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82,900 | A highest weight representation of the Virasoro algebra is a representation generated by a primary state: a vector v {\displaystyle v} such that L n > 0 v = 0 , L 0 v = h v , {\displaystyle L_{n>0}v=0,\quad L_{0}v=hv,} where the number h is called the conformal dimension or conformal weight of v {\displaystyle v} .A hi... | Virasoro algebra | 0.783967 |
82,901 | The character of a representation R {\displaystyle {\mathcal {R}}} of the Virasoro algebra is the function χ R ( q ) = Tr R q L 0 − c 24 . {\displaystyle \chi _{\mathcal {R}}(q)=\operatorname {Tr} _{\mathcal {R}}q^{L_{0}-{\frac {c}{24}}}.} The character of the Verma module V c , h {\displaystyle {\mathcal {V}}_{c,h}}... | Virasoro algebra | 0.783967 |
82,902 | The Witt algebra (the Virasoro algebra without the central extension) was discovered by É. Cartan (1909). Its analogues over finite fields were studied by E. Witt in about the 1930s. The central extension of the Witt algebra that gives the Virasoro algebra was first found (in characteristic p > 0) by R. E. Block (1966,... | Virasoro algebra | 0.783967 |
82,903 | The Virasoro algebra is spanned by generators Ln for n ∈ ℤ and the central charge c. These generators satisfy = 0 {\displaystyle =0} and The factor of 1 / 12 {\displaystyle 1/12} is merely a matter of convention. For a derivation of the algebra as the unique central extension of the Witt algebra, see derivation of the... | Virasoro algebra | 0.783967 |
82,904 | The Virasoro algebra is a subalgebra of the universal enveloping algebra of any affine Lie algebra, as shown by the Sugawara construction. In this sense, affine Lie algebras are extensions of the Virasoro algebra. | Virasoro algebra | 0.783967 |
82,905 | The Virasoro algebra is a central extension of the Lie algebra of meromorphic vector fields with two poles on a genus 0 Riemann surface. On a higher-genus compact Riemann surface, the Lie algebra of meromorphic vector fields with two poles also has a central extension, which is a generalization of the Virasoro algebra.... | Virasoro algebra | 0.783967 |
82,906 | The Virasoro algebra also has vertex algebraic and conformal algebraic counterparts, which basically come from arranging all the basis elements into generating series and working with single objects. | Virasoro algebra | 0.783967 |
82,907 | In two dimensions, the algebra of local conformal transformations is made of two copies of the Witt algebra. It follows that the symmetry algebra of two-dimensional conformal field theory is the Virasoro algebra. Technically, the conformal bootstrap approach to two-dimensional CFT relies on Virasoro conformal blocks, s... | Virasoro algebra | 0.783967 |
82,908 | In mathematics, the Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string theory. | Virasoro algebra | 0.783967 |
82,909 | If the limit of 1 A n ( x ) , {\displaystyle \mathbb {1} _{A_{n}}(x),} as n {\displaystyle n} goes to infinity, exists for all x {\displaystyle x} then Otherwise, the limit for ( A n ) {\displaystyle \left(A_{n}\right)} does not exist. It can be shown that the limit infimum is contained in the limit supremum: for examp... | Set-theoretic limit | 0.783966 |
82,910 | Set limits, particularly the limit infimum and the limit supremum, are essential for probability and measure theory. Such limits are used to calculate (or prove) the probabilities and measures of other, more purposeful, sets. For the following, ( X , F , P ) {\displaystyle (X,{\mathcal {F}},\mathbb {P} )} is a probabil... | Set-theoretic limit | 0.783966 |
82,911 | When f and g both take the values 0 or ∞ at P, the definition is essentially in limiting or removable singularity terms, by considering (up to sign) fagbwith a and b such that the function has neither a zero nor a pole at P. This is achieved by taking a to be the multiplicity of g at P, and −b the multiplicity of f at ... | Weil reciprocity | 0.783965 |
82,912 | In mathematics, the Weil reciprocity law is a result of André Weil holding in the function field K(C) of an algebraic curve C over an algebraically closed field K. Given functions f and g in K(C), i.e. rational functions on C, then f((g)) = g((f))where the notation has this meaning: (h) is the divisor of the function h... | Weil reciprocity | 0.783965 |
