MS: Well, I think-, well, usually, you're not prone to generalisation, Steve, and that was a very, very broad generalisation.
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Of course, as with any broad generalisation about religion, you can't push it too far.
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One big and global generalisation which would have been helpful is almost missing from "Good Economics".
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To make a huge generalisation, the practice of religion tends to make people either more proud or more humble.
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So I think, really, what we're talking about is building teams, Steve, not-, not your reference, not your-, your sweeping generalisation.
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He acknowledged that algorithms can lead to mistakes and over-generalisation, but said that should just open up opportunities for traditional fund managers.
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Bolton wants to win this boxing fight at any cost, so he is willing to use all rhetorical means necessary: exaggeration, generalisation and over-simplification.
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"One often hears that SWFs from emerging market and developing countries are non-transparent and consequently not as accountable ... The scoreboard results refute this generalisation," the authors wrote.
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For Europe, Israel's generalisation of the terrorism threat presents a problem, said Andrea Frontini, an analyst at the European Policy Centre, because it risks over-politicising counter-terrorism cooperation.
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Maybe that's a big generalisation, but finding them at the point I did it was very intense, very emotional music that spoke to a lot of the misfit kids out there.
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Brian Fagan's is the first general survey of its kind, and it is packed with intriguing details (like the Chinese training cormorants to catch fish for them) as well as with persuasive generalisation.
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That is a good example of a machine-learning phenomenon called "generalisation", in which neural networks can handle scenarios that are conceptually similar, but different in the specifics, to the ones they are trained on.
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It's probably a fair generalisation that most European church-goers are a lot more moderate and sensible than the far-rightists who are trying to woo them, but also stand a bit to the right of their own clergy and bishops.
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To begin with, offence can easily be caused by anything that sounds like a generalisation about a category of people from a certain race, ethnicity or religion along the lines of "the trouble with these people is that they......" And the offence is hugely magnified when it is implied because of their alleged characteristic, the people concerned don't quite qualify as members of the national family.
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Just as the André–Oort conjecture can be seen as a generalisation of the Manin–Mumford conjecture, so too the André–Oort conjecture can be generalised. The usual generalisation considered is the Zilber–Pink conjecture, an open problem which combines a generalisation of the André–Oort conjecture proposed by Richard Pink. and conjectures put forth by Boris Zilber...
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There is a generalisation of Serge Lang to abelian varieties (Lang, Abelian Varieties).
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Therefore, some degree of generalisation is unavoidable, even on the most literal view: the choice is simply between mechanical generalisation and intelligent generalisation. Regarding Islamic laws, there are various issues faced by Muslims in their daily lives. e.g. doubts in salāt and their corrections, conditions which invalidate a fast and the relevant compensations, rulings vis à vis correctness or incorrectness of various social and business practices e.g. Investing in Mutual Funds, Use of alcohol based perfumes and medicines, etc.
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Hermitian varieties are in a sense a generalisation of quadrics, and occur naturally in the theory of polarities.
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In mathematics, Pascal's simplex is a generalisation of Pascal's triangle into arbitrary number of dimensions, based on the multinomial theorem.
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The fractional Brownian motion is a Gaussian process whose covariance function is a generalisation of that of the Wiener process.
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Generalisation decrement is a type of learning that falls under the umbrella of associative learning. It is a concept where both animals and humans base current circumstances of learning through past events if the conditions of such an event is similar to the present one. The importance of applying associative theories to the context of human learning is due to the human behaviour of generalisation. Generalisation is when an association between a stimulus and a response will be generalised or applied superficially to a stimulus that is similar to the initial one.
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Vis versa, the generalisation rule is part of the definition of HM's type system and the implicit all-quantification a consequence.
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Ivor Grattan- Guinness finds the effectiveness in question eminently reasonable and explicable in terms of concepts such as analogy, generalisation and metaphor.
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Dyadic compacta and spaces satisfy the Suslin condition, and were introduced by Russian mathematician Pavel Alexandrov. Polyadic spaces are generalisation of dyadic spaces.
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In mathematics, the Arakawa–Kaneko zeta function is a generalisation of the Riemann zeta function which generates special values of the polylogarithm function.
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Commissioning by primary care groups or trusts is an internal market-like idea that could be seen as generalisation of general practitioner fundholding.
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The generalisation rule is also worth for closer look. Here, the all-quantification implicit in the premise \Gamma \vdash e : \sigma is simply moved to the right hand side of \vdash_D in the conclusion. This is possible, since \alpha does not occur free in the context. Again, while this makes the generalisation rule plausible, it is not really a consequence.
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Paul Yiu's generalisation of Gossard triangle. This generalisation is due to Paul Yiu. Let P be any point in the plane of the triangle ABC different from its centroid G. :Let the line PG meet the sidelines BC, CA and AB at X, Y and Z respectively. :Let the centroids of the triangles AYZ, BZX and CXY be Ga, Gb and Gc respectively.
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In mathematics, the Hasse derivative is a generalisation of the derivative which allows the formulation of Taylor's theorem in coordinate rings of algebraic varieties.
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The block Wiedemann algorithm for computing kernel vectors of a matrix over a finite field is a generalisation of an algorithm due to Don Coppersmith.
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In mathematics, the Nagata–Biran conjecture, named after Masayoshi Nagata and Paul Biran, is a generalisation of Nagata's conjecture on curves to arbitrary polarised surfaces.
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Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
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Cambridge: Cambridge University Press., the theory of generalizationNørreklit H., Nørreklit L. & Mitchell F. (2016). Understanding practice generalisation – opening the research/practice gap, Qualitative Research in Accounting & Management. 13, 3, 278-302.
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These crowdsourced projects aim at solving some issues raised by the replication crisis, more specifically by assessing the replicability of studies and generalisation of the results to other populations and contexts.
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Generalisation of "The aforementioned rules deal only with the international search and international preliminary examination and therefore not with the regional European search or examination." in Decision T 164/92, Reasons 8.4.
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Such a generalisation does not reflect actual past legal practice, but can only show which general principles are likely to have been typical for many (but not necessarily all) early Celtic laws.
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Cambridge: Cambridge University Press. requires that G =⟨S⟩. The definition presented above is a common generalisation of this. From a computational perspective, the formal definition of a straight-line program has some advantages.
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In statistical mechanics, the eight-vertex model is a generalisation of the ice-type (six-vertex) models; it was discussed by Sutherland, and Fan & Wu, and solved by Baxter in the zero-field case.
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Maximum entropy is a sufficient updating rule for radical probabilism. Richard Jeffrey's probability kinematics is a special case of maximum entropy inference. However, maximum entropy is not a generalisation of all such sufficient updating rules.
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In mathematics, and especially differential geometry and algebraic geometry, a stable principal bundle is a generalisation of the notion of a stable vector bundle to the setting of principal bundles. The concept of stability for principal bundles was introduced by Annamalai Ramanathan for the purpose of defining the moduli space of G-principal bundles over a Riemann surface, a generalisation of earlier work by David Mumford and others on the moduli spaces of vector bundles.Ramanathan, A., 1975. Stable principal bundles on a compact Riemann surface.
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In mathematics, the Fraňková-Helly selection theorem is a generalisation of Helly's selection theorem for functions of bounded variation to the case of regulated functions. It was proved in 1991 by the Czech mathematician Dana Fraňková.
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In mathematics, Schinzel's hypothesis H is one of the most famous open problems in the topic of number theory. It is a very broad generalisation of conjectures such as the twin prime conjecture named after Andrzej Schinzel.
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Behavioral medicine includes understanding the clinical applications of learning principles such as reinforcement, avoidance, generalisation, and discrimination, and of cognitive-social learning models as well, such as the cognitive-social learning model of relapse prevention by Marlatt.
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A lot more attention has been focused on the one-dimensional Dirac delta prime potential recently. A point on the one-dimensional line can be considered both as a point and as surface; as a point marks the boundary between two regions. Two generalisations of the Dirac delta-function to higher dimensions have thus been made: the generalisation to a multidimensional point, as well as the generalisation to a multidimensional surface. The former generalisations are known as point interactions, whereas the latter are known under different names, e.g.
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Thomas Murray MacRobert (4 April 1884, in Dreghorn, Ayrshire – 1 November 1962, in Glasgow) was a Scottish mathematician. He became professor of mathematics at the University of Glasgow and introduced the MacRobert E function, a generalisation of the generalised hypergeometric series.
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In mathematics, and particularly in category theory, a polygraph is a generalisation of a directed graph. It is also known as a computad. They were introduced as "polygraphs" by Albert BurroniA. Burroni. Higher-dimensional word problems with applications to equational logic.
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For a given number of phases, the Erlang distribution is the phase type distribution with smallest coefficient of variation. The hypoexponential distribution is a generalisation of the Erlang distribution by having different rates for each transition (the non-homogeneous case).
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DHOST theories were introduced in 2015 by David Langlois and Karim Noui. They are a generalisation of Beyond Horndeski (or GLPV) theories, which are themselves a generalisation of Horndeski theories. The equations of motion of Horndeski theories contain only two derivatives of the metric and the scalar field, and it was believed that only equations of motion of this form would not contain an extra scalar degree of freedom (which would lead to unwanted ghosts). However, it was first shown that a class of theories now named Beyond Horndeski also avoided the extra degree of freedom.
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Beacon Press, 1993.Teodor. "The nature and logic of the peasant economy 1: A Generalisation". The Journal of Peasant Studies 1.1 (1973): 63–80Alves, Leonardo Marcondes (2018). Give us this day our daily bread: The moral order of Pentecostal peasants in South Brazil.
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In mathematics, in the field of ring theory, a lattice is a module over a ring which is embedded in a vector space over a field, giving an algebraic generalisation of the way a lattice group is embedded in a real vector space.
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Then there exists a color c and an infinite set D of natural numbers, all colored with c, such that every finite sum over D also has color c. The Milliken–Taylor theorem is a common generalisation of Hindman's theorem and Ramsey's theorem.
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He also introduced the notion of coherence length in superconductors in his proposal for the non-local generalisation of the London equationsF. London, Superfluids, Vol. I: Macroscopic Theory of Superconductivity (Dover Publications, New York, 1961), p. 152. concerning electrodynamics in superfluids and superconductors.
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Computational thinking means thinking or solving problems like computer scientists. CT refers to thought processes required in understanding problems and formulating solutions. CT involves logic, assessment, patterns, automation, and generalisation. Career readiness can be integrated into learning and teaching environments in multiple ways.
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Hadronic matter can refer to 'ordinary' baryonic matter, made from hadrons (Baryons and mesons), or quark matter (a generalisation of atomic nuclei), i.e. the 'low' temperature QCD matter. It includes degenerate matter and the result of high energy heavy nuclei collisions. Distinct from dark matter.
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Subsequently, in April 2014, the Polymath project 8 lowered the bound to k ≤ 246. With current methods k ≤ 6 is the best attainable, and in fact k ≤ 12 and k ≤ 6 follow using current methods if the Elliott–Halberstam conjecture and its generalisation, respectively, hold.
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This is not the only way of generating such a conformal projection. For example, the 'exact' version of the Transverse Mercator projection on the ellipsoid is not a double projection. (It does, however, involve a generalisation of the conformal latitude to the complex plane).
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In probability and statistics, the class of exponential dispersion models (EDM) is a set of probability distributions that represents a generalisation of the natural exponential family.Jørgensen, B. (1987). Exponential dispersion models (with discussion). Journal of the Royal Statistical Society, Series B, 49 (2), 127-162.
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Cambridge Studies in Advanced Mathematics, Vol. 117 (2009) who only worked on schemes over fields. A generalisation to schemes over Dedekind schemes is due to Carlo Gasbarri.C. Gasbarri, Heights of Vector Bundles and the Fundamental Group Scheme of a Curve, Duke Mathematical Journal, Vol.
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Polyadic spaces were first studied by S. Mrówka in 1970 as a generalisation of dyadic spaces. The theory was developed further by R. H. Marty, János Gerlits and Murray G. Bell, the latter of whom introduced the concept of the more general centred spaces.
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Plural voting is the practice whereby one person might be able to vote multiple times in an election. It is not to be confused with a plurality voting system which does not necessarily involve plural voting. Weighted voting is a generalisation of plural voting.
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In particular, Gauss counted the number of solutions of the expression of an integer as a sum of three squares, and this is a generalisation of yet another result of Legendre,A.-M. Legendre, Hist. et Mém. Acad. Roy. Sci. Paris, 1785, pp. 514–515.
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In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem, about complex manifolds, which is itself a generalisation of the classical Riemann–Roch theorem for line bundles on compact Riemann surfaces. Riemann–Roch type theorems relate Euler characteristics of the cohomology of a vector bundle with their topological degrees, or more generally their characteristic classes in (co)homology or algebraic analogues thereof. The classical Riemann–Roch theorem does this for curves and line bundles, whereas the Hirzebruch–Riemann–Roch theorem generalises this to vector bundles over manifolds.
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Supermembranes are hypothesized objects that live in the 11-dimensional theory called M-Theory and should also exist in 11-dimensional supergravity. Supermembranes are a generalisation of superstrings to another dimension. Supermembranes are 2-dimensional surfaces. For example, they can be spherical or shaped like a torus.
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Certain heavy metals are known to enhance inter- system crossing (ISC). Generally, diamagnetic metals promote ISC and have a long triplet lifetime. In contrast, paramagnetic species deactivate excited states, reducing the excited-state lifetime and preventing photochemical reactions. However, exceptions to this generalisation include copper octaethylbenzochlorin.
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Traditionally these intellectual principles were analysed through the procedures of Aristotelian logic. The Akhbari scholar Muhammad Amin al- Asterabadi criticised this approach, arguing that since the alleged general principles were arrived at by way of generalisation from the existing practical rules, the whole process was circular.
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In mathematics, the analytic subgroup theorem is a significant result in modern transcendental number theory. It may be seen as a generalisation of Baker's theorem on linear forms in logarithms. Gisbert Wüstholz proved it in the 1980s. It marked a breakthrough in the theory of transcendental numbers.
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Ariadne was, in the main, well received. "An exception to the generalisation that all modern epics are tedious," declared The Cambridge Review. "Its plot is a model of epic construction in its compactness, directness and speed." Julian Bell, review of Ariadne in The Cambridge Review, 10 February 1933.
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The problem of the role class model is the redundancy, for example the method getName is visible in all of the role classes described in Figure 4. If this is considered inconvenient, the role class generalisation model as defined in Modelling Roles is a possible way to go.
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In functional analysis and quantum measurement theory, a positive operator- valued measure (POVM) is a measure whose values are positive semi-definite operators on a Hilbert space. POVMs are a generalisation of projection-valued measures (PVM) and, correspondingly, quantum measurements described by POVMs are a generalisation of quantum measurement described by PVMs (called projective measurements). In rough analogy, a POVM is to a PVM what a mixed state is to a pure state. Mixed states are needed to specify the state of a subsystem of a larger system (see purification of quantum state); analogously, POVMs are necessary to describe the effect on a subsystem of a projective measurement performed on a larger system.
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According to Snow Patrol frontman Gary Lightbody: "It's near the beginning of a dangerously reliant relationship. The album is full of songs like this. Rather than a break-up record this is a make-up record. That is a massive generalisation but it is a more positive record than the last".
