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https://en.wikipedia.org/wiki/John%20Todd
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John Todd or Tod may refer to:
Clergy
John Todd (abolitionist) (1818–1894), preacher and 'conductor' on the Underground Railroad
John Todd (author) (1800–1873), American minister and author
John Todd (bishop), Anglican bishop in the early 17th century
John Baptist Todd (1921–2017), Pakistani Franciscan priest
Mathematics, science, and medicine
John Todd (British biologist) (born 1958), British biologist working on diabetes mellitus
John Todd (Canadian biologist) (born 1939), Canadian biologist working in the field of ecological design
John (Jack) Todd (1911–2007), Northern Irish and American mathematician working in the field of numerical analysis
J. A. Todd (John Arthur Todd, 1908–1994), English mathematician
John Lancelot Todd (1876–1949), Canadian physician and parasitologist
John W. Todd (1912–1989), British physician and author
Politics and government
John Tod (1779–1830), American judge and politician
John Todd (politician) (), Canadian politician from the Northwest Territories
John Todd (Virginia soldier) (1750–1782), early Virginia official, Kentucky soldier, and great-uncle of Mary Todd Lincoln
John Blair Smith Todd (1814–1872), delegate to US Congress from Dakota Territory
John J. Todd (born 1927), Justice of the Minnesota Supreme Court
John Rawling Todd (1929–2002), British colonial civil servant
Sports
John Kennedy Tod (1852–1925), Scottish rugby union player
John Todd (footballer) (born 1938), Australian rules football player and coach
John Todd (rugby leagu
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https://en.wikipedia.org/wiki/Bessel
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Bessel may refer to:
Bessel beam
Bessel ellipsoid
Bessel function in mathematics
Bessel's inequality in mathematics
Bessel's correction in statistics.
Bessel filter, a linear filter often used in audio crossover systems
Bessel Fjord, NE Greenland
Bessel Fjord, NW Greenland
Bessel (crater), a small lunar crater
Bessel transform, also known as Fourier-Bessel transform or Hankel transform
Bessel window, in signal processing
Besselian date, see Epoch (astronomy)#Besselian years
, a German merchant ship in service 1928–45, latterly for the Kriegsmarine
People
Friedrich Wilhelm Bessel (1784–1846), German mathematician, astronomer, and systematizer of the Bessel functions
See also
Bessell
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https://en.wikipedia.org/wiki/Organic%20synthesis
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Organic synthesis is a special branch of chemical synthesis and is concerned with the intentional construction of organic compounds. Organic molecules are often more complex than inorganic compounds, and their synthesis has developed into one of the most important branches of organic chemistry. There are several main areas of research within the general area of organic synthesis: total synthesis, semisynthesis, and methodology.
Total synthesis
A total synthesis is the complete chemical synthesis of complex organic molecules from simple, commercially available petrochemical or natural precursors. Total synthesis may be accomplished either via a linear or convergent approach. In a linear synthesis—often adequate for simple structures—several steps are performed one after another until the molecule is complete; the chemical compounds made in each step are called synthetic intermediates. Most often, each step in a synthesis refers to a separate reaction taking place to modify the starting compound. For more complex molecules, a convergent synthetic approach may be preferable, one that involves individual preparation of several "pieces" (key intermediates), which are then combined to form the desired product. Convergent synthesis has the advantage of generating higher yield, compared to linear synthesis.
Robert Burns Woodward, who received the 1965 Nobel Prize for Chemistry for several total syntheses (e.g., his 1954 synthesis of strychnine), is regarded as the father of mo
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https://en.wikipedia.org/wiki/Edwin%20Baker%20%28CNIB%29
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Edwin Albert Baker, (January 9, 1893 – April 7, 1968) was a Canadian co-founder of the Canadian National Institute for the Blind (CNIB).
Born in Collins Bay, Ontario, he graduated with a Bachelor of Science in electrical engineering from Queen's University in 1914 and later that year enlisted with the Sixth Field Company, Canadian Engineers. In 1915, he was wounded in France, losing his sight in both eyes.
In 1918, he and six others founded the CNIB. He served as first Vice-President from 1918 to 1920 and Managing Director & General Secretary from 1920 until his retirement in 1962.
He married Jessie Robinson. They had three sons and a daughter.
Honours
In 1935, he was made an Officer of the Order of the British Empire.
In 1938, he was awarded an Honorary Doctor of Laws from Queen's University, and in 1945, the same from the University of Toronto.
Croix de Guerre
In 1967, he was made a Companion of the Order of Canada.
Related book
References
1893 births
1968 deaths
Canadian military personnel of World War I
Companions of the Order of Canada
Recipients of the Croix de Guerre (France)
Canadian Officers of the Order of the British Empire
People from Frontenac County
Queen's University at Kingston alumni
Canadian recipients of the Military Cross
Canadian blind people
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https://en.wikipedia.org/wiki/Nesbitt%27s%20inequality
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In mathematics, Nesbitt's inequality states that for positive real numbers a, b and c,
It is an elementary special case (N = 3) of the difficult and much studied Shapiro inequality, and was published at least 50 years earlier.
There is no corresponding upper bound as any of the 3 fractions in the inequality can be made arbitrarily large.
Proof
First proof: AM-HM inequality
By the AM-HM inequality on ,
Clearing denominators yields
from which we obtain
by expanding the product and collecting like denominators. This then simplifies directly to the final result.
Second proof: Rearrangement
Suppose , we have that
define
The scalar product of the two sequences is maximum because of the rearrangement inequality if they are arranged the same way, call and the vector shifted by one and by two, we have:
Addition yields our desired Nesbitt's inequality.
Third proof: Sum of Squares
The following identity is true for all
This clearly proves that the left side is no less than for positive a, b and c.
Note: every rational inequality can be demonstrated by transforming it to the appropriate sum-of-squares identity, see Hilbert's seventeenth problem.
Fourth proof: Cauchy–Schwarz
Invoking the Cauchy–Schwarz inequality on the vectors yields
which can be transformed into the final result as we did in the AM-HM proof.
Fifth proof: AM-GM
Let . We then apply the AM-GM inequality to obtain the following
because
Substituting out the in favor of yields
which then simpl
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https://en.wikipedia.org/wiki/Toy%20theorem
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In mathematics, a toy theorem is a simplified instance (special case) of a more general theorem, which can be useful in providing a handy representation of the general theorem, or a framework for proving the general theorem. One way of obtaining a toy theorem is by introducing some simplifying assumptions in a theorem.
In many cases, a toy theorem is used to illustrate the claim of a theorem, while in other cases, studying the proofs of a toy theorem (derived from a non-trivial theorem) can provide insight that would be hard to obtain otherwise.
Toy theorems can also have educational value as well. For example, after presenting a theorem (with, say, a highly non-trivial proof), one can sometimes give some assurance that the theorem really holds, by proving a toy version of the theorem.
Examples
A toy theorem of the Brouwer fixed-point theorem is obtained by restricting the dimension to one. In this case, the Brouwer fixed-point theorem follows almost immediately from the intermediate value theorem.
Another example of toy theorem is Rolle's theorem, which is obtained from the mean value theorem by equating the function values at the endpoints.
See also
Corollary
Fundamental theorem
Lemma (mathematics)
Toy model
References
Mathematical theorems
Mathematical terminology
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https://en.wikipedia.org/wiki/Yield%20%28chemistry%29
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In chemistry, yield, also referred to as reaction yield, is a measure of the quantity of moles of a product formed in relation to the reactant consumed, obtained in a chemical reaction, usually expressed as a percentage. Yield is one of the primary factors that scientists must consider in organic and inorganic chemical synthesis processes. In chemical reaction engineering, "yield", "conversion" and "selectivity" are terms used to describe ratios of how much of a reactant was consumed (conversion), how much desired product was formed (yield) in relation to the undesired product (selectivity), represented as X, Y, and S.
Definitions
In chemical reaction engineering, "yield", "conversion" and "selectivity" are terms used to describe ratios of how much of a reactant has reacted—conversion, how much of a desired product was formed—yield, and how much desired product was formed in ratio to the undesired product—selectivity, represented as X,S, and Y.
According to the Elements of Chemical Reaction Engineering manual, yield refers to the amount of a specific product formed per mole of reactant consumed. In chemistry, mole is used to describe quantities of reactants and products in chemical reactions.
The Compendium of Chemical Terminology defined yield as the "ratio expressing the efficiency of a mass conversion process. The yield coefficient is defined as the amount of cell mass (kg) or product formed (kg,mol) related to the consumed substrate (carbon or nitrogen source o
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https://en.wikipedia.org/wiki/Klaus%20Fesser
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Klaus Fesser is a professor for theoretical physics at Department of Physics at the University of Greifswald, Germany.
Director
Now, he is the director of the Department of Physics.
Subjects of lectures
Seminar of theoretical physics
Laboratory practical course II
Theoretical solid-state physics II
Seminar: special problems of theoretical physics
Special chapters of the solid theory
Physical colloquium
Research field
low-dimensional condensed matter
nonlinear dynamics in plasma
bifurcation theory
carbon nanotube
External links
more details
21st-century German physicists
Living people
Academic staff of the University of Greifswald
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/James%20Berges
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James Berges was president of Emerson Electric Corp from 1999 until he retired in 2005. He resides in St. Louis, Missouri. He was involved in the company for over 30 years. Mr. Berges, with a degree in electrical engineering from the University of Notre Dame, previously worked for General Electric Corp. He earned compensation of $9.5 million in 2005.
External links
'Emerson President James G. Berges to Retire November 1' (Emerson News)
General Electric people
PPG Industries people
Living people
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Filter%20bank
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In signal processing, a filter bank (or filterbank) is an array of bandpass filters that separates the input signal into multiple components, each one carrying a single frequency sub-band of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components differently and recombine them into a modified version of the original signal. The process of decomposition performed by the filter bank is called analysis (meaning analysis of the signal in terms of its components in each sub-band); the output of analysis is referred to as a subband signal with as many subbands as there are filters in the filter bank. The reconstruction process is called synthesis, meaning reconstitution of a complete signal resulting from the filtering process.
In digital signal processing, the term filter bank is also commonly applied to a bank of receivers. The difference is that receivers also down-convert the subbands to a low center frequency that can be re-sampled at a reduced rate. The same result can sometimes be achieved by undersampling the bandpass subbands.
Another application of filter banks is signal compression when some frequencies are more important than others. After decomposition, the important frequencies can be coded with a fine resolution. Small differences at these frequencies are significant and a coding scheme that preserves these differences must be used. On the other hand, less important frequencies do not have to be exact.
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https://en.wikipedia.org/wiki/Rigidity%20%28mathematics%29
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In mathematics, a rigid collection C of mathematical objects (for instance sets or functions) is one in which every c ∈ C is uniquely determined by less information about c than one would expect.
The above statement does not define a mathematical property; instead, it describes in what sense the adjective "rigid" is typically used in mathematics, by mathematicians.
Examples
Some examples include:
Harmonic functions on the unit disk are rigid in the sense that they are uniquely determined by their boundary values.
Holomorphic functions are determined by the set of all derivatives at a single point. A smooth function from the real line to the complex plane is not, in general, determined by all its derivatives at a single point, but it is if we require additionally that it be possible to extend the function to one on a neighbourhood of the real line in the complex plane. The Schwarz lemma is an example of such a rigidity theorem.
By the fundamental theorem of algebra, polynomials in C are rigid in the sense that any polynomial is completely determined by its values on any infinite set, say N, or the unit disk. By the previous example, a polynomial is also determined within the set of holomorphic functions by the finite set of its non-zero derivatives at any single point.
Linear maps L(X, Y) between vector spaces X, Y are rigid in the sense that any L ∈ L(X, Y) is completely determined by its values on any set of basis vectors of X.
Mostow's rigidity theorem, which states th
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https://en.wikipedia.org/wiki/Stationary%20phase%20approximation
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In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to functions given by integration against a rapidly-varying complex exponential.
This method originates from the 19th century, and is due to George Gabriel Stokes and Lord Kelvin.
It is closely related to Laplace's method and the method of steepest descent, but Laplace's contribution precedes the others.
Basics
The main idea of stationary phase methods relies on the cancellation of sinusoids with rapidly varying phase. If many sinusoids have the same phase and they are added together, they will add constructively. If, however, these same sinusoids have phases which change rapidly as the frequency changes, they will add incoherently, varying between constructive and destructive addition at different times.
Formula
Letting denote the set of critical points of the function (i.e. points where ), under the assumption that is either compactly supported or has exponential decay, and that all critical points are nondegenerate (i.e. for ) we have the following asymptotic formula, as :
Here denotes the Hessian of , and denotes the signature of the Hessian, i.e. the number of positive eigenvalues minus the number of negative eigenvalues.
For , this reduces to:
In this case the assumptions on reduce to all the critical points being non-degenerate.
This is just the Wick-rotated version of the formula for the method of steepest descent.
An example
Consider a function
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https://en.wikipedia.org/wiki/Parallel%20tempering
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Parallel tempering, in physics and statistics, is a computer simulation method typically used to find the lowest energy state of a system of many interacting particles. It addresses the problem that at high temperatures, one may have a stable state different from low temperature, whereas simulations at low temperatures may become "stuck" in a metastable state. It does this by using the fact that the high temperature simulation may visit states typical of both stable and metastable low temperature states.
More specifically, parallel tempering (also known as replica exchange MCMC sampling), is a simulation method aimed at improving the dynamic properties of Monte Carlo method simulations of physical systems, and of Markov chain Monte Carlo (MCMC) sampling methods more generally. The replica exchange method was originally devised by Robert Swendsen and J. S. Wang, then extended by Charles J. Geyer, and later developed further by Giorgio Parisi,
Koji Hukushima and Koji Nemoto,
and others.
Y. Sugita and Y. Okamoto also formulated a molecular dynamics version of parallel tempering; this is usually known as replica-exchange molecular dynamics or REMD.
Essentially, one runs N copies of the system, randomly initialized, at different temperatures. Then, based on the Metropolis criterion one exchanges configurations at different temperatures. The idea of this method
is to make configurations at high temperatures available to the simulations at low temperatures and vice versa.
