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86,000 | The 523rd Aviation Regiment, of the Far East Military Okrug, was the first to receive the Su-17. The Su-17 was produced until 1990, producing 2867 units.The Su-17 resembles its predecessor, the Su-7, with weight-saving measures added at the cost of combat survivability, an example of which is the removal of pilot prote... | Su-22 Fitter | 0.782718 |
86,001 | Shortly after the Su-7 fighter-bomber was put into service, the Sukhoi Design Bureau was ordered to develop a modernization program. The program would be aimed primarily at updating on-board avionics and takeoff/landing characteristics. The concept of variable-geometry wings - something gaining wider attention at that ... | Su-22 Fitter | 0.782718 |
86,002 | S-22I The first prototype "Variable-Geometry" Su-7, converted from a production Su-7BM, first flown on 2 August 1966. S-32 The initial production version, dubbed Su-17 by the VVS – Soviet Air Forces. S-32M The Su-17 with the Lyul'ka AL-21F engine and re-structured fuselage plus several smaller modifications, resulting ... | Su-22 Fitter | 0.782718 |
86,003 | There are several equivalent views of the Dirichlet process. Besides the formal definition above, the Dirichlet process can be defined implicitly through de Finetti's theorem as described in the first section; this is often called the Chinese restaurant process. A third alternative is the stick-breaking process, which ... | Dirichlet process | 0.782718 |
86,004 | If we take the frequentist view of probability, we believe there is a true probability distribution P 0 {\displaystyle P_{0}} that generated the data. Then it turns out that the Dirichlet process is consistent in the weak topology, which means that for every weak neighbourhood U {\displaystyle U} of P 0 {\displaystyle ... | Dirichlet process | 0.782718 |
86,005 | The Dirichlet Process can be used as a prior distribution to estimate the probability distribution that generates the data. In this section, we consider the model P ∼ DP ( H , α ) X 1 , ⋯ , X n | P ∼ i.i.d. P . {\displaystyle {\begin{aligned}P&\sim {\textrm {DP}}(H,\alpha )\\X_{1},\cdots ,X_{n}|P&{\overset {\textrm {i.... | Dirichlet process | 0.782718 |
86,006 | A particularly important application of Dirichlet processes is as a prior probability distribution in infinite mixture models. The Dirichlet process was formally introduced by Thomas Ferguson in 1973. It has since been applied in data mining and machine learning, among others for natural language processing, computer v... | Dirichlet process | 0.782718 |
86,007 | In probability theory, Dirichlet processes (after the distribution associated with Peter Gustav Lejeune Dirichlet) are a family of stochastic processes whose realizations are probability distributions. In other words, a Dirichlet process is a probability distribution whose range is itself a set of probability distribut... | Dirichlet process | 0.782718 |
86,008 | This P {\displaystyle P} is a random variable itself and has a distribution. This distribution (over distributions) is called a Dirichlet process ( DP {\displaystyle \operatorname {DP} } ). In summary, this means that we get an equivalent procedure to the above algorithm: Draw a distribution P {\displaystyle P} from DP... | Dirichlet process | 0.782718 |
86,009 | They are, however, exchangeable. This fact can be shown by calculating the joint probability distribution of the observations and noticing that the resulting formula only depends on which x {\displaystyle x} values occur among the observations and how many repetitions they each have. Because of this exchangeability, de... | Dirichlet process | 0.782718 |
86,010 | The generative process is therefore that a sample is drawn from a Dirichlet process, and for each data point, in turn, a value is drawn from this sample distribution and used as the component distribution for that data point. The fact that there is no limit to the number of distinct components which may be generated ma... | Dirichlet process | 0.782718 |
86,011 | Dirichlet processes are frequently used in Bayesian nonparametric statistics. "Nonparametric" here does not mean a parameter-less model, rather a model in which representations grow as more data are observed. Bayesian nonparametric models have gained considerable popularity in the field of machine learning because of t... | Dirichlet process | 0.782718 |
