Edward S. Lewis and Charles E. Boozer in 1952. Mechanistic and kinetic studies were reported few years later by various researchers.
Thionyl chloride first reacts with the alcohol to form an alkyl chloro sulfite, actually forming an intimate ion pair. The second step is the concerted loss of a sulfur dioxide molecule and its replacement by the chloride, which was attached to the sulphite group. The difference between S1 and Si is actually that the ion pair is not completely dissociated, and therefore no real carbocation is formed, which else would lead to a racemisation.
This reaction type is linked to many forms of neighbouring group participation, for instance the reaction of the sulfur or nitrogen lone pair in sulfur mustard or nitrogen mustard to form the cationic intermediate.
This reaction mechanism is supported by
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https://en.wikipedia.org/wiki/Primary%20field
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In theoretical physics, a primary field, also called a primary operator, or simply a primary, is a local operator in a conformal field theory which is annihilated by the part of the conformal algebra consisting of the lowering generators. From the representation theory point of view, a primary is the lowest dimension operator in a given representation of the conformal algebra. All other operators in a representation are called descendants; they can be obtained by acting on the primary with the raising generators.
History of the concept
Primary fields in a D-dimensional conformal field theory were introduced in 1969 by Mack and Salam where they were called interpolating fields. They were then studied by Ferrara, Gatto, and Grillo who called them irreducible conformal tensors, and by Mack who called them lowest weights. Polyakov used an equivalent definition as fields which cannot be represented as derivatives of other fields.
The modern terms primary fields and descendants were introduced by Belavin, Polyakov and Zamolodchikov in the context of two-dimensional conformal field theory. This terminology is now used both for D=2 and D>2.
Conformal field theory in D>2 spacetime dimensions
In dimensions conformal primary fields can be defined in two equivalent ways. Campos Delgado provided a pedagogical proof of the equivalence.
First definition
Let be the generator of dilations and let be the generator of special conformal transformations. A conformal primary field ,
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https://en.wikipedia.org/wiki/Resummation
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In mathematics and theoretical physics, resummation is a procedure to obtain a finite result from a divergent sum (series) of functions. Resummation involves a definition of another (convergent) function in which the individual terms defining the original function are re-scaled, and an integral transformation of this new function to obtain the original function. Borel resummation is probably the most well-known example.
The simplest method is an extension of a variational approach to higher order based on a paper by R.P. Feynman and H. Kleinert.
In quantum mechanics it was extended to any order here, and in quantum field theory here.
See also Chapters 16–20 in the textbook cited below.
See also
Perturbation theory
Perturbation theory (quantum mechanics)
References
Books
Hagen Kleinert, Critical Properties of φ4-Theories, World Scientific (Singapore, 2001); Paperback (also available online) (together with V. Schulte-Frohlinde).
Quantum field theory
Summability methods
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https://en.wikipedia.org/wiki/Anomalous%20magnetic%20dipole%20moment
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In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. The magnetic moment, also called magnetic dipole moment, is a measure of the strength of a magnetic source.
The "Dirac" magnetic moment, corresponding to tree-level Feynman diagrams (which can be thought of as the classical result), can be calculated from the Dirac equation. It is usually expressed in terms of the g-factor; the Dirac equation predicts . For particles such as the electron, this classical result differs from the observed value by a small fraction of a percent. The difference is the anomalous magnetic moment, denoted and defined as
Electron
The one-loop contribution to the anomalous magnetic moment—corresponding to the first and largest quantum mechanical correction—of the electron is found by calculating the vertex function shown in the adjacent diagram. The calculation is relatively straightforward and the one-loop result is:
where is the fine-structure constant. This result was first found by Julian Schwinger in 1948 and is engraved on his tombstone. As of 2016, the coefficients of the QED formula for the anomalous magnetic moment of the electron are known analytically up to and have been calculated up to order :
The QED prediction agrees with the experimentally measured value to more than 10 significant figures, making the magnetic moment of the e
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https://en.wikipedia.org/wiki/Resolvent
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In mathematics, resolvent meaning "that which resolves" may refer to:
Resolvent formalism in operator theory
Resolvent set in operator theory, the set of points where an operator is "well-behaved"
in probability theory
Resolvent (Galois theory) of an equation for a permutation group, in particular:
Resolvent quadratic of a cubic equation
Resolvent cubic of a quartic equation
In logic:
Resolvent (logic), the clause produced by a resolution
In the consensus theorem, the term produced by a consensus in Boolean logic
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https://en.wikipedia.org/wiki/Frederic%20Parke
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Frederic Ira Parke is an American computer graphics researcher and academic. He did early work on animated computer renderings of human faces.
Parke graduated from the University of Utah with a BS degree in physics in 1965. He was then a graduate student of the University of Utah College of Engineering where he received his MS (1972) and PhD (1974) in computer science.
In 1972, in a project partially financed by DARPA, Parke made the first 3D animation of a representation of a human face, his wife's face. This animation used a wireframe geometry overlaid with Gouraud shading that produces approximate renderings of curved surfaces. The technique was invented by Parke's Utah colleague Henri Gouraud.
A Computer Animated Face
In 1974, he created a more complex, parametric model of a human face, demonstrating various expressions and speech synchronization. Snippets of this animation, along with Ed Catmull's 1972 animation of his left hand, were used in the 1976 film Futureworld. Several of the faces also appeared in the music video of Miley Cyrus' 2013 song "We Can't Stop".
He has worked at the New York Institute of Technology Computer Graphics Laboratory.
Parke teaches at Texas A&M University in the Visualization Sciences program.
References
External links
Homepage of Frederic I. Parke at Texas A&M University
1943 births
Living people
Computer graphics professionals
Texas A&M University faculty
University of Utah alumni
New York Institute of Technology faculty
Scien
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https://en.wikipedia.org/wiki/Tensor%20product%20of%20Hilbert%20spaces
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In mathematics, and in particular functional analysis, the tensor product of Hilbert spaces is a way to extend the tensor product construction so that the result of taking a tensor product of two Hilbert spaces is another Hilbert space. Roughly speaking, the tensor product is the metric space completion of the ordinary tensor product. This is an example of a topological tensor product. The tensor product allows Hilbert spaces to be collected into a symmetric monoidal category.
Definition
Since Hilbert spaces have inner products, one would like to introduce an inner product, and therefore a topology, on the tensor product that arises naturally from those of the factors. Let and be two Hilbert spaces with inner products and respectively. Construct the tensor product of and as vector spaces as explained in the article on tensor products. We can turn this vector space tensor product into an inner product space by defining
and extending by linearity. That this inner product is the natural one is justified by the identification of scalar-valued bilinear maps on and linear functionals on their vector space tensor product. Finally, take the completion under this inner product. The resulting Hilbert space is the tensor product of and
Explicit construction
The tensor product can also be defined without appealing to the metric space completion. If and are two Hilbert spaces, one associates to every simple tensor product the rank one operator from to that maps a given
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https://en.wikipedia.org/wiki/Robotic%20pet
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Robotic pets are artificially intelligent machines that are made to resemble actual pets. While the first robotic pets produced in the late 1990s, were not too advanced, they have since grown technologically. Many now use machine learning (algorithms that allow machines to adapt to experiences independent of humans), making them much more realistic. Most consumers buy robotic pets with the aim of getting similar companionship that real pets offer, without some of the drawbacks that come with caring for live animals. The pets on the market currently have a wide price range, from the low hundreds into the several thousands of dollars. Multiple studies have been done to show that we treat robotic pets in a similar way as actual pets, despite their obvious differences. However, there is some controversy regarding how ethical using robotic pets is, and whether or not they should be widely adopted in elderly care.
History
The first known robotic pet was a robot dog called Sparko, built by the American company Westinghouse in 1940. It never got sold due to poor public interest.
The first robotic pets to be put on the market were Hasbro's Furby in 1998 and Sony's AIBO in 1999. Since then, robotic pets have grown increasingly advanced.
The shapes of the robotic pet includes:
familiar animals
nonfamiliar animals
imaginary animals or characters
Some popular robotic pets today are:
Joy for All (by Hasbro) Companion Pets
Zoomer Interactive Animals (Usually Kittens and Puppies)
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https://en.wikipedia.org/wiki/Hyperconjugation
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In organic chemistry, hyperconjugation (σ-conjugation or no-bond resonance) refers to the delocalization of electrons with the participation of bonds of primarily σ-character. Usually, hyperconjugation involves the interaction of the electrons in a sigma (σ) orbital (e.g. C–H or C–C) with an adjacent unpopulated non-bonding p or antibonding σ* or π* orbitals to give a pair of extended molecular orbitals. However, sometimes, low-lying antibonding σ* orbitals may also interact with filled orbitals of lone pair character (n) in what is termed negative hyperconjugation. Increased electron delocalization associated with hyperconjugation increases the stability of the system. In particular, the new orbital with bonding character is stabilized, resulting in an overall stabilization of the molecule. Only electrons in bonds that are in the β position can have this sort of direct stabilizing effect — donating from a sigma bond on an atom to an orbital in another atom directly attached to it. However, extended versions of hyperconjugation (such as double hyperconjugation) can be important as well. The Baker–Nathan effect, sometimes used synonymously for hyperconjugation, is a specific application of it to certain chemical reactions or types of structures.
