source
stringlengths 31
207
| text
stringlengths 12
1.5k
|
|---|---|
https://en.wikipedia.org/wiki/The%20Tao%20of%20Physics
|
The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism is a 1975 book by physicist Fritjof Capra. A bestseller in the United States, it has been translated into 23 languages. Capra summarized his motivation for writing the book: “Science does not need mysticism and mysticism does not need science. But man needs both.”
Origin
According to the preface of the first edition, reprinted in subsequent editions, Capra struggled to reconcile theoretical physics and Eastern mysticism and was at first "helped on my way by 'power plants'" or psychedelics, with the first experience "so overwhelming that I burst into tears, at the same time, not unlike Castaneda, pouring out my impressions to a piece of paper". (p. 12, 4th ed.)
Capra later discussed his ideas with Werner Heisenberg in 1972, as he mentioned in the following interview excerpt:
I had several discussions with Heisenberg. I lived in England then [circa 1972], and I visited him several times in Munich and showed him the whole manuscript chapter by chapter. He was very interested and very open, and he told me something that I think is not known publicly because he never published it. He said that he was well aware of these parallels. While he was working on quantum theory he went to India to lecture and was a guest of Tagore. He talked a lot with Tagore about Indian philosophy. Heisenberg told me that these talks had helped him a lot with his work in physics, because they showed him th
|
https://en.wikipedia.org/wiki/Chisini%20mean
|
In mathematics, a function f of n variables x1, ..., xn leads to a Chisini mean M if, for every vector ⟨x1, ..., xn⟩, there exists a unique M such that
f(M,M, ..., M) = f(x1,x2, ..., xn).
The arithmetic, harmonic, geometric, generalised, Heronian and quadratic means are all Chisini means, as are their weighted variants.
While Oscar Chisini was arguably the first to deal with "substitution means" in some depth in 1929, the idea of defining a mean as above is quite old, appearing (for example) in early works of Augustus De Morgan.
See also
Fréchet mean
Generalized mean
Jensen's inequality
Quasi-arithmetic mean
Stolarsky mean
References
Mathematical analysis
Means
|
https://en.wikipedia.org/wiki/Oscar%20Chisini
|
Oscar Chisini (14 March 1889 – 10 April 1967) was an Italian mathematician. He introduced the Chisini mean in 1929.
Biography
Chisini was born in Bergamo.
In 1929, he founded the Institute of Mathematics (Istituto di Matematica) at the University of Milan, along with Gian Antonio Maggi and Giulio Vivanti. He then held the position of chairman of the Institute from the early 1930s until 1959.
He graduated from the University of Bologna in 1912, having studied under Federigo Enriques. In 1952 he had the appellation "Federigo Enriques" attached to the Institute, to commemorate his memory. This name has been maintained by the Institute, and by the Department of Mathematics (which it became) since 1982.
He was a major contributor to the Enciclopedia Italiana, and from 1946–1967 editor of the journal Il periodico di matematiche.
The Chisini conjecture in algebraic geometry is a uniqueness question for morphisms of generic smooth projective surfaces, branched on a cuspidal curve. A special case is the question of the uniqueness of the covering of the projective plane, branched over a generic curve of degree at least five.
Chisini died in Milan in 1967.
References
External links
Biography and Work of Chisini at the MacTutor History of Mathematics archive
Obituary (in Italian)
1889 births
1967 deaths
19th-century Italian mathematicians
Scientists from Bergamo
20th-century Italian mathematicians
Italian statisticians
Algebraic geometers
Italian algebraic geometers
|
https://en.wikipedia.org/wiki/HPF
|
HPF may refer to:
High-pass filter
High Performance Fortran
High-power field, in microscopy
Hindustan Photo Films, an Indian film manufacturer
Historic Preservation Fund, in the United States
Hours post fertilization, a metric for developmental biology
Human Proteome Folding Project
Hyperpalatable food
|
https://en.wikipedia.org/wiki/Super%20Harvard%20Architecture%20Single-Chip%20Computer
|
The Super Harvard Architecture Single-Chip Computer (SHARC) is a high performance floating-point and fixed-point DSP from Analog Devices. SHARC is used in a variety of signal processing applications ranging from audio processing, to single-CPU guided artillery shells to 1000-CPU over-the-horizon radar processing computers. The original design dates to about January 1994.
SHARC processors are typically intended to have a good number of serial links to other SHARC processors nearby, to be used as a low-cost alternative to SMP.
Architecture
The SHARC is a Harvard architecture word-addressed VLIW processor; it knows nothing of 8-bit or 16-bit values since each address is used to point to a whole 32-bit word, not just an octet. It is thus neither little-endian nor big-endian, though a compiler may use either convention if it implements 64-bit data and/or some way to pack multiple 8-bit or 16-bit values into a single 32-bit word. In C, the characters are 32-bit as they are the smallest addressable words by standard.
The word size is 48-bit for instructions, 32-bit for integers and normal floating-point, and 40-bit for extended floating-point. Code and data are normally fetched from on-chip memory, which the user must split into regions of different word sizes as desired. Small data types may be stored in wider memory, simply wasting the extra space. A system that does not use 40-bit extended floating-point might divide the on-chip memory into two sections, a 48-bit one for code
|
https://en.wikipedia.org/wiki/Magnetic%20helicity
|
In plasma physics, magnetic helicity is a measure of the linkage, twist, and writhe of a magnetic field. In ideal magnetohydrodynamics, magnetic helicity is conserved. When a magnetic field contains magnetic helicity, it tends to form large-scale structures from small-scale ones. This process can be referred to as an inverse transfer in Fourier space.
This second property makes magnetic helicity special: three-dimensional turbulent flows tend to "destroy" structure, in the sense that large-scale vortices break up into smaller and smaller ones (a process called "direct energy cascade", described by Lewis Fry Richardson and Andrey Nikolaevich Kolmogorov). At the smallest scales, the vortices are dissipated in heat through viscous effects. Through a sort of "inverse cascade of magnetic helicity", the opposite happens: small helical structures (with a non-zero magnetic helicity) lead to the formation of large-scale magnetic fields. This is for example visible in the heliospheric current sheet, a large magnetic structure in the Solar System.
Magnetic helicity is of great relevance in several astrophysical systems, where the resistivity is typically very low so that magnetic helicity is conserved to a very good approximation. For example: magnetic helicity dynamics are important in solar flares and coronal mass ejections. Magnetic helicity is present in the solar wind. Its conservation is significant in dynamo processes. It also plays a role in fusion research, for example in rev
|
https://en.wikipedia.org/wiki/Hydrodynamical%20helicity
|
In fluid dynamics, helicity is, under appropriate conditions, an invariant of the Euler equations of fluid flow, having a topological interpretation as a measure of linkage and/or knottedness of vortex lines in the flow. This was first proved by Jean-Jacques Moreau in 1961 and Moffatt derived it in 1969 without the knowledge of Moreau's paper. This helicity invariant is an extension of Woltjer's theorem for magnetic helicity.
Let be the velocity field and the corresponding vorticity field. Under the following three conditions, the vortex lines are transported with (or 'frozen in') the flow: (i) the fluid is inviscid; (ii) either the flow is incompressible (), or it is compressible with a barotropic relation between pressure and density ; and (iii) any body forces acting on the fluid are conservative. Under these conditions, any closed surface whose normal vectors are orthogonal to the vorticity (that is, ) is, like vorticity, transported with the flow.
Let be the volume inside such a surface. Then the helicity in , denoted , is defined by the volume integral
For a localised vorticity distribution in an unbounded fluid, can be taken to be the whole space, and is then the total helicity of the flow. is invariant precisely because the vortex lines are frozen in the flow and their linkage and/or knottedness is therefore conserved, as recognized by Lord Kelvin (1868). Helicity is a pseudo-scalar quantity: it changes sign under change from a right-handed to a left-han
|
https://en.wikipedia.org/wiki/Alan%20Tower%20Waterman
|
Alan Tower Waterman (June 4, 1892 – November 30, 1967) was an American physicist.
Biography
Born in Cornwall-on-Hudson, New York, he grew up in Northampton, Massachusetts. His father was a professor of physics at Smith College. Alan also became a physicist, doing his undergraduate and doctoral work at Princeton University from which he obtained his Ph.D. in 1916.
He joined the faculty of the University of Cincinnati, and married Vassar graduate Mary Mallon. (sister of H. Neil Mallon) there in August 1917. He later became a professor at Yale University, and moved to North Haven, Connecticut in 1929. During World War II, he took leave of absence from Yale to become director of field operations for the Office of Scientific Research and Development and the family moved to Cambridge, MA. He continued his government work and became deputy chief of the Office of Naval Research. In 1950, he was appointed by President Truman as first director of the U.S. National Science Foundation (NSF) Waterman was awarded the Public Welfare Medal from the National Academy of Sciences in 1960. He served as director until 1963, when he retired and was subsequently awarded the Presidential Medal of Freedom.
Alan and Mary had six children: Alan Jr, an atmospheric physicist who taught at Stanford University, Neil, Barbara, Anne, and Guy, writer, climber, and conservationist. A daughter Mary died in childhood.
Possessed of a gentle nature, Alan Waterman was known for his calm and reasoned point of vi
|
https://en.wikipedia.org/wiki/Mary-Dell%20Chilton
|
Mary-Dell Chilton (born February 2, 1939, in Indianapolis, Indiana) is one of the founders of modern plant biotechnology.
Early life and education
Chilton attended private school for her early education. She earned both a B.S. and Ph.D. in chemistry from the University of Illinois Urbana-Champaign. She later completed postdoctoral work at the University of Washington at Seattle
Career and research
Chilton taught and performed research at Washington University in St. Louis. While on faculty there in the late 1970s and early 1980s, she led a collaborative research study that produced the first transgenic plants.
Chilton was the first (1977) to demonstrate the presence of a fragment of Agrobacterium Ti plasmid DNA in the nuclear DNA of crown gall tissue. Her research on Agrobacterium also showed that the genes responsible for causing disease could be removed from the bacterium without adversely affecting its ability to insert its own DNA into plant cells and modify the plant's genome. Chilton described what she had done as disarming the bacterial plasmid responsible for the DNA transfer. She and her collaborators produced the first genetically modified plants using Agrobacterium carrying the disarmed Ti plasmid (1983). She has been called the "queen of Agrobacterium."
Chilton is author of more than 100 scientific publications. She is a Distinguished Science Fellow at Syngenta Biotechnology, Inc. She began her corporate career in 1983 with CIBA-Geigy Corporation (a legacy co
|
https://en.wikipedia.org/wiki/Mark%20Benton
|
Mark Benton (born 16 November 1965) is an English actor and television presenter known for his roles as Eddie in Early Doors, Howard in Northern Lights and Martin Pond in Barbara. Benton has also starred in the BBC One school-based drama series Waterloo Road as mathematics teacher Daniel "Chalky" Chalk from 2011 to 2014. In 2013, Benton took part in Strictly Come Dancing, and in 2015 he hosted the daytime game show The Edge.
Since 2018, Benton has played the leading role of Frank Hathaway in Shakespeare & Hathaway: Private Investigators on BBC1.
Early life
Benton was born in Guisborough, North Riding of Yorkshire, England, and attended Sarah Metcalfe Comprehensive School and, later, Stockton Billingham Technical College. Some of Benton's early acting experience came at Middlesbrough Youth Theatre with performances in plays such as Atmos Fear and Twist.
Career
Benton has a recurring role as Father McBride in the James Nesbitt series Murphy's Law and has starred with Vic and Bob in the series Randall and Hopkirk (Deceased) (2000 TV series), Catterick, and Monkey Trousers. In 1999, he played Mickey-O in "The Wedding", the last episode of series 5 of Ballykissangel. He also appeared as an earthly representative of the devil in the 2003 ITV drama The Second Coming and the 2005 ITV drama Planespotting. From 1999 to 2003 Benton played Martin Pond in sitcom Barbara. He has also starred in the BBC Three comedy I'm with Stupid and in the Doctor Who episode "Rose" as conspiracy theor
|
https://en.wikipedia.org/wiki/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa%20matrix
|
In the Standard Model of particle physics, the Cabibbo–Kobayashi–Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix which contains information on the strength of the flavour-changing weak interaction. Technically, it specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions. It is important in the understanding of CP violation. This matrix was introduced for three generations of quarks by Makoto Kobayashi and Toshihide Maskawa, adding one generation to the matrix previously introduced by Nicola Cabibbo. This matrix is also an extension of the GIM mechanism, which only includes two of the three current families of quarks.
The matrix
Predecessor – the Cabibbo matrix
In 1963, Nicola Cabibbo introduced the Cabibbo angle () to preserve the universality of the weak interaction.
Cabibbo was inspired by previous work by Murray Gell-Mann and Maurice Lévy,
on the effectively rotated nonstrange and strange vector and axial weak currents, which he references.
In light of current concepts (quarks had not yet been proposed), the Cabibbo angle is related to the relative probability that down and strange quarks decay into up quarks ( || and || , respectively). In particle physics jargon, the object that couples to the up quark via charged-current weak interaction is a superposition of down-type quarks, here denoted by .
Mathematically this is:
or using the Cabibbo angle:
Using the
|
https://en.wikipedia.org/wiki/MIT%20Laboratory%20for%20Information%20and%20Decision%20Systems
|
The MIT Laboratory for Information and Decision Systems (LIDS) is an interdisciplinary research laboratory of MIT, working on research in the areas of communications, control, and signal processing combining faculty from the School of Engineering (including the Department of Aeronautics and Astronautics), the Department of Mathematics and the MIT Sloan School of Management. The lab is located in the Dreyfoos Tower of the Stata Center and shares some research duties with MIT's Lincoln Laboratory and the independent Draper Laboratory.
History
The laboratory traces its beginnings to the MIT Servomechanisms Laboratory, where work on guidance systems and early computation was done during World War II.
Known as LIDS, the laboratory has hosted several luminaries over the years, including Claude Shannon and David Forney. , the current acting director is Prof. Sertac Karaman.
See also
Gordon S. Brown
References
External links
LIDS webpage
Laboratory for Information and Decision Systems
|
https://en.wikipedia.org/wiki/Martin%20David%20Kruskal
|
Martin David Kruskal (; September 28, 1925 – December 26, 2006) was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and from nonlinear analysis to asymptotic analysis. His most celebrated contribution was in the theory of solitons.