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Occasionally, a quasimetric is defined as a function that satisfies all axioms for a metric with the possible exception of symmetry:E.g. Steen & Seebach (1995).. The name of this generalisation is not entirely standardized. This book calls them "semimetrics". That same term is also frequently used for two other generalizations of metrics.
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Linnik obtained numerous results concerning infinitely divisible distributions. In particular, he proved the following generalisation of Cramér's theorem: any divisor of a convolution of Gaussian and Poisson random variables is also a convolution of Gaussian and Poisson. He has also coauthored the book on the arithmetics of infinitely divisible distributions.
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Industry analysts suggest that this trend plays a bigger part in driving upgrades to existing computer systems than technological advancements. A second meaning of the term of system requirements, is a generalisation of this first definition, giving the requirements to be met in the design of a system or sub-system.
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One generalisation of the problem involves multivariate normal distributions with unknown covariance matrices, and is known as the multivariate Behrens–Fisher problem.Belloni & Didier (2008) The nonparametric Behrens–Fisher problem does not assume that the distributions are normal. Tests include the Cucconi test of 1968 and the Lepage test of 1971.
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In mathematics, a topological space is usually defined in terms of open sets. However, there are many equivalent characterizations of the category of topological spaces. Each of these definitions provides a new way of thinking about topological concepts, and many of these have led to further lines of inquiry and generalisation.
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For yet another type of relevant generalisation, Hans Zantema suggested the notion of a k-semi-transitive orientation refining the notion of a semi- transitive orientation . The idea here is restricting ourselves to considering only directed paths of length not exceeding k while allowing violations of semi-transitivity on longer paths.
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This genus contains a number of species with different habits making generalisation difficult. The overall body size varies widely, ranging from 60–160 mm. The tail is 60–180 mm and the weight is recorded from 12–90 g. They inhabit a wide variety of habitats from rainforests to plains and grasslands.
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Some books claim the Packington Fishers descended from Nicholas, but this is recognised as a generalisation. Nicholas's line mostly descended to Sir Thomas Fisher of London and Middlesex and to Robert Fisher of Chetwynd. Another line from Osbernus led to Saint John Fisher, Bishop of Rochester, beheaded by Henry VIII in 1535.
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It was Maurice Fréchet who, in 1906, had distilled the essence of the Bolzano–Weierstrass property and coined the term compactness to refer to this general phenomenon (he used the term already in his 1904 paperFrechet, M. 1904. Generalisation d'un theorem de Weierstrass. Analyse Mathematique. which led to the famous 1906 thesis).
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Ubiquitous command and control posits for military organizations, a generalisation from hierarchies to networks which allows for the use of hierarchies when they are appropriate, and non-hierarchical networks when they are inappropriate. This includes the notion of mission agreement, to support "edge in" as well as "top-down" flow of intent.
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In mathematics, the notion of an (exact) dimension function (also known as a gauge function) is a tool in the study of fractals and other subsets of metric spaces. Dimension functions are a generalisation of the simple "diameter to the dimension" power law used in the construction of s-dimensional Hausdorff measure.
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A further generalisation allows k glasses (instead of two) out of the n glasses to be examined at each turn. An algorithm can be found to ring the bell in a finite number of turns as long as k ≥ (1 − 1/p)n where p is the greatest prime factor of n.
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A multi-component generalisation of the Kundu-Ekchaus equation (3), known as Radhakrishnan, Kundu and Laskshmanan (RKL) equation was proposed in nonlinear optics for fiber optics communication through soliton pulses in a birefringent non-Kerr medium and analysed subsequently for its exact soliton solution and other aspects in a series of papers.
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In his work The Unconscious as Infinite Sets, Matte Blanco proposes that the structure of the unconscious can be summarised by the principles of Generalisation and of Symmetry: 1) The principle of Generalization: here logic does not take account of individuals as such, it deals with them only as members of classes, and of classes of classes. 2) The principle of Symmetry: here the logic treats the converse of any relation as identical to it; that is, it deals with relationships as symmetrical'.Matte Blanco, I. (1975) The Unconscious as Infinite Sets. London: Karmac"Matte- Blanco, Ignacio" While the principle of Generalisation might be compatible with conventional logic, discontinuity is introduced by the principle of Symmetry under which relationships are treated as symmetrical, or reversible.
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Foxwell is known for his attack on the legacy of Ricardo,Henry, John F. (1982–83). "Comment: Ideology in the Ricardo Debate," Journal of Post Keynesian Economics, Vol. 5, No. 2, pp. 314–317. who he says introduced a “wrong twist” into mainstream economics, giving "modern socialism its fancied scientific basis" through his "crude generalisation".
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Probability kinetics is not the only sufficient updating rule for radical probabilism. Others have been advocated including E. T. Jaynes' maximum entropy principle, and Skyrms' principle of reflection. It turns out that probability kinematics is a special case of maximum entropy inference. However, maximum entropy is not a generalisation of all such sufficient updating rules.
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In mathematics and statistics, the quasi-arithmetic mean or generalised f-mean is one generalisation of the more familiar means such as the arithmetic mean and the geometric mean, using a function f. It is also called Kolmogorov mean after Russian mathematician Andrey Kolmogorov. It is a broader generalization than the regular generalized mean.
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They sought to address rack-rents, tithe collection, excessive priests' dues, evictions and other oppressive acts. As a result, they targeted landlords and tithe collectors. Over time, Whiteboyism became a general term for rural violence connected to secret societies. Because of this generalisation, the historical record for the Whiteboys as a specific organisation is unclear.
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There exists a generalisation of the first and second Blanuša snark in two infinite families of snarks of order 8n+10 denoted B_n^1 and B_n^2. The Blanuša snarks are the smallest members those two infinite families.Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, pp.
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Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics. It can be viewed as a generalisation of histogram density estimation with improved statistical properties. Apart from histograms, other types of density estimators include parametric, spline, wavelet and Fourier series.
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After 1930, the interests of Riesz shifted to potential theory and partial differential equations. He made use of "generalised potentials", generalisations of the Riemann–Liouville integral. In particular, Riesz discovered the Riesz potential, a generalisation of the Riemann–Liouville integral to dimension higher than one. In the 1940s and 1950s, Riesz worked on Clifford algebras.
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In mathematics of stochastic systems, the Runge–Kutta method is a technique for the approximate numerical solution of a stochastic differential equation. It is a generalisation of the Runge–Kutta method for ordinary differential equations to stochastic differential equations (SDEs). Importantly, the method does not involve knowing derivatives of the coefficient functions in the SDEs.
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The connection with the Euler characteristic χ suggests the correct generalisation: the 2n-sphere has no non-vanishing vector field for . The difference between even and odd dimensions is that, because the only nonzero Betti numbers of the m-sphere are b0 and bm, their alternating sum χ is 2 for m even, and 0 for m odd.
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In mathematics, the fundamental group scheme is a group scheme canonically attached to a scheme over a Dedekind scheme (e.g. the spectrum of a field or the spectrum of a discrete valuation ring). It is a generalisation of the étale fundamental group. Although its existence was conjectured by Alexander Grothendieck, the first construction is due to Madhav Nori,M.
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Indexed containers (also known as dependent polynomial functors) are a generalisation of containers, which can represent a wider class of types, such as vectors (sized lists). The element type (called the input type) is indexed by shape and position, so it can vary by shape and position, and the extension (called the output type) is also indexed by shape.
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A local volatility model, in mathematical finance and financial engineering, is one that treats volatility as a function of both the current asset level S_t and of time t . As such, a local volatility model is a generalisation of the Black–Scholes model, where the volatility is a constant (i.e. a trivial function of S_t and t ).
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Another generalisation is to calculate the number of coprime integer solutions m, n to the inequality :m^2+n^2\leq r^2.\, This problem is known as the primitive circle problem, as it involves searching for primitive solutions to the original circle problem.J. Wu, On the primitive circle problem, Monatsh. Math. 135 (2002), pp.69-81.
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The non-local kernel proposed by Pippard, inferred on the basis of Chambers' non-local generalisation of Ohm's law) can be deduced within the framework of the BCS (Bardeen, Cooper and Schrieffer) theory of superconductivityJ. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of Superconductivity, Phys. Rev., Vol. 108, No. 5, pp. 1175–1204 (1957).
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Some strong paradigms such as fara, fer, for, fyriValfrid Lindgren, Jonas, Orbok över Burträskmålet, 1940, pg. 39 ’fara’, pg. 60 ’hava’ are preserved, though often there is a generalisation of the singular present or infinitive and plural present, thus , , or , . Due to vowel-balance, even with a generalised paradigm there can be a vowel difference between and .
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The circulation problem and its variants are a generalisation of network flow problems, with the added constraint of a lower bound on edge flows, and with flow conservation also being required for the source and sink (i.e. there are no special nodes). In variants of the problem, there are multiple commodities flowing through the network, and a cost on the flow.
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The geometrical construction for locating the Yff center of congruence has an interesting generalization. The generalisation begins with an arbitrary point P in the plane of a triangle ABC. Then points D, E, F are taken on the sides BC, CA, AB such that ∠BPD = ∠DPC, ∠CPE = ∠EPA, and ∠APF = ∠FPB. The generalization asserts that the lines AD, BE, CF are concurrent.
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These edges will be bidirectional if both languages borrow from one another. A tree is thus a simple network, however there are many other types of network. A phylogentic network is one where the taxa are represented by nodes and their evolutionary relationships are represented by branches. Another type is that based on splits, and is a combinatorial generalisation of the split tree.
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In mathematics, a subalgebra is a subset of an algebra, closed under all its operations, and carrying the induced operations. "Algebra", when referring to a structure, often means a vector space or module equipped with an additional bilinear operation. Algebras in universal algebra are far more general: they are a common generalisation of all algebraic structures. "Subalgebra" can refer to either case.
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In Bayesian statistics, a credible interval is an interval within which an unobserved parameter value falls with a particular probability. It is an interval in the domain of a posterior probability distribution or a predictive distribution.Edwards, Ward, Lindman, Harold, Savage, Leonard J. (1963) "Bayesian statistical inference in psychological research". Psychological Review, 70, 193-242 The generalisation to multivariate problems is the credible region.
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This shows the fundamental importance of the fluctuation theorem (FT) in nonequilibrium statistical mechanics. The FT gives a generalisation of the second law of thermodynamics. It is then easy to prove the second law inequality and the Kawasaki identity. When combined with the central limit theorem, the FT also implies the Green–Kubo relations for linear transport coefficients close to equilibrium.
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In mathematics and computer science, a rational series is a generalisation of the concept of formal power series over a ring to the case when the basic algebraic structure is no longer a ring but a semiring, and the indeterminates adjoined are not assumed to commute. They can be regarded as algebraic expressions of a formal language over a finite alphabet.
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Brivaracetam is used to treat partial-onset seizures with or without secondary generalisation, in combination with other antiepileptic drugs. No data are available for its effectiveness and safety in patients younger than 16 years.Drugs.com: for Briviact. It is sometimes prescribed as an alternative to the drug's analogue levetiracetam to avoid neuropsychiatric adverse effects such as mood swings, anxiety, emotional lability, and depression.
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The multivariate stable distribution is a multivariate probability distribution that is a multivariate generalisation of the univariate stable distribution. The multivariate stable distribution defines linear relations between stable distribution marginals. In the same way as for the univariate case, the distribution is defined in terms of its characteristic function. The multivariate stable distribution can also be thought as an extension of the multivariate normal distribution.
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With his Russian colleague, V.I. Yukalov, he has introduced the "quantum decision theory", with the goal of establishing an holistic theoretical framework of decision making. Based on the mathematics of Hilbert spaces, it embraces uncertainty and enjoys non-additive probability for the resolution of complex choice situations with interference effects. The use of Hilbert spaces constitutes the simplest generalisation of the probability theory axiomatised by KolmogorovA.N. Kolmogorov.
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However, this filter is not a member of the class of filters, general mn-type image filters, which are a generalisation of m-type filters. Rather, it is a double application of the m-derived process and for those filters the arbitrary parameters are usually designated m1, m2, m3 etc., rather than m, m', m as here. The importance of the filter lies in its impedance properties.
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In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic to an open set in a Banach space (a more involved and formal definition is given below). Banach manifolds are one possibility of extending manifolds to infinite dimensions. A further generalisation is to Fréchet manifolds, replacing Banach spaces by Fréchet spaces.
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Generalisation of J is not part of this system, as it plays no part in the desired property. We call (Λ, Ρ) a Green's pair. There are several choices of partial transformation semigroup that yield the original relations. One example would be to take Λ to be the semigroup of all left translations on S1, restricted to S, and Ρ the corresponding semigroup of restricted right translations.
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The unitary group of a quadratic module is a generalisation of the linear algebraic group U just defined, which incorporates as special cases many different classical algebraic groups. The definition goes back to Anthony Bak's thesis.Bak, Anthony (1969), "On modules with quadratic forms", Algebraic K-Theory and its Geometric Applications (editors--Moss R. M. F., Thomas C. B.) Lecture Notes in Mathematics, Vol. 108, pp.
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It is a logical instrument for demonstrating language vagueness, undue generalisation, conflation, pseudo-agreement and effective communication. Næss developed a simplified, practical textbook embodying these advantages, entitled Communication and Argument, which became a valued introduction to this pragmatics or "language logic", and was used over many decades as a sine qua non for the preparatory examination at the University of Oslo, later known as "Examen Philosophicum" ("Exphil").
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In the technological theory of social production, the growth of output, measured in money units, is related to achievements in technological consumption of labour and energy. This theory is based on concepts of classical political economy and neo-classical economics and appears to be a generalisation of the known economic models, such as the neo-classical model of economic growth and input-output model.
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His study focused on the applications of functional analysis to quantum theory. He worked on the physical interpretation of non-self adjoining operators and he developed a theory of open systems which are physical systems which interact with the environment. These research is compiled in two monographs. After moving to Tbilissi with his family, he started working on a generalisation of the Cayley-Hamilton theorem.
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Goal programming is a branch of multiobjective optimization, which in turn is a branch of multi-criteria decision analysis (MCDA). It can be thought of as an extension or generalisation of linear programming to handle multiple, normally conflicting objective measures. Each of these measures is given a goal or target value to be achieved. Deviations are measured from these goals both above and below the target.
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It's too complicated. The Catholic version is familiar, more Irish somehow'. Wilson exempts Leitch from the generalisation, and finds a compelling, harsh metre in Gilchrist, a novel about a 'smudged' Ulster preacher on the run to Spain with the church funds. 'Leitch writes brilliantly about the kind of pessimistic Protestant lust that threatens to burst Gilchrist at the seams [...] Leitch has given us a definitive Protestant portrait.
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In mathematics, the André–Oort conjecture is an open problem in Diophantine geometry, a branch of number theory, that builds on the ideas found in the Manin–Mumford conjecture, which is now a theorem. A prototypical version of the conjecture was stated by Yves André in 1989. and a more general version was conjectured by Frans Oort in 1995.. The modern version is a natural generalisation of these two conjectures.
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A simple substitution, or more accurately a mono-alphabetic substitution ciphers is a generalisation of the Caesar cipher where there can be any permutation of the alphabet. For the simple substitution cipher there are 26! possible keys, which is huge, but even then, the cipher insecure. After methods of solution were demonstrated on the blackboard, each student was given practice problems, based on clear English text, to solve for themself.
