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Benzil (i.e. Bz2, systematically known as 1,2-diphenylethane-1,2-dione) is the organic compound with the formula (C6H5CO)2, generally abbreviated (PhCO)2. This yellow solid is one of the most common diketones. Its main use is as a photoinitiator in polymer chemistry.
(C6H5CO)2
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Eventual consistency is a weak guarantee – most stronger models, like linearizability, are trivially eventually consistent. Eventually-consistent services are often classified as providing BASE semantics (basically-available, soft-state, eventual consistency), in contrast to traditional ACID (atomicity, consistency, is...
Eventual consistency
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Chemical Process modeling is a technique used in chemical engineering process design. Process modeling is defined as the physical, mathematical or logical representation of the real process, system or phenomena using model library present in the process simulator software. In this technique by using process simulator s...
Modeling and simulation of batch distillation unit
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In some instances, bonobos have been shown to consume lower-order primates.Until the development of agriculture approximately 10,000 years ago, Homo sapiens employed a hunter-gatherer method as their sole means of food collection. This involved combining stationary food sources (such as fruits, grains, tubers, and mush...
Nonhuman primate
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Concerns about genetic diversity are therefore especially important with large mammals due to their small population size and high levels of human-caused population effects.A genetic bottleneck can occur when a population goes through a period of low number of individuals, resulting in a rapid decrease in genetic diver...
Genetic diversity
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In software engineering, a plain old Java object (POJO) is an ordinary Java object, not bound by any special restriction. The term was coined by Martin Fowler, Rebecca Parsons and Josh MacKenzie in September 2000: "We wondered why people were so against using regular objects in their systems and concluded that it was b...
Plain old Java object
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Arizona State University - Tempe, AZ California State University - Dominguez Hills, CA Carnegie Mellon University - Pittsburgh, PA Catholic University of America - Washington, DC CEA-Saclay - Gif-sur-Yvette, France Christopher Newport University, Newport News, VA Florida International University - Miami, FL Florida Sta...
CLAS detector
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A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the re...
Principle of Optimality
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Oceanography is sub-categorized into more specialized cross-disciplines, such as physical oceanography and marine biology. As the marine ecosystem is very large and diverse, marine biology is further divided into many subfields, including specializations in particular species.
Natural science
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In linear algebra, a square nonnegative matrix A {\displaystyle A} of order n {\displaystyle n} is said to be productive, or to be a Leontief matrix, if there exists a n × 1 {\displaystyle n\times 1} nonnegative column matrix P {\displaystyle P} such as P − A P {\displaystyle P-AP} is a positive matrix.
Productive matrix
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Immunohistochemistry using antibodies to ubiquitin can identify abnormal accumulations of this protein inside cells, indicating a disease process. These protein accumulations are referred to as inclusion bodies (which is a general term for any microscopically visible collection of abnormal material in a cell). Examples...
Ubiquitin
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Then Grinberg's theorem states that The proof is an easy consequence of Euler's formula. As a corollary of this theorem, if an embedded planar graph has only one face whose number of sides is not 2 mod 3, and the remaining faces all have numbers of sides that are 2 mod 3, then the graph is not Hamiltonian. To see this,...
Grinberg's theorem
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The Cosmological Advanced Survey Telescope for Optical and UV Research (CASTOR) is a proposed space telescope mission led by the Canadian Space Agency. With its 1-meter diameter primary mirror, CASTOR would provide imaging capabilities in the ultraviolet (UV) and blue-optical regions at a spatial resolution similar to ...
CASTOR (spacecraft)
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A planetary civilization or global civilization is a civilization of Type I on the Kardashev scale. This type of civilization is likely to be reliant on renewable energy sources such as stellar power, as well as powerful non-renewable sources such as nuclear fusion. A Type I civilization's energy consumption level is r...
Planetary civilization
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This is a prototypical example of a function space. One may similarly define 1 / f: ( x 1 , … , x n ) ↦ 1 / f ( x 1 , … , x n ) , {\displaystyle 1/f:(x_{1},\ldots ,x_{n})\mapsto 1/f(x_{1},\ldots ,x_{n}),} which is a function only if the set of the points (x1, …,xn) in the domain of f such that f(x1, …, xn) ≠ 0 contains...