He was a student at the University of Chicago and at New York University, where he completed his Ph.D. under Richard Courant in 1952. He spent much of his career at Princeton University, as a research scientist at the Plasma Physics Laboratory starting in 1951, and then as a professor of astronomy (1961), founder and chair of the Program in Applied and Computational Mathematics (1968), and professor of mathematics (1979). He retired from Princeton University in 1989 and joined the mathematics department of Rutgers University, holding the David Hilbert Chair of Mathematics.
Apart from serious mathematical work, Kruskal was known for mathematical diversions. For example, he invented the Kruskal Count, a magical effect that has been known to perplex professional magicians because it was based not on sleight of hand but on a mathematical phenomenon.
Personal life
Martin David Kruskal was born to a Jewish family in New York City and grew up in New Rochelle. He was generally known as Martin to the world and David to his family. His father, Joseph B. Kruskal Sr., was a successful fur wholesaler. His mother, Lillian Rose Vorhaus Kruska
|
https://en.wikipedia.org/wiki/Christopher%20Jackson%20%28politician%29
|
Christopher Murray Jackson (24 May 1935 – 13 December 2019) was a British businessman and Conservative Party politician who served as a Member of the European Parliament (MEP) from 1979 to 1994.
After a National Service Commission in the RAF as a pilot, Jackson read physics at Magdalen College, Oxford, of which he was an Open Exhibitioner. Whilst there he founded the Magnates Club which eventually became the Oxford University Guild Society. He then trained in management with Unilever, becoming a senior manager of the Group in 1967.
He contested East Ham South as a Conservative in the 1970 General Election and Northampton North in 1974.
He was Director of Corporate Development of the Spillers Group from 1974 to 1979.
He was elected as the Member of the European Parliament for Kent East from 1979 (the first European Parliament Elections) to 1994, he served as Conservative Spokesman on Development Policy; Agriculture; Economic Affairs and Foreign Affairs. In 1984 he proposed the inclusion of subsidiarity in the Draft Treaty on European Union and led a European Parliament delegation, including Altiero Spinelli to the UK for discussions on the Draft Treaty with the Conservative, Labour, and Liberal parties, the CBI and the TUC. He was a Member of the ACP-European Economic Community Joint Assembly of which he was Rapporteur-General in 1985. He became Deputy Leader of Conservative MEPs in 1989, remaining in that position until 1991, and Co-President of the EP Working Group on
|
https://en.wikipedia.org/wiki/Jet
|
Jet, Jets, or The Jet(s) may refer to:
Aerospace
Jet aircraft, an aircraft propelled by jet engines
Jet airliner
Jet engine
Jet fuel
Jet Airways, an Indian airline
Wind Jet (ICAO: JET), an Italian airline
Journey to Enceladus and Titan (JET), a proposed astrobiology orbiter to Saturn
Jet pack, a backpack personal flying device containing a jet motor
Fighter jet, a military aircraft
Aircraft
Business jet
Boeing Business Jet
Very light jet
Cirrus Vision SF50, originally called "The-Jet by Cirrus"
Eclipse 400, originally called "Eclipse Concept Jet"
Honda HA-420 HondaJet
Piper PA-47 PiperJet
Other areas of science, math, and technology
Jet (fluid), a coherent stream of fluid that is projected into a surrounding medium, usually from some kind of a nozzle or aperture
Jet (gemstone), a black or brown semi-precious mineraloid
Jet (mathematics), an operation on a differentiable function
Jet (particle physics), a narrow cone of hadrons and other particles produced by the hadronization of a quark or gluon
Jet bundle, a fiber bundle of jets in differential topology
Jet group, a group of jets in differential topology
Jet stream, in meteorology, commonly referred to as "jet"
Astrophysical jet, in astrophysics, a stream of matter emitted along the axis of a rotating astronomical body
Joint European Torus, an experimental nuclear fusion machine
Junctional ectopic tachycardia, a rare cardiac arrhythmia that sometimes occurs after surgery in infants
People
J
|
https://en.wikipedia.org/wiki/Isogeny
|
In mathematics, particularly in algebraic geometry, an isogeny is a morphism of algebraic groups (also known as group varieties) that is surjective and has a finite kernel.
If the groups are abelian varieties, then any morphism of the underlying algebraic varieties which is surjective with finite fibres is automatically an isogeny, provided that . Such an isogeny then provides a group homomorphism between the groups of -valued points of and , for any field over which is defined.
The terms "isogeny" and "isogenous" come from the Greek word ισογενη-ς, meaning "equal in kind or nature". The term "isogeny" was introduced by Weil; before this, the term "isomorphism" was somewhat confusingly used for what is now called an isogeny.
Case of abelian varieties
For abelian varieties, such as elliptic curves, this notion can also be formulated as follows:
Let E1 and E2 be abelian varieties of the same dimension over a field k. An isogeny between E1 and E2 is a dense morphism of varieties that preserves basepoints (i.e. f maps the identity point on E1 to that on E2).
This is equivalent to the above notion, as every dense morphism between two abelian varieties of the same dimension is automatically surjective with finite fibres, and if it preserves identities then it is a homomorphism of groups.
Two abelian varieties E1 and E2 are called isogenous if there is an isogeny . This can be shown to be an equivalence relation; in the case of elliptic curves, symmetry is due to the ex
|
https://en.wikipedia.org/wiki/Semi-empirical%20mass%20formula
|
In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass of an atomic nucleus from its number of protons and neutrons. As the name suggests, it is based partly on theory and partly on empirical measurements. The formula represents the liquid-drop model proposed by George Gamow, which can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. It was first formulated in 1935 by German physicist Carl Friedrich von Weizsäcker, and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today.
The formula gives a good approximation for atomic masses and thereby other effects. However, it fails to explain the existence of lines of greater binding energy at certain numbers of protons and neutrons. These numbers, known as magic numbers, are the foundation of the nuclear shell model.
The liquid-drop model
The liquid-drop model was first proposed by George Gamow and further developed by Niels Bohr and John Archibald Wheeler. It treats the nucleus as a drop of incompressible fluid of very high density, held together by the nuclear force (a residual effect of the strong force), there is a similarity to the structure of a spherical liquid drop. While a crude model, the liquid-drop mod
|
https://en.wikipedia.org/wiki/Hypervalent%20molecule
|
In chemistry, a hypervalent molecule (the phenomenon is sometimes colloquially known as expanded octet) is a molecule that contains one or more main group elements apparently bearing more than eight electrons in their valence shells. Phosphorus pentachloride (), sulfur hexafluoride (), chlorine trifluoride (), the chlorite () ion, and the triiodide () ion are examples of hypervalent molecules.
Definitions and nomenclature
Hypervalent molecules were first formally defined by Jeremy I. Musher in 1969 as molecules having central atoms of group 15–18 in any valence other than the lowest (i.e. 3, 2, 1, 0 for Groups 15, 16, 17, 18 respectively, based on the octet rule).
Several specific classes of hypervalent molecules exist:
Hypervalent iodine compounds are useful reagents in organic chemistry (e.g. Dess–Martin periodinane)
Tetra-, penta- and hexavalent phosphorus, silicon, and sulfur compounds (e.g. PCl5, PF5, SF6, sulfuranes and persulfuranes)
Noble gas compounds (ex. xenon tetrafluoride, XeF4)
Halogen polyfluorides (ex. chlorine pentafluoride, ClF5)
N-X-L notation
N-X-L nomenclature, introduced collaboratively by the research groups of Martin, Arduengo, and Kochi in 1980, is often used to classify hypervalent compounds of main group elements, where:
N represents the number of valence electrons
X is the chemical symbol of the central atom
L the number of ligands to the central atom
Examples of N-X-L nomenclature include:
XeF2, 10-Xe-2
PCl5, 10-P-5
SF6, 12-S-6
IF7,
|
https://en.wikipedia.org/wiki/Thomas%20Simpson
|
Thomas Simpson FRS (20 August 1710 – 14 May 1761) was a British mathematician and inventor known for the eponymous Simpson's rule to approximate definite integrals. The attribution, as often in mathematics, can be debated: this rule had been found 100 years earlier by Johannes Kepler, and in German it is called Keplersche Fassregel.
Biography
Simpson was born in Sutton Cheney, Leicestershire. The son of a weaver, Simpson taught himself mathematics. At the age of nineteen, he married a fifty-year old widow with two children. As a youth, he became interested in astrology after seeing a solar eclipse. He also dabbled in divination and caused fits in a girl after 'raising a devil' from her. After this incident, he and his wife had to flee to Derby. He moved with his wife and children to London at age twenty-five, where he supported his family by weaving during the day and teaching mathematics at night.
From 1743, he taught mathematics at the Royal Military Academy, Woolwich. Simpson was a fellow of the Royal Society. In 1758, Simpson was elected a foreign member of the Royal Swedish Academy of Sciences.
He died in Market Bosworth, and was laid to rest in Sutton Cheney. A plaque inside the church commemorates him.
Early work
Simpson's treatise entitled The Nature and Laws of Chance and The Doctrine of Annuities and Reversions were based on the work of De Moivre and were attempts at making the same material more brief and understandable. Simpson stated this clearly in The N
|
https://en.wikipedia.org/wiki/Louis%20Couturat
|
Louis Couturat (; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido.
Life and education
Born in Ris-Orangis, Essonne, France. In 1887 he entered École Normale Supérieure to study philosophy and mathematics. In 1895 he lectured in philosophy at the University of Toulouse and 1897 lectured in philosophy of mathematics at the University of Caen Normandy, taking a stand in favor of transfinite numbers. After a time in Hanover studying the writings of Leibniz, he became an assistant to Henri-Louis Bergson at the Collège de France in 1905.
Career
He was the French advocate of the symbolic logic that emerged in the years before World War I, thanks to the writings of Charles Sanders Peirce, Giuseppe Peano and his school, and especially to The Principles of Mathematics by Couturat's friend and correspondent Bertrand Russell. Like Russell, Couturat saw symbolic logic as a tool to advance both mathematics and the philosophy of mathematics. In this, he was opposed by Henri Poincaré, who took considerable exception to Couturat's efforts to interest the French in symbolic logic. With the benefit of hindsight, we can see that Couturat was in broad agreement with the logicism of Russell, while Poincaré anticipated Brouwer's intuitionism.
His first major publication was De Platonicis mythis (1896). In 1901, he published La Logique de Leibniz, a detailed study of Leibniz the logician, ba
|
https://en.wikipedia.org/wiki/Taut%20submanifold
|
In mathematics, a (compact) taut submanifold N of a space form M is a compact submanifold with the property that for every the distance function
is a perfect Morse function.
If N is not compact, one needs to consider the restriction of the to any of their sublevel sets.
References
Differential geometry
Morse theory
|
https://en.wikipedia.org/wiki/Space%20form
|
In mathematics, a space form is a complete Riemannian manifold M of constant sectional curvature K. The three most fundamental examples are Euclidean n-space, the n-dimensional sphere, and hyperbolic space, although a space form need not be simply connected.
Reduction to generalized crystallography
The Killing–Hopf theorem of Riemannian geometry states that the universal cover of an n-dimensional space form with curvature is isometric to , hyperbolic space, with curvature is isometric to , Euclidean n-space, and with curvature is isometric to , the n-dimensional sphere of points distance 1 from the origin in .
By rescaling the Riemannian metric on , we may create a space of constant curvature for any . Similarly, by rescaling the Riemannian metric on , we may create a space of constant curvature for any . Thus the universal cover of a space form with constant curvature is isometric to .
This reduces the problem of studying space forms to studying discrete groups of isometries of which act properly discontinuously. Note that the fundamental group of , , will be isomorphic to . Groups acting in this manner on are called crystallographic groups. Groups acting in this manner on and are called Fuchsian groups and Kleinian groups, respectively.
See also
Borel conjecture
References
Riemannian geometry
Conjectures
|
https://en.wikipedia.org/wiki/Bias%20%28disambiguation%29
|
Bias is an inclination toward something, or a predisposition, partiality, prejudice, preference, or predilection.
Bias may also refer to:
Scientific method and statistics
The bias introduced into an experiment through a confounder
Algorithmic bias, machine learning algorithms that exhibit politically unacceptable behavior
Cultural bias, interpreting and judging phenomena in terms particular to one's own culture
Funding bias, bias relative to the commercial interests of a study's financial sponsor
Infrastructure bias, the influence of existing social or scientific infrastructure on scientific observations
Publication bias, bias toward publication of certain experimental results
Bias (statistics), the systematic distortion of a statistic
Biased sample, a sample falsely taken to be typical of a population
Estimator bias, a bias from an estimator whose expectation differs from the true value of the parameter
Personal equation, a concept in 19th- and early 20th-century science that each observer had an inherent bias when it came to measurements and observations
Reporting bias, a bias resulting from what is and is not reported in research, either by participants in the research or by the researcher.
Cognitive science
Cognitive bias, any of a wide range of effects identified in cognitive science.
Confirmation bias, tendency of people to favor information that confirm their beliefs of hypothesis
See List of cognitive biases for a comprehensive list
Mathematics an
|
https://en.wikipedia.org/wiki/Projectionless%20C%2A-algebra
|
In mathematics, a projectionless C*-algebra is a C*-algebra with no nontrivial projections. For a unital C*-algebra, the projections 0 and 1 are trivial. While for a non-unital C*-algebra, only 0 is considered trivial. The problem of whether simple infinite-dimensional C*-algebras with this property exist was posed in 1958 by Irving Kaplansky, and the first example of one was published in 1981 by Bruce Blackadar. For commutative C*-algebras, being projectionless is equivalent to its spectrum being connected. Due to this, being projectionless can be considered as a noncommutative analogue of a connected space.
Examples
C, the algebra of complex numbers.
The reduced group C*-algebra of the free group on finitely many generators.
The Jiang-Su algebra is simple, projectionless, and KK-equivalent to C.
Dimension drop algebras
Let be the class consisting of the C*-algebras for each , and let be the class of all C*-algebras of the form
,
where are integers, and where belong to .
Every C*-algebra A in is projectionless, moreover, its only projection is 0.