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https://en.wikipedia.org/wiki/FRC
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FRC may refer to:
Education
Feather River College, in California, United States
FIRST Robotics Competition, an annual international robotics competition for students aged 14-18
Fort Richmond Collegiate, a high school in Winnipeg, Manitoba, Canada
Government
Family Records Centre, a defunct British genealogical library
Federal Radio Commission, a defunct regulatory agency of the United States federal government
Federal Republic of China, a proposed federal republic encompassing mainland China, Macau, and Hong Kong
Financial Reporting Council, an independent regulator in the United Kingdom and Ireland
Federal Record Centers, maintained by NARA
First Responders Children's Foundation, an American non-profit organization. See Disney Princess.
Religion
Family Research Council, an American conservative Christian organization
Family Rosary Crusade, a Roman Catholic prayer movement
Family Rosary Crusade (TV program), a Philippine television program
Free Reformed Churches (disambiguation)
Technology
Fast Response Car, of the Singapore Police Force
Fast Response Cutter of the United States Coast Guard
Fiber-reinforced composite
Fiber-reinforced concrete
Field-reversed configuration
Flame-resistant clothing
Frame rate control
Music
"F.R.C." (song), a 1991 single by Australian rock band The Screaming Jets
Other uses
Cajun French (ISO 639-3 language code)
Fatah - Revolutionary Council, a terrorist organization
Federacion de Radioaficionados de Cuba, a Cub
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https://en.wikipedia.org/wiki/Robert%20d%27Escourt%20Atkinson
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Robert d'Escourt Atkinson (born 11 April 1898, Rhayader, Wales – died 28 October 1982, Bloomington, Indiana) was a British astronomer, physicist and inventor.
Biography
Robert d'Escourt Atkinson was born in Wales on April 11, 1898. He went to Manchester Grammar School and received a degree in physics from Oxford in 1922. He worked in the Clarendon Laboratory and then went to Göttingen, where he received a Ph.D. in physics in 1928. After teaching physics at the Berlin Technische Hochscule for a year, Atkinson was appointed Assistant Professor of Physics at Rutgers University. He taught at Rutgers University in New Jersey from 1929 to 1937, when he became Chief Assistant at the Royal Greenwich Observatory. During World War II, Atkinson was called away from this position to do anti-magnetic mine work. In 1944, he was lent out to the Ballistic Research Laboratory at Aberdeen Proving Ground in Maryland, where he worked under famed astronomer Edwin Hubble. Atkinson stayed there for two years then returned to Royal Greenwich Observatory. A large amount of his remaining years at the Royal Observatory were spent overseeing the move of the entire Observatory to Herstmonceux Castle in Sussex. In 1964, Atkinson retired from the Royal Observatory and came to Indiana University as a visiting professor. He became an adjunct professor in 1973 and a professor emeritus in 1979 at Indiana University. Also involved in professional associations, Atkinson was a founder-member of the Royal Insti
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https://en.wikipedia.org/wiki/Rigidity
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Rigid or rigidity may refer to:
Mathematics and physics
Stiffness, the property of a solid body to resist deformation, which is sometimes referred to as rigidity
Structural rigidity, a mathematical theory of the stiffness of ensembles of rigid objects connected by hinges
Rigidity (electromagnetism), the resistance of a charged particle to deflection by a magnetic field
Rigidity (mathematics), a property of a collection of mathematical objects (for instance sets or functions)
Rigid body, in physics, a simplification of the concept of an object to allow for modelling
Rigid transformation, in mathematics, a rigid transformation preserves distances between every pair of points
Rigidity (chemistry), the tendency of a substance to retain/maintain their shape when subjected to outside force
(Modulus of) rigidity or shear modulus (material science), the tendency of a substance to retain/maintain their shape when subjected to outside force
Medicine
Rigidity (neurology), an increase in muscle tone leading to a resistance to passive movement throughout the range of motion
Rigidity (psychology), an obstacle to problem solving which arises from over-dependence on prior experiences
Other uses
Real rigidity, and nominal rigidity, the resistance of prices and wages to market changes in macroeconomics
Ridgid, a brand of tools
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https://en.wikipedia.org/wiki/Fetal%20pig
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Fetal pigs are unborn pigs used in elementary as well as advanced biology classes as objects for dissection. Pigs, as a mammalian species, provide a good specimen for the study of physiological systems and processes due to the similarities between many pig and human organs.
Use in biology labs
Along with frogs and earthworms, fetal pigs are among the most common animals used in classroom dissection. There are several reasons for this, the main reason being that pigs, like humans, are mammals. Shared traits include common hair, mammary glands, live birth, similar organ systems, metabolic levels, and basic body form. They also allow for the study of fetal circulation, which differs from that of an adult. Secondly, fetal pigs are easy to obtain because they are by-products of the pork industry. Fetal pigs are the unborn piglets of sows that were killed by the meat-packing industry. These pigs are not bred and killed for this purpose, but are extracted from the deceased sow’s uterus. Fetal pigs not used in classroom dissections are often used in fertilizer or simply discarded. Thirdly, fetal pigs are cheap, which is an essential component for dissection use by schools. They can be ordered for about $30 at biological product companies. Fourthly, fetal pigs are easy to dissect because of their soft tissue and incompletely developed bones that are still made of cartilage. In addition, they are relatively large with well-developed organs that are easily visible. As long as the pork
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https://en.wikipedia.org/wiki/Chromatic%20polynomial
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The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff to study the four color problem. It was generalised to the Tutte polynomial by Hassler Whitney and W. T. Tutte, linking it to the Potts model of statistical physics.
History
George David Birkhoff introduced the chromatic polynomial in 1912, defining it only for planar graphs, in an attempt to prove the four color theorem. If denotes the number of proper colorings of G with k colors then one could establish the four color theorem by showing for all planar graphs G. In this way he hoped to apply the powerful tools of analysis and algebra for studying the roots of polynomials to the combinatorial coloring problem.
Hassler Whitney generalised Birkhoff’s polynomial from the planar case to general graphs in 1932. In 1968, Ronald C. Read asked which polynomials are the chromatic polynomials of some graph, a question that remains open, and introduced the concept of chromatically equivalent graphs. Today, chromatic polynomials are one of the central objects of algebraic graph theory.
Definition
For a graph G, counts the number of its (proper) vertex k-colorings.
Other commonly used notations include , , or .
There is a unique polynomial which evaluated at any integer k ≥ 0 coincides with ; it is called the chromatic polynomial of G.
For examp
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https://en.wikipedia.org/wiki/Res
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Res or RES may refer to:
Sciences
Computing
Russian and Eurasian Security Network
Spanish Supercomputing Network (Red Española de Supercomputación)
Energy
RES - The School for Renewable Energy Science
US Renewable Electricity Standard
Renewable Energy Systems, a UK company
Mathematics
Residue (complex analysis) function
Medicine
Reticuloendothelial system, in anatomy
Archaeology
Répertoire d'Épigraphie Sémitique, a journal publishing Semitic language inscriptions
Latin word meaning "thing"
Entity (disambiguation)
Object (philosophy)
The first word of several Latin phrases:
Res divina (service of the gods)
Res extensa Descartes' physical world
Res gestae (Things done)
Res inter alios acta (A thing done between others)
Res ipsa loquitur (The thing speaks for itself)
Res judicata (A matter [already] judged)
Res nullius (An unowned thing)
Res publica (A public thing), the origin of the word republic
Organizations
Rail Express Systems
Railway Enthusiasts Society, New Zealand
Royal Economic Society, UK
Royal Entomological Society
Places
Resistencia International Airport (IATA airport code: RES)
People
Res (singer), American singer
Arts, entertainment, and media
Literature
RES (magazine), bimonthly
Music
Songs
"R.E.S.", a song by Cardiacs from The Seaside
"The Res", a song by the American band Bright from their self-titled album
See also
RE5 (disambiguation)
Rez (disambiguation)
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https://en.wikipedia.org/wiki/Cyclic%20homology
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In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds. These notions were independently introduced by Boris Tsygan (homology) and Alain Connes (cohomology) in the 1980s. These invariants have many interesting relationships with several older branches of mathematics, including de Rham theory, Hochschild (co)homology, group cohomology, and the K-theory. Contributors to the development of the theory include Max Karoubi, Yuri L. Daletskii, Boris Feigin, Jean-Luc Brylinski, Mariusz Wodzicki, Jean-Louis Loday, Victor Nistor, Daniel Quillen, Joachim Cuntz, Ryszard Nest, Ralf Meyer, and Michael Puschnigg.
Hints about definition
The first definition of the cyclic homology of a ring A over a field of characteristic zero, denoted
HCn(A) or Hnλ(A),
proceeded by the means of the following explicit chain complex related to the Hochschild homology complex of A, called the Connes complex:
For any natural number n ≥ 0, define the operator which generates the natural cyclic action of on the n-th tensor product of A:
Recall that the Hochschild complex groups of A with coefficients in A itself are given by setting for all n ≥ 0. Then the components of the Connes complex are defined as , and the differential is the restriction of the Hochschild differential to this quotient. One can check that the Hochschild differential does
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https://en.wikipedia.org/wiki/Indeterminate%20%28variable%29
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In mathematics, particularly in formal algebra, an indeterminate is a symbol that is treated as a variable, but does not stand for anything else except itself. It may be used as a placeholder in objects such as polynomials and formal power series. In particular:
It does not designate a constant or a parameter of the problem.
It is not an unknown that could be solved for.
It is not a variable designating a function argument, or a variable being summed or integrated over.
It is not any type of bound variable.
It is just a symbol used in an entirely formal way.
When used as placeholders, a common operation is to substitute mathematical expressions (of an appropriate type) for the indeterminates.
By a common abuse of language, mathematical texts may not clearly distinguish indeterminates from ordinary variables.
Polynomials
A polynomial in an indeterminate is an expression of the form , where the are called the coefficients of the polynomial. Two such polynomials are equal only if the corresponding coefficients are equal. In contrast, two polynomial functions in a variable may be equal or not at a particular value of .
For example, the functions
are equal when and not equal otherwise. But the two polynomials
are unequal, since 2 does not equal 5, and 3 does not equal 2. In fact,
does not hold unless and . This is because is not, and does not designate, a number.
The distinction is subtle, since a polynomial in can be changed to a function in by substitution
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https://en.wikipedia.org/wiki/Yakov%20Perelman
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Yakov Isidorovich Perelman (; – 16 March 1942) was a Russian Empire and Soviet science writer and author of many popular science books, including Physics Can Be Fun and Mathematics Can Be Fun (both translated from Russian into English).
Life and work
Perelman was born in 1882 in the town of Białystok, Russian Empire. He obtained the Diploma in Forestry from the Imperial Forestry Institute (Now Saint-Petersburg State Forestry University) in Saint Petersburg, in 1909. He was influenced by Ernst Mach and probably the Russian Machist Alexander Bogdanov in his pedagogical approach to popularising science. After the success of "Physics for Entertainment", Perelman set out to produce other books, in which he showed himself to be an imaginative populariser of science. Especially popular were "Arithmetic for entertainment", "Mechanics for entertainment", "Geometry for Entertainment", "Astronomy for entertainment", "Lively Mathematics", " Physics Everywhere", and "Tricks and Amusements".
His famous books on physics and astronomy were translated into various languages by the erstwhile Soviet Union.
The scientist Konstantin Tsiolkovsky thought highly of Perelman's talents and creative genius, writing of him in the preface of Interplanetary Journeys: "The author has long been known by his popular, witty and quite scientific works on physics, astronomy and mathematics, which are, moreover written in a marvelous language and are very readable."
Perelman has also authored a number of te
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https://en.wikipedia.org/wiki/Chicken%20wire%20%28chemistry%29
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In chemistry the term chicken wire is used in different contexts. Most of them relate to the similarity of the regular hexagonal (honeycomb-like) patterns found in certain chemical compounds to the mesh structure commonly seen in real chicken wire.
Examples
Polycyclic aromatic hydrocarbons
Polycyclic aromatic hydrocarbons or graphenes—including fullerenes, carbon nanotubes, and graphite—have a hexagonal structure that is often described as chicken wire-like.
Hexagonal molecular structures
A hexagonal structure that is often described as chicken wire-like can also be found in other types of chemical compounds such as:
Non-aromatic polycyclic hydrocarbons, e.g. steroids like cholesterol
Flat hexagonal hydrogen bonded trimesic acid (benzene-1,3,5-tricarboxylic acid), boric acid, or melamine-cyanuric acid complexes
Interwoven molecule chains in the inorganic polymer NaAuS
Complexes of the protein clathrin
Additional information
Bond line notation
The skeletal formula is a method to draw structural formulas of organic compounds where lines represent the chemical bonds and the vertices represent implicit carbon atoms. This notation is sometimes jestingly called chicken wire notation.
Placeholder for organic compounds
Chicken wire is sometimes used as a placeholder name for any organic compound, similar to the use of the name John Doe.
Chemical joke
It is an old joke in chemistry to draw a polycyclic hexagonal chemical structure and call this fictional compound ch
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https://en.wikipedia.org/wiki/Borel%27s%20lemma
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In mathematics, Borel's lemma, named after Émile Borel, is an important result used in the theory of asymptotic expansions and partial differential equations.
Statement
Suppose U is an open set in the Euclidean space Rn, and suppose that f0, f1, ... is a sequence of smooth functions on U.
If I is any open interval in R containing 0 (possibly I = R), then there exists a smooth function F(t, x) defined on I×U, such that
for k ≥ 0 and x in U.
Proof
Proofs of Borel's lemma can be found in many text books on analysis, including and , from which the proof below is taken.
Note that it suffices to prove the result for a small interval I = (−ε,ε), since if ψ(t) is a smooth bump function with compact support in (−ε,ε) equal identically to 1 near 0, then ψ(t) ⋅ F(t, x) gives a solution on R × U. Similarly using a smooth partition of unity on Rn subordinate to a covering by open balls with centres at δ⋅Zn, it can be assumed that all the fm have compact support in some fixed closed ball C. For each m, let
where εm is chosen sufficiently small that
for |α| < m. These estimates imply that each sum
is uniformly convergent and hence that
is a smooth function with
By construction
Note: Exactly the same construction can be applied, without the auxiliary space U, to produce a smooth function on the interval I for which the derivatives at 0 form an arbitrary sequence.
