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https://en.wikipedia.org/wiki/Sato%E2%80%93Tate%20conjecture
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In mathematics, the Sato–Tate conjecture is a statistical statement about the family of elliptic curves Ep obtained from an elliptic curve E over the rational numbers by reduction modulo almost all prime numbers p. Mikio Sato and John Tate independently posed the conjecture around 1960.
If Np denotes the number of points on the elliptic curve Ep defined over the finite field with p elements, the conjecture gives an answer to the distribution of the second-order term for Np. By Hasse's theorem on elliptic curves,
as , and the point of the conjecture is to predict how the O-term varies.
The original conjecture and its generalization to all totally real fields was proved by Laurent Clozel, Michael Harris, Nicholas Shepherd-Barron, and Richard Taylor under mild assumptions in 2008, and completed by Thomas Barnet-Lamb, David Geraghty, Harris, and Taylor in 2011. Several generalizations to other algebraic varieties and fields are open.
Statement
Let E be an elliptic curve defined over the rational numbers without complex multiplication. For a prime number p, define θp as the solution to the equation
Then, for every two real numbers and for which
Details
By Hasse's theorem on elliptic curves, the ratio
is between -1 and 1. Thus it can be expressed as cos θ for an angle θ; in geometric terms there are two eigenvalues accounting for the remainder and with the denominator as given they are complex conjugate and of absolute value 1. The Sato–Tate conjecture, when E doesn't hav
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https://en.wikipedia.org/wiki/Levitation%20%28physics%29
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Levitation (from Latin , ) is the process by which an object is held aloft in a stable position, without mechanical support via any physical contact.
Levitation is accomplished by providing an upward force that counteracts the pull of gravity (in relation to gravity on earth), plus a smaller stabilizing force that pushes the object toward a home position whenever it is a small distance away from that home position. The force can be a fundamental force such as magnetic or electrostatic, or it can be a reactive force such as optical, buoyant, aerodynamic, or hydrodynamic.
Levitation excludes floating at the surface of a liquid because the liquid provides direct mechanical support. Levitation excludes hovering flight by insects, hummingbirds, helicopters, rockets, and balloons because the object provides its own counter-gravity force.
Physics
Levitation (on Earth or any planetoid) requires an upward force that cancels out the weight of the object, so that the object does not fall (accelerate downward) or rise (accelerate upward). For positional stability, any small displacement of the levitating object must result in a small change in force in the opposite direction. the small changes in force can be accomplished by gradient field(s) or by active regulation. If the object is disturbed, it might oscillate around its final position, but its motion eventually decreases to zero due to damping effects. (In a turbulent flow, the object might oscillate indefinitely.)
Levitation tech
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https://en.wikipedia.org/wiki/Multinomial%20theorem
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In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem from binomials to multinomials.
Theorem
For any positive integer and any non-negative integer , the multinomial formula describes how a sum with terms expands when raised to an arbitrary power :
where
is a multinomial coefficient. The sum is taken over all combinations of nonnegative integer indices through such that the sum of all is . That is, for each term in the expansion, the exponents of the must add up to . Also, as with the binomial theorem, quantities of the form that appear are taken to equal 1 (even when equals zero).
In the case , this statement reduces to that of the binomial theorem.
Example
The third power of the trinomial is given by
This can be computed by hand using the distributive property of multiplication over addition, but it can also be done (perhaps more easily) with the multinomial theorem. It is possible to "read off" the multinomial coefficients from the terms by using the multinomial coefficient formula. For example:
has the coefficient
has the coefficient
Alternate expression
The statement of the theorem can be written concisely using multiindices:
where
and
Proof
This proof of the multinomial theorem uses the binomial theorem and induction on .
First, for , both sides equal since there is only one term in the sum. For the induction step, suppose
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https://en.wikipedia.org/wiki/Independent%20component%20analysis
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In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statistically independent from each other. ICA is a special case of blind source separation. A common example application is the "cocktail party problem" of listening in on one person's speech in a noisy room.
Introduction
Independent component analysis attempts to decompose a multivariate signal into independent non-Gaussian signals. As an example, sound is usually a signal that is composed of the numerical addition, at each time t, of signals from several sources. The question then is whether it is possible to separate these contributing sources from the observed total signal. When the statistical independence assumption is correct, blind ICA separation of a mixed signal gives very good results. It is also used for signals that are not supposed to be generated by mixing for analysis purposes.
A simple application of ICA is the "cocktail party problem", where the underlying speech signals are separated from a sample data consisting of people talking simultaneously in a room. Usually the problem is simplified by assuming no time delays or echoes. Note that a filtered and delayed signal is a copy of a dependent component, and thus the statistical independence assumption is not violated.
Mixing weights for constructing the obse
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https://en.wikipedia.org/wiki/MAGENTA
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In cryptography, MAGENTA is a symmetric key block cipher developed by Michael Jacobson Jr. and Klaus Huber for Deutsche Telekom. The name MAGENTA is an acronym for Multifunctional Algorithm for General-purpose Encryption and Network Telecommunication Applications. (The color magenta is also part of the corporate identity of Deutsche Telekom.) The cipher was submitted to the Advanced Encryption Standard process, but did not advance beyond the first round; cryptographic weaknesses were discovered and it was found to be one of the slower ciphers submitted.
MAGENTA has a block size of 128 bits and key sizes of 128, 192 and 256 bits. It is a Feistel cipher with six or eight rounds.
After the presentation of the cipher at the first AES conference, several cryptographers immediately found vulnerabilities. These were written up and presented at the second AES conference (Biham et al., 1999).
References
External links
John Savard's description of Magenta
SCAN's entry for the cipher
Deutsche Telekom
Feistel ciphers
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https://en.wikipedia.org/wiki/Autolysis
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Autolysis may refer to:
Autolysis (biology), the destruction (or lysis) of a cell by its own enzymes
Autocatalysis, in chemistry, the production of a substance which catalyzes a chemical reaction it was made in, or catalyzes its own transformation into another compound
Autolysis (alcohol fermentation), the complex chemical reactions that take place when wine or beer spends time in contact with the (dead) yeast after fermentation
Breadmaking#Preparation, the rest period in which dough is left without yeast or starter to autolyse for improved gluten development
Autolysing yeast, the natural process by which yeast breaks down its own proteins to simpler compounds, in the production of commercial extract
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https://en.wikipedia.org/wiki/Brian%20Duffy%20%28astronaut%29
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Brian Duffy (born June 20, 1953, Boston, Massachusetts) is a retired U.S. Air Force colonel and a former NASA astronaut. He flew aboard four Space Shuttle missions.
Education
Duffy graduated from Rockland High School, Rockland, Massachusetts in 1971. In 1975 he received a Bachelor of Science degree in mathematics from the United States Air Force Academy and completed Undergraduate Pilot Training as part of Class 76-10 at Columbus Air Force Base, Mississippi, in August 1976. In 1981 he received a Master of Science degree in systems management from the University of Southern California.
Military career
After graduating from the USAF Academy in 1975, Duffy was selected to fly the F-15 and was stationed at Langley Air Force Base, Virginia, until 1979, when he transferred to Kadena Air Base, Okinawa, Japan. He flew F-15s there until 1982 when he was selected to attend the U.S. Air Force Test Pilot School at Edwards Air Force Base in California and then became the Director of F-15 Flight Test at Eglin Air Force Base, Florida.
Duffy logged over 5,000 hours of flight time in more than 25 different aircraft.
NASA career
Selected by NASA in June 1985, Duffy became an astronaut in July 1986. He participated in the development and testing of displays, flight crew procedures, and computer software to be used on Shuttle flights. He served as spacecraft communicator (CAPCOM) in Mission Control during numerous Space Shuttle missions. He also served as Assistant Director (Technical) and
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https://en.wikipedia.org/wiki/Algebraic%20K-theory
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Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important outstanding problem is to compute the K-groups of the integers.
K-theory was discovered in the late 1950s by Alexander Grothendieck in his study of intersection theory on algebraic varieties. In the modern language, Grothendieck defined only K0, the zeroth K-group, but even this single group has plenty of applications, such as the Grothendieck–Riemann–Roch theorem. Intersection theory is still a motivating force in the development of (higher) algebraic K-theory through its links with motivic cohomology and specifically Chow groups. The subject also includes classical number-theoretic topics like quadratic reciprocity and embeddings of number fields into the real numbers and complex numbers, as well as more modern concerns like the construction of higher regulators and special values of L-functions.
The lower K-groups were discovered first, in the sense that adequate descriptions of these groups in terms of other algebraic structures were found. For example, if F is a field, then is isomorphic to the integers Z and is closely related to the notion of vector space dimension. For a commutati
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https://en.wikipedia.org/wiki/Stirling%20%28disambiguation%29
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Stirling is a city and former ancient burgh in Scotland.
Stirling may also refer to:
Mathematics
Stirling's approximation, a formula to approximate large factorials
Stirling number
Stirling permutation
Physics and Engineering
Stirling cycle, a thermodynamic cycle for Stirling devices.
Stirling engine, a type of heat engine. See also Applications of the Stirling engine.
Stirling radioisotope generator, a type of radioisotope generator based on a Stirling engine.
Advanced Stirling radioisotope generator, a power system developed at NÄSA's Glenn Research Center.
Places
Scotland
Stirling (council area)
Stirling (Scottish Parliament constituency)
Stirling (UK Parliament constituency)
Stirling (Parliament of Scotland constituency), which ceased to exist in 1707
Stirling Sill, an outcropping or sill that underlies a large part of central Scotland
Stirling Village, Aberdeenshire
Stirlingshire, Scotland, a historic county and registration county.
Australia
Mount Stirling, Victoria
Stirling, South Australia, a town east of Adelaide
Stirling, Australian Capital Territory
Stirling, Victoria, an abandoned township near Tambo Crossing
Stirling Park, part of Stirling Linear Park, South Australia
Western Australia
City of Stirling, Perth
Stirling, Western Australia, a Perth suburb within the City of Stirling
Division of Stirling, electoral district in the Australian House of Representatives
Stirling County, Western Australia
Electoral district of Stirling, an e
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https://en.wikipedia.org/wiki/Product%20cipher
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In cryptography, a product cipher combines two or more transformations in a manner intending that the resulting cipher is more secure than the individual components to make it resistant to cryptanalysis. The product cipher combines a sequence of simple transformations such as substitution (S-box), permutation (P-box), and modular arithmetic. The concept of product ciphers is due to Claude Shannon, who presented the idea in his foundational paper, Communication Theory of Secrecy Systems. A particular product cipher design where all the constituting transformation functions have the same structure is called an iterative cipher with the term "rounds" applied to the functions themselves.
For transformation involving reasonable number of n message symbols, both of the foregoing cipher systems (the S-box and P-box) are by themselves wanting. Shannon suggested using a combination of S-box and P-box transformation—a product cipher. The combination could yield a cipher system more powerful than either one alone. This approach of alternatively applying substitution and permutation transformation has been used by IBM in the Lucifer cipher system, and has become the standard for national data encryption standards such as the Data Encryption Standard and the Advanced Encryption Standard. A product cipher that uses only substitutions and permutations is called a SP-network. Feistel ciphers are an important class of product ciphers.
References
Sources
External links
The Cryptography
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https://en.wikipedia.org/wiki/Threshold%20potential
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In electrophysiology, the threshold potential is the critical level to which a membrane potential must be depolarized to initiate an action potential. In neuroscience, threshold potentials are necessary to regulate and propagate signaling in both the central nervous system (CNS) and the peripheral nervous system (PNS).
Most often, the threshold potential is a membrane potential value between –50 and –55 mV, but can vary based upon several factors. A neuron's resting membrane potential (–70 mV) can be altered to either increase or decrease likelihood of reaching threshold via sodium and potassium ions. An influx of sodium into the cell through open, voltage-gated sodium channels can depolarize the membrane past threshold and thus excite it while an efflux of potassium or influx of chloride can hyperpolarize the cell and thus inhibit threshold from being reached.
Discovery
Initial experiments revolved around the concept that any electrical change that is brought about in neurons must occur through the action of ions. The German physical chemist Walther Nernst applied this concept in experiments to discover nervous excitability, and concluded that the local excitatory process through a semi-permeable membrane depends upon the ionic concentration. Also, ion concentration was shown to be the limiting factor in excitation. If the proper concentration of ions was attained, excitation would certainly occur. This was the basis for discovering the threshold value.
Along with reconst
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https://en.wikipedia.org/wiki/GMR%20%28cryptography%29
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In cryptography, GMR is a digital signature algorithm named after its inventors Shafi Goldwasser, Silvio Micali and Ron Rivest.
As with RSA the security of the system is related to the difficulty of factoring very large numbers. But, in contrast to RSA, GMR is secure against adaptive chosen-message attacks, which is the currently accepted security definition for signature schemes— even when an attacker receives signatures for messages of his choice, this does not allow them to forge a signature for a single additional message.
External links
Digital signature schemes
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https://en.wikipedia.org/wiki/John%20M.%20Grunsfeld
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John Mace Grunsfeld (born 10 October 1958) is an American physicist and a former NASA astronaut. He is a veteran of five Space Shuttle flights and has served as NASA Chief Scientist. His academic background includes research in high energy astrophysics, cosmic ray physics and the emerging field of exoplanet studies with specific interest in future astronomical instrumentation. After retiring from NASA in 2009, he served as the deputy director of the Space Telescope Science Institute in Baltimore, Maryland. In January 2012, he returned to NASA and served as associate administrator of NASA's Science Mission Directorate (SMD). Grunsfeld announced his retirement from NASA in April 2016.
Personal life
Grunsfeld was born in Chicago, Illinois, to Ernest Alton 'Tony' Grunsfeld III, a distinguished Chicago architect, and Sally Mace Grunsfeld; grandson of architect Ernest Grunsfeld Jr., architect of the Adler Planetarium. He is married to the former Carol E. Schiff, with whom he has two children. Grunsfeld enjoys mountaineering, flying, sailing, bicycling, and music. His father, Ernest Grunsfeld III, died in 2011 at the age of 81.
