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94,100 | It should be contrasted with what is sometimes called schooling. Schooling occurs when many opponents correctly call against a player with the best hand, whereas implicit collusion occurs when an opponent incorrectly calls against a player with the best hand. One conclusion of Morton's theorem is that, in a loose hold'... | Morton's theorem | 0.779305 |
94,101 | However, this is an optical illusion caused by perspective; in reality, the "rays" (i.e. bands of shadow) run near-parallel to each other.Also around the antisolar point, the gegenschein is often visible in a moonless night sky away from city lights, arising from the backscatter of sunlight by interplanetary dust. In a... | Anthelic point | 0.779303 |
94,102 | The Poynting vector occurs in Poynting's theorem only through its divergence ∇ ⋅ S, that is, it is only required that the surface integral of the Poynting vector around a closed surface describe the net flow of electromagnetic energy into or out of the enclosed volume. This means that adding a solenoidal vector field (... | Poynting flux | 0.779301 |
94,103 | The Poynting vector appears in Poynting's theorem (see that article for the derivation), an energy-conservation law: where Jf is the current density of free charges and u is the electromagnetic energy density for linear, nondispersive materials, given by where E is the electric field; D is the electric displacement fie... | Poynting flux | 0.779301 |
94,104 | So if one accepts the validity of the Poynting vector description of electromagnetic energy transfer, then Poynting's theorem is simply a statement of the conservation of energy. If electromagnetic energy is not gained from or lost to other forms of energy within some region (e.g., mechanical energy, or heat), then ele... | Poynting flux | 0.779301 |
94,105 | In Poynting's original paper and in most textbooks, the Poynting vector S {\displaystyle \mathbf {S} } is defined as the cross product where bold letters represent vectors and E is the electric field vector; H is the magnetic field's auxiliary field vector or magnetizing field.This expression is often called the Abraha... | Poynting flux | 0.779301 |
94,106 | The two alternative definitions of the Poynting vector are equal in vacuum or in non-magnetic materials, where B = μ0H. In all other cases, they differ in that S = (1/μ0) E × B and the corresponding u are purely radiative, since the dissipation term −J ⋅ E covers the total current, while the E × H definition has contri... | Poynting flux | 0.779301 |
94,107 | The "microscopic" (differential) version of Maxwell's equations admits only the fundamental fields E and B, without a built-in model of material media. Only the vacuum permittivity and permeability are used, and there is no D or H. When this model is used, the Poynting vector is defined as where μ0 is the vacuum permea... | Poynting flux | 0.779301 |
94,108 | The Verlet integration would automatically handle the velocity imparted by the collision in the latter case; however, note that this is not guaranteed to do so in a way that is consistent with collision physics (that is, changes in momentum are not guaranteed to be realistic). Instead of implicitly changing the velocit... | Verlet integration | 0.7793 |
94,109 | The content covers more than 200 years of chemistry and has been abstracted from several thousands of journal titles, books and patents. Today the data is drawn from selected journals (400 titles) and chemistry patents, and the excerption process for each reaction or substance data included needs to meet three conditio... | Reaxys | 0.7793 |
94,110 | Reaxys is a web-based tool for the retrieval of information about chemical compounds and data from published literature, including journals and patents. The information includes chemical compounds, chemical reactions, chemical properties, related bibliographic data, substance data with synthesis planning information, a... | Reaxys | 0.7793 |
94,111 | One of the primary goals of Reaxys is to provide research chemists with access to experimentally measured data – reactions, physical, chemical or pharmacological – in one universal and factual platform. Content covers organic, medicinal, synthetic, agro, fine, catalyst, inorganic and process chemistry and provides info... | Reaxys | 0.7793 |