References
C*-algebras
|
https://en.wikipedia.org/wiki/Mendel
|
Mendel may refer to:
People
Mendel (name), includes a list of people with the name
Gregor Mendel (1822–1884), the "father of modern genetics"
Mendel (Hungarian family), a prominent Hungarian family that flourished in the 15th century
Yiddish diminutive of Hebrew name Menahem or Menachem
Other
Mendel University Brno in the Czech Republic (formerly Mendel University of Agriculture and Forestry)
Mendel Biotechnology, a plant biotechnology company in Hayward, California
Mendel (lunar crater), a crater on the Moon
Mendel (Martian crater)
3313 Mendel, an asteroid named after Gregor Mendel
Mendelpass, a mountain pass in Northern Italy
RepRap 2.0 (Mendel), a self-replicating machine
See also
Mendel Polar Station in Antarctica
L. Mendel Rivers (1905–1970), US Congressman
USS L. Mendel Rivers (SSN-686), a US submarine
Mendele
Mandel
Mendelssohn
Mendl, a surname
Mende (disambiguation)
|
https://en.wikipedia.org/wiki/Reductive%20group
|
In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a representation that has a finite kernel and is a direct sum of irreducible representations. Reductive groups include some of the most important groups in mathematics, such as the general linear group GL(n) of invertible matrices, the special orthogonal group SO(n), and the symplectic group Sp(2n). Simple algebraic groups and (more generally) semisimple algebraic groups are reductive.
Claude Chevalley showed that the classification of reductive groups is the same over any algebraically closed field. In particular, the simple algebraic groups are classified by Dynkin diagrams, as in the theory of compact Lie groups or complex semisimple Lie algebras. Reductive groups over an arbitrary field are harder to classify, but for many fields such as the real numbers R or a number field, the classification is well understood. The classification of finite simple groups says that most finite simple groups arise as the group G(k) of k-rational points of a simple algebraic group G over a finite field k, or as minor variants of that construction.
Reductive groups have a rich representation theory in various contexts. First, one can study the representations of a reductive group G over a field k as an algebraic group, which are actions of G on k-vector spaces. But also, one can study the complex represen
|
https://en.wikipedia.org/wiki/Mahler%20measure
|
In mathematics, the Mahler measure of a polynomial with complex coefficients is defined as
where factorizes over the complex numbers as
The Mahler measure can be viewed as a kind of height function. Using Jensen's formula, it can be proved that this measure is also equal to the geometric mean of for on the unit circle (i.e., ):
By extension, the Mahler measure of an algebraic number is defined as the Mahler measure of the minimal polynomial of over . In particular, if is a Pisot number or a Salem number, then its Mahler measure is simply .
The Mahler measure is named after the German-born Australian mathematician Kurt Mahler.
Properties
The Mahler measure is multiplicative:
where is the norm of .
Kronecker's Theorem: If is an irreducible monic integer polynomial with , then either or is a cyclotomic polynomial.
(Lehmer's conjecture) There is a constant such that if is an irreducible integer polynomial, then either or .
The Mahler measure of a monic integer polynomial is a Perron number.
Higher-dimensional Mahler measure
The Mahler measure of a multi-variable polynomial is defined similarly by the formula
It inherits the above three properties of the Mahler measure for a one-variable polynomial.
The multi-variable Mahler measure has been shown, in some cases, to be related to special values
of zeta-functions and -functions. For example, in 1981, Smyth proved the formulas
where is the Dirichlet L-function, and
where is the Riemann zeta
|
https://en.wikipedia.org/wiki/Identity%20component
|
In mathematics, specifically group theory, the identity component of a group G refers to several closely related notions of the largest connected subgroup of G containing the identity element.
In point set topology, the identity component of a topological group G is the connected component G0 of G that contains the identity element of the group. The identity path component of a topological group G is the path component of G that contains the identity element of the group.
In algebraic geometry, the identity component of an algebraic group G over a field k is the identity component of the underlying topological space. The identity component of a group scheme G over a base scheme S is, roughly speaking, the group scheme G0 whose fiber over the point s of S is the connected component (Gs)0 of the fiber Gs, an algebraic group.
Properties
The identity component G0 of a topological or algebraic group G is a closed normal subgroup of G. It is closed since components are always closed. It is a subgroup since multiplication and inversion in a topological or algebraic group are continuous maps by definition. Moreover, for any continuous automorphism a of G we have
a(G0) = G0.
Thus, G0 is a characteristic subgroup of G, so it is normal.
The identity component G0 of a topological group G need not be open in G. In fact, we may have G0 = {e}, in which case G is totally disconnected. However, the identity component of a locally path-connected space (for instance a Lie group) is a
|
https://en.wikipedia.org/wiki/Cross-link
|
In chemistry and biology a cross-link is a bond or a short sequence of bonds that links one polymer chain to another. These links may take the form of covalent bonds or ionic bonds and the polymers can be either synthetic polymers or natural polymers (such as proteins).
In polymer chemistry "cross-linking" usually refers to the use of cross-links to promote a change in the polymers' physical properties.
When "crosslinking" is used in the biological field, it refers to the use of a probe to link proteins together to check for protein–protein interactions, as well as other creative cross-linking methodologies.
Although the term is used to refer to the "linking of polymer chains" for both sciences, the extent of crosslinking and specificities of the crosslinking agents vary greatly.
Synthetic polymers
Crosslinking generally involves covalent bonds that join two polymer chains. The term curing refers to the crosslinking of thermosetting resins, such as unsaturated polyester and epoxy resin, and the term vulcanization is characteristically used for rubbers. When polymer chains are crosslinked, the material becomes more rigid. The mechanical properties of a polymer depends strongly on the cross-link density. Low cross-link densities increase the viscosities of polymer melts. Intermediate cross-link densities transform gummy polymers into materials that have elastomeric properties and potentially high strengths. Very high cross-link densities can cause materials to become very
|
https://en.wikipedia.org/wiki/Euler%E2%80%93Tricomi%20equation
|
In mathematics, the Euler–Tricomi equation is a linear partial differential equation useful in the study of transonic flow. It is named after mathematicians Leonhard Euler and Francesco Giacomo Tricomi.
It is elliptic in the half plane x > 0, parabolic at x = 0 and hyperbolic in the half plane x < 0.
Its characteristics are
which have the integral
where C is a constant of integration. The characteristics thus comprise two families of semicubical parabolas, with cusps on the line x = 0, the curves lying on the right hand side of the y-axis.
Particular solutions
A general expression for particular solutions to the Euler–Tricomi equations is:
where
These can be linearly combined to form further solutions such as:
for k = 0:
for k = 1:
etc.
The Euler–Tricomi equation is a limiting form of Chaplygin's equation.
See also
Burgers equation
Chaplygin's equation
Bibliography
A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC Press, 2002.
External links
Tricomi and Generalized Tricomi Equations at EqWorld: The World of Mathematical Equations.
Partial differential equations
Equations of fluid dynamics
Leonhard Euler
|
https://en.wikipedia.org/wiki/Robomow
|
Robomow (also known as Friendly Robotics) is a manufacturer of robotic lawn mowers. Founded in Even Yehuda, Israel in 1995 by Udi Peless and Shai Abramson, the company provides robotic lawnmowers to the United States and Europe, with prices ranging from hundreds to thousands of dollars/Euros. Robomow mowers are rechargeable, environmentally-friendly designed to meet all safety standards. Robomow also comes with its own mobile application (the Robomow app) for remote and interactive control. The company has been mentioned in several magazines including: Design News, Business Wire, Washington Home and Garden and Vanity Fair. In May 2017, MTD Products Inc announced their intent to purchase Friendly Robotics. In July 2017, MTD Products announced the completion of the purchase of Robomow.
History
Robotic Lawn Mowers
Robomow was originally named ‘Friendly Machines’ with the goal of constructing robots that will, as Udi Peless says in Space Daily, "move in and around the home, doing the mundane tasks that people do not like to do anymore".
The Robomow Classic model debuted in the GLEE exhibition in Birmingham, UK in 1997 and was the ‘father’ of Friendly Robotics’ official first model. This Classic model was launched for sale in 1998, selling approximately 4000 units between 1998 and 2001.
The company name was changed to Friendly Robotics in 1999.
In 2000, the second generation of robotic mowers arrived: the Robomow ‘RL’ platform. Compared to the Robomow Classic, Robomow RL was
|
https://en.wikipedia.org/wiki/GNU%20Radio
|
GNU Radio is a free software development toolkit that provides signal processing blocks to implement software-defined radios and signal processing systems. It can be used with external radio frequency (RF) hardware to create software-defined radios, or without hardware in a simulation-like environment. It is widely used in hobbyist, academic, and commercial environments to support both wireless communications research and real-world radio systems.
Overview
The GNU Radio software provides the framework and tools to build and run software radio or just general signal-processing applications. The GNU Radio applications themselves are generally known as "flowgraphs", which are a series of signal processing blocks connected together, thus describing a data flow.
As with all software-defined radio systems, reconfigurability is a key feature. Instead of using different radios designed for specific but disparate purposes, a single, general-purpose, radio can be used as the radio front-end, and the signal-processing software (here, GNU Radio), handles the processing specific to the radio application.
These flowgraphs can be written in either C++ or Python. The GNU Radio infrastructure is written entirely in C++, and many of the user tools (such as GNU Radio Companion) are written in Python.
GNU Radio is a signal processing package and part of the GNU Project. It is distributed under the terms of the GNU General Public License (GPL), and most of the project code is copyrighted by
|
https://en.wikipedia.org/wiki/Modular%20lattice
|
In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self-dual condition,
Modular law implies
where are arbitrary elements in the lattice, ≤ is the partial order, and ∨ and ∧ (called join and meet respectively) are the operations of the lattice. This phrasing emphasizes an interpretation in terms of projection onto the sublattice , a fact known as the diamond isomorphism theorem. An alternative but equivalent condition stated as an equation (see below) emphasizes that modular lattices form a variety in the sense of universal algebra.
Modular lattices arise naturally in algebra and in many other areas of mathematics. In these scenarios, modularity is an abstraction of the 2nd Isomorphism Theorem. For example, the subspaces of a vector space (and more generally the submodules of a module over a ring) form a modular lattice.
In a not necessarily modular lattice, there may still be elements for which the modular law holds in connection with arbitrary elements and (for ). Such an element is called a modular element. Even more generally, the modular law may hold for any and a fixed pair . Such a pair is called a modular pair, and there are various generalizations of modularity related to this notion and to semimodularity.
Modular lattices are sometimes called Dedekind lattices after Richard Dedekind, who discovered the modular identity in several motivating examples.
Introduction
The modular law can be see
|
https://en.wikipedia.org/wiki/ICEE
|
ICEE may refer to:
Conferences
International Conference on Electrical Engineering organized by the International Association of Engineers
International Conference on Emerging Electronics organized by the IEEE
International Conference on Emission Electronics organized by the IEEE
Fourth International Conference on Environmental Education (ICEE), an environmental conference held in Ahmedabad, India in November 2007
International Conference on Environmental Ergonomics organized by the International Society of Environmental Ergonomics
International Conference on Environmental Enrichment organized by the volunteer organization Shape of Enrichment, Inc.
Fourth International Conference on Environmental Education
Companies and other organizations
The Icee Company - The Icee Company (previously Western Icee and Icee USA) is an American beverage company located in La Vergne, Tennessee, United States.
The Innovation Cluster for Entrepreneurship Education of the Erasmus+ Programme
The Institute for Community and Economic Engagement at the University of North Carolina at Greensboro
The International Committee for Exhibitions and Exchanges of the International Council of Museums
Other uses
The Innovation, Collaboration and Exchange Environment of the Defence Research and Development Canada government agency
Instrument Concepts for Europa Exploration of the Europa Multiple-Flyby Mission (also known as the Europa Clipper)
Ice-E, a character originating in the video game Undertale, and re
|
https://en.wikipedia.org/wiki/Karl%20Schroeder
|
Karl Schroeder () (born September 4, 1962) is a Canadian science fiction author and a professional futurist. His novels present far-future speculations on topics such as nanotechnology, terraforming, augmented reality, and interstellar travel, and are deeply philosophical. More recently he also focuses on near-future topics. Several of his short stories feature the character Gennady Malianov.
Biography
Schroeder was born in a Mennonite family in Brandon, Manitoba. In 1986 he moved to Toronto, where he now lives with his wife Janice Beitel and daughter. After publishing a dozen short stories, Schroeder published his first novel, Ventus, in 2000. A prequel to Ventus, Lady of Mazes, was published in 2005. He has published seven more novels and is co-author (with Cory Doctorow) of the self-help book The Complete Idiot's Guide to Publishing Science Fiction. Schroeder currently writes, consults in the area of futures studies.
In October, 2011, Karl Schroeder was awarded a Master of Design degree in Strategic Foresight and Innovation from OCAD University in Toronto, Ontario, Canada.
Awards
1982. Pierian Spring Best Story award for The Great Worm.
1989. Context '89 fiction contest winner for The Cold Convergence.
1993. Prix Aurora Award for Best Short Work in English for The Toy Mill.
2001. New York Times Notable book for Ventus.
2003. Prix Aurora Award for best Canadian SF novel for Permanence.
2006/2007: Sun of Suns: Kirkus Best Book of 2006, 2007 Aurora finalist, 2007
|
https://en.wikipedia.org/wiki/Norman%20Levinson
|
Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing. He worked closely with Norbert Wiener in his early career. He joined the faculty of the Massachusetts Institute of Technology in 1937. In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society and in 1971 the Chauvenet Prize (after winning in 1970 the Lester R. Ford Award) of the Mathematical Association of America for his paper A Motivated Account of an Elementary Proof of the Prime Number Theorem. In 1974 he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey.
He received both his bachelor's degree and his master's degree in electrical engineering from MIT in 1934, where he had studied under Norbert Wiener and took almost all of the graduate-level courses in mathematics. He received the MIT Redfield Proctor Traveling Fellowship to study at the University of Cambridge, with the assurance that MIT would reward him with a PhD upon his return regardless of whatever he produced at Cambridge. Within the first four months in Cambridge, he had already produced two papers. In 1935, MIT awarded him with the PhD in mathematics.
His death in 1975 was caused by a
|
https://en.wikipedia.org/wiki/Jacob%20Millman
|
Jacob Millman (1911 in Novohrad-Volynskyi, Russian Empire – May 22, 1991 in Longboat Key, Florida) was a professor of electrical engineering at Columbia University. He immigrated to the United States in 1913 with his mother, Gertrude (Nachshen) Millman and sister Rebecca.
Millman received a PhD from MIT in 1935. He joined Columbia University in 1951, and retired in 1975. From 1941 to 1987, Millman wrote eight textbooks on electronics, and he helped develop radar systems. Millman's theorem (otherwise known as the parallel generator theorem) is named after him. He received in 1970 the IEEE Education Medal.
Millman died of pneumonia at his home in Longboat Key, Florida in 1991.