Education
Grunsfeld graduated from Highland Park High School in Highland Park, Illinois, in 1976. He attended the Massachusetts Institute of Technology, earning a Bachelor of Science in physics in 1980. He then attended the University of Chicago, earning a Master of Science in physics in 1984 and a Doctor of Philosophy in physics in 1988.
Organizations
Am
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https://en.wikipedia.org/wiki/Holdfast%20%28biology%29
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A holdfast is a root-like structure that anchors aquatic sessile organisms, such as seaweed, other sessile algae, stalked crinoids, benthic cnidarians, and sponges, to the substrate.
Holdfasts vary in shape and form depending on both the species and the substrate type. The holdfasts of organisms that live in muddy substrates often have complex tangles of root-like growths. These projections are called haptera and similar structures of the same name are found on lichens. The holdfasts of organisms that live in sandy substrates are bulb-like and very flexible, such as those of sea pens, thus permitting the organism to pull the entire body into the substrate when the holdfast is contracted. The holdfasts of organisms that live on smooth surfaces (such as the surface of a boulder) have flattened bases which adhere to the surface. The organism derives no nutrition from this intimate contact with the substrate, as the process of liberating nutrients from the substrate requires enzymatically eroding the substrate away, thereby increasing the risk of organism falling off the substrate.
The claw-like holdfasts of kelps and other algae differ from the roots of land plants, in that they have no absorbent function, instead serving only as an anchor.
References
Plant morphology
es:Rizoide
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https://en.wikipedia.org/wiki/Propyl%20group
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In organic chemistry, propyl is a three-carbon alkyl substituent with chemical formula for the linear form. This substituent form is obtained by removing one hydrogen atom attached to the terminal carbon of propane. A propyl substituent is often represented in organic chemistry with the symbol Pr (not to be confused with the element praseodymium).
An isomeric form of propyl is obtained by moving the point of attachment from a terminal carbon atom to the central carbon atom, named 1-methylethyl or isopropyl. To maintain four substituents on each carbon atom, one hydrogen atom has to be moved from the middle carbon atom to the carbon atom which served as attachment point in the n-propyl variant, written as .
Linear propyl is sometimes termed normal and hence written with a prefix n- (i.e., n-propyl), as the absence of the prefix n- does not indicate which attachment point is chosen, i.e. absence of prefix does not automatically exclude the possibility of it being the branched version (i.e. i-propyl or isopropyl).
In addition, there is a third, cyclic, form called cyclopropyl, or c-propyl. It is not isomeric with the other two forms, having a different chemical formula ( vs ), not just a different connectivity of the atoms.
Examples
n-Propyl acetate is an ester which has the n-propyl group attached to the oxygen atom of the acetate group.
Other examples
Isopropyl alcohol
References
Alkyl groups
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https://en.wikipedia.org/wiki/American%20Society%20of%20Civil%20Engineers
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The American Society of Civil Engineers (ASCE) is a tax-exempt professional body founded in 1852 to represent members of the civil engineering profession worldwide. Headquartered in Reston, Virginia, it is the oldest national engineering society in the United States. Its constitution was based on the older Boston Society of Civil Engineers from 1848.
ASCE is dedicated to the advancement of the science and profession of civil engineering and the enhancement of human welfare through the activities of society members. It has more than 143,000 members in 177 countries. Its mission is to provide essential value to members, their careers, partners, and the public; facilitate the advancement of technology; encourage and provide the tools for lifelong learning; promote professionalism and the profession; develop and support civil engineers.
History
The first serious and documented attempts to organize civil engineers as a professional society in the newly created United States were in the early 19th century. In 1828, John Kilbourn of Ohio, managed a short-lived "Civil Engineering Journal", editorializing about the recent incorporation of the Institution of Civil Engineers in Great Britain that same year, Kilbourn suggested that the American corps of engineers could constitute an American society of civil engineers. Later, in 1834, an American trade periodical, the "American Railroad Journal" advocated for similar national organization of civil engineers.
Institution of American Ci
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https://en.wikipedia.org/wiki/WAKE%20%28cipher%29
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In cryptography, WAKE is a stream cipher designed by David Wheeler in 1993.
WAKE stands for Word Auto Key Encryption. The cipher works in cipher feedback mode, generating keystream blocks from previous ciphertext blocks. WAKE uses an S-box with 256 entries of 32-bit words.
The cipher is fast, but vulnerable to chosen plaintext and chosen ciphertext attacks.
See also
TEA, XTEA
References
External links
A Bulk Data Encryption Algorithm
Stream ciphers
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https://en.wikipedia.org/wiki/List%20of%20Historic%20Civil%20Engineering%20Landmarks
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The following is a list of Historic Civil Engineering Landmarks as designated by the American Society of Civil Engineers since it began the program in 1964. The designation is granted to projects, structures, and sites in the United States (National Historic Civil Engineering Landmarks) and the rest of the world (International Historic Civil Engineering Landmarks). As of 2019, there are over 280 landmarks that have been approved by the ASCE Board of Direction.
Sections or chapters of the American Society of Civil Engineers may also designate state or local landmarks within their areas; those landmarks are not listed here.
See also
List of Historic Mechanical Engineering Landmarks
References
External links
American Society of Civil Engineers Historic Landmarks
Civil engineering
American Society of Civil Engineers
Civil engineering
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https://en.wikipedia.org/wiki/New%20Civil%20Engineer
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New Civil Engineer is the monthly magazine for members of the Institution of Civil Engineers (ICE), the UK chartered body that oversees the practice of civil engineering in the UK. First published in May 1972, it is today published by Metropolis. Under its previous publisher, Ascential, who, as Emap, acquired the title and editorial control from the ICE in 1995, the ICE regularly discussed the magazine's content through an editorial advisory board and a supervisory board.
Available in print and online after the appropriate subscription has been taken out (it is free for members of the ICE), the magazine is aimed at professionals in the civil engineering industry. It contains industry news and analysis, letters from subscribers, a directory of companies, with listings arranged by companies’ areas of work, and an appointments section. It also occasionally has details of university courses and graduate positions.
In 2013 it had a net circulation of more than 50,000 per issue. Two years later, this had dropped to 42,805, of which some 39,000 related to copies distributed to ICE members. Previously printed on a weekly basis the magazine switched to a monthly format in December 2015.
New Civil Engineer was a co-founder of the British Construction Industry Awards.
In January 2017, Ascential announced its intention to sell 13 titles including New Civil Engineer; the 13 "heritage titles" were to be "hived off into a separate business while buyers are sought." The brands were purc
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https://en.wikipedia.org/wiki/IPN
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IPN may refer to:
Payments
Instant payment notification
Chemistry
Interpenetrating polymer network, form of chemical copolymer
Isopropyl nitrate, a liquid monopropellant
Industry
IPN, a type of I-beam used on European standards
Outer space
Interplanetary Internet
InterPlaNet
InterPlanetary Network, a group of spacecraft equipped with gamma-ray burst detectors
Medicine and anatomy
Infectious pancreatic necrosis, disease in fish
Interpeduncular nucleus, a region of the brain
Other
Independent Practitioners Network association for practitioners in psychotherapy, counselling, and related fields
Index of Place Names in Great Britain
World Bank's Inspection Panel of the World Bank Group
Instytut Pamięci Narodowej (Institute of National Remembrance), a Polish historical research institute
Instituto Pedro Nunes, technology transfer center of the University of Coimbra
Instituto Politécnico Nacional (National Polytechnic Institute), Mexican university
International Policy Network (1971–2011), former British think tank
International Polio Network, former name of Post-Polio Health International
IPN, IATA code for Usiminas Airport in Minas Gerais, Brazil
International pitch notation, a method to specify musical pitch
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https://en.wikipedia.org/wiki/Mental%20image
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In the philosophy of mind, neuroscience, and cognitive science, a mental image is an experience that, on most occasions, significantly resembles the experience of "perceiving" some object, event, or scene but occurs when the relevant object, event, or scene is not actually present to the senses. There are sometimes episodes, particularly on falling asleep (hypnagogic imagery) and waking up (hypnopompic imagery), when the mental imagery may be dynamic, phantasmagoric, and involuntary in character, repeatedly presenting identifiable objects or actions, spilling over from waking events, or defying perception, presenting a kaleidoscopic field, in which no distinct object can be discerned. Mental imagery can sometimes produce the same effects as would be produced by the behavior or experience imagined.
The nature of these experiences, what makes them possible, and their function (if any) have long been subjects of research and controversy in philosophy, psychology, cognitive science, and, more recently, neuroscience. As contemporary researchers use the expression, mental images or imagery can comprise information from any source of sensory input; one may experience auditory images, olfactory images, and so forth. However, the majority of philosophical and scientific investigations of the topic focus on visual mental imagery. It has sometimes been assumed that, like humans, some types of animals are capable of experiencing mental images. Due to the fundamentally introspective (r
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https://en.wikipedia.org/wiki/Poincar%C3%A9%20lemma
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In mathematics, the Poincaré lemma gives a sufficient condition for a closed differential form to be exact (while an exact form is necessarily closed). Precisely, it states that every closed p-form on an open ball in Rn is exact for p with . The lemma was introduced by Henri Poincaré in 1886.
Especially in calculus, the Poincaré lemma also says that every closed 1-form on a simply connected open subset in is exact.
In the language of cohomology, the Poincaré lemma says that the k-th de Rham cohomology group of a contractible open subset of a manifold M (e.g., ) vanishes for . In particular, it implies that the de Rham complex yields a resolution of the constant sheaf on M. The singular cohomology of a contractible space vanishes in positive degree, but the Poincaré lemma does not follow from this, since the fact that the singular cohomology of a manifold can be computed as the de Rham cohomology of it, that is, the de Rham theorem, relies on the Poincaré lemma. It does, however, mean that it is enough to prove the Poincaré lemma for open balls; the version for contractible manifolds then follows from the topological consideration.
The Poincaré lemma is also a special case of the homotopy invariance of de Rham cohomology; in fact, it is common to establish the lemma by showing the homotopy invariance or at least a version of it.
Proofs
Direct proof
We shall prove the lemma for an open subset that is star-shaped or a cone over ; i.e., if is in , then is in for . This
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https://en.wikipedia.org/wiki/Mary%20Somerville
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Mary Somerville (; , formerly Greig; 26 December 1780 – 29 November 1872) was a Scottish scientist, writer, and polymath. She studied mathematics and astronomy, and in 1835 she and Caroline Herschel were elected as the first female Honorary Members of the Royal Astronomical Society.
When John Stuart Mill organized a massive petition to Parliament to give women the right to vote, he made sure that the first signature on the petition would be Somerville's.
When she died in 1872, The Morning Post declared in her obituary that "Whatever difficulty we might experience in the middle of the nineteenth century in choosing a king of science, there could be no question whatever as to the queen of science". One of the earliest uses of the word scientist was in a review by William Whewell of Somerville's second book On the Connexion of the Physical Sciences. However, the word was not used to describe Somerville herself; she was known and celebrated as a mathematician or a philosopher.
Somerville College, a college of the University of Oxford, is named after her, reflecting the virtues of liberalism and academic success which the college wished to embody. She is featured on the front of the Royal Bank of Scotland polymer £10 note launched in 2017 along with a quotation from her work On the Connection of the Physical Sciences.
Early life and education
Somerville, the daughter of Vice-Admiral Sir William George Fairfax, was related to several prominent Scottish houses through her mothe
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https://en.wikipedia.org/wiki/Gradient%20conjecture
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In mathematics, the gradient conjecture, due to René Thom (1989), was proved in 2000 by three Polish mathematicians, Krzysztof Kurdyka (University of Savoie, France), Tadeusz Mostowski (Warsaw University, Poland) and Adam Parusiński (University of Angers, France).
The conjecture states that given a real-valued analytic function f defined on Rn and a trajectory x(t) of the gradient vector field of f having a limit point x0 ∈ Rn, where f has an isolated critical point at x0, there exists a limit (in the projective space PRn-1) for the secant lines from x(t) to x0, as t tends to zero.
The proof depends on a theorem due to Stanis%C5%82aw %C5%81ojasiewicz.
References
R. Thom (1989) "Problèmes rencontrés dans mon parcours mathématique: un bilan", Publications Math%C3%A9matiques de l%27IH%C3%89S 70: 200 to 214. (This gradient conjecture due to René Thom was in fact well-known among specialists by the early 70's, having been often discussed during that period by Thom during his weekly seminar on singularities at the IHES.)
In 2000 the conjecture was proven correct in Annals of Mathematics 152: 763 to 792. The proof is available here.
Theorems in analysis
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https://en.wikipedia.org/wiki/Radial
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Radial is a geometric term of location which may refer to:
Mathematics and Direction
Vector (geometric), a line
Radius, adjective form of
Radial distance (geometry), a directional coordinate in a polar coordinate system
Radial set
A bearing from a waypoint, such as a VHF omnidirectional range
Biology
Radial artery, the main artery of the lateral aspect of the forearm
Radial nerve, supplies the posterior portion of the upper limb
Radial symmetry, one of the types of distribution of body parts or shapes in biology
Radius (bone), a bone of the forearm
Technology
Radial (radio), lines which radiate from a radio antenna
Radial axle, on a locomotive or carriage
Radial compressor
Radial delayed blowback
Radial engine
Radial tire
Radial, Inc., e-commerce business
See also
Axial (disambiguation)
Radiate (disambiguation)
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https://en.wikipedia.org/wiki/H-space
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In mathematics, an H-space is a homotopy-theoretic version of a generalization of the notion of topological group, in which the axioms on associativity and inverses are removed.
Definition
An H-space consists of a topological space , together with an element of and a continuous map , such that and the maps and are both homotopic to the identity map through maps sending to . This may be thought of as a pointed topological space together with a continuous multiplication for which the basepoint is an identity element up to basepoint-preserving homotopy.