See also
References
Partial differential equations
Lemmas in analysis
Asymptotic analysis
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https://en.wikipedia.org/wiki/Riemann%E2%80%93Lebesgue%20lemma
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In mathematics, the Riemann–Lebesgue lemma, named after Bernhard Riemann and Henri Lebesgue, states that the Fourier transform or Laplace transform of an L1 function vanishes at infinity. It is of importance in harmonic analysis and asymptotic analysis.
Statement
Let be an integrable function, i.e. is a measurable function such that
and let be the Fourier transform of , i.e.
Then vanishes at infinity: as .
Because the Fourier transform of an integrable function is continuous, the Fourier transform is a continuous function vanishing at infinity. If denotes the vector space of continuous functions vanishing at infinity, the Riemann–Lebesgue lemma may be formulated as follows: The Fourier transformation maps to .
Proof
We will focus on the one-dimensional case , the proof in higher dimensions is similar. First, suppose that is continuous and compactly supported. For , the substitution leads to
.
This gives a second formula for . Taking the mean of both formulas, we arrive at the following estimate:
.
Because is continuous, converges to as for all . Thus, converges to 0 as due to the dominated convergence theorem.
If is an arbitrary integrable function, it may be approximated in the norm by a compactly supported continuous function. For , pick a compactly supported continuous function such that . Then
Because this holds for any , it follows that as .
Other versions
The Riemann–Lebesgue lemma holds in a variety of other situations.
If , then the Rie
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https://en.wikipedia.org/wiki/Dirichlet%E2%80%93Jordan%20test
|
In mathematics, the Dirichlet–Jordan test gives sufficient conditions for a real-valued, periodic function f to be equal to the sum of its Fourier series at a point of continuity. Moreover, the behavior of the Fourier series at points of discontinuity is determined as well (it is the midpoint of the values of the discontinuity). It is one of many conditions for the convergence of Fourier series.
The original test was established by Peter Gustav Lejeune Dirichlet in 1829, for piecewise monotone functions. It was extended in the late 19th century by Camille Jordan to functions of bounded variation (any function of bounded variation is the difference of two increasing functions).
Dirichlet–Jordan test for Fourier series
The Dirichlet–Jordan test states that if a periodic function is of bounded variation on a period, then the Fourier series converges, as , at each point of the domain to
In particular, if is continuous at , then the Fourier series converges to . Moreover, if is continuous everywhere, then the convergence is uniform.
Stated in terms of a periodic function of period 2π, the Fourier series coefficients are defined as
and the partial sums of the Fourier series are
The analogous statement holds irrespective of what the period of f is, or which version of the Fourier series is chosen.
There is also a pointwise version of the test: if is a periodic function in , and is of bounded variation in a neighborhood of , then the Fourier series at converges to the li
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https://en.wikipedia.org/wiki/Progressive%20function
|
In mathematics, a progressive function ƒ ∈ L2(R) is a function whose Fourier transform is supported by positive frequencies only:
It is called super regressive if and only if the time reversed function f(−t) is progressive, or equivalently, if
The complex conjugate of a progressive function is regressive, and vice versa.
The space of progressive functions is sometimes denoted , which is known as the Hardy space of the upper half-plane. This is because a progressive function has the Fourier inversion formula
and hence extends to a holomorphic function on the upper half-plane
by the formula
Conversely, every holomorphic function on the upper half-plane which is uniformly square-integrable on every horizontal line
will arise in this manner.
Regressive functions are similarly associated with the Hardy space on the lower half-plane .
Hardy spaces
Types of functions
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https://en.wikipedia.org/wiki/Fixed-point%20space
|
In mathematics, a Hausdorff space X is called a fixed-point space if every continuous function has a fixed point.
For example, any closed interval [a,b] in is a fixed point space, and it can be proved from the intermediate value property of real continuous function. The open interval (a, b), however, is not a fixed point space. To see it, consider the function
, for example.
Any linearly ordered space that is connected and has a top and a bottom element is a fixed point space.
Note that, in the definition, we could easily have disposed of the condition that the space is Hausdorff.
References
Vasile I. Istratescu, Fixed Point Theory, An Introduction, D. Reidel, the Netherlands (1981).
Andrzej Granas and James Dugundji, Fixed Point Theory (2003) Springer-Verlag, New York,
William A. Kirk and Brailey Sims, Handbook of Metric Fixed Point Theory (2001), Kluwer Academic, London
Fixed points (mathematics)
Topology
Topological spaces
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https://en.wikipedia.org/wiki/Local%20property
|
In mathematics, a mathematical object is said to satisfy a property locally, if the property is satisfied on some limited, immediate portions of the object (e.g., on some sufficiently small or arbitrarily small neighborhoods of points).
Properties of a point on a function
Perhaps the best-known example of the idea of locality lies in the concept of local minimum (or local maximum), which is a point in a function whose functional value is the smallest (resp., largest) within an immediate neighborhood of points. This is to be contrasted with the idea of global minimum (or global maximum), which corresponds to the minimum (resp., maximum) of the function across its entire domain.
Properties of a single space
A topological space is sometimes said to exhibit a property locally, if the property is exhibited "near" each point in one of the following ways:
Each point has a neighborhood exhibiting the property;
Each point has a neighborhood base of sets exhibiting the property.
Here, note that condition (2) is for the most part stronger than condition (1), and that extra caution should be taken to distinguish between the two. For example, some variation in the definition of locally compact can arise as a result of the different choices of these conditions.
Examples
Locally compact topological spaces
Locally connected and Locally path-connected topological spaces
Locally Hausdorff, Locally regular, Locally normal etc...
Locally metrizable
Properties of a pair of spaces
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https://en.wikipedia.org/wiki/Zipping%20%28computer%20science%29
|
In computer science, zipping is a function which maps a tuple of sequences into a sequence of tuples. This name zip derives from the action of a zipper in that it interleaves two formerly disjoint sequences. The inverse function is unzip.
Example
Given the three words cat, fish and be where |cat| is 3, |fish| is 4 and |be| is 2. Let denote the length of the longest word which is fish; . The zip of cat, fish, be is then 4 tuples of elements:
where # is a symbol not in the original alphabet. In Haskell this truncates to the shortest sequence , where :
zip3 "cat" "fish" "be"
-- [('c','f','b'),('a','i','e')]
Definition
Let Σ be an alphabet, # a symbol not in Σ.
Let x1x2... x|x|, y1y2... y|y|, z1z2... z|z|, ... be n words (i.e. finite sequences) of elements of Σ. Let denote the length of the longest word, i.e. the maximum of |x|, |y|, |z|, ... .
The zip of these words is a finite sequence of n-tuples of elements of , i.e. an element of :
,
where for any index , the wi is #.
The zip of x, y, z, ... is denoted zip(x, y, z, ...) or x ⋆ y ⋆ z ⋆ ...
The inverse to zip is sometimes denoted unzip.
A variation of the zip operation is defined by:
where is the minimum length of the input words. It avoids the use of an adjoined element , but destroys information about elements of the input sequences beyond .
In programming languages
Zip functions are often available in programming languages, often referred to as . In Lisp-dialects one can simply the desired functi
|
https://en.wikipedia.org/wiki/IARC
|
IARC may refer to:
International Aerial Robotics Competition
International Age Rating Coalition
International Agency for Research on Cancer
International Arctic Research Center
Israel Amateur Radio Club
iArc, South Korean architecture firm
IAR Systems C/C++ compiler (IAR C)
See also
Indian Association for Research in Computing Science (IARCS)
|
https://en.wikipedia.org/wiki/Birkhoff%20interpolation
|
In mathematics, Birkhoff interpolation is an extension of polynomial interpolation. It refers to the problem of finding a polynomial of degree such that only certain derivatives have specified values at specified points:
where the data points and the nonnegative integers are given. It differs from Hermite interpolation in that it is possible to specify derivatives of at some points without specifying the lower derivatives or the polynomial itself. The name refers to George David Birkhoff, who first studied the problem in 1906.
Existence and uniqueness of solutions
In contrast to Lagrange interpolation and Hermite interpolation, a Birkhoff interpolation problem does not always have a unique solution. For instance, there is no quadratic polynomial such that and . On the other hand, the Birkhoff interpolation problem where the values of and are given always has a unique solution.
An important problem in the theory of Birkhoff interpolation is to classify those problems that have a unique solution. Schoenberg formulates the problem as follows. Let denote the number of conditions (as above) and let be the number of interpolation points. Given a matrix , all of whose entries are either or , such that exactly entries are , then the corresponding problem is to determine such that
The matrix is called the incidence matrix. For example, the incidence matrices for the interpolation problems mentioned in the previous paragraph are:
Now the question is: Does a Birkhof
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https://en.wikipedia.org/wiki/Nitroamine
|
In organic chemistry, nitroamines are organic compounds with the general chemical structure . They consist of a nitro group () bonded to an amine. The parent inorganic compound, where both R substituents are hydrogen, is nitramide, .
References
Functional groups
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https://en.wikipedia.org/wiki/Superadditivity
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In mathematics, a function is superadditive if
for all and in the domain of
Similarly, a sequence is called superadditive if it satisfies the inequality
for all and
The term "superadditive" is also applied to functions from a boolean algebra to the real numbers where such as lower probabilities.
Examples of superadditive functions
The map is a superadditive function for nonnegative real numbers because the square of is always greater than or equal to the square of plus the square of for nonnegative real numbers and :
The determinant is superadditive for nonnegative Hermitian matrix, that is, if are nonnegative Hermitian then This follows from the Minkowski determinant theorem, which more generally states that is superadditive (equivalently, concave) for nonnegative Hermitian matrices of size : If are nonnegative Hermitian then
Horst Alzer proved that Hadamard's gamma function is superadditive for all real numbers with
Mutual information
Properties
If is a superadditive function whose domain contains then To see this, take the inequality at the top: Hence
The negative of a superadditive function is subadditive.
Fekete's lemma
The major reason for the use of superadditive sequences is the following lemma due to Michael Fekete.
Lemma: (Fekete) For every superadditive sequence the limit is equal to the supremum (The limit may be positive infinity, as is the case with the sequence for example.)
The analogue of Fekete's lemma hold
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https://en.wikipedia.org/wiki/Hanbury%20Brown%20and%20Twiss%20effect
|
In physics, the Hanbury Brown and Twiss (HBT) effect is any of a variety of correlation and anti-correlation effects in the intensities received by two detectors from a beam of particles. HBT effects can generally be attributed to the wave–particle duality of the beam, and the results of a given experiment depend on whether the beam is composed of fermions or bosons. Devices which use the effect are commonly called intensity interferometers and were originally used in astronomy, although they are also heavily used in the field of quantum optics.
History
In 1954, Robert Hanbury Brown and Richard Q. Twiss introduced the intensity interferometer concept to radio astronomy for measuring the tiny angular size of stars, suggesting that it might work with visible light as well. Soon after they successfully tested that suggestion: in 1956 they published an in-lab experimental mockup using blue light from a mercury-vapor lamp, and later in the same year, they applied this technique to measuring the size of Sirius. In the latter experiment, two photomultiplier tubes, separated by a few meters, were aimed at the star using crude telescopes, and a correlation was observed between the two fluctuating intensities. Just as in the radio studies, the correlation dropped away as they increased the separation (though over meters, instead of kilometers), and they used this information to determine the apparent angular size of Sirius.
This result was met with much skepticism in the physics c
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https://en.wikipedia.org/wiki/Air%20shower%20%28physics%29
|
Air showers are extensive cascades of subatomic particles and ionized nuclei, produced in the atmosphere when a primary cosmic ray enters the atmosphere. When a particle of the cosmic radiation, which could be a proton, a nucleus, an electron, a photon, or (rarely) a positron, interacts with the nucleus of a molecule in the atmosphere, it produces a vast number of secondary particles, which make up the shower. In the first interactions of the cascade especially hadrons (mostly light mesons like pions and kaons) are produced and decay rapidly in the air, producing other particles and electromagnetic radiation, which are part of the shower components. Depending on the energy of the cosmic ray, the detectable size of the shower can reach several kilometers in diameter.
The absorbed ionizing radiation from cosmic radiation is largely from muons, neutrons, and electrons, with a dose rate that varies in different parts of the world and is based largely on the geomagnetic field, altitude, and solar cycle. Airline crews are exposed to more radiation from cosmic rays if they routinely work flight routes that take them close to the North or South pole at high altitudes, where the shielding by the geomagnetic field is minimal.
The air shower phenomenon was unknowingly discovered by Bruno Rossi in 1933 in a laboratory experiment. In 1937 Pierre Auger, unaware of Rossi's earlier report, detected the same phenomenon and investigated it in some detail. He concluded that cosmic-ray particl
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https://en.wikipedia.org/wiki/Developmental%20Studies%20Hybridoma%20Bank
|
The Developmental Studies Hybridoma Bank (DSHB) is a National Resource established by the National Institutes of Health (NIH) in 1986 to bank and distribute at cost hybridomas and the monoclonal antibodies (mAbs) they produce to the basic science community worldwide. It is housed in the Department of Biology at the University of Iowa.
Mission
The mission of the DSHB is four-fold:
Keep product prices low to facilitate research (currently 40.00 USD per ml of supernatant).
Serve as a repository to relieve scientists of the time and expense of distributing hybridomas and the mAbs they produce.
Assure the scientific community that mAbs with limited demand remain available.
Maintain the highest product quality, provide prompt customer service and technical assistance.
Description
The DSHB is directed by David R. Soll at the University of Iowa. There are currently over 5000 hybridomas in the DSHB collection. The DSHB has obtained hybridomas from a variety of individuals and institutions, the latter including the Muscular Dystrophy Association, the National Cancer Institute, the NIH Common Fund, and the European Molecular Biology Laboratory (EMBL). The DSHB eagerly awaits new contributions. First time customers must agree to the DSHB terms of usage that products will be used for research purposes only, and that they cannot be commercialized or distributed to a third party. Researchers also agree to acknowledge both the DSHB and the contributing investigator and institution in p
|
https://en.wikipedia.org/wiki/Plateau%20%28mathematics%29
|
A plateau of a function is a part of its domain where the function has constant value.