94,112 | The company would later add another executive role with Chief Sustainability Officer in 2021.April 2021 saw robot manufacturer Comau and Rockwell Automation partner to simplify robot integration for industries.Another partnership came with Cisco in May 2021 to combat rapidly evolving industrial cybersecurity threats by... | Rockwell Automation | 0.779296 |
94,113 | Blake Moret was elected the incoming Chairman by the board of directors.On June 11, 2018, Rockwell Automation made a $1 billion equity investment in PTC, acquiring an 8.4% ownership stake.In February 2019, Rockwell Automation and Schlumberger entered a joint venture to create Sensia, the oil and gas industry's first fu... | Rockwell Automation | 0.779296 |
94,114 | Fiix – Provider of artificial intelligence-enabled computerized maintenance management systems.Oylo – Provider of industrial control system (ICS) cybersecurity services including assessments, turnkey implementations, managed services, and incident response.Kalypso – Software delivery and consulting firm specializing in... | Rockwell Automation | 0.779296 |
94,115 | Knowledge Lens – The Bengaluru, India-based company provides enterprise data services, combining digital technologies with deep data science, AI, and engineering expertise. Knowledge Lens joins Rockwell’s Kalypso organization.Clearpath Robotics – Manufactures and sells the OTTO line of self-driving vehicles for industr... | Rockwell Automation | 0.779296 |
94,116 | In recent years, Rockwell Automation has grown through acquisitions of companies specializing in software services for supply chain management, systems integrators, cloud-native smart manufacturing platforms, simulation capabilities, manufacturing execution systems, and cybersecurity services. | Rockwell Automation | 0.779296 |
94,117 | The radial part of the Laplacian in this case leads to a hypergeometric differential equation, the theory of which was treated in detail by Weyl. Weyl's approach was subsequently generalised by Harish-Chandra to study zonal spherical functions and the corresponding Plancherel theorem for more general semisimple Lie gro... | Zonal spherical function | 0.779294 |
94,118 | The structure of the Hecke algebra. Harish-Chandra and Godement proved that, as convolution algebras, there are natural isomorphisms between Cc∞(K \ G / K ) and Cc∞(A)W, the subalgebra invariant under the Weyl group. This is straightforward to establish for SL(2,R). | Zonal spherical function | 0.779294 |
94,119 | The principal series representation σ is realised on L2(K) as ( σ ( g ) ξ ) ( k ) = α ′ ( g − 1 k ) − 1 ξ ( U ( g − 1 k ) ) , {\displaystyle (\sigma (g)\xi )(k)=\alpha ^{\prime }(g^{-1}k)^{-1}\,\xi (U(g^{-1}k)),} where g = U ( g ) ⋅ X ( g ) {\displaystyle g=U(g)\cdot X(g)} is the Iwasawa decomposition of g with U(g) in... | Zonal spherical function | 0.779294 |
94,120 | If G is a non-compact semisimple Lie group, its maximal compact subgroup K acts by conjugation on the component P in the Cartan decomposition. If A is a maximal Abelian subgroup of G contained in P, then A is diffeomorphic to its Lie algebra under the exponential map and, as a further generalisation of the polar decomp... | Zonal spherical function | 0.779294 |
94,121 | For complex groups, the theory simplifies significantly, because G is the complexification of K, and the formulas are related to analytic continuations of the Weyl character formula on K. The abstract functional analytic theory of zonal spherical functions was first developed by Roger Godement. Apart from their group t... | Zonal spherical function | 0.779294 |
94,122 | The spectrum of the commutative Banach *-algebra of biinvariant L1 functions is larger; when G is a semisimple Lie group with maximal compact subgroup K, additional characters come from matrix coefficients of the complementary series, obtained by analytic continuation of the spherical principal series. Zonal spherical ... | Zonal spherical function | 0.779294 |
94,123 | In mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K (often a maximal compact subgroup) that arises as the matrix coefficient of a K-invariant vector in an irreducible representation of G. The key examples are the matrix coefficie... | Zonal spherical function | 0.779294 |
94,124 | If ψ is a zonal spherical function, then, regarded as a function on G/K, it is an eigenfunction of the Laplacian there, an elliptic differential operator with real analytic coefficients. By analytic elliptic regularity, ψ is a real analytic function on G/K, and hence G. Harish-Chandra used these facts about the structu... | Zonal spherical function | 0.779294 |
