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83,500 | For many years, the stereochemistry of the Wittig reaction, in terms of carbon-carbon bond formation, had been assumed to correspond directly with the Z/E stereochemistry of the alkene products. However, certain reactants do not follow this simple pattern. Lithium salts can also exert a profound effect on the stereoche... | Phosphonium ylide | 0.783761 |
83,501 | Under lithium-free conditions, the stereochemistry of the product 5 is due to the kinetically controlled addition of the ylide 1 to the carbonyl 2. When lithium is present, there may be equilibration of the intermediates, possibly via betaine species 3a and 3b. Bruce E. Maryanoff and A. B. Reitz identified the issue ab... | Phosphonium ylide | 0.783761 |
83,502 | For the reaction with aldehydes, the double bond geometry is readily predicted based on the nature of the ylide. With unstabilised ylides (R3 = alkyl) this results in (Z)-alkene product with moderate to high selectivity. If the reaction is performed in dimethylformamide in the presence of lithium iodide or sodium iodid... | Phosphonium ylide | 0.783761 |
83,503 | The Wittig reaction was reported in 1954 by Georg Wittig and his coworker Ulrich Schöllkopf. In part for this contribution, Wittig was awarded the Nobel Prize in Chemistry in 1979. | Phosphonium ylide | 0.783761 |
83,504 | Mechanistic studies have focused on unstabilized ylides, because the intermediates can be followed by NMR spectroscopy. The existence and interconversion of the betaine (3a and 3b) is subject of ongoing research. For lithium-free Wittig reactions, studies support a concerted formation of the oxaphosphetane without inte... | Phosphonium ylide | 0.783761 |
83,505 | After formally defining the convergence of sequences and accumulation points of sequences, one can also prove the Bolzano–Weierstrass theorem using nested intervals. In a follow-up, the fact, that Cauchy sequences are convergent (and that all convergent sequences are Cauchy sequences) can be proven. This in turn allows... | Nested sequence of closed intervals | 0.78376 |
83,506 | In two dimensions there is a similar result: nested closed disks in the plane must have a common intersection. This result was shown by Hermann Weyl to classify the singular behaviour of certain differential equations. | Nested sequence of closed intervals | 0.78376 |
83,507 | In mathematical analysis, nested intervals provide one method of axiomatically introducing the real numbers as the completion of the rational numbers, being a necessity for discussing the concepts of continuity and differentiability. Historically, Isaac Newton's and Gottfried Wilhelm Leibniz's discovery of differential... | Nested sequence of closed intervals | 0.78376 |
83,508 | In linear algebra, eigenvalues and eigenvectors play a fundamental role, since, given a linear transformation, an eigenvector is a vector whose direction is not changed by the transformation, and the corresponding eigenvalue is the measure of the resulting change of magnitude of the vector. More precisely, if the trans... | Characteristic polynomial of a graph | 0.783759 |
83,509 | The above definition of the characteristic polynomial of a matrix A ∈ M n ( F ) {\displaystyle A\in M_{n}(F)} with entries in a field F {\displaystyle F} generalizes without any changes to the case when F {\displaystyle F} is just a commutative ring. Garibaldi (2004) defines the characteristic polynomial for elements o... | Characteristic polynomial of a graph | 0.783759 |
83,510 | In 2007, Behavioral and Brain Sciences published a target article that put forth a biological model of intelligence based on 37 peer-reviewed neuroimaging studies (Jung & Haier, 2007). Their review of a wealth of data from functional imaging (functional magnetic resonance imaging and positron emission tomography) and s... | Neuroscience of intelligence | 0.783759 |
83,511 | Neuroscience and intelligence refers to the various neurological factors that are partly responsible for the variation of intelligence within species or between different species. A large amount of research in this area has been focused on the neural basis of human intelligence. Historic approaches to studying the neur... | Neuroscience of intelligence | 0.783759 |