More formally, let U, V be topological spaces. A plateau for a function f: U → V is a path-connected set of points P of U such that for some y we have
f (p) = y
for all p in P.
Examples
Plateaus can be observed in mathematical models as well as natural systems. In nature, plateaus can be observed in physical, chemical and biological systems. An example of an observed plateau in the natural world is in the tabulation of biodiversity of life through time.
See also
Level set
Contour line
Minimal surface
References
Topology
|
https://en.wikipedia.org/wiki/Lindel%C3%B6f%20hypothesis
|
In mathematics, the Lindelöf hypothesis is a conjecture by Finnish mathematician Ernst Leonard Lindelöf (see ) about the rate of growth of the Riemann zeta function on the critical line. This hypothesis is implied by the Riemann hypothesis. It says that for any ε > 0,
as t tends to infinity (see big O notation). Since ε can be replaced by a smaller value, the conjecture can be restated as follows: for any positive ε,
The μ function
If σ is real, then μ(σ) is defined to be the infimum of all real numbers a such that ζ(σ + iT ) = O(T a). It is trivial to check that μ(σ) = 0 for σ > 1, and the functional equation of the zeta function implies that μ(σ) = μ(1 − σ) − σ + 1/2. The Phragmén–Lindelöf theorem implies that μ is a convex function. The Lindelöf hypothesis states μ(1/2) = 0, which together with the above properties of μ implies that μ(σ) is 0 for σ ≥ 1/2 and 1/2 − σ for σ ≤ 1/2.
Lindelöf's convexity result together with μ(1) = 0 and μ(0) = 1/2 implies that 0 ≤ μ(1/2) ≤ 1/4. The upper bound of 1/4 was lowered by Hardy and Littlewood to 1/6 by applying Weyl's method of estimating exponential sums to the approximate functional equation. It has since been lowered to slightly less than 1/6 by several authors using long and technical proofs, as in the following table:
Relation to the Riemann hypothesis
(1918–1919) showed that the Lindelöf hypothesis is equivalent to the following statement about the zeros of the zeta function: for every ε > 0, the number of zeros with rea
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https://en.wikipedia.org/wiki/Alfred%20Gray%20%28mathematician%29
|
Alfred Gray (October 22, 1939 – October 27, 1998) was an American mathematician whose main research interests were in differential geometry. He also made contributions in the fields of complex variables and differential equations.
Short biography
Alfred Gray was born in Dallas, Texas to Alfred James Gray & Eloise Evans and studied mathematics at the University of Kansas.
He received a Ph.D. from the University of California, Los Angeles in 1964 and spent four years at University of California, Berkeley.
From 1970–1998 he was a professor at the University of Maryland, College Park.
He died in Bilbao, Spain of a heart attack while working with students in a computer lab at Colegio Mayor Miguel de Unamuno around 4 AM, on October 27, 1998.
Mathematical contributions
In the broad area of differential geometry, he made specific contributions in classifying various types of geometrical structures, such as (Kähler manifolds and almost Hermitian manifolds).
Gray introduced the concept of a nearly Kähler manifold, gave topological obstructions to the existence of geometrical structures, made several contributions in the computation of the volume of tubes and balls, curvature identities, etc.
He published a book on tubes and is the author of two textbooks and over one hundred scientific articles.
His books were translated into Spanish, Italian, Russian and German.
He was a pioneer in the use of computer graphics in teaching differential geometry (particularly the geometry of cu
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https://en.wikipedia.org/wiki/Allee%20effect
|
The Allee effect is a phenomenon in biology characterized by a correlation between population size or density and the mean individual fitness (often measured as per capita population growth rate) of a population or species.
History and background
Although the concept of Allee effect had no title at the time, it was first described in the 1930s by its namesake, Warder Clyde Allee. Through experimental studies, Allee was able to demonstrate that goldfish have a greater survival rate when there are more individuals within the tank. This led him to conclude that aggregation can improve the survival rate of individuals, and that cooperation may be crucial in the overall evolution of social structure. The term "Allee principle" was introduced in the 1950s, a time when the field of ecology was heavily focused on the role of competition among and within species. The classical view of population dynamics stated that due to competition for resources, a population will experience a reduced overall growth rate at higher density and increased growth rate at lower density. In other words, individuals in a population would be better off when there are fewer individuals around due to a limited amount of resources (see logistic growth). However, the concept of the Allee effect introduced the idea that the reverse holds true when the population density is low. Individuals within a species often require the assistance of another individual for more than simple reproductive reasons in order to
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https://en.wikipedia.org/wiki/Swizzling
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Swizzling may refer to:
Pointer swizzling – a computer science term.
Swizzling (computer graphics) – a computer graphics term.
Method swizzling
Texture swizzling – in computer graphics, a way to store texture maps while respecting locality of reference.
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https://en.wikipedia.org/wiki/Swizzle
|
Swizzle or swizzling may refer to:
Human movement
Swizzle (acro dance), a type of movement for two people in acro dance
Swizzle (figure skating), a type of movement in figure skating
Computer science
Swizzling (computer graphics), a method of rearranging the elements of a vector
Pointer swizzling, the manipulation of object references
Other uses
Swizzle stick, a device used for stirring drinks
Rum Swizzle, a type of cocktail
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https://en.wikipedia.org/wiki/Pointer%20swizzling
|
In computer science, pointer swizzling is the conversion of references based on name or position into direct pointer references (memory addresses). It is typically performed during deserialization or loading of a relocatable object from a disk file, such as an executable file or pointer-based data structure.
The reverse operation, replacing memory pointers with position-independent symbols or positions, is sometimes referred to as unswizzling, and is performed during serialization (saving).
Example
It is easy to create a linked list data structure using elements like this:
struct node {
int data;
struct node *next;
};
But saving the list to a file and then reloading it will (on most operating systems) break every link and render the list useless because the nodes will almost never be loaded into the same memory locations. One way to usefully save and retrieve the list is to assign a unique id number to each node and then unswizzle the pointers by turning them into a field indicating the id number of the next node:
struct node_saved {
int data;
int id_number;
int id_number_of_next_node;
};
Records like these can be saved to a file in any order and reloaded without breaking the list. Other options include saving the file offset of the next node or a number indicating its position in the sequence of saved records, or simply saving the nodes in-order to the file.
After loading such a list, finding a node based on its number is cumber
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https://en.wikipedia.org/wiki/General%20Atomics
|
General Atomics (GA) is an American energy and defense corporation headquartered in San Diego, California, specializing in research and technology development. This includes physics research in support of nuclear fission and nuclear fusion energy. The company also provides research and manufacturing services for remotely operated surveillance aircraft, including the Predator drones, airborne sensors, and advanced electric, electronic, wireless, and laser technologies.
History
General Atomics was founded on July 18, 1955, in San Diego, California, by Frederic de Hoffmann with assistance from notable physicists Edward Teller and Freeman Dyson. Originally the company was part of the General Atomic division of General Dynamics "for harnessing the power of nuclear technologies for the benefit of mankind".
GA's first offices were in the General Dynamics facility on Hancock Street in San Diego. GA also used a schoolhouse on San Diego's Barnard Street as its temporary headquarters, which it would later "adopt" as part of its Education Outreach program. In 1956, San Diego voters approved the transfer of land to GA for permanent facilities in Torrey Pines, and the John Jay Hopkins Laboratory for Pure and Applied Science was formally dedicated there on June 25, 1959. The Torrey Pines facility continues to serve as the company's headquarters today.
General Atomics's initial projects were the TRIGA nuclear research reactor, which was designed so that it was guaranteed to be safe by th
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https://en.wikipedia.org/wiki/Invariance%20theorem
|
Invariance theorem may refer to:
Invariance of domain, a theorem in topology
A theorem pertaining to Kolmogorov complexity
A result in classical mechanics for adiabatic invariants
A theorem of algorithmic probability
See also
Invariant (mathematics)
|
https://en.wikipedia.org/wiki/David%20C.%20Queller
|
David C. Queller is an evolutionary biologist at Washington University in St. Louis. He received his BA from The University of Illinois in 1976, and his PhD from the University of Michigan in 1982. Queller became a faculty member at Rice University in 1989 and remained there until 2011 when he was named Spencer T. Olin Professor of Biology at Washington University in St. Louis. Since the late 1980s, Queller has collaborated extensively with his wife and colleague Joan E. Strassmann. Empirically, Queller and Strassmann worked primarily with social insects until they made the switch to the social amoebae, Dictyostelium discoideum, in 1998.
Honors
Fellow, American Association for the Advancement of Science, 2004
Fellow, American Academy of Arts and Sciences, 2008
References
External links
David C. Queller Washington University Website
Strassmann / Queller Lab website
Evolutionary biologists
University of Illinois alumni
University of Michigan alumni
Rice University faculty
Living people
Year of birth missing (living people)
20th-century American biologists
21st-century American biologists
Washington University in St. Louis faculty
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https://en.wikipedia.org/wiki/Joan%20E.%20Strassmann
|
Joan E. Strassmann is a North American evolutionary biologist and the Charles Rebstock Professor of Biology at the Washington University in St. Louis. She is known for her work on social evolution and particularly how cooperation prospers in the face of evolutionary conflicts.
Her dissertation research explored theories of social behavior and evolution using individually marked social wasps in wild colonies. In 2011, Strassmann joined the Biology Department of Washington University in St. Louis. after leaving Rice University where she worked for the previous 31 years. Strassman earned a bachelor's degree in zoology from the University of Michigan and a Ph.D. in zoology from the University of Texas.
She is a member of the National Academy of Sciences (2013). She has received a John Simon Guggenheim Memorial Fellowship (2004), was elected a Fellow of the Animal Behavior Society (2002), the American Association for the Advancement of Science (2004), and the American Academy of Arts and Sciences (2008), and served as president of the Animal Behavior Society (2012).
Dr. Strassmann has a blog where she shares her beliefs on teaching, learning, and science. She believes that Wikipedia is a good resource for learning and teaching. Dr. Strassmann has also addressed the need for diversity among academicians.
Honors
Fellow, Animal Behavior Society, 2002
Fellow, American Association for the Advancement of Science, 2004
Fellow, American Academy of Arts and Sciences, 2008
Member, Nati
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https://en.wikipedia.org/wiki/Computational%20indistinguishability
|
In computational complexity and cryptography, two families of distributions are computationally indistinguishable if no efficient algorithm can tell the difference between them except with negligible probability.
Formal definition
Let and be two distribution ensembles indexed by a security parameter n (which usually refers to the length of the input); we say they are computationally indistinguishable if for any non-uniform probabilistic polynomial time algorithm A, the following quantity is a negligible function in n:
denoted . In other words, every efficient algorithm As behavior does not significantly change when given samples according to Dn or En in the limit as . Another interpretation of computational indistinguishability, is that polynomial-time algorithms actively trying to distinguish between the two ensembles cannot do so: that any such algorithm will only perform negligibly better than if one were to just guess.
Related notions
Implicit in the definition is the condition that the algorithm, , must decide based on a single sample from one of the distributions. One might conceive of a situation in which the algorithm trying to distinguish between two distributions, could access as many samples as it needed. Hence two ensembles that cannot be distinguished by polynomial-time algorithms looking at multiple samples are deemed indistinguishable by polynomial-time sampling'. If the polynomial-time algorithm can generate samples in polynomial time, or has access to
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https://en.wikipedia.org/wiki/The%20Man%20Who%20Counted
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The Man Who Counted (original Portuguese title: O Homem que Calculava) is a book on recreational mathematics and curious word problems by Brazilian writer Júlio César de Mello e Souza, published under the pen name Malba Tahan. Since its first publication in 1938, the book has been immensely popular in Brazil and abroad, not only among mathematics teachers but among the general public as well.
The book has been published in many other languages, including Catalan, English (in the UK and in the US), German, Italian, and Spanish, and is recommended as a paradidactic source in many countries. It earned its author a prize from the Brazilian Literary Academy.
Plot summary
First published in Brazil in 1949, O Homem que Calculava is a series of tales in the style of the Arabian Nights, but revolving around mathematical puzzles and curiosities. The book is ostensibly a translation by Brazilian scholar Breno de Alencar Bianco of an original manuscript by Malba Tahan, a thirteenth-century Persian scholar of the Islamic Empire – both equally fictitious.
The first two chapters tell how Hanak Tade Maia was traveling from Samarra to Baghdad when he met Beremiz Samir, a young lad from Khoy with amazing mathematical abilities. The traveler then invited Beremiz to come with him to Baghdad, where a man with his abilities will certainly find profitable employment. The rest of the book tells of various incidents that befell the two men along the road and in Baghdad. In all those events, Ber
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https://en.wikipedia.org/wiki/Top%20quark%20condensate
|
In particle physics, the top quark condensate theory (or top condensation) is an alternative to the Standard Model fundamental Higgs field, where the Higgs boson is a composite field, composed of the top quark and its antiquark.
The top quark-antiquark pairs are bound together by a new force called topcolor, analogous to the binding of Cooper pairs in a BCS superconductor, or mesons in the strong interactions. The top quark is very heavy, with a measured mass of approximately 174 GeV (comparable to the electroweak scale), and so its Yukawa coupling is of order unity, suggesting the possibility of strong coupling dynamics at high energy scales. This model attempts to explain how the electroweak scale may match the top quark mass.
History
The idea was described by Yoichiro Nambu and subsequently developed by Miransky, Tanabashi, and Yamawaki (1989) and Bardeen, Hill, and Lindner (1990), who connected the theory to the renormalization group, and improved its predictions.