82,913 | Software reliability testing is being used as a tool to help assess these software engineering technologies.To improve the performance of software product and software development process, a thorough assessment of reliability is required. Testing software reliability is important because it is of great use for software... | Software reliability testing | 0.783963 |
82,914 | The application of computer software has crossed into many different fields, with software being an essential part of industrial, commercial and military systems. Because of its many applications in safety critical systems, software reliability is now an important research area. Although software engineering is becomin... | Software reliability testing | 0.783963 |
82,915 | In mathematics, specifically in symplectic geometry, the symplectic cut is a geometric modification on symplectic manifolds. Its effect is to decompose a given manifold into two pieces. There is an inverse operation, the symplectic sum, that glues two manifolds together into one. The symplectic cut can also be viewed a... | Symplectic cut | 0.783963 |
82,916 | Most cryptocurrencies use blockchain technology to record transactions. For example, the bitcoin network and Ethereum network are both based on blockchain. The criminal enterprise Silk Road, which operated on Tor, utilized cryptocurrency for payments, some of which the US federal government has seized through research ... | Blockchain | 0.783963 |
82,917 | The UPS measures experimental molecular orbital energies for comparison with theoretical values from quantum chemistry, which was also extensively developed in the 1960s. The photoelectron spectrum of a molecule contains a series of peaks each corresponding to one valence-region molecular orbital energy level. Also, th... | Ultraviolet photoelectron spectroscopy | 0.783959 |
82,918 | Software Intelligence has been used by Kirk Paul Lafler, an American engineer, entrepreneur, and consultant, and founder of Software Intelligence Corporation in 1979. At that time, it was mainly related to SAS activities, in which he has been an expert since 1979.In the early 1980s, Victor R. Basili participated in dif... | Software intelligence | 0.783958 |
82,919 | The Cavendish Astrophysics Group (formerly the Radio Astronomy Group) is based at the Cavendish Laboratory at the University of Cambridge. The group operates all of the telescopes at the Mullard Radio Astronomy Observatory except for the 32m MERLIN telescope, which is operated by Jodrell Bank. The group is the second l... | Cavendish Astrophysics Group | 0.783957 |
82,920 | Sir Martin Ryle, 1918–1984, Nobel Prize for Physics, founder of the group, former British Astronomer Royal Tony Hewish, Nobel Prize for Physics, designed the telescope which discovered the first pulsars Malcolm Longair Jacksonian Professor of Natural Philosophy, former head of the Cavendish Laboratory Jocelyn Bell Burn... | Cavendish Astrophysics Group | 0.783957 |
82,921 | The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature (LPSN) and National Center for Biotechnology Information (NCBI). Family Ignavibacteriaceae Iino et al. 2010 Ignavibacterium Iino et al. 2010 Ignavibacterium album Iino et al. 2010 Family Melioribacteraceae Podosokors... | Ignavibacteriales | 0.783956 |
82,922 | Simple module Indecomposable module Representation of an associative algebra | Irreducible representation | 0.783955 |
82,923 | In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic structure A {\displaystyle A} is a nonzero representation that has no proper nontrivial subrepresentation ( ρ | W , W ) {\displaystyle (\rho |_{W},... | Irreducible representation | 0.783955 |
82,924 | It is notable for being the vertex figure of the complex Witting polytope, which shares 240 vertices with the eight-dimensional semiregular 421 polytope whose vertices in turn represent the root vectors of the simple Lie group E 8 {\displaystyle \mathrm {E} _{8}} .There are 72 compact and paracompact Coxeter groups of ... | 72 (number) | 0.783955 |
82,925 | Inside E n {\displaystyle \mathrm {E} _{n}} Lie algebras: 72 is the number of vertices of the six-dimensional 122 polytope, which also contains as facets 720 edges, 702 polychoral 4-faces, of which 270 are four-dimensional 16-cells, and two sets of 27 demipenteract 5-faces. These 72 vertices are the root vectors of the... | 72 (number) | 0.783955 |