83,512 | Substituting equations (1.2.1) into (1.1.1) and (1.1.2) yields the spectral domain Greens function relating the radiated electric field to its source currents: where, is the tensor Green's function in the spectral domain. Note that the spatial domain convolution has been transformed into a simple multiplication in the ... | Frequency selective surfaces | 0.783759 |
83,513 | The diffuson is a mathematical object, which often appears in the theory of disordered electronic systems (a part of condensed matter physics). In a disordered system, the motion of an electron is not ballistic, but diffusive: i.e., the electron does not move along a straight line, but experiences a series of random sc... | Diffuson | 0.783759 |
83,514 | The bidual or second dual of a TVS X , {\displaystyle X,} often denoted by X ′ ′ , {\displaystyle X^{\prime \prime },} is the strong dual of the strong dual of X {\displaystyle X}: where X b ′ {\displaystyle X_{b}^{\prime }} denotes X ′ {\displaystyle X^{\prime }} endowed with the strong dual topology b ( X ′ , X ) . {... | Strong dual topology | 0.783758 |
83,515 | In the geometry of hyperbolic 3-space, the order-7-4 triangular honeycomb (or 3,7,4 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,7,4}. It has four order-7 triangular tilings, {3,7}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infi... | Order-7-3 apeirogonal honeycomb | 0.783756 |
83,516 | The chiral anomaly in either chiral or vector field theories with fermions. This has close connection with topology through the notion of instantons. In QCD this anomaly causes the decay of a pion to two photons. The gauge anomaly, which must cancel in any consistent physical theory. In the electroweak theory this canc... | Pure gauge | 0.783756 |
83,517 | In organic chemistry, when a single organic molecule has two different functional groups, it is called a bifunctional molecule . A bifunctional molecule has the properties of two different types of functional groups, such as an alcohol (−OH), amide (−CONH2), aldehyde (−CHO), nitrile (−CN) or carboxylic acid (−COOH). Ma... | Bifunctional | 0.783756 |
83,518 | In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action. It states that the dynamics of a physical system are determined by a variational problem for a functional based on a single function, the Lagrangian, which may contain all physical information concerning the ... | Hamilton's principle | 0.783756 |
83,519 | Microsoft Windows is not shipped with support for X, but many third-party implementations exist, as free and open source software such as Cygwin/X, and proprietary products such as Exceed, MKS X/Server, Reflection X, X-Win32 and Xming. There are also Java implementations of X servers. WeirdX runs on any platform suppor... | X Window | 0.783756 |
83,520 | See also more rigorous derivation Euler–Lagrange equation Requiring that the true trajectory q(t) be a stationary point of the action functional S {\displaystyle {\mathcal {S}}} is equivalent to a set of differential equations for q(t) (the Euler–Lagrange equations), which may be derived as follows. Let q(t) represent ... | Hamilton's principle | 0.783756 |
83,521 | This strand involves formalizing semiotic methods of analysis and implementing them as algorithms on computers to process large digital data sets. These data sets are typically textual but semiotics opens the way for analysis of all manner of other data. Existing work provides methods for automated opposition analysis ... | Computational semiotics | 0.783755 |
83,522 | Silicon hyperconjugation explains specific observations regarding chemical kinetics and stereochemistry of organic reactions with reactants containing silicon. The picture below shows the partial overlap of the C-Si σ orbital with the C-X (leaving group) σ*orbital (2b). This donation of electron density into the anti-b... | Silicon hyperconjugation | 0.783755 |
83,523 | The beta-silicon effect in organosilicon chemistry, also called silicon hyperconjugation, is a special type of hyperconjugation that describes the stabilizing influence of a silicon atom on the development of positive charge at a carbon atom one position removed (β) from the silicon atom. The C-Si σ orbital is said to ... | Silicon hyperconjugation | 0.783755 |
83,524 | A common theme of this work is the adoption of a sign-theoretic perspective on issues of artificial intelligence and knowledge representation. Many of its applications lie in the field of human-computer interaction (HCI) and fundamental devices of recognition. One part of this field, known as algebraic semiotics, combi... | Computational semiotics | 0.783755 |