Multivariate function
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These processes can be used to form complex shapes out of different types of ductile metal tubing. Freeform-bending processes, like three-roll-pushbending, shape the workpiece kinematically, thus the bending contour is not dependent on the tool geometry.
Pipe and tube bender
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A fairly simple non-linear function, the sigmoid function such as the logistic function also has an easily calculated derivative, which can be important when calculating the weight updates in the network. It thus makes the network more easily manipulable mathematically, and was attractive to early computer scientists w...
Artificial neurons
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In applications to theoretical computer science, one wishes to devise network configurations for which the Cheeger constant is high (at least, bounded away from zero) even when |V(G)| (the number of computers in the network) is large. For example, consider a ring network of N ≥ 3 computers, thought of as a graph GN. Nu...
Isoperimetric number
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In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is t...
Euler's method
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This is sufficient to guarantee that a right-Noetherian ring is right Goldie. The converse does not hold: every right Ore domain is a right Goldie domain, and hence so is every commutative integral domain. A consequence of Goldie's theorem, again due to Goldie, is that every semiprime principal right ideal ring is isom...
Noncommutative algebra
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Proponents of geometric algebra strive to work with real algebras wherever that is possible. They argue that it is generally possible (and usually enlightening) to identify the presence of an imaginary unit in a physical equation. Such units arise from one of the many quantities in a real Clifford algebra that square t...
Dirac algebra
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When simulating the motion of particles through an accelerator or beam transport line, it is often desirable to describe the overall properties of an ensemble of particles, rather than track the motion of each particle individually. : 155 By Liouville's Theorem it can be shown that the density occupied on a position an...
Courant–Snyder parameters
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TAA is used in many modern video games and game engines, however all previous implementations have used some form of manually written heuristics to prevent temporal artifacts such as ghosting and flickering. One example of this is neighborhood clamping which forcefully prevents samples collected in previous frames from...
Deep learning anti-aliasing
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In classical electromagnetic theory, an ideal source of light with constant intensity can be modeled by a spatially and temporally coherent electromagnetic wave of a single frequency. Such a light source can be modeled by, E ( x , t ) = E 0 sin ⁡ ( k x − ω t + ϕ ) {\displaystyle E(x,t)=E_{0}\sin(kx-\omega t+\phi )} whe...
Photon Statistics
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CSA/ASCE Civil Engineering Abstracts encompasses global, indexing, and abstracting coverage of civil engineering technical literature. Coverage also includes the complementary fields of forensic engineering, engineering services management, engineering services marketing, engineering education, theoretical mechanics, t...
Metals Abstracts
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RFC 7027: "Elliptic Curve Cryptography (ECC) Brainpool Curves for Transport Layer Security (TLS)". RFC 7251: "AES-CCM Elliptic Curve Cryptography (ECC) Cipher Suites for TLS". RFC 7301: "Transport Layer Security (TLS) Application-Layer Protocol Negotiation Extension".
TLS 1.2
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As announced above, one can identify any matrix in this Lie algebra with an Euler vector ω = ( x , y , z ) ∈ R 3 , {\displaystyle {\boldsymbol {\omega }}=(x,y,z)\in \mathbb {R} ^{3},} ω ^ = ω ⋅ L = x L x + y L y + z L z = ∈ s o ( 3 ) . {\displaystyle {\widehat {\boldsymbol {\omega }}}={\boldsymbol {\omega }}\cdot {\bo...
Space of 3D rotations
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He received his M.Sc. in geology from University of Tübingen, then went on to receive his Ph.D. in geology from Australian National University.
Stephan Matthai
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Dimensioning a new network determines the minimum capacity requirements that will still allow the Teletraffic Grade of Service (GoS) requirements to be met. To do this, dimensioning involves planning for peak-hour traffic, i.e. that hour during the day during which traffic intensity is at its peak.The dimensioning proc...
Network design
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The augmented Lagrangian method was rejuvenated by the optimization systems LANCELOT, ALGENCAN and AMPL, which allowed sparse matrix techniques to be used on seemingly dense but "partially separable" problems. The method is still useful for some problems.Around 2007, there was a resurgence of augmented Lagrangian metho...