Applications
Hyperconjugation can be used to rationalize a variety of chemical phenomena, including the anomeric effect, the gauche effect, the rotational barrier of ethane, the beta-silicon effect, the vibrational frequency o
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https://en.wikipedia.org/wiki/Digitonin
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Digitonin is a steroidal saponin (saraponin) obtained from the foxglove plant Digitalis purpurea. Its aglycone is digitogenin, a spirostan steroid. It has been investigated as a detergent, as it effectively water-solubilizes lipids. As such, it has several potential membrane-related applications in biochemistry, including solubilizing membrane proteins, precipitating cholesterol, and permeabilizing cell membranes.
Digitonin is sometimes confused with the cardiac drugs digoxin and digitoxin; all three can be extracted from the same source.
Chemical properties
Critical micelle concentration = < 0.5 mM
Average micellar weight = 70000
Aggregation number = 60
References
Spiro compounds
Steroidal glycosides
Saponins
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https://en.wikipedia.org/wiki/Index%20Fungorum
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Index Fungorum is an international project to index all formal names (scientific names) in the fungus kingdom. the project is based at the Royal Botanic Gardens, Kew, one of three partners along with Landcare Research and the Institute of Microbiology, Chinese Academy of Sciences.
It is somewhat comparable to the International Plant Names Index (IPNI), in which the Royal Botanic Gardens is also involved. A difference is that where IPNI does not indicate correct names, the Index Fungorum does indicate the status of a name. In the returns from the search page a currently correct name is indicated in green, while others are in blue (a few, aberrant usages of names are indicated in red). All names are linked to pages giving the correct name, with lists of synonyms.
Index Fungorum is one of three nomenclatural repositories recognized by the Nomenclature Committee for Fungi; the others are MycoBank and Fungal Names.
Current names in Index Fungorum (Species Fungorum)
The main part of Index Fungorum is intended to be a global list of all fungal names which have ever been validly defined, but many of them are conflicting or no longer used. Species Fungorum is a closely related project based at the Royal Botanical Gardens, Kew supported by CABI to decide a consistent subset of the Index Fungorum names which can be recommended as currently valid. It is possible to search in either the Index Fungorum or the Species Fungorum list separately and the Index Fungorum results also give
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https://en.wikipedia.org/wiki/ABTS
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In biochemistry, ABTS (2,2'-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid)) is a chemical compound used to observe the reaction kinetics of specific enzymes. A common use for it is in the enzyme-linked immunosorbent assay (ELISA) to detect the binding of molecules to each other.
It is commonly used as a substrate with hydrogen peroxide for a peroxidase enzyme (such as horseradish peroxidase) or alone with blue multicopper oxidase enzymes (such as laccase or bilirubin oxidase). Its use allows the reaction kinetics of peroxidases themselves to be followed. In this way it also can be used to indirectly follow the reaction kinetics of any hydrogen peroxide-producing enzyme, or to simply quantify the amount of hydrogen peroxide in a sample.
The formal reduction potentials for ABTS are high enough for it to act as an electron donor for the reduction of oxo species such as molecular oxygen and hydrogen peroxide, particularly at the less-extreme pH values encountered in biological catalysis. Under these conditions, the sulfonate groups are fully deprotonated and the mediator exists as a dianion.
ABTS–· + e– → ABTS2– E° = 0.67 V vs SHE
ABTS + e– → ABTS–· E° = 1.08 V vs SHE
This compound is chosen because the enzyme facilitates the reaction with hydrogen peroxide, turning it into a green and soluble end-product. Its new absorbance maximum of 420 nm light (ε = 3.6 × 104 M–1 cm–1) can easily be followed with a spectrophotometer, a common laboratory instrument.
It is sometimes u
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https://en.wikipedia.org/wiki/Flowing-afterglow%20mass%20spectrometry
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Flowing-afterglow mass spectrometry (FA-MS), is an analytical chemistry technique for the sensitive detection of trace gases. Trace gas molecules are ionized by the production and flow of thermalized hydrated hydronium cluster ions in a plasma afterglow of helium or argon carrier gas along a flow tube following the introduction of a humid air sample. These ions react in multiple collisions with water molecules, their isotopic compositions reach equilibrium and the relative magnitudes of their isotopomers are measured by mass spectrometry.
Brief History
Over the years many variations of the instrument have been made. In the beginning during the 1960s there was the study of flowing afterglow plasma. This study was done by Eldon Ferguson, Art Schmeltekopf and Fred Fehsenfeld at National Bureau of Standards in Boulder, Colorado. Then in the 1970s it was flowing drift tube, flowing afterglow Langmuir probe (FALP), and variable temperature flowing afterglow Langmuir probe (VT-FLAP). With the addition of the drift tube the kinetics of a reaction could be studied in the gas phase. With the flowing afterglow Langmuir probe the electron density within the reaction region of the drift tube can be studied. With the VT-FLAP version of flowing afterglow the reactions temperature dependence could be studied. Now in the 2000s the ambient version of flowing afterglow mass spectrometry is flowing atmospheric pressure afterglow mass spectrometry (FAPA-MS).The FAPA allows for simple or no sam
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https://en.wikipedia.org/wiki/Hoagland-Pincus%20Conference%20Center
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The Hoagland-Pincus Conference Center is a conference facility of the University of Massachusetts Medical School.
It is named for Hudson Hoagland and Gregory Goodwin Pincus, the co-founders of the Worcester Foundation for Experimental Biology.
It is located in Shrewsbury, Massachusetts at the site of the former Worcester Foundation for Experimental Biology, where the first birth control pill was developed.
External links
Official site
Buildings and structures in Shrewsbury, Massachusetts
UMass Chan Medical School
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https://en.wikipedia.org/wiki/Eaton%20MTL
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Eaton MTL is a division of Eaton Corporation which produces electronic instrumentation and protection equipment for telecommunication and process control systems, including power systems, safety interfaces and surge protection. It has manufacturing facilities in Luton, UK; Chennai, India; Melbourne, Florida, USA and Brisbane, Australia.
History
MTL Instruments was founded as a private company in 1971. In 2005 the company acquired GeCma Components GmbH, which manufactures computer terminals for use in hazardous areas. In 2007 MTL acquired three companies: ELPRO Technologies, which specialises in industrial wireless equipment and radio telemetry; RTK Instruments, which manufactures alarm equipment for process control systems; and Ocean Technical Systems, which provides remote instrumentation for offshore drilling vessels, tankers and pipelines. In 2008, MTL Instruments was purchased by Cooper Industries of Houston, Texas, under that company's Crouse-Hinds division.
References
External links
MTL corporate website
2008 mergers and acquisitions
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https://en.wikipedia.org/wiki/GeoGebra
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GeoGebra (a portmanteau of geometry and algebra) is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is available on multiple platforms, with apps for desktops (Windows, macOS and Linux), tablets (Android, iPad and Windows) and web. It is presently owned by Indian edutech firm Byju's.
History
GeoGebra's creator, Markus Hohenwarter, started the project in 2001 as part of his master's thesis at the University of Salzburg. After a successful Kickstarter campaign, GeoGebra expanded its offering to include an iPad, an Android and a Windows Store app version. In 2013, GeoGebra incorporated Xcas into its CAS view. The project is now freeware (with open-source portions) and multi-lingual, and Hohenwarter continues to lead its development at the University of Linz.
GeoGebra includes both commercial and not-for-profit entities that work together from the head office in Linz, Austria, to expand the software and cloud services available to users.
In December 2021, GeoGebra was acquired by edtech conglomerate Byju's for approximately $100 million USD.
Features
GeoGebra is an interactive mathematics software suite for learning and teaching science, technology, engineering, and mathematics from primary school up to the university level. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynom
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https://en.wikipedia.org/wiki/Constrained%20geometry%20complex
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In organometallic chemistry, a "constrained geometry complex" (CGC) is a kind of catalyst used for the production of polyolefins such as polyethylene and polypropylene. The catalyst was one of the first major departures from metallocene-based catalysts and ushered in much innovation in the development of new plastics.
Structure
CGC complexes feature a pi-bonded moiety (e.g. cyclopentadienyl) linked to one of the other ligands on the same metal centre in such a way that the angle at this metal between the centroid of the pi-system and the additional ligand is smaller than in comparable unbridged complexes. More specifically, the term CGC was used for ansa-bridged cyclopentadienyl amido complexes, although the definition goes far beyond this class of compounds. The term CGC is frequently used in connection with other more or less related ligand systems that may or may not be isolobal and/or isoelectronic with the ansa-bridged cyclopentadienyl amido ligand system. Furthermore, the term is frequently used for related complexes with long ansa-bridges that induce no strain. Ansa-bridged cyclopentadienyl amido complexes are known for the Group 3, 4, 5, 6 and some Group 8 metals, with the Group 4 congeners being the most studied ones.