The renormalization group reveals that top quark condensation is fundamentally based upon the ‘infrared fixed point’ for the top quark Higgs-Yukawa coupling, proposed by Pendleton and Ross (1981). and Hill,
The ‘infrared’ fixed point originally predicted that the top quark would be heavy, contrary to the prevailing view of the early 1980s. Indeed, the top quark was discovered in 1995 at the large mass of 174 GeV. The infrared-fixed point implies that it is strongly coupled to the Higgs boson at very high energ
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https://en.wikipedia.org/wiki/Variational%20inequality
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In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set. The mathematical theory of variational inequalities was initially developed to deal with equilibrium problems, precisely the Signorini problem: in that model problem, the functional involved was obtained as the first variation of the involved potential energy. Therefore, it has a variational origin, recalled by the name of the general abstract problem. The applicability of the theory has since been expanded to include problems from economics, finance, optimization and game theory.
History
The first problem involving a variational inequality was the Signorini problem, posed by Antonio Signorini in 1959 and solved by Gaetano Fichera in 1963, according to the references and : the first papers of the theory were and , . Later on, Guido Stampacchia proved his generalization to the Lax–Milgram theorem in in order to study the regularity problem for partial differential equations and coined the name "variational inequality" for all the problems involving inequalities of this kind. Georges Duvaut encouraged his graduate students to study and expand on Fichera's work, after attending a conference in Brixen on 1965 where Fichera presented his study of the Signorini problem, as reports: thus the theory become widely known throughout France. Also in 1965, Stampacchia and Jacques-Louis Lions extended
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https://en.wikipedia.org/wiki/Riesz%20function
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In mathematics, the Riesz function is an entire function defined by Marcel Riesz in connection with the Riemann hypothesis, by means of the power series
If we set we may define it in terms of the coefficients of the Laurent series development of the hyperbolic (or equivalently, the ordinary) cotangent around zero. If
then F may be defined as
The values of ζ(2k) approach one for increasing k, and comparing the series for the Riesz function with that for shows that it defines an entire function. Alternatively, F may be defined as
denotes the rising factorial power in the notation of D. E. Knuth and the number Bn are the Bernoulli number. The series is one of alternating terms and the function quickly tends to minus infinity for increasingly negative values of x. Positive values of x are more interesting and delicate.
Riesz criterion
It can be shown that
for any exponent e larger than 1/2, where this is big O notation; taking values both positive and negative. Riesz showed that the Riemann hypothesis is equivalent to the claim that the above is true for any e larger than 1/4. In the same paper, he added a slightly pessimistic note too: «Je ne sais pas encore decider si cette condition facilitera la vérification de l'hypothèse» ("I do not know how to decide if this condition will facilitate the verification of the hypothesis").
Mellin transform of the Riesz function
The Riesz function is related to the Riemann zeta function via its Mellin transform. If we take
we see t
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https://en.wikipedia.org/wiki/Braided%20monoidal%20category
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In mathematics, a commutativity constraint on a monoidal category is a choice of isomorphism for each pair of objects A and B which form a "natural family." In particular, to have a commutativity constraint, one must have for all pairs of objects .
A braided monoidal category is a monoidal category equipped with a braiding—that is, a commutativity constraint that satisfies axioms including the hexagon identities defined below. The term braided references the fact that the braid group plays an important role in the theory of braided monoidal categories. Partly for this reason, braided monoidal categories and other topics are related in the theory of knot invariants.
Alternatively, a braided monoidal category can be seen as a tricategory with one 0-cell and one 1-cell.
Braided monoidal categories were introduced by André Joyal and Ross Street in a 1986 preprint. A modified version of this paper was published in 1993.
The hexagon identities
For along with the commutativity constraint to be called a braided monoidal category, the following hexagonal diagrams must commute for all objects . Here is the associativity isomorphism coming from the monoidal structure on :
Properties
Coherence
It can be shown that the natural isomorphism along with the maps coming from the monoidal structure on the category , satisfy various coherence conditions, which state that various compositions of structure maps are equal. In particular:
The braiding commutes with the units
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https://en.wikipedia.org/wiki/Pierre%20Cartier%20%28mathematician%29
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Pierre Émile Cartier (born 10 June 1932) is a French mathematician. An associate of the Bourbaki group and at one time a colleague of Alexander Grothendieck, his interests have ranged over algebraic geometry, representation theory, mathematical physics, and category theory.
He studied at the École Normale Supérieure in Paris under Henri Cartan and André Weil. Since his 1958 thesis on algebraic geometry he has worked in a number of fields. He is known for the introduction of the Cartier operator in algebraic geometry in characteristic p, and for work on duality of abelian varieties and on formal groups. He is the eponym of Cartier divisors and Cartier duality.
From 1961 to 1971 he was a professor at the University of Strasbourg. In 1970 he was an Invited Speaker at the International Congress of Mathematicians in Nice. He was awarded the 1978 Prize Ampère of the French Academy of Sciences. In 2012 he became a fellow of the American Mathematical Society.
Publications
(1st edition 1969)
(1st edition 1992)
Freedom in Mathematics, Springer India, 2016 (with Cédric Villani, Jean Dhombres, Gerhard Heinzmann), .
Translation from the French language edition: Mathématiques en liberté, La Ville Brûle, Montreuil 2012, .
Pierre Cartier: Alexander Grothendieck. A country known only by name. Notices AMS, vol. 62, 2015, no. 4, pp. 373–382, PDF.
as editor
(1st edition 1990)
See also
Cotangent complex
Dieudonné module
MacMahon's master theorem
References
External links
Car
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https://en.wikipedia.org/wiki/Root%20test
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In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series. It depends on the quantity
where are the terms of the series, and states that the series converges absolutely if this quantity is less than one, but diverges if it is greater than one. It is particularly useful in connection with power series.
Root test explanation
The root test was developed first by Augustin-Louis Cauchy who published it in his textbook Cours d'analyse (1821). Thus, it is sometimes known as the Cauchy root test or Cauchy's radical test. For a series
the root test uses the number
where "lim sup" denotes the limit superior, possibly +∞. Note that if
converges then it equals C and may be used in the root test instead.
The root test states that:
if C < 1 then the series converges absolutely,
if C > 1 then the series diverges,
if C = 1 and the limit approaches strictly from above then the series diverges,
otherwise the test is inconclusive (the series may diverge, converge absolutely or converge conditionally).
There are some series for which C = 1 and the series converges, e.g. , and there are others for which C = 1 and the series diverges, e.g. .
Application to power series
This test can be used with a power series
where the coefficients cn, and the center p are complex numbers and the argument z is a complex variable.
The terms of this series would then be given by an = cn(z − p)n. One then applies the root test to the an as above.
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https://en.wikipedia.org/wiki/Nome%20%28mathematics%29
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In mathematics, specifically the theory of elliptic functions, the nome is a special function that belongs to the non-elementary functions. This function is of great importance in the description of the elliptic functions, especially in the description of the modular identity of the Jacobi theta function, the Hermite elliptic transcendents and the Weber modular functions, that are used for solving equations of higher degrees.
Definition
The nome function is given by
where and are the quarter periods, and and are the fundamental pair of periods, and is the half-period ratio. The nome can be taken to be a function of any one of these quantities; conversely, any one of these quantities can be taken as functions of the nome. Each of them uniquely determines the others when . That is, when , the mappings between these various symbols are both 1-to-1 and onto, and so can be inverted: the quarter periods, the half-periods and the half-period ratio can be explicitly written as functions of the nome. For general with , is not a single-valued function of . Explicit expressions for the quarter periods, in terms of the nome, are given in the linked article.
Notationally, the quarter periods and are usually used only in the context of the Jacobian elliptic functions, whereas the half-periods and are usually used only in the context of Weierstrass elliptic functions. Some authors, notably Apostol, use and to denote whole periods rather than half-periods.
The nome is freq
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https://en.wikipedia.org/wiki/Quarter%20period
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In mathematics, the quarter periods K(m) and iK ′(m) are special functions that appear in the theory of elliptic functions.
The quarter periods K and iK ′ are given by
and
When m is a real number, 0 < m < 1, then both K and K ′ are real numbers. By convention, K is called the real quarter period and iK ′ is called the imaginary quarter period. Any one of the numbers m, K, K ′, or K ′/K uniquely determines the others.
These functions appear in the theory of Jacobian elliptic functions; they are called quarter periods because the elliptic functions and are periodic functions with periods and However, the function is also periodic with a smaller period (in terms of the absolute value) than , namely .
Notation
The quarter periods are essentially the elliptic integral of the first kind, by making the substitution . In this case, one writes instead of , understanding the difference between the two depends notationally on whether or is used. This notational difference has spawned a terminology to go with it:
is called the parameter
is called the complementary parameter
is called the elliptic modulus
is called the complementary elliptic modulus, where
the modular angle, where
the complementary modular angle. Note that
The elliptic modulus can be expressed in terms of the quarter periods as
and
where and are Jacobian elliptic functions.
The nome is given by
The complementary nome is given by
The real quarter period can be expressed as a Lamb
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https://en.wikipedia.org/wiki/Kraft%E2%80%93McMillan%20inequality
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In coding theory, the Kraft–McMillan inequality gives a necessary and sufficient condition for the existence of a prefix code (in Leon G. Kraft's version) or a uniquely decodable code (in Brockway McMillan's version) for a given set of codeword lengths. Its applications to prefix codes and trees often find use in computer science and information theory.
Kraft's inequality was published in . However, Kraft's paper discusses only prefix codes, and attributes the analysis leading to the inequality to Raymond Redheffer. The result was independently discovered in . McMillan proves the result for the general case of uniquely decodable codes, and attributes the version for prefix codes to a spoken observation in 1955 by Joseph Leo Doob.
Applications and intuitions
Kraft's inequality limits the lengths of codewords in a prefix code: if one takes an exponential of the length of each valid codeword, the resulting set of values must look like a probability mass function, that is, it must have total measure less than or equal to one. Kraft's inequality can be thought of in terms of a constrained budget to be spent on codewords, with shorter codewords being more expensive. Among the useful properties following from the inequality are the following statements:
If Kraft's inequality holds with strict inequality, the code has some redundancy.
If Kraft's inequality holds with equality, the code in question is a complete code.
If Kraft's inequality does not hold, the code is not uniqu
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https://en.wikipedia.org/wiki/Rad%C3%B3%27s%20theorem%20%28harmonic%20functions%29
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See also Rado's theorem (Ramsey theory)
In mathematics, Radó's theorem is a result about harmonic functions, named after Tibor Radó. Informally, it says that any "nice looking" shape without holes can be smoothly deformed into a disk.
Suppose Ω is an open, connected and convex subset of the Euclidean space R2 with smooth boundary ∂Ω and suppose that D is the unit disk. Then, given any homeomorphism
μ : ∂D → ∂Ω, there exists a unique harmonic function u : D → Ω such that u = μ on ∂D and u is a diffeomorphism.
References
R. Schoen, S. T. Yau. (1997) Lectures on Harmonic Maps. International Press, Inc., Boston, Massachusetts. , page 4.
Theorems in harmonic analysis
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https://en.wikipedia.org/wiki/Search%20problem
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In the mathematics of computational complexity theory, computability theory, and decision theory, a search problem is a type of computational problem represented by a binary relation. Intuitively, the problem consists in finding structure "y" in object "x". An algorithm is said to solve the problem if at least one corresponding structure exists, and then one occurrence of this structure is made output; otherwise, the algorithm stops with an appropriate output ("not found" or any message of the like).
Every search problem also has a corresponding decision problem, namely
This definition may be generalized to n-ary relations using any suitable encoding which allows multiple strings to be compressed into one string (for instance by listing them consecutively with a delimiter).
More formally, a relation R can be viewed as a search problem, and a Turing machine which calculates R is also said to solve it. More formally, if R is a binary relation such that field(R) ⊆ Γ+ and T is a Turing machine, then T calculates R if:
If x is such that there is some y such that R(x, y) then T accepts x with output z such that R(x, z) (there may be multiple y, and T need only find one of them)
If x is such that there is no y such that R(x, y) then T rejects x
(Note that the graph of a partial function is a binary relation, and if T calculates a partial function then there is at most one possible output.)
Such problems occur very frequently in graph theory and combinatorial optimization, fo
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https://en.wikipedia.org/wiki/Petr%20Paucek
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Petr Paucek is a Czech-born biophysicist and biomedical researcher and an associate professor of biology at Portland State University.
Early life and education
Paucek attended the Academy of Science at Prague, where he obtained doctorates in biophysics and physiology, and later trained at the Medical College of Ohio (subsequently renamed The University of Toledo Health Science Campus) and the Oregon Health & Science University. He relocated from Oregon to Maine in 2005 to conduct research at the Thomas M. Teague Biotechnology Center in Fairfield.
Career
He has co-authored a number of frequently-cited articles in Circulation Research, the Journal of Biological Chemistry, and the American Journal of Physiology.
References
External links
Comprehensive CV
Personal website
American biophysicists
American people of Czech descent
Czechoslovak emigrants to the United States
Living people
Oregon Health & Science University alumni
Portland State University faculty
University of Toledo faculty
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Maximal%20subgroup
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In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra.
In group theory, a maximal subgroup H of a group G is a proper subgroup, such that no proper subgroup K contains H strictly. In other words, H is a maximal element of the partially ordered set of subgroups of G that are not equal to G. Maximal subgroups are of interest because of their direct connection with primitive permutation representations of G. They are also much studied for the purposes of finite group theory: see for example Frattini subgroup, the intersection of the maximal subgroups.
In semigroup theory, a maximal subgroup of a semigroup S is a subgroup (that is, a subsemigroup which forms a group under the semigroup operation) of S which is not properly contained in another subgroup of S. Notice that, here, there is no requirement that a maximal subgroup be proper, so if S is in fact a group then its unique maximal subgroup (as a semigroup) is S itself. Considering subgroups, and in particular maximal subgroups, of semigroups often allows one to apply group-theoretic techniques in semigroup theory. There is a one-to-one correspondence between idempotent elements of a semigroup and maximal subgroups of the semigroup: each idempotent element is the identity element of a unique maximal subgroup.
Existence of maximal subgroup
Any proper subgroup of a finite group is contained in some maximal subgroup, since the proper subgroups form a finite parti
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https://en.wikipedia.org/wiki/Enumerator
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Enumerator may refer to:
Iterator (computer science)
An enumerator in the context of iteratees
in computer programming, a value of an enumerated type
Enumerator (computer science), a Turing machine that lists elements of some set S.
a census taker, a person performing door-to-door around census, to count the people and gather demographic data.
a person employed in the counting of votes in an election.