83,525 | The engineering and physical sciences award was founded in 2013. Every year there are 12 laureates from areas spanning physics, chemistry and more. The math and computing award was launched on Ada Lovelace Day, 2016. Every year there are five laureates from mathematics, five laureates from computing and one laureate fo... | Suffrage Science award | 0.783755 |
83,526 | Life Sciences award winners are: Kelly Nguyen (scientist), MRC Laboratory of Molecular Biology Naomi Matsuura, University of Toronto, Canada Elspeth Garman, University of Oxford, UK Veronique Miron, University of Edinburgh, UK Cécile Martinat, I-STEM, France Zena Werb, University of California, San Francisco, USA Saman... | Suffrage Science award | 0.783755 |
83,527 | The Vienna Technical Museum (German: Technisches Museum Wien) is located in Vienna (Austria), in the Penzing district, at Mariahilferstraße 212. The decision to establish a technical museum was made in 1908, and construction of the building started in 1909. On June 20, 1909, Emperor Franz Josef laid the foundation ston... | Vienna Technical Museum | 0.783755 |
83,528 | The consortium aimed to promote the applications of computer science to meet the needs of research and, secondly, university teaching. Over time the consortium diversified its activities and developed services related to electronic publishing, digital libraries, high-performance computing, software development, and tec... | Consorzio Interuniversitario Lombardo per l'Elaborazione Automatica | 0.783754 |
83,529 | AstroSoc also participate in the university's Astronomy in the City events, which include astronomy and astrophysics talks, and the chance for the general public to observe the night sky. The Society hosts a number of social events throughout the year, including an annual formal dinner, summer camping trip, and bar cra... | Birmingham University Astronomical Society | 0.783752 |
83,530 | It is also the custodian of the University's historic Cooke refractor, which was purchased in 1910 as a part of the original observatory on the Edgebaston campus and is now situated in a dome on top of the Poynting Building. The society also runs programmes to improve the public understanding of astronomy. These includ... | Birmingham University Astronomical Society | 0.783752 |
83,531 | In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a subgraph that is isomorphic to H. Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing w... | Subgraph isomorphism | 0.783751 |
83,532 | The Computer Science Society at the University of Birmingham, often referred to as CSS, is the official Computer Science society at the University of Birmingham. The society has won two awards in 2017, namely the "Society of the Year" and "Outstanding Event" awards and since then have also won the "Community Award" in ... | Birmingham University Astronomical Society | 0.783751 |
83,533 | SPIKE was developed by Ron Shamir's computational biology group in cooperation with the group of Yosef Shiloh, an Israel Prize recipient for his research in systems biology, and the group of Karen Avraham, a leading researcher of human deafness, all from Tel Aviv University. | SPIKE (database) | 0.78375 |
83,534 | Nature Nanotechnology is a monthly peer-reviewed scientific journal published by Nature Publishing Group. It was established in October 2006. The editor-in-chief is Fabio Pulizzi. It covers all aspects of nanoscience and nanotechnology. | Nature Nanotechnology | 0.78375 |
83,535 | In 2001 the National Science Foundation (NSF) sponsored a workshop, at the American Museum of Natural History in New York to develop the outlines of a web-based system for a collaborative, media-rich research tool for morphological phylogenetics. An application prototype presented at the workshop was later refined with... | Morphobank | 0.78375 |
83,536 | Rationale for the software was described in the journal Cladistics. MorphoBank has also received support from NESCENT and the San Diego Supercomputer Center. Since 2018, MorphoBank has been supported in part by Phoenix Bioinformatics, a non-profit company founded to sustain databases for the basic sciences. A permanent... | Morphobank | 0.78375 |