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Nonuniform sampling is a branch of sampling theory involving results related to the Nyquist–Shannon sampling theorem. Nonuniform sampling is based on Lagrange interpolation and the relationship between itself and the (uniform) sampling theorem. Nonuniform sampling is a generalisation of the Whittaker–Shannon–Kotelnikov (WSK) sampling theorem. The sampling theory of Shannon can be generalized for the case of nonuniform samples, that is, samples not taken equally spaced in time.
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A related problem is to determine the lowest-energy arrangement of identically interacting points that are constrained to lie within a given surface. The Thomson problem deals with the lowest energy distribution of identical electric charges on the surface of a sphere. The Tammes problem is a generalisation of this, dealing with maximising the minimum distance between circles on sphere. This is analogous to distributing non-point charges on a sphere.
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It includes "delightful passages ... both of natural description and of inspired reflection [yet] it affects a system without having an intelligible clue to one." The Excursion suffers from what Hazlitt highlights as a major flaw in contemporary poetry in general: it tends toward excessive generalisation, "abstraction". Thus it ends up being both inadequate philosophy and poetry that has detached itself from the essence and variety of life.Park 1971, p. 233.
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Graph theory is the branch of mathematics dealing with graphs. In network analysis, graphs are used extensively to represent a network being analysed. The graph of a network captures only certain aspects of a network; those aspects related to its connectivity, or, in other words, its topology. This can be a useful representation and generalisation of a network because many network equations are invariant across networks with the same topology.
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In the case of a central simple algebra A over a field F, the reduced norm provides a generalisation of the determinant giving a map K1(A) → F∗ and SK1(A) may be defined as the kernel. Wang's theorem states that if A has prime degree then SK1(A) is trivial,Gille & Szamuely (2006) p.47 and this may be extended to square-free degree.Gille & Szamuely (2006) p.
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In computer programming, predicate dispatch is a generalisation of multiple dispatch ("multimethods") that allows the method to call to be selected at runtime based on arbitrary decidable logical predicates and/or pattern matching attached to a method declaration. Raku supports predicate dispatch using "where" clauses that can execute arbitrary code against any function or method parameter. Julia has a package for it with PatternDispatch.jl but otherwise natively supports multiple dispatch.
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Weighted round robin (WRR) is a scheduling algorithm used in networks to schedule data flows, but also used to schedule processes. Weighted round robin is a generalisation of Round-robin scheduling. It serves a set of queues or tasks. Whereas round-robin cycles over the queues/tasks and gives one service opportunity per cycle, weighted round robin offers to each a fixed number of opportunities, the work weight, set at configuration.
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The unitary highest weight representations of these algebras have a classification analogous to that for the Virasoro algebra, with a continuum of representations together with an infinite discrete series. The existence of these discrete series was conjectured by Daniel Friedan, Zongan Qiu, and Stephen Shenker (1984). It was proven by Peter Goddard, Adrian Kent and David Olive (1986), using a supersymmetric generalisation of the coset construction or GKO construction.
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In number theory, a Hecke character is a generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of L-functions larger than Dirichlet L-functions, and a natural setting for the Dedekind zeta-functions and certain others which have functional equations analogous to that of the Riemann zeta-function. A name sometimes used for Hecke character is the German term Größencharakter (often written Grössencharakter, Grossencharacter, etc.).
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The naming of the theorem as Petr–Douglas–Neumann theorem, or as the PDN-theorem for short, is due to Stephen B Gray. This theorem has also been called Douglas's theorem, the Douglas–Neumann theorem, the Napoleon–Douglas–Neumann theorem and Petr's theorem. The PDN-theorem is a generalisation of the Napoleon's theorem which is concerned about arbitrary triangles and of the van Aubel's theorem which is related to arbitrary quadrilaterals.
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Seppo Linnainmaa in 1970 is said to have developed the Backpropagation Algorithm but the origins of the algorithm go back to the 1960s with many contributors. It is a generalisation of the least mean squares algorithm in the linear perceptron and the Delta Learning Rule. It implements gradient descent search through the space possible network weights, iteratively reducing the error, between the target values and the network outputs.
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In the 2019 general election, many of these constituencies uncharacteristically supported the Conservative Party. Press coverage described the red wall as having "turned blue", "crumbled", "fallen", or having been "demolished". The red wall metaphor has been criticised as a generalisation. Lewis Baston argues that the "red wall" is politically diverse, and includes bellwether seats which swung with the national trend, as well as former mining and industrial seats which show a more unusual shift.
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In quantum field theory, a Slavnov–Taylor identity is the non-Abelian generalisation of a Ward–Takahashi identity, which in turn is an identity between correlation functions that follows from the global or gauged symmetries of a theory, and which remains valid after renormalization. The identity was originally discovered by Gerard 't Hooft , and it is named after Andrei Slavnov and John C. Taylor who rephrased the identity to hold off the mass shell. .
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For example, they showed that: ::All computable functions on the real numbers are the unique solutions to a single finite system of algebraic formulae. The second generalisation, created with Viggo Stoltenberg-Hansen, focuses on implementing data types using approximations contained in the ordered structures of domain theory. The general theories have been applied as formal methods in microprocessor verifications, data types, and tools for volume graphics and modelling excitable media including the heart.
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Later, composers such as Gottfried Michael Koenig and Iannis Xenakis had computers generate the sounds of the composition as well as the score. Koenig produced algorithmic composition programs which were a generalisation of his own serial composition practice. This is not exactly similar to Xenakis' work as he used mathematical abstractions and examined how far he could explore these musically. Koenig's software translated the calculation of mathematical equations into codes which represented musical notation.
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In constructive mathematics, a pseudo-order is a constructive generalisation of a linear order to the continuous case. The usual trichotomy law does not hold in the constructive continuum because of its indecomposability, so this condition is weakened. A pseudo-order is a binary relation satisfying the following conditions: # It is not possible for two elements to each be less than the other. That is, \forall x,y: eg\;(x < y \;\wedge\; y < x).
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Graefe studied physics at the University of Kaiserslautern, completing her doctorate there in 2009. Her dissertation, Quantum-classical correspondence for a Bose-Hubbard dimer and its non- Hermitian generalisation, was supervised by Hans-Jürgen Korsch. She did postdoctoral research in quantum chaos at the University of Bristol before joining Imperial College. There, she was supported as a L'Oréal-UNESCO For Women in Science Fellow prior to her position as a Royal Society University Research Fellow.
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In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to multiple-input and multiple-output (MIMO) systems.Chen, p. 1038 The matrix relates the outputs of the system to its inputs. It is a particularly useful construction for linear time-invariant (LTI) systems because it can be expressed in terms of the s-plane.
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The size of the budget has implications for the promotional mix, the media mix and market coverage. As a generalisation, very large budgets are required to sustain national television campaigns. Advertisers with tight budgets may forced to use less effective media alternatives. However, even advertisers with small budgets may be able to incorporate expensive main media, by focusing on narrow geographic markets, buying spots in non-peak time periods and carefully managing advertising schedules.
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"Not many songwriters begin a melody with a major seventh interval; perhaps that's why there are few memorable examples."Neely, Blake (2009). Piano For Dummies, p.201. . However, two songs provide exceptions to this generalisation: Cole Porter's "I love you" (1944) opens with a descending major seventh and Jesse Harris's "Don't Know Why",(made famous by Norah Jones in her 2002 debut album, Come Away with Me), starts with an ascending one.
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It provides useful identities relating the solutions, and is also useful as a part of other techniques such as the method of variation of parameters. It is especially useful for equations such as Bessel's equation where the solutions do not have a simple analytical form, because in such cases the Wronskian is difficult to compute directly. A generalisation to first-order systems of homogeneous linear differential equations is given by Liouville's formula.
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For example, the meat cabinet at the supermarket might use a merchandise outpost to suggest a range of marinades or spice rubs to complement particular cuts of meat. As a generalisation, merchandise outposts are updated regularly so that they maintain a sense of novelty."Interior Design Tips: 6 Steps to Design Your Retail Shop", Retail Shop Design According to Ziethaml et al., layout affects how easy or difficult it is to navigate through a system.
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In 1897, he defended his doctoral thesis On a generalisation of a continuous fraction. He was an Invited Speaker of the ICM in 1904 at Heidelberg. By the time he was only 40 years of age, Voronoy started feeling sick to his stomach. He wrote in his diary: > I am making great progress with the question under study [indefinite > quadratic forms]; however, at the same time my health is becoming worse and > worse.
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Grünbaum's rotationally symmetrical 5-set Venn diagram, 1975 Grünbaum also devised a multi-set generalisation of Venn diagrams. He was an editor and a frequent contributor to Geombinatorics. Grünbaum's classic monograph Convex Polytopes, first published in 1967, became the main textbook on the subject. His monograph Tilings and Patterns, coauthored with G. C. Shephard, helped to rejuvenate interest in this classic field, and has proved popular with nonmathematical audiences, as well as with mathematicians.
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In mathematics, the Yoneda lemma is arguably the most important result in category theory. It is an abstract result on functors of the type morphisms into a fixed object. It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a miniature category with just one object and only isomorphisms). It allows the embedding of any category into a category of functors (contravariant set-valued functors) defined on that category.
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Hart's most important contribution was contained in his paper Extension of Terquem's theorem respecting the circle which bisects three sides of a triangle (1861). Hart wrote this paper after an carrying out an investigation suggested by William Rowan Hamilton in a letter to Hart. In addition, Hart corresponded with George Salmon on the same topic. This paper contains the result which became known as Hart's Theorem, which is a generalisation of Feuerbach's Theorem.
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In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function. The hyperbolic secant function is equivalent to the reciprocal hyperbolic cosine, and thus this distribution is also called the inverse-cosh distribution. Generalisation of the distribution gives rise to the Meixner distribution, also known as the Natural Exponential Family - Generalised Hyperbolic Secant or NEF-GHS distribution.
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85 opened study of the Turing degrees of the recursively enumerable sets which turned out to possess a very complicated and non-trivial structure. He also has a significant contribution in the subject of mass problems where he introduced the generalisation of Turing degrees, called "Muchnik degrees" in his work On Strong and Weak Reducibilities of Algorithmic Problems published in 1963.A. A. Muchnik, On strong and weak reducibility of algorithmic problems.
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Contrary to his father, who allegedly only accepted facts and had little interest in generalisation, Le Sage was primarily interested in general and abstract principles. Le Sage took the first regular education at the college of Geneva, where he was friendly connected with Jean-André Deluc. Besides philosophy, he studied mathematics under Gabriel Cramer, and physics under Jean-Louis Calandrini. Later he decided to study medicine in Basel, where he also gave private lessons in mathematics.
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A Lagged Fibonacci generator (LFG or sometimes LFib) is an example of a pseudorandom number generator. This class of random number generator is aimed at being an improvement on the 'standard' linear congruential generator. These are based on a generalisation of the Fibonacci sequence. The Fibonacci sequence may be described by the recurrence relation: :S_n = S_{n-1} + S_{n-2} Hence, the new term is the sum of the last two terms in the sequence.
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Akhbārīs claim to follow Hadith directly, without the need for generalisation, or of finding the reason for the decision. This, according to Usulis, is a logical impossibility. Hadith takes the form of case law, that is to say the narration of decisions taken in a concrete situation. To "follow" such a decision one must know which features of the situation are or are not relevant to the decision, as exactly the same set of facts will never occur twice.
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A square pyramid and the associated abstract polytope. In mathematics, an abstract polytope is an algebraic partially ordered set or poset which captures the combinatorial properties of a traditional polytope without specifying purely geometric properties such as angles or edge lengths. A polytope is a generalisation of polygons and polyhedra into any number of dimensions. An ordinary geometric polytope is said to be a realization in some real N-dimensional space, typically Euclidean, of the corresponding abstract polytope.
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Regge calculus is a formalism which chops up a Lorentzian manifold into discrete 'chunks' (four- dimensional simplicial blocks) and the block edge lengths are taken as the basic variables. A discrete version of the Einstein–Hilbert action is obtained by considering so-called deficit angles of these blocks, a zero deficit angle corresponding to no curvature. This novel idea finds application in approximation methods in numerical relativity and quantum gravity, the latter using a generalisation of Regge calculus.
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Let k be a positive integer. In number theory, Jordan's totient function J_k(n) of a positive integer n is the number of k-tuples of positive integers all less than or equal to n that form a coprime (k+1)-tuple together with n. (A tuple is coprime if and only if it is coprime as a set.) This is a generalisation of Euler's totient function, which is J_1. The function is named after Camille Jordan.
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KonkaniDisambiguation: Konkani is a name given to a group of several cognate dialects spoken along the narrow strip of land called Konkan, on the west coast of India. This is, however, somewhat an over-generalisation. Geographically, Konkan is defined roughly as the area between the river Damanganga to the north and river Kali to the south, the north-south length being approx. 650 km and east-west breadth about 50 km, going to 96 km in some places.
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This is within a constant factor of the t = O(d\log_2 n) lower bound. Chan et al. (2011) also provided a generalisation of COMP to a simple noisy model, and similarly produced an explicit performance bound, which was again only a constant (dependent on the likelihood of a failed test) above the corresponding lower bound. In general, the number of tests required in the Bernoulli noise case is a constant factor larger than in the noiseless case.
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Sample truncation is a pervasive issue in quantitative social sciences when using observational data, and consequently the development of suitable estimation techniques has long been of interest in econometrics and related disciplines. In the 1970s, James Heckman noted the similarity between truncated and otherwise non-randomly selected samples, and developed the Heckman correction. Estimation of truncated regression models is usually done via parametric maximum likelihood method. More recently, various semi- parametric and non-parametric generalisation were proposed in the literature, e.g.
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Example bigraph with sharing in which the node of control M is shared by the two nodes of control S. This is represented by M being in the intersection of the two S-nodes. Bigraphs with sharing are a generalisation of Milner's formalisation that allows for a straightforward representation of overlapping or intersecting spatial locations. In bigraphs with sharing, the place graph is defined as a directed acyclic graph (DAG), i.e. prnt is a binary relation instead of a map.
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Geodat was unusual in the 1980s in that the software was often given away free, while data downloads or tapes were charged. Geodat set out a quality management process for digitisation covering acquisition, cataloguing, map stability, transformation algorithms, merging and node coalescing. Geodat also set out a quality standard for comparing digitised maps with source maps, based on using generalisation and interpolation against a maximum orthogonal offset distance. Originally delivered as five large tapes, MundoCart was burned on CD-ROM in 1987.
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CMAC, represented as a 2D space In the adjacent image, there are two inputs to the CMAC, represented as a 2D space. Two quantising functions have been used to divide this space with two overlapping grids (one shown in heavier lines). A single input is shown near the middle, and this has activated two memory cells, corresponding to the shaded area. If another point occurs close to the one shown, it will share some of the same memory cells, providing generalisation.
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It was further elaborated by Ronald L. Iman and coauthors in 1981. Detailed computer codes and manuals were later published. In the context of statistical sampling, a square grid containing sample positions is a Latin square if (and only if) there is only one sample in each row and each column. A Latin hypercube is the generalisation of this concept to an arbitrary number of dimensions, whereby each sample is the only one in each axis-aligned hyperplane containing it.