Applications
Like Group 4 metallocenes, suitable Group 4 CGCs may be activated for the polymerisation of ethylene and alpha-olefins by reaction with co-catalysts, e.g. methylaluminoxane (MAO), tris(pentafluorophenyl)boranes, and trityl borates. T
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https://en.wikipedia.org/wiki/Cornell%20Laboratory%20for%20Accelerator-based%20Sciences%20and%20Education
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The Cornell Laboratory for Accelerator-based ScienceS and Education (CLASSE) is a particle accelerator facility located in Wilson Laboratory on the Cornell University campus in Ithaca, NY. CLASSE was formed by merging the Cornell High-Energy Synchrotron Source (CHESS) and the Laboratory for Elementary-Particle Physics (LEPP) in July 2006. Nigel Lockyer is the Director of CLASSE in spring of 2023.
The Wilson Synchrotron Lab, which houses both the Cornell Electron Storage Ring (CESR) and CHESS, is named after Robert R. Wilson, known for his work as a group leader in the Manhattan Project, for being the first director of the Fermi National Accelerator Laboratory, and for contributing to the design of CESR.
LEPP
The Laboratory for Elementary-Particle Physics (LEPP) is a high-energy physics laboratory studying fundamental particles and their interactions.
The 768-meter Cornell Electron Storage Ring (CESR) is in operation below the campus athletic fields. CESR is an electron-positron collider operating at a center-of-mass energy in the range of 3.5-12 GeV. Completed in 1979, CESR stores beams accelerated by the Cornell Synchrotron.
Adding to a long history of significant developments, such as superconducting radio frequency cavities and pretzel orbits, the accelerator group is now developing an entirely new type of superconducting linear accelerator called the Energy Recovery Linear accelerator (ERL). The group is also involved in the design of damping rings, tracking simulati
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https://en.wikipedia.org/wiki/Orthographical%20variant
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In biology, within the science of scientific nomenclature, i.e. the naming of organisms, an orthographical variant (abbreviated orth. var.) in botany or an orthographic error in zoology, is a spelling mistake, typing mistake or writing mistake within a scientific publication that resulted in a somewhat different name being accidentally used for an already-named organism. The rules that govern what to do when this happens are laid out in the relevant codes of nomenclature.
In botanical names
In botanical nomenclature, an orthographical variant (abbreviated orth. var.) is a variant spelling of the same name. For example, Hieronima and Hyeronima are orthographical variants of Hieronyma. One of the spellings must be treated as the correct one. In this case, the spelling Hieronyma has been conserved and is to be used as the correct spelling.
An inadvertent use of one of the other spellings has no consequence: the name is to be treated as if it were correctly spelled. Any subsequent use is to be corrected.
Orthographical variants are treated in Art 61 of the ICBN.
In zoological names
In zoology, "orthographical variants" in the formal sense do not exist; a misspelling or orthographic error is treated as a lapsus, a form of inadvertent error. The first reviser is allowed to choose one variant for mandatory further use, but in other ways, these errors generally have no further formal standing. Inadvertent misspellings are treated in Art. 32-33 of the ICZN.
References
Botanica
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https://en.wikipedia.org/wiki/Prelog%20strain
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In organic chemistry, transannular strain (also called Prelog strain after chemist Vladimir Prelog) is the unfavorable interactions of ring substituents on non-adjacent carbons. These interactions, called transannular interactions, arise from a lack of space in the interior of the ring, which forces substituents into conflict with one another. In medium-sized cycloalkanes, which have between 8 and 11 carbons constituting the ring, transannular strain can be a major source of the overall strain, especially in some conformations, to which there is also contribution from large-angle strain and Pitzer strain. In larger rings, transannular strain drops off until the ring is sufficiently large that it can adopt conformations devoid of any negative interactions.
Transannular strain can also be demonstrated in other cyclo-organic molecules, such as lactones, lactams, ethers, cycloalkenes, and cycloalkynes. These compounds are not without significance, since they are particularly useful in the study of transannular strain. Furthermore, transannular interactions are not relegated to only conflicts between hydrogen atoms, but can also arise from larger, more complicated substituents interacting across a ring.
Thermodynamics
By definition, strain implies discomfiture, so it should follow that molecules with large amounts of transannular strain should have higher energies than those without. Cyclohexane, for the most part, is without strain and is therefore quite stable and low in ener
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https://en.wikipedia.org/wiki/Cajal
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Cajal:
Santiago Ramón y Cajal, Spanish histologist, physician, pathologist
Fortún Garcés Cajal, medieval Spanish nobleman
Nicolae Cajal (1919–2004), Romanian Jewish physician, academic, politician, philanthropist
Cajal Institute, a neuroscience research center in Madrid, Spain.
Cajal cells
Cajal–Retzius cell
Interstitial cell of Cajal (ICC)
Cajal bodies (CBs)
Cajal (crater), a tiny lunar impact crater
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https://en.wikipedia.org/wiki/Nicolas%20Lemery
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Nicolas Lémery (or Lemery as his name appeared in his international publications) (17 November 1645 – 19 June 1715), French chemist, was born at Rouen. He was one of the first to develop theories on acid-base chemistry.
Life
After learning pharmacy in his native town he became a pupil of Christophe Glaser in Paris, and then went to Montpellier, where he began to lecture on chemistry. He next established a pharmacy in Paris, still continuing his lectures, but following 1683, being a Calvinist, he was obliged to retire to England. In the following year he returned to France, and turning Catholic in 1686 was able to reopen his shop and resume his lectures. He died in Paris on 19 June 1715.
Lemery did not concern himself much with theoretical speculations, but holding chemistry to be a demonstrative science, confined himself to the straightforward exposition of facts and experiments. In consequence, his lecture-room was thronged with people of all sorts, anxious to hear a man who shunned the barren obscurities of the alchemists, and did not regard the quest of the philosopher's stone and the elixir of life as the sole end of his science. Of his Cours de chymie (1675) he lived to see 13 editions, and for a century it maintained its reputation as a standard work.
In 1680, using the corpuscular theory as a basis, Lemery stipulated that the acidity of any substance consisted in its pointed particles, while alkalis were endowed with pores of various sizes. A molecule, according
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https://en.wikipedia.org/wiki/Golisano%20College%20of%20Computing%20and%20Information%20Sciences
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The B. Thomas Golisano College of Computing and Information Sciences is one of the largest colleges at the Rochester Institute of Technology (RIT), and is home to the institute's computing education and research facilities. Golisano College is home to RIT's computer science, cybersecurity, information sciences and technologies, and software engineering departments, and to the Ph.D. program in computing and information sciences, and the School of Interactive Games & Media.
Golisano College is housed in a 125,000 square foot facility, opened in 2003 on RIT's campus in Rochester, New York. In 2020, the facility added an additional 52,000 square foot building, which joins the original Golisano College on all three floors and houses the ESL Global Cybersecurity Institute.
History
In 1972, RIT began offering one of its first computer science programs. Originally named computer systems, the program offered students the opportunity to earn a bachelor of technology degree. In 1996, RIT introduced an undergraduate program in software engineering, one of the first programs of its kind. Later, in 2003, the software engineering program would become one of the first such programs to receive ABET accreditation.
In the late 1990s, the dean of RIT's College of Applied Science and Technology, made a proposition to create a new college that would focus on the growing fields of computer science, information technology and software engineering. In February 2001, B. Thomas Golisano, chairman and
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https://en.wikipedia.org/wiki/Fr%C3%A9chet%20derivative
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In mathematics, the Fréchet derivative is a derivative defined on normed spaces. Named after Maurice Fréchet, it is commonly used to generalize the derivative of a real-valued function of a single real variable to the case of a vector-valued function of multiple real variables, and to define the functional derivative used widely in the calculus of variations.
Generally, it extends the idea of the derivative from real-valued functions of one real variable to functions on normed spaces. The Fréchet derivative should be contrasted to the more general Gateaux derivative which is a generalization of the classical directional derivative.
The Fréchet derivative has applications to nonlinear problems throughout mathematical analysis and physical sciences, particularly to the calculus of variations and much of nonlinear analysis and nonlinear functional analysis.
Definition
Let and be normed vector spaces, and be an open subset of A function is called Fréchet differentiable at if there exists a bounded linear operator such that
The limit here is meant in the usual sense of a limit of a function defined on a metric space (see Functions on metric spaces), using and as the two metric spaces, and the above expression as the function of argument in As a consequence, it must exist for all sequences of non-zero elements of that converge to the zero vector Equivalently, the first-order expansion holds, in Landau notation
If there exists such an operator it is unique, so
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https://en.wikipedia.org/wiki/Dancing%20Links
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In computer science, dancing links (DLX) is a technique for adding and deleting a node from a circular doubly linked list. It is particularly useful for efficiently implementing backtracking algorithms, such as Knuth's Algorithm X for the exact cover problem. Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm that finds all solutions to the exact cover problem. Some of the better-known exact cover problems include tiling, the n queens problem, and Sudoku.
The name dancing links, which was suggested by Donald Knuth, stems from the way the algorithm works, as iterations of the algorithm cause the links to "dance" with partner links so as to resemble an "exquisitely choreographed dance." Knuth credits Hiroshi Hitotsumatsu and Kōhei Noshita with having invented the idea in 1979, but it is his paper which has popularized it.
Implementation
As the remainder of this article discusses the details of an implementation technique for Algorithm X, the reader is strongly encouraged to read the Algorithm X article first.