83,537 | Teams of scientists studying phylogenetics to build the Tree of Life assemble large spreadsheets of observations about species (referred to as "matrices"). These teams require simultaneous access by each team member to a single and secure copy of the team's data during a scientific research project. This single copy of... | Morphobank | 0.78375 |
83,538 | It has also been used more broadly in evolutionary and paleontological research to host curated images associated with published research on lacewing insects geckos, raptor birds, dinosaurs, frogs and nematodes. MorphoBank is increasingly used in conjunction with the Paleobiology Database.Example published projects: Pr... | Morphobank | 0.78375 |
83,539 | C3iDE initially optimises the subpopulations in a partially co-adaptive fashion. During the initial optimisation of a subpopulation, only a subset of the other subcomponents is considered for the co-adaptation. This subset increases stepwise until all subcomponents are considered. This makes C3iDE very effective on lar... | Constructive cooperative coevolution | 0.783747 |
83,540 | The constructive cooperative coevolutionary algorithm (also called C3) is a global optimisation algorithm in artificial intelligence based on the multi-start architecture of the greedy randomized adaptive search procedure (GRASP). It incorporates the existing cooperative coevolutionary algorithm (CC). The considered pr... | Constructive cooperative coevolution | 0.783747 |
83,541 | In number theory, Mazur's control theorem, introduced by Mazur (1972), describes the behavior in Zp extensions of the Selmer group of an abelian variety over a number field. | Mazur's control theorem | 0.783747 |
83,542 | It provides C++ APIs for physical accurate simulation and aims to model coupled industrial dynamic systems including fluid, solid, multi-body dynamics and beyond. SPHysics is an open source SPH implementation in Fortran SPLASH is an open source (GPL) visualisation tool for SPH simulations SYMPLER: A freeware SYMbolic P... | Smoothed Particle Hydrodynamics | 0.783746 |
83,543 | RealFlow Commercial SPH solver for the cinema industry. RheoCube is a commercial SaaS product by Lorenz Research for the study and prediction of complex-fluid rheology and stability SimPARTIX is a commercial simulation package for SPH and Discrete element method (DEM) simulations from Fraunhofer IWM SPH-flow SPHERA SPH... | Smoothed Particle Hydrodynamics | 0.783746 |
83,544 | Algodoo is a 2D simulation framework for education using SPH AQUAgpusph is the free (GPLv3) SPH of the researchers, by the researchers, for the researchers dive solutions is a commercial web-based SPH engineering software for CFD purposes DualSPHysics is a mostly open source SPH code based on SPHysics and using GPU com... | Smoothed Particle Hydrodynamics | 0.783746 |
83,545 | Finally, unlike grid-based techniques, which must track fluid boundaries, SPH creates a free surface for two-phase interacting fluids directly since the particles represent the denser fluid (usually water) and empty space represents the lighter fluid (usually air). For these reasons, it is possible to simulate fluid mo... | Smoothed Particle Hydrodynamics | 0.783746 |
83,546 | In information theory and computer science, the Damerau–Levenshtein distance (named after Frederick J. Damerau and Vladimir I. Levenshtein) is a string metric for measuring the edit distance between two sequences. Informally, the Damerau–Levenshtein distance between two words is the minimum number of operations (consis... | Damerau–Levenshtein distance | 0.783745 |
83,547 | Damerau–Levenshtein distance plays an important role in natural language processing. In natural languages, strings are short and the number of errors (misspellings) rarely exceeds 2. In such circumstances, restricted and real edit distance differ very rarely. Oommen and Loke even mitigated the limitation of the restric... | Damerau–Levenshtein distance | 0.783745 |
83,548 | Since DNA frequently undergoes insertions, deletions, substitutions, and transpositions, and each of these operations occurs on approximately the same timescale, the Damerau–Levenshtein distance is an appropriate metric of the variation between two strands of DNA. More common in DNA, protein, and other bioinformatics r... | Damerau–Levenshtein distance | 0.783745 |
83,549 | In mathematics, a radially unbounded function is a function f: R n → R {\displaystyle f:\mathbb {R} ^{n}\rightarrow \mathbb {R} } for which Or equivalently, Such functions are applied in control theory and required in optimization for determination of compact spaces. Notice that the norm used in the definition can be a... | Radially unbounded function | 0.783744 |