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"They abound in speeches and descriptions, such as he himself might make either to himself or others, lolling on his couch of a morning, but do not carry the reader out of the poet's mind to the scenes and events recorded."Hazlitt 1930, vol. 11, p. 74. In this Byron follows most of his contemporaries, as Hazlitt argued in many of his critical writings, the tendency of the age, in imaginative literature as well as philosophical and scientific, being toward generalisation, "abstraction".
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Blockbusting is a solved combinatorial game introduced in 1987 by Elwyn Berlekamp illustrating a generalisation of overheating. The analysis of Blockbusting may be used as the basis of a strategy for the combinatorial game of Domineering. Blockbusting is a partisan game for two players known as Red and Blue (or Right and Left) played on an n \times 1 strip of squares called "parcels". Each player, in turn, claims and colors one previously unclaimed parcel until all parcels have been claimed.
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These can be defined with either the input orientation (fix outputs and measure maximal possible reduction in inputs) or the output orientation (fix inputs and measure maximal possible expansion in outputs). A generalisation of these is the so-called Directional Distance Function, where one can select any direction (or orientation) for measuring the production efficiency. The most popular for estimating production efficiency are Data Envelopment Analysis Charnes, A., Cooper, W., and Rhodes, E. (1978). Measuring the efficiency of decision making units.
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The eight-vertex model, which has also been exactly solved, is a generalisation of the (square-lattice) six- vertex model: to recover the six-vertex model from the eight-vertex model, set the energies for vertex configurations 7 and 8 to infinity. Six-vertex models have been solved in some cases for which the eight-vertex model has not; for example, Nagle's solution for the three-dimensional KDP model and Yang's solution of the six-vertex model in a horizontal field.
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It then coordinates action towards social integration and solidarity. Finally, communicative action is the process through which people form their identities. Following Weber again, an increasing complexity arises from the structural and institutional differentiation of the lifeworld, which follows the closed logic of the systemic rationalisation of our communications. There is a transfer of action co-ordination from 'language' over to 'steering media', such as money and power, which bypass consensus- oriented communication with a 'symbolic generalisation of rewards and punishments'.
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Just because all successful endeavour engenders pleasure does not necessarily entail that pleasure is the sole objective of all endeavour. He uses William James's analogy to illustrate this fallacy: although an ocean liner always consumes coal on its trans-Atlantic voyages, it is unlikely that the sole purpose of these voyages is coal consumption. The third argument, unlike the first two, contains no non sequitur that Feinberg can see. He nevertheless adjudges that such a sweeping generalisation is unlikely to be true.
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He is usually credited with the proof of the Pythagorean theorem using similar triangles. However, Thabit Ibn Qurra (AD 901), an Arab mathematician, had produced a generalisation of the Pythagorean theorem applicable to all triangles six centuries earlier. It is a reasonable conjecture that Wallis was aware of Thabit's work. Wallis was also inspired by the works of Islamic mathematician Sadr al-Tusi, the son of Nasir al-Din al- Tusi, particularly by al-Tusi's book written in 1298 on the parallel postulate.
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The first step was to clarify the concept of the reaction field introduced by Onsager. Once this had been done it was possible to see how a generalisation of Onsager's equation for ε(0) to the frequency-dependent case would be obtained. Such an equation was published in a short note in 1964 in the Proceedings of the Physical Society of London 84, 616. The justification of this equation had first appeared in an Electrical Research report, which Scaife published in 1965.
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As a result of a faulty generalisation, it is very often incorrectly said that cumulonimbus and the updraughts under them are always turbulent. This fallacy originates from the fact that cumulonimbus are actually extremely turbulent at high altitude, and therefore, one might falsely deduce that cumulonimbus are turbulent at all altitudes. Reliable studies and glider pilots' experience have demonstrated that updraughts under cumulonimbus were generally smooth. As seen above, updraughts under a cumulonimbus are often dynamic and thus will be very smooth.
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The second chapter gives a broad generalisation of how differences in physical traits occur between the inhabitants of the various climes (a demarcation based on latitude). Communities that live close to the equator, for example, are described as having black skins, small statures, and thick woolly hair, as a protective response to the burning heat of that location. By contrast, communities that have settled in high northern regions are defined by their colder environment and its greater share of moisture.
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Modulations which have an order of 4 and above usually are termed as higher-order modulations. Examples of these are quadrature phase shift keying (QPSK) and its generalisation as m-ary quadrature amplitude modulation (m-QAM). Because existing computers and automation systems are based on binary logic most of the modulations have an order which is a power of two: 2, 4, 8, 16, etc. In principle, however, the order of a modulation can be any integer greater than one.
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One specific type of Framework is called the "Enterprise Reference Architecture." According to Bernus & Noran (2010): > Several proposals emerged in those two decades – e.g. PERA (Williams 1994), > CIMOSA (CIMOSA Association 1996), ARIS (Scheer 1999), GRAI-GIM (Doumeingts, > 1987), and the IFIP-IFAC Task Force, based on a thorough review of these as > well as their proposed generalisation (Bernus and Nemes, 1994) developed > GERAM (IFIP-IFAC Task Force, 1999) which then became the basis of > ISO15704:2000 “Industrial automation systems – Requirements for enterprise- > reference architectures and methodologies”...
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Ever since Tarkhanov's findings demonstrated sexual arousal in frogs to result from the state of seminal vesicles, the attempted elucidation of their role in other animals' sexual behaviour has been the object of experimental effort. No generalisation has yet appeared, however. The study performed by Beach & Wilson (University of California, Berkeley) in 1964 discovered that these glands do not participate in the regulation of sexual arousal of male rats in the similar manner. Whether the regularity observed in frogs is applicable to humans remains unknown.
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In queueing theory, a discipline within the mathematical theory of probability, the M/M/c queue (or Erlang–C model) is a multi-server queueing model. In Kendall's notation it describes a system where arrivals form a single queue and are governed by a Poisson process, there are c servers and job service times are exponentially distributed. It is a generalisation of the M/M/1 queue which considers only a single server. The model with infinitely many servers is the M/M/∞ queue.
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In mathematical logic, the cut rule is an inference rule of sequent calculus. It is a generalisation of the classical modus ponens inference rule. Its meaning is that, if a formula A appears as a conclusion in one proof and a hypothesis in another, then another proof in which the formula A does not appear can be deduced. In the particular case of the modus ponens, for example occurrences of man are eliminated of Every man is mortal, Socrates is a man to deduce Socrates is mortal.
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As a very broad generalisation, many politicians seek certainties and facts whilst scientists typically offer probabilities and caveats. However, politicians' ability to be heard in the mass media frequently distorts the scientific understanding by the public. Examples in Britain include the controversy over the MMR inoculation, and the 1988 forced resignation of a government minister, Edwina Currie, for revealing the high probability that battery eggs were contaminated with Salmonella."1988: Egg industry fury over salmonella claim", "On This Day," BBC News, December 3, 1988.
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However, example a represents a number of Old English clauses with object following a non-finite verb form, with the superficial structure verb-subject-verb object. A more substantial number of clauses contain a single finite verb form followed by an object, superficially verb-subject-object. Again, a generalisation is captured by describing these as subject–verb–object (SVO) modified by V2. Thus Old English can be described as intermediate between SOV languages (like German and Dutch) and SVO languages (like Swedish and Icelandic).
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They are typically divided into low and high grade, typically corresponding to indolent (slow-growing) lymphomas and aggressive lymphomas, respectively. As a generalisation, indolent lymphomas respond to treatment and are kept under control (in remission) with long-term survival of many years, but are not cured. Aggressive lymphomas usually require intensive treatments, with some having a good prospect for a permanent cure.Merck Manual home edition, Non-Hodgkin Lymphomas Prognosis and treatment depends on the specific type of lymphoma as well as the stage and grade.
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By addressing communication deficits, the person will be supported to express their needs and feelings by means other than challenging behavior. Working from the premise that people with autism are predominantly visual learners, intervention strategies are based around physical and visual structure, schedules, work systems and task organization. Individualized systems aim to address difficulties with communication, organisation, generalisation, concepts, sensory processing, change and relating to others. Whereas some interventions focus on addressing areas of weakness, the TEACCH approach works with existing strengths and emerging skill areas.
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See Charles-Adolphe Wurtz's report on the Karlsruhe Congress. Nevertheless, many chemists found equivalent weights to be a useful tool even if they did not subscribe to atomic theory. Equivalent weights were a useful generalisation of Joseph Proust's law of definite proportions (1794) that enabled chemistry to become a quantitative science. French chemist Jean-Baptiste Dumas (1800–84) became one of the more influential opponents of atomic theory, after having embraced it earlier in his career, but was a staunch supporter of equivalent weights.
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These filters are electrical wave filters designed using the image method. They are an invention of Otto Zobel at AT&T; Corp..Zobel, 1923 They are a generalisation of the m-type filter in that a transform is applied that modifies the transfer function while keeping the image impedance unchanged. For filters that have only one stopband there is no distinction with the m-type filter. However, for a filter that has multiple stopbands, there is the possibility that the form of the transfer function in each stopband can be different.
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Because Williams is an empiricist he thinks science can inform metaphysics, especially cosmology, as characterised above. He also thinks logic as well as common sense tell us something about time and our concept of time. He notes that science and logic and the canonical logic of science do not have any temporal reference. When a scientist proposes a law of nature or a scientific generalisation the scientist proposes a statement that holds regardless of temporal reference to a certain time or to the fact that a certain time is now.
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The Greeks had dealt with geometric quantities but had not thought of them in the same way as numbers to which the usual rules of arithmetic could be applied. By introducing arithmetical operations on quantities previously regarded as geometric and non-numerical, Thabit started a trend which led eventually to the generalisation of the number concept. In some respects, Thabit is critical of the ideas of Plato and Aristotle, particularly regarding motion. It would seem that here his ideas are based on an acceptance of using arguments concerning motion in his geometrical arguments.
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Such approaches are often implemented in social network analysis software such as UCInet. The alternative approach is to use cliques of fixed size k. The overlap of these can be used to define a type of k-regular hypergraph or a structure which is a generalisation of the line graph (the case when k=2) known as a "Clique graph". The clique graphs have vertices which represent the cliques in the original graph while the edges of the clique graph record the overlap of the clique in the original graph.
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Interaction nets are a graphical model of computation devised by Yves Lafont in 1990 as a generalisation of the proof structures of linear logic. An interaction net system is specified by a set of agent types and a set of interaction rules. Interaction nets are an inherently distributed model of computation in the sense that computations can take place simultaneously in many parts of an interaction net, and no synchronisation is needed. The latter is guaranteed by the strong confluence property of reduction in this model of computation.
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Ethologists expressed concern about the adequacy of some of the research on which attachment theory was based, particularly the generalisation to humans from animal studies. Schur, discussing Bowlby's use of ethological concepts (pre-1960) commented that these concepts as used in attachment theory had not kept up with changes in ethology itself. Ready to explore Ethologists and others writing in the 1960s and 1970s questioned the types of behaviour used as indications of attachment, and offered alternative approaches. For example, crying on separation from a familiar person was suggested as an index of attachment.
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This species is an armored catfish which, since the 1990s, has started to be offered quite regularly as an aquarium fish under the name "Pineapple Pleco". The term "pleco" here is of course a popular generalisation, as taxonomy has never placed this fish in the former genus Plecostomus. The armour is also pleasantly spiked along the sides of the fish, which causes the pineapple resemblance celebrated in the commercial name of the species. Additionally, under the L-number system used by hobbyists, it as referred to as both L152 and L095.
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Fleiss' kappa is a generalisation of Scott's pi statistic, a statistical measure of inter-rater reliability. It is also related to Cohen's kappa statistic and Youden's J statistic which may be more appropriate in certain instances. Whereas Scott's pi and Cohen's kappa work for only two raters, Fleiss' kappa works for any number of raters giving categorical ratings, to a fixed number of items. It can be interpreted as expressing the extent to which the observed amount of agreement among raters exceeds what would be expected if all raters made their ratings completely randomly.
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In some cases the fundamental group of a manifold can be shown to be linear by using representations coming from a geometric structure. For example, all closed surfaces of genus at least 2 are hyperbolic Riemann surfaces. Via the uniformisation theorem this gives rise to a representation of its fundamental group in the isometry group of the hyperbolic plane, which is isomorphic to PSL2(R) and this realises the fundamental group as a Fuchsian group. A generalisation of this construction is given by the notion of a (G,X)-structure on a manifold.
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MGS (a General Model of Simulation) is a domain-specific language used for specification and simulation of dynamical systems with dynamical structure, developed at IBISC (Computer Science, Integrative Biology and Complex Systems) at Université d'Évry Val-d'Essonne (University of Évry). MGS is particularly aimed at modelling biological systems. The MGS computational model is a generalisation of cellular automata, Lindenmayer systems, Paun systems and other computational formalisms inspired by chemistry and biology. It manipulates collections - sets of positions, filled with some values, in a lattice with a user-defined topology.
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Colour plate from the War of the Rebellion Atlas depicting Union and Confederate uniforms It is generally supposed that Union soldiers wore blue uniforms and Confederate soldiers wore grey ones. However, this was only a generalisation. Both the Union and the Confederacy drew up uniform regulations, but as a matter of practical reality neither side was able to fully equip its men at the outbreak of the war. Existing state units and quickly raised volunteer regiments on both sides wore a wide variety of styles and colours in the early stages of the war.
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2007 Today Carménère is rarely used, with Château Clerc Milon, a fifth growth Bordeaux, being one of the few to still retain Carménère vines. As of July 2019, Bordeaux wineries authorized the use of four new red grapes to combat temperature increases in Bordeaux. These newly approved grapes are Marselan, Touriga Nacional, Castets, and Arinarnoa. As a very broad generalisation, Cabernet Sauvignon (Bordeaux's second-most planted grape variety) dominates the blend in red wines produced in the Médoc and the rest of the left bank of the Gironde estuary.
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He also condemned Social Darwinism as an erroneous generalisation of Darwin's Theory of Evolution. In the early years of the reign of Alexander II, Pobedonostsev maintained, though keeping aloof from the Slavophiles, that Western institutions were radically bad in themselves and totally inapplicable to Russia since they had no roots in Russian history and culture and did not correspond to the spirit of Russian people. In that period, he contributed several papers to Alexander Herzen's radical periodical Voices from Russia. He denounced democracy as "the insupportable dictatorship of vulgar crowd".
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It is a powerful generalisation of Hamiltonian theory that remains valid for curved spacetime. The equations for the Hamiltonian involve only six degrees of freedom described by g_{rs},p^{rs} for each point of the surface on which the state is considered. The g_{m0} (m = 0, 1, 2, 3) appear in the theory only through the variables g^{r0}, ( -{g^{00}} ) ^{-1/2} which occur as arbitrary coefficients in the equations of motion. There are four constraints or weak equations for each point of the surface x^0 = constant.
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With angle A opposite side a and angle B opposite side b, some triangles with B=2A are generated byDeshpande,M. N., "Some new triples of integers and associated triangles", Mathematical Gazette 86, November 2002, 464–466. :a=n^2, \, :b = mn \, :c=m^2 - n^2, \, with integers m, n such that 0 < n < m < 2n. All triangles with B = 2A (whether integer or not) haveWillson, William Wynne, "A generalisation of the property of the 4, 5, 6 triangle", Mathematical Gazette 60, June 1976, 130–131. a(a+c)=b^2.