94,125 | Harish-Chandra proved that zonal spherical functions can be characterised as those normalised positive definite K-invariant functions on G/K that are eigenfunctions of D(G/K), the algebra of invariant differential operators on G. This algebra acts on G/K and commutes with the natural action of G by left translation. It... | Zonal spherical function | 0.779294 |
94,126 | One of the simplest classical Lie algebraic arguments is to note that, since Δ is an elliptic operator with analytic coefficients, by analytic elliptic regularity any eigenfunction is necessarily real analytic. Hence, if the zonal spherical function corresponds to the matrix coefficient for a vector v and representatio... | Zonal spherical function | 0.779294 |
94,127 | The theory of zonal spherical functions for SL(2,R) originated in the work of Mehler in 1881 on hyperbolic geometry. He discovered the analogue of the Plancherel theorem, which was rediscovered by Fock in 1943. The corresponding eigenfunction expansion is termed the Mehler–Fock transform. It was already put on a firm f... | Zonal spherical function | 0.779294 |
94,128 | Spherical functions for Euclidean motion groups and compact Lie groups. Spherical functions for p-adic Lie groups. These were studied in depth by Satake and Macdonald. Their study, and that of the associated Hecke algebras, was one of the first steps in the extensive representation theory of semisimple p-adic Lie group... | Zonal spherical function | 0.779294 |
94,129 | The theory of zonal functions that are not necessarily positive-definite. These are given by the same formulas as above, but without restrictions on the complex parameter s or ρ. They correspond to non-unitary representations. Harish-Chandra's eigenfunction expansion and inversion formula for spherical functions. This ... | Zonal spherical function | 0.779294 |
94,130 | {\displaystyle P=\{g\in G|\tau (g)=g^{-1}\}.} Under the exponential map, P is diffeomorphic to the -1 eigenspace of τ in the Lie algebra of G. Since τ preserves K, it induces an automorphism of the Hecke algebra Cc(K\G/K). On the other hand, if F lies in Cc(K\G/K), then F(τg) = F(g−1),so that τ induces an anti-automorp... | Zonal spherical function | 0.779294 |
94,131 | If G is a complex semisimple Lie group, it is the complexification of its maximal compact subgroup K. If g {\displaystyle {\mathfrak {g}}} and k {\displaystyle {\mathfrak {k}}} are their Lie algebras, then g = k ⊕ i k . {\displaystyle {\mathfrak {g}}={\mathfrak {k}}\oplus i{\mathfrak {k}}.} Let T be a maximal torus in ... | Zonal spherical function | 0.779294 |
94,132 | {\displaystyle \int _{G}|f(g)|^{2}\,dg=\int _{X}|\chi (\pi (f))|^{2}\,d\mu (\chi ).} μ is called the Plancherel measure. Since π(G)' is the centre of the von Neumann algebra generated by G, it also gives the measure associated with the direct integral decomposition of H1 in terms of the irreducible representations σχ. | Zonal spherical function | 0.779294 |
94,133 | The image forms a dense * subalgebra of A(K\G/K). The restriction of a * homomorphism χ continuous for the operator norm is also continuous for the norm ||·||1. Since the Banach space dual of L1 is L∞, it follows that χ ( π ( F ) ) = ∫ G F ( g ) h ( g ) d g , {\displaystyle \chi (\pi (F))=\int _{G}F(g)h(g)\,dg,} for so... | Zonal spherical function | 0.779294 |
94,134 | The pair (G, K) is said to be a Gelfand pair if one, and hence all, of the following algebras are commutative: π ( G ) ′ {\displaystyle \pi (G)^{\prime }} C c ( K ∖ G / K ) {\displaystyle C_{c}(K\backslash G/K)} A ( K ∖ G / K ) . {\displaystyle A(K\backslash G/K).} Since A(K\G/K) is a commutative C* algebra, by the Gel... | Zonal spherical function | 0.779294 |
94,135 | Thus the commutant of π is generated as a von Neumann algebra by operators P ρ ( f ) P = ∫ G f ( g ) ( P ρ ( g ) P ) d g {\displaystyle P\rho (f)P=\int _{G}f(g)(P\rho (g)P)\,dg} where f is a continuous function of compact support on G.However Pρ(f) P is just the restriction of ρ(F) to H1, where F ( g ) = ∫ K ∫ K f ( k ... | Zonal spherical function | 0.779294 |
94,136 | Let G be a locally compact unimodular topological group and K a compact subgroup and let H1 = L2(G/K). Thus, H1 admits a unitary representation π of G by left translation. This is a subrepresentation of the regular representation, since if H= L2(G) with left and right regular representations λ and ρ of G and P is the o... | Zonal spherical function | 0.779294 |