Main ideas
The idea of DLX is based on the observation that in a circular doubly linked list of nodes,
x.left.right ← x.right;
x.right.left ← x.left;
will remove node x from the list, while
x.left.right ← x;
x.right.left ← x;
will restore x'''s position in the list, assuming that x.right and x.left have been left unmodified. This works regardless of the number of elements in the list, even if that number is 1.
Knuth observed that
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https://en.wikipedia.org/wiki/Worm-like%20chain
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The worm-like chain (WLC) model in polymer physics is used to describe the behavior of polymers that are semi-flexible: fairly stiff with successive segments pointing in roughly the same direction, and with persistence length within a few orders of magnitude of the polymer length. The WLC model is the continuous version of the Kratky–Porod model.
Model elements
The WLC model envisions a continuously flexible isotropic rod. This is in contrast to the freely-jointed chain model, which is only flexible between discrete freely hinged segments. The model is particularly suited for describing stiffer polymers, with successive segments displaying a sort of cooperativity: nearby segments are roughly aligned. At room temperature, the polymer adopts a smoothly curved conformation; at K, the polymer adopts a rigid rod conformation.
For a polymer of maximum length , parametrize the path of the polymer as . Allow to be the unit tangent vector to the chain at point , and to be the position vector along the chain, as shown to the right. Then:
and the end-to-end distance .
The energy associated with the bending of the polymer can be written as:
where is the polymer's characteristic persistence length, is the Boltzmann constant, and is the absolute temperature. At finite temperatures, the end-to end distance of the polymer will be significantly shorter than the maximum length . This is caused by thermal fluctuations, which result in a coiled, random configuration of the undistu
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https://en.wikipedia.org/wiki/John%20Clive%20Ward
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John Clive Ward, (1 August 1924 – 6 May 2000) was a Anglo-Australian physicist who made significant contributions to quantum field theory, condensed-matter physics, and statistical mechanics. Andrei Sakharov called Ward one of the titans of quantum electrodynamics.
Ward introduced the Ward–Takahashi identity. He was one of the authors of the Standard Model of gauge particle interactions: his contributions were published in a series of papers he co-authored with Abdus Salam. He is also credited with being an early advocate of the use of Feynman diagrams. It has been said that physicists have made use of his principles and developments "often without knowing it, and generally without quoting him." The Ising model was another one of his research interests.
In 1955, Ward was recruited to work at the Atomic Weapons Research Establishment at Aldermaston. There, he independently derived a version of the Teller–Ulam design, for which he has been called the "father of the British H-bomb".
Early life
John Clive Ward was born in East Ham, London, on 1 August 1924. He was the son of Joseph William Ward, a civil servant who worked in Inland Revenue, and his wife Winifred Palmer, a schoolteacher. He had a sister, Mary Patricia. He attended Chalkwell Elementary School and Westcliff High School for Boys. In 1938 he sat for and won a £100 scholarship to Bishop Stortford College. He took the Higher School Certificate Examination in 1942, receiving distinctions in Mathematics, Physics, Ch
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https://en.wikipedia.org/wiki/Bullet-nose%20curve
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In mathematics, a bullet-nose curve is a unicursal quartic curve with three inflection points, given by the equation
The bullet curve has three double points in the real projective plane, at and , and , and and , and is therefore a unicursal (rational) curve of genus zero.
If
then
are the two branches of the bullet curve at the origin.
References
Plane curves
Algebraic curves
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https://en.wikipedia.org/wiki/Cl%C3%A9lie
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In mathematics, a Clélie or Clelia curve is a curve on a sphere with the property:
If the surface of a sphere is described as usual by the longitude (angle ) and the colatitude (angle ) then
.
The curve was named by Luigi Guido Grandi after Clelia Borromeo.
Viviani's curve and spherical spirals are special cases of Clelia curves. In practice Clelia curves occur as polar orbits of satellites with circular orbits, whose traces on the earth include the poles. If the orbit is a geosynchronous one, then and the trace is a Viviani's curve.
Parametric representation
If the sphere is parametrized by
and the angles are linearly connected by , then one gets a parametric representation of a Clelia curve:
Examples
Any Clelia curve meets the poles at least once.
Spherical spirals:
A spherical spiral usually starts at the south pole and ends at the north pole (or vice versa).
Viviani's curve:
Trace of a polar orbit of a satellite:
In case of the curve is periodic, if is rational (see rose). For example: In case of the period is . If is a non rational number, the curve is not periodic.
The table (second diagram) shows the floor plans of Clelia curves. The lower four curves are spherical spirals. The upper four are polar orbits. In case of the lower arcs are hidden exactly by the upper arcs. The picture in the middle (circle) shows the floor plan of a Viviani's curve. The typical 8-shaped appearance can only achieved by the projection along the x-axis.
Reference
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https://en.wikipedia.org/wiki/Cochleoid
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In geometry, a cochleoid is a snail-shaped curve similar to a strophoid which can be represented by the polar equation
the Cartesian equation
or the parametric equations
The cochleoid is the inverse curve of Hippias' quadratrix.
Notes
References
Cochleoid in the Encyclopedia of Mathematics
Liliana Luca, Iulian Popescu: A Special Spiral: The Cochleoid. Fiabilitate si Durabilitate - Fiability & Durability no 1(7)/ 2011, Editura "Academica Brâncuşi" , Târgu Jiu,
Roscoe Woods: The Cochlioid. The American Mathematical Monthly, Vol. 31, No. 5 (May, 1924), pp. 222–227 (JSTOR)
Howard Eves: A Graphometer. The Mathematics Teacher, Vol. 41, No. 7 (November 1948), pp. 311-313 (JSTOR)
External links
cochleoid at 2dcurves.com
Plane curves
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https://en.wikipedia.org/wiki/Hessian%20form%20of%20an%20elliptic%20curve
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In geometry, the Hessian curve is a plane curve similar to folium of Descartes. It is named after the German mathematician Otto Hesse.
This curve was suggested for application in elliptic curve cryptography, because arithmetic in this curve representation is faster and needs less memory than arithmetic in standard Weierstrass form.
Definition
Let be a field and consider an elliptic curve in the following special case of Weierstrass form over :
where the curve has discriminant
Then the point has order 3.
To prove that has order 3, note that the tangent to at is the line which intersects with multiplicity 3 at .
Conversely, given a point of order 3 on an elliptic curve both defined over a field one can put the curve into Weierstrass form with so that the tangent at is the line . Then the equation of the curve is with .
To obtain the Hessian curve, it is necessary to do the following transformation:
First let denote a root of the polynomial
Then
Note that if has a finite field of order , then every element of has a unique cube root; in general, lies in an extension field of K.
Now by defining the following value another curve, C, is obtained, that is birationally equivalent to E:
which is called cubic Hessian form (in projective coordinates)
in the affine plane (satisfying and ).
Furthermore, (otherwise, the curve would be singular).
Starting from the Hessian curve, a birationally equivalent Weierstrass equation is given by
under t
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https://en.wikipedia.org/wiki/Trident%20curve
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In mathematics, a trident curve (also trident of Newton or parabola of Descartes) is any member of the family of curves that have the formula:
Trident curves are cubic plane curves with an ordinary double point in the real projective plane at x = 0, y = 1, z = 0; if we substitute x = and y = into the equation of the trident curve, we get
which has an ordinary double point at the origin. Trident curves are therefore rational plane algebraic curves of genus zero.
References
External links
Cubic curves
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https://en.wikipedia.org/wiki/Viviani%27s%20curve
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In mathematics, Viviani's curve, also known as Viviani's window, is a figure eight shaped space curve named after the Italian mathematician Vincenzo Viviani. It is the intersection of a sphere with a cylinder that is tangent to the sphere and passes through two poles (a diameter) of the sphere (see diagram). Before Viviani this curve was studied by Simon de La Loubère and Gilles de Roberval.
The orthographic projection of Viviani's curve onto a plane perpendicular to the line through the crossing point and the sphere center is the lemniscate of Gerono, while the stereographic projection is a hyperbola or the lemniscate of Bernoulli, depending on which point on the same line is used to project.
In 1692 Viviani solved the following task: Cut out of a half sphere (radius ) two windows, such that the remaining surface (of the half sphere) can be squared, i.e. a square with the same area can be constructed using only compasses and ruler. His solution has an area of (see below).
Equations
In order to keep the proof for squaring simple,
the sphere has the equation
and
the cylinder is upright with equation .
The cylinder has radius and is tangent to the sphere at point
Properties of the curve
Floor plan, elevation and side plan
Elimination of , , respectively yields:
The orthogonal projection of the intersection curve onto the
--plane is the circle with equation
--plane the parabola with equation
--plane the algebraic curve with the equation
Parametric rep
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https://en.wikipedia.org/wiki/Watt%27s%20curve
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In mathematics, Watt's curve is a tricircular plane algebraic curve of degree six. It is generated by two circles of radius b with centers distance 2a apart (taken to be at (±a, 0)). A line segment of length 2c attaches to a point on each of the circles, and the midpoint of the line segment traces out the Watt curve as the circles rotate partially back and forth or completely around. It arose in connection with James Watt's pioneering work on the steam engine.
