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https://en.wikipedia.org/wiki/Extracellular%20fluid
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In cell biology, extracellular fluid (ECF) denotes all body fluid outside the cells of any multicellular organism. Total body water in healthy adults is about 50–60% (range 45 to 75%) of total body weight; women and the obese typically have a lower percentage than lean men. Extracellular fluid makes up about one-third of body fluid, the remaining two-thirds is intracellular fluid within cells. The main component of the extracellular fluid is the interstitial fluid that surrounds cells.
Extracellular fluid is the internal environment of all multicellular animals, and in those animals with a blood circulatory system, a proportion of this fluid is blood plasma. Plasma and interstitial fluid are the two components that make up at least 97% of the ECF. Lymph makes up a small percentage of the interstitial fluid. The remaining small portion of the ECF includes the transcellular fluid (about 2.5%). The ECF can also be seen as having two components – plasma and lymph as a delivery system, and interstitial fluid for water and solute exchange with the cells.
The extracellular fluid, in particular the interstitial fluid, constitutes the body's internal environment that bathes all of the cells in the body. The ECF composition is therefore crucial for their normal functions, and is maintained by a number of homeostatic mechanisms involving negative feedback. Homeostasis regulates, among others, the pH, sodium, potassium, and calcium concentrations in the ECF. The volume of body fluid, b
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https://en.wikipedia.org/wiki/SubSpace%20%28video%20game%29
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SubSpace is a 2D space shooter video game created in 1995 and released in 1997 by Virgin Interactive which was a finalist for the Academy of Interactive Arts & Sciences Online Game of the Year Award in 1998. SubSpace incorporates quasi-realistic zero-friction physics into a massively multiplayer online game.
The game is no longer operated by VIE; instead, fans and players of the game provide servers and technical updates.
The action is viewed from above, which presents challenges very different from those of a three-dimensional game. The game has no built-in story or set of goals; players may enter a variety of servers, each of which have differing objectives, maps, sounds, and graphics.
SubSpace is considered an early entry in the massively multiplayer online genre due to its unprecedented player counts.
History
SubSpace evolved from a game originally called Sniper (1995), a project to test the effects and severity of lag in a massively multiplayer environment over dialup connections.
After its creators realized its viability as an actual game, public beta testing began in February, 1996, and it became fully public later that year.
The game was released commercially in December 1997 with a list price of US$27.99 for unlimited play, requiring no monthly or hourly fees. The game was originally developed by Burst, led by Jeff Petersen, Rod Humble and Juan Sanchez, for the US branch of the now-defunct Virgin Interactive. The title was showcased at E3 1997.
When the
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https://en.wikipedia.org/wiki/Sampling%20theory
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sampling theory may mean:
Nyquist–Shannon sampling theorem, digital signal processing (DSP)
Statistical sampling
Fourier sampling
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https://en.wikipedia.org/wiki/Princeton%20Sound%20Lab
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The Princeton Sound Lab is a research laboratory in the Department of Computer Science at Princeton University, in collaboration with the Department of Music. The Sound Lab conducts research in a variety of areas in computer music, including physical modeling, audio analysis, audio synthesis, programming languages for audio and multimedia, interactive controller design, psychoacoustics, and real-time systems for composition and performance.
External links
Princeton University
Audio engineering
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https://en.wikipedia.org/wiki/Asymmetric
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Asymmetric may refer to:
Asymmetry in geometry, chemistry, and physics
Computing
Asymmetric cryptography, in public-key cryptography
Asymmetric digital subscriber line, Internet connectivity
Asymmetric multiprocessing, in computer architecture
Other
Asymmetric relation, in set theory
Asymmetric synthesis, in organic synthesis
Asymmetric warfare, in modern war
Asymmetric Publications, a video game company
Asymmetry (Mallory Knox album), 2014
Asymmetry (Karnivool album)
Asymmetry (population ethics)
Asymmetry (novel), a 2018 novel by Lisa Halliday
See also
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https://en.wikipedia.org/wiki/Max%20Mathews
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Max Vernon Mathews (November 13, 1926 in Columbus, Nebraska, US – April 21, 2011 in San Francisco, CA, US) was an American pioneer of computer music.
Biography
Max Vernon Mathews was born in Columbus, Nebraska, by two science schoolteachers. His father in particular taught physics, chemistry and biology in the Peru High School of Nebraska, where he was also the principal. His father allowed him to learn and play in the physics, biology and chemistry laboratories, where he enjoyed making lots of things from motors to mercury barometers. At the age of 9, when students are usually introduced to algebra, he started to study by himself the subject with few other students. That was because the vast majority of population there were farmers and their sons weren't interested about learning algebra, since it isn't useful for the everyday work. In the same way he studied calculus, but he never graduated from high school.
After a period as a radar repairman in the navy, where he felt in love with electronics, Mathews decide to study electrical engineering at the California Institute of Technology and the Massachusetts Institute of Technology, receiving a Sc.D. in 1954. Working at Bell Labs, Mathews wrote MUSIC, the first widely used program for sound generation, in 1957. For the rest of the century, he continued as a leader in digital audio research, synthesis, and human-computer interaction as it pertains to music performance. In 1968, Mathews and L. Rosler developed Graphic 1, an
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https://en.wikipedia.org/wiki/ESD
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ESD may refer to:
Science
ESD (gene), a human gene/enzyme
Electrostatic discharge, a sudden flow of electricity between two electrically charged objects
Electrostatic-sensitive device, any component which can be damaged by common static charges
Energy spectral density, a part of a function in statistical signal processing
Environmental secondary detector, a gaseous detection device used with environmental scanning electron microscopes
Equivalent spherical diameter, a diameter of a sphere of equivalent volume
Extreme subdwarf, a type of star
Medicine
End-systolic dimension, the diameter across a ventricle in the heart
Endoscopic submucosal dissection, a medical therapy with endoscopy
Education
Education for sustainable development, international learning methodology
Educational service district (disambiguation), regional education unit in some U.S. states
Episcopal School of Dallas, day school in Texas, U.S.
Evangelical School for the Deaf, in Luquillo, Puerto Rico
Government and law
Electronic services delivery, government services provided through the Internet or other electronic means
Empire State Development Corporation, an American public benefit umbrella organization
Employment Security Department, a Washington state unemployment agency
Examination support document, a submission to the United States Patent and Trademark Office
Technology
Electronic smoking device, a device that simulates the feeling of smoking
Electronic software distribution
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https://en.wikipedia.org/wiki/Wes%20Jackson
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Wes Jackson (born 1936) co-founded the Land Institute with Dana Jackson. He is also a member of the World Future Council.
Early life and education
Jackson was born and raised on a farm near Topeka, Kansas. After earning a BA in biology from Kansas Wesleyan University, an MA in botany from the University of Kansas, and a PhD in genetics from North Carolina State University, Wes Jackson established and served as chair of one of the United States' first environmental studies programs at California State University, Sacramento.
Jackson then chose to leave academia, returning to his native Kansas, where he founded a non-profit organization, The Land Institute, in 1976. The Land Institute is working to develop perennial grains, pulses, and oilseed-bearing plants to be grown in ecologically intensified, diverse crop mixtures under its Natural Systems Agriculture program. In tandem with these sustainable agriculture efforts, the Ecosphere Studies program seeks to change the way people think about the world and their place in it, through educational and cultural projects with a perennial perspective. Jackson stepped down from the presidency of The Land Institute in 2016, but still works in the Ecosphere Studies program.
Work with The Land Institute
The Land Institute has explored alternatives in appropriate technology, environmental ethics, and education, but a research program in sustainable agriculture eventually became central to its work. In 1978, Jackson proposed the developme
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https://en.wikipedia.org/wiki/Ecological%20genetics
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Ecological genetics is the study of genetics in natural populations. Traits in a population can be observed and quantified to represent a species adapting to a changing environment.
This contrasts with classical genetics, which works mostly on crosses between laboratory strains, and DNA sequence analysis, which studies genes at the molecular level.
Research in this field is on traits of ecological significance—that is, traits related to fitness, which affect an organism's survival and reproduction. Examples might be: flowering time, drought tolerance, polymorphism, mimicry, and avoidance of attacks by predators.
Ecological genetics is an especially useful tool when studying endangered species. Meta-barcoding and eDNA are used to examine the biodiversity of species in an ecosystem.
Research usually involves a mixture of field and laboratory studies. Samples of natural populations may be taken back to the laboratory for their genetic variation to be analyzed. Changes in the populations at different times and places will be noted, and the pattern of mortality in these populations will be studied. Research is often done on insects and other organisms such as microbial communities, that have short generation times.
History
Although work on natural populations had been done previously, it is acknowledged that the field was founded by the English biologist E.B. Ford (1901–1988) in the early 20th century. Ford was taught genetics at Oxford University by Julian Huxley, and start
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https://en.wikipedia.org/wiki/Char%20%28chemistry%29
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Char is the solid material that remains after light gases (e.g. coal gas) and tar have been driven out or released from a carbonaceous material during the initial stage of combustion, which is known as carbonization, charring, devolatilization or pyrolysis.
Further stages of efficient combustion (with or without char deposits) are known as gasification reactions, ending quickly when the reversible gas phase of the water gas shift reaction is reached.
See also
Biochar
Charcoal
Coke (fuel)
Petroleum coke
Shale oil extraction
Spent shale
Oil shale
Coal
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https://en.wikipedia.org/wiki/Formal%20group%20law
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In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by . The term formal group sometimes means the same as formal group law, and sometimes means one of several generalizations. Formal groups are intermediate between Lie groups (or algebraic groups) and Lie algebras. They are used in algebraic number theory and algebraic topology.
Definitions
A one-dimensional formal group law over a commutative ring R is a power series F(x,y) with coefficients in R, such that
F(x,y) = x + y + terms of higher degree
F(x, F(y,z)) = F(F(x,y), z) (associativity).
The simplest example is the additive formal group law F(x, y) = x + y.
The idea of the definition is that F should be something like the formal power series expansion of the product of a Lie group, where we choose coordinates so that the identity of the Lie group is the origin.
More generally, an n-dimensional formal group law is a collection of n power series
Fi(x1, x2, ..., xn, y1, y2, ..., yn) in 2n variables, such that
F(x,y) = x + y + terms of higher degree
F(x, F(y,z)) = F(F(x,y), z)
where we write F for (F1, ..., Fn), x for (x1, ..., xn), and so on.
The formal group law is called commutative if F(x,y) = F(y,x). If R is torsionfree, then one can embed R into a Q-algebra and use the exponential and logarithm to write any one-dimensional formal group law F as F(x,y) = exp(log(x) + log(y)), so F is necessarily commutative. Mor
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https://en.wikipedia.org/wiki/Paillier%20cryptosystem
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The Paillier cryptosystem, invented by and named after Pascal Paillier in 1999, is a probabilistic asymmetric algorithm for public key cryptography. The problem of computing n-th residue classes is believed to be computationally difficult. The decisional composite residuosity assumption is the intractability hypothesis upon which this cryptosystem is based.
The scheme is an additive homomorphic cryptosystem; this means that, given only the public key and the
encryption of and , one can compute the encryption of .
Algorithm
The scheme works as follows:
Key generation
Choose two large prime numbers and randomly and independently of each other such that . This property is assured if both primes are of equal length.
Compute and . lcm means Least Common Multiple.
Select random integer where
Ensure divides the order of by checking the existence of the following modular multiplicative inverse: ,
where function is defined as .
Note that the notation does not denote the modular multiplication of times the modular multiplicative inverse of but rather the quotient of divided by , i.e., the largest integer value to satisfy the relation .
The public (encryption) key is .
The private (decryption) key is
If using p,q of equivalent length, a simpler variant of the above key generation steps would be to set and , where .
The simpler variant is recommended for implementational purposes, because in the general form the calculation time of can be very high with sufficien
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https://en.wikipedia.org/wiki/Constantin%20Coand%C4%83
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Constantin Coandă (4 March 1857 – 30 September 1932) was a Romanian soldier and politician.
Biography
Constantin Coandă was born in Craiova. He reached the rank of general in the Romanian Army, and later became a mathematics professor at the National School of Bridges and Roads in Bucharest. Among his seven children was Henri Coandă, the discoverer of the Coandă effect.
During World War I, for a short time (24 October – 29 November 1918), he was the Prime Minister of Romania and the Foreign Affairs Minister. He participated in the signing of the Treaty of Neuilly between the Allies of World War I and Bulgaria.
On 8 December 1920, during his term as President of the Senate of Romania (representing Alexandru Averescu's People's Party), he was badly wounded by a bomb set up by the terrorist and anarchist Max Goldstein.
Military functions
Platoon commander in the 1st Artillery Regiment (1877 – 1883)
Positions in military education at the Bucharest School of Artillery, Engineering and Naval Officers and at the Superior School of War
Command and staff functions
Commander of the 2nd Artillery Regiment
Commander of the 5th Army Corps
Secretary General of the Ministry of War
Commander of the Bucharest Citadel
Military attaché in Berlin, Vienna and Paris
Director of the Artillery Department of the Ministry of War
Head of department in the General Staff
Inspector General of Artillery.
Other positions
Teacher at the Bucharest Bridge and Roads School
Delega
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https://en.wikipedia.org/wiki/Transmittance
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In optical physics, transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is the ratio of the transmitted to incident electric field.
Internal transmittance refers to energy loss by absorption, whereas (total) transmittance is that due to absorption, scattering, reflection, etc.
Mathematical definitions
Hemispherical transmittance
Hemispherical transmittance of a surface, denoted T, is defined as
where
Φet is the radiant flux transmitted by that surface;
Φei is the radiant flux received by that surface.
Spectral hemispherical transmittance
Spectral hemispherical transmittance in frequency and spectral hemispherical transmittance in wavelength of a surface, denoted Tν and Tλ respectively, are defined as
where
Φe,νt is the spectral radiant flux in frequency transmitted by that surface;
Φe,νi is the spectral radiant flux in frequency received by that surface;
Φe,λt is the spectral radiant flux in wavelength transmitted by that surface;
Φe,λi is the spectral radiant flux in wavelength received by that surface.
Directional transmittance
Directional transmittance of a surface, denoted TΩ, is defined as
where
Le,Ωt is the radiance transmitted by that surface;
Le,Ωi is the radiance received by that surface.