82,926 | In software engineering, the active record pattern is an architectural pattern. It is found in software that stores in-memory object data in relational databases. It was named by Martin Fowler in his 2003 book Patterns of Enterprise Application Architecture. The interface of an object conforming to this pattern would i... | Active record pattern | 0.783954 |
82,927 | A collection in a space X {\displaystyle X} is countably locally finite (or σ-locally finite) if it is the union of a countable family of locally finite collections of subsets of X {\displaystyle X} . Countably local finiteness is a key hypothesis in the Nagata–Smirnov metrization theorem, which states that a topologic... | Countably locally finite collection | 0.783953 |
82,928 | The set packing problem is not only NP-complete, but its optimization version (general maximum set packing problem) has been proven as difficult to approximate as the maximum clique problem; in particular, it cannot be approximated within any constant factor. The best known algorithm approximates it within a factor of ... | Set packing | 0.783952 |
82,929 | In the set cover problem, we are given a family S {\displaystyle {\mathcal {S}}} of subsets of a universe U {\displaystyle {\mathcal {U}}} , and the goal is to determine whether we can choose t sets that together contain every element of U {\displaystyle {\mathcal {U}}} . These sets may overlap. The optimization versio... | Set packing | 0.783952 |
82,930 | The problem is clearly in NP since, given t {\displaystyle t} subsets, we can easily verify that they are pairwise disjoint in polynomial time. The optimization version of the problem, maximum set packing, asks for the maximum number of pairwise disjoint sets in the list. It is a maximization problem that can be formul... | Set packing | 0.783952 |
82,931 | In the set packing decision problem, the input is a pair ( U , S ) {\displaystyle ({\mathcal {U}},{\mathcal {S}})} and an integer t {\displaystyle t} ; the question is whether there is a set packing of size t {\displaystyle t} or more. In the set packing optimization problem, the input is a pair ( U , S ) {\displaystyl... | Set packing | 0.783952 |
82,932 | Among other contributions, he solved the Sidon set union problem, worked on restrictions of Fourier and Radon transforms to curves, and generalized von Neumann's inequality. In operator theory, the Drury–Arveson space is named after William Arveson and him.His research now pertains to the interplay between matrix theor... | Stephen Drury (mathematician) | 0.783951 |
82,933 | Stephen William Drury is a Anglo-Canadian mathematician and professor of mathematics at McGill University. He specializes in mathematical analysis, harmonic analysis and linear algebra. He received his doctorate from the University of Cambridge in 1970 under the supervision of Nicholas Varopoulos and completed his post... | Stephen Drury (mathematician) | 0.783951 |
82,934 | Training usually takes place at a residential school, with courses taking anything between 9 and 13 weeks although divers with existing qualifications, such as former military divers can take courses which build on their existing knowledge and experience. During training, divers will be taught how to use common types o... | Diving systems technician | 0.78395 |
82,935 | Intertidal ecology is the study of ecosystems between the low- and high-water lines along a shore. At low water, the intertidal zone is exposed (or emersed), whereas at high water, it is underwater (or immersed). Intertidal ecologists therefore study the interactions between intertidal organisms and their environment, ... | Tidal constituent | 0.78395 |
82,936 | In mathematics, the Karoubi conjecture is a conjecture by Max Karoubi (1979) that the algebraic and topological K-theories coincide on C* algebras spatially tensored with the algebra of compact operators. It was proved by Andrei Suslin and Mariusz Wodzicki (1990, theorem 6, 1992). | Karoubi conjecture | 0.78395 |
82,937 | The Weak Interaction Studies with 32Ar Decay (WISArD) experiment is a permanent experimental setup located in the ISOLDE facility, at CERN. The purpose of the experiment is to investigate the weak interaction by looking for beta-delayed protons emitted from a nucleus. In the absence of online isotope production during ... | WISArD experiment | 0.78395 |
82,938 | By comparing the energy of the protons emitted, in the same and in opposite hemispheres of the experimental setup with respect to the beta particle, a kinematical shift between the two cases can be measured. This kinematical shift carries the information needed to deduce the beta-neutrino correlation and thus provides ... | WISArD experiment | 0.78395 |