References
External links
NY Times Obituary
1911 births
1991 deaths
People from Zviahel
People from Novograd-Volynsky Uyezd
People from Longboat Key, Florida
Emigrants from the Russian Empire to the United States
Massachusetts Institute of Technology alumni
Columbia University faculty
Columbia School of Engineering and Applied Science faculty
|
https://en.wikipedia.org/wiki/Biorthogonal%20system
|
In mathematics, a biorthogonal system is a pair of indexed families of vectors
such that
where and form a pair of topological vector spaces that are in duality, is a bilinear mapping and is the Kronecker delta.
An example is the pair of sets of respectively left and right eigenvectors of a matrix, indexed by eigenvalue, if the eigenvalues are distinct.
A biorthogonal system in which and is an orthonormal system.
Projection
Related to a biorthogonal system is the projection
where its image is the linear span of and the kernel is
Construction
Given a possibly non-orthogonal set of vectors and the projection related is
where is the matrix with entries
and then is a biorthogonal system.
See also
References
Jean Dieudonné, On biorthogonal systems Michigan Math. J. 2 (1953), no. 1, 7–20
Topological vector spaces
|
https://en.wikipedia.org/wiki/Genetic%20genealogy
|
Genetic genealogy is the use of genealogical DNA tests, i.e., DNA profiling and DNA testing, in combination with traditional genealogical methods, to infer genetic relationships between individuals. This application of genetics came to be used by family historians in the 21st century, as DNA tests became affordable. The tests have been promoted by amateur groups, such as surname study groups or regional genealogical groups, as well as research projects such as the Genographic Project.
about 30 million people had been tested. As the field developed, the aims of practitioners broadened, with many seeking knowledge of their ancestry beyond the recent centuries, for which traditional pedigrees can be constructed.
History
The investigation of surnames in genetics can be said to go back to George Darwin, a son of Charles Darwin and Charles' first cousin Emma Darwin. In 1875, George Darwin used surnames to estimate the frequency of first-cousin marriages and calculated the expected incidence of marriage between people of the same surname (isonymy). He arrived at a figure of 1.5% for cousin-marriage in the population of London, higher (3%-3.5%) among the upper classes and lower (2.25%) among the general rural population.
Surname studies
A famous study in 1998 examined the lineage of descendants of Thomas Jefferson's paternal line and male lineage descendants of the freed slave Sally Hemings.
Bryan Sykes, a molecular biologist at Oxford University, tested the new methodology in
|
https://en.wikipedia.org/wiki/Software%20prototyping
|
Software prototyping is the activity of creating prototypes of software applications, i.e., incomplete versions of the software program being developed. It is an activity that can occur in software development and is comparable to prototyping as known from other fields, such as mechanical engineering or manufacturing.
A prototype typically simulates only a few aspects of, and may be completely different from, the final product.
Prototyping has several benefits: the software designer and implementer can get valuable feedback from the users early in the project. The client and the contractor can compare if the software made matches the software specification, according to which the software program is built. It also allows the software engineer some insight into the accuracy of initial project estimates and whether the deadlines and milestones proposed can be successfully met. The degree of completeness and the techniques used in prototyping have been in development and debate since its proposal in the early 1970s.
Overview
The purpose of a prototype is to allow users of the software to evaluate developers' proposals for the design of the eventual product by actually trying them out, rather than having to interpret and evaluate the design based on descriptions. Software prototyping provides an understanding of the software's functions and potential threats or issues. Prototyping can also be used by end users to describe and prove requirements that have not been considered,
|
https://en.wikipedia.org/wiki/DFT%20matrix
|
In applied mathematics, a DFT matrix is an expression of a discrete Fourier transform (DFT) as a transformation matrix, which can be applied to a signal through matrix multiplication.
Definition
An N-point DFT is expressed as the multiplication , where is the original input signal, is the N-by-N square DFT matrix, and is the DFT of the signal.
The transformation matrix can be defined as , or equivalently:
,
where is a primitive Nth root of unity in which . We can avoid writing large exponents for using the fact that for any exponent we have the identity This is the Vandermonde matrix for the roots of unity, up to the normalization factor. Note that the normalization factor in front of the sum ( ) and the sign of the exponent in ω are merely conventions, and differ in some treatments. All of the following discussion applies regardless of the convention, with at most minor adjustments. The only important thing is that the forward and inverse transforms have opposite-sign exponents, and that the product of their normalization factors be 1/N. However, the choice here makes the resulting DFT matrix unitary, which is convenient in many circumstances.
Fast Fourier transform algorithms utilize the symmetries of the matrix to reduce the time of multiplying a vector by this matrix, from the usual . Similar techniques can be applied for multiplications by matrices such as Hadamard matrix and the Walsh matrix.
Examples
Two-point
The two-point DFT is a simple case, in w
|
https://en.wikipedia.org/wiki/Generative%20topographic%20map
|
Generative topographic map (GTM) is a machine learning method that is a probabilistic counterpart of the self-organizing map (SOM), is probably convergent and does not require a shrinking neighborhood or a decreasing step size. It is a generative model: the data is assumed to arise by first probabilistically picking a point in a low-dimensional space, mapping the point to the observed high-dimensional input space (via a smooth function), then adding noise in that space. The parameters of the low-dimensional probability distribution, the smooth map and the noise are all learned from the training data using the expectation-maximization (EM) algorithm. GTM was introduced in 1996 in a paper by Christopher Bishop, Markus Svensen, and Christopher K. I. Williams.
Details of the algorithm
The approach is strongly related to density networks which use importance sampling and a multi-layer perceptron to form a non-linear latent variable model. In the GTM the latent space is a discrete grid of points which is assumed to be non-linearly projected into data space. A Gaussian noise assumption is then made in data space so that the model becomes a constrained mixture of Gaussians. Then the model's likelihood can be maximized by EM.
In theory, an arbitrary nonlinear parametric deformation could be used. The optimal parameters could be found by gradient descent, etc.
The suggested approach to the nonlinear mapping is to use a radial basis function network (RBF) to create a nonlinear map
|
https://en.wikipedia.org/wiki/Targeting
|
Targeting may refer to:
Biology
Gene targeting
Protein targeting
Marketing
Behavioral targeting
Targeted advertising
Target market
Geotargeting, in internet marketing
Other uses
Targeting (gridiron football), a penalty
Targeting (politics), to determine where to spend the resources of time, money, manpower and attention when campaigning for election
Targeting (video games), a controversial strategy in online gaming where a player continuously attacks the same opponent
Targeting (warfare), to select objects or installations to be attacked, taken, or destroyed
Targeting pod, in warfare
Targeting tower, a radio frequency antenna
Geographic targeting
Inflation targeting, in economics
See also
Goal (disambiguation)
Target (disambiguation)
|
https://en.wikipedia.org/wiki/Igor%20Shafarevich
|
Igor Rostislavovich Shafarevich (; 3 June 1923 – 19 February 2017) was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry. Outside mathematics, he wrote books and articles that criticised socialism and other books which were described as anti-semitic.
Mathematics
From his early years, Shafarevich made fundamental contributions to several parts of mathematics
including algebraic number theory, algebraic geometry and arithmetic algebraic geometry. In particular, in algebraic number theory, the Shafarevich–Weil theorem extends the commutative reciprocity map to the case of Galois groups, which are central extensions of abelian groups by finite groups.
Shafarevich was the first mathematician to give a completely self-contained formula for the Hilbert pairing, thus initiating an important branch of the study of explicit formulas in number theory. Another famous (and slightly incomplete) result is Shafarevich's theorem on solvable Galois groups, giving the realization of every finite solvable group as a Galois group over the rationals.
Another development is the Golod–Shafarevich theorem on towers of unramified extensions of number fields.
Shafarevich and his school greatly contributed to the study of algebraic geometry of surfaces. He started a famous Moscow seminar on classification of algebraic surfaces that updated the treatment of birational geometry around 1960 and was largely responsible for the early introduction of the
|
https://en.wikipedia.org/wiki/David%20Crane%20%28programmer%29
|
David Patrick Crane (born 1953 in Nappanee, Indiana, United States) is an American video game designer and programmer.
Crane originally worked in the field of hardware design for National Semiconductor. He went to college at DeVry Institute of Technology in Phoenix, Arizona and graduated with a Bachelor of Science in Electrical Engineering Technology degree in 1975. Crane started his programming career at Atari, making games for the Atari 2600. He also worked on the operating system for the Atari 800 computer. After meeting co-worker Alan Miller in a tennis game, Miller told Crane about a plan he had to leave Atari and found a company that would give game designers more recognition. From this meeting, Crane left Atari in 1979 and co-founded Activision, along with Miller, Jim Levy, Bob Whitehead, and Larry Kaplan. His games won many awards while he was at Activision. At Activision, he was best known as the designer of Pitfall!. Pitfall! was a huge hit; it maintained the top slot on the Billboard charts for 64 weeks and was named video game of the year in 1982. Over four million copies of the game were sold in the 1980s. It was the second best-selling game for the Atari 2600 after Pac-Man.
Crane said that he left because the newly appointed CEO of Activision, Bruce Davis, offered a pay cut with the promise of a vaguely worded incentive program. He then spent a year working at Hasbro, then joining the design staff of Absolute Entertainment. Although Absolute was based in New
|
https://en.wikipedia.org/wiki/Negative%20frequency
|
In mathematics, signed frequency (negative and positive frequency) expands upon the concept of frequency, from just an absolute value representing how often some repeating event occurs, to also have a positive or negative sign representing one of two opposing orientations for occurrences of those events. The following examples help illustrate the concept:
For a rotating object, the absolute value of its frequency of rotation indicates how many rotations the object completes per unit of time, while the sign could indicate whether it is rotating clockwise or counterclockwise.
Mathematically speaking, the vector has a positive frequency of +1 radian per unit of time and rotates counterclockwise around the unit circle, while the vector has a negative frequency of -1 radian per unit of time, which rotates clockwise instead.
For a harmonic oscillator such as a pendulum, the absolute value of its frequency indicates how many times it swings back and forth per unit of time, while the sign could indicate in which of the two opposite directions it started moving.
For a periodic function represented in a Cartesian coordinate system, the absolute value of its frequency indicates how often in its domain it repeats its values, while changing the sign of its frequency could represent a reflection around its y-axis.
Sinusoids
Let be a nonnegative angular frequency with units of radians per unit of time and let be a phase in radians. A function has slope When used as the argument o
|
https://en.wikipedia.org/wiki/List%20of%20organic%20reactions
|
Well-known reactions and reagents in organic chemistry include
0-9
1,2-Wittig rearrangement
1,3-Dipolar cycloaddition
2,3-Wittig rearrangement
A
Abramovitch–Shapiro tryptamine synthesis
Acetalisation
Acetoacetic ester condensation
Achmatowicz reaction
Acylation
Acyloin condensation
Adams' catalyst
Adams decarboxylation
Adkins catalyst
Adkins–Peterson reaction
Akabori amino acid reaction
Alcohol oxidation
Alder ene reaction
Alder–Stein rules
Aldol addition
Aldol condensation
Algar–Flynn–Oyamada reaction
Alkylimino-de-oxo-bisubstitution
Alkyne trimerisation
Alkyne zipper reaction
Allan–Robinson reaction
Allylic rearrangement
Amadori rearrangement
Amine alkylation
Angeli–Rimini reaction
Andrussov oxidation
Appel reaction
Arbuzov reaction, Arbusow reaction
Arens–Van Dorp synthesis, Isler modification
Aromatic nitration
Arndt–Eistert synthesis
Aston–Greenburg rearrangement
Auwers synthesis
Aza-Cope rearrangement
Azo coupling
B
Baeyer–Drewson indigo synthesis
Baeyer–Villiger oxidation, Baeyer–Villiger rearrangement
Bakeland process (Bakelite)
Baker–Venkataraman rearrangement, Baker–Venkataraman transformation
Baldwin's rules
Bally–Scholl synthesis
Balz–Schiemann reaction
Bamberger rearrangement
Bamberger triazine synthesis
Bamford–Stevens reaction
Barbier reaction
Barbier–Wieland degradation
Bardhan–Sengupta phenanthrene synthesis
Barfoed's test
Bargellini reaction
Bartoli indole synthesis, Bartoli reaction
Barton decarboxylation
Barton reaction
Barton–Kellogg reaction
Barton–
|
https://en.wikipedia.org/wiki/Scorer%27s%20function
|
In mathematics, the Scorer's functions are special functions studied by and denoted Gi(x) and Hi(x).
Hi(x) and -Gi(x) solve the equation
and are given by
The Scorer's functions can also be defined in terms of Airy functions:
References
Special functions
|
https://en.wikipedia.org/wiki/Approximation%20theory
|
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. What is meant by best and simpler will depend on the application.
A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon summation of a series of terms based upon orthogonal polynomials.
One problem of particular interest is that of approximating a function in a computer mathematical library, using operations that can be performed on the computer or calculator (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with polynomial or rational (ratio of polynomials) approximations.
The objective is to make the approximation as close as possible to the actual function, typically with an accuracy close to that of the underlying computer's floating point arithmetic. This is accomplished by using a polynomial of high degree, and/or narrowing the domain over which the polynomial has to approximate the function.
Narrowing the domain can often be done through the use of various addition or scaling formulas for the function being approximated. Modern mathematical libraries often reduce the domain into many tiny segments and use a low-degree polynomial for each segment.
Optimal polynomials
Once the domain (typically an interval) and degree of the polynomial a
|
https://en.wikipedia.org/wiki/Lattice%20field%20theory
|
In physics, lattice field theory is the study of lattice models of quantum field theory, that is, of field theory on a space or spacetime that has been discretised onto a lattice.
Details
Although most lattice field theories are not exactly solvable, they are of tremendous appeal because they can be studied by simulation on a computer, often using Markov chain Monte Carlo methods. One hopes that, by performing simulations on larger and larger lattices, while making the lattice spacing smaller and smaller, one will be able to recover the behavior of the continuum theory as the continuum limit is approached.
Just as in all lattice models, numerical simulation gives access to field configurations that are not accessible to perturbation theory, such as solitons. Likewise, non-trivial vacuum states can be discovered and probed.
The method is particularly appealing for the quantization of a gauge theory through the Wilson action. Most quantization methods keep Poincaré invariance manifest but sacrifice manifest gauge symmetry by requiring gauge fixing. Only after renormalization can gauge invariance be recovered. Lattice field theory differs from these in that it keeps manifest gauge invariance, but sacrifices manifest Poincaré invariance—recovering it only after renormalization. The articles on lattice gauge theory and lattice QCD explore these issues in greater detail.