Spectral directional transmittance
Spectral directional transmittance in frequency and s
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https://en.wikipedia.org/wiki/Slater%20determinant
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In quantum mechanics, a Slater determinant is an expression that describes the wave function of a multi-fermionic system. It satisfies anti-symmetry requirements, and consequently the Pauli principle, by changing sign upon exchange of two electrons (or other fermions). Only a small subset of all possible fermionic wave functions can be written as a single Slater determinant, but those form an important and useful subset because of their simplicity.
The Slater determinant arises from the consideration of a wave function for a collection of electrons, each with a wave function known as the spin-orbital , where denotes the position and spin of a single electron. A Slater determinant containing two electrons with the same spin orbital would correspond to a wave function that is zero everywhere.
The Slater determinant is named for John C. Slater, who introduced the determinant in 1929 as a means of ensuring the antisymmetry of a many-electron wave function, although the wave function in the determinant form first appeared independently in Heisenberg's and Dirac's articles three years earlier.
Definition
Two-particle case
The simplest way to approximate the wave function of a many-particle system is to take the product of properly chosen orthogonal wave functions of the individual particles. For the two-particle case with coordinates and , we have
This expression is used in the Hartree method as an ansatz for the many-particle wave function and is known as a Hartree produ
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https://en.wikipedia.org/wiki/Homotopy%20principle
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In mathematics, the homotopy principle (or h-principle) is a very general way to solve partial differential equations (PDEs), and more generally partial differential relations (PDRs). The h-principle is good for underdetermined PDEs or PDRs, such as the immersion problem, isometric immersion problem, fluid dynamics, and other areas.
The theory was started by Yakov Eliashberg, Mikhail Gromov and Anthony V. Phillips. It was based on earlier results that reduced partial differential relations to homotopy, particularly for immersions. The first evidence of h-principle appeared in the Whitney–Graustein theorem. This was followed by the Nash–Kuiper isometric C1 embedding theorem and the Smale–Hirsch immersion theorem.
Rough idea
Assume we want to find a function ƒ on Rm which satisfies a partial differential equation of degree k, in co-ordinates . One can rewrite it as
where stands for all partial derivatives of ƒ up to order k. Let us exchange every variable in for new independent variables
Then our original equation can be thought as a system of
and some number of equations of the following type
A solution of
is called a non-holonomic solution, and a solution of the system which is also solution of our original PDE is called a holonomic solution.
In order to check whether a solution to our original equation exists, one can first check if there is a non-holonomic solution. Usually this is quite easy, and if there is no non-holonomic solution, then our original equatio
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https://en.wikipedia.org/wiki/ISPW
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The IRCAM Signal Processing Workstation (ISPW) was a hardware digital audio workstation developed by IRCAM and the Ariel Corporation in the late 1980s. In French, the ISPW is referred to as the SIM (Station d'informatique musicale). Eric Lindemann was the principal designer of the ISPW hardware as well as manager of the overall hardware/software effort.
It consisted of up to three customized DSP boards that could be plugged into the expansion bus on a NeXT Computer (a "cube"). The ISPW could then run a customized real-time audio processing server on the hardware boards controlled by a client application on the NeXT.
Each ISPW card had two Intel i860 microprocessors (running at 80 MFLOPS). An additional card with eight channels of audio I/O was also available for multi-channel sound recording and playback. A three-board ISPW provided what was at the time unsurpassed signal processing and audio synthesis power on a single workstation. A single ISPW card cost approximately $12,000US (not including the computer), which made it prohibitively expensive outside of research institutes and universities.
And the I860 board :
The main server software developed by IRCAM for the ISPW was called FTS ("Faster Than Sound"). The main NeXT client application was a graphical program called Max, developed by Miller Puckette. A commercial version of Max (without the FTS server) was licensed by IRCAM to Opcode Systems (and, later, Cycling '74).
Max/FTS eventually migrated to a softwa
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https://en.wikipedia.org/wiki/Adam%20Powell%20%28game%20designer%29
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Adam James Powell (born 20 December 1976) is a Welsh computer programmer, game designer and businessman. He is the co-founder of Neopets and Meteor Games.
Career
Powell attended the University of Nottingham from 1995 to 1998 studying for a computer science degree. During his time at Nottingham, Powell created Dark Heart released in 1996, a popular MUD based on the DikuMUD code.
In 1997, Powell started Shout! Advertising, a UK-based advertising company which operated the third largest click-through program on the Internet by mid-1999. He also co-founded Netmagic, a successful business which designed and sold online banner advertising. Then in July 1999, he founded Powlex, which focused on web page design.
Neopets
Powell first had the idea of Neopets in 1997, while studying at the University of Nottingham.
He and Donna Powell (formerly Donna Williams) started programming the site in September 1999, and launched the site two months later on 15 November 1999. Powell programmed the entire site, and created most of the original activities and games.
In April 2000, Powell negotiated a significant investment in Neopets.com and transferred the company from the UK to Los Angeles, US. After the relocation, Powell remained on staff as creative director and technical lead. Under Powell's management, Neopets went from its initial launch to over 140 million accounts and 5 billion pageviews per month. On 20 June 2005, Viacom bought Neopets, Inc. for US$160 million.
Powell continued t
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https://en.wikipedia.org/wiki/NTRUEncrypt
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The NTRUEncrypt public key cryptosystem, also known as the NTRU encryption algorithm, is an NTRU lattice-based alternative to RSA and elliptic curve cryptography (ECC) and is based on the shortest vector problem in a lattice (which is not known to be breakable using quantum computers).
It relies on the presumed difficulty of factoring certain polynomials in a truncated polynomial ring into a quotient of two polynomials having very small coefficients. Breaking the cryptosystem is strongly related, though not equivalent, to the algorithmic problem of lattice reduction in certain lattices. Careful choice of parameters is necessary to thwart some published attacks.
Since both encryption and decryption use only simple polynomial multiplication, these operations are very fast compared to other asymmetric encryption schemes, such as RSA, ElGamal and elliptic curve cryptography. However, NTRUEncrypt has not yet undergone a comparable amount of cryptographic analysis in deployed form.
A related algorithm is the NTRUSign digital signature algorithm.
Specifically, NTRU operations are based on objects in a truncated polynomial ring with convolution multiplication and all polynomials in the ring have integer coefficients and degree at most N-1:
That in this ring has the effect that multiplying a polynomial by rotates the coefficients of the polynomial. A map of the form for a fixed thus produces a new polynomial where every coefficient depends on as many coefficients from as
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https://en.wikipedia.org/wiki/NTRU
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NTRU is an open-source public-key cryptosystem that uses lattice-based cryptography to encrypt and decrypt data. It consists of two algorithms: NTRUEncrypt, which is used for encryption, and NTRUSign, which is used for digital signatures. Unlike other popular public-key cryptosystems, it is resistant to attacks using Shor's algorithm. NTRUEncrypt was patented, but it was placed in the public domain in 2017. NTRUSign is patented, but it can be used by software under the GPL.
History
The first version of the system, which was called NTRU, was developed in 1996 by mathematicians Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman. That same year, the developers of NTRU joined with Daniel Lieman and founded the company NTRU Cryptosystems, Inc., and were given a patent on the cryptosystem. The name "NTRU", chosen for the company and soon applied to the system as well, was originally derived from the pun Number Theorists 'R' Us or, alternatively, stood for Number Theory Research Unit. In 2009, the company was acquired by Security Innovation, a software security corporation. In 2013, Damien Stehle and Ron Steinfeld created a provably secure version of NTRU, which is being studied by a post-quantum crypto group chartered by the European Commission.
In May 2016, Daniel Bernstein, Chitchanok Chuengsatiansup, Tanja Lange and Christine van Vredendaal released NTRU Prime, which adds defenses against potential attack to NTRU by eliminating algebraic structure they considered worriso
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https://en.wikipedia.org/wiki/Timing%20attack
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In cryptography, a timing attack is a side-channel attack in which the attacker attempts to compromise a cryptosystem by analyzing the time taken to execute cryptographic algorithms. Every logical operation in a computer takes time to execute, and the time can differ based on the input; with precise measurements of the time for each operation, an attacker can work backwards to the input. Finding secrets through timing information may be significantly easier than using cryptanalysis of known plaintext, ciphertext pairs. Sometimes timing information is combined with cryptanalysis to increase the rate of information leakage.
Information can leak from a system through measurement of the time it takes to respond to certain queries. How much this information can help an attacker depends on many variables: cryptographic system design, the CPU running the system, the algorithms used, assorted implementation details, timing attack countermeasures, the accuracy of the timing measurements, etc. Timing attacks can be applied to any algorithm that has data-dependent timing variation. Removing timing-dependencies is difficult in some algorithms that use low-level operations that frequently exhibit varied execution time.
Timing attacks are often overlooked in the design phase because they are so dependent on the implementation and can be introduced unintentionally with compiler optimizations. Avoidance of timing attacks involves design of constant-time functions and careful testing of the
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https://en.wikipedia.org/wiki/Wendell%20Meredith%20Stanley
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Wendell Meredith Stanley (16 August 1904 – 15 June 1971) was an American biochemist, virologist and Nobel laureate.
Biography
Stanley was born in Ridgeville, Indiana, and earned a BSc in chemistry at Earlham College in Richmond, Indiana. He then studied at the University of Illinois, gaining an MS in science in 1927 followed by a PhD in chemistry two years later. His later accomplishments include writing the book "Chemistry: A Beautiful Thing" and being a Pulitzer Prize nominee.
Research
As a member of National Research Council he moved temporarily for academic work with Heinrich Wieland in Munich before he returned to the States in 1931. On return he was approved as an assistant at The Rockefeller Institute for Medical Research. He remained with the Institute until 1948, becoming an Associate Member in 1937, and a Member in 1940. In 1948, he became Professor of Biochemistry at the University of California, Berkeley and built the Virus Laboratory and a free-standing Department of Biochemistry building, which is now called Stanley Hall.
Stanley's work contributed to on lepracidal compounds, diphenyl stereochemistry and the chemistry of the sterols. His research on the virus causing the mosaic disease in tobacco plants led to the isolation of a nucleoprotein which displayed tobacco mosaic virus activity.
Stanley was elected to the American Philosophical Society in 1940 and the United States National Academy of Sciences in 1941. He was awarded the Nobel Prize in Chemistr
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https://en.wikipedia.org/wiki/Zeroisation
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In cryptography, zeroisation (also spelled zeroization) is the practice of erasing sensitive parameters (electronically stored data, cryptographic keys, and critical security parameters) from a cryptographic module to prevent their disclosure if the equipment is captured. This is generally accomplished by altering or deleting the contents to prevent recovery of the data.
Mechanical
When encryption was performed by mechanical devices, this would often mean changing all the machine's settings to some fixed, meaningless value, such as zero. On machines with letter settings rather than numerals, the letter 'O' was often used instead. Some machines had a button or lever for performing this process in a single step. Zeroisation would typically be performed at the end of an encryption session to prevent accidental disclosure of the keys, or immediately when there was a risk of capture by an adversary.
Software
In modern software based cryptographic modules, zeroisation is made considerably more complex by issues such as virtual memory, compiler optimisations and use of flash memory. Also, zeroisation may need to be applied not only to the key, but also to a plaintext and some intermediate values. A cryptographic software developer must have an intimate understanding of memory management in a machine, and be prepared to zeroise data whenever a sensitive device might move outside the security boundary. Typically this will involve overwriting the data with zeroes, but in the case of
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https://en.wikipedia.org/wiki/L7
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L7 or L-7 may refer to:
Music
L7 (band), a grunge/metal band from Los Angeles, California
L7 (album), a 1988 album by the band
L-Seven, a post-punk band from Detroit, Michigan
Mathematics and technology
ISO/IEC 8859-13 (Latin-7), an 8-bit character encoding
L7, the application layer in the OSI model of computer communications
A layer 7 switch or load balancer
The Lp space for p=7 in mathematics
Transportation
Vehicles
D-Lieferwagen L-7, a 1927–1930 German three-wheel truck
IM L7, a 2022–present Chinese full-size luxury electric sedan
Landsat 7, an Earth observation satellite
Other
L7, IATA code for Laoag International Airlines
Other uses
Royal Ordnance L7, british and the NATO standard 105mm tank and light-field cannon
L7 (machine gun), a Belgian 7.62 mm general-purpose machine gun
Motorola SLVR L7, a mobile phone
See also
7L (disambiguation)
Bustin' Out of L Seven, an album by Rick James
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https://en.wikipedia.org/wiki/Absorptivity
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In science, absorptivity may refer to:
Molar absorptivity, in chemistry, a measurement of how strongly a chemical species absorbs light at a given wavelength
Absorptance, in physics, the fraction of radiation absorbed at a given wavelength
, information on the radiometrical aspect
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https://en.wikipedia.org/wiki/S-1%20block%20cipher
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In cryptography, the S-1 block cipher was a block cipher posted in source code form on Usenet on 11 August 1995. Although incorrect security markings immediately indicated a hoax, there were several features of the code which suggested it might be leaked source code for the Skipjack cipher, which was still classified at the time.
However once David Wagner had discovered a severe design flaw, involving the key schedule but not the underlying round function, it was generally accepted as being a hoax—but one with an astonishing amount of work behind it. Bruce Schneier noted that S-1 contained a feature never seen before in the open literature; a G-table that results in key and data dependent rotation of S-boxes to use in a given round. When Skipjack was eventually declassified in 1998, it was indeed found to be totally unlike S-1.
References
See also
Iraqi block cipher
Block ciphers
Internet hoaxes
1995 hoaxes
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https://en.wikipedia.org/wiki/Iraqi%20block%20cipher
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In cryptography, the Iraqi block cipher was a block cipher published in C source code form by anonymous FTP upload around July 1999, and widely distributed on Usenet. It is a five round unbalanced Feistel cipher operating on a 256 bit block with a 160 bit key.
The source code shows that the algorithm operates on blocks of 32 bytes (or 256 bits). That's four times larger than DES or 3DES (8 bytes) and twice as big as Twofish or AES (16 bytes).
It also shows that the key size can vary from 160 to 2048 bits.