One says that a topological space is an H-space if there exists and such that the triple is an H-space as in the above definition. Alternatively, an H-space may be defined without requiring homotopies to fix the basepoint , or by requiring to be an exact identity, without any consideration of homotopy. In the case of a CW complex, all three of these definitions are in fact equivalent.
Examples and properties
The standard definition of the fundamental group, together with the fact that it is a group, can be rephrased as saying that the loop space of a pointed topological space has the structure of an H-group, as equipped with the standard operations of concatenation and inversion. Furthermore a continuous basepoint preserving map of pointed topological space induces a H-homomorphism of the corresponding loop spaces; this reflects the group homomorphism on fundamental groups induced by a continuous map.
It is straigh
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https://en.wikipedia.org/wiki/Animals%20in%20space
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Animals in space originally served to test the survivability of spaceflight, before human spaceflights were attempted. Later, other non-human animals were flown to investigate various biological processes and the effects microgravity and space flight might have on them. Bioastronautics is an area of bioengineering research that spans the study and support of life in space. To date, seven national space programs have flown animals into space: the United States, Soviet Union, France, Argentina, China, Japan and Iran.
A wide variety of animals have been launched into space, including monkeys and apes, dogs, cats, tortoises, mice, rats, rabbits, fish, frogs, spiders, quail eggs (which hatched in 1990 on Mir), and insects. The US launched the first Earthlings into space - fruit flies in 1947 - and flights carrying primates primarily between 1949 and 1961, with one flight in 1969 and one in 1985. France launched two monkey-carrying flights in 1967. The Soviet Union and Russia launched monkeys between 1983 and 1996. During the 1950s and 1960s, the Soviet space program used a number of dogs for sub-orbital and orbital space flights.
Two tortoises and several varieties of plants were the first inhabitants of Earth to circle the Moon, on the September 1968 Zond 5 mission. Turtles followed on the November 1968 Zond 6 circumlunar mission, and four turtles flew to the Moon on Zond 7 in August 1969. In 1972 five mice, Fe, Fi, Fo, Fum, and Phooey, orbited the Moon a record 75 times in Apo
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https://en.wikipedia.org/wiki/Arbitrary-precision%20arithmetic
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In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision.
Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits.
Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required. It should not be confused with the symbolic computation provided by many computer algebra systems, which represent numbers by expressions such as , and can thus represent any computable number with infinite precision.
Applications
A common application is public-key cryptography, whose algorithms commonly employ arithmetic with integers having hundreds of digits. Another is in situations where artificial limits and overflows would be inappropriate. It is also useful for checking the results of fixed-precision calculations
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https://en.wikipedia.org/wiki/List%20of%20inequalities
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This article lists Wikipedia articles about named mathematical inequalities.
Inequalities in pure mathematics
Analysis
Agmon's inequality
Askey–Gasper inequality
Babenko–Beckner inequality
Bernoulli's inequality
Bernstein's inequality (mathematical analysis)
Bessel's inequality
Bihari–LaSalle inequality
Bohnenblust–Hille inequality
Borell–Brascamp–Lieb inequality
Brezis–Gallouet inequality
Carleman's inequality
Chebyshev–Markov–Stieltjes inequalities
Chebyshev's sum inequality
Clarkson's inequalities
Eilenberg's inequality
Fekete–Szegő inequality
Fenchel's inequality
Friedrichs's inequality
Gagliardo–Nirenberg interpolation inequality
Gårding's inequality
Grothendieck inequality
Grunsky's inequalities
Hanner's inequalities
Hardy's inequality
Hardy–Littlewood inequality
Hardy–Littlewood–Sobolev inequality
Harnack's inequality
Hausdorff–Young inequality
Hermite–Hadamard inequality
Hilbert's inequality
Hölder's inequality
Jackson's inequality
Jensen's inequality
Khabibullin's conjecture on integral inequalities
Kantorovich inequality
Karamata's inequality
Korn's inequality
Ladyzhenskaya's inequality
Landau–Kolmogorov inequality
Lebedev–Milin inequality
Lieb–Thirring inequality
Littlewood's 4/3 inequality
Markov brothers' inequality
Mashreghi–Ransford inequality
Max–min inequality
Minkowski's inequality
Poincaré inequality
Popoviciu's inequality
Prékopa–Leindler inequality
Rayleigh–Faber–Krahn inequality
Remez inequality
Riesz
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https://en.wikipedia.org/wiki/RCT
|
RCT may refer to:
Science and technology
Random conical tilt, a technique used in cryogenic electron microscopy
Rational choice theory, a framework for understanding social and economic behavior
Reverse conducting thyristor
Ritchey–Chrétien telescope
Rubber Chemistry and Technology, a scientific journal
Reversible Color Transform, a technique in computer graphics
Medicine
Randomized controlled trial, a research method used in medical and social sciences
Radiochemotherapy, the combination of chemotherapy and radiotherapy to treat cancer
Root canal treatment, dental treatment to treat nerve damage of the tooth
Reverse cholesterol transport, pathway by which peripheral cell cholesterol can be returned to the liver for recycling to extrahepatic tissues, hepatic storage, or excretion into the intestine in bile
Organizations
Ranipokhari Corner Team, a Nepalese football club
RC Toulonnais, a rugby union club from Toulon, France
Register of Clinical Technologists (UK)
Rehabilitation and Research Centre for Torture Victims
Rose City Transit, a former mass transit company in Portland, Oregon
Royal Corps of Transport
Rural Community Transportation, a public bus system in Vermont
Other uses
Rameau Catalogue Thématique, a numbering system used to catalogue the works of Jean-Philippe Rameau
Regents Competency Test, an alternative standardized test for special education high school students in New York State
Regimental combat team
Relational-cultural therapy
Rh
|
https://en.wikipedia.org/wiki/IBL
|
IBL may refer to:
Technology
International Brain Laboratory, a collaborative research group in neuroscience
Image-based lighting, an image rendering technique
Inbred backcross lines, a breeding technique
InBound Links, a metric used by search engines
Instance-based learning, a family of machine learning algorithms (e.g. KNN, PEL-C, IBL-1, IBL-2 and IBL-3)
Indigo Bay Lodge Airport, an airport in Mozambique (IATA code IBL)
Ion beam lithography, a microfabrication technique
Sports
Indonesian Basketball League, formerly called the National Basketball League
Indian Badminton League
Intercounty Baseball League, a baseball league in Canada
International Basketball League (1999–2001), basketball league in the United States
International Basketball League (2005–2014), a basketball league in the United States
Italian Baseball League
Israel Baseball League
Other
In before lock, an Internet slang
Inquiry-based learning, a teaching method
International Brotherhood of Longshoremen, a labor union in North America
Industrial Bus Lines, an American bus company
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https://en.wikipedia.org/wiki/Paul%20Erd%C5%91s
|
Paul Erdős ( ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered around discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics.
Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed. He firmly believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mathematicians. He was known both for his social practice of mathematics, working with more than 500 collaborators, and for his eccentric lifestyle; Time magazine called him "The Oddball's Oddball". He devoted his waking hours to mathematics, even into his later years—indeed, his death came at a mathematics conference in Warsaw. Erdős's prolific output with co-authors prompted the creation of the Erdős number, the number of steps in the shortest path between a mathematician and Erdős in terms of co-authorships.
Life
Paul Erdős
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https://en.wikipedia.org/wiki/DEC%20Systems%20Research%20Center
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The Systems Research Center (SRC) was a research laboratory created by Digital Equipment Corporation (DEC) in 1984, in Palo Alto, California.
DEC SRC was founded by a group of computer scientists, led by Robert Taylor, who left the Computer Science Laboratory (CSL) of Xerox PARC after an internal power struggle. SRC survived the takeover of DEC by Compaq in 1998. It was renamed to "Compaq Systems Research Center". When Compaq was acquired by Hewlett-Packard in 2002, SRC was merged with other HP corporate research labs and relocated there.
After Taylor's retirement, the lab was directed by Roy Levin and then by Lyle Ramshaw.
Some of the critical developments made at SRC include the Modula-3 programming language; the snoopy cache, used in the first multiprocessor workstation, the Firefly, built from MicroVAX 78032 microprocessors; the first multi-threaded Unix system, Taos; the first user interface editor; early networked window systems, Trestle. AltaVista was jointly developed by researchers from DEC's Network Systems Laboratory, Western Research Laboratory and Systems Research Center. Among the researchers at SRC, there are Butler Lampson, Chuck Thacker, and Leslie Lamport, all recipients of the ACM A.M. Turing Award.
A later inhabitant of this building is A9.com, a research part of Amazon.com.
References
External links
Downloadable SRC publications
Archived SRC Lab site
Educational buildings in Santa Clara County, California
Systems Research Center
Laboratories i
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https://en.wikipedia.org/wiki/Bottom-up
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Bottom-up may refer to:
Bottom-up analysis, a fundamental analysis technique in accounting and finance
Bottom-up parsing, a computer science strategy
Bottom-up processing, in Pattern recognition (psychology)
Bottom-up theories of galaxy formation and evolution
Bottom-up tree automaton, in data structures
Bottom-up integration testing, in software testing
Top-down and bottom-up design, strategies of information processing and knowledge ordering
Bottom-up proteomics, a laboratory technique involving proteins
Bottom Up Records, a record label founded by Shyheim
Bottom-up approach of the Holocaust, a viewpoint on the causes of the Holocaust
See also
Bottoms Up (disambiguation)
Top-down (disambiguation)
Capsizing, when a boat is turned upside down
Mundanity, a precursor of social movements
Social movements, bottom-up societal reform
Turtling (sailing)
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https://en.wikipedia.org/wiki/Awl
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Awl may refer to:
Tools
Bradawl, a woodworking hand tool for making small holes
Scratch awl, a woodworking layout and point-making tool used to scribe a line
Stitching awl, a tool for piercing holes in a variety of materials such as leather or canvases
Biology
Butterfly species called "awl", of the family Hesperiidae
Awls, genus Hasora
Awl-flies, family Xylophagidae
Awl nematode, or genus Dolichodorus
People
Aime M. Awl (1887–1973), American scientific illustrator
Farah Awl (1937–1991), Somali writer
William Maclay Awl (1799–1876), American psychiatrist and politician
Other uses
AA-4 'Awl', the NATO reporting name for the Raduga K-9 air-to-air missile
Academic Word List, a word frequency list from a broad range of academic texts
Alliance for Workers' Liberty, a Trotskyist group in Britain
Arizona Winter League, a former instructional baseball league
The Awl, a current events and culture website in New York City
Statement List (German: Anweisungsliste (AWL)), an instruction list language of Siemens
Alas Nacionales, a former airline, ICAO airline code AWL
See also
Owl (disambiguation)
Aul, a type of fortified village found throughout the Caucasus mountains and Central Asia
Ahlspiess or awl pike, a 15th–16th century thrusting spear
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https://en.wikipedia.org/wiki/Frobenius%20theorem%20%28differential%20topology%29
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In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields. The theorem generalizes the existence theorem for ordinary differential equations, which guarantees that a single vector field always gives rise to integral curves; Frobenius gives compatibility conditions under which the integral curves of r vector fields mesh into coordinate grids on r-dimensional integral manifolds. The theorem is foundational in differential topology and calculus on manifolds.
Contact geometry studies 1-forms that maximally violates the assumptions of Frobenius' theorem. An example is shown on the right.
Introduction
One-form version
Suppose we are to find the trajectory of a particle in a subset of 3D space, but we do not know its trajectory formula. Instead, we know only that its trajectory satisfies , where are smooth functions of . Then, we can know only for sure that, if at some moment in time, the particle is at location , then its velocity at that moment is restricted within the plane with equation
In other words, we can draw a "local plane" at each point in 3D space, and w
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https://en.wikipedia.org/wiki/Sober%20space
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In mathematics, a sober space is a topological space X such that every (nonempty) irreducible closed subset of X is the closure of exactly one point of X: that is, every irreducible closed subset has a unique generic point.
Definitions
Sober spaces have a variety of cryptomorphic definitions, which are documented in this section. All except the definition in terms of nets are described in. In each case below, replacing "unique" with "at most one" gives an equivalent formulation of the T0 axiom. Replacing it with "at least one" is equivalent to the property that the T0 quotient of the space is sober, which is sometimes referred to as having "enough points" in the literature.
In terms of morphisms of frames and locales
A topological space X is sober if every map that preserves all joins and all finite meets from its partially ordered set of open subsets to is the inverse image of a unique continuous function from the one-point space to X.
This may be viewed as a correspondence between the notion of a point in a locale and a point in a topological space, which is the motivating definition.
Using completely prime filters
A filter F of open sets is said to be completely prime if for any family of open sets such that , we have that for some i. A space X is sober if it each completely prime filter is the neighbourhood filter of a unique point in X.
In terms of nets
A net is self-convergent if it converges to every point in , or equivalently if its eventuality filter i
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https://en.wikipedia.org/wiki/Integrability
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Integrability may refer to:
Bronshtein-integrability (informal)
Frobenius integrability
Riemann-integrability
Lebesgue-integrability; see Lebesgue integral
Liouville-integrability
Darboux-integrability
See also
Integrable system (mathematics, physics)
System integration (information technology)
Interoperability (information technology)
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https://en.wikipedia.org/wiki/Type%20safety
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In computer science, type safety and type soundness are the extent to which a programming language discourages or prevents type errors. Type safety is sometimes alternatively considered to be a property of facilities of a computer language; that is, some facilities are type-safe and their usage will not result in type errors, while other facilities in the same language may be type-unsafe and a program using them may encounter type errors. The behaviors classified as type errors by a given programming language are usually those that result from attempts to perform operations on values that are not of the appropriate data type, e.g., adding a string to an integer when there's no definition on how to handle this case. This classification is partly based on opinion.