Further reading
Creutz, M., Quarks, gluons and lattices, Cambridge University Press, Cambridge, (1985).
|
https://en.wikipedia.org/wiki/Willem%20%27s%20Gravesande
|
Willem Jacob 's Gravesande (26 September 1688 – 28 February 1742) was a Dutch mathematician and natural philosopher, chiefly remembered for developing experimental demonstrations of the laws of classical mechanics and the first experimental measurement of kinetic energy. As professor of mathematics, astronomy, and philosophy at Leiden University, he helped to propagate Isaac Newton's ideas in Continental Europe.
Life
Born in 's-Hertogenbosch, 's Gravesande studied law at Leiden University, where he defended a thesis on suicide and earned a doctorate in 1707. He then practised law in The Hague while also participating in intellectual discussions and cultivating his interest in the mathematical sciences. His Essai de perspective ("Essay on Perspective"), published in 1711, was praised by the influential Swiss mathematician Johann Bernoulli. In The Hague, 's Gravesande also helped to establish the Journal littéraire ("Literary journal"), a learned periodical first published in 1713.
In 1715, 's Gravesande visited London as part of a Dutch delegation sent to welcome the Hanoverian succession in Great Britain. In London, 's Gravesande met both King George I and Isaac Newton, and was elected a Fellow of the Royal Society. In 1717 he became professor of mathematics and astronomy in Leiden. From that position, he was instrumental in introducing Newton's work to the Netherlands. He also obtained the chairs of civil and military architecture in 1730 and philosophy in 1734. As
|
https://en.wikipedia.org/wiki/Stanley%27s%20reciprocity%20theorem
|
In combinatorial mathematics, Stanley's reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any rational cone (defined below) and the generating function of the cone's interior.
Definitions
A rational cone is the set of all d-tuples
(a1, ..., ad)
of nonnegative integers satisfying a system of inequalities
where M is a matrix of integers. A d-tuple satisfying the corresponding strict inequalities, i.e., with ">" rather than "≥", is in the interior of the cone.
The generating function of such a cone is
The generating function Fint(x1, ..., xd) of the interior of the cone is defined in the same way, but one sums over d-tuples in the interior rather than in the whole cone.
It can be shown that these are rational functions.
Formulation
Stanley's reciprocity theorem states that for a rational cone as above, we have
Matthias Beck and Mike Develin have shown how to prove this by using the calculus of residues. Develin has said that this amounts to proving the result "without doing any work".
Stanley's reciprocity theorem generalizes Ehrhart-Macdonald reciprocity for Ehrhart polynomials of rational convex polytopes.
See also
Ehrhart polynomial
References
Algebraic combinatorics
Theorems in combinatorics
|
https://en.wikipedia.org/wiki/Sex%20%28disambiguation%29
|
Sex is the biological distinction of an organism between male and female.
Sex or SEX may also refer to:
Biology and behaviour
Animal sexual behaviour
Copulation (zoology)
Group sex
Human female sexuality
Human male sexuality
Human sexual activity
Non-penetrative sex, or sexual outercourse
Sex drive, a person's overall sexual drive or desire for sexual activity
Sexual intercourse, also called copulation or coitus
Transgender sexuality
Gender, the distinction between male and female or masculinity and femininity within an individual's gender identity
Sex–gender distinction
Human sexuality
Mating types, a distinction of gametes, whether in anisogamous or isogamous species
Sexing, the act of discerning the sex of an animal
Sexual reproduction, a process of combining and mixing genetic traits, associated with the generation of new individuals, by means of meiosis and fertilization
Genetic recombination, the process of mixing genetic traits solely, occurring both in organisms with sexual or asexual reproduction
Art and entertainment
Film and television
Sex (film), a 1920 film by Fred Niblo
Sex: The Annabel Chong Story, a 1999 documentary film
"Sex" (Kath & Kim episode)
Sex (TV series), an Australian television series
Literature
Sex (book), a 1992 book by Madonna and Steven Meisel
Sex (play), a 1926 play by Mae West
Music
SEX, pseudonym of American rapper Young Thug
Albums
Sex (Elli Kokkinou album), 2005
Sex (The Necks album), 1989
Sex (The 1975 EP), 2012
Sex (Tila Tequila EP
|
https://en.wikipedia.org/wiki/Basal
|
Basal or basilar is a term meaning base, bottom, or minimum.
Science
Basal (anatomy), an anatomical term of location for features associated with the base of an organism or structure
Basal (medicine), a minimal level that is necessary for health or life, such as a minimum insulin dose
Basal (phylogenetics), a relative position in a phylogenetic tree closer to the root
Places
Basal, Hungary, a village in Hungary
Basal, Pakistan, a village in the Attock District
Other
Basal plate (disambiguation)
Basal sliding, the act of a glacier sliding over the bed before it due to meltwater increasing the water pressure underneath the glacier causing it to be lifted from its bed
Basal conglomerate, see conglomerate (geology)
See also
Basel (disambiguation)
Basil (disambiguation)
|
https://en.wikipedia.org/wiki/Wannier%20function
|
The Wannier functions are a complete set of orthogonal functions used in solid-state physics. They were introduced by Gregory Wannier in 1937. Wannier functions are the localized molecular orbitals of crystalline systems.
The Wannier functions for different lattice sites in a crystal are orthogonal, allowing a convenient basis for the expansion of electron states in certain regimes. Wannier functions have found widespread use, for example, in the analysis of binding forces acting on electrons.
Definition
Although, like localized molecular orbitals, Wannier functions can be chosen in many different ways, the original, simplest, and most common definition in solid-state physics is as follows. Choose a single band in a perfect crystal, and denote its Bloch states by
where uk(r) has the same periodicity as the crystal. Then the Wannier functions are defined by
,
where
R is any lattice vector (i.e., there is one Wannier function for each Bravais lattice vector);
N is the number of primitive cells in the crystal;
The sum on k includes all the values of k in the Brillouin zone (or any other primitive cell of the reciprocal lattice) that are consistent with periodic boundary conditions on the crystal. This includes N different values of k, spread out uniformly through the Brillouin zone. Since N is usually very large, the sum can be written as an integral according to the replacement rule:
where "BZ" denotes the Brillouin zone, which has volume Ω.
Properties
On the basis
|
https://en.wikipedia.org/wiki/Everything%20Sucks%20%28Descendents%20album%29
|
Everything Sucks is the fifth studio album by American punk rock band the Descendents, released on September 24, 1996, through Epitaph Records. It was their first album of new studio material since 1987's All, after which singer Milo Aukerman had left the band to pursue a career in biochemistry. The remaining members (bassist Karl Alvarez, guitarist Stephen Egerton, and drummer Bill Stevenson) had changed the band's name to All and released eight albums between 1988 and 1995 with singers Dave Smalley, Scott Reynolds, and Chad Price. When Aukerman decided to return to music the group chose to operate as two acts simultaneously, playing with Aukerman as the Descendents and with Price as All. It is considered a return to the band's angrier hardcore punk such as the Fat EP and Milo Goes to College.
Everything Sucks was the first Descendents release to chart, reaching #132 on the Billboard 200 and #4 on Top Heatseekers, supported by the singles "I'm the One" and "When I Get Old". Aukerman returned to his biochemistry career following the album's supporting tours, reuniting with them again in 2004 for Cool to Be You, and again in 2010 for live performances.
Background
The Descendents formed in 1978 in Manhattan Beach, California, with an initial recording lineup of Tony Lombardo (bass guitar), Frank Navetta (guitar), and Bill Stevenson (drums). Adding singer Milo Aukerman in 1980, the band released three albums over the next six years, weathering several lineup changes (Navetta
|
https://en.wikipedia.org/wiki/William%20Ernest%20Hocking
|
William Ernest Hocking (August 10, 1873 – June 12, 1966) was an American idealist philosopher at Harvard University. He continued the work of his philosophical teacher Josiah Royce (the founder of American idealism) in revising idealism to integrate and fit into empiricism, naturalism and pragmatism. He said that metaphysics has to make inductions from experience: "That which does not work is not true." His major field of study was the philosophy of religion, but his 22 books included discussions of philosophy and human rights, world politics, freedom of the press, the philosophical psychology of human nature; education; and more. In 1958 he served as president of the Metaphysical Society of America. He led a highly influential study of missions in mainline Protestant churches in 1932. His "Laymen's Inquiry" recommended a greater emphasis on education and social welfare, transfer of power to local groups, less reliance on evangelizing and conversion, and a much more respectful appreciation for local religions.
Early life and education
William Ernest Hocking was born in 1873 to William Hocking (1839–1903) and Julia Pratt (1848–1936) in Cleveland, Ohio. He was of Cornish American heritage. He attended public schools through high school. He worked first as a mapmaker, illustrator and printer's devil, before entering Iowa State College of Agriculture and Mechanical Arts in 1894, where he intended to be an engineer. Reading William James' work The Principles of Psychology made
|
https://en.wikipedia.org/wiki/Hough%20function
|
In applied mathematics, the Hough functions are the eigenfunctions of Laplace's tidal equations which govern fluid motion on a rotating sphere. As such, they are relevant in geophysics and meteorology where they form part of the solutions for atmospheric and ocean waves. These functions are named in honour of Sydney Samuel Hough.
Each Hough mode is a function of latitude and may be expressed as an infinite sum of associated Legendre polynomials; the functions are orthogonal over the sphere in the continuous case. Thus they can also be thought of as a generalized Fourier series in which the basis functions are the normal modes of an atmosphere at rest.
See also
Secondary circulation
Legendre polynomials
Primitive equations
References
Further reading
Atmospheric dynamics
Physical oceanography
Fluid mechanics
Special functions
|
https://en.wikipedia.org/wiki/Bourgeois%20pseudoscience
|
Bourgeois pseudoscience () was a term of condemnation in the Soviet Union for certain scientific disciplines that were deemed unacceptable from an ideological point of view due to their incompatibility with Marxism–Leninism. For example, genetics was not acceptable due to the role of random mutations of an individual organism in evolution, which was perceived as incompatible with the "universal laws of history" that applied to masses universally, as postulated by the Marxist ideology. At various times pronounced "bourgeois pseudosciences" were: genetics, cybernetics, quantum physics, theory of relativity, sociology and particular directions in comparative linguistics (Japhetic theory). This attitude was most prevalent during the rule of Joseph Stalin.
Notably, the term was not used by Stalin himself, who rejected the notion that science can have a class nature. Stalin removed all mention of “bourgeois biology” from Trofim Lysenko’s report, The State of Biology in the Soviet Union, and in the margin next to the statement that “any science is based on class” Stalin wrote, “Ha-ha-ha!! And what about mathematics? Or Darwinism?” The term was mostly used by Stalinist philosophers, such as Mark Moisevich Rosenthal and Pavel Yudin, who use it in the 1951 and 1954 editions of their Short Philosophical Dictionary: "Eugenics is a bourgeois pseudoscience", "Weismannism-Morganism - bourgeois pseudoscience, designed to justify capitalism".
Psychology was declared "bourgeois pseudoscience
|
https://en.wikipedia.org/wiki/R.%20A.%20McConnell
|
Robert A. McConnell (1914—2006) was an American physicist and parapsychologist.
McConnell was born in Pennsylvania in 1914, and studied at Carnegie Institute of Technology obtaining a B.S. in physics in 1935 and a Ph.D. from the University of Pittsburgh in 1947. He worked as a physicist at a U.S. Naval aircraft factory and at the Massachusetts Institute of Technology Radiation Laboratory. He also worked in radar moving target indication, iconoscope, and ultrasonic microwaves.
He earned a Doctor of Philosophy degree in engineering physics. McConnell was the first president of the Parapsychological Association and a Fellow of the American Psychological Society. He was Research Professor Emeritus of Biological Sciences at the University of Pittsburgh.
Selected works
Encounters with Parapsychology (1982, )
Parapsychology and Self-Deception in Science (1983, )
An Introduction to Parapsychology in the Context of Science (1983, )
Parapsychology in Retrospect (1987, )
Far Out in the New Age: The Subversion of Science by Cultural Communism (1995, )
Joyride To Infinity: A Scientific Study of the Doomsday Literature (2000, )
God.org Are You There?: On the Deeper Meaning of ESP (2001, )
Can We Win This War?: ISLAM (2002, )
References
External links
Robert A. McConnell, from the Parapsychological Association site
Home page of R. A. McConnell
1914 births
2006 deaths
20th-century American physicists
American parapsychologists
Radar pioneers
University of Pittsburgh faculty
Carnegie
|
https://en.wikipedia.org/wiki/Spearfish
|
Spearfish may refer to:
Places
Spearfish, South Dakota, United States
North Spearfish, South Dakota, United States
Spearfish Formation, a geologic formation in the United States
Biology
Tetrapturus, a genus of marlin with shorter rostrum (a.k.a. snout or bill) and stunted sail behind the dorsal fin
Longbill spearfish, native to the Atlantic Ocean
Mediterranean spearfish, native to the Mediterranean Sea
Shortbill spearfish, native to the Indo-Pacific
Roundscale spearfish, native to the Eastern Atlantic to the western Mediterranean
Spearfish remora, a species of remora found around the world in tropical and subtropical seas
Spearfish Fisheries Center, one of 70 fish hatcheries as part of the National Fish Hatchery System of the U.S. Fish and Wildlife Service
Military
Spearfish torpedo, or simply Spearfish, is a modern torpedo built by GEC-Marconi
Fairey Spearfish, a prototype dive bomber of the immediate post World War II period
HMS Spearfish (69S), a 1936 British S-class submarine lost in World War II
USS Spearfish (SS-190), a US submarine in World War II
|
https://en.wikipedia.org/wiki/Karl%20Ernst%20Krafft
|
Karl Ernst Krafft (10 May 1900 – 8 January 1945) was a Swiss astrologer, born in Basel. He worked on the fields of astrology and graphology.
Astrology career
After studying in the University of Basel and Geneva, he graduated with a degree in mathematics. For the best part of ten years he worked on a massive book entitled Traits of Astro-Biology. This expounded his own theory of "Typocosmy": the prediction of the future based on the study of an individual's personality, or type. Krafft opened an office in Zürich, where he provided horoscopes and investment advice. Krafft's business collapsed, as did and his own investments (which were decided via divination).