82,939 | One of the application domains where DSA have found the most amount of success is that of artificial intelligence. In particular, several architectures have been developed for the acceleration of Deep Neural Networks (DNN). In the following sections, we report some examples. | Domain-specific architecture | 0.783948 |
82,940 | These programmable processing units found widespread adoption both in gaming consoles and personal computers. With the improvement of the hardware/software stack for both NVIDIA and AMD GPUs, these architectures are being used more and more for the acceleration of massively and embarrassingly parallel tasks, even outsi... | Domain-specific architecture | 0.783948 |
82,941 | Google's TPU was developed in 2015 to accelerate DNN inference since the company projected that the use of voice search would require to double the computational resources allocated at the time for neural network inference.The TPU was designed to be a co-processor communicating via a PCIe bus, to be easily incorporated... | Domain-specific architecture | 0.783948 |
82,942 | Aside from an application in artificial intelligence, DSAs are being adopted in many domains within scientific computing, image processing, and networking. | Domain-specific architecture | 0.783948 |
82,943 | Anton3 is a DSA designed to efficiently compute molecular-dynamics simulations. It uses a specialized 3D torus topology interconnection network to connect several computing nodes. Each computing node contains a set of 64 cores interconnected through a mesh. The cores implement a specialized deep pipeline to efficiently... | Domain-specific architecture | 0.783948 |
82,944 | Invest saved resources into arithmetic units or bigger memories: since a remarkable amount of hardware resources can be saved by dropping general-purpose architectural optimizations such as out-of-order execution, prefetching, address coalescing, and hardware speculation, the resources saved should be re-invested to ma... | Domain-specific architecture | 0.783948 |
82,945 | (As mentioned above, Principia itself was already known to be incomplete for some non-arithmetic statements.) According to the theorem, within every sufficiently powerful recursive logical system (such as Principia), there exists a statement G that essentially reads, "The statement G cannot be proved." Such a statement... | Ramified Theory of Types | 0.783947 |
82,946 | In 1930, Gödel's completeness theorem showed that first-order predicate logic itself was complete in a much weaker sense—that is, any sentence that is unprovable from a given set of axioms must actually be false in some model of the axioms. However, this is not the stronger sense of completeness desired for Principia M... | Ramified Theory of Types | 0.783947 |
82,947 | The Principia covered only set theory, cardinal numbers, ordinal numbers, and real numbers. Deeper theorems from real analysis were not included, but by the end of the third volume it was clear to experts that a large amount of known mathematics could in principle be developed in the adopted formalism. It was also clea... | Ramified Theory of Types | 0.783947 |
82,948 | To do this, conversational interfaces use natural language processing (NLP) to allow computers to understand, analyze, and create meaning from human language. Unlike word processors, NLP considers the structure of human language (i.e., words make phrases; phrases make sentences which convey the idea or intent the user ... | Conversational interfaces | 0.783945 |
82,949 | In organic chemistry, the term acetylenic designates A doubly unsaturated position (sp-hybridized) on a molecular framework, for instance in an alkyne such as acetylene; An ethynyl fragment, HC ≡ {\displaystyle \equiv } C–, or substituted homologue. | Acetylenic | 0.783945 |
82,950 | The Journal of Energy Engineering is a quarterly peer-reviewed scientific journal published by the American Society of Civil Engineers. It covers civil engineering as related to the production, distribution, and storage of energy. | Journal of Energy Engineering | 0.783945 |
82,951 | It was called Polychrome and used RGBw LED which have been calibrated as Tim Pritlove shown in a Talk about the Project on Aug. 16. The electrical engineering and computer science students of the Budapest University of Technology and Economics turn their Schönherz Dormitory into a giant display ("the Matrix") at their ... | Matrix (blinkenlights) | 0.783945 |