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Randall Swingler, a communist poet, responded to the essay in an article "The Right to Free Expression" in Polemic 5. Swingler did not disagree that a writer must stand against the enemies of intellectual liberty nor with Orwell's case against the totalitarian cultural policies of the Soviet Union. His complaint was that it was impossible to reply to Orwell's essay because it was pitched at a level of "intellectual swashbucklery", persuasive generalisation and unsupported assertion. Orwell had a marginal column in which he responded to what he saw as a personal attack with sarcastic comments.
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A slightly more explicit description of the kuṭṭaka was later given in Brahmagupta, Brāhmasphuṭasiddhānta, XVIII, 3–5 (in , cited in ). this is a procedure close to (a generalisation of) the Euclidean algorithm, which was probably discovered independently in India. Āryabhaṭa seems to have had in mind applications to astronomical calculations. Brahmagupta (628 CE) started the systematic study of indefinite quadratic equations—in particular, the misnamed Pell equation, in which Archimedes may have first been interested, and which did not start to be solved in the West until the time of Fermat and Euler.
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The particle filter could be considered as a generalisation of the UKF. It makes no assumptions about the distributions of the errors in the filter and neither does it require the equations to be linear. Instead it generates a large number of random potential states ("particles") and then propagates this "cloud of particles" through the equations, resulting in a different distribution of particles at the output. The resulting distribution of particles can then be used to calculate a mean or variance, or whatever other statistical measure is required.
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If the Gaussian curvature of a surface is everywhere positive, then the Euler characteristic is positive so is homeomorphic (and therefore diffeomorphic) to . If in addition the surface is isometrically embedded in , the Gauss map provides an explicit diffeomorphism. As Hadamard observed, in this case the surface is convex; this criterion for convexity can be viewed as a 2-dimensional generalisation of the well-known second derivative criterion for convexity of plane curves. Hilbert proved that every isometrically embedded closed surface must have a point of positive curvature.
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It is a generalisation of earlier neural network architectures such as recurrent neural networks, liquid-state machines and echo-state networks. Reservoir computing also extends to physical systems that are not networks in the classical sense, but rather continuous systems in space and/or time: e.g. a literal "bucket of water" can serve as a reservoir that performs computations on inputs given as perturbations of the surface. The resultant complexity of such recurrent neural networks was found to be useful in solving a variety of problems including language processing and dynamic system modeling.
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In mathematics, particularly category theory, a representable functor is a certain functor from an arbitrary category into the category of sets. Such functors give representations of an abstract category in terms of known structures (i.e. sets and functions) allowing one to utilize, as much as possible, knowledge about the category of sets in other settings. From another point of view, representable functors for a category C are the functors given with C. Their theory is a vast generalisation of upper sets in posets, and of Cayley's theorem in group theory.
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On 29 July 1985, Wrigley was appointed as Director-General of ASIO. As Director-General, Wrigley implemented several rigorous reforms to the agency, continuing a trend begun under the directorship of Sir Edward Woodward by further reducing the level of specialisation and increasing generalisation. He also oversaw the moving of ASIO's headquarters from Melbourne to Canberra in 1986. A number of experienced officers resigned from ASIO after Wrigley abolished benefits and allowances for senior officers moving to Canberra, which had been negotiated with the Hawke Government under his predecessor Harvey Barnett.
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If G is cyclic then the transfer takes any element y of G to y[G:H]. A simple case is that seen in the Gauss lemma on quadratic residues, which in effect computes the transfer for the multiplicative group of non-zero residue classes modulo a prime number p, with respect to the subgroup {1, −1}. One advantage of looking at it that way is the ease with which the correct generalisation can be found, for example for cubic residues in the case that p − 1 is divisible by three.
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Rough sets can be also defined, as a generalisation, by employing a rough membership function instead of objective approximation. The rough membership function expresses a conditional probability that x belongs to X given \textstyle \R. This can be interpreted as a degree that x belongs to X in terms of information about x expressed by \textstyle \R. Rough membership primarily differs from the fuzzy membership in that the membership of union and intersection of sets cannot, in general, be computed from their constituent membership as is the case of fuzzy sets.
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The simplest possible generalisation of a graph of groups is a 2-dimensional complex of groups. These are modeled on orbifolds arising from cocompact properly discontinuous actions of discrete groups on 2-dimensional simplicial complexes that have the structure of CAT(0) spaces. The quotient of the simplicial complex has finite stabiliser groups attached to vertices, edges and triangles together with monomorphisms for every inclusion of simplices. A complex of groups is said to be developable if it arises as the quotient of a CAT(0) simplicial complex.
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In mathematics, in particular abstract algebra and topology, a homotopy Lie algebra (or L_\infty-algebra) is a generalisation of the concept of a differential graded Lie algebra. To be a little more specific, the Jacobi identity only holds up to homotopy. Therefore, a differential graded Lie algebra can be seen as a homotopy Lie algebra where the Jacobi identity holds on the nose. These homotopy algebras are useful in classifying deformation problems over characteristic 0 in deformation theory because deformation functors are classified by quasi-isomorphism classes of L_\infty-algebras.
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Among all closed manifolds with non-positive sectional curvature, flat manifolds are characterized as precisely those with an amenable fundamental group. This is a consequence of the Adams-Ballmann theorem (1998), which establishes this characterization in the much more general setting of discrete cocompact groups of isometries of Hadamard spaces. This provides a far-reaching generalisation of Bieberbach's theorem. The discreteness assumption is essential in the Adams-Ballmann theorem: otherwise, the classification must include symmetric spaces, Bruhat-Tits buildings and Bass-Serre trees in view of the "indiscrete" Bieberbach theorem of Caprace-Monod.
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An alternate, though related, approach is to apply a local volatility model, where volatility is treated as a deterministic function of both the current asset level S_t and of time t . As such, a local volatility model is a generalisation of the Black–Scholes model, where the volatility is a constant. The concept was developed when Bruno Dupire and Emanuel Derman and Iraj Kani noted that there is a unique diffusion process consistent with the risk neutral densities derived from the market prices of European options. See #Development for discussion.
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However, some generalisation of Beijing cuisine can be characterised as follows: Foods that originated in Beijing are often snacks rather than main courses, and they are typically sold by small shops or street vendors. There is emphasis on dark soy paste, sesame paste, sesame oil and scallions, and fermented tofu is often served as a condiment. In terms of cooking techniques, methods relating to different ways of frying are often used. There is less emphasis on rice as an accompaniment as compared to many other regions in China, as local rice production in Beijing is limited by the relatively dry climate.
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An extreme version of crimping was shanghaiing, when seamen "would be rendered senseless – either by drink, drugs or blunt instrument – and then were signed-on to a ship". Folksinger and author Stan Hugill published, in 1967, a book on this topic, Sailortown, but his account has been criticized for "relying almost exclusively on generalisation, titillation and shock- value". During the nineteenth century, throughout the world, religious denominations established institutions in sailortowns to cater to the spiritual needs of sailors. One example was the Liverpool Sailors' Home project which was launched at a public meeting called by Liverpool’s Mayor in October 1844.
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In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix. Specifically, a complex number λ is said to be in the spectrum of a bounded linear operator T if T-\lambda I is not invertible, where I is the identity operator. The study of spectra and related properties is known as spectral theory, which has numerous applications, most notably the mathematical formulation of quantum mechanics. The spectrum of an operator on a finite-dimensional vector space is precisely the set of eigenvalues.
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Marc R. Wilkins is an Australian scientist who is credited with the defining the concept of the proteome. Wilkins is a Professor in the School of Biotechnology and Biomolecular Sciences at the University of New South Wales, Sydney. Wilkins coined the term proteome in 1994 whilst developing the concept as a PhD student at Macquarie University, Sydney, Australia, describing it as the 'PROTein complement expressed by a genOME'. The term is a generalisation of the concept of the genome to encompass the set of all proteins that can be produced through the genome through alternative splicing and post- transcriptional modification of messenger RNA.
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For example, they showed that ::On any discrete data type, functions are definable as the unique solutions of small finite systems of equations if, and only if, they are computable by algorithms. The results combined techniques of universal algebra and recursion theory, including term rewriting and Matiyasevich's theorem. For the other problems, he and his co-workers have developed two independent disparate generalisations of classical computability/recursion theory, which are equivalent for many continuous data types. The first generalisation, created with Jeffrey Zucker, focuses on imperative programming with abstract data types and covers specifications and verification using Hoare logic.
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Rényi proved, using the large sieve, that there is a number K such that every even number is the sum of a prime number and a number that can be written as the product of at most K primes. Chen's theorem, a strengthening of this result, shows that the theorem is true for K = 2, for all sufficiently large even numbers. The case K = 1 is the still-unproven Goldbach conjecture. In information theory, he introduced the spectrum of Rényi entropies of order α, giving an important generalisation of the Shannon entropy and the Kullback–Leibler divergence.
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Neolithic clay amulet (retouched), part of the Tărtăria tablets set, dated to 5500-5300 BC and associated with the Turdaş-Vinča culture. The Vinča symbols on it predate the proto-Sumerian pictographic script. Discovered in 1961 at Tărtăria, Alba County, Romania by the archaeologist Nicolae Vlassa. The Starčevo-Criş culture, representing the generalisation of the early Neolithic in the Intra-Carpathian territory, has been regarded by some as the prolongation of the Gura Baciului-Cârcea/Precriş culture, disregarding that it is probably the result of a new south Balkan migration (the Presesklo culture) arriving in Transylvania via Banat.
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A further generalisation and refinement of these results due to Samson Abramsky, Rui Soares Barbosa and Shane Mansfield appeared in 2017, proving a precise quantifiable relationship between the probability of successfully computing any given non-linear function and the degree of contextuality present in the l2-MBQC as measured by the contextual fraction. Specifically, (1-p_s) \geq \left( 1-CF(e) \right) . u(f) where p_s, CF(e), u(f) \in [0,1] are the probability of success, the contextual fraction of the measurement statistics e, and a measure of the non-linearity of the function to be computed f , respectively.
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Leonhard Euler in 1750 introduced a generalisation of Newton's laws of motion for rigid bodies called Euler's laws of motion, later applied as well for deformable bodies assumed as a continuum. If a body is represented as an assemblage of discrete particles, each governed by Newton's laws of motion, then Euler's laws can be derived from Newton's laws. Euler's laws can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle structure. Newton's laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames.
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Closely linked to these cohomology theories, he originated topos theory as a generalisation of topology (relevant also in categorical logic). He also provided an algebraic definition of fundamental groups of schemes and more generally the main structures of a categorical Galois theory. As a framework for his coherent duality theory he also introduced derived categories, which were further developed by Verdier. The results of work on these and other topics were published in the EGA and in less polished form in the notes of the Séminaire de géométrie algébrique (SGA) that he directed at the IHÉS.
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In mathematics, in the theory of Hopf algebras, a Hopf algebroid is a generalisation of weak Hopf algebras, certain skew Hopf algebras and commutative Hopf k-algebroids. If k is a field, a commutative k-algebroid is a cogroupoid object in the category of k-algebras; the category of such is hence dual to the category of groupoid k-schemes. This commutative version has been used in 1970-s in algebraic geometry and stable homotopy theory. The generalization of Hopf algebroids and its main part of the structure, associative bialgebroids, to the noncommutative base algebra was introduced by J.-H.
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Brown algae have adapted to a wide variety of marine ecological niches including the tidal splash zone, rock pools, the whole intertidal zone and relatively deep near shore waters. They are an important constituent of some brackish water ecosystems, and have colonized freshwater on a maximum of six known occasions. A large number of Phaeophyceae are intertidal or upper littoral, and they are predominantly cool and cold water organisms that benefit from nutrients in up welling cold water currents and inflows from land; Sargassum being a prominent exception to this generalisation. Brown algae growing in brackish waters are almost solely asexual.
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Some works on dependability John C. Knight, Elisabeth A. Strunk, Kevin J. Sullivan: Towards a Rigorous Definition of Information System Survivability use structured information systems, e.g. with SOA, to introduce the attribute survivability, thus taking into account the degraded services that an Information System sustains or resumes after a non-maskable failure. The flexibility of current frameworks encourage system architects to enable reconfiguration mechanisms that refocus the available, safe resources to support the most critical services rather than over-provisioning to build failure-proof system. With the generalisation of networked information systems, accessibility was introduced to give greater importance to users' experience.
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He is known as the father of commercial forestry in Iran due to empowering the field of greenery with genetically modified trees in Iran. Lotfi A. Zadeh:is a mathematician, electrical engineer, computer scientist, artificial intelligence researcher and professor emeritus of computer science at the University of California, Berkeley. Zadeh, in his theory of fuzzy sets, proposed using a membership function (with a range covering the interval [0,1]) operating on the domain of all possible values. He proposed new operations for the calculus of logic and showed that fuzzy logic was a generalisation of classical and Boolean logic.
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One of the origins of the mathematical theory of arithmetic groups is algebraic number theory. The classical reduction theory of quadratic and Hermitian forms by Charles Hermite, Hermann Minkowski and others can be seen as computing fundamental domains for the action of certain arithmetic groups on the relevant symmetric spaces. The topic was related to Minkowski's Geometry of numbers and the early development of the study of arithmetic invariant of number fields such as the discriminant. Arithmetic groups can be thought of as a vast generalisation of the unit groups of number fields to a noncommutative setting.
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The report argued that too many buildings, sports clubs, car parks, and roads all defeated the purpose of parks as open spaces. The Sherwood Arboretum stands in stark contradiction to this generalisation. The park's vistas, river frontage, subtropical mature trees and mature plantings of Queensland pines, native figs and specimens of rare Queensland native plums in a setting of grassed open spaces, open lagoons and shrubby borderlines, demonstrate an established sub-tropical garden character and are well appreciated by the public. Indeed, Sherwood Arboretum is listed as the third or fourth most visited park in Brisbane.
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This gives rise to characteristically broad pulses (duty cycle 67%). The signal format Alternate-Phase Return-to-Zero (APRZ) can be viewed as a generalisation of CSRZ in which the phase alternation can take up any value ΔΦ (and not necessarily only π) and the duty cycle is also a free parameter. CSRZ can be used to generate specific optical modulation formats, e.g. CSRZ- OOK, in which data is coded on the intensity of the signal using a binary scheme (light on=1, light off=0), or CSRZ-DPSK, in which data is coded on the differential phase of the signal, etc.
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There are many other equivalent ways to define a topological space: in other words the concepts of neighbourhood, or that of open or closed sets can be reconstructed from other starting points and satisfy the correct axioms. Another way to define a topological space is by using the Kuratowski closure axioms, which define the closed sets as the fixed points of an operator on the power set of X. A net is a generalisation of the concept of sequence. A topology is completely determined if for every net in X the set of its accumulation points is specified.
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In higher-dimensional algebra (HDA), a double groupoid is a generalisation of a one-dimensional groupoid to two dimensions, and the latter groupoid can be considered as a special case of a category with all invertible arrows, or morphisms. Double groupoids are often used to capture information about geometrical objects such as higher-dimensional manifolds (or n-dimensional manifolds). In general, an n-dimensional manifold is a space that locally looks like an n-dimensional Euclidean space, but whose global structure may be non-Euclidean. Double groupoids were first introduced by Ronald Brown in 1976, in ref.