Alternating direction method of multipliers
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Ivar Ekeland is an expert on variational analysis, which studies mathematical optimization of spaces of functions. His research on periodic solutions of Hamiltonian systems and particularly to the theory of Kreĭn indices for linear systems (Floquet theory) was described in his monograph.
Ivar Ekeland
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UVGI is often used to disinfect equipment such as safety goggles, instruments, pipettors, and other devices. Lab personnel also disinfect glassware and plasticware this way. Microbiology laboratories use UVGI to disinfect surfaces inside biological safety cabinets ("hoods") between uses.
UV water disinfection
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A large part of the research involving PCO is now looking into utilising the anion as a synthetic building block to derive phosphorus containing analogues of small molecules. The first major breakthrough in this area came from Goicoechea et al. in 2013; they published the reaction between the PCO anion and ammonium sal...
Phosphaethynolate
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As has been suggested in earlier sections much of geometric algebra generalises well into higher dimensions. The geometric algebra for the real space Rn is Cln(R), and the subspace of bivectors is ⋀2Rn. The number of simple bivectors needed to form a general bivector rises with the dimension, so for n odd it is (n − 1)...
Oriented plane segment
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The number of its elements shall be denoted by ϕ(z) (analogously to Euler's totient function φ(n) for integers n). For Gaussian primes it immediately follows that ϕ(p) = |p|2 − 1 and for arbitrary composite Gaussian integers z = i k ∏ m p m ν m {\displaystyle z=i^{k}\prod _{m}{p_{m}}^{\nu _{m}}} Euler's product formula...
Gaussian primes
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Braunstein's devices are the forerunners of contemporary LED lighting and semiconductor lasers, which typically employ III-V semiconductors. The 2000 and 2014 Nobel Prizes in Physics were awarded for further advances in closely related fields.Braunstein was raised in New York City. He earned a doctorate in physics from...
Rubin Braunstein
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In February 2009, under the auspices of the Association for the Advancement of Artificial Intelligence (AAAI), Eric Horvitz chaired a meeting of leading computer scientists, artificial intelligence researchers and roboticists at the Asilomar conference center in Pacific Grove, California. The goal was to discuss the po...
Technological Singularity
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Some ideas on calculus later appeared in Indian mathematics, at the Kerala school of astronomy and mathematics. Madhava of Sangamagrama in the 14th century, and later mathematicians of the Kerala school, stated components of calculus such as the Taylor series and infinite series approximations. However, they did not co...
History of calculus
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The following outline is provided as an overview of and topical guide to electronics: Electronics – branch of physics, engineering and technology dealing with electrical circuits that involve active semiconductor components and associated passive interconnection technologies.
Outline of electronics
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In physics, the atomic form factor, or atomic scattering factor, is a measure of the scattering amplitude of a wave by an isolated atom. The atomic form factor depends on the type of scattering, which in turn depends on the nature of the incident radiation, typically X-ray, electron or neutron. The common feature of al...
Atomic scattering factor
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Ferris constructed gaseous simulations of the atmospheres of Jupiter and Titan and analyzed their composition using a combination of photochemistry techniques, including x-ray photoelectron spectroscopy and infrared spectroscopy. Information gained from these studies could then be directly compared to measurements of t...
James Ferris
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In mathematics there is a close link between map coloring and graph coloring, since every map showing different areas has a corresponding graph. By far the most famous result in this area is the four color theorem, which states that any planar map can be colored with at most four colors.
Map coloring
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He unsuccessfully tried to solve a problem posed by Archimedes of cutting a sphere into two volumes of a given ratio, which was later solved by 10th century mathematician Abū Ja'far al-Khāzin. His only known surviving work on astronomy was on the calculation of azimuths. He was also known to make astronomical observati...
Al-Mahani
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Pharmacognosy Reviews is a peer-reviewed open-access medical journal published by Pharmacognosy Network Worldwide (Phcog.net). The journal publishes articles on the subject of pharmacognosy, natural products, and phytochemistry. It is indexed with Caspur, EBSCO, ProQuest, and Scopus. Phcog.net appeared on Beall's list ...