82,952 | Few governments maintain detailed demographic statistics of their amateur radio operator populations, aside from recording the total number of licensed operators. The majority of amateur radio operators worldwide reside in the United States, Japan, and the nations of East Asia, North America, and Europe. The top five c... | Ham radio operator | 0.783944 |
82,953 | The Felkin model (1968) named after Hugh Felkin also predicts the stereochemistry of nucleophilic addition reactions to carbonyl groups. Felkin argued that the Cram model suffered a major drawback: an eclipsed conformation in the transition state between the carbonyl substituent (the hydrogen atom in aldehydes) and the... | Chiral induction | 0.783944 |
82,954 | The Cram's rule of asymmetric induction developed by Donald J. Cram in 1952 is an early concept relating to the prediction of stereochemistry in certain acyclic systems. In full the rule is: In certain non-catalytic reactions that diastereomer will predominate, which could be formed by the approach of the entering grou... | Chiral induction | 0.783944 |
82,955 | Most countries do not have a minimum age requirement in order to earn an amateur radio license and become an amateur radio operator. Although the number of amateur radio operators in many countries increases from year to year, the average age of amateur radio operators is relatively high. In some countries, the average... | Ham radio operator | 0.783944 |
82,956 | The composition of functions creates the algebraic structure of a monoid. When the set S has only two elements, the monoid is known as the dyadic monoid. The dyadic monoid can be visualized as an infinite binary tree; more generally, if the set S has p elements, then the monoid may be represented as a p-adic tree. The ... | Self-similarity | 0.783944 |
82,957 | The polar Felkin–Anh model postulates that the observed stereochemistry arises due to hyperconjugative stabilization arising from the anti-periplanar interaction between the C-X antibonding σ* orbital and the forming bond. Improving Felkin–Anh selectivity for organometal additions to aldehydes can be achieved by using ... | Chiral induction | 0.783944 |
82,958 | In the late 1700s, Germany experienced several outbreaks of an illness connected to eating specific sausages. In 1817, the German neurologist Justinus Kerner detected rod-shaped cells in his investigations into this so-called sausage poisoning. In 1897, the Belgian biology professor Emile van Ermengem published his fin... | Clostridium | 0.783942 |
82,959 | For a dark-energy-dominated universe, the evolution of the scale factor in the Friedmann–Lemaître–Robertson–Walker metric is easily obtained solving the Friedmann equations: a ( t ) ∝ exp ( H 0 t ) {\displaystyle a(t)\propto \exp(H_{0}t)} Here, the coefficient H 0 {\displaystyle H_{0}} in the exponential, the Hubble ... | Scale factor cosmology | 0.783938 |
82,960 | This is an extension of Szemerédi's regularity lemma that partitions any given graph into bounded number parts such that edges between the parts behave almost randomly. Similarly, the hypergraph counting lemma is a generalization of the graph counting lemma that estimates number of copies of a fixed graph as a subgraph... | Hypergraph regularity method | 0.783937 |
82,961 | In mathematics, the hypergraph regularity method is a powerful tool in extremal graph theory that refers to the combined application of the hypergraph regularity lemma and the associated counting lemma. It is a generalization of the graph regularity method, which refers to the use of Szemerédi's regularity and counting... | Hypergraph regularity method | 0.783937 |
82,962 | In fact, this approach yields first quantitative bounds for the theorems. This theorem roughly implies that any dense subset of Z d {\displaystyle \mathbb {Z} ^{d}} contains any finite pattern of Z d {\displaystyle \mathbb {Z} ^{d}} . The case when d = 1 {\displaystyle d=1} and the pattern is arithmetic progression of ... | Hypergraph regularity method | 0.783937 |
82,963 | In fact, by a relatively simple application of the triangle removal lemma, one can prove that every dense subset of Z {\displaystyle \mathbb {Z} } contains an arithmetic progression of length 3. The hypergraph regularity method and hypergraph removal lemma can prove high-dimensional and ring analogues of density versio... | Hypergraph regularity method | 0.783937 |