A detailed analysis of the source code of the algorithm shows that it uses a 256-byte S-Box that is key-dependant (as on Blowfish, it uses a first fixed S table that will generate, with the key, the second S-Box used for encryption/decryption). The algorithm also uses a 16-column x 16-row P-Box, which is also key-dependent and also initialized from a fixed P table. Each round uses one row from P-Box and 16 columns, which means that the algorithm can use up to 16 rounds.
A comment suggests that it is of Iraqi origin. However, like the S-1 block cipher, it is generally regarded as a hoax, although of lesser quality than S-1. Although the comment suggests that it is Iraqi in origin, all comments, variable and function names and printed strings are in English rather than Arabic; the code is fairly inefficient (including some pointless operations), and the cipher's security may be flawed (no proof).
Because it has a constant key schedule the cipher is vulnerable to a slide at
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https://en.wikipedia.org/wiki/Gromov%E2%80%93Hausdorff%20convergence
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In mathematics, Gromov–Hausdorff convergence, named after Mikhail Gromov and Felix Hausdorff, is a notion for convergence of metric spaces which is a generalization of Hausdorff convergence.
Gromov–Hausdorff distance
The Gromov–Hausdorff distance was introduced by David Edwards in 1975, and it was later rediscovered and generalized by Mikhail Gromov in 1981. This distance measures how far two compact metric spaces are from being isometric. If X and Y are two compact metric spaces, then dGH (X, Y) is defined to be the infimum of all numbers dH(f(X), g(Y)) for all (compact) metric spaces M and all isometric embeddings f : X → M and g : Y → M. Here dH denotes Hausdorff distance between subsets in M and the isometric embedding is understood in the global sense, i.e. it must preserve all distances, not only infinitesimally small ones; for example no compact Riemannian manifold admits such an embedding into Euclidean space of the same dimension.
The Gromov–Hausdorff distance turns the set of all isometry classes of compact metric spaces into a metric space, called Gromov–Hausdorff space, and it therefore defines a notion of convergence for sequences of compact metric spaces, called Gromov–Hausdorff convergence. A metric space to which such a sequence converges is called the Gromov–Hausdorff limit of the sequence.
Some properties of Gromov–Hausdorff space
The Gromov–Hausdorff space is path-connected, complete, and separable. It is also geodesic, i.e., any two of its points are
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https://en.wikipedia.org/wiki/Tetration
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In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though and the left-exponent xb are common.
Under the definition as repeated exponentiation, means , where copies of are iterated via exponentiation, right-to-left, i.e. the application of exponentiation times. is called the "height" of the function, while is called the "base," analogous to exponentiation. It would be read as "the th tetration of ".
It is the next hyperoperation after exponentiation, but before pentation. The word was coined by Reuben Louis Goodstein from tetra- (four) and iteration.
Tetration is also defined recursively as
allowing for attempts to extend tetration to non-natural numbers such as real and complex numbers.
The two inverses of tetration are called super-root and super-logarithm, analogous to the nth root and the logarithmic functions. None of the three functions are elementary.
Tetration is used for the notation of very large numbers.
Introduction
The first four hyperoperations are shown here, with tetration being considered the fourth in the series. The unary operation succession, defined as , is considered to be the zeroth operation.
Addition copies of 1 added to combined by succession.
Multiplication copies of combined by addition.
Exponentiation copies of combined by multiplication.
Tetration copies of combined by exponentiation, right-to-left.
Note that nested expon
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https://en.wikipedia.org/wiki/Shielding%20effect
|
In chemistry, the shielding effect sometimes referred to as atomic shielding or electron shielding describes the attraction between an electron and the nucleus in any atom with more than one electron. The shielding effect can be defined as a reduction in the effective nuclear charge on the electron cloud, due
to a difference in the attraction forces on the electrons in the atom. It is a special case of electric-field screening.
This effect also has some significance in many projects in material sciences.
Strength per electron shell
The wider the electron shells are in space, the weaker is the electric interaction between the electrons and the nucleus due to screening. In general we can order the electron shells (s,p,d,f) as such
where S is the screening strength that a given orbital provides to the rest of the electrons.
Description
In hydrogen, or any other atom in group 1A of the periodic table (those with only one valence electron), the force on the electron is just as large as the electromagnetic attraction from the nucleus of the atom. However, when more electrons are involved, each electron (in the nth-shell) experiences not only the electromagnetic attraction from the positive nucleus, but also repulsion forces from other electrons in shells from 1 to n. This causes the net force on electrons in outer shells to be significantly smaller in magnitude; therefore, these electrons are not as strongly bonded to the nucleus as electrons closer to the nucleus. This pheno
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https://en.wikipedia.org/wiki/Polylogarithm
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In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function of order and argument . Only for special values of does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function. In quantum statistics, the polylogarithm function appears as the closed form of integrals of the Fermi–Dirac distribution and the Bose–Einstein distribution, and is also known as the Fermi–Dirac integral or the Bose–Einstein integral. In quantum electrodynamics, polylogarithms of positive integer order arise in the calculation of processes represented by higher-order Feynman diagrams.
The polylogarithm function is equivalent to the Hurwitz zeta function — either function can be expressed in terms of the other — and both functions are special cases of the Lerch transcendent. Polylogarithms should not be confused with polylogarithmic functions, nor with the offset logarithmic integral , which has the same notation without the subscript.
The polylogarithm function is defined by a power series in , which is also a Dirichlet series in :
This definition is valid for arbitrary complex order and for all complex arguments with ; it can be extended to by the process of analytic continuation. (Here the denominator is understood as ). The special case involves the ordinary natural logarithm, , while the special cases and are called the dilogarithm (also referred to as Spence's function) and trilogarithm
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https://en.wikipedia.org/wiki/TNI
|
TNI or Tni may refer to:
Satna Airport, IATA code TNI
Tahitian Noni International, Inc.
Taqramiut Nipingat Inc., an Inuit broadcasting organization in Quebec, Canada
Telephone Network Interface; see Network interface device (NID)
Tentara Nasional Indonesia; abbreviation of the Indonesian National Armed Forces.
Texas Neurosciences Institute, a research and neurological clinical center
Thai-Nichi Institute of Technology a private college in Thailand
Transnationality Index
Transnational Institute
The National Interest
The New Inquiry
Trichoplusia ni, the cabbage looper moth
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https://en.wikipedia.org/wiki/Nikolay%20Yakovlevich%20Sonin
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Nikolay Yakovlevich Sonin (Russian: Никола́й Я́ковлевич Со́нин, February 22, 1849 – February 27, 1915) was a Russian mathematician.
Biography
He was born in Tula and attended Lomonosov University, studying mathematics and physics there from 1865 to 1869. His advisor was Nikolai Bugaev. He obtained a master's degree with a thesis submitted in 1871, then he taught at the University of Warsaw where he obtained a doctorate in 1874. He was appointed to a chair in the University of Warsaw in 1876. In 1894, Sonin moved to St. Petersburg, where he taught at the University for Women.
Sonin worked on special functions, in particular cylindrical functions. For instance, the Sonine formula is a formula given by Sonin for the integral of the product of three Bessel functions. He is furthermore credited with the introduction of the associated Laguerre polynomials. He also contributed to the Euler–Maclaurin summation formula.
Other topics Sonin studied include Bernoulli polynomials and approximate computation of definite integrals, continuing Chebyshev's work on numerical integration. Together with Andrey Markov, Sonin prepared a two volume edition of Chebyshev's works in French and Russian. He died in St. Petersburg.
References
External links
1849 births
1915 deaths
Moscow State University alumni
University of Warsaw alumni
Academic staff of the University of Warsaw
Mathematical analysts
Mathematicians from the Russian Empire
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https://en.wikipedia.org/wiki/Bingham%20plastic
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In materials science, a Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is named after Eugene C. Bingham who proposed its mathematical form.
It is used as a common mathematical model of mud flow in drilling engineering, and in the handling of slurries. A common example is toothpaste, which will not be extruded until a certain pressure is applied to the tube. It is then pushed out as a relatively coherent plug.
Explanation
Figure 1 shows a graph of the behaviour of an ordinary viscous (or Newtonian) fluid in red, for example in a pipe. If the pressure at one end of a pipe is increased this produces a stress on the fluid tending to make it move (called the shear stress) and the volumetric flow rate increases proportionally. However, for a Bingham Plastic fluid (in blue), stress can be applied but it will not flow until a certain value, the yield stress, is reached. Beyond this point the flow rate increases steadily with increasing shear stress. This is roughly the way in which Bingham presented his observation, in an experimental study of paints. These properties allow a Bingham plastic to have a textured surface with peaks and ridges instead of a featureless surface like a Newtonian fluid.
Figure 2 shows the way in which it is normally presented currently. The graph shows shear stress on the vertical axis and shear rate on the horizontal one. (Volumetric flow rate depends on the size
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https://en.wikipedia.org/wiki/Leonard%20Hayflick
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Leonard Hayflick (born 20 May 1928) is a Professor of Anatomy at the UCSF School of Medicine, and was Professor of Medical Microbiology at Stanford University School of Medicine. He is a past president of the Gerontological Society of America and was a founding member of the council of the National Institute on Aging (NIA). The recipient of a number of research prizes and awards, including the 1991 Sandoz Prize for Gerontological Research, he has studied the aging process for more than fifty years. He is known for discovering that normal human cells divide for a limited number of times in vitro (refuting the contention by Alexis Carrel that normal body cells are immortal). This is known as the Hayflick limit. His discoveries overturned a 60-year old dogma that all cultured cells are immortal. Hayflick demonstrated that normal cells have a memory and can remember at what doubling level they have reached. He demonstrated that his normal human cell strains were free from contaminating viruses. His cell strain WI-38 soon replaced primary monkey kidney cells and became the substrate for the production of most of the world's human virus vaccines. Hayflick discovered that the etiological agent of primary atypical pneumonia (also called "walking pneumonia") was not a virus as previously believed. He was the first to cultivate the causative organism called a mycoplasma, the smallest free-living organism, which Hayflick isolated on a unique culture medium that bears his name. He named
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https://en.wikipedia.org/wiki/Closure%20operator
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In mathematics, a closure operator on a set S is a function from the power set of S to itself that satisfies the following conditions for all sets
{| border="0"
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| (cl is extensive),
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| (cl is increasing),
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| (cl is idempotent).
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Closure operators are determined by their closed sets, i.e., by the sets of the form cl(X), since the closure cl(X) of a set X is the smallest closed set containing X. Such families of "closed sets" are sometimes called closure systems or "Moore families". A set together with a closure operator on it is sometimes called a closure space. Closure operators are also called "hull operators", which prevents confusion with the "closure operators" studied in topology.
History
E. H. Moore studied closure operators in his 1910 Introduction to a form of general analysis, whereas the concept of the closure of a subset originated in the work of Frigyes Riesz in connection with topological spaces. Though not formalized at the time, the idea of closure originated in the late 19th century with notable contributions by Ernst Schröder, Richard Dedekind and Georg Cantor.
Examples
The usual set closure from topology is a closure operator. Other examples include the linear span of a subset of a vector space, the convex hull or affine hull of a subset of a vector space or the lower semicontinuous hull of a function , where is e.g. a normed space, defined implicitly , where is the epigraph of a function .
The relative interior is not a closur
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https://en.wikipedia.org/wiki/Transduction
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Transduction (trans- + -duc- + -tion, "leading through or across") can refer to:
Signal transduction, any process by which a biological cell converts one kind of signal or stimulus into another
Olfactory transduction
Sugar signal transduction
Transduction (biophysics), the conveyance of energy from a donor electron to a receptor electron, during which the class of energy changes
Transduction (genetics), the transfer of DNA from one cell to another using a virus or viral vector
Tbx18 transduction, a cardiac therapy method
Transduction (machine learning), the process of directly drawing conclusions about new data from previous data, without constructing a model
Transduction (physiology), the transportation of stimuli to the nervous system
Transduction (psychology), reasoning from specific cases to general cases, typically employed by children during their development
A process by which a transducer converts one type of energy to another
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https://en.wikipedia.org/wiki/Key%20distribution%20center
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In cryptography, a key distribution center (KDC) is part of a cryptosystem intended to reduce the risks inherent in exchanging keys. KDCs often operate in systems within which some users may have permission to use certain services at some times and not at others.
Security overview
For instance, an administrator may have established a policy that only certain users may back up to tape. Many operating systems can control access to the tape facility via a "system service". If that system service further restricts the tape drive to operate only on behalf of users who can submit a service-granting ticket when they wish to use it, there remains only the task of distributing such tickets to the appropriately permitted users. If the ticket consists of (or includes) a key, one can then term the mechanism which distributes it a KDC. Usually, in such situations, the KDC itself also operates as a system service.
Operation
A typical operation with a KDC involves a request from a user to use some service. The KDC will use cryptographic techniques to authenticate requesting users as themselves. It will also check whether an individual user has the right to access the service requested. If the authenticated user meets all prescribed conditions, the KDC can issue a ticket permitting access.
KDCs mostly operate with symmetric encryption.
In most (but not all) cases the KDC shares a key with each of all the other parties.
The KDC produces a ticket based on a server key.
The client rece
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https://en.wikipedia.org/wiki/Iosif%20Shklovsky
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Iosif Samuilovich Shklovsky (; sometimes transliterated Josif, Josif, Shklovskii, Shklovskij) (1 July 1916 – 3 March 1985) was a Soviet astronomer and astrophysicist. He is remembered for work in theoretical astrophysics and other topics, as well as for his 1962 book on extraterrestrial life, the revised and expanded version of which was co-authored by American astronomer Carl Sagan in 1966 as Intelligent Life in the Universe.
He won the Lenin Prize in 1960 and the Bruce Medal in 1972. Asteroid 2849 Shklovskij and the crater Shklovsky (on the Martian moon Phobos) are named in his honor. He was a Corresponding Member of Soviet Academy of Sciences since 1966.
Early life
Shklovsky was born in Hlukhiv, a city in the Ukrainian part of the Russian Empire, into a poor Ukrainian Jewish family. After graduating from the seven-year secondary school, he worked as a foreman on building Baikal Amur Mainline. In 1933 Shklovsky entered the Physico-Mathematical Faculty of the Moscow State University.
There he studied until 1938, when he took a Postgraduate Course at the Astrophysics Department of the Sternberg State Astronomical Institute and remained working in the Institute until the end of his life. He died in Moscow, aged 68.