Enumerator polynomial
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https://en.wikipedia.org/wiki/Pixar%20Image%20Computer
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The Pixar Image Computer is a graphics computer originally developed by the Graphics Group, the computer division of Lucasfilm, which was later renamed Pixar. Aimed at commercial and scientific high-end visualization markets, such as medicine, geophysics and meteorology, the original machine was advanced for its time, but sold poorly.
History
Creation
When George Lucas recruited people from NYIT in 1979 to start their Computer Division, the group was set to develop digital optical printing, digital audio, digital non-linear editing and computer graphics. Computer graphics quality was just not good enough due to technological limitations at the time. The team then decided to solve the problem by starting a hardware project, building what they would call the Pixar Image Computer, a machine with more computational power that was able to produce images with higher resolution.
Availability
About three months after their acquisition by Steve Jobs on February 3, 1986, the computer became commercially available for the first time, and was aimed at commercial and scientific high-end visualization markets, such as medical imaging, geophysics, and meteorology. The machine sold for $135,000, but also required a $35,000 workstation from Sun Microsystems or Silicon Graphics (in total, ). The original machine was well ahead of its time and generated many single sales, for labs and research. However, the system did not sell in quantity.
In 1987, Pixar redesigned the machine to create t
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https://en.wikipedia.org/wiki/Vinge
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Vinge is a surname shared by several notable people, among them being:
Joan D. Vinge (born 1948), an American science fiction author
Vernor Vinge (born 1944), a retired San Diego State University Professor of Mathematics, computer scientist, and science fiction author
See also
Ving (disambiguation)
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https://en.wikipedia.org/wiki/Animal%20embryonic%20development
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In developmental biology, animal embryonic development, also known as animal embryogenesis, is the developmental stage of an animal embryo. Embryonic development starts with the fertilization of an egg cell (ovum) by a sperm cell, (spermatozoon). Once fertilized, the ovum becomes a single diploid cell known as a zygote. The zygote undergoes mitotic divisions with no significant growth (a process known as cleavage) and cellular differentiation, leading to development of a multicellular embryo after passing through an organizational checkpoint during mid-embryogenesis. In mammals, the term refers chiefly to the early stages of prenatal development, whereas the terms fetus and fetal development describe later stages.
The main stages of animal embryonic development are as follows:
The zygote undergoes a series of cell divisions (called cleavage) to form a structure called a morula.
The morula develops into a structure called a blastula through a process called blastulation.
The blastula develops into a structure called a gastrula through a process called gastrulation.
The gastrula then undergoes further development, including the formation of organs (organogenesis).
The embryo then transforms into the next stage of development, the nature of which varies between different animal species (examples of possible next stages include a fetus and a larva).
Fertilization and the zygote
The egg cell is generally asymmetric, having an animal pole (future ectoderm).
It is covered w
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https://en.wikipedia.org/wiki/Concrete%20Roman
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Concrete Roman is a slab serif typeface designed by Donald Knuth using his METAFONT program. It was intended to accompany the Euler mathematical font which it partners in Knuth's book Concrete Mathematics. It has a darker appearance than its more famous sibling, Computer Modern. Some favour it for use on the computer screen because of this, as the thinner strokes of Computer Modern can make it hard to read at low resolutions.
External links
Computer Modern family, for general use select .otf fonts
Typefaces designed by Donald Knuth
Slab serif typefaces
TeX
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https://en.wikipedia.org/wiki/Alan%20Bond%20%28engineer%29
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Alan Bond (born 1944) is a British mechanical and aerospace engineer, who served as Managing Director of Reaction Engines Ltd and associated with Project Daedalus, Blue Streak missile, HOTOL, Reaction Engines Skylon and the Reaction Engines A2 hypersonic passenger aircraft.
Career
Alan Bond is an engineer, with a degree in Mechanical Engineering. He worked on liquid rocket engines, principally the RZ.2 (liquid oxygen / kerosene) and the RZ.20 (liquid oxygen / liquid hydrogen) at Rolls-Royce under the tutelage of Val Cleaver, and he was also involved with flight trials of the Blue Streak at Woomera.
He then worked for about 20 years at UK Atomic Energy Authority's Culham Laboratory on nuclear fusion, on the JET and RFX nuclear research projects. He was engaged in studies for the application of fusion to interplanetary space travel. He is the leading author of the report on the Project Daedalus interstellar, fusion powered starship concept, published by the British Interplanetary Society.
In the 1980s, he was one of the creators of the HOTOL space plane project, along with Dr. Bob Parkinson of British Aerospace. Alan Bond brought a precooled jet engine design he had invented to the HOTOL project, and this became the Rolls-Royce RB545 rocket engine.
In 1989, he formed Reaction Engines Limited (REL) with fellow rocket engineers, Richard Varvill and John Scott-Scott. REL is developing a single-stage orbital space plane Skylon, and other advanced vehicles including the Reacti
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https://en.wikipedia.org/wiki/Minkowski%27s%20question-mark%20function
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In mathematics, Minkowski's question-mark function, denoted , is a function with unusual fractal properties, defined by Hermann Minkowski in 1904. It maps quadratic irrational numbers to rational numbers on the unit interval, via an expression relating the continued fraction expansions of the quadratics to the binary expansions of the rationals, given by Arnaud Denjoy in 1938. It also maps rational numbers to dyadic rationals, as can be seen by a recursive definition closely related to the Stern–Brocot tree.
Definition and intuition
One way to define the question-mark function involves the correspondence between two different ways of representing fractional numbers using finite or infinite binary sequences. Most familiarly, a string of 0's and 1's with a single point mark ".", like "11.001001000011111..." can be interpreted as the binary representation of a number. In this case this number is
There is a different way of interpreting the same sequence, however, using continued fractions.
Interpreting the fractional part "0.001001000011111..." as a binary number in the same way, replace each consecutive block of 0's or 1's by its run length (or, for the first block of zeroes, its run length plus one), in this case generating the sequence . Then, use this sequence as the coefficients of a continued fraction:
The question-mark function reverses this process: it translates the continued-fraction of a given real number into a run-length encoded binary sequence, and then reinter
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https://en.wikipedia.org/wiki/Glossary%20of%20game%20theory
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Game theory is the branch of mathematics in which games are studied: that is, models describing human behaviour. This is a glossary of some terms of the subject.
Definitions of a game
Notational conventions
Real numbers .
The set of players .
Strategy space , where
Player i's strategy space is the space of all possible ways in which player i can play the game.
A strategy for player i
is an element of
.
Complements
an element of , is a tuple of strategies for all players other than i.
Outcome space is in most textbooks identical to -
Payoffs , describing how much gain (money, pleasure, etc.) the players are allocated by the end of the game.
Normal form game
A game in normal form is a function:
Given the tuple of strategies chosen by the players, one is given an allocation of payments (given as real numbers).
A further generalization can be achieved by splitting the game into a composition of two functions:
the outcome function of the game (some authors call this function "the game form"), and:
the allocation of payoffs (or preferences) to players, for each outcome of the game.
Extensive form game
This is given by a tree, where at each vertex of the tree a different player has the choice of choosing an edge. The outcome set of an extensive form game is usually the set of tree leaves.
Cooperative game
A game in which players are allowed to form coalitions (and to enforce coalitionary discipline). A cooperative game is given by stating a val
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https://en.wikipedia.org/wiki/Jacobi%20triple%20product
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In mathematics, the Jacobi triple product is the mathematical identity:
for complex numbers x and y, with |x| < 1 and y ≠ 0.
It was introduced by in his work Fundamenta Nova Theoriae Functionum Ellipticarum.
The Jacobi triple product identity is the Macdonald identity for the affine root system of type A1, and is the Weyl denominator formula for the corresponding affine Kac–Moody algebra.
Properties
The basis of Jacobi's proof relies on Euler's pentagonal number theorem, which is itself a specific case of the Jacobi Triple Product Identity.
Let and . Then we have
The Jacobi Triple Product also allows the Jacobi theta function to be written as an infinite product as follows:
Let and
Then the Jacobi theta function
can be written in the form
Using the Jacobi Triple Product Identity we can then write the theta function as the product
There are many different notations used to express the Jacobi triple product. It takes on a concise form when expressed in terms of q-Pochhammer symbols:
where is the infinite q-Pochhammer symbol.
It enjoys a particularly elegant form when expressed in terms of the Ramanujan theta function. For it can be written as
Proof
Let
Substituting for and multiplying the new terms out gives
Since is meromorphic for , it has a Laurent series
which satisfies
so that
and hence
Evaluating
Showing that is technical. One way is to set and show both the numerator and the denominator of
are weight 1/2 modular under , since t
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https://en.wikipedia.org/wiki/Don%20Kirkham
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Don Kirkham (February 11, 1908 – March 7, 1998) was an American soil scientist regarded as the founder of mathematical soil physics. His special interest was the flow of water through soils and drainage of agricultural land. He was awarded the 1983/4 Wolf Prize in Agriculture and the Robert E. Horton Medal in 1995.
Selected publications
References
External links
.
Don and Betty Kirkham soil physics award and Kirkham conferences, Soil Science Society of America.
1908 births
1998 deaths
American hydrologists
20th-century American physicists
Wolf Prize in Agriculture laureates
Fellows of the American Physical Society
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https://en.wikipedia.org/wiki/Wendell%20L.%20Roelofs
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Wendell L. Roelofs (born July 26, 1938) was the first researcher to characterize insect sex pheromone structures, developing microchemical techniques for the isolation and identification of pheromone components.
Education and career
Roelofs obtained his BS in chemistry in 1960 from Central College in Pella, Iowa and his PhD in organic chemistry from Indiana University in 1964. He is the Liberty Hyde Bailey Professor of Insect Biochemistry in the Department of Entomology at Cornell University in Ithaca, New York.
Award
Roelofs received the National Medal of Science from President Ronald Reagan in 1983.
References
(letter to the editor)
Sound recording, on side 2 of 1 cassette
External links
Roelofs homepage at Cornell University
1938 births
Living people
21st-century American chemists
Central College (Iowa) alumni
Cornell University faculty
Indiana University alumni
National Medal of Science laureates
People from Geneva, New York
People from Orange City, Iowa
Scientists from New York (state)
Wolf Prize in Agriculture laureates
Chemical ecologists
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https://en.wikipedia.org/wiki/Jay%20Laurence%20Lush
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Jay Laurence Lush (January 3, 1896 – May 22, 1982) was a pioneering animal geneticist who made important contributions to livestock breeding. He is sometimes known as the father of modern scientific animal breeding. Lush received National Medal of Science in 1968 and the Wolf Prize in 1979.
Lush was introduced to mathematics and genetics during his BSc studies of animal husbandry at the Kansas State Agricultural College (now Kansas State University). He completed his MSc in 1918 at Kansas State, and his PhD in genetics at the University of Wisconsin–Madison (1922).
Lush advocated breeding not based on subjective appearance of the animal, but on quantitative statistics and genetic information. Lush authored a classic textbook Animal Breeding Plans in 1937 which greatly influenced animal breeding around the world.
From 1930 to 1966, Lush was the Charles F. Curtiss Distinguished Professor in Agriculture at Iowa State University. He was elected to the United States National Academy of Sciences in 1967.
Lush won the Borden Award for research in dairy production from the American Dairy Science Association and both the Armour Award for animal breeding and genetics and the Morrison Award from the American Society of Animal Science. In 1979, he was awarded the Wolf Prize in Agriculture.
Bibliography
References
1896 births
1982 deaths
American geneticists
Iowa State University faculty
Kansas State University alumni
University of Wisconsin–Madison College of Agricultura
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https://en.wikipedia.org/wiki/Biligiriranga%20Hills
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The Biligirirangana Hills or Biligirirangan Hills (as referred to in biology and geology) is a hill range situated in south-western Karnataka, at its border with Tamil Nadu (Erode District) in South India. The area is called Biligiri Ranganatha Swamy Temple Wildlife Sanctuary or simply BRT Wildlife Sanctuary. It is a protected reserve under the Wildlife Protection Act of 1972. Being close to the Eastern Ghats as well as the Western Ghats, the sanctuary has floral and faunal associations with both regions. The site was declared a tiger reserve in January 2011 by the Government of Karnataka, a few months after approval from India's National Tiger Conservation Authority.
Location
The hills are located at the north-west of the Western Ghats and the westernmost edge of the Eastern Ghats. Thus this area supports a diverse flora and fauna in view of the various habitat types present. A wildlife sanctuary of was created around the temple on 27 June 1974, and enlarged to on 14 January 1987. The sanctuary derives its name Biligiri (white hill in Kannada) from the white rock face that constitutes the major hill crowned with the temple of Lord Ranganathaswamy (Lord Vishnu) or from the white mist and the silver clouds that cover these hills for a greater part of the year. An annual festival of Lord Vishnu, held in the month of April, draws pilgrims from far and wide. Once in two years, the Soliga Tribals present a 1-foot and 9 inches slipper, made of skin, to the deity in Biligirirang
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https://en.wikipedia.org/wiki/Peter%20Liese
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Peter Liese (born 20 May 1965) is a German physician and politician who has been serving as a Member of the European Parliament since 1994. He is a member of the Christian Democratic Union, part of the European People's Party.
Education
1991: Second state examination in medicine
1989-1992: Graduated as doctor at the Institute of Humane Genetics of the University of Bonn
Early career
until 1994: Ward doctor in Paderborn children's hospital
since 1994: Doctor in general practice and internist
Political career
Career in state politics
Former member of the Land executive of the Young Union, North Rhine-Westphalia
1991-1997: District Chairman of the Junge Union
Member of the Land executive of the CDU, North Rhine-Westphalia
1989-1994: Member of Bestwig local council
Member of the European Parliament, 1994–present
Liese sits on the European Parliament's Committee on the Environment, Public Health and Food Safety, where he serves as the European People's Party Group’s coordinator. In this capacity, he was responsible for writing reports on including aviation within the European Union Emission Trading Scheme (2007) and an ETS reform (2021). In 2020, he also joined the Special Committee on Beating Cancer.