86,012 | In order to interpret the credible sets as confidence sets, a Bernstein–von Mises theorem is needed. In case of the Dirichlet process we compare the posterior distribution with the empirical process P n = 1 n ∑ i = 1 n δ X i {\displaystyle \mathbb {P} _{n}={\frac {1}{n}}\sum _{i=1}^{n}\delta _{X_{i}}} . Suppose F {\dis... | Dirichlet process | 0.782718 |
86,013 | The difference from the traditional Rogowski coil is that the sensor can be manufactured using a planar coil rather than a toroidal coil. In order to reject the influence of conductors outside the sensor's measurement region, these planar Rogowski current sensors use a concentric coil geometry instead of a toroidal geo... | Rogowski coil | 0.782717 |
86,014 | A Rogowski coil, named after Walter Rogowski, is an electrical device for measuring alternating current (AC) or high-speed current pulses. It sometimes consists of a helical coil of wire with the lead from one end returning through the centre of the coil to the other end so that both terminals are at the same end of th... | Rogowski coil | 0.782717 |
86,015 | XPath engines were also not optimized. Increasingly, however, XSLT processors use optimization techniques found in functional programming languages and database query languages, such as static rewriting of an expression tree (e.g., to move calculations out of loops), and lazy pipelined evaluation to reduce the memory f... | XSLT | 0.782717 |
86,016 | This separation is reflected in the design of XSLT processing APIs (such as JAXP). Early XSLT processors had very few optimizations. Stylesheet documents were read into Document Object Models and the processor would act on them directly. | XSLT | 0.782717 |
86,017 | Real-time economic data, and other official statistics, are often based on preliminary estimates, and therefore are frequently adjusted as better estimates become available. These later adjusted data are called "revised data". The terms real-time economic data and real-time economic analysis were coined by Francis X. D... | Real-time information | 0.782716 |
86,018 | Metal has been available since June 2, 2014 on iOS devices powered by Apple A7 or later, and since June 8, 2015 on Macs (2012 models or later) running OS X El Capitan.On June 5, 2017, at WWDC, Apple announced the second version of Metal, to be supported by macOS High Sierra, iOS 11 and tvOS 11. Metal 2 is not a separat... | Metal (API) | 0.782716 |
86,019 | Metal Performance Shaders is a highly optimized library of graphics functions that can help application developers achieve great performance at the same time decrease work on maintaining GPU family specific functions. It provides functions including: Image filtering algorithms Neural network processing Advanced math op... | Metal (API) | 0.782716 |
86,020 | The field of asymptotics is normally first encountered in school geometry with the introduction of the asymptote, a line to which a curve tends at infinity. The word Ασύμπτωτος (asymptotos) in Greek means non-coincident and puts strong emphasis on the point that approximation does not turn into coincidence. It is a sal... | Asymptotology | 0.782715 |
86,021 | In physics and other fields of science, one frequently comes across problems of an asymptotic nature, such as damping, orbiting, stabilization of a perturbed motion, etc. Their solutions lend themselves to asymptotic analysis (perturbation theory), which is widely used in modern applied mathematics, mechanics and physi... | Asymptotology | 0.782715 |
86,022 | LK-99 (from the Lee-Kim 1999 research) is a gray–black, polycrystalline compound, identified as a copper-doped lead‒oxyapatite. A team from Korea University led by Lee Sukbae (이석배) and Kim Ji-Hoon (김지훈) began studying this material as a potential superconductor starting in 1999.: 1 In July 2023, they published preprint... | LK-99 | 0.782715 |
86,023 | In organic chemistry, an aza-crown ether is an aza analogue of a crown ether (cyclic polyether). That is, it has a nitrogen atom (amine linkage, −NH− or >N−) in place of each oxygen atom (ether linkage, −O−) around the ring. While the parent crown ethers have the formulae (CH2CH2O)n, the parent aza-crown ethers have th... | Aza-crown ether | 0.782713 |