Research
He specialized in theoretical astrophysics and radio astronomy, as well as the Sun's corona, supernovae, and cosmic rays and their origins. He showed, in 1946, that the radio-wave radiation from the Sun emanates from the ionized layers of its corona, an
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https://en.wikipedia.org/wiki/Fibonacci%20polynomials
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In mathematics, the Fibonacci polynomials are a polynomial sequence which can be considered as a generalization of the Fibonacci numbers. The polynomials generated in a similar way from the Lucas numbers are called Lucas polynomials.
Definition
These Fibonacci polynomials are defined by a recurrence relation:
The Lucas polynomials use the same recurrence with different starting values:
They can be defined for negative indices by
The Fibonacci polynomials form a sequence of orthogonal polynomials with and .
Examples
The first few Fibonacci polynomials are:
The first few Lucas polynomials are:
Properties
The degree of Fn is n − 1 and the degree of Ln is n.
The Fibonacci and Lucas numbers are recovered by evaluating the polynomials at x = 1; Pell numbers are recovered by evaluating Fn at x = 2.
The ordinary generating functions for the sequences are:
The polynomials can be expressed in terms of Lucas sequences as
They can also be expressed in terms of Chebyshev polynomials and as
where is the imaginary unit.
Identities
As particular cases of Lucas sequences, Fibonacci polynomials satisfy a number of identities, such as
Closed form expressions, similar to Binet's formula are:
where
are the solutions (in t) of
For Lucas Polynomials n > 0, we have
A relationship between the Fibonacci polynomials and the standard basis polynomials is given by
For example,
Combinatorial interpretation
If F(n,k) is the coefficient of xk in Fn(x), namely
then F(n
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https://en.wikipedia.org/wiki/ICMC
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ICMC may refer to:
International Catholic Migration Commission
International Computer Music Conference
The Indiana College Mathematics Competition
International Cryptographic Module Conference
Integrated Currency Management Centre
Inter College Music Competition
Integrated Call Management Centre
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https://en.wikipedia.org/wiki/Perry%20R.%20Cook
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Perry R. Cook (born September 25, 1955) is an American computer music researcher and professor emeritus of computer science and music at Princeton University. He was also founder and head of the Princeton Sound Lab.
Cook has worked in the areas of physical modeling, singing voice synthesis, music information retrieval, principles of computer music controller design, audio analysis and real-time computer music programming languages and systems, and has written a number of books on these subjects. Together with Gary Scavone, he authored the Synthesis Toolkit and with Ge Wang the ChucK programming language. He is also a co-founder, with Dan Trueman in 2005, of the Princeton Laptop Orchestra (PLOrk). Cook was an invited keynote speaker at NIME-07, held in New York City in June, 2007. He is a Fellow of the Association for Computing Machinery (2008) and the Guggenheim Foundation (2003).
Cook is also an avid conch shell musician, including the ancient conch-shell Peruvian instrument known as pututus.
Cook is a founding advisor (since 2008) to Smule, a successful mobile music app company.
In 2012, Cook and Ajay Kapur received an NSF-funded grant to create a programming and technology curriculum for art schools. Beginning in 2013 with Ajay Kapur and others, Cook co-founded Kadenze, an online arts education company.
His adviser was Julius Orion Smith III at Stanford.
References
External links
Princeton SoundLab
Synthesis Toolkit
Princeton Laptop Orchestra
ChucK programm
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https://en.wikipedia.org/wiki/Unit%20generator
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Unit generators (or ugens) are the basic formal units in many MUSIC-N-style computer music programming languages. They are sometimes called opcodes (particularly in Csound), though this expression is not accurate in that these are not machine-level instructions.
Unit generators form the building blocks for designing synthesis and signal processing algorithms in software. For example, a simple unit generator called OSC could generate a sinusoidal waveform of a specific frequency (given as an input or argument to the function or class that represents the unit generator). ENV could be a unit generator that delineates a breakpoint function. Thus ENV could be used to drive the amplitude envelope of the oscillator OSC through the equation OSC*ENV. Unit generators often use predefined arrays of values for their functions (which are filled with waveforms or other shapes by calling a specific generator function).
The unit generator theory of sound synthesis was first developed and implemented by Max Mathews and his colleagues at Bell Labs in the 1950s.
Code example
In the SuperCollider language, the .ar method in the SinOsc class is a UGen that generates a sine wave. The example below makes a sine wave at frequency 440, phase 0, and amplitude 0.5.
<nowiki>SinOsc.ar(440, 0, 0.5);</nowiki>
See also
Tuning generator
Acoustics software
Audio programming languages
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https://en.wikipedia.org/wiki/Vito%20Volterra
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Vito Volterra (, ; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations, being one of the founders of functional analysis.
Biography
Born in Ancona, then part of the Papal States, into a very poor Jewish family: his father was Abramo Volterra and his mother, Angelica Almagià. Abramo Volterra died in 1862 when Vito was two years old. The family moved to Turin, and then to Florence, where he studied at the Dante Alighieri Technical School and the Galileo Galilei Technical Institute.
Volterra showed early promise in mathematics before attending the University of Pisa, where he fell under the influence of Enrico Betti, and where he became professor of rational mechanics in 1883. He immediately started work developing his theory of functionals which led to his interest and later contributions in integral and integro-differential equations. His work is summarised in his book Theory of functionals and of Integral and Integro-Differential Equations (1930).
In 1892, he became professor of mechanics at the University of Turin and then, in 1900, professor of mathematical physics at the University of Rome La Sapienza. Volterra had grown up during the final stages of the Risorgimento when the Papal States were finally annexed by Italy and, like his mentor Betti, he was an enthusiastic patriot, being named by the king Victor Emmanuel III as a senator of the Kingdom of Italy in 1905. In the
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https://en.wikipedia.org/wiki/Zymogen
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In biochemistry, a zymogen (), also called a proenzyme (), is an inactive precursor of an enzyme. A zymogen requires a biochemical change (such as a hydrolysis reaction revealing the active site, or changing the configuration to reveal the active site) for it to become an active enzyme. The biochemical change usually occurs in Golgi bodies, where a specific part of the precursor enzyme is cleaved in order to activate it. The inactivating piece which is cleaved off can be a peptide unit, or can be independently-folding domains comprising more than 100 residues. Although they limit the enzyme's ability, these N-terminal extensions of the enzyme or a “prosegment” often aid in the stabilization and folding of the enzyme they inhibit.
The pancreas secretes zymogens partly to prevent the enzymes from digesting proteins in the cells in which they are synthesised. Enzymes like pepsin are created in the form of pepsinogen, an inactive zymogen. Pepsinogen is activated when chief cells release it into the gastric acid, whose hydrochloric acid partially activates it. Another partially inactivated pepsinogen completes the activation by removing the peptide, turning the pepsinogen into pepsin. Accidental activation of zymogens can happen when the secretion duct in the pancreas is blocked by a gallstone, resulting in acute pancreatitis.
Fungi also secrete digestive enzymes into the environment as zymogens. The external environment has a different pH than inside the fungal cell and this c
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https://en.wikipedia.org/wiki/Judy%20array
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In computer science, a Judy array is a data structure implementing a type of associative array with high performance and low memory usage. Unlike most other key-value stores, Judy arrays use no hashing, leverage compression on their keys (which may be integers or strings), and can efficiently represent sparse data; that is, they may have large ranges of unassigned indices without greatly increasing memory usage or processing time. They are designed to remain efficient even on structures with sizes in the peta-element range, with performance scaling on the order of O(log n). Roughly speaking, Judy arrays are highly optimized 256-ary radix trees.
Judy trees are usually faster than AVL trees, B-trees, hash tables and skip lists because they are highly optimized to maximize usage of the CPU cache. In addition, they require no tree balancing and no hashing algorithm is used.
History
The Judy array was invented by Douglas Baskins and named after his sister.
Benefits
Memory allocation
Judy arrays are dynamic and can grow or shrink as elements are added to, or removed from, the array. The memory used by Judy arrays is nearly proportional to the number of elements in the Judy array.
Speed
Judy arrays are designed to minimize the number of expensive cache-line fills from RAM, and so the algorithm contains much complex logic to avoid cache misses as often as possible. Due to these cache optimizations, Judy arrays are fast, especially for very large datasets. On data sets that are s
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https://en.wikipedia.org/wiki/Functional%20neuroimaging
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Functional neuroimaging is the use of neuroimaging technology to measure an aspect of brain function, often with a view to understanding the relationship between activity in certain brain areas and specific mental functions. It is primarily used as a research tool in cognitive neuroscience, cognitive psychology, neuropsychology, and social neuroscience.
Overview
Common methods of functional neuroimaging include
Positron emission tomography (PET)
Functional magnetic resonance imaging (fMRI)
Electroencephalography (EEG)
Magnetoencephalography (MEG)
Functional near-infrared spectroscopy (fNIRS)
Single-photon emission computed tomography (SPECT)
Functional ultrasound imaging (fUS)
PET, fMRI, fNIRS and fUS can measure localized changes in cerebral blood flow related to neural activity. These changes are referred to as activations. Regions of the brain which are activated when a subject performs a particular task may play a role in the neural computations which contribute to the behaviour. For instance, widespread activation of the occipital lobe is typically seen in tasks which involve visual stimulation (compared with tasks that do not). This part of the brain receives signals from the retina and is believed to play a role in visual perception.
Other methods of neuroimaging involve recording of electrical currents or magnetic fields, for example EEG and MEG. Different methods have different advantages for research; for instance, MEG measures brain activity with high t
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https://en.wikipedia.org/wiki/QMC
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QMC may refer to:
Quaid e Azam Medical College, a medical college in Bahawalpur, Pakistan
Quantum Monte Carlo, a class of computer algorithms
Quartermaster Corporal, a type of appointment in the British Household Cavalry
Quasi-Monte Carlo method, an integration method in mathematics
Queen Margaret College, now Queen Margaret University, in Edinburgh, Scotland
Queen Margaret College (Wellington), an all-girls high school in Wellington, New Zealand
Queen Mary Coast, a portion of the coast of Antarctica
Queen Mary College, a former college of the University of London, now part of Queen Mary University of London
Queen Mary's College, Chennai, a women's college in Chennai
Queen Mary's College, a Sixth Form College in Basingstoke, Hampshire, England
Queen's Medical Centre, a hospital in Nottingham, England
Quezon Memorial Circle, a national park and shrine in Quezon City, Philippines
Quine–McCluskey algorithm, a method used for the minimization of Boolean functions
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https://en.wikipedia.org/wiki/Keith%20number
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In recreational mathematics, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number in a given number base with digits such that when a sequence is created such that the first terms are the digits of and each subsequent term is the sum of the previous terms, is part of the sequence. Keith numbers were introduced by Mike Keith in 1987.
They are computationally very challenging to find, with only about 100 known.
Definition
Let be a natural number, let be the number of digits of in base , and let
be the value of each digit of .
We define the sequence by a linear recurrence relation. For ,
and for
If there exists an such that , then is said to be a Keith number.
For example, 88 is a Keith number in base 6, as
and the entire sequence
and .
Finding Keith numbers
Whether or not there are infinitely many Keith numbers in a particular base is currently a matter of speculation. Keith numbers are rare and hard to find. They can be found by exhaustive search, and no more efficient algorithm is known.
According to Keith, in base 10, on average Keith numbers are expected between successive powers of 10. Known results seem to support this.
Examples
14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909, 31331, 34285, 34348, 55604, 62662, 86935, 93993, 120284, 129106, 147640, 156146, 174680, 183186, 298320, 355419, 694280, 925993, 1084051, 7913837, 11436171, 33445755, 44121607, 1295720
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https://en.wikipedia.org/wiki/Periodogram
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In signal processing, a periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898. Today, the periodogram is a component of more sophisticated methods (see spectral estimation). It is the most common tool for examining the amplitude vs frequency characteristics of FIR filters and window functions. FFT spectrum analyzers are also implemented as a time-sequence of periodograms.
Definition
There are at least two different definitions in use today. One of them involves time-averaging, and one does not. Time-averaging is also the purview of other articles (Bartlett's method and Welch's method). This article is not about time-averaging. The definition of interest here is that the power spectral density of a continuous function, is the Fourier transform of its auto-correlation function (see Cross-correlation theorem, Spectral density#Power spectral density, and Wiener–Khinchin theorem):
Computation
For sufficiently small values of parameter an arbitrarily-accurate approximation for can be observed in the region of the function:
which is precisely determined by the samples that span the non-zero duration of (see Discrete-time Fourier transform).
And for sufficiently large values of parameter , can be evaluated at an arbitrarily close frequency by a summation of the form:
where is an integer. The periodicity of allows this to be written very simply in terms of a Discrete Fourier transform:
where is a pe
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https://en.wikipedia.org/wiki/H%C3%A9non%20map
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In mathematics, the Hénon map, sometimes called Hénon–Pomeau attractor/map, is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior. The Hénon map takes a point in the plane and maps it to a new point
The map depends on two parameters, and , which for the classical Hénon map have values of and . For the classical values the Hénon map is chaotic. For other values of and the map may be chaotic, intermittent, or converge to a periodic orbit. An overview of the type of behavior of the map at different parameter values may be obtained from its orbit diagram.
The map was introduced by Michel Hénon as a simplified model of the Poincaré section of the Lorenz model. For the classical map, an initial point of the plane will either approach a set of points known as the Hénon strange attractor, or diverge to infinity. The Hénon attractor is a fractal, smooth in one direction and a Cantor set in another. Numerical estimates yield a correlation dimension of 1.21 ± 0.01 or 1.25 ± 0.02 (depending on the dimension of the embedding space) and a Box Counting dimension of 1.261 ± 0.003 for the attractor of the classical map.
Attractor
The Hénon map maps two points into themselves: these are the invariant points. For the classical values of a and b of the Hénon map, one of these points is on the attractor:
This point is unstable. Points close to this fixed point and along the slope 1.924 will approach the f
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https://en.wikipedia.org/wiki/Netlib
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Netlib is a repository of software for scientific computing maintained by AT&T, Bell Laboratories, the University of Tennessee and Oak Ridge National Laboratory. Netlib comprises many separate programs and libraries. Most of the code is written in C and Fortran, with some programs in other languages.