Pharmacognosy Reviews
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A development in medical statistics is the use of out-of-sample cross validation techniques in meta-analysis. It forms the basis of the validation statistic, Vn, which is used to test the statistical validity of meta-analysis summary estimates. Essentially it measures a type of normalized prediction error and its distr...
Regression validation
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He graduated from University High School in Urbana, Illinois and from Harvard University before obtaining a doctorate in physics from Princeton University under the supervision of Edward Witten. Kachru was a junior fellow in the Harvard Society of Fellows. In 2017 he received a Simons Investigator Award.Kachru is best ...
Shamit Kachru
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Then they are independent, but not necessarily identically distributed, and their joint probability distribution is given by the Bapat–Beg theorem. From now on, we will assume that the random variables under consideration are continuous and, where convenient, we will also assume that they have a probability density fun...
Order statistic
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As such, the composition of two homeomorphisms is again a homeomorphism, and the set of all self-homeomorphisms X → X {\textstyle X\to X} forms a group, called the homeomorphism group of X, often denoted Homeo ( X ) . {\textstyle {\text{Homeo}}(X).} This group can be given a topology, such as the compact-open topology,...
Bicontinuous function
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We have seen how a reproducing kernel Hilbert space defines a reproducing kernel function that is both symmetric and positive definite. The Moore–Aronszajn theorem goes in the other direction; it states that every symmetric, positive definite kernel defines a unique reproducing kernel Hilbert space. The theorem first a...
Reproducing kernel Hilbert space
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One of the reasons behind the failure of the regular PINNs is soft-constraining of Dirichlet and Neumann boundary conditions which pose multi-objective optimization problems. This requires the need for manually weighing the loss terms to be able to optimize. Another reason is getting optimization itself. Posing PDE sol...
Physics-informed neural networks
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94,350
380–399.9 MHz: Terrestrial Trunked Radio (TETRA) service for emergency use 430–440 MHz: Amateur radio (70 cm band) 446.0–446.2 MHz: European unlicensed PMR service => PMR446 457–464 MHz: Scanning telemetry and telecontrol, assigned mostly to the water, gas, and electricity industries 606–614 MHz: Radio microphones and ...
Ultra-high frequency
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94,351
Recent encyclopaedias and popular accounts claim that the tenth century astronomer Ibn Yunus used a pendulum for time measurement, despite the fact that it has been known for nearly a hundred years that this is based on nothing more than an error made in 1684 by the Savilian Professor of Astronomy at Oxford Edward Bern...
Ibn Yunus
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In addition to its primary physics goals, NOνA will be able to improve upon the measurements of the already measured oscillation parameters. NOνA, like MINOS, is well suited to detecting muon neutrinos and so will be able to refine our knowledge of θ23. The NOνA near detector will be used to conduct measurements of neu...
NOvA
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Statistician David J. Bartholomew, of the London School of Economics, said that Gould erred in his use of factor analysis, irrelevantly concentrated upon the fallacy of reification (abstract as concrete), and ignored the contemporary scientific consensus about the existence of the psychometric g.Reviewing the book, Ste...
The Mismeasure of Man
0.79696
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One of the key facts about F is that it is (absolutely or completely) parallelizable, i.e. for n = dim F, there are n vector fields on F which form a basis at each point. As a result its Lie algebra is easy to understand; and the dual 1-forms on F have a particularly simple structure described by the Cartan structural ...
Riemannian connection on a surface
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Evolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve. It was first used by Lawrence J. Fogel in the US in 1960 in order to use simulated ev...
Evolutionary programming
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94,356
His simple and elegant theory shows that time is relative to an inertial frame. In an inertial frame, Newton's first law holds; it has its own local geometry, and therefore its own measurements of space and time; there is no 'universal clock'. An act of synchronization must be performed between two systems, at the leas...
Time in physics
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Meeting the following essential requirements of the Criteria List is a prerequisite for certification: Electricity must be sourced 100 % from renewable energy (from already existing or new power plants). Electricity providers must use a fixed amount per sold kilowatt-hour to promote new renewable energy development. In...