By the early 1930s, when Adolf Hitler had come to power, Krafft enjoyed a unique status among occultists and prophets in Germany. The National Socialists, later to become his patrons, at first posed a threat to him. Occultists, like Freemasons, were among those harassed and vilified by most National Socialists. While the Nazi state persecuted astrologers, Rudolf Hess and Heinrich Himmler consulted them. Krafft moved to Germany at the invitation of the Nazis and was endorsed by the Ministry of Propaganda. Kraff subsequently joined the Nazi Party and introduced anti-Semitic ideas into his work. Krafft moved into the orbit of the National Socialist elite in November 1939 when he made a remarkable prediction. He predicted that the Führer's life would be in danger between 7 and 10 November. He wrote, on 2 November to a frien
|
https://en.wikipedia.org/wiki/De%20Morgan%20Medal
|
The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society. The Society's most prestigious award, it is given in memory of Augustus De Morgan, who was the first President of the society.
The medal is awarded every third year (in years divisible by 3) to a mathematician who is normally resident in the United Kingdom on 1 January of the relevant year. The only grounds for the award of the medal are the candidate's contributions to mathematics.
In 1968, Mary Cartwright became the first woman to receive the award.
De Morgan Medal winners
Recipients of the De Morgan Medal include the following:
See also
Whitehead Prize
Fröhlich Prize
Senior Whitehead Prize
Berwick Prize
Naylor Prize and Lectureship
Pólya Prize (LMS)
List of mathematics awards
References
British science and technology awards
Awards established in 1884
Triennial events
Awards of the London Mathematical Society
1884 establishments in the United Kingdom
|
https://en.wikipedia.org/wiki/Logistic
|
Logistic may refer to:
Mathematics
Logistic function, a sigmoid function used in many fields
Logistic map, a recurrence relation that sometimes exhibits chaos
Logistic regression, a statistical model using the logistic function
Logit, the inverse of the logistic function
Logistic distribution, the derivative of the logistic function, a continuous probability distribution, used in probability theory and statistics
Mathematical logic, subfield of mathematics exploring the applications of formal logic to mathematics
Other uses
Logistics, the management of resources and their distributions
Logistic engineering, the scientific study of logistics
Military logistics, the study of logistics at the service of military units and operations
See also
Logic (disambiguation)
|
https://en.wikipedia.org/wiki/Dominance%20hierarchy
|
In biology, a dominance hierarchy (formerly and colloquially called a pecking order) is a type of social hierarchy that arises when members of animal social groups interact, creating a ranking system. A dominant higher-ranking individual is sometimes called an alpha, and a submissive lower-ranking individual is called a beta. Different types of interactions can result in dominance depending on the species, including ritualized displays of aggression or direct physical violence. In social living groups, members are likely to compete for access to limited resources and mating opportunities. Rather than fighting each time they meet, individuals of the same sex establish a relative rank, with higher-ranking individuals often gaining more access to resources and mates. Based on repetitive interactions, a social order is created that is subject to change each time a dominant animal is challenged by a subordinate one.
Definitions
Dominance is an individual's preferential access to resources over another based on coercive capacity based on strength, threat, and intimidation, compared to prestige (persuasive capacity based on skills, abilities, and knowledge). A dominant animal is one whose sexual, feeding, aggressive, and other behaviour patterns subsequently occur with relatively little influence from other group members. Subordinate animals are opposite; their behaviour is submissive, and can be relatively easily influenced or inhibited by other group members.
Dominance
For
|
https://en.wikipedia.org/wiki/Conserved%20current
|
In physics a conserved current is a current, , that satisfies the continuity equation . The continuity equation represents a conservation law, hence the name.
Indeed, integrating the continuity equation over a volume , large enough to have no net currents through its surface, leads to the conservation law
where is the conserved quantity.
In gauge theories the gauge fields couple to conserved currents. For example, the electromagnetic field couples to the conserved electric current.
Conserved quantities and symmetries
Conserved current is the flow of the canonical conjugate of a quantity possessing a continuous translational symmetry. The continuity equation for the conserved current is a statement of a conservation law.
Examples of canonical conjugate quantities are:
Time and energy - the continuous translational symmetry of time implies the conservation of energy
Space and momentum - the continuous translational symmetry of space implies the conservation of momentum
Space and angular momentum - the continuous rotational symmetry of space implies the conservation of angular momentum
Wave function phase and electric charge - the continuous phase angle symmetry of the wave function implies the conservation of electric charge
Conserved currents play an extremely important role in theoretical physics, because Noether's theorem connects the existence of a conserved current to the existence of a symmetry of some quantity in the system under study. In practical terms, all con
|
https://en.wikipedia.org/wiki/Compartmentalization
|
Compartmentalization or compartmentalisation may refer to:
Compartmentalization (biology)
Compartmentalization (engineering)
Compartmentalization (fire protection)
Compartmentalization (information security)
Compartmentalization (psychology)
Compartmentalization of decay in trees
|
https://en.wikipedia.org/wiki/Relict
|
A relict is a surviving remnant of a natural phenomenon.
Biology
A relict (or relic) is an organism that at an earlier time was abundant in a large area but now occurs at only one or a few small areas.
Geology and geomorphology
In geology, a relict is a structure or mineral from a parent rock that did not undergo metamorphosis when the surrounding rock did, or a rock that survived a destructive geologic process.
In geomorphology, a relict landform is a landform formed by either erosive or constructive surficial processes that are no longer active as they were in the past.
A glacial relict is a cold-adapted organism that is a remnant of a larger distribution that existed in the ice ages.
Human populations
As revealed by DNA testing, a relict population is an ancient people in an area, who have been largely supplanted by a later group of migrants and their descendants.
In various places around the world, minority ethnic groups represent lineages of ancient human migrations in places now occupied by more populous ethnic groups, whose ancestors arrived later. For example, the first human groups to inhabit the Caribbean islands were hunter-gatherer tribes from South and Central America. Genetic testing of natives of Cuba show that, in late pre-Columbian times, the island was home to agriculturalists of Taino ethnicity. In addition, a relict population of the original hunter-gatherers remained in western Cuba as the Ciboney people.
Other uses
In ecology, an ecosystem whi
|
https://en.wikipedia.org/wiki/Adams%20Prize
|
The Adams Prize is one of the most prestigious prizes awarded by the University of Cambridge. It is awarded each year by the Faculty of Mathematics at the University of Cambridge and St John's College to a UK-based mathematician for distinguished research in the Mathematical Sciences.
The prize is named after the mathematician John Couch Adams. It was endowed by members of St John's College and was approved by the senate of the university in 1848 to commemorate Adams' controversial role in the discovery of the planet Neptune. Originally open only to Cambridge graduates, the current stipulation is that the mathematician must reside in the UK and must be under forty years of age. Each year applications are invited from mathematicians who have worked in a specific area of mathematics. the Adams Prize is worth approximately £14,000. The prize is awarded in three parts. The first third is paid directly to the candidate; another third is paid to the candidate's institution to fund research expenses; and the final third is paid on publication of a survey paper in the winner's field in a major mathematics journal.
The prize has been awarded to many well known mathematicians, including
James Clerk Maxwell and Sir William Hodge. The first time it was awarded to a female mathematician was in 2002 when it was awarded to Susan Howson, then a lecturer at the University of Nottingham for her work on number theory and elliptic curves.
Subject area
2014–15: "Algebraic Geometry"
2015–16
|
https://en.wikipedia.org/wiki/List%20of%20mathematical%20societies
|
This article provides a list of mathematical societies.
International
African Mathematical Union
Association for Women in Mathematics
Circolo Matematico di Palermo
European Mathematical Society
European Women in Mathematics
Foundations of Computational Mathematics
International Association for Cryptologic Research
International Association of Mathematical Physics
International Linear Algebra Society
International Mathematical Union
International Statistical Institute
International Society for Analysis, its Applications and Computation
International Society for Mathematical Sciences
Kurt Gödel Society
Mathematical Council of the Americas (MCofA)
Mathematical Society of South Eastern Europe (MASSEE)
Mathematical Optimization Society
Maths Society
Ramanujan Mathematical Society
Quaternion Society
Society for Industrial and Applied Mathematics
Southeast Asian Mathematical Society (SEAMS)
Spectra (mathematical association)
Unión Matemática de América Latina y el Caribe (UMALCA)
Young Mathematicians Network
Honor societies
Kappa Mu Epsilon
Mu Alpha Theta
Pi Mu Epsilon
National and subnational
Arranged as follows: Society name in English (Society name in home-language; Abbreviation if used), Country and/or subregion/city if not specified in name.
This list is sorted by continent.
Africa
Algeria Mathematical Society
Gabon Mathematical Society
South African Mathematical Society
Asia
Bangladesh Mathematical Society
Calcutta Mathematical Soc
|
https://en.wikipedia.org/wiki/Methine%20group
|
In organic chemistry, a methine group or methine bridge is a trivalent functional group , derived formally from methane. It consists of a carbon atom bound by two single bonds and one double bond, where one of the single bonds is to a hydrogen. The group is also called methyne or methene, but its IUPAC systematic name is methylylidene or methanylylidene.
This group is sometimes called "methylidyne", however that name belongs properly to either the methylidyne group (connected to the rest of the molecule by a triple bond) or to the methylidyne radical (the two atoms as a free molecule with dangling bonds).
The name "methine" is also widely used in non-systematic nomenclature for the methanetriyl group (IUPAC): a carbon atom with four single bonds, where one bond is to a hydrogen atom ().
Overlapping methines
Two or more methine bridges can overlap, forming a chain or ring of carbon atoms connected by alternating single and double bonds, as in piperylene , or the compound
Every carbon atom in this molecule is a methine carbon atom, except for three; two that are attached to the two nitrogen atoms and not to any hydrogen atoms, and the carbon attached to the nitrogen atom, which is attached to two hydrogen atoms (far right). There is a five-carbon-atom poly-methine chain in the center of this molecule.
Chains of alternating single and double bonds often form conjugated systems. When closed, as in benzene , they often give aromatic character to the compound.
See also
|
https://en.wikipedia.org/wiki/Morphology%20%28biology%29
|
Morphology is a branch of biology dealing with the study of the form and structure of organisms and their specific structural features.
This includes aspects of the outward appearance (shape, structure, colour, pattern, size), i.e. external morphology (or eidonomy), as well as the form and structure of the internal parts like bones and organs, i.e. internal morphology (or anatomy). This is in contrast to physiology, which deals primarily with function. Morphology is a branch of life science dealing with the study of gross structure of an organism or taxon and its component parts.
History
The etymology of the word "morphology" is from the Ancient Greek (), meaning "form", and (), meaning "word, study, research".
While the concept of form in biology, opposed to function, dates back to Aristotle (see Aristotle's biology), the field of morphology was developed by Johann Wolfgang von Goethe (1790) and independently by the German anatomist and physiologist Karl Friedrich Burdach (1800).
Among other important theorists of morphology are Lorenz Oken, Georges Cuvier, Étienne Geoffroy Saint-Hilaire, Richard Owen, Karl Gegenbaur and Ernst Haeckel.
In 1830, Cuvier and E.G.Saint-Hilaire engaged in a famous debate, which is said to exemplify the two major deviations in biological thinking at the time – whether animal structure was due to function or evolution.
Divisions of morphology
Comparative morphology is analysis of the patterns of the locus of structures within the body pl
|
https://en.wikipedia.org/wiki/Salem%20Prize
|
The Salem Prize, in memory of Raphael Salem, is awarded each year to young researchers for outstanding contributions to the field of analysis. It is awarded by the School of Mathematics at the Institute for Advanced Study in Princeton and was founded by the widow of Raphael Salem in his memory. The prize is considered highly prestigious and many Fields Medalists previously received it. The prize was 5000 French Francs in 1990.
Past winners
(Note: a F symbol denotes mathematicians who later earned a Fields Medal).
See also
List of mathematics awards
References
Mathematics awards
|
https://en.wikipedia.org/wiki/Einselection
|
In quantum mechanics, einselections, short for "environment-induced superselection", is a name coined by Wojciech H. Zurek
for a process which is claimed to explain the appearance of wavefunction collapse and the emergence of classical descriptions of reality from quantum descriptions. In this approach, classicality is described as an emergent property induced in open quantum systems by their environments. Due to the interaction with the environment, the vast majority of states in the Hilbert space of a quantum open system become highly unstable due to entangling interaction with the environment, which in effect monitors selected observables of the system. After a decoherence time, which for macroscopic objects is typically many orders of magnitude shorter than any other dynamical timescale, a generic quantum state decays into an uncertain state which can be expressed as a mixture of simple pointer states. In this way the environment induces effective superselection rules. Thus, einselection precludes stable existence of pure superpositions of pointer states. These 'pointer states' are stable despite environmental interaction. The einselected states lack coherence, and therefore do not exhibit the quantum behaviours of entanglement and superposition.
Advocates of this approach argue that since only quasi-local, essentially classical states survive the decoherence process, einselection can in many ways explain the emergence of a (seemingly) classical reality in a fundamen
|
https://en.wikipedia.org/wiki/Branching%20fraction
|
In particle physics and nuclear physics, the branching fraction (or branching ratio) for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to either the radioactive decay of atoms or the decay of elementary particles. It is equal to the ratio of the partial decay constant to the overall decay constant. Sometimes a partial half-life is given, but this term is misleading; due to competing modes, it is not true that half of the particles will decay through a particular decay mode after its partial half-life. The partial half-life is merely an alternate way to specify the partial decay constant , the two being related through:
For example, for spontaneous decays of 132Cs, 98.1% are ε (electron capture) or β+ (positron) decays, and 1.9% are β− (electron) decays. The partial decay constants can be calculated from the branching fraction and the half-life of 132Cs (6.479 d), they are: 0.10 d−1 (ε + β+) and 0.0020 d−1 (β−). The partial half-lives are 6.60 d (ε + β+) and 341 d (β−). Here the problem with the term partial half-life is evident: after (341+6.60) days almost all the nuclei will have decayed, not only half as one may initially think.
Isotopes with significant branching of decay modes include copper-64, arsenic-74, rhodium-102, indium-112, iodine-126 and holmium-164.
References
External links
LBNL Isotopes Project
Particle Data Group (listings for particle physics)
Nuc
|
https://en.wikipedia.org/wiki/List%20of%20unsolved%20problems%20in%20computer%20science
|
This article is a list of notable unsolved problems in computer science. A problem in computer science is considered unsolved when no solution is known, or when experts in the field disagree about proposed solutions.
Computational complexity
P versus NP problem
What is the relationship between BQP and NP?
NC = P problem
NP = co-NP problem
P = BPP problem
P = PSPACE problem
L = NL problem
PH = PSPACE problem
L = P problem
L = RL problem
Unique games conjecture
Is the exponential time hypothesis true?