86,024 | In physics, Peek's law defines the electric potential gap necessary for triggering a corona discharge between two wires: e v = m v g v r ln ( S r ) {\displaystyle e_{v}=m_{v}g_{v}r\ln \left({S \over r}\right)} ev is the "visual critical corona voltage" or "corona inception voltage" (CIV), the voltage required to init... | Peek's law | 0.782712 |
86,025 | In September 2015, the first peer-reviewed academic journal dedicated to cryptocurrency and blockchain technology research, Ledger, was announced. The inaugural issue was published in December 2016. The journal covers aspects of mathematics, computer science, engineering, law, economics and philosophy that relate to cr... | Blockchain technology | 0.782712 |
86,026 | In January 2015, the size had grown to almost 30 GB, and from January 2016 to January 2017, the bitcoin blockchain grew from 50 GB to 100 GB in size. The ledger size had exceeded 200 GB by early 2020.The words block and chain were used separately in Satoshi Nakamoto's original paper, but were eventually popularized as ... | Blockchain technology | 0.782712 |
86,027 | Blockchain technology, such as cryptocurrencies and non-fungible tokens (NFTs), has been used in video games for monetization. Many live-service games offer in-game customization options, such as character skins or other in-game items, which the players can earn and trade with other players using in-game currency. Some... | Blockchain technology | 0.782712 |
86,028 | In March 2021, Bill Gates stated that "Bitcoin uses more electricity per transaction than any other method known to mankind", adding "It's not a great climate thing. "Nicholas Weaver, of the International Computer Science Institute at the University of California, Berkeley, examined blockchain's online security, and th... | Blockchain technology | 0.782712 |
86,029 | Bromocresol purple is used in medical laboratories to measure albumin. Use of BCP in this application may provide some advantage over older methods using bromocresol green. In microbiology, it is used for staining dead cells based on their acidity, and for the isolation and assaying of lactic acid bacteria.In photograp... | Bromocresol purple | 0.782712 |
86,030 | Similar to bromocresol green, the structure of bromocresol purple changes with pH. Changing the level of acidity causes a shift in the equilibrium between two different structures that have different colors. In near-neutral or alkaline solution, the chemical has a sulfonate structure that gives the solution a purple co... | Bromocresol purple | 0.782712 |
86,031 | As in the finite case, determining the Cartan–Weyl basis is an important step in determining the structure of affine Lie algebras. Fix a finite-dimensional, simple, complex Lie algebra g {\displaystyle {\mathfrak {g}}} with Cartan subalgebra h {\displaystyle {\mathfrak {h}}} and a particular root system Δ {\displaystyl... | Affine Lie algebra | 0.782711 |
86,032 | The Dynkin diagram of each affine Lie algebra consists of that of the corresponding simple Lie algebra plus an additional node, which corresponds to the addition of an imaginary root. Of course, such a node cannot be attached to the Dynkin diagram in just any location, but for each simple Lie algebra there exists a num... | Affine Lie algebra | 0.782711 |
86,033 | The affine Lie algebra corresponding to a finite-dimensional semisimple Lie algebra is the direct sum of the affine Lie algebras corresponding to its simple summands. There is a distinguished derivation of the affine Lie algebra defined by δ ( a ⊗ t m + α c ) = t d d t ( a ⊗ t m ) . {\displaystyle \delta (a\otimes t^{m... | Affine Lie algebra | 0.782711 |
86,034 | If g {\displaystyle {\mathfrak {g}}} is a finite-dimensional simple Lie algebra, the corresponding affine Lie algebra g ^ {\displaystyle {\hat {\mathfrak {g}}}} is constructed as a central extension of the loop algebra g ⊗ C {\displaystyle {\mathfrak {g}}\otimes \mathbb {\mathbb {C} } } , with one-dimensional center C... | Affine Lie algebra | 0.782711 |
86,035 | Therefore the root α {\displaystyle \alpha } is infinitely degenerate with respect to this abelian subalgebra. Appending the derivation described above to the abelian subalgebra turns the abelian subalgebra into a Cartan subalgebra for the affine Lie algebra, with eigenvalues ( α 1 , ⋯ , α d i m h , 0 , n ) {\displayst... | Affine Lie algebra | 0.782711 |