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Almost all of Northern Australia is a huge ancient craton that has not experienced geological upheaval since the end of the Precambrian. The only exception to this generalisation is the Wet Tropics of northern Queensland, where active volcanoes have been present as recently as the Pleistocene. The vast craton in the north and west contains a number of quite rugged mountain ranges, of which the highest are the MacDonnell and Musgrave Ranges on the southern border of the Northern Territory. These rise to over , but the most spectacular features are the deep gorges of rivers such as the Finke.
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Contrary to this, in dimension two work of Ivan Fesenko on two- dimensional generalisation of Tate's thesis includes an integral representation of a zeta integral closely related to the zeta function. In this new situation, not possible in dimension one, the poles of the zeta function can be studied via the zeta integral and associated adele groups. Related conjecture of on the positivity of the fourth derivative of a boundary function associated to the zeta integral essentially implies the pole part of the generalized Riemann hypothesis. proved that the latter, together with some technical assumptions, implies Fesenko's conjecture.
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The term Silat Melayu ("Malay silat") was originally used in reference to the Riau Archipelago in Indonesia but is today commonly used for referring to systems created in Peninsular Malaysia. Generally speaking, Silat Melayu is often associated with fixed hand positions, low stances and slow dance-like movements. While this generalisation does not necessarily reflect the reality of silat techniques, it has had a notable influence on the stereotypical way the art is portrayed in Malaysia, Singapore, and to some extent Brunei. Pencak silat is one of the sports included in the Southeast Asian Games and other region-wide competitions.
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In algebraic geometry and differential geometry, the Nonabelian Hodge correspondence or Corlette–Simpson correspondence (named after Kevin Corlette and Carlos Simpson) is a correspondence between Higgs bundles and representations of the fundamental group of a smooth, projective complex algebraic variety, or a compact Kähler manifold. The theorem can be considered a vast generalisation of the Narasimhan–Seshadri theorem which defines a correspondence between stable vector bundles and unitary representations of the fundamental group of a compact Riemann surface. In fact the Narasimhan–Seshadri theorem may be obtained as a special case of the nonabelian Hodge correspondence by setting the Higgs field to zero.
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In the area of artificial intelligence, he is best known for his influential early work on the complexity of nonmonotonic logics and on (generalised) hypertree decompositions, a framework for obtaining tractable structural classes of constraint satisfaction problems, and a generalisation of the notion of tree decomposition from graph theory. This work has also had substantial impact in database theory, since it is known that the problem of evaluating conjunctive queries on relational databases is equivalent to the constraint satisfaction problem. His recent work on XML query languages (notably XPath) has helped create the complexity-theoretical foundations of this area.
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Edited by George Eisenman. — NY.: Marcel Dekker, Inc. 1967 His achievements in solving the fundamental problems of chemical thermodynamics are noteworthy. Special mention should be made of the generalisation of the stability conditions for the Gibbs equilibrium to heterogeneous (multicomponent, multiphase) systems (1954). M. Shultz developed a method for calculating changes in the thermodynamic properties of a heterogeneous system from data on the composition of the coexisting phases and on the change in the chemical potential of only one component («method of the third component», so called else «Shultz-Storonkin’s method»). In the frame of the thermodynamic theory existing is the «Filippov-Shultz rule».
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The Conclusions of the Council of the European Union, which founded the European initiative for the exchange of young officers, inspired by Erasmus, have translated these objectives into concrete measures, such as: • Measures aimed at increasing the number of exchanges, such as the generalisation of the Bologna process, mutual recognition of the outcomes of exchanges in professional training, greater use of Erasmus mobility for students and personnel, opening of national educational opportunities to young European officers; • Measures aimed at teaching/learning about Europe and its defence, such as the creation of a common module on the Common Security and Defence Policy, promotion of the learning of several foreign languages.
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A linear system of divisors algebraicizes the classic geometric notion of a family of curves, as in the Apollonian circles. In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family. These arose first in the form of a linear system of algebraic curves in the projective plane. It assumed a more general form, through gradual generalisation, so that one could speak of linear equivalence of divisors D on a general scheme or even a ringed space (X, OX).
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After the Kosovo War, the citizens & supporters returned to its stadium stands. Although numerously fighting relegation throughout the seasons during the 2000s one thing was for sure, the “Ferki Aliu Stadium” would always be packed to the rafters during every home game. The clubs’ ultras group “Forca” gained a nation wide generalisation during that period due to many opposing teams supporters being the subject of verbal and physical abuse when they would travel and watch their team play in the city of Vushtrri. Due to this the club was constantly fined and deducted points and became one of Kosovos most hated teams and fiercest cities to play away at.
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Staying within the world of semigroups, Green's relations can be extended to cover relative ideals, which are subsets that are only ideals with respect to a subsemigroup (Wallace 1963). For the second kind of generalisation, researchers have concentrated on properties of bijections between L- and R- classes. If x R y, then it is always possible to find bijections between Lx and Ly that are R-class-preserving. (That is, if two elements of an L-class are in the same R-class, then their images under a bijection will still be in the same R-class.) The dual statement for x L y also holds.
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There are more complex network architectures, including recurrent networks, that produce dynamics by introducing increasing orders of lagged variables to the input nodes. But in these cases it is very easy to over specify the lags and this can lead to over fitting and poor generalisation properties. Neural networks have several advantages; they are conceptually simple, easy to train and to use, have excellent approximation properties, the concept of local and parallel processing is important and this provides integrity and fault tolerant behaviour. The biggest criticism of the classical neural network models is that the models produced are completely opaque and usually cannot be written down or analysed.
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Further generalisation to locally compact abelian groups is required in number theory. In non-commutative harmonic analysis, the idea is taken even further in the Selberg trace formula, but takes on a much deeper character. A series of mathematicians applying harmonic analysis to number theory, most notably Martin Eichler, Atle Selberg, Robert Langlands, and James Arthur, have generalised the Poisson summation formula to the Fourier transform on non-commutative locally compact reductive algebraic groups G with a discrete subgroup \Gamma such that G/\Gamma has finite volume. For example, G can be the real points of GL_n and \Gamma can be the integral points of GL_n.
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To be widely useful, a transformation system must be able to handle many target programming languages, and must provide some means of specifying such front ends. A generalisation of semantic equivalence is the notion of program refinement: one program is a refinement of another if it terminates on all the initial states for which the original program terminates, and for each such state it is guaranteed to terminate in a possible final state for the original program. In other words, a refinement of a program is more defined and more deterministic than the original program. If two programs are refinements of each other, then the programs are equivalent.
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Other sections of the book deal with Cornish's theories about what he claims are the common roots of Wittgenstein's and Hitler's philosophies in mysticism, magic, and the "no-ownership" theory of mind. Cornish sees this as Wittgenstein's generalisation of Arthur Schopenhauer's account of the Unity of the Will, in which despite appearances, there is only a single Will acting through the bodies of all creatures. This doctrine, generalized to other mental faculties such as thinking, is presented in Ralph Waldo Emerson's "Essays". The doctrine, writes Cornish, was also held by the Oxford philosopher R. G. Collingwood who was one of Wittgenstein's electors to his Cambridge chair.
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Roman Britain in 410 Caesar's invasions of Britain brought descriptions of the peoples of what he called Britannia pars interior, "inland Britain", in 55 BC. Throughout Book 4 of his Geography, Strabo is consistent in spelling the island Britain (transliterated) as Prettanikē; he uses the terms Prettans or Brettans loosely to refer to the islands as a group – a common generalisation used by classical geographers. For example, in Geography 2.1.18, …οι νοτιώτατοι των Βρεττανών βορειότεροι τούτων εισίν ("…the most southern of the Brettans are further north than this").Translation by Roseman, op.cit. He was writing around AD 10, although the earliest surviving copy of his work dates from the 6th century.
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Logistic functions are used in logistic regression to model how the probability p of an event may be affected by one or more explanatory variables: an example would be to have the model : p = f(a + bx), where x is the explanatory variable, a and b are model parameters to be fitted, and f is the standard logistic function. Logistic regression and other log-linear models are also commonly used in machine learning. A generalisation of the logistic function to multiple inputs is the softmax activation function, used in multinomial logistic regression. Another application of the logistic function is in the Rasch model, used in item response theory.
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Steiner was regarded as a polymath and is often credited with having recast the role of the critic by having explored art and thought unbounded by national frontiers or academic disciplines. He advocated generalisation over specialisation, and insisted that the notion of being literate must encompass knowledge of both arts and sciences. Steiner believed that nationalism is too inherently violent to satisfy the moral prerogative of Judaism, having said "that because of what we are, there are things we can't do." Among Steiner's non-traditional views, in his autobiography titled Errata (1997), Steiner related his sympathetic stance towards the use of brothels since his college years at the University of Chicago.
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Thistles, even if one restricts the term to members of the Asteraceae, are too varied a group for generalisation; many are troublesome weeds, including some invasive species of Cirsium, Carduus, Silybum and Onopordum. Typical adverse effects are competition with crops and interference with grazing in pastures, where dense growths of spiny vegetation suppress forage plants and repel grazing animals from eating either the thistle plants or neighbouring forage. Some species, although not intensely poisonous, do affect the health of animals that swallow more than small amounts of the material.Watt, John Mitchell; Breyer-Brandwijk, Maria Gerdina: The Medicinal and Poisonous Plants of Southern and Eastern Africa 2nd ed Pub.
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In the book's introduction, Barrett criticises the trend amongst processual archaeologists to focus on the generalisation of past societies into a series of processes, instead arguing that archaeologists should instead think about the individuals of the past, who are otherwise forgotten. He therefore accepts the role that post-processual theory plays in the book, but argues that "this is not a book about archaeological theory", instead being "an empirical study aimed at building a history of the period between about 2900 and 1200 BC in southern Britain" a timespan that he considers to be "one of the most remarkable periods in European prehistory".Barrett 1994. pp. 1-7.
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In mathematics, structural Ramsey theory is a categorical generalisation of Ramsey theory, rooted in the idea that many important results of Ramsey theory have "similar" logical structure. The key observation is noting that these Ramsey-type theorems can be expressed as the assertion that a certain category (or class of finite structures) has the Ramsey property (defined below). Structural Ramsey theory began in the 1970s with the work of Nešetřil and Rödl, and is intimately connected to Fraïssé theory. It received some renewed interest in the mid-2000s due to the discovery of the Kechris–Pestov–Todorčević correspondence, which connected structural Ramsey theory to topological dynamics.
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Scott also began working on modal logic in this period, beginning a collaboration with John Lemmon, who moved to Claremont, California, in 1963. Scott was especially interested in Arthur Prior's approach to tense logic and the connection to the treatment of time in natural-language semantics, and began collaborating with Richard Montague (Copeland 2004), whom he had known from his days as an undergraduate at Berkeley. Later, Scott and Montague independently discovered an important generalisation of Kripke semantics for modal and tense logic, called Scott-Montague semantics (Scott 1970). John Lemmon and Scott began work on a modal-logic textbook that was interrupted by Lemmon's death in 1966.
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The work of Munthe-Kaas is centred on applications of differential geometry and Lie group techniques in geometric integration and structure preserving algorithms for numerical integration of differential equations. A central aspect is the analysis of structure preservation by algebraic and combinatorial techniques (B-series and Lie–Butcher series). In the mid-1990s Munthe-Kaas developed what are now known as Runge–Kutta–Munthe-Kaas methods, a generalisation of Runge–Kutta methods to integration of differential equations evolving on Lie groups. The analysis of numerical Lie group integrators leads to the study of new types of formal power series for flows on manifolds (Lie–Butcher series).
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In mathematics, a weakly symmetric space is a notion introduced by the Norwegian mathematician Atle Selberg in the 1950s as a generalisation of symmetric space, due to Élie Cartan. Geometrically the spaces are defined as complete Riemannian manifolds such that any two points can be exchanged by an isometry, the symmetric case being when the isometry is required to have period two. The classification of weakly symmetric spaces relies on that of periodic automorphisms of complex semisimple Lie algebras. They provide examples of Gelfand pairs, although the corresponding theory of spherical functions in harmonic analysis, known for symmetric spaces, has not yet been developed.
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A twisted Edwards curve of equation 10x^2+y^2=1+6x^2y^2 In algebraic geometry, the twisted Edwards curves are plane models of elliptic curves, a generalisation of Edwards curves introduced by Bernstein, Birkner, Joye, Lange and Peters in 2008.D. J. Bernstein, P. Birkner, M. Joye, T. Lange, C. Peters, Twisted Edwards Curves. The curve set is named after mathematician Harold M. Edwards. Elliptic curves are important in public key cryptography and twisted Edwards curves are at the heart of an electronic signature scheme called EdDSA that offers high performance while avoiding security problems that have surfaced in other digital signature schemes.
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This is a crude > generalisation, and of course all good publishers still have excellent > editors working for them, but the main shift from editorially led buying to > sales team buying, changed the flavour of publishing radically. ...there > were so many good editors on the freelance market, and so many people > writing who needed an opinion on their work. TLC was the first to establish > itself in Britain, and to remove the stigma of people paying for editorial > opinion and advice. After all, editing is a real skill, knowing the markets > is another skill, and in my view people writing should consider paying for > these skills—rather than expecting serious feedback for free.
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In X-ray computed tomography the lines on which the parameter is integrated are straight lines : the tomographic reconstruction of the parameter distribution is based on the inversion of the Radon transform. Although from a theoretical point of view many linear inverse problems are well understood, problems involving the Radon transform and its generalisations still present many theoretical challenges with questions of sufficiency of data still unresolved. Such problems include incomplete data for the x-ray transform in three dimensions and problems involving the generalisation of the x-ray transform to tensor fields. Solutions explored include Algebraic Reconstruction Technique, filtered backprojection, and as computing power has increased, iterative reconstruction methods such as iterative Sparse Asymptotic Minimum Variance.
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8 Darlington's insertion-loss method is a generalisation of the procedure used by Norton. In Norton's filter it can be shown that each filter is equivalent to a separate filter unterminated at the common end. Darlington's method applies to the more straightforward and general case of a 2-port LC network terminated at both ends. The procedure consists of the following steps: #determine the poles of the prescribed insertion-loss function, #from that find the complex transmission function, #from that find the complex reflection coefficients at the terminating resistors, #find the driving point impedance from the short-circuit and open-circuit impedances, #expand the driving point impedance into an LC (usually ladder) network.
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It was later shown by Hartle and Hawking that these solutions can be "glued" together to construct multi-blackhole solutions of charged blackholes. These charged blackholes are in static equilibrium with each other with the gravitational and the electrostatic forces cancelling each other out. The Majumdar–Papapetrou solution, thus, can be seen as early example of BPS configuration where static equilibrium results due to the cancellation of opposing forces. Examples of such BPS configurations include cosmic strings (attractive gravitational force balances with the repulsive scalar force), monopoles, BPS configurations of D-branes (cancellation of NS- NS and RR forces, NS-NS being the gravitational force and RR being the generalisation of the electrostatic force), etc.
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In 1955, Ehrenberg moved into marketing research working on consumer panels. His first milestone paper was "The Pattern of Consumer Purchases" Ehrenberg, A. (1959) The pattern of consumer Purchases, Applied Statistics, 8,1, 26–41. which showed the applicability of the negative binomial distribution to the numbers of purchases of a brand of consumer goods. In the early 1980s, with Gerald Goodhardt and Chris Chatfield, he extended the NBD model to account for brand choices. The generalisation to the multi-brand case was put forward in "The Dirichlet: A Comprehensive Model of Buying behaviour" Goodhardt G.J., Ehrenberg, A. and Chatfield (1984), The Dirichlet: A comprehensive model of buying behaviour, Journal of the Royal Statistical Society, Series A, 147, 621–655.