History
The project began with email distribution on UUCP, ARPANET and CSNET in the 1980s.
The code base of Netlib was written at a time when computer software was not yet considered merchandise. Therefore, no license terms or terms of use are stated for many programs. Before the Berne Convention Implementation Act of 1988 (and the earlier Copyright Act of 1976) works without an explicit copyright notice were public-domain software. Also, most of the Netlib code is work of US government employees and therefore in the public domain. While several packages therefore don't have explicit waiver/anti-copyright statements, for instance, the SLATEC package has an explicit statement.
Contents
Some well-known packages maintained in Netlib are:
AMPL Solver Library (ASL)
Basic Linear Algebra Subprograms (BLAS)
EISPACK
LAPACK
LINPACK
MINPACK
QUADPACK
The SLATEC package is special in that it comprises a number of other packages like BLAS and LINPACK.
Other projects
GNU Scientific Library (GSL), written in C and distributed under the GNU General Public License
References
External links
www.netlib.org
Numerical software
Public-domain software with source code
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https://en.wikipedia.org/wiki/Primitive%20ideal
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In mathematics, specifically ring theory, a left primitive ideal is the annihilator of a (nonzero) simple left module. A right primitive ideal is defined similarly. Left and right primitive ideals are always two-sided ideals.
Primitive ideals are prime. The quotient of a ring by a left primitive ideal is a left primitive ring. For commutative rings the primitive ideals are maximal, and so commutative primitive rings are all fields.
Primitive spectrum
The primitive spectrum of a ring is a non-commutative analog of the prime spectrum of a commutative ring.
Let A be a ring and the set of all primitive ideals of A. Then there is a topology on , called the Jacobson topology, defined so that the closure of a subset T is the set of primitive ideals of A containing the intersection of elements of T.
Now, suppose A is an associative algebra over a field. Then, by definition, a primitive ideal is the kernel of an irreducible representation of A and thus there is a surjection
Example: the spectrum of a unital C*-algebra.
See also
Dixmier mapping
Notes
References
External links
Ideals (ring theory)
Module theory
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https://en.wikipedia.org/wiki/Intramolecular%20reaction
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In chemistry, intramolecular describes a process or characteristic limited within the structure of a single molecule, a property or phenomenon limited to the extent of a single molecule.
Examples
intramolecular hydride transfer (transfer of a hydride ion from one part to another within the same molecule)
intramolecular hydrogen bond (a hydrogen bond formed between two functional groups of the same molecule)
cyclization of ω-haloalkylamines and alcohols to form the corresponding saturated nitrogen and oxygen heterocycles, respectively (an SN2 reaction within the same molecule)
In intramolecular organic reactions, two reaction sites are contained within a single molecule. This creates a very high effective concentration (resulting in high reaction rates), and, therefore, many intramolecular reactions that would not occur as an intermolecular reaction between two compounds take place.
Examples of intramolecular reactions are the Smiles rearrangement, the Dieckmann condensation and the Madelung synthesis.
Relative rates
Intramolecular reactions, especially ones leading to the formation of 5- and 6-membered rings, are rapid compared to an analogous intermolecular process. This is largely a consequence of the reduced entropic cost for reaching the transition state of ring formation and the absence of significant strain associated with formation of rings of these sizes. For the formation of different ring sizes via cyclization of substrates of varying tether length, the orde
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https://en.wikipedia.org/wiki/Physiological%20psychology
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Physiological psychology is a subdivision of behavioral neuroscience (biological psychology) that studies the neural mechanisms of perception and behavior through direct manipulation of the brains of nonhuman animal subjects in controlled experiments. This field of psychology takes an empirical and practical approach when studying the brain and human behavior. Most scientists in this field believe that the mind is a phenomenon that stems from the nervous system. By studying and gaining knowledge about the mechanisms of the nervous system, physiological psychologists can uncover many truths about human behavior. Unlike other subdivisions within biological psychology, the main focus of psychological research is the development of theories that describe brain-behavior relationships.
Physiological psychology studies many topics relating to the body's response to a behavior or activity in an organism. It concerns the brain cells, structures, components, and chemical interactions that are involved in order to produce actions. Psychologists in this field usually focus their attention to topics such as sleep, emotion, ingestion, senses, reproductive behavior, learning/memory, communication, psychopharmacology, and neurological disorders. The basis for these studies all surround themselves around the notion of how the nervous system intertwines with other systems in the body to create a specific behavior.
Nervous system
The nervous system can be described as a control system that
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https://en.wikipedia.org/wiki/142%20%28number%29
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142 (one hundred [and] forty-two) is the natural number following 141 and preceding 143.
In mathematics
There are 142 connected functional graphs on four labeled vertices, 142 planar graphs with 6 unlabeled vertices, and 142 partial involutions on five elements.
See also
The year AD 142 or 142 BC
List of highways numbered 142
References
Integers
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https://en.wikipedia.org/wiki/Aliquot%20sequence
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In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0.
Definition and overview
The aliquot sequence starting with a positive integer can be defined formally in terms of the sum-of-divisors function or the aliquot sum function in the following way:
If the condition is added, then the terms after 0 are all 0, and all aliquot sequences would be infinite, and we can conjecture that all aliquot sequences are convergent, the limit of these sequences are usually 0 or 6.
For example, the aliquot sequence of 10 is because:
Many aliquot sequences terminate at zero; all such sequences necessarily end with a prime number followed by 1 (since the only proper divisor of a prime is 1), followed by 0 (since 1 has no proper divisors). See for a list of such numbers up to 75. There are a variety of ways in which an aliquot sequence might not terminate:
A perfect number has a repeating aliquot sequence of period 1. The aliquot sequence of 6, for example, is
An amicable number has a repeating aliquot sequence of period 2. For instance, the aliquot sequence of 220 is
A sociable number has a repeating aliquot sequence of period 3 or greater. (Sometimes the term sociable number is used to encompass amicable numbers as well.) For instance, the aliquot sequence of 1264460 is
Some numbers have an aliqu
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https://en.wikipedia.org/wiki/Peter%20Lax
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Peter David Lax (born Lax Péter Dávid; 1 May 1926) is a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics.
Lax has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields.
In a 1958 paper Lax stated a conjecture about matrix representations for third order hyperbolic polynomials which remained unproven for over four decades. Interest in the "Lax conjecture" grew as mathematicians working in several different areas recognized the importance of its implications in their field, until it was finally proven to be true in 2003.
Life and education
Lax was born in Budapest, Hungary to a Jewish family. Lax began displaying an interest in mathematics at age twelve, and soon his parents hired Rózsa Péter as a tutor for him. His parents Klara Kornfield and Henry Lax were both physicians and his uncle Albert Kornfeld (also known as Albert Korodi) was a mathematician, as well as a friend of Leó Szilárd.
The family left Hungary on 15 November 1941, and traveled via Lisbon to the United States. As a high school student at Stuyvesant High School, Lax took no math classes but did compete on the school math team. During this time, he met with John von Neumann, Richard Courant, and Paul Erdős, who introduced him to Albert Einstein.
As he was still 17 when he finished high school, he could a
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https://en.wikipedia.org/wiki/Charting%20application
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A charting application is a computer program that is used to create a graphical representation (a chart) based on some non-graphical data that is entered by a user, most often through a spreadsheet application, but also through a dedicated specific scientific application (such as through a symbolic mathematics computing system, or a proprietary data collection application), or using an online spreadsheet service.
There are several online charting services available, the most popular one being the U.S. Department of Education's Institute of Education Sciences' NCES Chart.
See also
List of information graphics software
Charts
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https://en.wikipedia.org/wiki/Pelageya%20Polubarinova-Kochina
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Pelageya Yakovlevna Polubarinova-Kochina (; – 3 July 1999) was a Soviet and Russian applied mathematician, known for her work on fluid mechanics and hydrodynamics, particularly, the application of Fuchsian equations, as well in the history of mathematics. She was elected a corresponding member of the Academy of Sciences of the Soviet Union in 1946 and full member (academician) in 1958.
Biography
Born on in the Russian Empire to an accountant and a housewife, Pelageya was the second youngest of four children. She studied at a women's high school in Saint Petersburg and went on to Petrograd University (after the Russian Revolution). After her father died in 1918, she started working at the laboratory of geophysics under the supervision of Alexander Friedmann. There she met Nikolai Kochin; they were married in 1925 and had two daughters. The two taught at Petrograd University until 1934, when they moved to Moscow, where Nikolai Kochin took a teaching position at the Moscow University. In Moscow, Polubarinova-Kochina did research at the Steklov Institute until World War II, when she and their daughters were evacuated to Kazan while Kochin stayed in Moscow to work on aiding the military effort. He died before the war was over.
After the war, she edited his lectures and continued to teach applied mathematics. She was later head of the department of theoretical mechanics at the University of Novosibirsk and director of the department of applied hydrodynamics at the Hydrodynamic
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https://en.wikipedia.org/wiki/Astrophysics%20Data%20System
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The SAO/NASA Astrophysics Data System (ADS) is an online database of over 16 million astronomy and physics papers that are both from peer reviewed and non-peer reviewed sources. Abstracts are available online for free for almost all articles, and fully scanned articles are available in Graphics Interchange Format (GIF), and Portable Document Format (PDF) for older articles. It was developed by the National Aeronautics and Space Administration (NASA) and it is managed by the Smithsonian Astrophysical Observatory.
ADS is a powerful research tool with significant impact on the efficiency of astronomical research since it was started in 1992. Literature searches that would previously take days or weeks to retrieve the result, now take seconds via the ADS search engine, which is custom-built for astronomical needs. Studies have found that the monetary benefit to astronomy that the ADS saves is equivalent to several hundred million US dollars annually (2005).
ADS is used among astronomers worldwide, and therefore ADS usage statistics can be used to analyze global trends in astronomical research.
These studies have revealed that the amount of research an astronomer carries out is related to the per capita gross domestic product (GDP) of the country in which the scientist is based, and that the number of astronomers in a country is proportional to the GDP of that country. Consequently, the total amount of research done in a country is proportional to the square of its GDP divided
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https://en.wikipedia.org/wiki/List%20of%20neurological%20research%20methods
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There are numerous types of research methods used when conducting neurological research, all with the purpose of trying to view the activity that occurs within the brain during a certain activity or behavior. The disciplines within which these methods are used is quite broad, ranging from psychology to neuroscience to biomedical engineering to sociology. The following is a list of neuroimaging methods:
Electroencephalography (EEG)
Quantitative electroencephalography (QEEG)
Stereoelectroencephalography (SEEG)
Functional magnetic resonance imaging (fMRI)
Magnetoencephalography (MEG)
Near-infrared spectroscopy (NIRS)
Positron emission tomography (PET)
Single-unit recording
Transcranial direct-current stimulation (TDCS)
Transcranial magnetic stimulation (TMS)
See also
neuroimaging
functional neuroimaging
Neurological research methods
Research methods
Cognitive science lists
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https://en.wikipedia.org/wiki/Dicarbonyl
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In organic chemistry, a dicarbonyl is a molecule containing two carbonyl () groups. Although this term could refer to any organic compound containing two carbonyl groups, it is used more specifically to describe molecules in which both carbonyls are in close enough proximity that their reactivity is changed, such as 1,2-, 1,3-, and 1,4-dicarbonyls. Their properties often differ from those of monocarbonyls, and so they are usually considered functional groups of their own. These compounds can have symmetrical or unsymmetrical substituents on each carbonyl, and may also be functionally symmetrical (dialdehydes, diketones, diesters, etc.) or unsymmetrical (keto-esters, keto-acids, etc.).
1,2-Dicarbonyls
1,2-Dialdehyde
The only 1,2-dialdehyde is glyoxal, . Like many alkyldialdehydes, glyoxal is encountered almost exclusively as its hydrate and oligomers thereof. These derivatives often behave equivalently to the aldehydes since hydration is reversible. Glyoxal condenses readily with amines. Via such reactions, it is a precursor to many heterocycles, e.g. imidazoles.
1,2-Diketones
The principal diketone is diacetyl, also known as 2,3-butanedione, . 1,2-Diketones are often generated by oxidation (dehydrogenation) of the diols:
RCH(OH)CH(OH)R -> RC(O)C(O)R + 2 H2
2,3-Butanedione, 2,3-pentanedione, and 2,3-hexanedione are found in small amounts in various foods. They are used as aroma components in alcohol-free beverages and in baked goods. Benzil, , is the corresponding dip
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https://en.wikipedia.org/wiki/Galois%20module
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In mathematics, a Galois module is a G-module, with G being the Galois group of some extension of fields. The term Galois representation is frequently used when the G-module is a vector space over a field or a free module over a ring in representation theory, but can also be used as a synonym for G-module. The study of Galois modules for extensions of local or global fields and their group cohomology is an important tool in number theory.
Examples
Given a field K, the multiplicative group (Ks)× of a separable closure of K is a Galois module for the absolute Galois group. Its second cohomology group is isomorphic to the Brauer group of K (by Hilbert's theorem 90, its first cohomology group is zero).
If X is a smooth proper scheme over a field K then the ℓ-adic cohomology groups of its geometric fibre are Galois modules for the absolute Galois group of K.
Ramification theory
Let K be a valued field (with valuation denoted v) and let L/K be a finite Galois extension with Galois group G. For an extension w of v to L, let Iw denote its inertia group. A Galois module ρ : G → Aut(V) is said to be unramified if ρ(Iw) = {1}.
Galois module structure of algebraic integers
In classical algebraic number theory, let L be a Galois extension of a field K, and let G be the corresponding Galois group. Then the ring OL of algebraic integers of L can be considered as an OK[G]-module, and one can ask what its structure is. This is an arithmetic question, in that by the normal basis theorem one
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https://en.wikipedia.org/wiki/Vigna
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Vigna is a genus of plants in the legume family, Fabaceae, with a pantropical distribution. It includes some well-known cultivated species, including many types of beans. Some are former members of the genus Phaseolus. According to Hortus Third, Vigna differs from Phaseolus in biochemistry and pollen structure, and in details of the style and stipules.
Vigna is also commonly confused with the genus Dolichos, but the two differ in stigma structure.
Vigna are herbs or occasionally subshrubs. The leaves are pinnate, divided into 3 leaflets. The inflorescence is a raceme of yellow, blue, or purple pea flowers. The fruit is a legume pod of varying shapes containing seeds.