83,550 | In the mathematical areas of order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following: Let (L, ≤) be a complete lattice and let f: L → L be an monotonic function (w.r.t. ≤ ). Then the set of fixed points of f in L forms a complete lattice under ≤ .It wa... | Knaster–Tarski theorem | 0.783743 |
83,551 | Hyperelliptic curves can be defined over fields of any characteristic. Hence we consider an arbitrary field K {\displaystyle K} and its algebraic closure K ¯ {\displaystyle {\overline {K}}} . An (imaginary) hyperelliptic curve of genus g {\displaystyle g} over K {\displaystyle K} is given by an equation of the form whe... | Imaginary hyperelliptic curve | 0.783743 |
83,552 | The Abel-Jacobi theorem states that a divisor D = ∑ P ∈ E c P {\textstyle D=\sum _{P\in E}{c_{P}}} is principal if and only if D {\displaystyle D} has degree 0 and ∑ P ∈ E c P P = O {\textstyle \sum _{P\in E}{c_{P}P}=O} under the usual addition law for points on cubic curves. As two divisors D 1 , D 2 ∈ D i v 0 ( E ) ... | Imaginary hyperelliptic curve | 0.783743 |
83,553 | For elliptic curves the Jacobian turns out to simply be isomorphic to the usual group on the set of points on this curve, this is basically a corollary of the Abel-Jacobi theorem. To see this consider an elliptic curve E {\displaystyle E} over a field K {\displaystyle K} . The first step is to relate a divisor D {\disp... | Imaginary hyperelliptic curve | 0.783743 |
83,554 | Putting y = a ( x ) {\displaystyle y=a(x)} we find that y 2 = f ( x ) = a 2 ( x ) {\displaystyle y^{2}=f(x)=a^{2}(x)} and hence f ( x ) − a 2 ( x ) = 0 {\displaystyle f(x)-a^{2}(x)=0} .As f ( x ) − a 2 ( x ) {\displaystyle f(x)-a^{2}(x)} is a polynomial of degree 6, we have that f ( x ) − a 2 ( x ) {\displaystyle f(x)-... | Imaginary hyperelliptic curve | 0.783743 |
83,555 | The group law on elliptic curves is based on the fact that a straight line through two points lying on an elliptic curve has a unique third intersection point with the curve. Note that this is always true since O {\displaystyle O} lies on the curve. From the graph of C {\displaystyle C} it is clear that this does not n... | Imaginary hyperelliptic curve | 0.783743 |
83,556 | A hyperelliptic curve is a particular kind of algebraic curve. There exist hyperelliptic curves of every genus g ≥ 1 {\displaystyle g\geq 1} . If the genus of a hyperelliptic curve equals 1, we simply call the curve an elliptic curve. | Imaginary hyperelliptic curve | 0.783743 |
83,557 | As b = 0 {\displaystyle b=0} and b 2 = f ( a ) {\displaystyle b^{2}=f(a)} , it must be the case that f ( a ) = 0 {\displaystyle f(a)=0} and thus a {\displaystyle a} is a multiple root of f {\displaystyle f} . We conclude that the curve C: y 2 = f ( x ) {\displaystyle C:y^{2}=f(x)} has no singular points if and only if ... | Imaginary hyperelliptic curve | 0.783743 |
83,558 | However, heavy ion projectiles can easily recoil lighter ions which, if the geometry is right, can be ejected from the target and detected. This is the basis of the Elastic Recoil Detection (ERD, with synonyms ERDA, FRS, HFS) technique. | Rutherford backscattering spectrometry | 0.783742 |
83,559 | Rutherford backscattering spectrometry (RBS) is an analytical technique used in materials science. Sometimes referred to as high-energy ion scattering (HEIS) spectrometry, RBS is used to determine the structure and composition of materials by measuring the backscattering of a beam of high energy ions (typically protons... | Rutherford backscattering spectrometry | 0.783742 |
83,560 | The Institut de Robòtica i Informàtica Industrial, CSIC-UPC (IRI) (in Spanish: Instituto de Robótica e Informática Industrial, in English: Institute of Robotics and Industrial Informatics), is a Joint Research Center of the Spanish National Research Council (CSIC) and the Polytechnical University of Catalonia (UPC). Th... | Institut de Robòtica i Informàtica Industrial | 0.783742 |
83,561 | In geology the aspects of rock density are involved. | Mass distribution | 0.78374 |
83,562 | In astronomy mass distribution has decisive influence on the development e.g. of nebulae, stars and planets. The mass distribution of a solid defines its center of gravity and influences its dynamical behaviour - e.g. the oscillations and eventual rotation. | Mass distribution | 0.78374 |