86,036 | In order to obtain a basis of simple roots for the affine algebra, an extra simple root must be appended, and is given by where θ {\displaystyle \theta } is the highest root of g {\displaystyle {\mathfrak {g}}} , using the usual notion of height of a root. This allows definition of the extended Cartan matrix and extend... | Affine Lie algebra | 0.782711 |
86,037 | The representations are constructed in more detail as follows.Fix a Lie algebra g {\displaystyle {\mathfrak {g}}} and basis { J ρ } {\displaystyle \{J^{\rho }\}} . Then { J n ρ } = { J ρ ⊗ t n } {\displaystyle \{J_{n}^{\rho }\}=\{J^{\rho }\otimes t^{n}\}} is a basis for the corresponding loop algebra, and { J n ρ } ∪ {... | Affine Lie algebra | 0.782711 |
86,038 | Many new techniques have been developed and are used in order to more accurately gather evidence, or reevaluate old information. The use of these newly developed techniques and evaluations have become relevant in litigation and appeals. Forensic entomology not only uses arthropod biology, but it pulls from other scienc... | Forensic entomology | 0.78271 |
86,039 | Although many tools used in DFSS consulting such as response surface methodology, transfer function via linear and non linear modeling, axiomatic design, simulation have their origin in inferential statistics, statistical modeling may overlap with data analytics and mining, However, despite that DFSS as a methodology h... | Design for Six Sigma | 0.78271 |
86,040 | Traditional six sigma methodology, DMAIC, has become a standard process optimization tool for the chemical process industries. However, it has become clear that the promise of six sigma, specifically, 3.4 defects per million opportunities (DPMO), is simply unachievable after the fact. Consequently, there has been a gro... | Design for Six Sigma | 0.78271 |
86,041 | The methodology describes the detailed process for successfully applying DFSS methods and tools throughout the software product design, covering the overall Software Development life cycle: requirements, architecture, design, implementation, integration, optimization, verification and validation (RADIOV). The methodolo... | Design for Six Sigma | 0.78271 |
86,042 | In this way, DFSS is closely related to operations research (solving the knapsack problem), workflow balancing. DFSS is largely a design activity requiring tools including: quality function deployment (QFD), axiomatic design, TRIZ, Design for X, design of experiments (DOE), Taguchi methods, tolerance design, robustific... | Design for Six Sigma | 0.78271 |
86,043 | Response surface methodology and other DFSS tools uses statistical (often empirical) models, and therefore practitioners need to be aware that even the best statistical model is an approximation to reality. In practice, both the models and the parameter values are unknown, and subject to uncertainty on top of ignorance... | Design for Six Sigma | 0.78271 |
86,044 | This then encompasses applied physics, ceramics, composite materials, metals and metallurgy, polymer engineering, semiconductors, thin films, biomaterials, dental technology, as well as optics. The database indexes relevant materials science information from over 6,000 scientific journals that are part of the ISI datab... | Material Science Citation Index | 0.782709 |
86,045 | The Materials Science Citation Index is a citation index, established in 1992, by Thomson ISI (Thomson Reuters). Its overall focus is cited reference searching of the notable and significant journal literature in materials science. The database makes accessible the various properties, behaviors, and materials in the ma... | Material Science Citation Index | 0.782709 |
86,046 | For example we have the relation basic in quantum mechanics: D x − x D = 1. {\displaystyle Dx-xD=1.} The subring of operators that are polynomials in D with constant coefficients is, by contrast, commutative. It can be characterised another way: it consists of the translation-invariant operators. The differential opera... | Linear differential operator | 0.782708 |
86,047 | See also Jet (mathematics). In the development of holomorphic functions of a complex variable z = x + i y, sometimes a complex function is considered to be a function of two real variables x and y. Use is made of the Wirtinger derivatives, which are partial differential operators: This approach is also used to study fu... | Linear differential operator | 0.782708 |