Familiar food species include the adzuki bean (V. angularis), the black gram (V. mungo), the cowpea (V. unguiculata, including the variety known as the black-eyed pea), and the mung bean (V. radiata). Each of these may be used as a whole bean, a bean paste, or as bean sprouts.
The genus is named after Domenico Vigna, a seventeenth-century Italian botanist and director of the Orto botanico di Pisa.
Uses
Root tubers of Vigna species have itionally been used as food by the Indigenous Peoples of the Northern Territory.
Selected species
The genus Vigna contains at least 90 species, including:
Subgenus Ceratotropis
Vigna aconitifolia (Jacq.) Maréchal—moth bean, mat bean, Turkish gram
Vigna angularis (Willd.) Ohwi & H. Ohashi—adzuki bean, red bean
Vigna angularis var. angularis (Willd.) Ohwi & H. Ohashi
Vigna a
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https://en.wikipedia.org/wiki/Sympatric%20speciation
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Sympatric speciation is the evolution of a new species from a surviving ancestral species while both continue to inhabit the same geographic region. In evolutionary biology and biogeography, sympatric and sympatry are terms referring to organisms whose ranges overlap so that they occur together at least in some places. If these organisms are closely related (e.g. sister species), such a distribution may be the result of sympatric speciation. Etymologically, sympatry is derived from the Greek roots ("together") and ("homeland"). The term was coined by Edward Bagnall Poulton in 1904, who explains the derivation.
Sympatric speciation is one of three traditional geographic modes of speciation. Allopatric speciation is the evolution of species caused by the geographic isolation of two or more populations of a species. In this case, divergence is facilitated by the absence of gene flow. Parapatric speciation is the evolution of geographically adjacent populations into distinct species. In this case, divergence occurs despite limited interbreeding where the two diverging groups come into contact. In sympatric speciation, there is no geographic constraint to interbreeding. These categories are special cases of a continuum from zero (sympatric) to complete (allopatric) spatial segregation of diverging groups.
In multicellular eukaryotic organisms, sympatric speciation is a plausible process that is known to occur, but the frequency with which it occurs is not known.
In bacteria, h
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https://en.wikipedia.org/wiki/Spin%20probe
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A spin probe is a molecule with stable free radical character that carries a functional group. This group can be used to couple the probe to another molecule, e.g. a biomolecule.
Electron spin resonance can be employed to quantify the probe's concentration.
References
Molecular physics
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https://en.wikipedia.org/wiki/Charge%20carrier
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In physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. The term is used most commonly in solid state physics. In a conducting medium, an electric field can exert force on these free particles, causing a net motion of the particles through the medium; this is what constitutes an electric current.
The electron and the proton are the elementary charge carriers, each carrying one elementary charge (e), of the same magnitude and opposite sign.
In conductors
In conducting media, particles serve to carry charge:
In many metals, the charge carriers are electrons. One or two of the valence electrons from each atom are able to move about freely within the crystal structure of the metal. The free electrons are referred to as conduction electrons, and the cloud of free electrons is called a Fermi gas. Many metals have electron and hole bands. In some, the majority carriers are holes.
In electrolytes, such as salt water, the charge carriers are ions, which are atoms or molecules that have gained or lost electrons so they are electrically charged. Atoms that have gained electrons so they are negatively charged are called anions, atoms that have lost electrons so they are positively charged are called cations. Cations and anions of the dissociated liquid also serve as charge carriers in melted ionic solids (see e.g.
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https://en.wikipedia.org/wiki/Secondary%20emission
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In particle physics, secondary emission is a phenomenon where primary incident particles of sufficient energy, when hitting a surface or passing through some material, induce the emission of secondary particles. The term often refers to the emission of electrons when charged particles like electrons or ions in a vacuum tube strike a metal surface; these are called secondary electrons. In this case, the number of secondary electrons emitted per incident particle is called secondary emission yield. If the secondary particles are ions, the effect is termed secondary ion emission. Secondary electron emission is used in photomultiplier tubes and image intensifier tubes to amplify the small number of photoelectrons produced by photoemission, making the tube more sensitive. It also occurs as an undesirable side effect in electronic vacuum tubes when electrons from the cathode strike the anode, and can cause parasitic oscillation.
Applications
Secondary emissive materials
Commonly used secondary emissive materials include
alkali antimonide
Beryllium oxide (BeO)
Magnesium oxide (MgO)
Gallium phosphide (GaP)
Gallium arsenide phosphide (GaAsP)
Lead oxide (PbO)
Photo multipliers and similar devices
In a photomultiplier tube, one or more electrons are emitted from a photocathode and accelerated towards a polished metal electrode (called a dynode).
They hit the electrode surface with sufficient energy to release a number of electrons through secondary emission. These
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https://en.wikipedia.org/wiki/Photocathode
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A photocathode is a surface engineered to convert light (photons) into electrons using the photoelectric effect. Photocathodes are important in accelerator physics where they are utilised in a photoinjector to generate high brightness electron beams. Electron beams generated with photocathodes are commonly used for free electron lasers and for ultrafast electron diffraction. Photocathodes are also commonly used as the negatively charged electrode in a light detection device such as a photomultiplier, phototube and image intensifier.
Important Properties
Quantum Efficiency (QE)
Quantum efficiency is a unitless number that measures the sensitivity of the photocathode to light. It is the ratio of the number of electrons emitted to the number of incident photons. This property depends on the wavelength of light being used to illuminate the photocathode. For many applications, QE is the most important property as the photocathodes are used solely for converting photons into an electrical signal.
Quantum efficiency may be calculated from photocurrent (), laser power (), and either the photon energy () or laser wavelength () using the following equation.
Mean Transverse Energy (MTE) and Thermal Emittance
For some applications, the initial momentum distribution of emitted electrons is important and the mean transverse energy (MTE) and thermal emittance are popular metrics for this. The MTE is the mean of the squared momentum in a direction along the photocathode's surface
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https://en.wikipedia.org/wiki/Standard%20diving%20dress
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Standard diving dress, also known as hard-hat or copper hat equipment, deep sea diving suit or heavy gear, is a type of diving suit that was formerly used for all relatively deep underwater work that required more than breath-hold duration, which included marine salvage, civil engineering, pearl shell diving and other commercial diving work, and similar naval diving applications. Standard diving dress has largely been superseded by lighter and more comfortable equipment.
Standard diving dress consists of a diving helmet made from copper and brass or bronze, clamped over a watertight gasket to a waterproofed canvas suit, an air hose from a surface-supplied manually operated pump or low pressure breathing air compressor, a diving knife, and weights to counteract buoyancy, generally on the chest, back and shoes. Later models were equipped with a diver's telephone for voice communications with the surface. The term deep sea diving was used to distinguish diving with this equipment from shallow water diving using a shallow water helmet, which was not sealed to the suit.
Some variants used rebreather systems to extend the use of gas supplies carried by the diver, and were effectively self-contained underwater breathing apparatus, and others were suitable for use with helium based breathing gases for deeper work. Divers could be deployed directly by lowering or raising them using the lifeline, or could be transported on a diving stage. Most diving work using standard dress was don
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https://en.wikipedia.org/wiki/Jacobson%20density%20theorem
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In mathematics, more specifically non-commutative ring theory, modern algebra, and module theory, the Jacobson density theorem is a theorem concerning simple modules over a ring .
The theorem can be applied to show that any primitive ring can be viewed as a "dense" subring of the ring of linear transformations of a vector space. This theorem first appeared in the literature in 1945, in the famous paper "Structure Theory of Simple Rings Without Finiteness Assumptions" by Nathan Jacobson. This can be viewed as a kind of generalization of the Artin-Wedderburn theorem's conclusion about the structure of simple Artinian rings.
Motivation and formal statement
Let be a ring and let be a simple right -module. If is a non-zero element of , (where is the cyclic submodule of generated by ). Therefore, if are non-zero elements of , there is an element of that induces an endomorphism of transforming to . The natural question now is whether this can be generalized to arbitrary (finite) tuples of elements. More precisely, find necessary and sufficient conditions on the tuple and separately, so that there is an element of with the property that for all . If is the set of all -module endomorphisms of , then Schur's lemma asserts that is a division ring, and the Jacobson density theorem answers the question on tuples in the affirmative, provided that the are linearly independent over .
With the above in mind, the theorem may be stated this way:
The Jacobson density theorem
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https://en.wikipedia.org/wiki/Newtonian%20limit
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In physics, the Newtonian limit is a mathematical approximation applicable to physical systems exhibiting (1) weak gravitation, (2) objects moving slowly compared to the speed of light, and (3) slowly changing (or completely static) gravitational fields. Under these conditions, Newton's law of universal gravitation may be used to obtain values that are accurate. In general, and in the presence of significant gravitation, the general theory of relativity must be used.
In the Newtonian limit, spacetime is approximately flat and the Minkowski metric may be used over finite distances. In this case 'approximately flat' is defined as space in which gravitational effect approaches 0, mathematically actual spacetime and Minkowski space are not identical, Minkowski space is an idealized model.
Special relativity
In special relativity, Newtonian behaviour can in most cases be obtained by performing the limit . In this limit, the often appearing gamma factor becomes 1
and the Lorentz transformations between reference frames turn into Galileo transformations
General relativity
The geodesic equation for a free particle on curved spacetime with metric can be derived from the action
If the spacetime-metric is
then, ignoring all contributions of order the action becomes
which is the action that reproduces the Newtonian equations of motion of a particle in a gravitational potential
See also
Classical limit
References
Special relativity
Dynamical systems
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https://en.wikipedia.org/wiki/Eugene%20Koonin
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Eugene Viktorovich Koonin (Russian: Евге́ний Ви́кторович Ку́нин; born October 26, 1956) is a Russian-American biologist and Senior Investigator at the National Center for Biotechnology Information (NCBI). He is a recognised expert in the field of evolutionary and computational biology.
Education
Koonin gained a Master of Science in 1978 and a PhD in 1983 in molecular biology, both from the Department of Biology at Moscow State University. His PhD thesis, titled "Multienzyme organization of encephalomyocarditis virus replication complexes", was supervised by Vadim I. Agol.
Research
From 1985 until 1991, Koonin worked as a research scientist in computational biology in the Institutes of Poliomyelitis and Microbiology at the USSR Academy of Medical Sciences, studying virus biochemistry and bacterial genetics. In 1991, Koonin moved to the NCBI, where he has held a Senior Investigator position since 1996.
Koonin's principal research goals include the comparative analysis of sequenced genomes and automatic methods for genome-scale annotation of gene functions. He also researches in the application of comparative genomics for phylogenetic analysis, reconstruction of ancestral life forms and building large-scale evolutionary scenarios, as well as mathematical modeling of genome evolution. Koonin's research also investigates computational study of the major transitions in the evolution of life (such as the origin of eukaryotes), the evolution of eukaryotic signaling and development
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https://en.wikipedia.org/wiki/Simics
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Simics is a full-system simulator or virtual platform used to run unchanged production binaries of the target hardware. Simics was originally developed by the Swedish Institute of Computer Science (SICS), and then spun off to Virtutech for commercial development in 1998. Virtutech was acquired by Intel in 2010. Currently, Simics is provided by Intel in a public release and sold commercially by Wind River Systems, which was in the past a subsidiary of Intel.
Simics contains both instruction set simulators and hardware models, and is or has been used to simulate systems such as Alpha, ARM (32- and 64-bit), IA-64, MIPS (32- and 64-bit), MSP430, PowerPC (32- and 64-bit), RISC-V (32- and 64-bit), SPARC-V8 and V9, and x86 and x86-64 CPUs.
Many different operating systems have been run on various simulated virtual platforms, including Linux, MS-DOS, Windows, VxWorks, OSE, Solaris, FreeBSD, QNX, RTEMS, UEFI, and Zephyr.
The NetBSD AMD64 port was initially developed using Simics before the public release of the chip. The purpose of simulation in Simics is often to develop software for a particular type of hardware without requiring access to that precise hardware, using Simics as a virtual platform. This can applied both to pre-release and pre-silicon software development for future hardware, as well as for existing hardware. Intel uses Simics to provide its ecosystem with access to future platform months or years ahead of the hardware launch.
The current version of Simics is
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https://en.wikipedia.org/wiki/Eckmann%E2%80%93Hilton%20argument
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In mathematics, the Eckmann–Hilton argument (or Eckmann–Hilton principle or Eckmann–Hilton theorem) is an argument about two unital magma structures on a set where one is a homomorphism for the other. Given this, the structures are the same, and the resulting magma is a commutative monoid. This can then be used to prove the commutativity of the higher homotopy groups. The principle is named after Beno Eckmann and Peter Hilton, who used it in a 1962 paper.
The Eckmann–Hilton result
Let be a set equipped with two binary operations, which we will write and , and suppose:
and are both unital, meaning that there are identity elements and of such that and , for all .
for all .
Then and are the same and in fact commutative and associative.
Remarks
The operations and are often referred to as monoid structures or multiplications, but this suggests they are assumed to be associative, a property that is not required for the proof. In fact, associativity follows. Likewise, we do not have to require that the two operations have the same neutral element; this is a consequence.
Proof
First, observe that the units of the two operations coincide:
.
Now, let .
Then . This establishes that the two operations coincide and are commutative.
For associativity, .
Two-dimensional proof
The above proof also has a "two-dimensional" presentation that better illustrates the application to higher homotopy groups.
For this version of the proof, we write the two operations as vertic
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https://en.wikipedia.org/wiki/Hasan-i%20Sabbah
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Hasan-i Sabbah (; 1050 – 12 June 1124) was a religious and military leader, founder of the Nizari Ismaili sect and also the Hashshashin also known as the Order of Assassins.
Alongside his role as a formidable leader, Sabbah was an accomplished scholar of mathematics, most notably in geometry, as well as astronomy and philosophy, especially in epistemology. He came to be known in the West as the Old Man of the Mountain, a name given to him in the writings of Marco Polo that referenced the sect's possession of the commanding mountain fortress of Alamut Castle.
Sources
Hasan is thought to have written an autobiography, which did not survive but seems to underlie the first part of an anonymous Isma'ili biography entitled Sargozasht-e Seyyednā (). The latter is known only from quotations made by later Persian authors. Hasan also wrote a treatise, in Persian, on the doctrine of ta'līm, called, al-Fusul al-arba'a The text is no longer in existence, but fragments are cited or paraphrased by al-Shahrastānī and several Persian historians.