Liese is a substitute for the Committee on Industry, Research and Energy, a member of the Delegation for relations with the countries of Central America and a substitute for the Delegation to the EU-Mexico Joint Parliamentary Committee. He was part of the Parliament's d
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https://en.wikipedia.org/wiki/ShmooCon
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ShmooCon is an American hacker convention organized by The Shmoo Group. There are typically 40 different talks and presentations on a variety of subjects related to computer security and cyberculture. Multiple events are held at the convention related to cryptography and computer security such as Shmooganography, Hack Fortress, a locksport village hosted by TOOOL DC, and Ghost in the Shellcode. ShmooCon 2021 was not held in January due to the COVID-19 pandemic. The next event is set for January 20-22, 2023
History
From 2005 to 2010, ShmooCon was held at the Marriott Wardman Park in Washington, D.C.
ShmooCon VII and VII (2011–2012) were held at the Washington Hilton in Washington, D.C.
ShmooCon IX was held at the Hyatt Regency Washington in Washington, D.C.
ShmooCon X and later returned to the Washington Hilton in Washington, D.C.
ShmooCon I: February 4–6, 2005: ≈ 400 attendees
ShmooCon II: January 13–15, 2006: ≈ 700 attendees
ShmooCon III: March 23–25, 2007: Sold out; > 900 attendees
ShmooCon IV: February 15–17, 2008: Sold out; > 1200 attendees
ShmooCon V: February 6–8, 2009: Sold out; > 1600 attendees
ShmooCon VI: February 5–7, 2010: Sold out; around 1600 attendees
ShmooCon VII: January 28–30, 2011: Sold out; > 1600 attendees
ShmooCon VIII: January 27–29, 2012: Sold out; > 1800 attendees
ShmooCon IX: February 15–17, 2013: Sold out; > 1600 attendees
ShmooCon X: January 17–19, 2014: Sold out; > 1900 attendees
ShmooCon XI: January 16–18, 2015: Sold out; > 1900
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https://en.wikipedia.org/wiki/Lancetfish
|
Lancetfishes are large oceanic predatory fishes in the genus Alepisaurus ("scaleless lizard") in the monogeneric family Alepisauridae.
Lancetfishes grow up to in length. Very little is known about their biology, though they are widely distributed in all oceans, except the polar seas. Specimens have been recorded as far north as Greenland. They are often caught as bycatch by vessels long-lining for tuna.
The generic name is from Greek a- meaning "without", meaning "scale", and sauros meaning "lizard".
Species
The two currently recognized extant species in this genus are:
Alepisaurus brevirostris Gibbs, 1960 (short-snouted lancetfish)
Alepisaurus ferox R. T. Lowe, 1833 (long-snouted lancetfish)
The anatomic difference between the two species is the shape of the snout, which is long and pointed in A. ferox, and slightly shorter in A. brevirostris. The long-snouted lancetfish is found in the tropical and northern sub-tropical waters of the Pacific ocean. The short-snouted lancetfish lives in the Atlantic ocean's tropics, subtropics, and southern sub-tropics of the Pacific ocean. A third recognized species, A. paronai D'Erasmo, 1923, is a fossil known from Middle Miocene-aged strata from Italy.
Description
Lancetfish possess a long and very high dorsal fin, soft-rayed from end to end, with an adipose fin behind it. The dorsal fin has 41 to 44 rays and occupies the greater length of the back. This fin is rounded in outline, about twice as high as the fish is deep, and can
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https://en.wikipedia.org/wiki/Flagship%20species
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In conservation biology, a flagship species is a species chosen to raise support for biodiversity conservation in a given place or social context. Definitions have varied, but they have tended to focus on the strategic goals and the socio-economic nature of the concept, to support the marketing of a conservation effort. The species need to be popular, to work as symbols or icons, and to stimulate people to provide money or support.
Species selected since the idea was developed in 1980s include widely recognised and charismatic species like the black rhinoceros, the Bengal tiger, and the Asian elephant. Some species such as the Chesapeake blue crab and the Pemba flying fox, the former of which is locally significant to Northern America, have suited a cultural and social context.
Utilizing a flagship species has limitations. It can skew management and conservation priorities, which may conflict. Stakeholders may be negatively affected if the flagship species is lost. The use of a flagship may have limited effect, and the approach may not protect the species from extinction: all of the top ten charismatic groups of animal, including tigers, lions, elephants and giraffes, are endangered.
Definitions
The term flagship is linked to the metaphor of representation. In its popular usage, flagships are viewed as ambassadors or icons for a conservation project or movement. The geographer Maan Barua noted that metaphors influence what people understand and how they act; that mammal
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https://en.wikipedia.org/wiki/Nikos%20Vakalis
|
Nikos Vakalis (December 1939 – 23 March 2017) was a Member of the European Parliament (MEP) from 2004 to 2009.
Biography
He studied Physics with a scholarship at the Aristotle University of Thessaloniki. He served as a reservist officer (head of Faculty) in the Artillery. He founded the Frontistirio Vakalis in 1967. After studying the British educational system he founded in 1972 the College of Advance Education collaborating with the British examining bodies Cambridge, AEB and JMB.
In 1999 he extended his activities founding the publishing house Publications Vakali. He also entered the market of Information Technology with the founding of the training company e-master, and the company executive training market with the founding of the Business Training Centre.
He wrote and published the books "About Friction", "Mechanics", "Electricity" and "Thermodynamics" and many collections of exercises.
He was married to Helen Mpousiou and had two sons, Andonis who is 38 (Bachelor and Master in Finance from the University of London, England. Master in Educational Management from the Institute of Education, University of London, England) and Manolis who is 33 (Bachelor in Information Technology from the University of Sussex, England).
Trade-union and Political activities
He was:
Chairman of Students of Physics of the Aristotle University of Thessaloniki.
A founding member of New Democracy, Thessaloniki
General Secretary of the Management Committee of New Democracy (Thessaloniki P
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https://en.wikipedia.org/wiki/Software%20transactional%20memory
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In computer science, software transactional memory (STM) is a concurrency control mechanism analogous to database transactions for controlling access to shared memory in concurrent computing. It is an alternative to lock-based synchronization. STM is a strategy implemented in software, rather than as a hardware component. A transaction in this context occurs when a piece of code executes a series of reads and writes to shared memory. These reads and writes logically occur at a single instant in time; intermediate states are not visible to other (successful) transactions. The idea of providing hardware support for transactions originated in a 1986 paper by Tom Knight. The idea was popularized by Maurice Herlihy and J. Eliot B. Moss. In 1995 Nir Shavit and Dan Touitou extended this idea to software-only transactional memory (STM). Since 2005, STM has been the focus of intense research and support for practical implementations is growing.
Performance
Unlike the locking techniques used in most modern multithreaded applications, STM is often very optimistic: a thread completes modifications to shared memory without regard for what other threads might be doing, recording every read and write that it is performing in a log. Instead of placing the onus on the writer to make sure it does not adversely affect other operations in progress, it is placed on the reader, who after completing an entire transaction verifies that other threads have not concurrently made changes to memory th
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https://en.wikipedia.org/wiki/Nymph%20%28disambiguation%29
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In Greek mythology, a nymph or nymphe () is a female nature-spirit.
Nymph or nymphe may also mean:
Flora and fauna
Nymph (biology), the immature form of an insect having incomplete metamorphosis
Nymph (fishing), a lure that imitates an insect nymph
Jungle nymph, a type of large stick insect found in Malaysia
Water nymph, several species of aquatic plants in the Nymphaeaceae family
Literature
The Nymphs (poem), by Leigh Hunt, published in 1818
Nymph, the "Beta Angeloid: Electronic Warfare Type" in the anime Sora no Otoshimono from the manga series Heaven's Lost Property
Movies and television
Nymph (1973 film), a 1973 American film
The Nymph (Ninfa plebea), a 1996 Italian film directed by Lina Wertmüller
Nymph (2009 film), a 2009 Thai film
Nymphs (TV series), a 2013 Finnish television series
Music
Nymphs (band), a 1990s US-American alternative rock band
Nymphs (album), an album by The Nymphs released in 1991
"Nymph", a song by Brooke Candy from the 2019 album Sexorcism
Nymph (album), a 2022 album by British rapper Shygirl
Ships
, various French Navy ships
, a Royal Navy sloop launched in 1778
, the name of several Royal Navy ships
, a United States Navy steamer that served in the American Civil War
Other uses
875 Nymphe, a minor planet that orbits the Sun
NAC Freelance, an airplane originally known as the BN-3 Nymph
Nymph (Central Figure for "The Three Graces"), a bronze sculpture in Washington, D.C.
Nymph (Dungeons & Dragons), a monster in the Dungeons & Dragons role-
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https://en.wikipedia.org/wiki/Stieltjes%20constants
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In mathematics, the Stieltjes constants are the numbers that occur in the Laurent series expansion of the Riemann zeta function:
The constant is known as the Euler–Mascheroni constant.
Representations
The Stieltjes constants are given by the limit
(In the case n = 0, the first summand requires evaluation of 00, which is taken to be 1.)
Cauchy's differentiation formula leads to the integral representation
Various representations in terms of integrals and infinite series are given in works of Jensen, Franel, Hermite, Hardy, Ramanujan, Ainsworth, Howell, Coppo, Connon, Coffey, Choi, Blagouchine and some other authors. In particular, Jensen-Franel's integral formula, often erroneously attributed to Ainsworth and Howell, states that
where δn,k is the Kronecker symbol (Kronecker delta). Among other formulae, we find
see.
As concerns series representations, a famous series implying an integer part of a logarithm was given by Hardy in 1912
Israilov gave semi-convergent series in terms of Bernoulli numbers
Connon, Blagouchine and Coppo gave several series with the binomial coefficients
where Gn are Gregory's coefficients, also known as reciprocal logarithmic numbers (G1=+1/2, G2=−1/12, G3=+1/24, G4=−19/720,... ).
More general series of the same nature include these examples
and
or
where are the Bernoulli polynomials of the second kind and are the polynomials given by the generating equation
respectively (note that ).
Oloa and Tauraso showed that
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https://en.wikipedia.org/wiki/David%20Kaplan%20%28philosopher%29
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David Benjamin Kaplan (; born September 17, 1933) is an American philosopher. He is the Hans Reichenbach Professor of Scientific Philosophy at the UCLA Department of Philosophy. His philosophical work focuses on the philosophy of language, logic, metaphysics, epistemology and the philosophy of Frege and Russell. He is best known for his work on demonstratives, propositions, and reference in intensional contexts. He was elected a Fellow of the American Academy of Arts & Sciences in 1983 and a Corresponding Fellow of the British Academy in 2007.
Education and career
Kaplan began as an undergraduate at UCLA in 1951, admitted on academic probation "owing to poor grades." While he started as a music major due to his interest in jazz, he was soon persuaded by his academic counselor Veronica Kalish to take the logic course taught by her husband Donald Kalish. Kaplan went on to earn a BA in philosophy in 1956 and a BA in mathematics in 1957, continuing in the department of philosophy as a graduate student. He was the last doctoral student supervised by Rudolf Carnap, receiving his PhD in 1964 with a thesis entitled Foundations of Intensional Logic. His work continues the strongly formal approach to philosophy long associated with UCLA (as represented by mathematician-logician-philosophers such as Alonzo Church and Richard Montague).
In most years, Kaplan teaches an upper division course on philosophy of language, focusing on the work of either Gottlob Frege, Bertrand Russell, or P
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https://en.wikipedia.org/wiki/Hector%20Ruiz
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Hector de Jesus Ruiz Cardenas (born December 25, 1945) is the chairman and CEO of Advanced Nanotechnology Solutions, Inc. and former CEO & executive chairman of semiconductor company Advanced Micro Devices, Inc. (AMD).
Ruiz is the author of Slingshot: AMD’s Fight To Free An Industry From The Ruthless Grip Of Intel, "a book that memorializes his bet-the-company decision in 2005 to file an antitrust case against its much larger rival." The book also "elaborates on his humble upbringing as well as advice and lessons learned from relatives and teachers."
Education
Ruiz was born in the border town of Piedras Negras, Coahuila, Mexico. As a teenager, he walked across the Mexico – United States border every day to attend a high school in nearby Eagle Pass, Texas, from which he graduated as valedictorian just three years after beginning to learn English. Ruiz earned a BS and MS in electrical engineering from the University of Texas at Austin in 1968 and 1970 respectively and a PhD from Rice University in 1973.
In 2012, Ruiz—along with former First Lady Laura Bush, Charles Matthews, Melinda Perrin, Julius Glickman and Admiral William H. McRaven—was named a Distinguished Alumnus of the University of Texas.
Career
Ruiz worked at Texas Instruments for six years and Motorola for 22 years, rising to become president of Motorola's Semiconductor Products Sector before being recruited in 2000 by AMD founder Jerry Sanders to serve as AMD's president and chief operating officer, and to beco
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https://en.wikipedia.org/wiki/Prime%20Sentinel
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Prime Sentinels are an advanced type of fictional Sentinel appearing in American comic books published by Marvel Comics. They are depicted as a human/machine hybrid that uses nanotechnology from the "Days of Future Past" alternate future.
Creation
The Prime Sentinels were created when Bastion initiated the Operation: Zero Tolerance program. These Sentinels were actually humans who had been fitted with cybernetic nanotech implants which, upon activation, transformed the humans into armored beings with powerful weapons systems. These altered humans were set up as sleeper agents, unaware of their natures until a signal from the Operation: Zero Tolerance base activated their programming. These Sentinels were used by Bastion to capture Professor X for his own purposes, as well as attack various mutants associated with the X-Men across the country. Bastion and his Prime Sentinels were eventually defeated by the X-Men with help from the government agency S.H.I.E.L.D., who shut down Operation: Zero Tolerance.
It was assumed that the threat of the Prime Sentinels and their second generation was over, upon the arrest of Bastion and the end of Operation: Zero Tolerance. However, when the mutant race endured another extinct event with the release of the Terrigen Mists into the atmosphere, the Omega Sentinels now revering the Terrigen Mists that's poisoning mutants, returned violently when the mutants were at their lowest.