86,048 | In differential topology, the exterior derivative and Lie derivative operators have intrinsic meaning. In abstract algebra, the concept of a derivation allows for generalizations of differential operators, which do not require the use of calculus. Frequently such generalizations are employed in algebraic geometry and c... | Linear differential operator | 0.782708 |
86,049 | The differential operator P {\displaystyle P} is elliptic if its symbol is invertible; that is for each nonzero θ ∈ T ∗ X {\displaystyle \theta \in T^{*}X} the bundle map σ P ( θ , … , θ ) {\displaystyle \sigma _{P}(\theta ,\dots ,\theta )} is invertible. On a compact manifold, it follows from the elliptic theory that ... | Linear differential operator | 0.782708 |
86,050 | Multi-tip scanning tunneling microscopy (Multi-tip STM) extends scanning tunneling microscopy (STM) from imaging to dedicated electrical measurements at the nanoscale like a ″multimeter at the nanoscale″. In materials science, nanoscience, and nanotechnology, it is desirable to measure electrical properties at a partic... | Multi-tip scanning tunneling microscopy | 0.782707 |
86,051 | 1,2-Bis(dimethylarsino)benzene (diars) is the organoarsenic compound with the formula C6H4(As(CH3)2)2. The molecule consists of two dimethylarsino groups attached to adjacent carbon centers of a benzene ring. It is a chelating ligand in coordination chemistry. This colourless oil is commonly abbreviated "diars." | 1,2-Bis(dimethylarsino)benzene | 0.782705 |
86,052 | Related, but non-chelating organoarsenic ligands include triphenylarsine and trimethylarsine. Work on diars preceded the development of the chelating diphosphine ligands such as dppe, which are now prevalent in homogeneous catalysis. Diars is a bidentate ligand used in coordination chemistry. It was first described in ... | 1,2-Bis(dimethylarsino)benzene | 0.782705 |
86,053 | Goal-based agents further expand on the capabilities of the model-based agents, by using "goal" information. Goal information describes situations that are desirable. This provides the agent a way to choose among multiple possibilities, selecting the one which reaches a goal state. Search and planning are the subfields... | Artificial agent | 0.782703 |
86,054 | More importantly, it has a number of practical advantages that have helped move AI research forward. It provides a reliable and scientific way to test programs; researchers can directly compare or even combine different approaches to isolated problems, by asking which agent is best at maximizing a given "goal function"... | Artificial agent | 0.782703 |
86,055 | Philosophically, this definition of artificial intelligence avoids several lines of criticism. Unlike the Turing test, it does not refer to human intelligence in any way. Thus, there is no need to discuss if it is "real" vs "simulated" intelligence (i.e., "synthetic" vs "artificial" intelligence) and does not indicate ... | Artificial agent | 0.782703 |
86,056 | (In the automation and engineering environments, the hardware engineer or architect encompasses the electronics engineering and electrical engineering fields, with subspecialities in analog, digital, or electromechanical systems.) The hardware systems architect or hardware architect is responsible for: Interfacing with... | Hardware architect | 0.782701 |
86,057 | A neural radiance field (NeRF) is a method based on deep learning for reconstructing a three-dimensional representation of a scene from two-dimensional images. It is a graphics primitive which can be optimized from a set of 2D images to produce a 3D scene. The NeRF model can learn the scene geometry, camera poses, and ... | Neural radiance field | 0.7827 |
86,058 | There is not always a clear distinction between tracing and other forms of logging, except that the term tracing is almost never applied to logging that is a functional requirement of a program (therefore excluding logging of data from an external source, such as data acquisition in a high-energy physics experiment, an... | Event logging | 0.782697 |
86,059 | In software engineering, tracing involves a specialized use of logging to record information about a program's execution. This information is typically used by programmers for debugging purposes, and additionally, depending on the type and detail of information contained in a trace log, by experienced system administra... | Event logging | 0.782697 |