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From there, "shamanism" was picked up by anthropologists to describe any cultural practice that involves vision-seeking and communication with the spirits, no matter how diverse the cultures included in this generalisation. Native American and First Nations spiritual people use terms in their own languages to describe their traditions; their spiritual teachers, leaders or elders are not called "shamans". However, with Michael Harner's invention and promotion of "core shamanism" in the 1980s, the term "shaman" began to be misapplied to Native American ways by cultural outsiders; this is due to Harner's unfounded claim that the ways of several North American tribes share core elements with those of the Siberian Shamans.Harner, Michael The Way of the Shaman.
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As Anjali's family were not in favour of her decision of marrying Abhishek, he is informed that Anjali has married the person she has been engaged to and did not care to tell him that Anjali has actually died and visit him, even when he was in hospital recovering from injuries after the accident. Abhishek's grandfather had faked an invitation card to Anjali's wedding only to keep him away from further mental trauma. This angers Abhishek and he starts to hate women with the generalisation that all women are like Anjali. After a long gap Aishwarya (Deepika Padukone) joins the company he works in which is owned by his uncle as an assistant manager.
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In the past, there was a vogue for drilling children in grammatical exercises, using imitation and elicitation, but such methods fell into disuse when it became apparent that there was little generalisation to everyday situations. Contemporary approaches to enhancing development of language structure, for younger children at least, are more likely to adopt 'milieu' methods, in which the intervention is interwoven into natural episodes of communication, and the therapist builds on the child's utterances, rather than dictating what will be talked about. Interventions for older children, may be more explicit, telling the children what areas are being targeted and giving explanations regarding the rules and structures they are learning, often with visual supports.Bryan, A., Colourful Semantics.
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On 22 August 2006 the draft proposal was rewritten with two changes from the previous draft. The first was a generalisation of the name of the new class of planets (previously the draft resolution had explicitly opted for the term 'pluton'), with a decision on the name to be used postponed. Many geologists had been critical of the choice of name for Pluto-like planets, being concerned about the term pluton which has been used for years within the geological community to represent a form of magmatic intrusion; such formations are fairly common balls of rock. Confusion was thought undesirable due to the status of planetology as a field closely allied to geology.
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There are marked stylistic differences between the composers of North, South and Central Germany such that further generalisation is inaccurate. The North German Praeludium (an important form consisting of alternating sections of free material written in the largely misunderstood stylus phantasticus and fugal material) reached its zenith in Dieterich Buxtehude, informed by Matthias Weckmann and Heinrich Scheidemann (influenced most strongly by Jan Peeterszoon Sweelinck and by the Italian school transported to North Germany by Heinrich Schütz and Samuel Scheidt). Georg Böhm remained firmly representative of the South German School, though Johann Pachelbel's influence as a teacher extended across North, South and Central Germany. Baroque organ music arguably reached its height in the works of Johann Sebastian Bach.
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2 which would have proven at least as useful in case of a divorce as it would for the reason given by Caesar, to determine the inheritance of the partner who survived the other. It is likely that there were other elements covering various issues of kinship relations in early Celtic laws, for instance covering adoption, expulsion of antisocial kin members, and inheritance rules in case that a whole lineage would be heirless, but there is too little available information on this subject from late prehistory to allow for more than a generalisation of similarities in these areas as found in early medieval Irish and Welsh law.for possibilities see Charles-Edwards 1993.
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To save time batches of his writing were typeset on arrival, so one part was being printed "while the other part was still uncoiling from my brain in Cambridge." Napier did not insist on the usual concise review, but as it was still arriving in mid May stopped it at what became 85 pages, one of the longest reviews the quarterly ever published. The British Association for the Advancement of Science annual meeting was held at Cambridge in June 1845, giving its president John Herschel a platform to counter Vestiges. His presidential address contrasted the "sound and thoughtful and sobering discipline" of the scientific brotherhood with the "over-hasty generalisation" and "pure speculation" of the unnamed book.
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The court said it thus found the question too complicated to be solved by broad generalisation. Moreover, "once one departs from the case in which the unfairness to the customer and the anticompetitive nature of the monopoly is as plain and obvious as it appeared to the House of Lords in British Leyland, the jurisprudential and economic basis for the doctrine becomes extremely fragile." The Privy Council did not perceive in this case "the features of unfairness and abuse of monopoly power which underlay the decision in British Leyland" as "plainly and obviously present." Therefore, they reversed the order of the Court of Appeal on the copyright issue and reinstated that of the trial court.
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It can be proved by direct analysis of the doubling of a point on E. Some years later André Weil took up the subject, producing the generalisation to Jacobians of higher genus curves over arbitrary number fields in his doctoral dissertation published in 1928. More abstract methods were required, to carry out a proof with the same basic structure. The second half of the proof needs some type of height function, in terms of which to bound the 'size' of points of A(K). Some measure of the co-ordinates will do; heights are logarithmic, so that (roughly speaking) it is a question of how many digits are required to write down a set of homogeneous coordinates.
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His third suggested generalisation is to incorporate adjustment of the money supply: > Instead of assuming, as before, that the supply of money is given, we can > assume that there is a given monetary system... monetary authorities will > prefer to create new money rather than allow interest rates to rise... Any > change in liquidity preference or monetary policy will shift the LL [i.e. > LM] curve...'Liquidity preference' is misprinted as 'liquidity of > preference' in 'Critical essays in monetary theory'. Presumably we should write M(r) in place of M. A similar dependence was proposed around the same time by Pigou. In Ambrosi's words: > According to Pigou the quantity of money is not given.
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In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated. This can be thought of as a generalisation of many classical methods—the method of moments, least squares, and maximum likelihood—as well as some recent methods like M-estimators. The basis of the method is to have, or to find, a set of simultaneous equations involving both the sample data and the unknown model parameters which are to be solved in order to define the estimates of the parameters. Various components of the equations are defined in terms of the set of observed data on which the estimates are to be based.
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Williams’ early research was in elementary particle physics, then during her second postdoctoral position she started working in classical general relativity. Eventually she combined these two interests by working in quantum gravity in an attempt to find a unified theory of quantum mechanics and general relativity. Her particular approach, called Regge calculus, is a version of discrete gravity where curved space-times are approximated by collections of flat simplices. This may be thought of as a generalisation of geodesic domes to higher dimensions. Williams’ work on Regge calculus includes the classical evolution of model universes, and numerical simulations of discrete quantum gravity, together with investigations of the relationship between Regge calculus and the continuum theory.
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Tower blocks in Ladywood The Ladywood ward combines areas of varying land-use, such that no generalisation is possible. There is the city centre (the economically valuable Central business district), the affluent Jewellery Quarter, and Broad Street areas which have become fashionable for "luxury flat" living, the Lee Bank area (now known as Park Central) which has been fully redeveloped, and there is the remainder of the ward, which is Ladywood itself (here referred to as "remainder Ladywood" – i.e., what is Ladywood itself) which is relatively economically impoverished. Most of "remainder Ladywood" was redeveloped during the 1960s, with decaying terraced slums being cleared to make way for new low- rise housing and high-rise flats.
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Distribution law or the Nernst's distribution law gives a generalisation which governs the distribution of a solute between two non miscible solvents. This law was first given by Nernst who studied the distribution of several solutes between different appropriate pairs of solvents. C1/C2 = Kd Where Kd is called the distribution coefficient or the partition coefficient. Concentration of X in solvet A/concentration of X in solvent B=Kď If C1 denotes the concentration of solute X in solvent A & C2 denotes the concentration of solute X in solvent B; Nernst's distribution law can be expressed as C1/C2 = Kd. This law is only valid if the solute is in the same molecular form in both the solvents.
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It was criticised by some reviewers for the seemingly arbitrary cut-off of 1922, for a certain amount of generalisation and excessive detail in other parts, and has to some extent been superseded by later more nuanced works that make a greater distinction between the individual Constructivists. However, there was also general praise for the achievement of what was clearly a very difficult task that nobody else had been able to tackle in an area that was previously largely unknown to Western scholars. Gray's publishers asked her to write a book specifically about Constructivism and she won a Leverhulme Trust award to pay for the research but was unable to proceed as the British Council would not endorse the project because she had no university degree.
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The phenomenon of static equilibrium for a system of point charges is well known in Newtonian theory, where the mutual gravitational and electrostatic forces can be balanced by fine-tuning the charge suitably with the particle masses. The corresponding generalisation, in the form of static solutions of the coupled, source-free Einstein-Maxwell equations, was discovered by Majumdar and Papapetrou independently in 1947. These gravitational fields assume no spatial symmetry and also contain geodesics which are incomplete. While work continued on understanding these solutions better, a renewed interest in this metric was generated by the important observation of Israel and Wilson in 1972 that static black-hole spacetimes with the mass being equal to the magnitude of the charge are of Majumdar–Papapetrou form.
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Wood's early works in chemistry involved polymerisation and fermentation, under Sir William Ramsay and then Arthur Harden. As a medical statistician, she compared food prices with wages and rent, the generalisation of statistical correlations on death rates, and mortality rates for cancer and diabetes. Her work during the war remains unpublished, but two posthumous papers concern the effects of higher education on fertility, and the correlation between economic class and child mental development. Her sole- author paper on trends in wages in London 1900–1912 was read before a meeting of the Royal Statistical Society on 18 November 1913, which RSS president F. Y. Edgeworth commented made "an important contribution to the art of measuring changes in the value of money".
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After World War I finished, Vauck undertook study of mathematics and physics at the Technical University of Dresden. In 1922, he passed the exam for a higher education office, and two years later, under supervision of Gerhard Kowalewski, Vauck was promoted to Dr. phil with a thesis titled A generalisation of Bolzano's continuous but non-differentiable function () which is within Mathematics Subject Classification 26 Real functions. Vauck's first career position was as a teacher at the secondary school in Thum and then from 1926 as a teacher at the secondary school in Bautzen. After the war from 1948, he became a teacher in Bautzen and later became a lecturer in physics and electrical engineering at the engineering school in Bautzen.
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Binary space partitioning is a generic process of recursively dividing a scene into two until the partitioning satisfies one or more requirements. It can be seen as a generalisation of other spatial tree structures such as k-d trees and quadtrees, one where hyperplanes that partition the space may have any orientation, rather than being aligned with the coordinate axes as they are in k-d trees or quadtrees. When used in computer graphics to render scenes composed of planar polygons, the partitioning planes are frequently chosen to coincide with the planes defined by polygons in the scene. The specific choice of partitioning plane and criterion for terminating the partitioning process varies depending on the purpose of the BSP tree.
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According to the National Statistical Institute of Bulgaria, Bulgarian Turks make up 12% of short term migrants, 13% of long term migrants, and 12% of the labour migrants. However, it is unlikely that this generalisation shows a true indication of the ethnic make-up of Bulgarian citizens living abroad because Bulgarian citizens of Turkish origin make up entire majorities in some countries. For example, out of the 10,000 to 30,000 people from Bulgaria living in the Netherlands, the majority, of about 80%, are ethnic Turks from Bulgaria who have come from the south-eastern Bulgarian district of Kurdzhali.. Moreover, the Bulgarian Turks are the fastest-growing group of immigrants in the Netherlands. There is also about 30,000 Bulgarian Turks living in Sweden,.
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Basal rosettes of dark green leaves bear trumpet-shaped flowers in shades of white, violet or purple in spring and summer. Despite the zygomorphic nectar-producing flowers (which are considered an ancestral character) and the overall trend in Gesneriaceae, resurrection plant is only rarely pollinated by bees and does not have specific pollinators. Rather its evolution has switched in the direction of providing pollen as a reward and generalisation of pollinating insects - a trend that is observed in the other two European members (Jankaea and Ramonda) of the more tropically and subtropically spread family Gesneriaceae. Active pollinators of Haberlea are found to be syrphids (hoverflies) and Lasioglossum morio (Hymenoptera, Halictidae) which are characterised by low preferential behaviour regarding the plants that they visit for food.
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Noun reduplication, though nearly absent in Standard Chinese, is found in Cantonese and southwestern dialects of Mandarin. For instance, in Sichuan Mandarin, bāobāo 包包 (handbag) is used whereas Beijing use bāor 包儿. One notable exception is the colloquial use of bāobāo 包包 by non-Sichuanese speakers to denote a perceived fancy, attractive, or "cute" purse (somewhat equivalent to the English "baggie"). However, there are few nouns that can be reduplicated in Standard Chinese, and reduplication denotes generalisation and uniformity: rén 人 (human being) and rénrén 人人 (everybody (in general, in common)), jiājiāhùhù 家家户户 (every household (uniformly)) – in the latter jiā and hù additionally duplicate the meaning of household, which is a common way of creating compound words in Chinese.
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Twisted geometries are discrete geometries that play a role in loop quantum gravity and spin foam models, where they appear in the semiclassical limit of spin networks. A twisted geometry can be visualized as collections of polyhedra dual to the nodes of the spin network's graph. Intrinsic and extrinsic curvatures are defined in a manner similar to Regge calculus, but with the generalisation of including a certain type of metric discontinuities: the face shared by two adjacent polyhedra has a unique area, but its shape can be different. This is a consequence of the quantum geometry of spin networks: ordinary Regge calculus is "too rigid" to account for all the geometric degrees of freedom described by the semiclassical limit of a spin network.
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The Council for Aboriginal Reconciliation's booklet, Understanding Country, formally seeks to introduce non-indigenous Australians to Aboriginal perspectives on the environment. It makes the following generalisation about Aboriginal myths and mythology: > ...they generally describe the journeys of ancestral beings, often giant > animals or people, over what began as a featureless domain. Mountains, > rivers, waterholes, animal and plant species, and other natural and cultural > resources came into being as a result of events which took place during > these Dreamtime journeys. Their existence in present-day landscapes is seen > by many indigenous peoples as confirmation of their creation beliefs... > The routes taken by the Creator Beings in their Dreamtime journeys across > land and sea... link many sacred sites together in a web of Dreamtime tracks > criss-crossing the country.
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F. A. M. Frescura, B. J. Hiley: Algebras, quantum theory and pre- space, p. 3–4 (published in Revista Brasileira de Fisica, Volume Especial, Julho 1984, Os 70 anos de Mario Schonberg, pp. 49-86) Bohm and Hiley expanded on the concept that "relativistic quantum mechanics can be expressed completely through the interweaving of three basic algebras, the bosonic, the fermionic and the Clifford" and that in this manner "the whole of relativistic quantum mechanics can also be put into an implicate order" as suggested in earlier publications of David Bohm from 1973 and 1980.D. Bohm, B. J. Hiley: Generalisation of the twistor to Clifford algebras as a basis for geometry, published in Revista Brasileira de Fisica, Volume Especial, Os 70 anos de Mario Schönberg, pp.