Grüner Strom Label
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94,358
Fabricated geomembranes can be accordion folded or rolled up to facilitate deployment and reduce double folds as shown in photographs.Factory fabrication reduces field seaming by 70 to 90% depending on the geometry of the installation and weight of the geomembrane material used, which reduces field testing and patching...
Fabricated geomembranes
0.796959
94,359
The tensor product of two irreducible representations V 1 , V 2 {\displaystyle V_{1},V_{2}} of a group or Lie algebra is usually not irreducible. It is therefore of interest to attempt to decompose V 1 ⊗ V 2 {\displaystyle V_{1}\otimes V_{2}} into irreducible pieces. This decomposition problem is known as the Clebsch–G...
Symmetric and alternating squares
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94,360
Physics Bulletin said about the book, "No matter how gently one introduces students to the concept of Dirac’s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of". American Scientist called it "An e...
Principles of Quantum Mechanics
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Since 2012, Goriely has done some work related to the brain modeling. With his collaborators, he has developed models for axon growth based on the combined mechanics of microtubules extension, growth cone connection,. At the tissue level, with his collaborators, he developed new constitutive models for brain tissue val...
Alain Goriely
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94,362
They could also be used in tents and awnings.Because the solar cells could be made transparent, Konarka was also developing a version of its solar cells that could be laminated to windows to generate electricity and serve as a window tinting.However, the technology had several drawbacks. The solar cells only lasted a c...
Konarka Technologies
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94,363
For any finite polynomial set F ⊂ k, one can compute a reduced triangular set C ⊂ ⟨ F ⟩ {\displaystyle C\subset \langle F\rangle } such that all polynomial g in F reduces to zero by pseudo-division w.r.t C.Different concepts and algorithms extended the work of Wen-Tsun Wu. In the early 1990s, the notion of a regular ch...
Triangular decomposition
0.796958
94,364
Every smooth convex surface collapses to a point under the mean-curvature flow, without other singularities, and converges to the shape of a sphere as it does so. For surfaces of dimension two or more this is a theorem of Gerhard Huisken; for the one-dimensional curve-shortening flow it is the Gage–Hamilton–Grayson the...
Mean curvature flow
0.796958
94,365
In statistics, the order of a kernel is the degree of the first non-zero moment of a kernel.
Order of a kernel
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CANaerospace - Stock (for the aviation industry) CAN Kingdom - Kvaser (embedded control system) CCP/XCP (automotive ECU calibration) GMLAN - General Motors (for General Motors) RV-C - RVIA (used for recreational vehicles) SafetyBUS p - Pilz (used for industrial automation) UAVCAN (aerospace and robotics) CSP (CubeSat S...
CAN Bus
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In contrast a re-evaluation of Thom's fieldwork by Clive Ruggles argued that Thom's claims of high accuracy astronomy were not fully supported by the evidence. Nevertheless, Thom's legacy remains strong, Edwin C. Krupp wrote in 1979, "Almost singlehandedly he has established the standards for archaeo-astronomical field...
Archaeoastronomy
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Since A {\displaystyle A} and − B {\displaystyle -B} do not share any eigenvalue, p {\displaystyle p} and q {\displaystyle q} are coprime. Hence there exist polynomials f {\displaystyle f} and g {\displaystyle g} such that p ( z ) f ( z ) + q ( z ) g ( z ) ≡ 1 {\displaystyle p(z)f(z)+q(z)g(z)\equiv 1} . By the Cayley–H...
Sylvester equation
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He was educated at Bootham School, a private school in York, and at Balliol College, Oxford. After obtaining a Doctor of Philosophy with a thesis entitled A structural investigation of some compounds showing charge-transfer properties, he became lecturer in chemistry at the (new) University of Stirling and was first wa...
Peter Murray-Rust
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"Golden oldies: classic articles from the world of statistics and probability: 'the teaching of statistics'". Annals of Mathematical Statistics. 3 (1): 63–71.
Harold Hotelling
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Applicative universal grammar, or AUG, is a universal semantic metalanguage intended for studying the semantic processes in particular languages. This is a linguistic theory that views the formation of phrase structure by analogy to function application in an applicative programming language. Among the innovations in t...