94,137 | S/KEY is a trademark of Telcordia Technologies, formerly known as Bell Communications Research (Bellcore). S/KEY is also sometimes referred to as Lamport's scheme, after its author, Leslie Lamport. It was developed by Neil Haller, Phil Karn and John Walden at Bellcore in the late 1980s. With the expiration of the basic... | S/KEY | 0.779293 |
94,138 | The creation of the Max Planck Harvard Research Center for the Archaeoscience of the Ancient Mediterranean (MHAAM) was announced in February 2017 at Harvard University. It was inaugurated with a workshop and a signing ceremony at Harvard University on October 10, 2017, when the president of the Max Planck Society, Mart... | Max Planck Harvard Research Center for the Archaeoscience of the Ancient Mediterranean | 0.779292 |
94,139 | Term Rewriting Systems, Terese, Cambridge Tracts in Theoretical Computer Science, 2003. (book weblink) Term Rewriting and All That, Franz Baader and Tobias Nipkow, Cambridge University Press, 1998 (book weblink) John Harrison, Handbook of Practical Logic and Automated Reasoning, Cambridge University Press, 2009, ISBN 9... | Newman's lemma | 0.779291 |
94,140 | H. S. M. Coxeter, S. L. Greitzer: Geometry Revisited. MAA, Washington 1967, pp. 52-54 Peter N. Oliver: Consequences of Varignon Parallelogram Theorem. Mathematics Teacher, Band 94, Nr. 5, Mai 2001, pp. 406-408 | Varignon's theorem | 0.779287 |
94,141 | There are three techniques in IGA that permit to enlarge the space of basis functions without touching the geometry and its parametrization.The first one is known as knot insertion (or h-refinement in the FEA framework), where Ξ ¯ = { ξ 1 ¯ = ξ 1 , ξ 2 ¯ , . . . | Isogeometric analysis | 0.779284 |
94,142 | Isogeometric analysis is a computational approach that offers the possibility of integrating finite element analysis (FEA) into conventional NURBS-based CAD design tools. Currently, it is necessary to convert data between CAD and FEA packages to analyse new designs during development, a difficult task since the two com... | Isogeometric analysis | 0.779284 |
94,143 | In the framework of IGA, the notions of both control mesh and physical mesh are defined.A control mesh is made by the so called control points and it is obtained by a piecewise linear interpolation of them. Control points play also the role of degrees of freedom (DOFs).The physical mesh lays directly on the geometry an... | Isogeometric analysis | 0.779284 |
94,144 | A free magma MX on a set X is the "most general possible" magma generated by X (i.e., there are no relations or axioms imposed on the generators; see free object). The binary operation on MX is formed by wrapping each of the two operands in parenthesis and juxtaposing them in the same order. For example: a • b = (a)(b)... | Unital magma | 0.779282 |
94,145 | The category of magmas, denoted Mag, is the category whose objects are magmas and whose morphisms are magma homomorphisms. The category Mag has direct products, and there is an inclusion functor: Set → Med ↪ Mag as trivial magmas, with operations given by projection x T y = y . An important property is that an injectiv... | Unital magma | 0.779282 |
94,146 | The Jacobi and Dedekind ellipsoids are both equilibrium figures for a body of rotating homogeneous self-gravitating fluid. However, while the Jacobi ellipsoid spins bodily, with no internal flow of the fluid in the rotating frame, the Dedekind ellipsoid maintains a fixed orientation, with the constituent fluid circulat... | Jacobi ellipsoid | 0.779281 |
94,147 | In statistics, an L-statistic is a statistic (function of a data set) that is a linear combination of order statistics; the "L" is for "linear". These are more often referred to by narrower terms according to use, namely: L-estimator, using L-statistics as estimators for parameters L-moment, L-statistic analogs of the ... | L-statistic | 0.779277 |
94,148 | Separate access control lists on every file provide flexible information sharing, but complete privacy when needed. Multics has a number of standard mechanisms to allow engineers to analyze the performance of the system, as well as a number of adaptive performance optimization mechanisms. Due to its many novel and valu... | Multics operating system | 0.779277 |