The equation of the curve can be given in polar coordinates as
Derivation
Polar coordinates
The polar equation for the curve can be derived as follows:
Working in the complex plane, let the centers of the circles be at a and −a, and the connecting segment have endpoints at −a+bei λ and a+bei ρ. Let the angle of inclination of the segment be ψ with its midpoint at rei θ. Then the endpoints are also given by rei θ ± cei ψ. Setting expressions for the same points equal to each other gives
Add these and divide by two to get
Comparing radii and arguments gives
Similarly, subtracting the first two equations and dividing by 2 gives
Write
Then
Cartesian coordinates
Expanding the polar equation gives
Letting d 2=a2+b2–c2 simplifies this to
Form of the curve
The construction requires a quadrilateral with sides 2a, b, 2c, b. Any side must be less than the sum of the remaining sides, so the curve is empty (at least in the real plane) unless a<b+c and c<b+a.
The curve has a crossing point at the origin if there is a tria
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https://en.wikipedia.org/wiki/Primitive%20permutation%20group
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In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action preserves are the trivial partitions into either a single set or into |X| singleton sets. Otherwise, if G is transitive and G does preserve a nontrivial partition, G is called imprimitive.
While primitive permutation groups are transitive, not all transitive permutation groups are primitive. The simplest example is the Klein four-group acting on the vertices of a square, which preserves the partition into diagonals. On the other hand, if a permutation group preserves only trivial partitions, it is transitive, except in the case of the trivial group acting on a 2-element set. This is because for a non-transitive action, either the orbits of G form a nontrivial partition preserved by G, or the group action is trivial, in which case all nontrivial partitions of X (which exists for |X| ≥ 3) are preserved by G.
This terminology was introduced by Évariste Galois in his last letter, in which he used the French term équation primitive for an equation whose Galois group is primitive.
Properties
In the same letter in which he introduced the term "primitive", Galois stated the following theorem:If G is a primitive solvable group acting on a finite set X, then the order of X is a power of a prime number p. Further, X may be identified with an affine space over the finite field with p elements, and G acts on X as a subgroup of t
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https://en.wikipedia.org/wiki/Nanoelectrochemistry
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Nanoelectrochemistry is a branch of electrochemistry that investigates the electrical and electrochemical properties of materials at the nanometer size regime. Nanoelectrochemistry plays significant role in the fabrication of various sensors, and devices for detecting molecules at very low concentrations.
Mechanism
Two transport mechanisms are fundamental for nanoelectrochemistry: electron transfer and mass transport. The formulation of theoretical models allows to understand the role of the different species involved in the electrochemical reactions.
The electron transfer between the reactant and the nanoelectrode can be explained by the combination of various theories based on the Marcus theory.
Mass transport, that is the diffusion of the reactant molecules from the electrolyte bulk to the nanoelectrode, is influenced by the formation of a double electric layer at the electrode/electrolyte interface. At the nanoscale it is necessary to theorize a dynamic double electric layer which takes into account an overlap of the Stern layer and the diffuse layer.
Knowledge of the mechanisms involved allows to build computational models that combine the density functional theory with electron transfer theories and the dynamic double electric layer.
In the field of molecular modelling, accurate models could predict the behaviour of the system as reactants, electrolyte or electrode change.
Interface effect
The role of the surface is strongly reaction-specific: in fact, one site ca
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https://en.wikipedia.org/wiki/Hartmut%20Heinrich
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Hartmut Heinrich (born 5 March 1952 in Northeim, Lower Saxony) is a German marine geologist and climatologist. Heinrich was Head of the Marine Physics Department at the Federal Maritime and Hydrographic Agency (BSH) in Hamburg until September 2017. He was actively involved in global Argo Ocean Observing Programme, environmental research and administration, and adaptation to climate change. In 1988 he described the suddenly occurring climate changes in the history of the Earth, which have since been named after him, Heinrich events.
Since October 2017 he is freelancer (10°E maritime consulting) for climate and environment. In October 2017 the Free and Hanseatic City honoured his important contribution to climatic research with the title "Professor honoris causa".
Heinrich studied geology at the University of Göttingen and attained a doctorate at the University of Kiel in marine geology. The discovery that was named for him, Heinrich events, periods of substantial ice output of the continental ice sheets by which the global climate is strongly affected, were subsequently confirmed by investigations of ice core samples from the Greenland ice sheet by the Greenland ice core project (GRIP). Heinrich warns of the consequences of global warming that could occur precipitously and of far larger effects on navigation, coastal populations and the marine environment.
Selected publications
References
1952 births
Living people
People from Northeim
German climatologists
21st-century Ge
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https://en.wikipedia.org/wiki/Osculating%20plane
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In mathematics, particularly in differential geometry, an osculating plane is a plane in a Euclidean space or affine space which meets a submanifold at a point in such a way as to have a second order of contact at the point. The word osculate is from the Latin osculatus which is a past participle of osculari, meaning to kiss. An osculating plane is thus a plane which "kisses" a submanifold.
The osculating plane in the geometry of Euclidean space curves can be described in terms of the Frenet-Serret formulas as the linear span of the tangent and normal vectors.
See also
Normal plane (geometry)
Osculating circle
References
Differential geometry
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https://en.wikipedia.org/wiki/Hom%20functor
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In mathematics, specifically in category theory, hom-sets (i.e. sets of morphisms between objects) give rise to important functors to the category of sets. These functors are called hom-functors and have numerous applications in category theory and other branches of mathematics.
Formal definition
Let C be a locally small category (i.e. a category for which hom-classes are actually sets and not proper classes).
For all objects A and B in C we define two functors to the category of sets as follows:
{| class=wikitable
|-
! Hom(A, –) : C → Set
! Hom(–, B) : C → Set
|-
| This is a covariant functor given by:
Hom(A, –) maps each object X in C to the set of morphisms, Hom(A, X)
Hom(A, –) maps each morphism f : X → Y to the function
Hom(A, f) : Hom(A, X) → Hom(A, Y) given by
for each g in Hom(A, X).
| This is a contravariant functor given by:
Hom(–, B) maps each object X in C to the set of morphisms, Hom(X, B)
Hom(–, B) maps each morphism h : X → Y to the function
Hom(h, B) : Hom(Y, B) → Hom(X, B) given by
for each g in Hom(Y, B).
|}
The functor Hom(–, B) is also called the functor of points of the object B.
Note that fixing the first argument of Hom naturally gives rise to a covariant functor and fixing the second argument naturally gives a contravariant functor. This is an artifact of the way in which one must compose the morphisms.
The pair of functors Hom(A, –) and Hom(–, B) are related in a natural manner. For any pair of morphisms f : B → B′ and h : A′ → A the fol
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https://en.wikipedia.org/wiki/The%20Computer%20Journal
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The Computer Journal is a peer-reviewed scientific journal covering computer science and information systems. Established in 1958, it is one of the oldest computer science research journals. It is published by Oxford University Press on behalf of BCS, The Chartered Institute for IT. The authors of the best paper in each annual volume receive the Wilkes Award from BCS, The Chartered Institute for IT.
Editors-in-chief
The following people have been editor-in-chief:
1958–1969 Eric N. Mutch
1969–1992 Peter Hammersley
1993–2000 C. J. van Rijsbergen
2000–2008 Fionn Murtagh
2008–2012 Erol Gelenbe
2012–2016 Fionn Murtagh
2016–2020 Steve Furber
2021–present Tom Crick
References
External links
Official website
History of the journal
Wilkes Award
British Computer Society
Computer science in the United Kingdom
Computer science journals
English-language journals
Oxford University Press academic journals
Academic journals established in 1958
1958 establishments in England
Academic journals associated with learned and professional societies
8 times per year journals
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https://en.wikipedia.org/wiki/Mathematical%20Association
|
The Mathematical Association is a professional society concerned with mathematics education in the UK.
History
It was founded in 1871 as the Association for the Improvement of Geometrical Teaching and renamed to the Mathematical Association in 1894. It was the first teachers' subject organisation formed in England. In March 1927, it held a three-day meeting in Grantham to commemorate the bicentenary of the death of Sir Isaac Newton, attended by Sir J. J. Thomson (discoverer of the electron), Sir Frank Watson Dyson – the Astronomer Royal, Sir Horace Lamb, and G. H. Hardy.
In 1951, Mary Cartwright became the first female president of the Mathematical Association.
In the 1960s, when comprehensive education was being introduced, the Association was in favour of the 11-plus system. For maths teachers training at university, a teaching award that was examined was the Diploma of the Mathematical Association, later known as the Diploma in Mathematical Education of the Mathematical Association.
Function
It exists to "bring about improvements in the teaching of mathematics and its applications, and to provide a means of communication among students and teachers of mathematics". Since 1894 it has published The Mathematical Gazette. It is one of the participating bodies in the quadrennial British Congress of Mathematics Education, organised by the Joint Mathematical Council, and it holds its annual general meeting as part of the Congress.
Structure
It is based in the south-east of L
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https://en.wikipedia.org/wiki/Naum%20Idelson
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Naum Ilyich Idelson () (March 1(13), 1885, Saint Petersburg - July 14, 1951, Leningrad) was a Soviet theoretical astronomer and expert in history of physics and mathematics.
The crater Idelson on the Moon is named after him.