Applicative universal grammar
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94,372
Peter Bernd Schneider (born 9 January 1953 in Karlsruhe) is a German mathematician, specializing in the p-adic aspects of algebraic number theory, arithmetic algebraic geometry, and representation theory.
Peter Schneider (mathematician)
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Because of energy limitations, oxygen and nitrogen do not react at ambient temperatures. But at high temperatures, they undergo an endothermic reaction producing various oxides of nitrogen. Such temperatures arise inside an internal combustion engine or a power station boiler, during the combustion of a mixture of air ...
Nitrogen oxide emissions
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94,374
Brandt-Pearce majored in electrical engineering at Rice University, graduating in 1985. She then worked for several years for Lockheed Corporation, at NASA's Johnson Space Center. Returning to Rice for graduate study, she earned a master's degree in 1989 and completed her Ph.D. in 1993.
Maïté Brandt-Pearce
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Atmospheric chemistry is a branch of atmospheric science in which the chemistry of the Earth's atmosphere and that of other planets is studied. It is a multidisciplinary field of research and draws on environmental chemistry, physics, meteorology, computer modeling, oceanography, geology and volcanology and other disci...
Atmospheric Sciences
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94,376
Over the years, AURA expanded its focus to include Solar Astronomy and the Gemini 8-meter telescopes, going on to partner with other consortia such as WIYN (Wisconsin Indiana Yale & NOAO) and SOAR (Southern Astrophysical Research). In the 1980s, AURA took on the management of the Space Telescope Science Institute, open...
Association of Universities for Research in Astronomy
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COMBREX is a multifaceted project that aims to bring together the computational and experimental communities of biologists in the interest of improving our understanding of microbial gene function and accelerating the annotation of microbial gene function. The COMBREX project was co-founded by Simon Kasif, Richard Robe...
Combrex
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94,378
In cell biology, microsomes are heterogeneous vesicle-like artifacts (~20-200 nm diameter) re-formed from pieces of the endoplasmic reticulum (ER) when eukaryotic cells are broken-up in the laboratory; microsomes are not present in healthy, living cells.Rough (containing ribosomes) and smooth (without ribosomes) micros...
Microsome
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On June 26, 2007, the University of Arizona announced it would take over research at the Biosphere 2. The announcement ended fears that the structure would be demolished. University officials said private gifts and grants enabled them to cover research and operating costs for three years with the possibility of extendi...
Biosphere 2
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Primary facilities within the ACL include advanced toxic agent laboratories, environmental chambers, and secure work spaces for classified materials. Chemical agent operations in this building include analytical chemistry, Chemical Weapons Convention (CWC) treaty support, filtration, decontamination and evaluation of c...
Edgewood Chemical Biological Center
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Each server is able to support 32 players. The games developers have commented that the engine used in the game features technology which could not be easily implemented on any other platform, such as procedurally generated water and waves, as well as volumetric clouds.Following the games release, many issues with netw...
Warhawk (2007 video game)
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Computing with Realizational Morphology In Computational Linguistics and Intelligent Text Processing, Alexander Gelbukh (ed. ), Lecture Notes in Computer Science, Volume 2588, pages 205–216, Springer Verlag, Heidelberg. 2003. The Insufficiency of Paper-and-Pencil Linguistics: the Case of Finnish Prosody In Intelligent ...
Lauri Karttunen
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A. K. M. Fazle Hussain (Bengali: এ.কে.এম. ফজলে হুসাইন; born 20 January 1943, in Bangladesh) is a professor of mechanical engineering at Texas Tech University.
Fazle Hussain
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Quantum computation studies quantum phenomena applications beyond the scope of classical approximation for the purpose of informing artificial intelligence processing and communication. Various models of quantum computation exist, but the most popular models incorporate concepts of qubits and quantum gates (or gate-bas...
Superconductive quantum computing
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94,385
Social cognitive optimization (SCO) is a population-based metaheuristic optimization algorithm which was developed in 2002. This algorithm is based on the social cognitive theory, and the key point of the ergodicity is the process of individual learning of a set of agents with their own memory and their social learning...