Type enforcement can be static, catching potential errors at compile time, or dynamic, associating type information with values at run-time and consulting them as needed to detect imminent errors, or a combination of both. Dynamic type enforcement often allows programs to run that would be invalid under static enforcement.
In the context of static (compile-time) type systems, type safety usually involves (among other things) a guarantee that the eventual value of any expression will be a legitimate member of that expression's static type. The precise requirement is more subtle than this — see, for example, subtyping and polymorphism for complications.
Definitions
Intuitively, type soundness is captured by Robin Mil
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https://en.wikipedia.org/wiki/Eduard%20von%20Hartmann
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Karl Robert Eduard von Hartmann (23 February 1842 – 5 June 1906) was a German philosopher, independent scholar and author of Philosophy of the Unconscious (1869). His notable ideas include the theory of the Unconscious and a pessimistic interpretation of the "best of all possible worlds" concept in metaphysics.
Biography
Von Hartmann was born in Berlin, the son of Prussian Major General Robert von Hartmann and was educated with the intention of him pursuing a military career. In 1858 he entered the Guards Artillery Regiment of the Prussian Army and attended the United Artillery and Engineering School. He achieved the rank of first lieutenant but took leave from the army in 1865 due to a chronic knee problem. After some hesitation between pursuing music or philosophy, he decided to make the latter his profession, and in 1867 earned his Ph.D. from the University of Rostock. In 1868 he formally resigned from the army. After the great success of his first work Philosophy of the Unconscious (1869)—the publication of which led to Von Hartmann being embroiled in the pessimism controversy in Germany—he rejected professorships offered to him by the universities of Leipzig, Göttingen and Berlin.
He subsequently returned to Berlin. For many years, he lived a retired life of study as an independent scholar, doing most of his work in bed, while suffering great pain.
Von Hartmann married Agnes Taubert (1844–1877) on 3 July 1872 in Charlottenburg. After her death, he married Alma Lorenz
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https://en.wikipedia.org/wiki/Imago
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In biology, the imago (Latin for "image") is the last stage an insect attains during its metamorphosis, its process of growth and development; it is also called the imaginal stage, the stage in which the insect attains maturity. It follows the final ecdysis of the immature instars.
In a member of the Ametabola or Hemimetabola, in which metamorphosis is "incomplete", the final ecdysis follows the last immature or nymphal stage.
In members of the Holometabola, in which there is a pupal stage, the final ecdysis follows emergence from the pupa, after which the metamorphosis is complete, although there is a prolonged period of maturation in some species.
The imago is the only stage during which the insect is sexually mature and, if it is a winged species, has functional wings. The imago often is referred to as the adult stage.
Members of the order Ephemeroptera (mayflies) do not have a pupal stage, but they briefly pass through an extra winged stage called the subimago. Insects at this stage have functional wings but are not yet sexually mature.
The Latin plural of imago is imagines, and this is the term generally used by entomologists –
however, imagoes is also acceptable.
See also
Imaginal disc
References
Insect developmental biology
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https://en.wikipedia.org/wiki/Parameterized%20complexity
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In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output. The complexity of a problem is then measured as a function of those parameters. This allows the classification of NP-hard problems on a finer scale than in the classical setting, where the complexity of a problem is only measured as a function of the number of bits in the input. This appears to have been first demonstrated in . The first systematic work on parameterized complexity was done by .
Under the assumption that P ≠ NP, there exist many natural problems that require superpolynomial running time when complexity is measured in terms of the input size only but that are computable in a time that is polynomial in the input size and exponential or worse in a parameter . Hence, if is fixed at a small value and the growth of the function over is relatively small then such problems can still be considered "tractable" despite their traditional classification as "intractable".
The existence of efficient, exact, and deterministic solving algorithms for NP-complete, or otherwise NP-hard, problems is considered unlikely, if input parameters are not fixed; all known solving algorithms for these problems require time that is exponential (so in particular superpolynomial) in the total size of the input. However, some problems can be solved by
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https://en.wikipedia.org/wiki/BTK
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BTK, Btk, etc. may refer to:
Biology and medicine
Bacillus thuringiensis kurstaki (Btk), a soil-dwelling bacterium also used as an insecticide
Bruton's tyrosine kinase, a protein
Btk-type zinc finger or Btk motif (BM), a zinc-binding motif present in some eukaryotic signalling proteins
Medicine
BTK (below-the-knee amputation), amputation of the lower limb between the knee joint and the ankle joint
Music
"BTK", a song by American band Exodus on their 2014 album Blood In, Blood Out
"B.T.K. (Dennis Rader)", a song by Japanese band Church of Misery on their 2013 album "Thy Kingdom Scum"
"Bind Torture Kill", a song by American band Suffocation on their 2006 self-titled album
Bind, Torture, Kill, a 2006 album by Belgian band Suicide Commando
Birth Through Knowledge, a Canadian hip-hop/rock band
Telecommunications
Bulgarian Telecommunications Company, (БТК in Cyrillic)
Information and Communication Technologies Authority in Turkey, (abbreviated as BTK in Turkish)
Transportation
Baku–Tbilisi–Kars railway connecting Azerbaijan, Georgia and Turkey
ICAO airline code for Indonesian airline Batik Air
IATA airport code for Bratsk Airport, Russia
Other uses
BTK, the ISO 639-2 and ISO 639-5 codes for Batak languages
Dennis Rader (born 1945), American serial killer known as "BTK"
Kaiser-Fleetwings XBTK, a US Navy dive and torpedo bomber
Pillars of Truth (Boutokaan Te Koaua), a political party in Kiribati
See also
Born to Kill (disambiguation)
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https://en.wikipedia.org/wiki/1985%20in%20science
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The year 1985 in science and technology involved many significant events, listed below.
Astronomy and space exploration
January 7 – Japan Aerospace Exploration Agency launches Sakigake, Japan's first interplanetary spacecraft and the first deep space probe to be launched by any country other than the United States or the Soviet Union.
Chemistry
The fullerene Buckminsterfullerene (C60) is first intentionally prepared by Harold Kroto, James R. Heath, Sean O'Brien, Robert Curl and Richard Smalley at Rice University in the United States.
Computer science
March – The GNU Manifesto, written by Richard Stallman, is first published.
March 15 – The first commercial Internet domain name, in the top-level domain .com, is registered in the name symbolics.com by Symbolics Inc., a computer systems firm in Cambridge, Massachusetts.
November 20 – Microsoft Windows operating system released.
Environment
May 16 – Scientists of the British Antarctic Survey announce discovery of the ozone hole.
Exploration
September 1 – The wreck of the RMS Titanic (1912) in the North Atlantic is located by a joint American-French expedition led by Dr. Robert Ballard (WHOI) and Jean-Louis Michel (Ifremer) using side-scan sonar from RV Knorr.
Mathematics
March – Louis de Branges de Bourcia publishes proof of de Branges's theorem.
September – Dennis Sullivan publishes proof of the No wandering domain theorem.
December – Publication of the ATLAS of Finite Groups.
Jean-Pierre Serre provides partial
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https://en.wikipedia.org/wiki/1981%20in%20science
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The year 1981 in science and technology involved many significant events, listed below.
Biology
September – Pantanal Matogrossense National Park designated in Brazil.
Publication of Stephen Jay Gould's critique of biological determinism, The Mismeasure of Man, in the United States.
Chemistry
A German research team led by Peter Armbruster and Gottfried Münzenberg at the GSI Helmholtz Centre for Heavy Ion Research (GSI Helmholtzzentrum für Schwerionenforschung) in Darmstadt bombard a target of bismuth-209 with accelerated nuclei of chromium-54 to produce 5 atoms of the isotope bohrium-262
Computer science
March 5 – The ZX81, a pioneering British home computer, is launched by Sinclair Research, going on to sell over 1.5 million units worldwide.
April 3 – The Osborne 1, the first successful portable computer, is unveiled at the West Coast Computer Faire in San Francisco.
July 9 – Nintendo releases the arcade game Donkey Kong featuring the debut of Mario.
August 12 – The IBM Personal Computer is released.
September 12 – The Chaos Computer Club, a European association of hackers, is established in Berlin by Wau Holland and others.
Mathematics
Alexander Merkurjev proves the norm residue isomorphism theorem for the case and .
Medicine
April 26 – Dr. Michael R. Harrison of the University of California, San Francisco, performs the world's first human open fetal surgery.
June 5 – AIDS pandemic begins when the United States Centers for Disease Control and Prevention rep
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https://en.wikipedia.org/wiki/David%20Gelernter
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David Hillel Gelernter (born March 5, 1955) is an American computer scientist, artist, and writer. He is a professor of computer science at Yale University.
Gelernter is known for contributions to parallel computation in the 1980s, and for books on topics such as computed worlds (Mirror Worlds). Gelernter is also known for his belief, expressed in his book America-Lite: How Imperial Academia Dismantled Our Culture (and Ushered in the Obamacrats), that liberal academia has a destructive influence on American society. He is in addition known for his views against women in the workforce, and his rejection of the scientific consensus regarding anthropogenic climate change and evolution.
In 1993 Gelernter was sent a mail bomb by Ted Kaczynski, known as the Unabomber. He opened it and the resulting explosion almost killed him, leaving him with permanent loss of use of his right hand as it destroyed 4 fingers, and permanent damage to his right eye.
Early life and education
Gelernter grew up on Long Island, New York. His father Herbert Gelernter was a physicist who, in the late 1950s and 1960s, became a pioneer in artificial intelligence and taught computer science at State University of New York at Stony Brook. Gelernter's grandfather was a rabbi, and Gelernter grew up as a Reform Jew; he later became a follower of Orthodox Judaism.
He received his Bachelor of Arts and Master of Arts degrees in Classical Hebrew literature from Yale University in 1976. He earned his Ph.D. from S
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https://en.wikipedia.org/wiki/Coherent%20sheaf
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In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information.
Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an abelian category, and so they are closed under operations such as taking kernels, images, and cokernels. The quasi-coherent sheaves are a generalization of coherent sheaves and include the locally free sheaves of infinite rank.
Coherent sheaf cohomology is a powerful technique, in particular for studying the sections of a given coherent sheaf.
Definitions
A quasi-coherent sheaf on a ringed space is a sheaf of -modules which has a local presentation, that is, every point in has an open neighborhood in which there is an exact sequence
for some (possibly infinite) sets and .
A coherent sheaf on a ringed space is a sheaf satisfying the following two properties:
is of finite type over , that is, every point in has an open neighborhood in such that there is a surjective morphism for some natural number ;
for any open set , any natural number , and any morphism of -modules, the kernel of is of finite type.
Morphisms between (quasi-)coherent sheaves are the same as morphisms of sheaves of -modules.
The case of schemes
When is a scheme, the genera
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https://en.wikipedia.org/wiki/Message%20forgery
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In cryptography, message forgery is sending a message so to deceive the recipient about the actual sender's identity. A common example is sending a spam or prank e-mail as if it were originated from an address other than the one which was really used.
See also
Authentication
Message authentication code
Stream cipher attack
Cryptographic attacks
Practical jokes
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https://en.wikipedia.org/wiki/K%C3%A4hler%20differential
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In mathematics, Kähler differentials provide an adaptation of differential forms to arbitrary commutative rings or schemes. The notion was introduced by Erich Kähler in the 1930s. It was adopted as standard in commutative algebra and algebraic geometry somewhat later, once the need was felt to adapt methods from calculus and geometry over the complex numbers to contexts where such methods are not available.
Definition
Let and be commutative rings and be a ring homomorphism. An important example is for a field and a unital algebra over (such as the coordinate ring of an affine variety). Kähler differentials formalize the observation that the derivatives of polynomials are again polynomial. In this sense, differentiation is a notion which can be expressed in purely algebraic terms. This observation can be turned into a definition of the module
of differentials in different, but equivalent ways.
Definition using derivations
An -linear derivation on is an -module homomorphism to an -module satisfying the Leibniz rule (it automatically follows from this definition that the image of is in the kernel of ). The module of Kähler differentials is defined as the -module for which there is a universal derivation . As with other universal properties, this means that is the best possible derivation in the sense that any other derivation may be obtained from it by composition with an -module homomorphism. In other words, the composition with provides, for every , an -modu
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https://en.wikipedia.org/wiki/Mosaic%20%28genetics%29
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Mosaicism or genetic mosaicism is a condition in which a multicellular organism possesses more than one genetic line as the result of genetic mutation. This means that various genetic lines resulted from a single fertilized egg. Mosaicism is one of several possible causes of chimerism, wherein a single organism is composed of cells with more than one distinct genotype.
Genetic mosaicism can result from many different mechanisms including chromosome nondisjunction, anaphase lag, and endoreplication. Anaphase lagging is the most common way by which mosaicism arises in the preimplantation embryo. Mosaicism can also result from a mutation in one cell during development, in which case the mutation will be passed on only to its daughter cells (and will be present only in certain adult cells). Somatic mosaicism is not generally inheritable as it does not generally affect germ cells.
History
In 1929, Alfred Sturtevant studied mosaicism in Drosophila, a genus of fruit fly. Muller in 1930 demonstrated that mosaicism in Drosophila is always associated with chromosomal rearrangements and Schultz in 1936 showed that in all cases studied these rearrangements were associated with heterochromatic inert regions, several hypotheses on the nature of such mosaicism were proposed. One hypothesis assumed that mosaicism appears as the result of a break and loss of chromosome segments. Curt Stern in 1935 assumed that the structural changes in the chromosomes took place as a result of somatic cross
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https://en.wikipedia.org/wiki/Schinzel%27s%20hypothesis%20H
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In mathematics, Schinzel's hypothesis H is one of the most famous open problems in the topic of number theory. It is a very broad generalization of widely open conjectures such as the twin prime conjecture. The hypothesis is named after Andrzej Schinzel.