86,060 | The API separator is a gravity separation device designed using Stokes' law principles that define the rise velocity of oil droplets based on their density, size and water properties. The design of the separator is based on the specific gravity difference between the oil and the wastewater because that difference is mu... | API oil–water separator | 0.782697 |
86,061 | This is useful for many areas of research including immunology and stem cell research. High quality of modern microscopes and imaging software also permits subcellular imaging in live animals that in turn allows studying cell biology at molecular level in vivo. | Intravital microscopy | 0.782696 |
86,062 | In mathematics, the H-derivative is a notion of derivative in the study of abstract Wiener spaces and the Malliavin calculus. | H-derivative | 0.782694 |
86,063 | Self-developing radiochromic film can provide very high resolution measurements, for dosimetry and profiling purposes, particularly in radiotherapy physics. == References == | X-ray detector | 0.782694 |
86,064 | In theoretical physics, a gravitational anomaly is an example of a gauge anomaly: it is an effect of quantum mechanics — usually a one-loop diagram—that invalidates the general covariance of a theory of general relativity combined with some other fields. The adjective "gravitational" is derived from the symmetry of a g... | Diffeo anomaly | 0.782694 |
86,065 | The theorem of Bertini has been generalized in various ways. For example, a result due to Steven Kleiman asserts the following (cf. Kleiman's theorem): for a connected algebraic group G, and any homogeneous G-variety X, and two varieties Y and Z mapping to X, let Yσ be the variety obtained by letting σ ∈ G act on Y. Th... | Bertini's theorem | 0.782694 |
86,066 | In mathematics, the theorem of Bertini is an existence and genericity theorem for smooth connected hyperplane sections for smooth projective varieties over algebraically closed fields, introduced by Eugenio Bertini. This is the simplest and broadest of the "Bertini theorems" applying to a linear system of divisors; sim... | Bertini's theorem | 0.782694 |
86,067 | Organic Chemistry, Fessenden & Fessenden, 6th Edition, Ralph J. Fessenden et al. For Antoine constants: http://webbook.nist.gov/cgi/cbook.cgi?ID=C103731&Units=SI&Mask=4#ref-10 | Ethyl phenyl ether | 0.782693 |
86,068 | The physics of this process was first explained by Dungey (1961).If one assumed that magnetopause was just a boundary between a magnetic field in a vacuum and a plasma with a weak magnetic field embedded in it, then the magnetopause would be defined by electrons and ions penetrating one gyroradius into the magnetic fie... | Magnetopause | 0.782692 |
86,069 | The Tango Platform is an augmented reality computing platform, developed and authored by the Advanced Technology and Projects (ATAP), a skunkworks division of Google. It uses computer vision and internal sensors (like gyroscopes) to enable mobile devices, such as smartphones and tablets, to detect their position relati... | 3D user interaction | 0.782692 |
86,070 | This is technically called a time-like Killing vector. Because the system has a time translation symmetry, Noether's theorem guarantees that it has a conserved energy. Because a stationary system also has a well defined rest frame in which its momentum can be considered to be zero, defining the energy of the system als... | Mass in general relativity | 0.782692 |
86,071 | Great effort has been expended on proving positivity theorems for the masses just defined, not least because positivity, or at least the existence of a lower limit, has a bearing on the more fundamental question of boundedness from below: if there were no lower limit to the energy, then no isolated system would be abso... | Mass in general relativity | 0.782692 |
86,072 | The Higgs boson validates the Standard Model through the mechanism of mass generation. As more precise measurements of its properties are made, more advanced extensions may be suggested or excluded. As experimental means to measure the field's behaviours and interactions are developed, this fundamental field may be bet... | Higgs physics | 0.782687 |
86,073 | 168 is an even number, a composite number, an abundant number, and an idoneal number.There are 168 primes less than 1000. 168 is the product of the first two perfect numbers. 168 is the order of the group PSL(2,7), the second smallest nonabelian simple group. From Hurwitz's automorphisms theorem, 168 is the maximum pos... | 168 (number) | 0.782686 |