94,149 | Jerome H. Saltzer, Introduction to Multics (MIT Project MAC, 1974) is a considerably longer introduction to the system, geared towards actual users. Elliott I. Organick, The Multics System: An Examination of Its Structure (MIT Press, 1972) is the standard work on the system, although it documents an early version, and ... | Multics operating system | 0.779277 |
94,150 | In molecular biology the FGGY carbohydrate kinase family is a family of evolutionarily related carbohydrate kinase enzymes. These enzymes include L-fuculokinase EC 2.7.1.51 (gene fucK); gluconokinase EC 2.7.1.12 (gene gntK); glycerol kinase EC 2.7.1.30 (gene glpK); xylulokinase EC 2.7.1.17 (gene xylB); D-ribulose kinas... | FGGY carbohydrate kinase family | 0.779272 |
94,151 | In the geometry of hyperbolic 3-space, the cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from cube, octahedron, and cuboctahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named by its two regular cells. A geometric honeycomb is a space-fillin... | Truncated cubic-octahedral honeycomb | 0.779271 |
94,152 | It turns out that the Weierstrass function is far from being an isolated example: although it is "pathological", it is also "typical" of continuous functions: In a topological sense: the set of nowhere-differentiable real-valued functions on is comeager in the vector space C(; R) of all continuous real-valued function... | Weierstrass function | 0.77927 |
94,153 | In the NFW profile, the density of dark matter as a function of radius is given by: ρ ( r ) = ρ 0 r R s ( 1 + r R s ) 2 {\displaystyle \rho (r)={\frac {\rho _{0}}{{\frac {r}{R_{s}}}\left(1~+~{\frac {r}{R_{s}}}\right)^{2}}}} where ρ0 and the "scale radius", Rs, are parameters which vary from halo to halo. The integrated... | Navarro–Frenk–White profile | 0.77927 |
94,154 | Where the domain of the function is the natural numbers, sufficient conditions for the definition to be valid are that the value of f(0) (i.e., base case) is given, and that for n > 0, an algorithm is given for determining f(n) in terms of n, f ( 0 ) , f ( 1 ) , … , f ( n − 1 ) {\displaystyle f(0),f(1),\dots ,f(n-1)} (... | Recursively define | 0.77927 |
94,155 | Most recursive definitions have two foundations: a base case (basis) and an inductive clause. The difference between a circular definition and a recursive definition is that a recursive definition must always have base cases, cases that satisfy the definition without being defined in terms of the definition itself, and... | Recursively define | 0.779269 |
94,156 | In both Gutin & Toft (2000) and Soifer (2008), Vizing mentions that his work was motivated by a theorem of Shannon (1949) showing that multigraphs could be colored with at most (3/2)Δ colors. Although Vizing's theorem is now standard material in many graph theory textbooks, Vizing had trouble publishing the result init... | Vizing's theorem | 0.779269 |
94,157 | In 1969, Branko Grünbaum conjectured that every 3-regular graph with a polyhedral embedding on any two-dimensional oriented manifold such as a torus must be of class one. In this context, a polyhedral embedding is a graph embedding such that every face of the embedding is topologically a disk and such that the dual gra... | Vizing's theorem | 0.779269 |
94,158 | If the graph is empty, the theorem trivially holds. Let m > 0 and suppose a proper (Δ+1)-edge-coloring exists for all G − xy where xy ∈ E. We say that color α ∈ {1,...,Δ+1} is missing in x ∈ V with respect to proper (Δ+1)-edge-coloring c if c(xy) ≠ α for all y ∈ N(x). Also, let α/β-path from x denote the unique maximal... | Vizing's theorem | 0.779269 |
94,159 | In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than the maximum degree Δ of the graph. At least Δ colors are always necessary, so the undirected graphs may be partitioned into two classes: "class one" graphs for which Δ... | Vizing's theorem | 0.779268 |
94,160 | Misra & Gries (1992) describe a polynomial time algorithm for coloring the edges of any graph with Δ + 1 colors, where Δ is the maximum degree of the graph. That is, the algorithm uses the optimal number of colors for graphs of class two, and uses at most one more color than necessary for all graphs. Their algorithm fo... | Vizing's theorem | 0.779268 |
94,161 | In organic chemistry, a methine group or methine bridge is a trivalent functional group =CH−, derived formally from methane. It consists of a carbon atom bound by two single bonds and one double bond, where one of the single bonds is to a hydrogen. The group is also called methyne or methene, but its IUPAC systematic n... | Methine group | 0.779267 |