83,563 | In physics and mechanics, mass distribution is the spatial distribution of mass within a solid body. In principle, it is relevant also for gases or liquids, but on Earth their mass distribution is almost homogeneous. | Mass distribution | 0.78374 |
83,564 | The highest injection pressure is up to 160 MPa. In order to achieve high efficiency, Daimler-Benz installed a single wastegate turbocharger and an air-to-air intercooler. The turbocharger's exhaust turbine is relatively small to achieve good turbo response; it has a fixed turbine geometry, and a wastegate. | Unimog 405 | 0.783739 |
83,565 | However, a hardware machine and its programming can be designed to perform an almost illimitable number of abstract and physical tasks. Within the computer and software engineering disciplines (and, often, other engineering disciplines, such as communications), then, the term system came to be defined as containing all... | Systems architecture | 0.783739 |
83,566 | Systems architecture depends heavily on practices and techniques which were developed over thousands of years in many other fields, perhaps the most important being civil architecture. Prior to the advent of digital computers, the electronics and other engineering disciplines used the term "system" as it is still commo... | Systems architecture | 0.783739 |
83,567 | The Matrix Market exchange formats are a set of human readable, ASCII-based file formats designed to facilitate the exchange of matrix data. The file formats were designed and adopted for the Matrix Market, a NIST repository for test data for use in comparative studies of algorithms for numerical linear algebra. | Matrix Market exchange formats | 0.783738 |
83,568 | Examples in physics of equations defined by a potential include the electromagnetic field, the gravitational field, and, in fluid dynamics, potential flow, which is an approximation to fluid flow assuming constant density, zero viscosity, and irrotational flow. One example of a fluid dynamic application of a conformal ... | Conformal projection | 0.783737 |
83,569 | Conformal mappings are invaluable for solving problems in engineering and physics that can be expressed in terms of functions of a complex variable yet exhibit inconvenient geometries. By choosing an appropriate mapping, the analyst can transform the inconvenient geometry into a much more convenient one. For example, o... | Conformal projection | 0.783737 |
83,570 | The introduction of translations in the Poincaré group again preserves angles. A larger group of conformal maps for relating solutions of Maxwell's equations was identified by Ebenezer Cunningham (1908) and Harry Bateman (1910). Their training at Cambridge University had given them facility with the method of image cha... | Conformal projection | 0.783737 |
83,571 | Many specialists and professionals consider Vitruvius' theories as the foundations of architectural technology. Vitruvius' attempt to classify building types, styles, materials and construction methods influenced the creation of many disciplines such as civil engineering, structural engineering, architectural technolog... | Architectural technology | 0.783736 |
83,572 | Simics is a full-system simulator or virtual platform used to run unchanged production binaries of the target hardware. Simics was originally developed by the Swedish Institute of Computer Science (SICS), and then spun off to Virtutech for commercial development in 1998. Virtutech was acquired by Intel in 2010. Current... | Simics | 0.783735 |
83,573 | The Barratt–Priddy theorem states that these "stable homology groups" are the same: for n ≥ 2 k {\displaystyle n\geq 2k} , there is a natural isomorphism H k ( Σ n ) ≅ H k ( Map 0 ( S n , S n ) ) . {\displaystyle H_{k}(\Sigma _{n})\cong H_{k}({\text{Map}}_{0}(S^{n},S^{n})).} This isomorphism holds with integral coeffic... | Barratt–Priddy theorem | 0.783734 |
83,574 | The mapping space Map 0 ( S n , S n ) {\displaystyle \operatorname {Map} _{0}(S^{n},S^{n})} is the topological space of all continuous maps f: S n → S n {\displaystyle f\colon S^{n}\to S^{n}} from the n-dimensional sphere S n {\displaystyle S^{n}} to itself, under the topology of uniform convergence (a special case o... | Barratt–Priddy theorem | 0.783734 |