Statement
The hypothesis claims that for every finite collection of nonconstant irreducible polynomials over the integers with positive leading coefficients, one of the following conditions holds:
There are infinitely many positive integers such that all of are simultaneously prime numbers, or
There is an integer (called a "fixed divisor"), which depends on the polynomials, which always divides the product . (Or, equivalently: There exists a prime such that for every there is an such that divides .)
The second condition is satisfied by sets such as , since is always divisible by 2. It is easy to see that this condition prevents the first condition from being true. Schinzel's hypothesis essentially claims that condition 2 is the only way condition 1 can fail to hold.
No effective technique is known for determining whether the first condition holds for a given set of polynomials, but the second one is straightforward to check: Let and compute the greatest common divisor of successive values of . One can see by extrapolating with finite differences that this divisor will also divide all other values of too.
Schinzel's hypothesis builds on the earlier Bunyakovsky conjecture, for a single polynomial, and on the
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https://en.wikipedia.org/wiki/Stone%27s%20representation%20theorem%20for%20Boolean%20algebras
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In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first half of the 20th century. The theorem was first proved by Marshall H. Stone. Stone was led to it by his study of the spectral theory of operators on a Hilbert space.
Stone spaces
Each Boolean algebra B has an associated topological space, denoted here S(B), called its Stone space. The points in S(B) are the ultrafilters on B, or equivalently the homomorphisms from B to the two-element Boolean algebra. The topology on S(B) is generated by a (closed) basis consisting of all sets of the form
where b is an element of B. This is the topology of pointwise convergence of nets of homomorphisms into the two-element Boolean algebra.
For every Boolean algebra B, S(B) is a compact totally disconnected Hausdorff space; such spaces are called Stone spaces (also profinite spaces). Conversely, given any topological space X, the collection of subsets of X that are clopen (both closed and open) is a Boolean algebra.
Representation theorem
A simple version of Stone's representation theorem states that every Boolean algebra B is isomorphic to the algebra of clopen subsets of its Stone space S(B). The isomorphism sends an element to the set of all ultrafilters that contain b. This is a clopen set because of the choice of topology on S(B) and because
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https://en.wikipedia.org/wiki/Elastase
|
In molecular biology, elastase is an enzyme from the class of proteases (peptidases) that break down proteins. In particular, it is a serine protease.
Forms and classification
Eight human genes exist for elastase:
Some bacteria (including Pseudomonas aeruginosa) also produce elastase. In bacteria, elastase is considered a virulence factor.
Function
Elastase breaks down elastin, an elastic fibre that, together with collagen, determines the mechanical properties of connective tissue. The neutrophil form breaks down the Outer membrane protein A (OmpA) of E. coli and other Gram-negative bacteria. Elastase also has the important immunological role of breaking down Shigella virulence factors. This is accomplished through the cleavage of peptide bonds in the target proteins. The specific peptide bonds cleaved are those on the carboxyl side of small, hydrophobic amino acids such as glycine, alanine, and valine. For more on how this is accomplished, see serine protease.
The role of human elastase in disease
A1AT
Elastase is inhibited by the acute-phase protein α1-antitrypsin (A1AT), which binds almost irreversibly to the active site of elastase and trypsin. A1AT is normally secreted by the liver cells into the serum. Alpha-1 antitrypsin deficiency (A1AD) leads to uninhibited destruction of elastic fibre by elastase; the main result is emphysema.
Cyclic neutropenia
The rare disease cyclic neutropenia (also called "cyclic hematopoeiesis") is an autosomal dominant genetic di
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https://en.wikipedia.org/wiki/Guillaume-Fran%C3%A7ois%20Rouelle
|
Guillaume François Rouelle (, 15 September 1703 – 3 August 1770) was a French chemist and apothecary. In 1754 he introduced the concept of a base into chemistry as a substance which reacts with an acid to form a salt.
He is known as l'Aîné (the elder) to distinguish him from his younger brother, Hilaire Rouelle, who was also a chemist and known as the discoverer of urea.
Rouelle started as an apothecary.
He later started a public course in his laboratory in 1738, in 1742 he was appointed experimental demonstrator of chemistry at the Jardin du Roi in Paris. he was especially influential and popular as a teacher, and taught many students among whom were Denis Diderot, Antoine-Laurent de Lavoisier, Joseph Proust and Antoine-Augustin Parmentier.
He was elected a foreign member of the Royal Swedish Academy of Sciences in 1749.
In addition to his investigation of neutral salts, he published papers on the inflammation of turpentine and other essential oils by nitric acid, and the methods of embalming practised in Ancient Egypt.
Why bases for neutral salts were called bases
The modern meaning of the word "base" and its general introduction into the chemical vocabulary are usually attributed to Rouelle, who used the term "Base" in a memoir on salts written in 1754 (see The Origin of the Term "Base" by William B. Jensen). In this paper, which was an extension of an earlier memoir on the same subject written in 1744, Rouelle pointed out that the number of known salts had increased
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https://en.wikipedia.org/wiki/AM-GM%20Inequality
|
In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same (in which case they are both that number).
The simplest non-trivial case – i.e., with more than one variable – for two non-negative numbers and , is the statement that
with equality if and only if .
This case can be seen from the fact that the square of a real number is always non-negative (greater than or equal to zero) and from the elementary case of the binomial formula:
Hence , with equality precisely when , i.e. . The AM–GM inequality then follows from taking the positive square root of both sides and then dividing both sides by 2.
For a geometrical interpretation, consider a rectangle with sides of length and , hence it has perimeter and area . Similarly, a square with all sides of length has the perimeter and the same area as the rectangle. The simplest non-trivial case of the AM–GM inequality implies for the perimeters that and that only the square has the smallest perimeter amongst all rectangles of equal area.
The simplest case is implicit in Euclid's Elements, Book 5, Proposition 25.
Extensions of the AM–GM inequality are available to include weights or generalized means.
Background
The arithmetic mean, or less precisel
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https://en.wikipedia.org/wiki/A1%20broth
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An A1 broth is a liquid culture medium used in microbiology for the detection of fecal coliforms in foods, treated wastewater and seawater bays using the most probable number (MPN) method. It is prepared according to the formulation of Andrews and Presnell given below. It is used with a Durham tube, a positive tube being one that exhibits a trapped bubble of gas.
Typical formula (g/L)
Directions
Suspend the dry ingredients in one liter of cold distilled water. Gently heat until completely dissolved and distribute 9 mL into test tubes with an inverted Durham tube. Sterilize in an autoclave at 121°C for 15 minutes. If needed, prepare multi-strength broth weighing the appropriate quantity of the dry medium. The final pH is 6.9 ± 0.1.
Widespread usage
Variants of this test has been used for potable water across the globe, for example by the Cree community of Split Lake, Manitoba, by the Mapuche people of Maquehue, Chile and in Singapore, Malaysia and Thailand
References
Microbiological media
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https://en.wikipedia.org/wiki/WLS
|
WLS may refer to:
Arts, entertainment, and media
WLS (AM), a radio station in Chicago, Illinois, US
WLS-FM, a radio station in Chicago, Illinois, US
WLS-TV, a television station in Chicago, Illinois, US
DWLS, a radio station in Metro Manila, Philippines
Biology and healthcare
GPR177, Wntless, or WLS, a human gene
Weight loss surgery
Computing and technology
Oracle WebLogic Server, a Java application server
White light scanner, for measuring surface height
Wavelength shifter, material that absorbs a wavelength and emits another
Other uses
Wisconsin Lutheran Seminary, US
WLS, the Chapman code for Wales
Weighted least squares, in statistics
West London Synagogue
Westchester Library System, New York, US
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https://en.wikipedia.org/wiki/Behavioral%20neuroscience
|
Behavioral neuroscience, also known as biological psychology, biopsychology, or psychobiology, is the application of the principles of biology to the study of physiological, genetic, and developmental mechanisms of behavior in humans and other animals.
History
Behavioral neuroscience as a scientific discipline emerged from a variety of scientific and philosophical traditions in the 18th and 19th centuries. René Descartes proposed physical models to explain animal as well as human behavior. Descartes suggested that the pineal gland, a midline unpaired structure in the brain of many organisms, was the point of contact between mind and body. Descartes also elaborated on a theory in which the pneumatics of bodily fluids could explain reflexes and other motor behavior. This theory was inspired by moving statues in a garden in Paris.
Other philosophers also helped give birth to psychology. One of the earliest textbooks in the new field, The Principles of Psychology by William James, argues that the scientific study of psychology should be grounded in an understanding of biology.
The emergence of psychology and behavioral neuroscience as legitimate sciences can be traced from the emergence of physiology from anatomy, particularly neuroanatomy. Physiologists conducted experiments on living organisms, a practice that was distrusted by the dominant anatomists of the 18th and 19th centuries. The influential work of Claude Bernard, Charles Bell, and William Harvey helped to convinc
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https://en.wikipedia.org/wiki/Photohydrogen
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In photochemistry, photohydrogen is hydrogen produced with the help of artificial or natural light. This is how the leaf of a tree splits water molecules into protons (hydrogen ions), electrons (to make carbohydrates) and oxygen (released into the air as a waste product). Photohydrogen may also be produced by the photodissociation of water by ultraviolet light.
Photohydrogen is sometimes discussed in the context of obtaining renewable energy from sunlight, by using microscopic organisms such as bacteria or algae. These organisms create hydrogen with the help of hydrogenase enzymes which convert protons derived from the water splitting reaction into hydrogen gas which can then be collected and used as a biofuel.
See also
Solar hydrogen panel
Photofermentation
Biological hydrogen production (Algae)
Photoelectrochemical cell
Photosynthesis
Hydrogen cycle
Hydrogen economy
References
Biofuels technology
Hydrogen production
Photochemistry
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https://en.wikipedia.org/wiki/Kronecker%27s%20theorem
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In mathematics, Kronecker's theorem is a theorem about diophantine approximation, introduced by .
Kronecker's approximation theorem had been firstly proved by L. Kronecker in the end of the 19th century. It has been now revealed to relate to the idea of n-torus and Mahler measure since the later half of the 20th century. In terms of physical systems, it has the consequence that planets in circular orbits moving uniformly around a star will, over time, assume all alignments, unless there is an exact dependency between their orbital periods.
Statement
Kronecker's theorem is a result in diophantine approximations applying to several real numbers xi, for 1 ≤ i ≤ n, that generalises Dirichlet's approximation theorem to multiple variables.
The classical Kronecker approximation theorem is formulated as follows.
Given real n-tuples and , the condition:
holds if and only if for any with
the number is also an integer.
In plainer language the first condition states that the tuple can be approximated arbitrarily well by linear combinations of the s (with integer coefficients) and integer vectors.
For the case of a and , Kronecker's Approximation Theorem can be stated as follows. For any with irrational and there exist integers and with , such that
Relation to tori
In the case of N numbers, taken as a single N-tuple and point P of the torus
T = RN/ZN,
the closure of the subgroup <P> generated by P will be finite, or some torus T′ contained in T. The original K
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https://en.wikipedia.org/wiki/Malanga
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Malanga may refer to:
Biology
Botany
Xanthosoma, a tropical and sub-tropical edible or ornamental plant, or its starchy bulbotubers
Eddoe (Colocasia esculenta antiquorum), a tropical vegetable closely related to taro
Zoology
Erebus ephesperis, also known as Erebus malanga, a moth species
Eilema triplaiola, also known as Ilema malanga, a moth species
Film
Malanga (film), 1986 Pakistani film
Music
, Colombian rock band
, Venezuelan pop rock or Venezuelan rock band
People
Malanga (dancer) (1885–1927), Cuban rumba dancer born José Rosario Oviedo
Christian Malanga (born 1983), Congolese politician
Gerard Malanga (born 1943), American poet and filmmaker
Steven Malanga, American journalist
Places
Malanga, neighbourhood in Maputo, Mozambique
Malanga, ancient name of Kanchipuram, India
Char Malanga, village in Bangladesh
Malangas, Zamboanga Sibugay, a town in the Philippines
Malangas Coal Reservation
Malangas Institute
See also
Malagan
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https://en.wikipedia.org/wiki/Dienes
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Dienes may refer to:
Dienes (surname), including a list of people with the name
the plural of diene, a class of organic chemical compound
Base ten blocks used in mathematics education, also known as Dienes blocks or simply dienes
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https://en.wikipedia.org/wiki/Meso
|
Meso or mesos may refer to:
Apache Mesos, a computer clustering management platform
Meso, in-game currency for the massively multiplayer online role-playing game MapleStory
Meso compound, a stereochemical classification in chemistry
Mesolithic, archaeological period between the Upper Paleolithic and the Neolithic
Mesopotamia, the first major river civilization, known today as Iraq
Mesoamerica, Americas, or Native Americans
Mesothelioma, a form of cancer
Mesoscopic physics, subdiscipline of condensed matter physics that deals with materials of an intermediate size
Multiple Equivalent Simultaneous Offers, a strategy used in negotiation
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https://en.wikipedia.org/wiki/1968%20in%20science
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The year 1968 in science and technology involved some significant events, listed below.
Astronomy
Thomas Gold explains the recently discovered radio pulsars as rapidly rotating neutron stars; subsequent observations confirm the suggestion.
Computer science
April – First book printed completely using electronic composition, the United States edition of Andrew Garve's thriller The Long Short Cut.
July 18 – The semiconductor chip company Intel is founded by Gordon E. Moore and Robert Noyce in Mountain View, California.
December 9 – In what becomes retrospectively known as "The Mother of All Demos", Douglas Engelbart of Stanford Research Institute's Augmentation Research Center demonstrates for the first time the computer mouse, the video conference, teleconferencing, hypertext, word processing, hypermedia, object addressing, the dynamic linker and a collaborative real-time editor using NLS.
Mathematics
Beniamino Segre describes a version of the tennis ball theorem.
Medicine
January 2 – Dr. Christiaan Barnard performs the second successful human heart transplant, in South Africa, on Philip Blaiberg, who survives for nineteen months.