94,162 | In molecular biology, CD11 is a member of the C/D class of snoRNA which contain the C (UGAUGA) and D (CUGA) box motifs. Most of the members of the box C/D family function in directing site-specific 2'-O-methylation of substrate RNAs. | Small nucleolar RNA CD11 | 0.779266 |
94,163 | A regular map between complex algebraic varieties is a holomorphic map. (There is actually a slight technical difference: a regular map is a meromorphic map whose singular points are removable, but the distinction is usually ignored in practice.) In particular, a regular map into the complex numbers is just a usual hol... | Regular map (algebraic geometry) | 0.779266 |
94,164 | A morphism between algebraic varieties that is a homeomorphism between the underlying topological spaces need not be an isomorphism (a counterexample is given by a Frobenius morphism t ↦ t p {\displaystyle t\mapsto t^{p}} .) On the other hand, if f is bijective birational and the target space of f is a normal variety, ... | Regular map (algebraic geometry) | 0.779266 |
94,165 | This is an algebraic analog of Hartogs' extension theorem. There is also a relative version of this fact; see . | Regular map (algebraic geometry) | 0.779266 |
94,166 | (More abstractly, this is the induced map from the residue field of the generic point of Y to that of X.) Conversely, every inclusion of fields k ( Y ) ↪ k ( X ) {\displaystyle k(Y)\hookrightarrow k(X)} is induced by a dominant rational map from X to Y. Hence, the above construction determines a contravariant-equivalen... | Regular map (algebraic geometry) | 0.779266 |
94,167 | A morphism f:X→Y of algebraic varieties is said to be dominant if it has dense image. For such an f, if V is a nonempty open affine subset of Y, then there is a nonempty open affine subset U of X such that f(U) ⊂ V and then f #: k → k {\displaystyle f^{\#}:k\to k} is injective. Thus, the dominant map f induces an inj... | Regular map (algebraic geometry) | 0.779266 |
94,168 | A regular map whose inverse is also regular is called biregular, and the biregular maps are the isomorphisms of algebraic varieties. Because regular and biregular are very restrictive conditions – there are no non-constant regular functions on projective varieties – the concepts of rational and birational maps are wide... | Regular map (algebraic geometry) | 0.779266 |
94,169 | In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called a regular map. A morphism from an algebraic variety to the affine line is also called a regular function. | Regular map (algebraic geometry) | 0.779266 |
94,170 | The technical condition that G has no f-torsion is referred to by the authors as "f-regularity". In fact, one can state a stronger version of this theorem. Let M(A) be the category of A-modules (whose morphisms are A-module homomorphisms) and let Mf(A) be the full subcategory of f-regular modules. In this notation, we ... | Beauville–Laszlo theorem | 0.779265 |
94,171 | Theorem: Given A, f, F, G, and φ as above, if G has no f-torsion, then there exist an A-module M and isomorphisms α: M f → ∼ F β: M ⊗ A A ^ → ∼ G {\displaystyle \alpha \colon M_{f}{\xrightarrow {\sim }}F\qquad \beta \colon M\otimes _{A}{\hat {A}}{\xrightarrow {\sim }}G} consistent with the isomorphism φ: φ is equal to ... | Beauville–Laszlo theorem | 0.779265 |
94,172 | {\displaystyle \phi \colon G_{f}{\xrightarrow {\sim }}F\otimes _{A_{f}}{\hat {A}}_{f}=F\otimes _{A}{\hat {A}}.} Now consider the converse situation: we have a ring A and an element f, and two modules: an Af-module F and an Â-module G, together with an isomorphism φ as above. Geometrically, we are given a scheme X and b... | Beauville–Laszlo theorem | 0.779265 |
94,173 | (Despite the notational temptation to write G = M ^ {\displaystyle G={\widehat {M}}} , meaning the completion of the A-module M at the ideal Af, unless A is noetherian and M is finitely-generated, the two are not in fact equal. This phenomenon is the main reason that the theorem bears the names of Beauville and Laszlo;... | Beauville–Laszlo theorem | 0.779265 |
94,174 | The intersection of Df and Spec  is a "punctured infinitesimal neighborhood" D0 about (f), equal to Spec  ⊗A Af = Spec Âf. Suppose now that we have an A-module M; geometrically, M is a sheaf on Spec A, and we can restrict it to both the principal open set Df and the infinitesimal neighborhood Spec Â, yielding an Af-m... | Beauville–Laszlo theorem | 0.779265 |