References
Further reading
Russian astronomers
1885 births
1951 deaths
Scientists from Saint Petersburg
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https://en.wikipedia.org/wiki/DPLL%20algorithm
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In logic and computer science, the Davis–Putnam–Logemann–Loveland (DPLL) algorithm is a complete, backtracking-based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem.
It was introduced in 1961 by Martin Davis, George Logemann and Donald W. Loveland and is a refinement of the earlier Davis–Putnam algorithm, which is a resolution-based procedure developed by Davis and Hilary Putnam in 1960. Especially in older publications, the Davis–Logemann–Loveland algorithm is often referred to as the "Davis–Putnam method" or the "DP algorithm". Other common names that maintain the distinction are DLL and DPLL.
Implementations and applications
The SAT problem is important both from theoretical and practical points of view. In complexity theory it was the first problem proved to be NP-complete, and can appear in a broad variety of applications such as model checking, automated planning and scheduling, and diagnosis in artificial intelligence.
As such, writing efficient SAT solvers has been a research topic for many years. GRASP (1996-1999) was an early implementation using DPLL. In the international SAT competitions, implementations based around DPLL such as zChaff and MiniSat were in the first places of the competitions in 2004 and 2005.
Another application that often involves DPLL is automated theorem proving or satisfiability modulo theories (SMT), which is a SAT problem in which proposit
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https://en.wikipedia.org/wiki/Martin%20van%20Marum
|
Martin(us) van Marum (; 20 March 1750, Delft – 26 December 1837, Haarlem) was a Dutch physician, inventor, scientist and teacher, who studied medicine and philosophy in Groningen. Van Marum introduced modern chemistry in the Netherlands after the theories of Lavoisier, and several scientific applications for general use. He became famous for his demonstrations with instruments, most notable the Large electricity machine, to show statical electricity and chemical experiments while curator for the Teylers Museum.
He researched on the validity of Boyle's law on gases other than air. He found that ammonium gas deviated from Boyle's law with increasing pressure, and it liquified at 7 atm. With this, he was the first to liquify ammonium.
Biography
Early career
Born in Delft, Van Marum moved to Haarlem in 1776 because the Haarlemmers had more taste in the sciences than anywhere else in the Netherlands. After his arrival in Haarlem he began to practise medicine, but devoted himself mainly to lecturing on physical subjects and creating instruments to demonstrate physical theory. He must have made a big impression on Haarlem society, because he became a member of the Dutch Society of Science in the same year, but was named director and curator of their cabinet of curiosities in the next year.
Van Marum received at first no salary, but by scaring off the former cabinet concierge Nicolaus Linder, he was able to collect Linder's' annual salary of 100 guilders, and when the cabinet m
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https://en.wikipedia.org/wiki/Quasi-invariant%20measure
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In mathematics, a quasi-invariant measure μ with respect to a transformation T, from a measure space X to itself, is a measure which, roughly speaking, is multiplied by a numerical function of T. An important class of examples occurs when X is a smooth manifold M, T is a diffeomorphism of M, and μ is any measure that locally is a measure with base the Lebesgue measure on Euclidean space. Then the effect of T on μ is locally expressible as multiplication by the Jacobian determinant of the derivative (pushforward) of T.
To express this idea more formally in measure theory terms, the idea is that the Radon–Nikodym derivative of the transformed measure μ′ with respect to μ should exist everywhere; or that the two measures should be equivalent (i.e. mutually absolutely continuous):
That means, in other words, that T preserves the concept of a set of measure zero. Considering the whole equivalence class of measures ν, equivalent to μ, it is also the same to say that T preserves the class as a whole, mapping any such measure to another such. Therefore, the concept of quasi-invariant measure is the same as invariant measure class.
In general, the 'freedom' of moving within a measure class by multiplication gives rise to cocycles, when transformations are composed.
As an example, Gaussian measure on Euclidean space Rn is not invariant under translation (like Lebesgue measure is), but is quasi-invariant under all translations.
It can be shown that if E is a separable Banach space
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https://en.wikipedia.org/wiki/Conchospiral
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In mathematics, a conchospiral a specific type of space spiral on the surface of a cone (a conical spiral), whose floor projection is a logarithmic spiral.
Conchospirals are used in biology for modelling snail shells, and flight paths of insects and in electrical engineering for the construction of antennas.
Parameterization
In cylindrical coordinates, the conchospiral is described by the parametric equations:
The projection of a conchospiral on the plane is a logarithmic spiral.
The parameter controls the opening angle of the projected spiral, while the parameter controls the slope of the cone on which the curve lies.
History
The name "conchospiral" was given to these curves by 19th-century German mineralogist Georg Amadeus Carl Friedrich Naumann, in his study of the shapes of sea shells.
Applications
The conchospiral has been used in the design for radio antennas. In this application, it has the advantage of producing a radio beam in a single direction, towards the apex of the cone.
References
External links
Spirals
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https://en.wikipedia.org/wiki/Cro%20%28TV%20series%29
|
Cro is an American animated television series produced by the Children's Television Workshop (now known as Sesame Workshop) and Film Roman. It was partially funded by the National Science Foundation. Every episode has an educational theme, introducing basic concepts of physics, mechanical engineering, and technology. The show's narrator is an orange woolly mammoth named Phil, who was found frozen in ice by a scientist named Dr. C and her assistant, Mike. After they defrost him, Phil tells both of them about life in the Ice Age, including stories about his friend Cro, a Cro-Magnon boy.
The show debuted on September 18, 1993, on ABC. ABC canceled the series in 1994, which caused the Children's Television Workshop to plan its own TV channel so that it would not have to rely on other companies to air its shows. The new channel, Noggin, debuted in 1999 and aired Cro reruns from its launch date until 2004. From 2000 to 2002, Cro also aired on Nickelodeon during the "Noggin on Nick" block.
The series' story editors were Sindy McKay and Mark Zaslove, who was also the developer of the show. The premise of using woolly mammoths as a teaching tool for the principles of technology was inspired by The Way Things Work, a book by David Macaulay. Cro was created with the help of a developmental psychologist, Dr. Susan Mendelsohn, and its educational content was heavily researched. According to the Children's Television Workshop, testing of over 2,600 viewers aged 6-12 found that they were
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https://en.wikipedia.org/wiki/W%C3%B6hler%20synthesis
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The Wöhler synthesis is the conversion of ammonium cyanate into urea. This chemical reaction was described in 1828 by Friedrich Wöhler. It is often cited as the starting point of modern organic chemistry. Although the Wöhler reaction concerns the conversion of ammonium cyanate, this salt appears only as an (unstable) intermediate. Wöhler demonstrated the reaction in his original publication with different sets of reactants: a combination of cyanic acid and ammonia, a combination of silver cyanate and ammonium chloride, a combination of lead cyanate and ammonia and finally from a combination of mercury cyanate and cyanatic ammonia (which is again cyanic acid with ammonia).
Modified versions of the Wöhler synthesis
The reaction can be demonstrated by starting with solutions of potassium cyanate and ammonium chloride which are mixed, heated and cooled again. An additional proof of the chemical transformation is obtained by adding a solution of oxalic acid which forms urea oxalate as a white precipitate.
Alternatively the reaction can be carried out with lead cyanate and ammonia. The actual reaction taking place is a double displacement reaction to form ammonium cyanate:
Ammonium cyanate decomposes to ammonia and cyanic acid which in turn react to produce urea:
Complexation with oxalic acid drives this chemical equilibrium to completion.
Debate
It is disputed that Wöhler's synthesis sparked the downfall of the theory of vitalism, which states that organic matter possessed a
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https://en.wikipedia.org/wiki/Crossed%20product
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In mathematics, and more specifically in the theory of von Neumann algebras, a crossed product
is a basic method of constructing a new von Neumann algebra from
a von Neumann algebra acted on by a group. It is related to
the semidirect product construction for groups. (Roughly speaking, crossed product is the expected structure for a group ring of a semidirect product group. Therefore crossed products have a ring theory aspect also. This article concentrates on an important case, where they appear in functional analysis.)
Motivation
Recall that if we have two finite groups and N with an action of G on N we can form the semidirect product . This contains N
as a normal subgroup, and the action of G on N is given by conjugation in the semidirect product. We can replace N by its complex group algebra C[N], and again form a product in a similar way; this algebra is a sum of subspaces gC[N] as g runs through the elements of G, and is the group algebra of .
We can generalize this construction further by replacing C[N]
by any algebra A acted on by G to get a crossed product
, which is the sum of subspaces
gA and where the action of G on A is given by conjugation in the crossed product.
The crossed product of a von Neumann algebra by a group G acting on it is similar except that we have to be more careful about topologies, and need to construct a Hilbert space acted on by the crossed product. (Note that the von Neumann algebra crossed product is usually larger than the algebraic
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https://en.wikipedia.org/wiki/Phil%20Lapsley
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Philip D. Lapsley (born 1965) is an electrical engineer, hacker, author and entrepreneur.
Early life
Lapsley attended the University of California, Berkeley in the 1980s, graduating with a B.S. and M.S. in electrical engineering and computer science in 1988 and 1991. While there he became involved in the Berkeley UNIX project and co-founded the eXperimental Computing Facility, where he was involved in defending against the Morris worm in 1988.
Lapsley received an M.B.A. from the MIT Sloan School of Management.