82,964 | For all l ≥ k ≥ 2 {\displaystyle l\geq k\geq 2} and every μ > 0 {\displaystyle \mu >0} , there exists ζ > 0 {\displaystyle \zeta >0} and n 0 > 0 {\displaystyle n_{0}>0} so that the following holds. Suppose F ( k ) {\displaystyle {\mathcal {F}}^{(k)}} is a k {\displaystyle k} -uniform hypergraph on l {\displaystyle l} v... | Hypergraph regularity method | 0.783937 |
82,965 | For the algorithm and the corresponding computer code see. The theoretical result can be formulated as follows. Universal approximation theorem: Let {\displaystyle } be a finite segment of the real line, s = b − a {\displaystyle s=b-a} and λ {\displaystyle \lambda } be any positive number. | Universal approximation theorem | 0.783934 |
82,966 | The first result on approximation capabilities of neural networks with bounded number of layers, each containing a limited number of artificial neurons was obtained by Maiorov and Pinkus. Their remarkable result revealed that such networks can be universal approximators and for achieving this property two hidden layers... | Universal approximation theorem | 0.783934 |
82,967 | Achieving useful universal function approximation on graphs (or rather on graph isomorphism classes) has been a longstanding problem. The popular graph convolutional neural networks (GCNs or GNNs) can be made as discriminative as the Weisfeiler–Leman graph isomorphism test. In 2020, a universal approximation theorem re... | Universal approximation theorem | 0.783934 |
82,968 | A spate of papers in the 1980s—1990s, from George Cybenko and Kurt Hornik etc, established several universal approximation theorems for arbitrary width and bounded depth. See for reviews. The following is the most often quoted: Such an f {\displaystyle f} can also be approximated by a network of greater depth by using ... | Universal approximation theorem | 0.783934 |
82,969 | The bounded depth and bounded width case was first studied by Maiorov and Pinkus in 1999. They showed that there exists an analytic sigmoidal activation function such that two hidden layer neural networks with bounded number of units in hidden layers are universal approximators. Using algorithmic and computer programmi... | Universal approximation theorem | 0.783934 |
82,970 | The question of minimal possible width for universality was first studied in 2021, Park et al obtained the minimum width required for the universal approximation of Lp functions using feed-forward neural networks with ReLU as activation functions. Similar results that can be directly applied to residual neural networks... | Universal approximation theorem | 0.783934 |
82,971 | In 2022, Shen Zuowei, Haizhao Yang, and Shijun Zhang obtained precise quantitative information on the depth and width required to approximate a target function by deep and wide ReLU neural networks. The arbitrary depth case was also studied by a number of authors such as Gustaf Gripenberg in 2003, Dmitry Yarotsky, Zhou... | Universal approximation theorem | 0.783934 |
82,972 | One of the first versions of the arbitrary width case was proven by George Cybenko in 1989 for sigmoid activation functions. Kurt Hornik, Maxwell Stinchcombe, and Halbert White showed in 1989 that multilayer feed-forward networks with as few as one hidden layer are universal approximators. Hornik also showed in 1991 th... | Universal approximation theorem | 0.783934 |
82,973 | Variants involving other operating systems include MAMP (macOS), SAMP (Solaris), FAMP (FreeBSD), iAMP (IBM i) and XAMPP (cross-platform).The web server or database management system also varies. LEMP is a version where Apache has been replaced with the more lightweight web server Nginx. A version where MySQL has been r... | LAMP stack | 0.783933 |
82,974 | MySQL's original role as the LAMP's relational database management system has since been alternately provisioned by others like PostgreSQL, MariaDB (a community-developed fork of MySQL developed by its original developers), and even NoSQL databases like MongoDB. MySQL is a multithreaded, multi-user, SQL database manage... | LAMP stack | 0.783933 |
82,975 | LAMP (Linux, Apache, MySQL, PHP/Perl/Python) is an acronym denoting one of the most common software stacks for many of the web's most popular applications. However, LAMP now refers to a generic software stack model and its components are largely interchangeable.Each letter in the acronym stands for one of its four open... | LAMP stack | 0.783933 |