86,074 | Respirocytes are hypothetical, microscopic, artificial red blood cells that are intended to emulate the function of their organic counterparts, so as to supplement or replace the function of much of the human body's normal respiratory system. Respirocytes were proposed by Robert A. Freitas Jr in his 1998 paper "A Mecha... | Respirocyte | 0.782686 |
86,075 | The discoveries were verified with spectra taken mostly from the telescopes of the Keck Observatory, and the European Southern Observatory. In a 1998 study led by Adam Riess, the High-Z Team became the first to publish evidence that the expansion of the Universe is accelerating (Riess et al. 1998, AJ, 116, 1009, submit... | High-Z Supernova Search Team | 0.782686 |
86,076 | 1998: Breakthrough of the Year, Science magazine 2006: Shaw Prize 2007: Gruber Prize in Cosmology 2011: Nobel Prize in Physics 2011: Albert Einstein Medal 2015: Breakthrough Prize in Fundamental Physics 2015: Wolf Prize in Physics | High-Z Supernova Search Team | 0.782685 |
86,077 | Reception for Sagan's work was generally positive. In The New York Times Book Review, novelist James Michener praised Cosmos as "a cleverly written, imaginatively illustrated summary of ... ruminations about our universe... His style is iridescent, with lights flashing upon unexpected juxtapositions of thought." The Am... | Cosmos (Sagan book) | 0.782685 |
86,078 | As of 2016, neither the launch vehicle nor precursory launch date have been set. The objective is to establish a widespread surface observation network on Mars to investigate the planet's atmospheric structure, physics and meteorology. The bulk of the mission consist of at least 16 MetNet impact landers deployed over t... | Mars MetNet | 0.782685 |
86,079 | Particularly in astronomy and physics, he said, the book inspired many people to become scientists. Sagan has also been called the "most successful popularizing scientist of our time," for his ability to draw such a large and varied audience.The popularity of Sagan's Cosmos has been referenced in arguments supporting i... | Cosmos (Sagan book) | 0.782685 |
86,080 | NASA scientist Ravi Kopparapu advocates studying UAP. We need to frame the current UAP/UFO question with the same level of active inquiry, one involving experts from academia in disciplines including astronomy, meteorology and physics, as well as industry and government professionals with knowledge of military aircraft... | Extraterrestrial UFO hypothesis | 0.782685 |
86,081 | If the poset X is finite then the statement of the theorem has a clear interpretation that leads to the proof. The sequence of successive iterates, x n + 1 = f ( x n ) , n = 0 , 1 , 2 , … , {\displaystyle x_{n+1}=f(x_{n}),n=0,1,2,\ldots ,} where x0 is any element of X, is monotone increasing. By the finiteness of X, it... | Bourbaki–Witt theorem | 0.782684 |
86,082 | Bourbaki–Witt has other applications. In particular in computer science, it is used in the theory of computable functions. It is also used to define recursive data types, e.g. linked lists, in domain theory. | Bourbaki–Witt theorem | 0.782684 |
86,083 | This is allowed as, by assumption, the set is non-empty. Then f(x) > x, so f is an inflationary function with no fixed point, contradicting the theorem. This special case of Zorn's lemma is then used to prove the Hausdorff maximality principle, that every poset has a maximal chain, which is easily seen to be equivalent... | Bourbaki–Witt theorem | 0.782684 |
86,084 | The Bourbaki–Witt theorem has various important applications. One of the most common is in the proof that the axiom of choice implies Zorn's lemma. We first prove it for the case where X is chain complete and has no maximal element. Let g be a choice function on P ( X ) − { ∅ } . | Bourbaki–Witt theorem | 0.782684 |
86,085 | In mathematics, the Bourbaki–Witt theorem in order theory, named after Nicolas Bourbaki and Ernst Witt, is a basic fixed point theorem for partially ordered sets. It states that if X is a non-empty chain complete poset, and f: X → X {\displaystyle f:X\to X} such that f ( x ) ≥ x {\displaystyle f(x)\geq x} for all x , {... | Bourbaki–Witt theorem | 0.782684 |