Early life and conversion
Qom and Rayy
The possibly autobiographical information found in Sargozasht-i Seyyednā is the main source for Hasan's background and early life. According to this, Hasan-i Sabbāh was born in the city of Qom, Persia in the 1050s to a family of Twelver Shia. His father, a Kufan Arab reportedly of Yemenite origins, had left the Sawād of Kufa (located in modern Iraq) to settle in the town of Qom, one of the first centres of
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https://en.wikipedia.org/wiki/Tribology
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Tribology is the science and engineering of understanding friction, lubrication and wear phenomena for interacting surfaces in relative motion. It is highly interdisciplinary, drawing on many academic fields, including physics, chemistry, materials science, mathematics, biology and engineering. The fundamental objects of study in tribology are tribosystems, which are physical systems of contacting surfaces. Subfields of tribology include biotribology, nanotribology and space tribology. It is also related to other areas such as the coupling of corrosion and tribology in tribocorrosion and the contact mechanics of how surfaces in contact deform.
Approximately 20% of the total energy expenditure of the world is due to the impact of friction and wear in the transportation, manufacturing, power generation, and residential sectors.
This section will provide an overview of tribology, with links to many of the more specialized areas.
Etymology
The word tribology derives from the Greek root τριβ- of the verb , tribo, "I rub" in classic Greek, and the suffix -logy from , -logia "study of", "knowledge of". Peter Jost coined the word in 1966, in the eponymous report which highlighted the cost of friction, wear and corrosion to the UK economy.
History
Early history
Despite the relatively recent naming of the field of tribology, quantitative studies of friction can be traced as far back as 1493, when Leonardo da Vinci first noted the two fundamental 'laws' of friction. According to Le
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https://en.wikipedia.org/wiki/Artinian%20ring
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In mathematics, specifically abstract algebra, an Artinian ring (sometimes Artin ring) is a ring that satisfies the descending chain condition on (one-sided) ideals; that is, there is no infinite descending sequence of ideals. Artinian rings are named after Emil Artin, who first discovered that the descending chain condition for ideals simultaneously generalizes finite rings and rings that are finite-dimensional vector spaces over fields. The definition of Artinian rings may be restated by interchanging the descending chain condition with an equivalent notion: the minimum condition.
Precisely, a ring is left Artinian if it satisfies the descending chain condition on left ideals, right Artinian if it satisfies the descending chain condition on right ideals, and Artinian or two-sided Artinian if it is both left and right Artinian. For commutative rings the left and right definitions coincide, but in general they are distinct from each other.
The Wedderburn–Artin theorem characterizes every simple Artinian ring as a ring of matrices over a division ring. This implies that a simple ring is left Artinian if and only if it is right Artinian.
The same definition and terminology can be applied to modules, with ideals replaced by submodules.
Although the descending chain condition appears dual to the ascending chain condition, in rings it is in fact the stronger condition. Specifically, a consequence of the Akizuki–Hopkins–Levitzki theorem is that a left (resp. right) Artinian
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https://en.wikipedia.org/wiki/Three-spined%20stickleback
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The three-spined stickleback (Gasterosteus aculeatus) is a fish native to most inland and coastal waters north of 30°N. It has long been a subject of scientific study for many reasons. It shows great morphological variation throughout its range, ideal for questions about evolution and population genetics. Many populations are anadromous (they live in seawater but breed in fresh or brackish water) and very tolerant of changes in salinity, a subject of interest to physiologists. It displays elaborate breeding behavior (defending a territory, building a nest, taking care of the eggs and fry) and it can be social (living in shoals outside the breeding season) making it a popular subject of inquiry in fish ethology and behavioral ecology. Its antipredator adaptations, host-parasite interactions, sensory physiology, reproductive physiology, and endocrinology have also been much studied. Facilitating these studies is the fact that the three-spined stickleback is easy to find in nature and easy to keep in aquaria.
Description
This species can occasionally reach lengths of , but lengths of at maturity are more common. The body is laterally compressed. The base of the tail is slender. The caudal fin has 12 rays. The dorsal fin has 10–14 rays; in front of it are the three spines that give the fish its name (though some individuals may have only two or four). The third spine (the one closest to the dorsal fin) is much shorter than the other two. The back of each spine is joined to the
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https://en.wikipedia.org/wiki/Hasse%20principle
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In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the completions of the rational numbers: the real numbers and the p-adic numbers. A more formal version of the Hasse principle states that certain types of equations have a rational solution if and only if they have a solution in the real numbers and in the p-adic numbers for each prime p.
Intuition
Given a polynomial equation with rational coefficients, if it has a rational solution, then this also yields a real solution and a p-adic solution, as the rationals embed in the reals and p-adics: a global solution yields local solutions at each prime. The Hasse principle asks when the reverse can be done, or rather, asks what the obstruction is: when can you patch together solutions over the reals and p-adics to yield a solution over the rationals: when can local solutions be joined to form a global solution?
One can ask this for other rings or fields: integers, for instance, or number fields. For number fields, rather than reals and p-adics, one uses complex embeddings and -adics, for prime ideals .
Forms representing 0
Quadratic forms
The Hasse–Minkowski theorem states that the local–global principle holds for the problem of representing 0 by quadratic forms over the
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https://en.wikipedia.org/wiki/Jacobian%20variety
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In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles. It is the connected component of the identity in the Picard group of C, hence an abelian variety.
Introduction
The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete version of the Abel–Jacobi theorem, making the injectivity statement of Niels Abel into an isomorphism. It is a principally polarized abelian variety, of dimension g, and hence, over the complex numbers, it is a complex torus. If p is a point of C, then the curve C can be mapped to a subvariety of J with the given point p mapping to the identity of J, and C generates J as a group.
Construction for complex curves
Over the complex numbers, the Jacobian variety can be realized as the quotient space V/L, where V is the dual of the vector space of all global holomorphic differentials on C and L is the lattice of all elements of V of the form
where γ is a closed path in C. In other words,
with embedded in via the above map. This can be done explicitly with the use of theta functions.
The Jacobian of a curve over an arbitrary field was constructed by as part of his proof of the Riemann hypothesis for curves over a finite field.
The Abel–Jacobi theorem states that the torus thus built is a variety, the classical Jacobian of a curve, that indeed parametrizes the degree 0 line bundles, that is, it can be identified with its Picard variety of degree 0 div
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https://en.wikipedia.org/wiki/MNS
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MNS may refer to:
Maharashtra Navnirman Sena, Indian political party
The Malaysian Nature Society
Maki-Nakagawa-Sakata matrix in particle physics
Ministry of National Security of several countries
Minneapolis, Northfield and Southern Railway, reporting mark
Mirror neuron system
Mission Need Statement
MNS antigen system, a variant blood group
Monday Night Soccer, an Irish television programme
Movement for a New Society
National Syndicalists (Portugal), Movimento Nacional-Sindicalista
Manganese(II) sulfide, chemical symbol MnS
Mansi language, by ISO 639-3 language code
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https://en.wikipedia.org/wiki/Parochial%20school
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A parochial school is a private primary or secondary school affiliated with a religious organization, and whose curriculum includes general religious education in addition to secular subjects, such as science, mathematics and language arts. The word parochial comes from the same root as "parish", and parochial schools were originally the educational wing of the local parish church. Christian parochial schools are called "church schools" or "Christian schools."
In addition to schools run by Christian organizations, there are also religious schools affiliated with Jewish, Muslim, and other groups; however, these are not usually called "parochial" because of the term's historical association with Christian parishes.
United Kingdom
In British education, parish schools from the established church of the relevant constituent country formed the basis of the state-funded education system, and many schools retain a church connection while essentially providing secular education in accordance with standards set by the government of the country concerned. These are often primary schools, and may be designated as name C.E. School or name C.E. (Aided) School, depending on whether they are wholly or partly funded by the Church of England (the latter is more common).
In 2002, Frank Dobson proposed an amendment to the Education Bill (for England and Wales) which would limit the selection rights of faith schools by requiring them to offer at least a quarter of places to children of anoth
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https://en.wikipedia.org/wiki/Blinding%20%28cryptography%29
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In cryptography, blinding is a technique by which an agent can provide a service to (i.e., compute a function for) a client in an encoded form without knowing either the real input or the real output. Blinding techniques also have applications to preventing side-channel attacks on encryption devices.
More precisely, Alice has an input x and Oscar has a function f. Alice would like Oscar to compute for her without revealing either x or y to him. The reason for her wanting this might be that she doesn't know the function f or that she does not have the resources to compute it.
Alice "blinds" the message by encoding it into some other input E(x); the encoding E must be a bijection on the input space of f, ideally a random permutation. Oscar gives her f(E(x)), to which she applies a decoding D to obtain .
Not all functions allow for blind computation. At other times, blinding must be applied with care. An example of the latter is Rabin–Williams signatures. If blinding is applied to the formatted message but the random value does not honor Jacobi requirements on p and q, then it could lead to private key recovery. A demonstration of the recovery can be seen in discovered by Evgeny Sidorov.
The most common application of blinding is the blind signature. In a blind signature protocol, the signer digitally signs a message without being able to learn its content.
The one-time pad (OTP) is an application of blinding to the secure communication problem, by its very nature. Alice
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https://en.wikipedia.org/wiki/Connected%20sum
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In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the classification of closed surfaces.
More generally, one can also join manifolds together along identical submanifolds; this generalization is often called the fiber sum. There is also a closely related notion of a connected sum on knots, called the knot sum or composition of knots.
Connected sum at a point
A connected sum of two m-dimensional manifolds is a manifold formed by deleting a ball inside each manifold and gluing together the resulting boundary spheres.
If both manifolds are oriented, there is a unique connected sum defined by having the gluing map reverse orientation. Although the construction uses the choice of the balls, the result is unique up to homeomorphism. One can also make this operation work in the smooth category, and then the result is unique up to diffeomorphism. There are subtle problems in the smooth case: not every diffeomorphism between the boundaries of the spheres gives the same composite manifold, even if the orientations are chosen correctly. For example, Milnor showed that two 7-cells can be glued along their boundary so that the result is an exotic sphere homeomorphic but not diffeomorphic to a 7-sphere.
However, there is a canonical way to choose the gluing of and which gives a unique well-defined conn
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https://en.wikipedia.org/wiki/Homological%20conjectures%20in%20commutative%20algebra
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In mathematics, homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of interrelated (sometimes surprisingly so) conjectures relating various homological properties of a commutative ring to its internal ring structure, particularly its Krull dimension and depth.
The following list given by Melvin Hochster is considered definitive for this area. In the sequel, , and refer to Noetherian commutative rings; will be a local ring with maximal ideal , and and are finitely generated -modules.
The Zero Divisor Theorem. If has finite projective dimension and is not a zero divisor on , then is not a zero divisor on .
Bass's Question. If has a finite injective resolution then is a Cohen–Macaulay ring.
The Intersection Theorem. If has finite length, then the Krull dimension of N (i.e., the dimension of R modulo the annihilator of N) is at most the projective dimension of M.
The New Intersection Theorem. Let denote a finite complex of free R-modules such that has finite length but is not 0. Then the (Krull dimension) .
The Improved New Intersection Conjecture. Let denote a finite complex of free R-modules such that has finite length for and has a minimal generator that is killed by a power of the maximal ideal of R. Then .
The Direct Summand Conjecture. If is a module-finite ring extension with R regular (here, R need not be local but the problem reduces at once to the local case), then R
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https://en.wikipedia.org/wiki/Alexander%20R.%20Todd
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Alexander Robertus Todd, Baron Todd (2 October 1907 – 10 January 1997) was a British biochemist whose research on the structure and synthesis of nucleotides, nucleosides, and nucleotide coenzymes gained him the Nobel Prize for Chemistry in 1957.
Early life and education
Todd was born in Cathcart in outer Glasgow, the son of Alexander Todd, a clerk with the Glasgow Subway, and his wife, Jane Lowry.
He attended Allan Glen's School and graduated from the University of Glasgow with a bachelor's degree in 1928. He received a doctorate from Goethe University Frankfurt in 1931 for his thesis on the chemistry of the bile acids.
Todd was awarded an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851, and, after studying at Oriel College, Oxford, he gained another doctorate in 1933.
Career
Todd held posts with the Lister Institute, the University of Edinburgh (staff, 1934–1936) and the University of London, where he was appointed Reader in biochemistry.
In 1938, Alexander Todd spent six months as a visiting professor at California Institute of Technology, eventually declining an offer of faculty position. Todd became the Sir Samuel Hall Chair of Chemistry and director of the Chemical Laboratories of the University of Manchester in 1938, where he began working on nucleosides, compounds that form the structural units of nucleic acids (DNA and RNA).
In 1944, he was appointed to the 1702 Chair of Chemistry in the University of Cambridge, which he held until
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https://en.wikipedia.org/wiki/121%20%28number%29
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121 (one hundred [and] twenty-one) is the natural number following 120 and preceding 122.
In mathematics
One hundred [and] twenty-one is
a square (11 times 11)
the sum of the powers of 3 from 0 to 4, so a repunit in ternary. Furthermore, 121 is the only square of the form , where p is prime (3, in this case).
the sum of three consecutive prime numbers (37 + 41 + 43).
As , it provides a solution to Brocard's problem. There are only two other squares known to be of the form . Another example of 121 being one of the few numbers supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form (with being 2 and 5, respectively).
It is also a star number, a centered tetrahedral number, and a centered octagonal number.
In decimal, it is a Smith number since its digits add up to the same value as its factorization (which uses the same digits) and as a consequence of that it is a Friedman number (). But it cannot be expressed as the sum of any other number plus that number's digits, making 121 a self number.
In other fields
121 is also:
The electricity emergency telephone number in Egypt
The number for voicemail for mobile phones on the Vodafone network
The undiscovered chemical element unbiunium has the atomic number 121
The official end score for cribbage
The pennant number of RTS Moskva, the Russian Navy’s Black Sea flagship, which was damaged beyond repair on April 13, 2022.