Social cognitive optimization
0.796952
94,386
In geometry, a glide plane operation is a type of isometry of the Euclidean space: the combination of a reflection in a plane and a translation in that plane. Reversing the order of combining gives the same result. Depending on context, we may consider a reflection a special case, where the translation vector is the ze...
Glide planes
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However, the product of continuum many copies of the closed unit interval (with its usual topology) fails to be sequentially compact with respect to the product topology, even though it is compact by Tychonoff's theorem (e.g., see Wilansky 1970, p. 134).
Tychonoff theorem
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94,388
BCT1 is used in functional analysis to prove the open mapping theorem, the closed graph theorem and the uniform boundedness principle. BCT1 also shows that every nonempty complete metric space with no isolated point is uncountable. (If X {\displaystyle X} is a nonempty countable metric space with no isolated point, the...
Baire's theorem
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During his tenure, RIM@GT experienced an unprecedented growth, including (as of 2008) 36 faculty members as well as a dedicated interdisciplinary Ph.D. program in Robotics.
Henrik I. Christensen
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He then earned his M.S. and Ph.D. from Northwestern University in 1942 and 1943. The subject of his thesis was the 24-hour rhythms of the Norway rat.Calhoun met his future wife, Edith Gressley, at Northwestern, where she was a biology major and a student in one of his classes.
John B. Calhoun
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94,391
◻ {\displaystyle \square } Proof: By the theorem applied to S and S as an S-module, we see K(y1, ..., yn) is an S-free resolution of S/(y1, ..., yn). So, by definition, the i-th homology of K ( y 1 , … , y n ) ⊗ S M {\displaystyle K(y_{1},\dots ,y_{n})\otimes _{S}M} is the right-hand side of the above. On the other han...
Koszul complex
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Popular deep learning models are generally trained on very large datasets of media (such as publicly available images and the text of web pages) scraped from the Internet, much of which is copyrighted. (As of 2023, alternate open-source approaches like "The Stack" by Hugging Face are rare.) Because assembling these tra...
Artificial intelligence and copyright
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Metric tensors resulting from cases where the resultant differential equations can be solved exactly for a physically reasonable distribution of energy–momentum are called exact solutions. Examples of important exact solutions include the Schwarzschild solution and the Friedman-Lemaître-Robertson–Walker solution. The E...
Mathematics of general relativity
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In February 1946 he received an academic position at Pomona College, where he taught until 1988. Hansch completed sabbaticals at ETH Zurich with Vladimir Prelog and at University of Munich with Rolf Huisgen.Hansch taught Organic Chemistry for many years at Pomona College, and was known for giving complex lectures witho...
Corwin Hansch
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The "pearls" of the title include theorems, proofs, problems, and examples in graph theory. The book has ten chapters; after an introductory chapter on basic definitions, the remaining chapters material on graph coloring; Hamiltonian cycles and Euler tours; extremal graph theory; subgraph counting problems including co...
Pearls in Graph Theory
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Miller apologized for the "lack of clarity and due diligence" in a leaked early draft of his work. Richard D. De Veaux, Vice President of the American Statistical Association and Professor of Statistics at Williams College, commented "any estimates based on unverifiable or biased data are inaccurate, wrong and unfounde...
Steven J. Miller
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There are several applications of this theorem. In particular, given a dg-algebra, such as the de Rham algebra ( Ω ∙ ( X ) , d , ∧ ) {\displaystyle (\Omega ^{\bullet }(X),d,\wedge )} , or the Hochschild cohomology algebra, they can be equipped with an A ∞ {\displaystyle A_{\infty }} -structure.
Homotopy associative algebra
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These assessments are generally consistent with the conclusions of the Intergovernmental Panel on Climate Change. Some scientific bodies have recommended specific policies to governments, and science can play a role in informing an effective response to climate change. Policy decisions, however, may require value judge...
Scientific consensus on climate change
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He received an MEng in Mechanical Engineering from the University of Edinburgh in 2002. In 2006, Abercromby received a PhD in Kinesiology from the University of Houston. He was honoured as a Distinguished Alumnus by the University's Department of Health and Human Performance (HHP) in 2007.
Andrew Abercromby
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