82,976 | The Shockley–Ramo theorem is a method for calculating the electric current induced by a charge moving in the vicinity of an electrode. Previously named simply the "Ramo Theorem", the modified name was introduced by D.S. McGregor et al. in 1998 to recognize the contributions of both Shockley and Ramo to understanding th... | Shockley–Ramo theorem | 0.783931 |
82,977 | The theorem appeared in William Shockley's 1938 paper titled "Currents to Conductors Induced by a Moving Point Charge" and in Simon Ramo's 1939 paper titled "Currents Induced by Electron Motion". It is based on the concept that the current induced in the electrode is due to the instantaneous change of electrostatic flu... | Shockley–Ramo theorem | 0.783931 |
82,978 | The presence of endotoxins in the blood is called endotoxemia. High level of endotoxemia can lead to septic shock, while lower concentration of endotoxins in the bloodstream is called metabolic endotoxemia. Endotoxemia is associated with obesity, diet, cardiovascular diseases, and diabetes, while also host genetics mig... | Lipopolysaccharide | 0.783931 |
82,979 | However, it appears that LPS is nonessential in at least some Gram-negative bacteria, such as Neisseria meningitidis, Moraxella catarrhalis, and Acinetobacter baumannii. It has also been implicated in non-pathogenic aspects of bacterial ecology, including surface adhesion, bacteriophage sensitivity, and interactions wi... | Lipopolysaccharide | 0.783931 |
82,980 | The dew point is the temperature to which a parcel of air must be cooled in order to become saturated, and (unless super-saturation occurs) condenses to water. Water vapor normally begins to condense on condensation nuclei such as dust, ice, and salt in order to form clouds. The cloud condensation nuclei concentration ... | Convectional Precipitation | 0.783931 |
82,981 | A free group may be defined from a group presentation consisting of a set of generators with no relations. That is, every element is a product of some sequence of generators and their inverses, but these elements do not obey any equations except those trivially following from gg−1 = 1. The elements of a free group may ... | Schreier index formula | 0.78393 |
82,982 | The Nielsen–Schreier theorem is a non-abelian analogue of an older result of Richard Dedekind, that every subgroup of a free abelian group is free abelian.Jakob Nielsen (1921) originally proved a restricted form of the theorem, stating that any finitely-generated subgroup of a free group is free. His proof involves per... | Schreier index formula | 0.78393 |
82,983 | Suppose that g is a complex semisimple Lie algebra, with a Borel subalgebra b containing a Cartan subalgebra h. An irreducible finite-dimensional representation V of g splits as a sum of eigenspaces of h, and the highest weight space is 1-dimensional and is an eigenspace of b. The Weyl group W acts on the weights of V,... | Demazure character formula | 0.78393 |
82,984 | The Effelsberg radio telescope is operated by the Max Planck Institute for Radio Astronomy in Bonn, the radio astronomy institute of the Max-Planck-Gesellschaft. It was constructed from 1968 to 1971 and inaugurated on 1 August 1972. A major technical difficulty in building a radio telescope of 100 m diameter was how to... | Effelsberg 100-m Radio Telescope | 0.78393 |
82,985 | Theorem: Let R be a right Artinian ring with a simple right module UR, and let RU, D and E be given as in the previous paragraph. Then R U = C E ( C E ( R U ) ) {\displaystyle R_{U}=\mathrm {C} _{E}(\mathrm {C} _{E}(R_{U}))\,} .Remarks In this version, the rings are chosen with the intent of proving the Jacobson densit... | Double commutant theorem | 0.783929 |
82,986 | The following generalized version for Artinian rings (which include finite-dimensional algebras) appears in (Isaacs 2009, p.187). Given a simple R module UR, we will borrow notation from the above motivation section including RU and E=End(U). Additionally, we will write D=End(UR) for the subring of E consisting of R-ho... | Double commutant theorem | 0.783929 |
82,987 | In (Rowen 1980, p.154), a version is given for polynomial identity rings. The notation Z(R) will be used to denote the center of a ring R. Theorem: If R is a simple polynomial identity ring, and A is a simple Z(R) subalgebra of R, then CR(CR(A)) = A. RemarksThis version can be considered to be "between" the central sim... | Double commutant theorem | 0.783929 |