See also
List of highways numbered 121
Unit
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https://en.wikipedia.org/wiki/Bernard%20T.%20Feld
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Bernard Taub Feld (December 21, 1919 – February 19, 1993) was a professor of physics at the Massachusetts Institute of Technology. He helped develop the atomic bomb, and later led an international movement among scientists to banish nuclear weapons.
Early life
Feld was born in Brooklyn, New York. He graduated from the City College of New York with a bachelor of science degree in 1939. He began graduate school at Columbia University, but suspended his studies to join the American war effort. He spent the war serving as an assistant to Enrico Fermi and Leó Szilárd working on the Manhattan Project. After World War II, he returned to Columbia University to receive his PhD in 1945 with thesis advisor Willis Lamb.
Career
Feld was on the faculty of MIT from 1948 until he retired in 1990. During this time, he was President of the Albert Einstein Peace Prize Foundation, editor of the Bulletin of the Atomic Scientists, and head of the American Pugwash Committee.
Feld was a Ford Foundation Fellow and a visiting scientist at the European Center for Nuclear Research (CERN) in Geneva, Switzerland.
The Pugwash Conferences on Science and World Affairs won the Nobel Peace Prize in 1995. Feld was a leader in these conferences, serving as U.S. Chairman from 1963 to 1973 and as International Chairman from 1973 to 1978. It was in this role that he attracted the anger of Richard Nixon's White House. He was eleventh on Nixon's list of enemies, a fact that pleased him tremendously.
"O
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https://en.wikipedia.org/wiki/Cancellation%20property
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In mathematics, the notion of cancellativity (or cancellability) is a generalization of the notion of invertibility.
An element a in a magma has the left cancellation property (or is left-cancellative) if for all b and c in M, always implies that .
An element a in a magma has the right cancellation property (or is right-cancellative) if for all b and c in M, always implies that .
An element a in a magma has the two-sided cancellation property (or is cancellative) if it is both left- and right-cancellative.
A magma has the left cancellation property (or is left-cancellative) if all a in the magma are left cancellative, and similar definitions apply for the right cancellative or two-sided cancellative properties.
A left-invertible element is left-cancellative, and analogously for right and two-sided. If a⁻¹ is the inverse of a, then a ∗ b = a ∗ c implies a⁻¹ ∗ a ∗ b = a⁻¹ ∗ a ∗ c which implies b = c.
For example, every quasigroup, and thus every group, is cancellative.
Interpretation
To say that an element a in a magma is left-cancellative, is to say that the function is injective. That the function g is injective implies that given some equality of the form a ∗ x = b, where the only unknown is x, there is only one possible value of x satisfying the equality. More precisely, we are able to define some function f, the inverse of g, such that for all x . Put another way, for all x and y in M, if a * x = a * y, then x = y.
Similarly, to say that the element a is r
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https://en.wikipedia.org/wiki/Sturm%E2%80%93Liouville%20theory
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In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form:
for given functions , and , together with some boundary conditions at extreme values of . The goals of a given Sturm–Liouville problem are:
To find the for which there exists a non-trivial solution to the problem. Such values are called the eigenvalues of the problem.
For each eigenvalue , to find the corresponding solution of the problem. Such functions are called the eigenfunctions associated to each .
Sturm–Liouville theory is the general study of Sturm–Liouville problems. In particular, for a "regular" Sturm–Liouville problem, it can be shown that there are an infinite number of eigenvalues each with a unique eigenfunction, and that these eigenfunctions form an orthonormal basis of a certain Hilbert space of functions.
This theory is important in applied mathematics, where Sturm–Liouville problems occur very frequently, particularly when dealing with separable linear partial differential equations. For example, in quantum mechanics, the one-dimensional time-independent Schrödinger equation is a Sturm–Liouville problem.
Sturm–Liouville theory is named after Jacques Charles François Sturm (1803–1855) and Joseph Liouville (1809–1882) who developed the theory.
Main results
The main results in Sturm–Liouville theory apply to a Sturm–Liouville problem
on a finite interval that is "regular". The problem is said to be regular if:
t
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https://en.wikipedia.org/wiki/Field%20%28computer%20science%29
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In computer science, data that has several parts, known as a record, can be divided into fields (data fields). Relational databases arrange data as sets of database records, so called rows. Each record consists of several fields; the fields of all records form the columns.
Examples of fields: name, gender, hair colour.
In object-oriented programming, a field (also called data member or member variable) is a particular piece of data encapsulated within a class or object. In the case of a regular field (also called instance variable), for each instance of the object there is an instance variable: for example, an Employee class has a Name field and there is one distinct name per employee. A static field (also called class variable) is one variable, which is shared by all instances. Fields are abstracted by properties, which allow them to be read and written as if they were fields, but these can be translated to getter and setter method calls.
Fixed length
Fields that contain a fixed number of bits are known as fixed length fields. A four byte field for example may contain a 31 bit binary integer plus a sign bit (32 bits in all). A 30 byte name field may contain a person's name typically padded with blanks at the end.
The disadvantage of using fixed length fields is that some part of the field may be wasted but space is still required for the maximum length case. Also, where fields are omitted, padding for the missing fields is still required to maintain fixed start positions
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https://en.wikipedia.org/wiki/Envelope%20%28disambiguation%29
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An envelope is the paper container used to hold a letter being sent by post.
Envelope may also refer to:
Mathematics
Envelope (mathematics), a curve, surface, or higher-dimensional object defined as being tangent to a given family of lines or curves (or surfaces, or higher-dimensional objects, respectively)
Envelope (category theory)
Science
Viral envelope, the membranal covering surrounding the capsid of a virus
Cell envelope of a bacterium, consisting of the cell membrane, cell wall and outer membrane
, the fabric skin covering the airship
Building envelope, the exterior layer of a building that protects it from the elements
Envelope (motion), a solid representing all positions that an object may occupy during its normal range of motion
Envelope (music), the variation of a sound over time, as is used in sound synthesis
Envelope (radar), the volume of space where a radar system is required to reliably detect an object
Envelope (waves), a curve outlining the peak values of an oscillating waveform or signal
Envelope detector, an electronic circuit used to measure the envelope of a waveform
Flight envelope, the limits within which an aircraft can operate
Entertainment
Envelopes (band), an indie/pop band from Sweden and France, based in the UK
Envelope (film), a 2012 film
"Envelopes", a song by Frank Zappa from his 1982 album Ship Arriving Too Late to Save a Drowning Witch
Other uses
Envelope (military), attacking one or both of the enemy's flanks to enc
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https://en.wikipedia.org/wiki/American%20Computer%20Science%20League
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ACSL, or the American Computer Science League, is an international computer science competition among more than 300 schools. Originally founded in 1978 as the Rhode Island Computer Science League, it then became the New England Computer Science League. With countrywide and worldwide participants, it became the American Computer Science League. It has been in continuous existence since 1978.
Each yearly competition consists of four contests. All students at each school may compete but the team score is the sum of the best 3 or 5 top scores. Each contest consists of two parts: a written section (called "shorts") and a programming section. Written topics tested include "what does this program do?", digital electronics, Boolean algebra, computer numbering systems, recursive functions, data structures (primarily dealing with heaps, binary search trees, stacks, and queues), lisp programming, regular expressions and Finite State Automata, bit string flicking, graph theory, assembly programming and prefix/postfix/infix notation.
Divisions
There are five divisions in ACSL: Elementary, Classroom, Junior, Intermediate, and Senior. The Elementary Division is a non-programming competition for grades 3 - 6. It tests one topic per contest. The Classroom Division is a non-programming competition for all grades and consists of a 10 question test on 4 topics each contest. Junior Division is recommended for middle school students (no students above the ninth grade may compete in it).
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https://en.wikipedia.org/wiki/Thomas%20Muir%20%28mathematician%29
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Sir Thomas Muir (25 August 1844 – 21 March 1934) was a Scottish mathematician, remembered as an authority on determinants.
Life
He was born in Stonebyres in South Lanarkshire, and brought up in the small town of Biggar. He was educated at Wishaw Public School.
At the University of Glasgow he changed his studies from classics to mathematics after advice from the future Lord Kelvin. After graduating he held positions at the University of St Andrews and the University of Glasgow. From 1874 to 1892 he taught at Glasgow High School. In 1882 he published Treatise on the theory of determinants; then in 1890 he published a History of determinants. In his 1882 work, Muir rediscovered an important lemma that was first proved by Cayley 35 years earlier: In Glasgow he lived at Beechcroft in the Bothwell district.
In 1874 he was elected a Fellow of the Royal Society of Edinburgh, His proposers were William Thomson, Lord Kelvin, Hugh Blackburn, Philip Kelland and Peter Guthrie Tait. He won the Society's Keith Prize for 1881-1883 and a second time in 1895–1897. He served as the Society's Vice President 1888 to 1891. He won the Gunning Victoria Jubilee Prize for 1912 to 1916.
From 1892 to 1915 he was in South Africa as Superintendent General of Education, and also working at the University of the Cape. He was elected a Fellow of the Royal Society of Edinburgh and in 1900 a Fellow of the Royal Society. He was installed Companion of the Order of St Michael and St George (CMG) in 1901 and
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https://en.wikipedia.org/wiki/John%20William%20Heslop-Harrison
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Prof John William Heslop Harrison, FRS FRSE (1881–1967), was Professor of Botany at King's College, Durham University (now Newcastle University). He enjoyed a brilliant career, specialising in the genetics of moths, but is now best remembered for an alleged academic fraud.
Early life and education
He was born in Birtley on 22 January 1881, the son of George Heslop-Harrison, a pattern-maker at Birtley Iron Works. He was educated at Bede College School in Durham then Rutherford School for Boys in Newcastle upon Tyne. His mother was a keen gardener, and other influences such as his uncle, Rev J E Hull, and neighbour, Charles Robson, led him to an early interest in botany and natural history.
He then studied at Durham College of Science, graduating BSc in 1903. He did further postgraduate study at the University of Newcastle gaining an MSc in 1916 and doctorate (DSc) in 1917.
In 1921 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were James Hartley Ashworth, Sir Thomas Hudson Beare, Percy Hall Grimshaw, and James Ritchie. He served as the Society's Vice-President 1945–1948. He was elected a Fellow of the Royal Society of London in 1928.
He died in Birtley, Tyne and Wear on 23 January 1967.
Career
From 1903 to 1905 he was a schoolmaster in Gateshead and then until 1917 in Middlesbrough.
In 1917 he began lecturing in Genetics and Botany at the University of Newcastle being given a professorship in 1927. He remained in this role until retiring in 194
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https://en.wikipedia.org/wiki/Gerard%20%27t%20Hooft
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Gerardus (Gerard) 't Hooft (; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating the quantum structure of electroweak interactions".
His work concentrates on gauge theory, black holes, quantum gravity and fundamental aspects of quantum mechanics. His contributions to physics include a proof that gauge theories are renormalizable, dimensional regularization and the holographic principle.
Biography
Early life
Gerard 't Hooft was born in Den Helder on July 5, 1946, but grew up in The Hague. He was the middle child of a family of three. He comes from a family of scholars. His great uncle was Nobel prize laureate Frits Zernike, and his grandmother was married to Pieter Nicolaas van Kampen, a professor of zoology at Leiden University. His uncle Nico van Kampen was an (emeritus) professor of theoretical physics at Utrecht University, and his mother married a maritime engineer. Following his family's footsteps, he showed interest in science at an early age. When his primary school teacher asked him what he wanted to be when he grew up, he replied, "a man who knows everything."
After primary school Gerard attended the Dalton Lyceum, a school that applied the ideas of the Dalton Plan, an educational method that suited him well. He excelled at science and mathematics courses. At the age of sixteen he won a silver medal in th
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https://en.wikipedia.org/wiki/Martinus%20J.%20G.%20Veltman
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Martinus Justinus Godefriedus "Tini" Veltman (; 27 June 1931 – 4 January 2021) was a Dutch theoretical physicist. He shared the 1999 Nobel Prize in physics with his former PhD student Gerardus 't Hooft for their work on particle theory.
Biography
Martinus Justinus Godefriedus Veltman was born in Waalwijk, Netherlands, on 27 June 1931. His father was the head of the local primary school. Three of his father's siblings were primary school teachers. His mother's father was a contractor and also ran a café. He was the fourth child in a family with six children. He started studying mathematics and physics at Utrecht University in 1948.
As a youth he had a great interest in radio electronics, which was a difficult hobby to work on because the occupying German army had confiscated most of the available radio equipment.
In 1955, he became an assistant to Prof. Michels of the Van Der Waals laboratory in Amsterdam. Michels was an experimental physicist, working in high pressure physics. His primary task was the upkeep of a large library collection and occasional lecture preparations for Michels.
His research career advanced when he moved to Utrecht to work under Léon Van Hove in 1955. He received his MSc degree in 1956, after which he was drafted into military service for two years, returning in February 1959. Van Hove then hired him as a doctoral researcher. He obtained his PhD degree in theoretical physics in 1963 and became professor at Utrecht University in 1966.
In 1960, Va
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https://en.wikipedia.org/wiki/Thue%E2%80%93Morse%20sequence
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In mathematics, the Thue–Morse sequence or Prouhet–Thue–Morse sequence or parity sequence is the binary sequence (an infinite sequence of 0s and 1s) obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far. The first few steps of this procedure yield the strings 0 then 01, 0110, 01101001, 0110100110010110, and so on, which are prefixes of the Thue–Morse sequence. The full sequence begins:
01101001100101101001011001101001....
The sequence is named after Axel Thue and Marston Morse.
Definition
There are several equivalent ways of defining the Thue–Morse sequence.
Direct definition
To compute the nth element tn, write the number n in binary. If the number of ones in this binary expansion is odd then tn = 1, if even then tn = 0. That is, tn is the even parity bit for n. John H. Conway et al. called numbers n satisfying tn = 1 odious (for odd) numbers and numbers for which tn = 0 evil (for even) numbers. In other words, tn = 0 if n is an evil number and tn = 1 if n is an odious number.
Fast sequence generation
This method leads to a fast method for computing the Thue–Morse sequence: start with , and then, for each n, find the highest-order bit in the binary representation of n that is different from the same bit in the representation of . If this bit is at an even index, tn differs from , and otherwise it is the same as .
In pseudo-code form:
def generate_sequence(seq_length: int):
"""Thue–Morse sequence."""
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