94,175 | Although it has implications in algebraic geometry, the theorem is a local result and is stated in its most primitive form for commutative rings. If A is a ring and f is a nonzero element of A, then we can form two derived rings: the localization at f, Af, and the completion at Af, Â; both are A-algebras. In the follow... | Beauville–Laszlo theorem | 0.779265 |
94,176 | In mathematics, the Beauville–Laszlo theorem is a result in commutative algebra and algebraic geometry that allows one to "glue" two sheaves over an infinitesimal neighborhood of a point on an algebraic curve. It was proved by Arnaud Beauville and Yves Laszlo (1995). | Beauville–Laszlo theorem | 0.779265 |
94,177 | In neuroscience, a sensory map in the brain which has overlapping stimulus coding (e.g. location and quality) is called an orthogonal map. | Orthogonal (computing) | 0.779264 |
94,178 | In 1994 he was elected Fellow of the Royal Society of Edinburgh (FRSE) and Fellow of the Royal Society of Chemistry (FRSC), and in 2016 he was elected Member of Academia Europaea (MAE). He is currently a Member of Council of the Engineering and Physical Sciences Research Council (EPSRC). He has held a Leverhulme Trust ... | Martin Schröder (chemist) | 0.779262 |
94,179 | He has been a visiting professor at the University of Toronto, Canada, the University of Otago, Dunedin, New Zealand and the Université Louis Pasteur, Strasbourg, France, and has published over 540 publications and patents. His early independent research focussed on the chemistry of transition metal thioether and aza m... | Martin Schröder (chemist) | 0.779262 |
94,180 | After postdoctoral fellowships at the ETH, Zürich with Albert Eschenmoser, funded by a Royal Society-Swiss National Foundation Fellowship, and at the University of Cambridge with Jack Lewis, he was appointed to a senior demonstratorship at the University of Edinburgh in 1982. He was subsequently promoted to lecturer, r... | Martin Schröder (chemist) | 0.779262 |
94,181 | Martin Schröder was born in Taplow, Buckinghamshire of Estonian refugee parents in 1954, and was educated at Montem Primary School and Slough Grammar School. He is first in family to attend university, and was awarded a Bachelor of Science degree in chemistry from the University of Sheffield in 1975 and a PhD from Impe... | Martin Schröder (chemist) | 0.779262 |
94,182 | Martin Schröder in an inorganic chemist. He is Vice President and Dean for the Faculty of Science and Engineering and Professor of Chemistry in the Department of Chemistry at the University of Manchester since June 2015. He served previously as Executive Dean of the Faculty of Science from 2011 to 2015 and Professor of... | Martin Schröder (chemist) | 0.779262 |
94,183 | These changes of ISP-1 resulted in continued improvements in the profile of the compound.To further improve the activity and safety the side chain was shortened from 28 carbons to 14 carbons marked orange on illustration 1. To find the lead optimization a part of the fatty acid side chain was replaced with 1,4-disubsti... | Sphingosine-1-phosphate receptor modulator | 0.779261 |
94,184 | is a cover-to-cover English translation of the Russian peer-reviewed mathematics journal Sibirskii Matematicheskii Zhurnal, a publication of the Sobolev Institute of Mathematics of the Siberian Division of the Russian Academy of Sciences (Novosibirsk). Sibirskii Matematicheskii Zhurnal was established in 1960 and the S... | Siberian Mathematical Journal | 0.77926 |
94,185 | According to Georgia Institute of Technology research, prey and predator roles have cycles where the prey population may increase, thereby causing the predator population to increase as well. But sometimes the predator population overwhelms the prey to the point of devastating the prey population, subsequently resultin... | Predator–prey reversal | 0.779257 |
94,186 | A model called the Lotka–Volterra model after its founders, Alfred J. Lotka and Vito Volterra, focuses on studies of ecology and demographics while attempting to explain why certain plant and animal interactions occur the way they do. Although created in the early 1900s, this model has proven to be flexible and adaptab... | Predator–prey reversal | 0.779257 |
94,187 | NodeXL has been used by news outlets such as Foreign Policy to visualize the structure of conversations about political topics as well as by organizations like the World Bank to analyze voting data. NodeXL has been used as an analytical tool in dozens of research papers in the social, information, and computer sciences... | NodeXL | 0.779257 |