Career
Lapsley co-authored RFC 977, Network News Transfer Protocol (NNTP), an Internet standard for transmission of USENET news articles, and was the primary developer of the NNTP reference implementation, nntpd. After leaving Berkeley he co-founded Berkeley Design Technology, Inc., a digital signal processing technology advisory firm, and is the author of a book on DSP processors. He later co-founded SmartTouch, a biometric financial transaction processing company.
Lapsley worked at McKinsey & Company as a management consultant until 2008.
His book Exploding the Phone, on the history of phone phreaking, was published by Grove/Atlantic in February, 2013.
References
1965 births
Living people
American electrical engineers
American management consultants
McKinsey & Company people
MIT Sloan School of Management alumni
UC Berkeley College of Engineering alumni
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https://en.wikipedia.org/wiki/Dmitry%20Vadimovich%20Zelenin
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Dmitry Vadimovich Zelenin () (born 27 November 1962, in Moscow) is a Russian businessman and politician. During 2003-2011 he was governor of Tver Oblast, Russia.
Biography
Zelenin graduated from the Moscow Institute of Physics and Technology (Phystech) in 1986 and worked in the electronics industry until 1990 when he became commercial director of Resurs Bank and chief executive of this bank in 1995.
Zelenin was one of the top managers of Norilsk Nickel having joined in 1996 as first deputy general director. This company is one of the largest nickel producers in the world.
Dmitry Zelenin was elected governor of Tver Oblast in December 2003, bypassing incumbent Vladimir Platov, MVD officer Igor Zubov and communist Tatyana Astrakhankina. He was appointed for a second term by president Vladimir Putin in July 2007. In 2010, Zelenin caused a scandal when he posted photos of a salad containing an earthworm on his Twitter account, which was allegedly served to German President Christian Wulff. Sergei Prikhodko, foreign policy adviser to president Dmitry Medvedev, then asked him to resign. Zelenin resigned as governor in June 2011. The main reason was not the Kremlin incident, but the result of the Legislative Assembly election, where United Russia party suffered its second-worst electoral performance in the 2011 regional elections.
Zelenin is married with two daughters and a son.
References
External links
Personal website of Dmitry Zelenin
Moscow Institute of Physics and Te
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https://en.wikipedia.org/wiki/Leftist%20tree
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In computer science, a leftist tree or leftist heap is a priority queue implemented with a variant of a binary heap. Every node x has an s-value which is the distance to the nearest leaf in subtree rooted at x. In contrast to a binary heap, a leftist tree attempts to be very unbalanced. In addition to the heap property, leftist trees are maintained so the right descendant of each node has the lower s-value.
The height-biased leftist tree was invented by Clark Allan Crane. The name comes from the fact that the left subtree is usually taller than the right subtree.
A leftist tree is a mergeable heap. When inserting a new node into a tree, a new one-node tree is created and merged into the existing tree. To delete an item, it is replaced by the merge of its left and right sub-trees. Both these operations take O(log n) time. For insertions, this is slower than Fibonacci heaps, which support insertion in O(1) (constant) amortized time, and O(log n) worst-case.
Leftist trees are advantageous because of their ability to merge quickly, compared to binary heaps which take Θ(n). In almost all cases, the merging of skew heaps has better performance. However merging leftist heaps has worst-case O(log n) complexity while merging skew heaps has only amortized O(log n) complexity.
Bias
The usual leftist tree is a height-biased leftist tree. However, other biases can exist, such as in the weight-biased leftist tree.
S-value
The s-value (or rank) of a node is the distance from that no
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https://en.wikipedia.org/wiki/Don%20Mottram
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Don Mottram (born 1945 in Cheshire) is an English flavour chemist based at the School of Food Biosciences of the University of Reading.
Having obtained an honours degree in colour chemistry from the University of Leeds in 1967 he spent a year working as a volunteer with Voluntary Service Overseas in Dacca, Bangladesh (formerly East Pakistan) before returning to Leeds to study for a Ph.D. in colour chemistry. Following his graduation in 1971, Mottram took up a post at the Meat Research Institute at Langford, near Bristol, UK.
Mottram moved to the University of Reading in 1988. His research interests are mainly in the area of flavour chemistry, the analysis of flavour and the factors affecting its formation and retention in foods, especially meat.
Following the detection of the potential carcinogen acrylamide in a range of fried and oven-cooked foods, Mottram, in collaboration with Professor Bronek Wedzicha of the University of Leeds, provided an important breakthrough in understanding the origin of acrylamide in cooked foods which was published in Nature.
Recently, Mottram has collaborated with chef Heston Blumenthal of The Fat Duck restaurant in the village of Bray in Berkshire.
Mottram is married to Angela (née Cormacey) and they have two children.
External links
Mottram's site
References
Nature, 419, 448-449 (2002)
English chemists
Living people
1945 births
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https://en.wikipedia.org/wiki/Phenomenology%20%28physics%29
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In physics, phenomenology is the application of theoretical physics to experimental data by making quantitative predictions based upon known theories. It is related to the philosophical notion of the same name in that these predictions describe anticipated behaviors for the phenomena in reality. Phenomenology stands in contrast with experimentation in the scientific method, in which the goal of the experiment is to test a scientific hypothesis instead of making predictions.
Phenomenology is commonly applied to the field of particle physics, where it forms a bridge between the mathematical models of theoretical physics (such as quantum field theories and theories of the structure of space-time) and the results of the high-energy particle experiments. It is sometimes used in other fields such as in condensed matter physics and plasma physics, when there are no existing theories for the observed experimental data.
Applications in particle physics
Standard Model consequences
Within the well-tested and generally accepted Standard Model, phenomenology is the calculating of detailed predictions for experiments, usually at high precision (e.g., including radiative corrections).
Examples include:
Next-to-leading order calculations of particle production rates and distributions.
Monte Carlo simulation studies of physics processes at colliders.
Extraction of parton distribution functions from data.
CKM matrix calculations
The CKM matrix is useful in these predictions:
Appli
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https://en.wikipedia.org/wiki/C.%20C.%20Wei
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Chung Ching (C. C., Charles C.) Wei (July 12, 1914 – February 20, 1987) was a Chinese-born American businessman who created the Precision Club bidding system in contract bridge.
Biography
Wei was born in Sheng County, Zhejiang Province, China. He received his B.E. in electrical engineering from Shanghai Jiao Tong University in 1936. In 1942, during World War II, he went to the United States. After the war he became a successful entrepreneur in the shipping industry.
Wei was a member of the ACBL Greater New York Bridge Association. As a player, he was renowned for partnership agreements to compete vigorously through the 2-level, especially at matchpoints. He sometimes played at the Mayfair Club.
Wei died of complications from diabetes at age 72, in New York Hospital, then a resident of New York and Houston. He was survived by his wife Kathie Wei, a son, a daughter, and three stepchildren.
Achievements in bridge
In 1963, "with assistance from Alan Truscott" Wei developed the China bidding system, later called the Precision Club. He was not an expert player, and the system did not attract much attention from the bridge community. That changed when the Taiwan national team, trained and led by Wei, finished as runner-up in the 1969 Bermuda Bowl world team championship, relegating a strong North America team to third place. With two returning players and four new ones, Taiwan was losing finalists again in 1970, and these strong showings brought Wei and the Precision Club grea
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https://en.wikipedia.org/wiki/Multiple%20integral
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In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, or . Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables over a region in (real-number 3D space) are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration.
Introduction
Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the -axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where ) and the plane which contains its domain. If there are more variables, a multiple integral will yield hypervolumes of multidimensional functions.
Multiple integration of a function in variables: over a domain is most commonly represented by nested integral signs in the reverse order of execution (the leftmost integral sign is computed last), followed by the function and integrand arguments in proper order (the integral with respect to the rightmost argument is computed last). The domain of integration is either represented symbolically for every argument over each integral sign, or is abbreviated by a variable at the rightmost integral sign:
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https://en.wikipedia.org/wiki/Meyrin
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Meyrin () is a municipality of the Canton of Geneva, Switzerland.
The main site of CERN, the European particle physics research organisation, is in Meyrin. Meyrin was originally a small agricultural village until the 1950s, when construction of CERN began just to the north. It is now a commuter town dominated with apartment high-rises, and many of its residents work at CERN or in central Geneva. Geneva International Airport is partially located within Meyrin.
History
Meyrin is first mentioned in 1153 as Mairin.
Geography
Meyrin has an area, , of . Of this area, or 35.6% is used for agricultural purposes, while or 4.3% is forested. Of the rest of the land, or 59.1% is settled (buildings or roads), or 0.1% is either rivers or lakes and or 0.8% is unproductive land.
Of the built up area, industrial buildings made up 11.1% of the total area while housing and buildings made up 17.7% and transportation infrastructure made up 25.8%. while parks, green belts and sports fields made up 3.5%. Out of the forested land, all of the forested land area is covered with heavy forests. Of the agricultural land, 28.5% is used for growing crops and 4.8% is pastures, while 2.3% is used for orchards or vine crops. All the water in the municipality is in lakes.
The municipality is located on the right bank of the Rhone river and consists of the sub-sections or villages of CERN, Maisonnex, Mategnin, Citadelle, Aéroport - Tour-de-Contrôle, Aéroport - Papillons, Aéroport - Forestier,
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https://en.wikipedia.org/wiki/Daniel%20Borel
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Daniel Borel (born 14 February 1950) is a Swiss businessman and co-founder of technology firm Logitech.