Is the strong exponential time hypothesis (SETH) true?
Do one-way functions exist?
Is public-key cryptography possible?
Log-rank conjecture
Polynomial versus nondeterministic-polynomial time for specific algorithmic problems
Can integer factorization be done in polynomial time on a classical (non-quantum) computer?
Can the discrete logarithm be computed in polynomial time on a classical (non-quantum) computer?
Can the shortest vector of a lattice be computed in polynomial time on a classical or quantum computer?
Can clustered planar drawings be found in polynomial time?
Can the graph isomorphism problem be solved in polynomial time?
Can leaf powers and -leaf powers be recognized in polynomial time?
Can parity games be solved in polynomial time?
Can the rotation distance between two binary trees be computed in polynomial time?
Can graphs of bounded clique-width be recognized in polynomial time?
Can one find a simple closed quasigeodesic on a convex pol
|
https://en.wikipedia.org/wiki/Eduard%20Vogel
|
Eduard Vogel (7 March 1829February 1856) was a German explorer in Central Africa.
Early career
Vogel was born in Krefeld. He studied mathematics, botany and astronomy at Leipzig and Berlin, studying with Encke at the latter institution. In 1851, he was engaged as assistant astronomer to director John Russel Hind at George Bishop's private observatory in London. That year August Heinrich Petermann introduced Vogel to the Royal Geographical Society.
Africa commission
In 1853 Petermann arranged for Vogel to be chosen by the British government to join the Richardson, Overweg and Barth expedition with supplies. That expedition had been sent to Africa in 1849 to find a trade route that bypassed the Arabs. Vogel was to be a replacement for Richardson who had died two years earlier and was tasked to make geographical and meteorological observations and to collect botanical specimens. In 1853, the expedition was in the western Sudan.
Vogel sailed from England on 20 February 1853. The day Vogel left London, news had arrived that Overweg had also died, leaving Barth on his own.
Meeting Barth
On 25 July, Vogel left Tripoli with a caravan to catch up with Barth. Vogel arrived at the end of the Trans-Saharan trade route, Kuka, the capital of Bornu on 13 January 1854. Vogel's specimens, and the fact that both expedition engineers were soldiers, made the king there suspicious of his intentions, and Vogel's movements were severely restricted.
Instead of waiting for Barth to return, on
|
https://en.wikipedia.org/wiki/Mentalism
|
Mentalism is a performing art in which its practitioners, known as mentalists, appear to demonstrate highly developed mental or intuitive abilities. Performances may appear to include hypnosis, telepathy, clairvoyance, divination, precognition, psychokinesis, mediumship, mind control, memory feats, deduction, and rapid mathematics. Mentalists perform a theatrical act that includes special effects that may appear to employ psychic or supernatural forces but that are actually achieved by "ordinary conjuring means", natural human abilities (i.e. reading body language, refined intuition, subliminal communication, emotional intelligence), and an in-depth understanding of key principles from human psychology or other behavioral sciences.
Mentalism is commonly classified as a subcategory of magic and, when performed by a stage magician, may also be referred to as mental magic. However, many professional mentalists today may generally distinguish themselves from magicians, insisting that their art form leverages a distinct skillset. Instead of doing "magic tricks", mentalists argue that they produce psychological experiences for the mind and imagination, and expand reality with explorations of psychology, suggestion, and influence. Mentalists are also often considered psychic entertainers, although that category also contains non-mentalist performers such as psychic readers and bizarrists.
Some well-known magicians, such as Penn & Teller, and James Randi, argue that a key different
|
https://en.wikipedia.org/wiki/Dynamic%20Monte%20Carlo%20method
|
In chemistry, dynamic Monte Carlo (DMC) is a Monte Carlo method for modeling the dynamic behaviors of molecules by comparing the rates of individual steps with random numbers. It is essentially the same as Kinetic Monte Carlo. Unlike the Metropolis Monte Carlo method, which has been employed to study systems at equilibrium, the DMC method is used to investigate non-equilibrium systems such as a reaction, diffusion, and so-forth (Meng and Weinberg 1994). This method is mainly applied to analyze adsorbates' behavior on surfaces.
There are several well-known methods for performing DMC simulations, including the First Reaction Method (FRM) and Random Selection Method (RSM). Although the FRM and RSM give the same results from a given model, the computer resources are different depending on the applied system.
In the FRM, the reaction whose time is minimum on the event list is advanced. In the event list, the tentative times for all possible reactions are stored. After the selection of one event, the system time is advanced to the reaction time, and the event list is recalculated. This method is efficient in computation time because the reaction always occurs in one event. On the other hand, it consumes a lot of computer memory because of the event list. Therefore, it is difficult to apply to large-scale systems.
The RSM decides whether the reaction of the selected molecule proceeds or not by comparing the transition probability with a random number. In this method, the reaction
|
https://en.wikipedia.org/wiki/Isometry%20group
|
In mathematics, the isometry group of a metric space is the set of all bijective isometries (that is, bijective, distance-preserving maps) from the metric space onto itself, with the function composition as group operation. Its identity element is the identity function. The elements of the isometry group are sometimes called motions of the space.
Every isometry group of a metric space is a subgroup of isometries. It represents in most cases a possible set of symmetries of objects/figures in the space, or functions defined on the space. See symmetry group.
A discrete isometry group is an isometry group such that for every point of the space the set of images of the point under the isometries is a discrete set.
In pseudo-Euclidean space the metric is replaced with an isotropic quadratic form; transformations preserving this form are sometimes called "isometries", and the collection of them is then said to form an isometry group of the pseudo-Euclidean space.
Examples
The isometry group of the subspace of a metric space consisting of the points of a scalene triangle is the trivial group. A similar space for an isosceles triangle is the cyclic group of order two, C2. A similar space for an equilateral triangle is D3, the dihedral group of order 6.
The isometry group of a two-dimensional sphere is the orthogonal group O(3).
The isometry group of the n-dimensional Euclidean space is the Euclidean group E(n).
The isometry group of the Poincaré disc model of the hyperbolic
|
https://en.wikipedia.org/wiki/Cyclic%20voltammetry
|
In electrochemistry, cyclic voltammetry (CV) is a type of potentiodynamic measurement. In a cyclic voltammetry experiment, the working electrode potential is ramped linearly versus time. Unlike in linear sweep voltammetry, after the set potential is reached in a CV experiment, the working electrode's potential is ramped in the opposite direction to return to the initial potential. These cycles of ramps in potential may be repeated as many times as needed. The current at the working electrode is plotted versus the applied voltage (that is, the working electrode's potential) to give the cyclic voltammogram trace. Cyclic voltammetry is generally used to study the electrochemical properties of an analyte in solution or of a molecule that is adsorbed onto the electrode.
Experimental method
In cyclic voltammetry (CV), the electrode potential ramps linearly versus time in cyclical phases (Figure 2). The rate of voltage change over time during each of these phases is known as the experiment's scan rate (V/s). The potential is measured between the working electrode and the reference electrode, while the current is measured between the working electrode and the counter electrode. These data are plotted as current (i) versus applied potential (E, often referred to as just 'potential'). In Figure 2, during the initial forward scan (from t0 to t1) an increasingly reducing potential is applied; thus the cathodic current will, at least initially, increase over this time period, assuming
|
https://en.wikipedia.org/wiki/Shen%20Kuo
|
Shen Kuo (; 1031–1095) or Shen Gua, courtesy name Cunzhong (存中) and pseudonym Mengqi (now usually given as Mengxi) Weng (夢溪翁), was a Chinese polymath, scientist, and statesman of the Song dynasty (960–1279). Shen was a master in many fields of study including mathematics, optics, and horology. In his career as a civil servant, he became a finance minister, governmental state inspector, head official for the Bureau of Astronomy in the Song court, Assistant Minister of Imperial Hospitality, and also served as an academic chancellor. At court his political allegiance was to the Reformist faction known as the New Policies Group, headed by Chancellor Wang Anshi (1021–1085).
In his Dream Pool Essays or Dream Torrent Essays (; Mengxi Bitan) of 1088, Shen was the first to describe the magnetic needle compass, which would be used for navigation (first described in Europe by Alexander Neckam in 1187). Shen discovered the concept of true north in terms of magnetic declination towards the north pole, with experimentation of suspended magnetic needles and "the improved meridian determined by Shen's [astronomical] measurement of the distance between the pole star and true north". This was the decisive step in human history to make compasses more useful for navigation, and may have been a concept unknown in Europe for another four hundred years (evidence of German sundials made circa 1450 show markings similar to Chinese geomancers' compasses in regard to declination).
Alongside his colle
|
https://en.wikipedia.org/wiki/Marx%20generator
|
A Marx generator is an electrical circuit first described by Erwin Otto Marx in 1924. Its purpose is to generate a high-voltage pulse from a low-voltage DC supply. Marx generators are used in high-energy physics experiments, as well as to simulate the effects of lightning on power-line gear and aviation equipment. A bank of 36 Marx generators is used by Sandia National Laboratories to generate X-rays in their Z Machine.
Principle of operation
The circuit generates a high-voltage pulse by charging a number of capacitors in parallel, then suddenly connecting them in series. See the circuit diagram on the right. At first, n capacitors (C) are charged in parallel to a voltage VC by a DC power supply through the resistors (RC). The spark gaps used as switches have the voltage VC across them, but the gaps have a breakdown voltage greater than VC, so they all behave as open circuits while the capacitors charge. The last gap isolates the output of the generator from the load; without that gap, the load would prevent the capacitors from charging. To create the output pulse, the first spark gap is caused to break down (triggered); the breakdown effectively shorts the gap, placing the first two capacitors in series, applying a voltage of about 2VC across the second spark gap. Consequently, the second gap breaks down to add the third capacitor to the "stack", and the process continues to sequentially break down all of the gaps. This process of the spark gaps connecting the capacitors in
|
https://en.wikipedia.org/wiki/Difference%20of%20two%20squares
|
In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number. Every difference of squares may be factored according to the identity
in elementary algebra.
Proof
The proof of the factorization identity is straightforward. Starting from the left-hand side, apply the distributive law to get
By the commutative law, the middle two terms cancel:
leaving
The resulting identity is one of the most commonly used in mathematics. Among many uses, it gives a simple proof of the AM–GM inequality in two variables.
The proof holds in any commutative ring.
Conversely, if this identity holds in a ring R for all pairs of elements a and b, then R is commutative. To see this, apply the distributive law to the right-hand side of the equation and get
.
For this to be equal to , we must have
for all pairs a, b, so R is commutative.
Geometrical demonstrations
The difference of two squares can also be illustrated geometrically as the difference of two square areas in a plane. In the diagram, the shaded part represents the difference between the areas of the two squares, i.e. . The area of the shaded part can be found by adding the areas of the two rectangles; , which can be factorized to . Therefore, .
Another geometric proof proceeds as follows: We start with the figure shown in the first diagram below, a large square with a smaller square removed from it. The side of the entire square is a, and the side of the small rem
|
https://en.wikipedia.org/wiki/Encyclopedia%20of%20Genetics
|
The Encyclopedia of Genetics () is a print encyclopedia of genetics edited by Sydney Brenner and Jeffrey H. Miller. It has four volumes and 1,700 entries. It is available online at http://www.sciencedirect.com/science/referenceworks/9780122270802.
Genetics
Genetics literature
|
https://en.wikipedia.org/wiki/Encyclopedia%20of%20Evolution
|
The Encyclopedia of Evolution is a print encyclopedia of evolutionary biology edited by Mark Pagel and published in 2002 by Oxford University Press.
It consists of 370 original articles written by leading experts including Richard Dawkins, Stephen Jay Gould, and Jane Goodall, and was selected as one of the Outstanding Reference Sources of 2003 by American Libraries.
A similar book, the Cambridge Encyclopedia of Evolution is edited by Steve Jones.
References
External links
Oxford University Press: U.S. General Catalog
LCCN record of Library of Congress
Evolutionary biology literature
Encyclopedias of science
|
https://en.wikipedia.org/wiki/UA2%20experiment
|
The Underground Area 2 (UA2) experiment was a high-energy physics experiment at the Proton-Antiproton Collider (SpS) — a modification of the Super Proton Synchrotron (SPS) — at CERN. The experiment ran from 1981 until 1990, and its main objective was to discover the W and Z bosons. UA2, together with the UA1 experiment, succeeded in discovering these particles in 1983, leading to the 1984 Nobel Prize in Physics being awarded to Carlo Rubbia and Simon van der Meer. The UA2 experiment also observed the first evidence for jet production in hadron collisions in 1981, and was involved in the searches of the top quark and of supersymmetric particles. Pierre Darriulat was the spokesperson of UA2 from 1981 to 1986, followed by Luigi Di Lella from 1986 to 1990.
Background
Around 1968 Sheldon Glashow, Steven Weinberg, and Abdus Salam came up with the electroweak theory, which unified electromagnetism and weak interactions, and for which they shared the 1979 Nobel Prize in Physics. The theory postulated the existence of W and Z bosons, and the pressure on the research community to prove the existence of these particles experimentally was substantial. During the 70s it was established that the masses of the W and Z bosons were in the range of 60 to 80 GeV (W boson) and 75 to 92 GeV (Z boson) — energies too large to be accessible by any accelerator in operation at that time. In 1976, Carlo Rubbia, Peter McIntyre and David Cline proposed to modify a proton accelerator — at that time a pro
|
https://en.wikipedia.org/wiki/Fractional%20Fourier%20transform
|
In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate domain between time and frequency. Its applications range from filter design and signal analysis to phase retrieval and pattern recognition.
The FRFT can be used to define fractional convolution, correlation, and other operations, and can also be further generalized into the linear canonical transformation (LCT). An early definition of the FRFT was introduced by Condon, by solving for the Green's function for phase-space rotations, and also by Namias, generalizing work of Wiener on Hermite polynomials.
However, it was not widely recognized in signal processing until it was independently reintroduced around 1993 by several groups. Since then, there has been a surge of interest in extending Shannon's sampling theorem for signals which are band-limited in the Fractional Fourier domain.
A completely different meaning for "fractional Fourier transform" was introduced by Bailey and Swartztrauber as essentially another name for a z-transform, and in particular for the case that corresponds to a discrete Fourier transform shifted by a fractional amount in frequency space (multiplying the input by a linear chirp) and evaluating at a fractional set of frequency points (e.
|
https://en.wikipedia.org/wiki/Mohamed%20Elmasry
|
Mohamed Elmasry () (born December 24, 1943) is a Canadian engineering professor, imam, and Muslim community leader.