94,188 | Since SRISK is measured in terms of currency, the industry aggregates may also be related to Gross Domestic Product. As such one obtains a measure of domestic, systemically important banks. The SRISK Systemic Risk Indicator is computed automatically on a weekly basis and made available to the community. For the US mode... | Systemic risk | 0.779256 |
94,189 | In mathematics, the Abel–Jacobi map is a construction of algebraic geometry which relates an algebraic curve to its Jacobian variety. In Riemannian geometry, it is a more general construction mapping a manifold to its Jacobi torus. The name derives from the theorem of Abel and Jacobi that two effective divisors are lin... | Abel–Jacobi theorem | 0.779256 |
94,190 | The Heritage team is composed of amateur and professional astronomers, as well as people with backgrounds outside astronomy, and emphasizes the aesthetic nature of Hubble images. The Heritage Project is granted a small amount of time to observe objects which, for scientific reasons, may not have images taken at enough ... | Hubble Space Telescope | 0.779256 |
94,191 | An orbiting solar telescope was launched in 1962 by the United Kingdom as part of the Ariel programme, and in 1966 NASA launched the first Orbiting Astronomical Observatory (OAO) mission. OAO-1's battery failed after three days, terminating the mission. It was followed by Orbiting Astronomical Observatory 2 (OAO-2), wh... | Hubble Space Telescope | 0.779256 |
94,192 | After it was approved, she became the program scientist, setting up the steering committee in charge of making astronomer needs feasible to implement and writing testimony to Congress throughout the 1970s to advocate continued funding of the telescope. Her work as project scientist helped set the standards for NASA's o... | Hubble Space Telescope | 0.779256 |
94,193 | Roughly speaking, Littlewood's proof consists of Dirichlet's approximation theorem to show that sometimes many terms have about the same argument. In the event that the Riemann hypothesis is false, the argument is much simpler, essentially because the terms li ( x ρ ) {\displaystyle \operatorname {li} (x^{\rho })} fo... | Skewes's number | 0.779254 |
94,194 | In number theory, Skewes's number is any of several large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number x {\displaystyle x} for which π ( x ) > li ( x ) , {\displaystyle \pi (x)>\operatorname {li} (x),} where π is the prime-counting function and li is t... | Skewes's number | 0.779254 |
94,195 | László Lovász (1975) gives a simplified proof of Brooks' theorem. If the graph is not biconnected, its biconnected components may be colored separately and then the colorings combined. If the graph has a vertex v with degree less than Δ, then a greedy coloring algorithm that colors vertices farther from v before closer... | Brooks’ theorem | 0.779253 |
94,196 | The adverse effects include but are not limited to shortage of food, shootings of birds and nests, and removal of nestlings from nests. Due to the advances of cattle-breeding, involving indoor breeding and the utilization of dead cattle, many necrophagous birds, such as the Eurasian griffon, are losing access to nutrit... | Necrophage | 0.779252 |
94,197 | The research at the Centre focuses on: Astrochemistry Astrophysical masers The Cosmic Microwave Background Galaxy formation and evolution Gravitational lenses Theoretical astrophysics and cosmology Planetary nebulae Pulsars Stellar physics (including star formation and solar plasmas) Development of telescope receivers | Jodrell Bank Centre for Astrophysics | 0.779251 |
94,198 | The SKA will be the largest telescope in the world - construction is expected to start at the end of this decade. The JBCA is part of the School of Physics and Astronomy. The current director is Professor Michael Garrett. | Jodrell Bank Centre for Astrophysics | 0.779251 |
94,199 | The Jodrell Bank Centre for Astrophysics at the University of Manchester, is among the largest astrophysics groups in the UK. It includes the Jodrell Bank Observatory, the MERLIN/VLBI National Facility, and the Jodrell Bank Visitor Centre. The centre was formed after the merger of the Victoria University of Manchester ... | Jodrell Bank Centre for Astrophysics | 0.779251 |
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