November – Outbreak of acute gastroenteritis among schoolchildren in Norwalk, Ohio, caused by "Norwalk agent", the first identified norovirus.
Publication of a Harvard committee report on irreversible coma establishes a paradigm for defining brain death. France becomes the first European country to adopt brain death as a legal definition (
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https://en.wikipedia.org/wiki/RNC
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RNC may refer to:
Technology and sciences
Radio Network Controller, a governing element of a mobile phone network
Ribosome-nascent chain complex, in biology
Romanian National R&D Computer Network, registry for the .ro top-level domain
file extension for Relax NG files in compact syntax
Raster Navigational Charts (NOAA), a raster file format for nautical charts
Organisations
Royal Newfoundland Constabulary, a police force in Newfoundland and Labrador, Canada
Russia-NATO Council for cooperation between Russia and NATO military alliance
Politics
Republican National Committee, the principal campaign and fund-raising organization affiliated with the United States Republican Party
Republican National Convention, the nominating convention for the United States Republican Party
Rwanda National Congress, a political movement created by prominent Rwandan dissidents
Other
Riverside National Cemetery, a cemetery in Riverside, California for the interment of United States military personnel
Royal National College for the Blind, a college in Hereford, UK
Royal Niger Company, a mercantile company chartered by the British government in the nineteenth century
Rear naked choke, a martial arts move
NC (complexity), or RNC, a randomized complexity class in computational complexity theory
Nishinippon Broadcasting, a Japanese commercial broadcaster
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https://en.wikipedia.org/wiki/Einstein%E2%80%93Cartan%20theory
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In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation similar to general relativity. The theory was first proposed by Élie Cartan in 1922. Einstein–Cartan theory is the simplest Poincaré gauge theory.
Overview
Einstein–Cartan theory differs from general relativity in two ways: (1) it is formulated within the framework of Riemann–Cartan geometry, which possesses a locally gauged Lorentz symmetry, while general relativity is formulated within the framework of Riemannian geometry, which does not; (2) an additional set of equations are posed that relate torsion to spin. This difference can be factored into
by first reformulating general relativity onto a Riemann–Cartan geometry, replacing the Einstein–Hilbert action over Riemannian geometry by the Palatini action over Riemann–Cartan geometry; and second, removing the zero torsion constraint from the Palatini action, which results in the additional set of equations for spin and torsion, as well as the addition of extra spin-related terms in the Einstein field equations themselves.
The theory of general relativity was originally formulated in the setting of Riemannian geometry by the Einstein–Hilbert action, out of which arise the Einstein field equations. At the time of its original formulation, there was no concept of Riemann–Cartan geometry. Nor was there a sufficient awareness of the concept of gauge symmetry to understand that Rieman
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https://en.wikipedia.org/wiki/EECS
|
EECS may refer to:
Electrical engineering and computer science
European Energy Certificate System
See also
EEC (disambiguation)
|
https://en.wikipedia.org/wiki/Hilbert%27s%20program
|
In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early 1920s, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic.
Gödel's incompleteness theorems, published in 1931, showed that Hilbert's program was unattainable for key areas of mathematics. In his first theorem, Gödel showed that any consistent system with a computable set of axioms which is capable of expressing arithmetic can never be complete: it is possible to construct a statement that can be shown to be true, but that cannot be derived from the formal rules of the system. In his second theorem, he showed that such a system could not prove its own consistency, so it certainly cannot be used to prove the consistency of anything stronger with certainty. This refuted Hilbert's assumption that a finitistic system could be used to prove the consistency of itself, and therefore could not prove everything else.
Statement of Hilbert's program
The main goal of Hilbert's program was
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https://en.wikipedia.org/wiki/Reaction%20mechanism
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In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical reaction occurs.
A chemical mechanism is a theoretical conjecture that tries to describe in detail what takes place at each stage of an overall chemical reaction. The detailed steps of a reaction are not observable in most cases. The conjectured mechanism is chosen because it is thermodynamically feasible and has experimental support in isolated intermediates (see next section) or other quantitative and qualitative characteristics of the reaction. It also describes each reactive intermediate, activated complex, and transition state, which bonds are broken (and in what order), and which bonds are formed (and in what order). A complete mechanism must also explain the reason for the reactants and catalyst used, the stereochemistry observed in reactants and products, all products formed and the amount of each.
The electron or arrow pushing method is often used in illustrating a reaction mechanism; for example, see the illustration of the mechanism for benzoin condensation in the following examples section.
A reaction mechanism must also account for the order in which molecules react. Often what appears to be a single-step conversion is in fact a multistep reaction.
Reaction intermediates
Reaction intermediates are chemical species, often unstable and short-lived (however sometimes can be isolated), which are not reactants or products of the overall chemical reac
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https://en.wikipedia.org/wiki/Activated%20complex
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In chemistry an activated complex is defined by the International Union of Pure and Applied Chemistry (IUPAC) as "that assembly of atoms which corresponds to an arbitrary infinitesimally small region at or near the col (saddle point) of a potential energy surface". In other words, it refers to a collection of intermediate structures in a chemical reaction when bonds are breaking and new bonds are forming. It therefore represents not one defined state, but rather a range of transient configurations that a collection of atoms passes through in between clearly defined products and reactants.
Transition state theory (also known as activated complex theory) studies the kinetics of reactions that pass through a defined intermediate state with standard Gibbs energy of activation . The state represented by the double dagger symbol is known as the transition state and represents the exact configuration that has an equal probability of forming either the reactants or products of the given reaction.
The activated complex is often confused with the transition state and is used interchangeably in many textbooks. However, it differs from the transition state in that the transition state represents only the highest potential energy configuration of the atoms during the reaction while the activated complex refers to a range of configurations near the transition state that the atoms pass through in the transformation from products to reactants. This can be visualized in terms of a reaction
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https://en.wikipedia.org/wiki/Symbolic%20execution
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In computer science, symbolic execution (also symbolic evaluation or symbex) is a means of analyzing a program to determine what inputs cause each part of a program to execute. An interpreter follows the program, assuming symbolic values for inputs rather than obtaining actual inputs as normal execution of the program would. It thus arrives at expressions in terms of those symbols for expressions and variables in the program, and constraints in terms of those symbols for the possible outcomes of each conditional branch. Finally, the possible inputs that trigger a branch can be determined by solving the constraints.
The field of symbolic simulation applies the same concept to hardware. Symbolic computation applies the concept to the analysis of mathematical expressions.
Example
Consider the program below, which reads in a value and fails if the input is 6.
int f() {
...
y = read();
z = y * 2;
if (z == 12) {
fail();
} else {
printf("OK");
}
}
During a normal execution ("concrete" execution), the program would read a concrete input value (e.g., 5) and assign it to y. Execution would then proceed with the multiplication and the conditional branch, which would evaluate to false and print OK.
During symbolic execution, the program reads a symbolic value (e.g., λ) and assigns it to y. The program would then proceed with the multiplication and assign λ * 2 to z. When reaching the if statement, it would evaluate λ * 2 == 12. At this point of the program, λ c
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https://en.wikipedia.org/wiki/Parallel%20translation
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Parallel translation may refer to:
parallel transport, in mathematics
parallel text, in translation
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https://en.wikipedia.org/wiki/LEO%20%28website%29
|
LEO (meaning Link Everything Online) is an Internet-based electronic dictionary and translation dictionary initiated by the computer science department of the Technical University of Munich in Germany. After a spin-out, the dictionaries have been run since 3 April 2006 by the limited liability company Leo GmbH, formed by the members of the original Leo team, and are partially funded by commercial advertising on the website. Its dictionaries can be consulted free online from any web browser or from LEO's Lion downloadable user interface (GUI) which is free since version 3.0 (released 13 January 2009) to private users only and no longer sold as shareware. Corporate users and research institutions are however required to purchase a license.
Dictionaries
The website hosts eight free German language based bilingual dictionaries and forums for additional language queries. The dictionaries are characterized by providing translations in forms of hyperlinks to further dictionary queries, thereby facilitating back translations. The dictionaries are partly added to and corrected by large vocabulary donations of individuals or companies, partly through suggestions and discussions on the LEO language forums.
For any of the eight foreign languages, there's at least one (in the cases of English and French two) qualified employee in charge (whose mother tongue is either German and who has studied the respective other idiom or vice versa). These employees oversee the above-mentioned donati
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https://en.wikipedia.org/wiki/Swedish%20Institute%20of%20Space%20Physics
|
The Swedish Institute of Space Physics (, IRF) is a Swedish government agency. The institute's primary task is to carry out basic research, education and associated observatory activities in space physics, space technology and atmospheric physics.
Foundation
The IRF was founded in 1957 and the first Kiruna-designed satellite experiment was launched in 1968. The institute has about one hundred employees and has its head office in Kiruna. Other offices are situated in Umeå, Uppsala and Lund.
IRF, originally the Kiruna Geophysical Observatory, began as a department within the Royal Swedish Academy of Sciences. It has been a public research institute since 1973, under the auspices of the Swedish Ministry of Education and Culture.
Satellite experiments
IRF participates in several international satellite projects. At present, data from satellite instruments are being analysed to help us better comprehend the plasma-physical processes in the solar wind and around comets and planets. For example, the Swedish Viking and Freja satellites, with equipment from IRF on board, have greatly increased our knowledge of the auroral processes in the Earth’s magnetosphere, as have the microsatellites Astrid 1 and 2, launched in 1995 and 1998. IRF's own nano-satellite Munin (at 6 kg (13 lb) the smallest-ever research satellite) was launched in 2000. An IRF-built instrument on board the Indian satellite Chandrayaan-1 (launched 2008) collected data from the Moon and new techniques for making par
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https://en.wikipedia.org/wiki/Janna%20Levin
|
Janna J. Levin (born 1967) is an American theoretical cosmologist and a professor of physics and astronomy at Barnard College. She earned a Bachelor of Arts in astronomy and physics with a concentration in philosophy at Barnard College in 1988 and a PhD in theoretical physics at the Massachusetts Institute of Technology in 1993. Much of her work deals with looking for evidence to support the proposal that our universe might be finite in size due to its having a nontrivial topology. Other work includes black holes and chaos theory. She joined the faculty at Barnard College in January 2004 and is currently the Claire Tow Professor of Physics and Astronomy.
Biography
Levin was born to Yiddish-speaking Jewish parents in Texas. Her grandparents were immigrants from Eastern Europe, who eventually gave up keeping kosher. She describes her household as mostly not religious (Levin was not brought to synagogue and was not bat mitzvahed). Levin attended Columbia University for her bachelor's degree and MIT for her Ph.D, graduating in 1993. In 2002 she held a research fellowship at Cambridge University (England).
Janna Levin is a professor of physics and astronomy at Barnard College of Columbia University with a grant from the Tow Foundation. She researches black holes, the cosmology of extra dimensions, and gravitational waves in the shape of spacetime. In addition she is the director of sciences at Pioneer Works.
Levin is the author of the popular science book How the Universe Got
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https://en.wikipedia.org/wiki/Expression%20%28mathematics%29
|
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Many authors distinguish an expression from a formula, the former denoting a mathematical object, and the latter denoting a statement about mathematical objects. For example, is an expression, while is a formula. However, in modern mathematics, and in particular in computer algebra, formulas are viewed as expressions that can be evaluated to true or false, depending on the values that are given to the variables occurring in the expressions. For example takes the value false if is given a value less than –1, and the value true otherwise.
Examples
The use of expressions ranges from the simple:
(linear polynomial)
(quadratic polynomial)
(rational fraction)
to the complex:
Syntax versus semantics
Syntax
An expression is a syntactic construct. It must be well-formed: the allowed operators must have the correct number of inputs in the correct places, the characters that make up these inputs must be valid, have a clear order of operations, etc. Strings of symbols that violate the rules of syntax are not well-formed and are not valid mathematical expressions.
For example, in the usual notation of arithmetic
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https://en.wikipedia.org/wiki/1963%20in%20science
|
The year 1963 in science and technology involved some significant events, listed below.
Astronomy, astrophysics and space exploration
January 1 – Long-period comet C/1963 A1 (Ikeya) is discovered by a Japanese amateur.
January 4 – Soviet Luna reaches Earth orbit but fails to reach the Moon.
May 15 – Mercury program: NASA launches the last mission of the program Mercury 9. (On June 12 NASA Administrator James E. Webb tells Congress the program is complete.)
July 26 – Roy Kerr submits for publication his discovery of the Kerr metric, an exact solution to the Einstein field equation of general relativity, predicting a rotating black hole.
October 18 – Aboard the French Véronique AGI 47 sounding rocket, a bicolor cat designated C 341, later known as Félicette, becomes the first cat in space.
November 1 – The Arecibo Observatory, with the world's largest single-dish radio telescope, officially opens in Arecibo, Puerto Rico.
First definite identification of a radio source, 3C 48, with an optical object, later identified as a quasar, is published by Allan Sandage and Thomas A. Matthews; also Maarten Schmidt publishes significant observations on 3C 273.
Biology
Geneticist J. B. S. Haldane coins the word "clone".
Molecular biologist Emile Zuckerkandl and physical chemist Linus Pauling introduce the term paleogenetics.
Konrad Lorenz publishes On Aggression (Das sogenannte Böse: Zur Naturgeschichte der Aggression).
Niko Tinbergen poses his four questions to be asked of any
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https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider%20theorem
|
In mathematics, the Gelfond–Schneider theorem establishes the transcendence of a large class of numbers.
History
It was originally proved independently in 1934 by Aleksandr Gelfond and Theodor Schneider.
Statement
If a and b are complex algebraic numbers with a ≠ 0, 1, and b not rational, then any value of ab is a transcendental number.
Comments
The values of a and b are not restricted to real numbers; complex numbers are allowed (here complex numbers are not regarded as rational when they have an imaginary part not equal to 0, even if both the real and imaginary parts are rational).