83,575 | In homotopy theory, a branch of mathematics, the Barratt–Priddy theorem (also referred to as Barratt–Priddy–Quillen theorem) expresses a connection between the homology of the symmetric groups and mapping spaces of spheres. The theorem (named after Michael Barratt, Stewart Priddy, and Daniel Quillen) is also often stat... | Barratt–Priddy theorem | 0.783734 |
83,576 | One central analogy is the idea that GLn(F1) should be the symmetric group Σn. The higher K-groups Ki(R) of a ring R can be defined as K i ( R ) = π i ( B G L ∞ ( R ) + ) {\displaystyle K_{i}(R)=\pi _{i}(BGL_{\infty }(R)^{+})} According to this analogy, the K-groups Ki(F1) of F1 should be defined as πi(BGL∞(F1)+)=πi(BΣ... | Barratt–Priddy theorem | 0.783734 |
83,577 | The Barratt–Priddy theorem is sometimes colloquially rephrased as saying that "the K-groups of F1 are the stable homotopy groups of spheres". This is not a meaningful mathematical statement, but a metaphor expressing an analogy with algebraic K-theory. The "field with one element" F1 is not a mathematical object; it re... | Barratt–Priddy theorem | 0.783734 |
83,578 | The Barratt–Priddy theorem implies that the space BΣ∞+ resulting from applying Quillen's plus construction to BΣ∞ can be identified with Map0(S∞,S∞). (Since π1(Map0(S∞,S∞))≅H1(Σ∞)≅Z/2Z, the map φ: BΣ∞→Map0(S∞,S∞) satisfies the universal property of the plus construction once it is known that φ is a homology equivalence... | Barratt–Priddy theorem | 0.783734 |
83,579 | Today, OMDoc is used in the following settings: E-learning Creation of customized textbooks. Data exchange OMDoc import and export modules are available for many automated theorem provers and computer algebra systems. OMDoc is intended to be used for communication between mathematical web services. Document preparation... | OMDoc | 0.783733 |
83,580 | OMDoc allows for mathematical expressions on three levels: Object level Formulae, written in Content MathML (the non-presentational subset of MathML), OpenMath or languages for mathematical logic. Statement level Definitions, theorems, proofs, examples and the relations between them (e.g. “this proof proves that theore... | OMDoc | 0.783733 |
83,581 | It is planned to create the infrastructure for a “semantic web for technology and science” based on OMDoc. To this end, OMDoc is being extended towards sciences other than mathematics. The first result is PhysML, an OMDoc variant extended towards physics. For a better integration with other Semantic Web applications, a... | OMDoc | 0.783733 |
83,582 | 1QBit was founded as the first dedicated quantum computing software company in 2012. In 2013, 1QBit raised seed funding from US and Canadian angel investors, before closing a Series A financing round led by the Chicago Mercantile Exchange in 2014. On August 5, 2015 the World Economic Forum announced 1QBit as a recipien... | 1QBit | 0.783733 |
83,583 | 1QBit has divisions focused on universal quantum computing, advanced AI techniques, cloud based quantum processing, and hardware innovation. 1QBit's 1Qloud platform is focused on optimization including reformulating optimization problems into the quadratic unconstrained binary optimization (QUBO) format necessary to co... | 1QBit | 0.783733 |
83,584 | 1QB Information Technologies, Inc. (1QBit) is a quantum computing software company, based in Vancouver, British Columbia. 1QBit was founded on December 1, 2012 and has established hardware partnerships with Microsoft, IBM, Fujitsu and D-Wave Systems. While 1QBit develops general purpose algorithms for quantum computing... | 1QBit | 0.783733 |
83,585 | Let τ1 and τ2 be two topologies on a set X and let Bi(x) be a local base for the topology τi at x ∈ X for i = 1,2. Then τ1 ⊆ τ2 if and only if for all x ∈ X, each open set U1 in B1(x) contains some open set U2 in B2(x). Intuitively, this makes sense: a finer topology should have smaller neighborhoods. | Coarser (topology) | 0.78373 |
83,586 | An open (resp. closed) map f: X → Y remains open (resp. closed) if the topology on Y becomes finer or the topology on X coarser.One can also compare topologies using neighborhood bases. | Coarser (topology) | 0.78373 |
83,587 | Let τ1 and τ2 be two topologies on a set X. Then the following statements are equivalent: τ1 ⊆ τ2 the identity map idX: (X, τ2) → (X, τ1) is a continuous map. the identity map idX: (X, τ1) → (X, τ2) is a strongly/relatively open map. (The identity map idX is surjective and therefore it is strongly open if and only if i... | Coarser (topology) | 0.78373 |