Education
In 1973, Daniel Borel earned an engineering degree in Physics from the École Polytechnique Fédérale de Lausanne in Switzerland, and in 1977 received a Master of Science degree in Computer Science from Stanford University.
Business
Borel co-founded Logitech at his father-in-law's farm in 1981 with Pierluigi Zappacosta and Giacomo Marini. He served as Logitech's Chairman 1982 to 2008, and served as the company's CEO from 1982 to 1988, and again from 1992 to 1998. In 1988, he took the Logitech Group public on the Swiss stock market, and on the Nasdaq in 1997. He is currently serving as Chairman Emeritus on Logitech's board of directors.
Other endeavours
Borel was a member of the Nestlé Board of Directors from 2004-2016. He also serves on the board of Defitech, founded by him and his wife in 2001, a foundation that brings IT technology to disabled people. In addition, he founded and is chairman of swissUP, a foundation dedicated to promoting education in Switzerland.
In 2019, Borel participated in a fundraising campaign for Unibuddy, a London-based peer-to-peer EdTech platform founded in 2016 by Kimeshan Naidoo and Diego Fanara. Unibuddy raised a total of $5 million in its Series A investment round. Since then, Borel has continued to invest in further Unibuddy funding rounds and the company has raised $32 million to date including a $20 million Series B round
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https://en.wikipedia.org/wiki/Stream%20%28computing%29
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In computer science, a stream is a sequence of data elements made available over time. A stream can be thought of as items on a conveyor belt being processed one at a time rather than in large batches.
Streams are processed differently from batch data – normal functions cannot operate on streams as a whole, as they have potentially unlimited data, and formally, streams are codata (potentially unlimited), not data (which is finite). Functions that operate on a stream, producing another stream, are known as filters, and can be connected in pipelines, analogously to function composition. Filters may operate on one item of a stream at a time, or may base an item of output on multiple items of input, such as a moving average.
Examples
The term "stream" is used in a number of similar ways:
"Stream editing", as with sed, awk, and perl. Stream editing processes a file or files, in-place, without having to load the file(s) into a user interface. One example of such use is to do a search and replace on all the files in a directory, from the command line.
On Unix and related systems based on the C language, a stream is a source or sink of data, usually individual bytes or characters. Streams are an abstraction used when reading or writing files, or communicating over network sockets. The standard streams are three streams made available to all programs.
I/O devices can be interpreted as streams, as they produce or consume potentially unlimited data over time.
In object-oriented pr
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https://en.wikipedia.org/wiki/Combinatorial%20design
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Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in sudoku grids.
Combinatorial design theory can be applied to the area of design of experiments. Some of the basic theory of combinatorial designs originated in the statistician Ronald Fisher's work on the design of biological experiments. Modern applications are also found in a wide gamut of areas including finite geometry, tournament scheduling, lotteries, mathematical chemistry, mathematical biology, algorithm design and analysis, networking, group testing and cryptography.
Example
Given a certain number n of people, is it possible to assign them to sets so that each person is in at least one set, each pair of people is in exactly one set together, every two sets have exactly one person in common, and no set contains everyone, all but one person, or exactly one person? The answer depends on n.
This has a solution only if n has the form q2 + q + 1. It is less simple to prove that a solution exists if q is a prime power. It is conjectured that thes
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https://en.wikipedia.org/wiki/David%20Gregory-Kumar
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David Gregory-Kumar (born David Gregory) is a news correspondent for BBC Midlands Today, covering the English midlands. He is the science and environmental correspondent.
After graduating from university, Gregory worked on his PhD in physics in both Berlin and Milan, but largely just outside the city of Liverpool.
Gregory went on to work on the now defunct Science Line, Science Information Telephone Service.
Gregory had an interest in journalism, produced a regular newsletter while at university and went on to do freelance work for BBC Radio 5 Live. He then became 5 Live's science specialist for his first full-time role for the BBC.
He later joined BBC Midlands Today team as the regional science and environment correspondent, which he continues to do today. David Gregory also writes for BBC Online and works on BBC Radio with his reports usually on the local BBC radio stations in the West Midlands. On occasions, he has also co-presented the main edition of Midlands Today, the regional news program Inside Out, and Radio 4's Farming Today.
In 2012, David Gregory entered into a Civil Partnership with his partner Suraj Kumar. This was converted into a marriage in March 2016, followed by a ceremony in New York in June 2016. The couple have hyphenated their surnames to both become Gregory-Kumar. They have a daughter Marnie.
External links
Gregory's First Law Gregory-Kumar's BBC blog
BBC people
British male journalists
British LGBT journalists
Living people
Year of birt
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https://en.wikipedia.org/wiki/Polynucleotide
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In molecular biology, a polynucleotide () is a biopolymer composed of nucleotide monomers that are covalently bonded in a chain. DNA (deoxyribonucleic acid) and RNA (ribonucleic acid) are examples of polynucleotides with distinct biological functions. DNA consists of two chains of polynucleotides, with each chain in the form of a helix (like a spiral staircase).
Sequence
Although DNA and RNA do not generally occur in the same polynucleotide, the four species of nucleotides may occur in any order in the chain. The sequence of DNA or RNA species for a given polynucleotide is the main factor determining its function in a living organism or a scientific experiment.
Polynucleotides in organisms
Polynucleotides occur naturally in all living organisms. The genome of an organism consists of complementary pairs of enormously long polynucleotides wound around each other in the form of a double helix. Polynucleotides have a variety of other roles in organisms.
Polynucleotides in scientific experiments
Polynucleotides are used in biochemical experiments such as polymerase chain reaction (PCR) or DNA sequencing. Polynucleotides are made artificially from oligonucleotides, smaller nucleotide chains with generally fewer than 30 subunits. A polymerase enzyme is used to extend the chain by adding nucleotides according to a pattern specified by the scientist.
Prebiotic condensation of nucleobases with ribose
In order to understand how life arose, knowledge is required of the chemical p
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https://en.wikipedia.org/wiki/Arsenite
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In chemistry, an arsenite is a chemical compound containing an arsenic oxyanion where arsenic has oxidation state +3. Note that in fields that commonly deal with groundwater chemistry, arsenite is used generically to identify soluble AsIII anions. IUPAC have recommended that arsenite compounds are to be named as arsenate(III), for example ortho-arsenite is called trioxidoarsenate(III).
Ortho-arsenite contrasts to the corresponding anions of the lighter members of group 15, phosphite which has the structure and nitrite, which is bent.
A number of different arsenite anions are known:
ortho-arsenite, an ion of arsenous acid, with a pyramidal shape
meta-arsenite, a polymeric chain anion.
pyro-arsenite,
a polyarsenite,
a polyarsenite,
, a polymeric anion
In all of these the geometry around the AsIII centers are approximately trigonal, the lone pair on the arsenic atom is stereochemically active.
Well known examples of arsenites include sodium meta-arsenite which contains a polymeric linear anion, , and silver ortho-arsenite, , which contains the trigonal anion.
Preparation of arsenites
Some arsenite salts can be prepared from an aqueous solution of . Examples of these are the meta-arsenite salts and at low temperature, hydrogen arsenite salts can be prepared, such as , , and .
Arsenite minerals
A number of minerals contain arsenite anions: reinerite, ; finnemanite, ; paulmooreite, ; stenhuggarite, (contains a complex polymeric anion); schneiderhöhnite, FeFe; magnu
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https://en.wikipedia.org/wiki/Solvay%20Conference
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The Solvay Conferences () have been devoted to preeminent unsolved problems in both physics and chemistry. They began with the historic invitation-only 1911 Solvay Conference on Physics, considered a turning point in the world of physics, and are ongoing.
Since the success of 1911, they have been organised by the International Solvay Institutes for Physics and Chemistry, founded by the Belgian industrialist Ernest Solvay in 1912 and 1913, and located in Brussels. The institutes coordinate conferences, workshops, seminars, and colloquia. Recent Solvay Conferences entail a three year cycle: the Solvay Conference on Physics followed by a gap year, followed by the Solvay Conference on Chemistry.
Notable Solvay conferences
First conference
Hendrik Lorentz was chairman of the first Solvay Conference on Physics, held in Brussels from 30 October to 3 November 1911. The subject was Radiation and the Quanta. This conference looked at the problems of having two approaches, namely classical physics and quantum theory. Albert Einstein was the second youngest physicist present (the youngest one was Lindemann). Other members of the Solvay Congress were experts including Marie Curie, Ernest Rutherford and Henri Poincaré (see image for attendee list).
Third conference
The third Solvay Conference on Physics was held in April 1921, soon after World War I. Most German scientists were barred from attending. In protest at this action, Albert Einstein, although he had renounced German citizen
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https://en.wikipedia.org/wiki/QCI
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QCI may refer to:
QoS Class Identifier, a mechanism to ensure proper Quality of Service for bearer traffic in LTE networks
Quadratic configuration interaction, an extension of configuration interaction in quantum physics
Queen Charlotte Islands, an archipelago on the North Coast of British Columbia, Canada
Quality Council of India
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