In general, is multivalued, where ln stands for the natural logarithm. This accounts for the phrase "any value of" in the theorem's statement.
An equivalent formulation of the theorem is the following: if α and γ are nonzero algebraic numbers, and we take any non-zero logarithm of α, then is either rational or transcendental. This may be expressed as saying that if , are linearly independent over the rationals, then they are linearly independent over the algebraic numbers. The generalisation of this statement to more general linear forms in logarithms of several algebraic numbers is in the domain of transcendental number theory.
If the restriction that a and b be algebraic is removed, the statement does not remain true in general. For example,
Here, a is , which (as proven by the theorem itself) is transcendental rather than algebraic. Similarly, if and , which is transcendental
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https://en.wikipedia.org/wiki/Key%20schedule
|
In cryptography, the so-called product ciphers are a certain kind of cipher, where the (de-)ciphering of data is typically done as an iteration of rounds. The setup for each round is generally the same, except for round-specific fixed values called a round constant, and round-specific data derived from the cipher key called a round key. A key schedule is an algorithm that calculates all the round keys from the key.
Some types of key schedules
Some ciphers have simple key schedules. For example, the block cipher TEA splits the 128-bit key into four 32-bit pieces and uses them repeatedly in successive rounds.
DES has a key schedule in which the 56-bit key is divided into two 28-bit halves; each half is thereafter treated separately. In successive rounds, both halves are rotated left by one or two bits (specified for each round), and then 48 round key bits are selected by Permuted Choice 2 (PC-2) – 24 bits from the left half and 24 from the right. The rotations have the effect that a different set of bits is used in each round key; each bit is used in approximately 14 out of the 16 round keys.
To avoid simple relationships between the cipher key and the round keys, in order to resist such forms of cryptanalysis as related-key attacks and slide attacks, many modern ciphers use more elaborate key schedules to generate an "expanded key" from which round keys are drawn. Some ciphers, such as Rijndael (AES) and Blowfish, use the same operations as those used in the data path of t
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https://en.wikipedia.org/wiki/Duality%20%28mathematics%29
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In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of is , then the dual of is . Such involutions sometimes have fixed points, so that the dual of is itself. For example, Desargues' theorem is self-dual in this sense under the standard duality in projective geometry.
In mathematical contexts, duality has numerous meanings. It has been described as "a very pervasive and important concept in (modern) mathematics" and "an important general theme that has manifestations in almost every area of mathematics".
Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of the second type to some family of scalars. For instance, linear algebra duality corresponds in this way to bilinear maps from pairs of vector spaces to scalars, the duality between distributions and the associated test functions corresponds to the pairing in which one integrates a distribution against a test function, and Poincaré duality corresponds similarly to intersection number, viewed as a pairing between submanifolds of a given manifold.
From a category theory viewpoint, duality can also be seen as a functor, at least in the realm of vector spaces. This functor assigns to each space its dual space, and the pullback construction assigns to each ar
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https://en.wikipedia.org/wiki/1956%20in%20science
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The year 1956 in science and technology involved some significant events, listed below.
Biology
March – Denham Harman proposes the free-radical theory of aging.
Wesley K. Whitten reports developing eight-cell mouse ova to blastocyst stage in vitro.
Climatology
May – Gilbert Plass publishes his seminal article "The Carbon Dioxide Theory of Climate Change".
Computer science
July 13 – John McCarthy (Dartmouth), Marvin Minsky (MIT), Claude Shannon (Bell Labs) and Nathaniel Rochester (IBM) assemble the first coordinated research meeting on the topic of artificial intelligence, at Dartmouth College, Hanover, New Hampshire, in the United States.
September 13 – The hard disk drive is invented by an IBM team led by Reynold B. Johnson.
TX-0 transistorized computer completed at MIT Lincoln Laboratory in the United States.
Mathematics
February 1 – Joseph Kruskal publishes Kruskal's algorithm.
December – Martin Gardner begins his Mathematical Games column in Scientific American.
Henri Cartan and Samuel Eilenberg publish a text on homological algebra.
Jean-Pierre Serre publishes his "GAGA" paper in algebraic geometry and analytic geometry.
Medicine
April – Humphry Osmond first proposes use of the word psychedelic to describe the effect of certain drugs, at a meeting of the New York Academy of Sciences.
May 1 – Minamata disease epidemic is identified in Japan by Hajime Hosokawa.
June 1 – Elsie Stephenson becomes founding Director of the Nurse Teaching Unit, University of E
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https://en.wikipedia.org/wiki/Alexander%20Oparin
|
Alexander Ivanovich Oparin (; – April 21, 1980) was a Soviet biochemist notable for his theories about the origin of life, and for his book The Origin of Life. He also studied the biochemistry of material processing by plants and enzyme reactions in plant cells. He showed that many food production processes were based on biocatalysis and developed the foundations for industrial biochemistry in the USSR.
Life
Born in Uglich in 1894, Oparin graduated from the Moscow State University in 1917 and became a professor of biochemistry there in 1927. Many of his early papers were about plant enzymes and their role in metabolism. In 1924 he put forward a hypothesis suggesting that life on Earth developed through a gradual chemical evolution of carbon-based molecules in the Earth's primordial soup. In 1935, along with academician Alexey Bakh, he founded the Biochemistry Institute of the Soviet Academy of Sciences. In 1939, Oparin became a Corresponding Member of the Academy, and, in 1946, a full member. In 1940s and 1950s he supported the theories of Trofim Lysenko and Olga Lepeshinskaya, who made claims about "the origin of cells from noncellular matter". "Taking the party line" helped advance his career. In 1970, he was elected President of the International Society for the Study of the Origins of Life. He died in Moscow on April 21, 1980, and was interred in Novodevichy Cemetery in Moscow.
Oparin became Hero of Socialist Labour in 1969, received the Lenin Prize in 1974 and was awa
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https://en.wikipedia.org/wiki/G.%20I.%20Taylor
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Sir Geoffrey Ingram Taylor OM FRS FRSE (7 March 1886 – 27 June 1975) was a British physicist and mathematician, who made contributions to fluid dynamics and wave theory.
Early life and education
Taylor was born in St. John's Wood, London. His father, Edward Ingram Taylor, was an artist, and his mother, Margaret Boole, came from a family of mathematicians (his aunt was Alicia Boole Stott and his grandfather was George Boole). As a child he was fascinated by science after attending the Royal Institution Christmas Lectures, and performed experiments using paint rollers and sticky-tape.
Taylor read mathematics and physics at Trinity College, Cambridge from 1905 to 1908. He won several scholarships and prizes at Cambridge, one of which enabled him to study under J. J. Thomson.
Career and research
Taylor published his first paper while he was still an undergraduate. In it, he showed that interference of visible light produced fringes even with extremely weak light sources. The interference effects were produced with light from a gas light, attenuated through a series of dark glass plates, diffracting around a sewing needle. Three months were required to produce a sufficient exposure of the photographic plate. The paper does not mention quanta of light (photons) and does not reference Einstein's 1905 paper on the photoelectric effect, but today the result can be interpreted by saying that less than one photon on average was present at a time. Once it became widely accepted in aro
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https://en.wikipedia.org/wiki/Cusp%20form
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In number theory, a branch of mathematics, a cusp form is a particular kind of modular form with a zero constant coefficient in the Fourier series expansion.
Introduction
A cusp form is distinguished in the case of modular forms for the modular group by the vanishing of the constant coefficient a0 in the Fourier series expansion (see q-expansion)
This Fourier expansion exists as a consequence of the presence in the modular group's action on the upper half-plane via the transformation
For other groups, there may be some translation through several units, in which case the Fourier expansion is in terms of a different parameter. In all cases, though, the limit as q → 0 is the limit in the upper half-plane as the imaginary part of z → ∞. Taking the quotient by the modular group, this limit corresponds to a cusp of a modular curve (in the sense of a point added for compactification). So, the definition amounts to saying that a cusp form is a modular form that vanishes at a cusp. In the case of other groups, there may be several cusps, and the definition becomes a modular form vanishing at all cusps. This may involve several expansions.
Dimension
The dimensions of spaces of cusp forms are, in principle, computable via the Riemann–Roch theorem. For example, the Ramanujan tau function τ(n) arises as the sequence of Fourier coefficients of the cusp form of weight 12 for the modular group, with a1 = 1. The space of such forms has dimension 1, which means this definition is possib
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https://en.wikipedia.org/wiki/Eric%20Lander
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Eric Steven Lander (born February 3, 1957) is an American mathematician and geneticist who is a professor of biology at the Massachusetts Institute of Technology (MIT), and a professor of systems biology at Harvard Medical School. Eric Lander is founding director emeritus of the Broad Institute of MIT and Harvard. He is a 1987 MacArthur Fellow and Rhodes Scholar.
Lander served as the 11th director of the Office of Science and Technology Policy and Science Advisor to the President in Joe Biden's presidential Cabinet. In response to allegations that he had engaged in bullying and abusive conduct, Lander apologized and resigned from the Biden Administration effective February 18, 2022.
Early life and education
Lander was born in Brooklyn, New York City, to Jewish parents, the son of Rhoda G. Lander, a social studies teacher, and Harold Lander, an attorney. He was captain of the math team at Stuyvesant High School, graduating in 1974 as valedictorian and an International Mathematical Olympiad Silver Medalist for the U.S. At age 17, he wrote a paper on quasiperfect numbers for which he won the Westinghouse Science Talent Search.
After graduating from Stuyvesant High School as valedictorian in 1974, Lander graduated from Princeton University in 1978 as valedictorian and with a Bachelor of Arts in Mathematics. He completed his senior thesis, "On the structure of projective modules", under John Coleman Moore's supervision. He then moved to the University of Oxford where he was a
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https://en.wikipedia.org/wiki/Fine%20structure
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In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to electron spin and relativistic corrections to the non-relativistic Schrödinger equation. It was first measured precisely for the hydrogen atom by Albert A. Michelson and Edward W. Morley in 1887, laying the basis for the theoretical treatment by Arnold Sommerfeld, introducing the fine-structure constant.
Background
Gross structure
The gross structure of line spectra is the line spectra predicted by the quantum mechanics of non-relativistic electrons with no spin. For a hydrogenic atom, the gross structure energy levels only depend on the principal quantum number n. However, a more accurate model takes into account relativistic and spin effects, which break the degeneracy of the energy levels and split the spectral lines. The scale of the fine structure splitting relative to the gross structure energies is on the order of (Zα)2, where Z is the atomic number and α is the fine-structure constant, a dimensionless number equal to approximately 1/137.
Relativistic corrections
The fine structure energy corrections can be obtained by using perturbation theory. To perform this calculation one must add the three corrective terms to the Hamiltonian: the leading order relativistic correction to the kinetic energy, the correction due to the spin–orbit coupling, and the Darwin term coming from the quantum fluctuating motion or zitterbewegung of the electron.
These corrections can also be
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https://en.wikipedia.org/wiki/1939%20in%20science
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The year 1939 in science and technology involved some significant events, listed below.
Astronomy
Robert Oppenheimer jointly predicts two new types of celestial object:
With George Volkoff, he calculates the structure of neutron stars.
With Hartland Snyder, he predicts the existence of what will come to be called black holes.
Biology
Autumn – DDT's properties as an insecticide are discovered by Paul Müller of Geigy.
Cartography
Kavrayskiy VII projection devised by Vladimir V. Kavrayskiy.
Chemistry
January 7 – French physicist Marguerite Perey identifies francium, the last chemical element first discovered in nature, as a decay product of 227Ac.
April 30 – Nylon fabric is first introduced to the general public at the New York World's Fair.
July – Edward Adelbert Doisy of Saint Louis University publishes the chemical structure of vitamin K.
Linus Pauling publishes The Nature of the Chemical Bond, a compilation of a decade's work on chemical bonding, explaining hybridization theory, covalent bonding and ionic bonding as explained through electronegativity, and resonance as a means to explain, among other things, the structure of benzene.
Computer science
September 4 – Alan Turing and Gordon Welchman report to the United Kingdom Government Code and Cypher School, Bletchley Park.
October – John V. Atanasoff with Clifford Berry demonstrate the first prototype Atanasoff–Berry Computer at Iowa State University.
Publication of Vannevar Bush's article "Mechanization an
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https://en.wikipedia.org/wiki/Clandestine%20chemistry
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Clandestine chemistry is chemistry carried out in secret, and particularly in illegal drug laboratories. Larger labs are usually run by gangs or organized crime intending to produce for distribution on the black market. Smaller labs can be run by individual chemists working clandestinely in order to synthesize smaller amounts of controlled substances or simply out of a hobbyist interest in chemistry, often because of the difficulty in ascertaining the purity of other, illegally synthesized drugs obtained on the black market. The term clandestine lab is generally used in any situation involving the production of illicit compounds, regardless of whether the facilities being used qualify as a true laboratory.
History
Ancient forms of clandestine chemistry included the manufacturing of explosives.
Another old form of clandestine chemistry is the illegal brewing and distillation of alcohol. This is frequently done to avoid taxation on spirits.
From 1919 to 1933, the United States prohibited the sale, manufacture, or transportation of alcoholic beverages. This opened a door for brewers to supply their own town with alcohol. Just like modern-day drug labs, distilleries were placed in rural areas. The term moonshine generally referred to "corn whiskey", that is, a whiskey-like liquor made from corn. Today, American-made corn whiskey can be labeled or sold under that name, or as Bourbon or Tennessee whiskey, depending on the details of the production process.