82,988 | Therefore, by an isomorphism theorem for rings, RM is isomorphic to the quotient ring R/Ann(MR). Clearly when M is a faithful module, R and RM are isomorphic rings. So now E is a ring with RM as a subring, and CE(RM) may be formed. By definition one can check that CE(RM) = End(MR), the ring of R module endomorphisms of... | Double commutant theorem | 0.783929 |
82,989 | The centralizer of a subring S of R is given by C R ( S ) = { r ∈ R ∣ r s = s r for all s ∈ S } . {\displaystyle \mathrm {C} _{R}(S)=\{r\in R\mid rs=sr{\text{ for all }}s\in S\}.\,} Clearly CR(CR(S)) ⊇ S, but it is not always the case that one can say the two sets are equal. The double centralizer theorems give conditi... | Double commutant theorem | 0.783929 |
82,990 | The Von Neumann bicommutant theorem states that a *-subalgebra A of the algebra of bounded operators B(H) on a Hilbert space H is a von Neumann algebra (i.e. is weakly closed) if and only if A = CB(H)CB(H)(A). | Double commutant theorem | 0.783929 |
82,991 | Perhaps the most common version is the version for central simple algebras, as it appears in (Knapp 2007, p.115): Theorem: If A is a finite-dimensional central simple algebra over a field F and B is a simple subalgebra of A, then CA(CA(B)) = B, and moreover the dimensions satisfy d i m F ( B ) ⋅ d i m F ( C A ( B ) ) =... | Double commutant theorem | 0.783929 |
82,992 | The above formulas for the derivative of a vector function rely on the assumption that the basis vectors e1, e2, e3 are constant, that is, fixed in the reference frame in which the derivative of a is being taken, and therefore the e1, e2, e3 each has a derivative of identically zero. This often holds true for problems ... | Vector valued function | 0.783928 |
82,993 | The rock's mechanical or geomechanical properties are also used within petrophysics to determine the reservoir strength, elastic properties, hardness, ultrasonic behaviour, index characteristics and in situ stresses.Petrophysicists use acoustic and density measurements of rocks to compute their mechanical properties an... | Reservoir petrophysics | 0.783928 |
82,994 | These studies are combined with geological, geophysical, and reservoir engineering studies to model the reservoir and determine its economic feasibility. While most petrophysicists work in the hydrocarbon industry, some also work in the mining, water resources, geothermal energy, and carbon capture and storage industri... | Reservoir petrophysics | 0.783928 |
82,995 | Petrophysics (from the Greek πέτρα, petra, "rock" and φύσις, physis, "nature") is the study of physical and chemical rock properties and their interactions with fluids.A major application of petrophysics is in studying reservoirs for the hydrocarbon industry. Petrophysicists work together with reservoir engineers and g... | Reservoir petrophysics | 0.783928 |
82,996 | For each subinterval i = 1, 2, ..., n, let φi be the midpoint of the subinterval, and construct a sector with the center at the pole, radius r(φi), central angle Δφ and arc length r(φi)Δφ. The area of each constructed sector is therefore equal to Hence, the total area of all of the sectors is As the number of subinterv... | Polar plot | 0.783928 |
82,997 | The result was a combination of auger atom electron physics, electron microscopy, and argon etching.The main challenge in applying the technology to biological material was to invent a sample preparation procedure that would ensure that the atom and 3D structure remained stable while argon nano-etching occurred. During... | Auger architectomics | 0.783927 |
82,998 | Auger architectomics, which opens up individual cells to scan them, can be used to assess the effectiveness of such drugs by determining if a single cell can be "powered down" with targeted treatment. Based on the development of the anti-mitochondrial antifungal assay system, the University of the Free State scientists... | Auger architectomics | 0.783927 |
82,999 | Firstly, the biological sample is plated with gold to stabilise the outer structure and make it electron conductive. It is then scanned in SEM mode and the surface visually enlarged. Auger atom electron physics are applied and selected areas on the sample surface are beamed with electrons. The incident beam ejects an e... | Auger architectomics | 0.783927 |
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