83,588 | High energy physics and molecular biology are very different as scientific fields belonging to two different epistemic cultures. They also are very different in terms of academic authorship. Biagioli describes this difference in terms of publications culture regarding number of authors per paper, distribution of contri... | Epistemic cultures | 0.78373 |
83,589 | In practice, Knorr Cetina compares two contemporary important scientific fields: High energy physics and molecular biology. She worked as an anthropologist within two laboratories, along the line of the laboratory anthropology work by Latour and Woolgar. Her anthropological work is comparative and the two chosen scient... | Epistemic cultures | 0.78373 |
83,590 | The Groupement des écoles d'aéronautique (GEA France) (in English French aeronautical universities network) includes three French national aerospace engineering grandes écoles focused on this scope: École nationale de l'aviation civile (ÉNAC), Aix-en-Provence, Carcassonne, Castelnaudary, Toulouse, Muret, Montpellier, G... | Groupement des écoles d'aéronautique | 0.783728 |
83,591 | The Institut sino-européen d'ingénierie de l'aviation (Sino-European Institute of Aviation Engineering) of Tianjin has been created by the GEA grandes écoles, in partnership with DGAC and French companies (EADS, Airbus, Thales, Eurocopter, Safran) as part of a Franco-Chinese cooperation following the implantation of an... | Groupement des écoles d'aéronautique | 0.783728 |
83,592 | In mathematics, a lethargy theorem is a statement about the distance of points in a metric space from members of a sequence of subspaces; one application in numerical analysis is to approximation theory, where such theorems quantify the difficulty of approximating general functions by functions of special form, such as... | Lethargy theorem | 0.783728 |
83,593 | In polymer chemistry, a copolymer is a polymer derived from more than one species of monomer. The polymerization of monomers into copolymers is called copolymerization. Copolymers obtained from the copolymerization of two monomer species are sometimes called bipolymers. Those obtained from three and four monomers are c... | Copolymer | 0.783726 |
83,594 | The Telecommunications Industry Association's Telecommunications Infrastructure Standard for Data Centers specifies the minimum requirements for telecommunications infrastructure of data centers and computer rooms including single tenant enterprise data centers and multi-tenant Internet hosting data centers. The topolo... | Micro data center | 0.783724 |
83,595 | In physics, the view of the universe and its workings as the ebb and flow of information was first observed by Wheeler. Consequently, two views of the world emerged: the first one proposes that the universe is a quantum computer, while the other one proposes that the system performing the simulation is distinct from it... | Virtual reality simulation | 0.783722 |
83,596 | Motivations for the more recent alternatives to general relativity are almost all cosmological, associated with or replacing such constructs as "inflation", "dark matter" and "dark energy". The basic idea is that gravity agrees with general relativity at the present epoch but may have been quite different in the early ... | Modified gravity | 0.783722 |
83,597 | In 1984, Edelman published his regulator hypothesis of CAM and SAM action in the development and evolution of the animal body plan. Edelman would reiterate this hypothesis in his Neural Darwinism book in support of the mechanisms for degenerate neuronal group formation in the primary repertoire. The regulator hypothesi... | Neuronal group selection | 0.783719 |
83,598 | Edelman realized that in order to truly complete Darwin's program, he would need to link the developmental question to the larger issues of evolutionary biology. "How is an answer to the developmental genetic question (q.v.) reconciled with the relatively rapid changes in form occurring in relatively short evolutionary... | Neuronal group selection | 0.783719 |
83,599 | An early review of the book Neural Darwinism in The New York Review of Books by Israel Rosenfield invited a lively response on the part of the neurosciences community. Edelman's views would be seen as an attack on the dominant paradigm of computational algorithms in cognitive psychology and computational neuroscience –... | Neuronal group selection | 0.783719 |
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