Powers and abilities
Prime Sentinels are equipped with several
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https://en.wikipedia.org/wiki/John%20Mark%20Ockerbloom
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John Mark Ockerbloom (born 1966) is a digital library architect and planner in the library science field. Formerly at Carnegie Mellon University, from which he earned a PhD in computer science, he now works for the University of Pennsylvania. He is the editor of The Online Books Page, which lists over two million books including project Gutenberg titles, all of which are freely available for reading online or by download.
Education
Mark Ockerbloom attended Carnegie Mellon University in the 1990s and earned a PhD in computer science.
Career
Mark Ockerbloom works as a digital library planner and researcher at the University of Pennsylvania.
He is involved in the use of technology by the general public for the public good. He is the chair of the ILS-DI Task Group for the Digital Library Federation.
Free speech
In 1994, Mark Ockerbloom created Banned Books On-Line in response to the censoring of usenet newsgroups on Carnegie Mellon's servers. A number of organizations including Electronic Frontier Foundation and the American Civil Liberties Union were opposing the Communications Decency Act around that time and took note of Banned Books On-Line, linking to it from their websites.
In 1998, Mark Ockerbloom joined as a plaintiff along with columnist Rob Morse of the San Francisco Examiner, the ACLU and others in a federal lawsuit against a library using web filtering software. The Loudoun County Library in Virginia installed X-Stop filtering software created by Log-On Data
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https://en.wikipedia.org/wiki/Normal%20family
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In mathematics, with special application to complex analysis, a normal family is a pre-compact subset of the space of continuous functions. Informally, this means that the functions in the family are not widely spread out, but rather stick together in a somewhat "clustered" manner. Note that a compact family of continuous functions is automatically a normal family.
Sometimes, if each function in a normal family F satisfies a particular property (e.g. is holomorphic),
then the property also holds for each limit point of the set F.
More formally, let X and Y be topological spaces. The set of continuous functions has a natural topology called the compact-open topology. A normal family is a pre-compact subset with respect to this topology.
If Y is a metric space, then the compact-open topology is equivalent to the topology of compact convergence, and we obtain a definition which is closer to the classical one: A collection F of continuous functions is called a normal family
if every sequence of functions in F contains a subsequence which converges uniformly on compact subsets of X to a continuous function from X to Y. That is, for every sequence of functions in F, there is a subsequence and a continuous function from X to Y such that the following holds for every compact subset K contained in X:
where is the metric of Y.
Normal families of holomorphic functions
The concept arose in complex analysis, that is the study of holomorphic functions. In this case, X is an ope
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https://en.wikipedia.org/wiki/Ruby%20Payne-Scott
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Ruby Violet Payne-Scott (28 May 1912 – 25 May 1981) was an Australian pioneer in radiophysics and radio astronomy, and was one of two Antipodean women pioneers in radio astronomy and radio physics at the end of the second world war, Ruby Payne-Scott the Australian and Elizabeth Alexander the New Zealander.
Early life and education
Ruby Payne-Scott was born on 28 May 1912 in Grafton, New South Wales, the daughter of Cyril Payne-Scott and his wife Amy (née Neale). She later moved to Sydney to live with her aunt. There she attended the Penrith Public Primary School (1921–24), and the Cleveland-Street Girls' High School (1925–26), before completing her secondary schooling at Sydney Girls High School. Her school leaving certificate included honours in mathematics and botany.
She won two scholarships to undertake tertiary education at the University of Sydney, where she studied physics, chemistry, mathematics and botany. She earned a BSc in 1933—the third woman to graduate in physics there—followed by an MSc in physics in 1936 and a Diploma of Education in 1938.
Early career
In 1936, Payne-Scott conducted research with William H. Love at the Cancer Research Laboratory at the University of Sydney. They determined that the magnetism of the Earth had little or no effect on the vital processes of beings living on the Earth by cultivating chicken embryos with no observable differences, despite being in magnetic fields up to 5,000 times as powerful as that of the Earth. Some decades
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https://en.wikipedia.org/wiki/Elektron
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Elektron may refer to:
Elektron (alloy), a magnesium alloy
Elektron (company), a musical instrument company
Elektron (ISS), a Russian oxygen generator
Elektron (resin) or amber, a fossilised resin
Elektron (satellite), a series of four Soviet particle physics satellites
See also
Electron, a subatomic particle
Electron (disambiguation)
Tron (disambiguation)
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https://en.wikipedia.org/wiki/Radix%20tree
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In computer science, a radix tree (also radix trie or compact prefix tree or compressed trie) is a data structure that represents a space-optimized trie (prefix tree) in which each node that is the only child is merged with its parent. The result is that the number of children of every internal node is at most the radix of the radix tree, where is a positive integer and a power of 2, having ≥ 1. Unlike regular trees, edges can be labeled with sequences of elements as well as single elements. This makes radix trees much more efficient for small sets (especially if the strings are long) and for sets of strings that share long prefixes.
Unlike regular trees (where whole keys are compared en masse from their beginning up to the point of inequality), the key at each node is compared chunk-of-bits by chunk-of-bits, where the quantity of bits in that chunk at that node is the radix of the radix trie. When is 2, the radix trie is binary (i.e., compare that node's 1-bit portion of the key), which minimizes sparseness at the expense of maximizing trie depth—i.e., maximizing up to conflation of nondiverging bit-strings in the key. When ≥ 4 is a power of 2, then the radix trie is an -ary trie, which lessens the depth of the radix trie at the expense of potential sparseness.
As an optimization, edge labels can be stored in constant size by using two pointers to a string (for the first and last elements).
Note that although the examples in this article show strings as sequences
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https://en.wikipedia.org/wiki/Walther%20Flemming
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Walther Flemming (21 April 1843 – 4 August 1905) was a German biologist and a founder of cytogenetics.
He was born in Sachsenberg (now part of Schwerin) as the fifth child and only son of the psychiatrist Carl Friedrich Flemming (1799–1880) and his second wife, Auguste Winter. He graduated from the Gymnasium der Residenzstadt, where one of his colleagues and lifelong friends was writer Heinrich Seidel.
Career
Flemming trained in medicine at the University of Prague, graduating in 1868. Afterwards, he served in 1870–71 as a military physician in the Franco-Prussian War. From 1873 to 1876 he worked as a teacher at the University of Prague. In 1876 he accepted a post as a professor of anatomy at the University of Kiel. He became the director of the Anatomical Institute and stayed there until his death.
With the use of aniline dyes he was able to find a structure which strongly absorbed basophilic dyes, which he named chromatin. He identified that chromatin was correlated to threadlike structures in the cell nucleus – the chromosomes (meaning coloured bodies), which were named thus later by German anatomist Wilhelm von Waldeyer-Hartz (1841–1923). The Belgian scientist Edouard Van Beneden (1846–1910) had also observed them, independently. The centrosome was discovered jointly by Walther Flemming in 1875 and Edouard Van Beneden in 1876.
Flemming investigated the process of cell division and the distribution of chromosomes to the daughter nuclei, a process he called mitosis f
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https://en.wikipedia.org/wiki/DMF
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DMF may refer to:
Science and technology
Chemistry
Dimethylformamide, a common solvent
Dimethyl fumarate, a small molecule anti-inflammatory human medicine
2,5-Dimethylfuran, a liquid biofuel
Computing
Distribution Media Format, the computer floppy disk format
DivX Media Format, the media container format
Death Master File, a document listing deaths in the US
Medicine
Decay-missing-filled index for assessing dental caries prevalence as well as dental treatment needs among populations
Drug Master File, a document in the pharmaceutical industry
Other technology
Digital microfluidics, a fluid handling technique
Dual-mass flywheel, a rotating mechanical device
Other uses
Danish Musicians' Union, a Danish trade union
Defensive midfielder, in association football
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https://en.wikipedia.org/wiki/Bekenstein%20bound
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In physics, the Bekenstein bound (named after Jacob Bekenstein) is an upper limit on the thermodynamic entropy S, or Shannon entropy H, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximal amount of information required to perfectly describe a given physical system down to the quantum level. It implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy are finite. In computer science this implies that non-finite models such as Turing machines are not realizable as finite devices.
Equations
The universal form of the bound was originally found by Jacob Bekenstein in 1981 as the inequality
where S is the entropy, k is the Boltzmann constant, R is the radius of a sphere that can enclose the given system, E is the total mass–energy including any rest masses, ħ is the reduced Planck constant, and c is the speed of light. Note that while gravity plays a significant role in its enforcement, the expression for the bound does not contain the gravitational constant G, and so, it ought to apply to quantum field theory in curved spacetime.
The Bekenstein–Hawking boundary entropy of three-dimensional black holes exactly saturates the bound. The Schwarzschild radius is given by
and so the two-dimensional area of the black hole's event horizon is
and using the Planck length
the Bekenstein–Hawking entropy is
O
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https://en.wikipedia.org/wiki/Real%20coordinate%20space
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In mathematics, the real coordinate space of dimension , denoted or is the set of the -tuples of real numbers, that is the set of all sequences of real numbers.
Special cases are called the real line and the real coordinate plane .
With component-wise addition and scalar multiplication, it is a real vector space, and its elements are called coordinate vectors.
The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension as that of the vector space. Similarly, the Cartesian coordinates of the points of a Euclidean space of dimension form a real coordinate space of dimension .
These one to one correspondences between vectors, points and coordinate vectors explain the names of coordinate space and coordinate vector. It allows using geometric terms and methods for studying real coordinate spaces, and, conversely, to use methods of calculus in geometry. This approach of geometry was introduced by René Descartes in the 17th century. It is widely used, as it allows locating points in Euclidean spaces, and computing with them.
Definition and structures
For any natural number , the set consists of all -tuples of real numbers (). It is called the "-dimensional real space" or the "real -space".
An element of is thus a -tuple, and is written
where each is a real number. So, in multivariable calculus, the domain of a function of several real variables and the codomain of a real vector valued function are subsets of
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https://en.wikipedia.org/wiki/Euclidean%20topology
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In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on -dimensional Euclidean space by the Euclidean metric.
Definition
The Euclidean norm on is the non-negative function defined by
Like all norms, it induces a canonical metric defined by The metric induced by the Euclidean norm is called the Euclidean metric or the Euclidean distance and the distance between points and is
In any metric space, the open balls form a base for a topology on that space.
The Euclidean topology on is the topology by these balls.
In other words, the open sets of the Euclidean topology on are given by (arbitrary) unions of the open balls defined as for all real and all where is the Euclidean metric.
Properties
When endowed with this topology, the real line is a T5 space.
Given two subsets say and of with where denotes the closure of there exist open sets and with and such that
See also
References
Topology
Euclid
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https://en.wikipedia.org/wiki/Total%20relation
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In mathematics, a binary relation R ⊆ X×Y between two sets X and Y is total (or left total) if the source set X equals the domain {x : there is a y with xRy }. Conversely, R is called right total if Y equals the range {y : there is an x with xRy }.
When f: X → Y is a function, the domain of f is all of X, hence f is a total relation. On the other hand, if f is a partial function, then the domain may be a proper subset of X, in which case f is not a total relation.
"A binary relation is said to be total with respect to a universe of discourse just in case everything in that universe of discourse stands in that relation to something else."
Algebraic characterization
Total relations can be characterized algebraically by equalities and inequalities involving compositions of relations. To this end, let be two sets, and let For any two sets let be the universal relation between and and let be the identity relation on We use the notation for the converse relation of
is total iff for any set and any implies
is total iff
If is total, then The converse is true if
If is total, then The converse is true if
If is total, then The converse is true if
More generally, if is total, then for any set and any The converse is true if
Notes
References
Gunther Schmidt & Michael Winter (2018) Relational Topology
C. Brink, W. Kahl, and G. Schmidt (1997) Relational Methods in Computer Science, Advances in Computer Science, page 5,
Gunther Schmidt & Thomas
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https://en.wikipedia.org/wiki/Term%20symbol
|
In atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi-electron atom. So while the word symbol suggests otherwise, it represents an actual value of a physical quantity.
For a given electron configuration of an atom, its state depends also on its total angular momentum, including spin and orbital components, which are specified by the term symbol. The usual atomic term symbols assume LS coupling (also known as Russell–Saunders coupling) in which the all-electron total quantum numbers for orbital (L), spin (S) and total (J) angular momenta are good quantum numbers.
In the terminology of atomic spectroscopy, L and S together specify a term; L, S, and J specify a level; and L, S, J and the magnetic quantum number MJ specify a state. The conventional term symbol has the form 2S+1LJ, where J is written optionally in order to specify a level. L is written using spectroscopic notation: for example, it is written "S", "P", "D", or "F" to represent L = 0, 1, 2, or 3 respectively. For coupling schemes other that LS coupling, such as the jj coupling that applies to some heavy elements, other notations are used to specify the term.
Term symbols apply to both neutral and charged atoms, and to their ground and excited states. Term symbols usually specify the total for all electrons in an atom, but are sometimes used to describe electrons in a given subshell or set of subshells, for exampl
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https://en.wikipedia.org/wiki/Ranking
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A ranking is a relationship between a set of items such that, for any two items, the first is either "ranked higher than", "ranked lower than", or "ranked equal to" the second. In mathematics, this is known as a weak order or total preorder of objects. It is not necessarily a total order of objects because two different objects can have the same ranking. The rankings themselves are totally ordered. For example, materials are totally preordered by hardness, while degrees of hardness are totally ordered. If two items are the same in rank it is considered a tie.
By reducing detailed measures to a sequence of ordinal numbers, rankings make it possible to evaluate complex information according to certain criteria. Thus, for example, an Internet search engine may rank the pages it finds according to an estimation of their relevance, making it possible for the user quickly to select the pages they are likely to want to see.
Analysis of data obtained by ranking commonly requires non-parametric statistics.
Strategies for handling ties
It is not always possible to assign rankings uniquely. For example, in a race or competition two (or more) entrants might tie for a place in the ranking. When computing an ordinal measurement, two (or more) of the quantities being ranked might measure equal. In these cases, one of the strategies below for assigning the rankings may be adopted.
A common shorthand way to distinguish these ranking strategies is by the ranking numbers that would be prod
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