86,086 | Residue curve never reach an unstable node. Saddle: These are pure components or azeotropic points with an intermediate boiling temperature and vapor pressure in a distillation region. Residue curves move toward and then away from saddles but saddles are never end points. Only border lines start or end at saddles.The d... | Residue curve | 0.782684 |
86,087 | Evans, Lawrence C. (2010). Partial Differential Equations (2nd ed.). American Mathematical Society. | Rellich–Kondrachov theorem | 0.782683 |
86,088 | Since an embedding is compact if and only if the inclusion (identity) operator is a compact operator, the Rellich–Kondrachov theorem implies that any uniformly bounded sequence in W1,p(Ω; R) has a subsequence that converges in Lq(Ω; R). Stated in this form, in the past the result was sometimes referred to as the Rellic... | Rellich–Kondrachov theorem | 0.782683 |
86,089 | In mathematics, the Rellich–Kondrachov theorem is a compact embedding theorem concerning Sobolev spaces. It is named after the Austrian-German mathematician Franz Rellich and the Russian mathematician Vladimir Iosifovich Kondrashov. Rellich proved the L2 theorem and Kondrashov the Lp theorem. | Rellich–Kondrachov theorem | 0.782683 |
86,090 | On a compact manifold with C1 boundary, the Kondrachov embedding theorem states that if k > ℓ and k − n/p > ℓ − n/q then the Sobolev embedding W k , p ( M ) ⊂ W ℓ , q ( M ) {\displaystyle W^{k,p}(M)\subset W^{\ell ,q}(M)} is completely continuous (compact). | Rellich–Kondrachov theorem | 0.782683 |
86,091 | Table obtained from Lange's Handbook of Chemistry, 10th ed. Specific gravity is referenced to water at 15.6 °C. See also "Typical Freezing and Boiling Points of Aqueous Solutions of DOWTHERM SR-1 and DOWTHERM-SR4000" (PDF). | Ethylene glycol (data page) | 0.782681 |
86,092 | It can perform automatic system balancing based on Genetic Algorithm and statistics. Useful software packages to perform these tasks are PAMS and SHARE. | Reconfigurable Manufacturing Systems | 0.78268 |
86,093 | A logic control design methodology for sequencing and coordination control of large manufacturing systems results in reconfigurable and formally verifiable controllers that can be implemented on industrial PLCs. A Stream-of-Variations (SoV) methodology based on blending state-space control theory with in-process statis... | Reconfigurable Manufacturing Systems | 0.78268 |
86,094 | The other solution is nonperiodic, denoted fe n ( x , q ) {\displaystyle {\text{fe}}_{n}(x,q)} and ge n ( x , q ) {\displaystyle {\text{ge}}_{n}(x,q)} , respectively, and referred to as a Mathieu function of the second kind. This result can be formally stated as Ince's theorem: An equivalent statement of Floquet's theo... | Mathieu function | 0.782678 |
86,095 | Many properties of the Mathieu differential equation can be deduced from the general theory of ordinary differential equations with periodic coefficients, called Floquet theory. The central result is Floquet's theorem: It is natural to associate the characteristic numbers a ( q ) {\displaystyle a(q)} with those values ... | Mathieu function | 0.782678 |
86,096 | By decreasing q {\displaystyle q} , tunneling through the barriers becomes possible (in physical language), leading to a splitting of the characteristic numbers a → a ∓ {\displaystyle a\to a_{\mp }} (in quantum mechanics called eigenvalues) corresponding to even and odd periodic Mathieu functions. This splitting is obt... | Mathieu function | 0.782678 |
86,097 | (See Ince's Theorem above.) These classifications are summarized in the table below. The modified Mathieu function counterparts are defined similarly. | Mathieu function | 0.782678 |
86,098 | Several third-party programs have graphical user interfaces that can be used to generate graphs using gnuplot as the plotting engine. These include: gretl, a statistics package for econometrics JGNUPlot, a java-based GUI Kayali a computer algebra system xldlas, an old X11 statistics package gnuplotxyz, an old Windows p... | Gnuplot | 0.782677 |
86,099 | The ability of different transport modes to meet on time performance statistics depends on the degree to which they are affected by external factors. For example, rail services often operate on a separated right of way, and so are not affected by road congestion. Buses, unless they are separated from road traffic, will... | Schedule adherence | 0.782676 |
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