Psychoactive substanc
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https://en.wikipedia.org/wiki/BTX
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BTX may refer to:
Bildschirmtext, an interactive videotex system launched in 1983 in West Germany
BTX (chemistry), a mixture of benzene, toluene and xylenes
B't X, a science fiction manga and anime television series created by Masami Kurumada
BTX (form factor), a form factor for PC motherboards
Backstreets Magazine, also known as BTX, a popular Internet forum for fans of musician Bruce Springsteen
Batrachotoxin, a neurotoxic poison that blocks sodium channels
Botulinum toxin, the most potent neurotoxin known
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https://en.wikipedia.org/wiki/Norbert%20Wiener%20Prize%20in%20Applied%20Mathematics
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The Norbert Wiener Prize in Applied Mathematics is a $5000 prize awarded, every three years, for an outstanding contribution to "applied mathematics in the highest and broadest sense." It was endowed in 1967 in honor of Norbert Wiener by MIT's mathematics department and is provided jointly by the American Mathematical Society and Society for Industrial and Applied Mathematics and first issued in 1970. The recipient of the prize has to be a member of one of the awarding societies.
Winners
1970: Richard E. Bellman
1975: Peter D. Lax
1980: Tosio Kato and Gerald B. Whitham
1985: Clifford S. Gardner
1990: Michael Aizenman and Jerrold E. Marsden
1995: Hermann Flaschka and Ciprian Foias
2000: Alexandre J. Chorin and Arthur Winfree
2004: James A. Sethian
2007: Craig Tracy and Harold Widom
2010: David Donoho
2013: Andrew Majda
2016: Constantine M. Dafermos
2019: Marsha Berger and Arkadi Nemirovski
2022: Eitan Tadmor
See also
List of mathematics awards
Prizes named after people
References
External links
AMS webpage for the prize
SIAM webpage for the prize
Awards of the American Mathematical Society
Awards established in 1970
Triennial events
Awards of the Society for Industrial and Applied Mathematics
1970 establishments in the United States
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https://en.wikipedia.org/wiki/Paul%20Wild%20%28Swiss%20astronomer%29
|
Paul Wild (; 5 October 1925 – 2 July 2014) was a Swiss astronomer and director of the Astronomical Institute of the University of Bern, who discovered numerous comets, asteroids and supernovae.
Biography
Wild was born on 5 October 1925 in the village of Wädenswil near Zürich, Switzerland. From 1944 through 1950, he studied mathematics and physics at the ETH Zurich. Thereafter, he worked at the California Institute of Technology where he researched galaxies and supernovas under the leadership of countryman Fritz Zwicky from 1951 through 1955.
At the Zimmerwald Observatory, near Bern, Wild made his first cometary discovery C/1957 U1 (1957 IX) on 2 October 1957. The parabolic comet was later named "Latyshev-Wild–Burnham".
Professor Wild became director of the Astronomical Institute of the University of Bern in 1980, and remained in this position until 1991. He died on 2 July 2014 at the age of 88 in Bern.
Discoveries
During countless nights Wild observed the skies at the Zimmerwald Observatory near Bern and discovered numerous asteroids, comets and supernovae including:
4 periodic comets: 63P/Wild, 81P/Wild, 86P/Wild and 116P/Wild
3 parabolic comets: C/1957 U1, C/1967 C2 and C/1968 U1
The Apollo asteroid 1866 Sisyphus and the two Amor asteroids 2368 Beltrovata and 3552 Don Quixote
41 supernovae, as well as 8 co-discoveries. His first discovered supernova was SN 1954A, while his most recent is SN 1994M.
The best known discovery of a comet occurred on 6 January 1978.
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https://en.wikipedia.org/wiki/Sinc%20function
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In mathematics, physics and engineering, the sinc function, denoted by , has two forms, normalized and unnormalized.
In mathematics, the historical unnormalized sinc function is defined for by
Alternatively, the unnormalized sinc function is often called the sampling function, indicated as Sa(x).
In digital signal processing and information theory, the normalized sinc function is commonly defined for by
In either case, the value at is defined to be the limiting value
for all real (the limit can be proven using the squeeze theorem).
The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of ). As a further useful property, the zeros of the normalized sinc function are the nonzero integer values of .
The normalized sinc function is the Fourier transform of the rectangular function with no scaling. It is used in the concept of reconstructing a continuous bandlimited signal from uniformly spaced samples of that signal.
The only difference between the two definitions is in the scaling of the independent variable (the axis) by a factor of . In both cases, the value of the function at the removable singularity at zero is understood to be the limit value 1. The sinc function is then analytic everywhere and hence an entire function.
The function has also been called the cardinal sine or sine cardinal function. The term sinc was introduced by Philip M. Woodwar
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https://en.wikipedia.org/wiki/Yield
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Yield may refer to:
Measures of output/function
Computer science
Yield (multithreading) is an action that occurs in a computer program during multithreading
See generator (computer programming)
Physics/chemistry
Yield (chemistry), the amount of product obtained in a chemical reaction
The arrow symbol in a chemical equation
Yield (engineering), yield strength of a material as defined in engineering and material science
Fission product yield
Nuclear weapon yield
Earth science
Crop yield, measurement of the amount of a crop harvested, or animal products such as wool, meat or milk produced, per unit area of land
Yield (wine), the amount of grapes or wine that is produced per unit surface of vineyard
Ecological yield, the harvestable population growth of an ecosystem, most commonly measured in forestry and fishery
Specific yield, a measure of aquifer capacity
Yield (hydrology), the volume of water escaping from a spring
Production/manufacturing
Yield (casting)
Throughput yield, a manufacturing evaluation method
A measure of functioning devices in semiconductor testing, see Semiconductor device fabrication#Device test
The number of servings provided by a recipe and hulk
Finance
Yield (finance), a rate of return for a security
Dividend yield and earnings yield, measures of dividends paid on stock
Other uses
Yield (college admissions), a statistic describing what percent of applicants choose to enroll
Yield (album), by Pearl Jam
Yield sign, a traffic sign
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https://en.wikipedia.org/wiki/Bioacoustics
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Bioacoustics is a cross-disciplinary science that combines biology and acoustics. Usually it refers to the investigation of sound production, dispersion and reception in animals (including humans). This involves neurophysiological and anatomical basis of sound production and detection, and relation of acoustic signals to the medium they disperse through. The findings provide clues about the evolution of acoustic mechanisms, and from that, the evolution of animals that employ them.
In underwater acoustics and fisheries acoustics the term is also used to mean the effect of plants and animals on sound propagated underwater, usually in reference to the use of sonar technology for biomass estimation. The study of substrate-borne vibrations used by animals is considered by some a distinct field called biotremology.
History
For a long time humans have employed animal sounds to recognise and find them. Bioacoustics as a scientific discipline was established by the Slovene biologist Ivan Regen who began systematically to study insect sounds. In 1925 he used a special stridulatory device to play in a duet with an insect. Later, he put a male cricket behind a microphone and female crickets in front of a loudspeaker. The females were not moving towards the male but towards the loudspeaker. Regen's most important contribution to the field apart from realization that insects also detect airborne sounds was the discovery of tympanal organ's function.
Relatively crude electro-mechanical d
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https://en.wikipedia.org/wiki/Per-unit%20system
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In the power systems analysis field of electrical engineering, a per-unit system is the expression of system quantities as fractions of a defined base unit quantity. Calculations are simplified because quantities expressed as per-unit do not change when they are referred from one side of a transformer to the other. This can be a pronounced advantage in power system analysis where large numbers of transformers may be encountered. Moreover, similar types of apparatus will have the impedances lying within a narrow numerical range when expressed as a per-unit fraction of the equipment rating, even if the unit size varies widely. Conversion of per-unit quantities to volts, ohms, or amperes requires a knowledge of the base that the per-unit quantities were referenced to. The per-unit system is used in power flow, short circuit evaluation, motor starting studies etc.
The main idea of a per unit system is to absorb large differences in absolute values into base relationships. Thus, representations of elements in the system with per unit values become more uniform.
A per-unit system provides units for power, voltage, current, impedance, and admittance. With the exception of impedance and admittance, any two units are independent and can be selected as base values; power and voltage are typically chosen. All quantities are specified as multiples of selected base values. For example, the base power might be the rated power of a transformer, or perhaps an arbitrarily selected power w
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https://en.wikipedia.org/wiki/Crick%2C%20Brenner%20et%20al.%20experiment
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The Crick, Brenner et al. experiment (1961) was a scientific experiment performed by Francis Crick, Sydney Brenner, Leslie Barnett and R.J. Watts-Tobin.
It was a key experiment in the development of what is now known as molecular biology and led to a publication entitled "The General Nature of the Genetic Code for Proteins" and according to the historian of Science Horace Judson is "regarded...as a classic of intellectual clarity, precision and rigour". This study demonstrated that the genetic code is made up of a series of three base pair codons which code for individual amino acids. The experiment also elucidated the nature of gene expression and frame-shift mutations.
The experiment
In the experiment, proflavin-induced mutations of the T4 bacteriophage gene, rIIB, were isolated. Proflavin causes mutations by inserting itself between DNA bases, typically resulting in insertion or deletion of a single base pair.
Through the use of proflavin, the experimenters were able to insert or delete base pairs into their sequence of interest. When nucleotides were inserted or deleted, the gene would often be nonfunctional. However, if three base pairs were added or deleted, the gene would remain functional. This proved that the genetic code uses a codon of three nucleotide bases that corresponds to an amino acid. The mutants produced by Crick and Brenner that could not produce functional rIIB protein were the results of frameshift mutations, where the triplet code was disrupted.
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https://en.wikipedia.org/wiki/Localization%20of%20a%20category
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In mathematics, localization of a category consists of adding to a category inverse morphisms for some collection of morphisms, constraining them to become isomorphisms. This is formally similar to the process of localization of a ring; it in general makes objects isomorphic that were not so before. In homotopy theory, for example, there are many examples of mappings that are invertible up to homotopy; and so large classes of homotopy equivalent spaces. Calculus of fractions is another name for working in a localized category.
Introduction and motivation
A category C consists of objects and morphisms between these objects. The morphisms reflect relations between the objects. In many situations, it is meaningful to replace C by another category C''' in which certain morphisms are forced to be isomorphisms. This process is called localization.
For example, in the category of R-modules (for some fixed commutative ring R) the multiplication by a fixed element r of R is typically (i.e., unless r is a unit) not an isomorphism:
The category that is most closely related to R-modules, but where this map is an isomorphism turns out to be the category of -modules. Here is the localization of R with respect to the (multiplicatively closed) subset S consisting of all powers of r,
The expression "most closely related" is formalized by two conditions: first, there is a functor
sending any R-module to its localization with respect to S. Moreover, given any category C and any functor
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https://en.wikipedia.org/wiki/Sobolev%20space
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In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, i.e. a Banach space. Intuitively, a Sobolev space is a space of functions possessing sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and regularity of a function.
Sobolev spaces are named after the Russian mathematician Sergei Sobolev. Their importance comes from the fact that weak solutions of some important partial differential equations exist in appropriate Sobolev spaces, even when there are no strong solutions in spaces of continuous functions with the derivatives understood in the classical sense.
Motivation
In this section and throughout the article is an open subset of
There are many criteria for smoothness of mathematical functions. The most basic criterion may be that of continuity. A stronger notion of smoothness is that of differentiability (because functions that are differentiable are also continuous) and a yet stronger notion of smoothness is that the derivative also be continuous (these functions are said to be of class — see Differentiability classes). Differentiable functions are important in many areas, and in particular for differential equations. In the twentieth century, however, i
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https://en.wikipedia.org/wiki/LOKI97
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In cryptography, LOKI97 is a block cipher which was a candidate in the Advanced Encryption Standard competition. It is a member of the LOKI family of ciphers, with earlier instances being LOKI89 and LOKI91. LOKI97 was designed by Lawrie Brown, assisted by Jennifer Seberry and Josef Pieprzyk.
Like DES, LOKI97 is a 16-round Feistel cipher, and like other AES candidates, has a 128-bit block size and a choice of a 128-, 192- or 256-bit key length. It uses 16 rounds of a balanced Feistel network to process the input data blocks (see diagram right). The complex round function f incorporates two substitution-permutation layers in each round. The key schedule is also a Feistel structure – an unbalanced one unlike the main network — but using the same F-function.
The LOKI97 round function (shown right) uses two columns each with multiple copies of two basic S-boxes. These S-boxes are designed to be highly non-linear and have a good XOR profile. The permutations before and between serve to provide auto-keying and to diffuse the S-box outputs as quickly as possible.
The authors have stated that, "LOKI97 is a non-proprietary algorithm, available for royalty-free use worldwide as a possible replacement for the DES or other existing block ciphers." It was intended to be an evolution of the earlier LOKI89 and LOKI91 block ciphers.
It was the first published candidate in the Advanced Encryption Standard competition, and was quickly analysed and attacked. An analysis of some problems with
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https://en.wikipedia.org/wiki/Hadamard%27s%20inequality
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In mathematics, Hadamard's inequality (also known as Hadamard's theorem on determinants) is a result first published by Jacques Hadamard in 1893. It is a bound on the determinant of a matrix whose entries are complex numbers in terms of the lengths of its column vectors. In geometrical terms, when restricted to real numbers, it bounds the volume in Euclidean space of n dimensions marked out by n vectors vi for 1 ≤ i ≤ n in terms of the lengths of these vectors ||vi||.
Specifically, Hadamard's inequality states that if N is the matrix having columns vi, then
If the n vectors are non-zero, equality in Hadamard's inequality is achieved if and only if the vectors are orthogonal.
Alternate forms and corollaries
A corollary is that if the entries of an n by n matrix N are bounded by B, so |Nij|≤B for all i and j, then
In particular, if the entries of N are +1 and −1 only then
In combinatorics, matrices N for which equality holds, i.e. those with orthogonal columns, are called Hadamard matrices.
A positive-semidefinite matrix P can be written as N*N, where N* denotes the conjugate transpose of N (see Decomposition of a semidefinite matrix). Then
So, the determinant of a positive definite matrix is less than or equal to the product of its diagonal entries. Sometimes this is also known as Hadamard's inequality.
Proof
The result is trivial if the matrix N is singular, so assume the columns of N are linearly independent. By dividing each column by its length, it can be seen tha
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