Biography
He was born in Cairo, Egypt and received his Bachelor of Science in 1965 from Cairo University. He continued his studies in Canada earning masters and doctorate degrees in electrical engineering from the University of Ottawa in 1970 and 1974. He has worked in the area of digital integrated microchip design for over four decades.
From 1965 to 1968, Elmasry worked for Cairo University and from 1972 to 1974 for Bell-Northern Research in Ottawa, Ontario, Canada. Since 1974, he has been with the Department of Electrical and Computer Engineering at the University of Waterloo in Ontario where he is a founding Director of the VLSI (Microchip) Research Group.
As a spokesperson for Muslim causes through the Canadian Islamic Congress, he has been a regular contributor to The Globe and Mail. His remarks, especially those concerning the Israeli–Palestinian conflict, have drawn significant attention in the Canadian media. He has accused some of his opponents of being anti-Islam.
Elmasry has authored and co-authored more than 500 research papers and 16 books on integrated circuit design and design automation, as well as having several patents to his credit. He has edited the following books for the Institute of Electrical and Electronics Engineers: Digital MOS Integrated Circuits (1981); Digital VLSI Systems (1985), Digital MOS Integrated Circuits II (1991) and
|
https://en.wikipedia.org/wiki/Power%20stroke
|
Power Stroke may refer to:
In motoring:
Power stroke (engine), the stroke of a cyclic motor which generates force
Power Stroke, a family of Ford diesel engines
Other:
Power stroke (baseball), a batter who hits for extra bases
Power stroke (biology), the molecular interactions of muscle contraction
Power stroke (swimming), a propulsion kick
See also
Power Stroke Diesel 200, a NASCAR race
|
https://en.wikipedia.org/wiki/Jonathan%27s%20Space%20Report
|
Jonathan's Space Report (JSR) is a newsletter about the Space Age hosted at Jonathan's Space Page. It is written by Jonathan McDowell, a Center for Astrophysics Harvard & Smithsonian astrophysicist. It is updated as McDowell's schedule permits, but he tries to publish two issues each month. Originally the website was hosted on a Harvard University account, but it was moved in late 2003 to a dedicated domain.
Started in 1989, the newsletter reports on recent space launches, International Space Station activities, spacecraft developments, and newly released space-related data. McDowell's report occasionally corrects NASA's official web sites, or provides additional data on classified launches that aren't available elsewhere.
Associated projects on the JSR web site are:
A catalog of all known geosynchronous satellites and their current positions
A listing of satellite launch attempts
A cross-reference between catalog number and international designation of artificial satellites
A photo archive covering many launch attempts
A catalog of all spacecraft reentries
McDowell has long campaigned for U.S. compliance with the UN Convention on Registration of Outer Space Objects (1975) and UN Resolution 1721B (1961).
See also
Encyclopedia Astronautica
References
External links
Newsletters
Spaceflight
Academic journals established in 1989
Internet properties established in 1989
Space Age
|
https://en.wikipedia.org/wiki/Covariance%20and%20contravariance%20%28computer%20science%29
|
Many programming language type systems support subtyping. For instance, if the type is a subtype of , then an expression of type should be substitutable wherever an expression of type is used.
Variance is how subtyping between more complex types relates to subtyping between their components. For example, how should a list of s relate to a list of s? Or how should a function that returns relate to a function that returns ?
Depending on the variance of the type constructor, the subtyping relation of the simple types may be either preserved, reversed, or ignored for the respective complex types. In the OCaml programming language, for example, "list of Cat" is a subtype of "list of Animal" because the list type constructor is covariant. This means that the subtyping relation of the simple types is preserved for the complex types.
On the other hand, "function from Animal to String" is a subtype of "function from Cat to String" because the function type constructor is contravariant in the parameter type. Here, the subtyping relation of the simple types is reversed for the complex types.
A programming language designer will consider variance when devising typing rules for language features such as arrays, inheritance, and generic datatypes. By making type constructors covariant or contravariant instead of invariant, more programs will be accepted as well-typed. On the other hand, programmers often find contravariance unintuitive, and accurately tracking variance to avoid run
|
https://en.wikipedia.org/wiki/Hill%20cipher
|
In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once.
The following discussion assumes an elementary knowledge of matrices.
Encryption
Each letter is represented by a number modulo 26. Though this is not an essential feature of the cipher, this simple scheme is often used:
To encrypt a message, each block of n letters (considered as an n-component vector) is multiplied by an invertible n × n matrix, against modulus 26. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption.
The matrix used for encryption is the cipher key, and it should be chosen randomly from the set of invertible n × n matrices (modulo 26). The cipher can, of course, be adapted to an alphabet with any number of letters; all arithmetic just needs to be done modulo the number of letters instead of modulo 26.
Consider the message 'ACT', and the key below (or GYBNQKURP in letters):
Since 'A' is 0, 'C' is 2 and 'T' is 19, the message is the vector:
Thus the enciphered vector is given by:
which corresponds to a ciphertext of 'POH'. Now, suppose that our message is instead 'CAT', or:
This time, the enciphered vector is given by:
which corresponds to a ciphertext of 'FIN'. Every letter has changed. The Hill cipher has achieved Shannon's diffusion, and an
|
https://en.wikipedia.org/wiki/Grigory%20Margulis
|
Grigory Aleksandrovich Margulis (, first name often given as Gregory, Grigori or Gregori; born February 24, 1946) is a Russian-American mathematician known for his work on lattices in Lie groups, and the introduction of methods from ergodic theory into diophantine approximation. He was awarded a Fields Medal in 1978, a Wolf Prize in Mathematics in 2005, and an Abel Prize in 2020, becoming the fifth mathematician to receive the three prizes. In 1991, he joined the faculty of Yale University, where he is currently the Erastus L. De Forest Professor of Mathematics.
Biography
Margulis was born to a Russian family of Lithuanian Jewish descent in Moscow, Soviet Union. At age 16 in 1962 he won the silver medal at the International Mathematical Olympiad. He received his PhD in 1970 from the Moscow State University, starting research in ergodic theory under the supervision of Yakov Sinai. Early work with David Kazhdan produced the Kazhdan–Margulis theorem, a basic result on discrete groups. His superrigidity theorem from 1975 clarified an area of classical conjectures about the characterisation of arithmetic groups amongst lattices in Lie groups.
He was awarded the Fields Medal in 1978, but was not permitted to travel to Helsinki to accept it in person, allegedly due to antisemitism against Jewish mathematicians in the Soviet Union. His position improved, and in 1979 he visited Bonn, and was later able to travel freely, though he still worked in the Institute of Problems of Informat
|
https://en.wikipedia.org/wiki/Kirby%20calculus
|
In mathematics, the Kirby calculus in geometric topology, named after Robion Kirby, is a method for modifying framed links in the 3-sphere using a finite set of moves, the Kirby moves. Using four-dimensional Cerf theory, he proved that if M and N are 3-manifolds, resulting from Dehn surgery on framed links L and J respectively, then they are homeomorphic if and only if L and J are related by a sequence of Kirby moves. According to the Lickorish–Wallace theorem any closed orientable 3-manifold is obtained by such surgery on some link in the 3-sphere.
Some ambiguity exists in the literature on the precise use of the term "Kirby moves". Different presentations of "Kirby calculus" have a different set of moves and these are sometimes called Kirby moves. Kirby's original formulation involved two kinds of move, the "blow-up" and the "handle slide"; Roger Fenn and Colin Rourke exhibited an equivalent construction in terms of a single move, the Fenn–Rourke move, that appears in many expositions and extensions of the Kirby calculus. Dale Rolfsen's book, Knots and Links, from which many topologists have learned the Kirby calculus, describes a set of two moves: 1) delete or add a component with surgery coefficient infinity 2) twist along an unknotted component and modify surgery coefficients appropriately (this is called the Rolfsen twist). This allows an extension of the Kirby calculus to rational surgeries.
There are also various tricks to modify surgery diagrams. One such u
|
https://en.wikipedia.org/wiki/Peter%20Unger
|
Peter K. Unger (; born April 25, 1942) is a contemporary American philosopher and professor in the Department of Philosophy at New York University. His main interests lie in the fields of metaphysics, epistemology, ethics, and the philosophy of mind.
Biography
Unger attended Swarthmore College at the same time as David Lewis, earning a B.A. in philosophy in 1962, and Oxford University, where he studied under A. J. Ayer and earned a doctorate in 1966.
Unger has written a defense of profound philosophical skepticism. In Ignorance (1975), he argues that nobody knows anything and even that nobody is reasonable or justified in believing anything.
In Philosophical Relativity (1984), he argues that many philosophical questions cannot be definitively answered.
In the field of applied ethics, his best-known work is Living High and Letting Die (1996). In this text, Unger argues that the citizens of first-world countries have a moral duty to make large donations to life-saving charities (such as Oxfam and UNICEF), and that once they have given all of their own money and possessions, beyond what is needed to survive, they should give what belongs to others, even if having to beg, borrow, or steal in the process.
In "The Mental Problems of the Many" (2002), he argues for substantial interactionist dualism on questions of mind and matter: that each of us is an immaterial soul. The argument is extended and fortified in his 2006 book All the Power in the World.
In Empty Ideas (2014),
|
https://en.wikipedia.org/wiki/Blackwater%20river
|
A blackwater river is a type of river with a slow-moving channel flowing through forested swamps or wetlands. Most major blackwater rivers are in the Amazon Basin and the Southern United States. The term is used in fluvial studies, geology, geography, ecology, and biology. Not all dark rivers are blackwater in that technical sense. Some rivers in temperate regions, which drain or flow through areas of dark black loam, are simply black due to the color of the soil; these rivers are black mud rivers. There are also black mud estuaries.
Blackwater rivers are lower in nutrients than whitewater rivers and have ionic concentrations higher than rainwater. The unique conditions lead to flora and fauna that differ from both whitewater and clearwater rivers. The classification of Amazonian rivers into black, clear, and whitewater was first proposed by Alfred Russel Wallace in 1853 based on water colour, but the types were more clearly defined by chemistry and physics by from the 1950s to the 1980s. Although many Amazonian rivers fall clearly into one of these categories, others show a mix of characteristics and may vary depending on season and flood levels.
Comparison between white and black waters
Black and white waters differ significantly in their ionic composition, as shown in Table 1. Black waters are more acidic, resulting in an aluminum concentration greater than that of the more neutral white waters. The major difference is the concentrations of sodium, magnesium, calciu
|
https://en.wikipedia.org/wiki/Smith%20normal%20form
|
In mathematics, the Smith normal form (sometimes abbreviated SNF) is a normal form that can be defined for any matrix (not necessarily square) with entries in a principal ideal domain (PID). The Smith normal form of a matrix is diagonal, and can be obtained from the original matrix by multiplying on the left and right by invertible square matrices. In particular, the integers are a PID, so one can always calculate the Smith normal form of an integer matrix. The Smith normal form is very useful for working with finitely generated modules over a PID, and in particular for deducing the structure of a quotient of a free module. It is named after the Irish mathematician Henry John Stephen Smith.
Definition
Let A be a nonzero m×n matrix over a principal ideal domain R. There exist invertible and -matrices S, T (with coefficients in R) such that the product S A T is
and the diagonal elements satisfy for all . This is the Smith normal form of the matrix A. The elements are unique up to multiplication by a unit and are called the elementary divisors, invariants, or invariant factors. They can be computed (up to multiplication by a unit) as
where (called i-th determinant divisor) equals the greatest common divisor of the determinants of all minors of the matrix A and .
Algorithm
The first goal is to find invertible square matrices and such that the product is diagonal. This is the hardest part of the algorithm. Once diagonality is achieved, it becomes relatively eas
|
https://en.wikipedia.org/wiki/Kinetic%20isotope%20effect
|
In physical organic chemistry, a kinetic isotope effect (KIE) is the change in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced by one of its isotopes. Formally, it is the ratio of rate constants for the reactions involving the light (kL) and the heavy (kH) isotopically substituted reactants (isotopologues):
This change in reaction rate is a quantum mechanical effect that primarily results from heavier isotopologues having lower vibrational frequencies compared to their lighter counterparts. In most cases, this implies a greater energetic input needed for heavier isotopologues to reach the transition state (or, in rare cases, the dissociation limit), and consequently, a slower reaction rate. The study of kinetic isotope effects can help the elucidation of the reaction mechanism of certain chemical reactions and is occasionally exploited in drug development to improve unfavorable pharmacokinetics by protecting metabolically vulnerable C-H bonds.
Background
The kinetic isotope effect is considered to be one of the most essential and sensitive tools for the study of reaction mechanisms, the knowledge of which allows the improvement of the desirable qualities of the corresponding reactions. For example, kinetic isotope effects can be used to reveal whether a nucleophilic substitution reaction follows a unimolecular (SN1) or bimolecular (SN2) pathway.
In the reaction of methyl bromide and cyanide (shown in the introduction), the obs
|
https://en.wikipedia.org/wiki/Monarch%20%28disambiguation%29
|
A monarch is a ruler in a system (monarchy) where succession is hereditary.
Monarch or Monarchy may also refer to:
Biology
Danaus (genus), a genus of butterflies commonly called monarchs
Danaus plexippus, the North American butterfly most commonly referred to as the monarch butterfly
Monarch flycatcher or Monarchidae, a family of passerine birds
Places
Monarch, Alberta, Canada
Monarch, Colorado, United States
Monarch, Montana, an American unincorporated community
Monarch, Virginia, United States
Monarch, West Virginia, United States
Monarch, Wyoming, an American unincorporated community
Monarch Icefield, a large continental icecap in British Columbia, Canada
Monarch Lake, a reservoir in Colorado, United States
Monarch Mountain, a summit of the Pacific Ranges in British Columbia, Canada
Monarch Mountain (Alberta), a peak in the Victoria Cross Ranges in Canada
Monarch Pass, Colorado, United States
Monarch Ski Area, Colorado, United States
The Monarch (Canadian Rockies), a mountain in Canada
Entertainment
Monarch: Legacy of Monsters
Monarch (film), a 2000 British costume drama involving Henry VIII
Monarchy (TV series), a documentary television series about the British monarchy
Monarch (American TV series), an American TV series
Lord Monarch, a 1991 strategy war video game
Monarch: The Butterfly King, a 2007 personal computer game
Monarch, a fictional organization in the MonsterVerse film franchise
HMS Monarch, a fictional Royal Navy warship from the 2017 film Pirates of the
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.