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In astronomy, the distance to a visual binary star may be estimated from the masses of its two components, the size of their orbit, and the period of their orbit about one another. A dynamical parallax is an (annual) parallax which is computed from such an estimated distance. To calculate a dynamical parallax, the angular semi-major axis of the orbit of the stars is observed, as is their apparent brightness. By using Newton's generalisation of Kepler's Third Law, which states that the total mass of a binary system multiplied by the square of its orbital period is proportional to the cube of its semi-major axis, together with the mass-luminosity relation, the distance to the binary star can then be determined.
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However, this situation could be an artefact of the relative scarcity of Torosaurus remains and imperfect sampling. Longrich therefore concluded that the hypothesis was corroborated by the first prediction. Secondly, the hypothesis predicted that all Torosaurus specimens would be adults, while no Triceratops specimens would be very old. According to Longrich, this last point had not yet been established. Admittedly, in 2011 Horner had published an histological study showing that all Triceratops specimens investigated possessed a subadult bone structure,Horner, J.R., Lamm, E-T., 2011, "Ontogeny of the parietal frill of Triceratops: a preliminary histological analysis", Comptes Rendus de l’Academie des Sciences Paris série D 10: 439–452 but the sample had been too small to allow for a valid generalisation to all Triceratops fossils.
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Just as the most natural and general setting for continuity is topological spaces, the most natural and general setting for the study of uniform continuity are the uniform spaces. A function f : X → Y between uniform spaces is called uniformly continuous if for every entourage V in Y there exists an entourage U in X such that for every (x1, x2) in U we have (f(x1), f(x2)) in V. In this setting, it is also true that uniformly continuous maps transform Cauchy sequences into Cauchy sequences. Each compact Hausdorff space possesses exactly one uniform structure compatible with the topology. A consequence is a generalisation of the Heine-Cantor theorem: each continuous function from a compact Hausdorff space to a uniform space is uniformly continuous.
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Burgess, 1871–72 Spencer first articulated his evolutionary perspective in his essay, 'Progress: Its Law and Cause', published in Chapman's Westminster Review in 1857, and which later formed the basis of the First Principles of a New System of Philosophy (1862). In it he expounded a theory of evolution which combined insights from Samuel Taylor Coleridge's essay 'The Theory of Life' – itself derivative from Friedrich von Schelling's Naturphilosophie – with a generalisation of von Baer's law of embryological development. Spencer posited that all structures in the universe develop from a simple, undifferentiated, homogeneity to a complex, differentiated, heterogeneity, while being accompanied by a process of greater integration of the differentiated parts. This evolutionary process could be found at work, Spencer believed, throughout the cosmos.
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The first reason that can be cited for that is that it did not provide fresh information on the splitting of prime ideals in a Galois extension; a common way to explain the objective of a non-abelian class field theory is that it should provide a more explicit way to express such patterns of splitting.On the statistical level, the classical result on primes in arithmetic progressions of Dirichlet generalises to Chebotaryov's density theorem; what is asked for is a generalisation, of the same scope of quadratic reciprocity. The cohomological approach therefore was of limited use in even formulating non-abelian class field theory. Behind the history was the wish of Chevalley to write proofs for class field theory without using Dirichlet series: in other words to eliminate L-functions.
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It was at once evident to Rivers that "the names applied to the various forms of blood relationship did not correspond to those used by Europeans, but belonged to what is known as a 'classificatory system'; a man's 'brothers' or 'sisters' might include individuals we should call cousins and the key to this nomenclature is to be found in forms of social organisation especially in varieties of the institution of marriage." Rivers found that relationship terms were used to imply definite duties, privileges and mutual restrictions in conduct, rather than being biologically based as ours are. As Head puts it: "all these facts were clearly demonstrable by the genealogical method, a triumphant generalisation which has revolutionised ethnology." The Torres Straits expedition was "revolutionary" in many other respects as well.
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Category theorists will often think of the ring R and the category R as two different representations of the same thing, so that a particularly perverse category theorist might define a ring as a preadditive category with exactly one object (in the same way that a monoid can be viewed as a category with only one object—and forgetting the additive structure of the ring gives us a monoid). In this way, preadditive categories can be seen as a generalisation of rings. Many concepts from ring theory, such as ideals, Jacobson radicals, and factor rings can be generalized in a straightforward manner to this setting. When attempting to write down these generalizations, one should think of the morphisms in the preadditive category as the "elements" of the "generalized ring".
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In mathematics, the Plancherel theorem for spherical functions is an important result in the representation theory of semisimple Lie groups, due in its final form to Harish-Chandra. It is a natural generalisation in non-commutative harmonic analysis of the Plancherel formula and Fourier inversion formula in the representation theory of the group of real numbers in classical harmonic analysis and has a similarly close interconnection with the theory of differential equations. It is the special case for zonal spherical functions of the general Plancherel theorem for semisimple Lie groups, also proved by Harish-Chandra. The Plancherel theorem gives the eigenfunction expansion of radial functions for the Laplacian operator on the associated symmetric space X; it also gives the direct integral decomposition into irreducible representations of the regular representation on L2(X).
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Despite this, the fruitless search for a quantitative relationship allowing the logical derivation of prices from values (a labor theory of price) with the aid of mathematical functions has occupied many economists, producing the famous transformation problem literature. If, however, prices can fluctuate above or below value for all sorts of reasons, Marx's law of value is best seen as a "law of grand averages", an overall generalisation about economic exchange, and the quantitative relationships between labour hours worked and real prices charged for an output are best expressed in probabilistic terms. One might ask, how can "value" be transformed into "price" if a commodity by definition already has a value and a price? To understand this, one needs to recognise the process whereby products move into markets and are withdrawn from markets.
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This type of for-loop is a generalisation of the numeric range type of for-loop, as it allows for the enumeration of sets of items other than number sequences. It is usually characterized by the use of an implicit or explicit iterator, in which the loop variable takes on each of the values in a sequence or other data collection. A representative example in Python is: for item in some_iterable_object: do_something() do_something_else() Where is either a data collection that supports implicit iteration (like a list of employee's names), or may in fact be an iterator itself. Some languages have this in addition to another for-loop syntax; notably, PHP has this type of loop under the name , as well as a three-expression for-loop (see below) under the name .
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George C. Williams, Natural Selection: Domains, Levels and Challenges, (Oxford University Press, 1992), 23-55 > Williams became convinced that the genic neo-Darwinism of his earlier years, > while essentially correct as a theory of microevolutionary change, could not > account for evolutionary phenomena over longer time scales, and was thus an > "utterly inadequate account of the evolution of the Earth's biota" (1992, p. > 31). In particular, he became a staunch advocate of clade selection – a > generalisation of species selection to monophyletic clades of any rank – > which could potentially explain phenomena such as adaptive radiations, long- > term phylogenetic trends, and biases in rates of speciation/extinction. In > Natural Selection (1992), Williams argued that these phenomena cannot be > explained by selectively-driven allele substitutions within populations, the > evolutionary mechanism he had originally championed over all others.
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Other methods avoiding the spectral theorem were later developed independently by Levitan, Levinson and Yoshida, who used the fact that the resolvent of the singular differential operator could be approximated by compact resolvents corresponding to Sturm–Liouville problems for proper subintervals. Another method was found by Mark Grigoryevich Krein; his use of direction functionals was subsequently generalised by Izrail Glazman to arbitrary ordinary differential equations of even order. Weyl applied his theory to Carl Friedrich Gauss's hypergeometric differential equation, thus obtaining a far-reaching generalisation of the transform formula of Gustav Ferdinand Mehler (1881) for the Legendre differential equation, rediscovered by the Russian physicist Vladimir Fock in 1943, and usually called the Mehler–Fock transform. The corresponding ordinary differential operator is the radial part of the Laplacian operator on 2-dimensional hyperbolic space.
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He implores conservationists to take indigenous knowledge into account and form a judgment based on evidence for that particular situation and not generalisation (Ellen, 1993). Dr. Ellen recognises that individual subsistence techniques differ among particular populations and have different ecological profiles when it comes to energy transfer, limiting factors, and carrying capacity. The effect on the landscape is varied and is due to the degree of human effort that is required. Empirical knowledge of plants and animals and its broad understanding allows them to comfortably co-exist together and gives way to claims of mutual causation that gives rise to a complex notion of nature He includes that although uncut forest is recognised by Nuaulu as a single entity, it contrasts in different ways with other land types depending on context.
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The second rule states that if one cause is assigned to a natural effect, then the same cause so far as possible must be assigned to natural effects of the same kind: for example respiration in humans and in animals, fires in the home and in the Sun, or the reflection of light whether it occurs terrestrially or from the planets. An extensive explanation is given of the third rule, concerning the qualities of bodies, and Newton discusses here the generalisation of observational results, with a caution against making up fancies contrary to experiments, and use of the rules to illustrate the observation of gravity and space. Isaac Newton's statement of the four rules revolutionised the investigation of phenomena. With these rules, Newton could in principle begin to address all of the world's present unsolved mysteries.
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Nambooripad's partial order is a generalisation of an earlier known partial order on the set of idempotents in any semigroup. The partial order on the set E of idempotents in a semigroup S is defined as follows: For any e and f in E, e ≤ f if and only if e = ef = fe. Vagner in 1952 had extended this to inverse semigroups as follows: For any a and b in an inverse semigroup S, a ≤ b if and only if a = eb for some idempotent e in S. In the symmetric inverse semigroup, this order actually coincides with the inclusion of partial transformations considered as sets. This partial order is compatible with multiplication on both sides, that is, if a ≤ b then ac ≤ bc and ca ≤ cb for all c in S. Nambooripad extended these definitions to regular semigroups.
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Intervention is usually carried out by speech and language therapists, who use a wide range of techniques to stimulate language learning. In the past, there was a vogue for drilling children in grammatical exercises, using imitation and elicitation methods, but such methods fell into disuse when it became apparent that there was little generalisation to everyday situations. Contemporary approaches to enhancing development of language structure are more likely to adopt 'milieu' methods, in which the intervention is interwoven into natural episodes of communication, and the therapist builds on the child's utterances, rather than dictating what will be talked about. In addition, there has been a move away from a focus solely on grammar and phonology toward interventions that develop children's social use of language, often working in small groups that may include typically developing as well as language-impaired peers.
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In contrast to Comte, who stressed only the unity of scientific method, Spencer sought the unification of scientific knowledge in the form of the reduction of all natural laws to one fundamental law, the law of evolution. In this respect, he followed the model laid down by the Edinburgh publisher Robert Chambers in his anonymous Vestiges of the Natural History of Creation (1844). Although often dismissed as a lightweight forerunner of Charles Darwin's The Origin of Species, Chambers' book was in reality a programme for the unification of science which aimed to show that Laplace's nebular hypothesis for the origin of the solar system and Lamarck's theory of species transformation were both instances of 'one magnificent generalisation of progressive development' (Lewes' phrase). Chambers was associated with Chapman's salon and his work served as the unacknowledged template for the Synthetic Philosophy.
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A lot of the learning methods in machine learning work similar to each other, and are based on each other which makes it difficult to classify them in clear categories. But they can be broadly understood in 4 categories of learning methods, though these categories don't have clear boundaries and they tend to belong to multiple categories of learning methods \- #Hebbian - Neocognitron, Brain-state-in-a-box #Gradient Descent - ADALINE, Hopfield Network, Recurrent Neural Network #Competitive - Learning Vector Quantisation, Self-Organising Feature Map, Adaptive Resonance Theory #Stochastic - Boltzmann Machine, Cauchy Machine It is to be noted that though these learning rules might appear to be based on similar ideas, they do have subtle differences, as they are a generalisation or application over the previous rule, and hence it makes sense to study them separately based on their origins and intents.
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The University of Cambridge believes that their course's generalisation, rather than specialisation, gives their students an advantage. First, it allows students to experience subjects at university level before specialising. Second, many modern sciences exist at the boundaries of traditional disciplines, for example, applying methods from a different discipline. Third, this structure allows other scientific subjects, such as Mathematics (traditionally a very strong subject at Cambridge), Medicine and the History and Philosophy of Science, (and previously Computer sciences before it had been removed for 2020 entry) to link with the Natural Sciences Tripos so that once, say, the two-year Part I of the Medical Sciences tripos has been completed, one can specialise in another biological science in Part II during one's third year, and still come out with a science degree specialised enough to move into postgraduate studies, such as a PhD.
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PMIs have Sources of Authority (SoAs) and Attribute Authorities (AAs) that issue ACs to users, instead of certification authorities (CAs) that issue PKCs to users. Usually PMIs rely on an underlying PKI, since ACs have to be digitally signed by the issuing AA, and the PKI is used to validate the AA's signature. An X.509 AC is a generalisation of the well known X.509 public key certificate (PKC), in which the public key of the PKC has been replaced by any set of attributes of the certificate holder (or subject). Therefore, one could in theory use X.509 ACs to hold a user's public key as well as any other attribute of the user. (In a similar vein, X.509 PKCs can also be used to hold privilege attributes of the subject, by adding them to the subject directory attributes extension of an X.509 PKC).
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Alexander Grothendieck's work during the "Golden Age" period at the IHÉS established several unifying themes in algebraic geometry, number theory, topology, category theory and complex analysis. His first (pre-IHÉS) discovery in algebraic geometry was the Grothendieck–Hirzebruch–Riemann–Roch theorem, a generalisation of the Hirzebruch–Riemann–Roch theorem proved algebraically; in this context he also introduced K-theory. Then, following the programme he outlined in his talk at the 1958 International Congress of Mathematicians, he introduced the theory of schemes, developing it in detail in his Éléments de géométrie algébrique (EGA) and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time. He went on to introduce the étale cohomology theory of schemes, providing the key tools for proving the Weil conjectures, as well as crystalline cohomology and algebraic de Rham cohomology to complement it.
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The one given that name by Siegel (2013, 478) and by Wikipedia, however, relies on some later developments. Although it is an almost trivial consequence of Sprague and Grundy's results, which are also encapsulated in its statement and proof, it was not even formulated, let alone proved, by either of them. The maximum number of colors used by a greedy coloring algorithm is called the Grundy number, also after this work on games, as its definition has some formal similarities with the Sprague–Grundy theory.. In 1939 Grundy began research in algebraic geometry as a research student at the University of Cambridge, eventually specialising in the theory of ideals. In 1941 he won a Smith's Prize for an essay entitled On the theory of R-modules, and his first research paper in the area, A generalisation of additive ideal theory, was published in the following year.Grundy (1942).
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This is usually accounted for by the replacement of horizontal (or contrapuntal) composition, common in the music of the Renaissance, with a new emphasis on the vertical element of composed music. Modern theorists, however, tend to see this as an unsatisfactory generalisation. According to Carl Dahlhaus: Descriptions and definitions of harmony and harmonic practice often show bias towards European (or Western) musical traditions, although many cultures practice vertical harmony In addition, South Asian art music (Hindustani and Carnatic music) is frequently cited as placing little emphasis on what is perceived in western practice as conventional harmony; the underlying harmonic foundation for most South Asian music is the drone, a held open fifth interval (or fourth interval) that does not alter in pitch throughout the course of a composition. and Catherine Schmidt Jones, 'Listening to Indian Classical Music', Connexions, (accessed 16 November 2007) Pitch simultaneity in particular is rarely a major consideration.
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The Chebotarev density theorem may be viewed as a generalisation of Dirichlet's theorem on arithmetic progressions. A quantitative form of Dirichlet's theorem states that if N≥2 is an integer and a is coprime to N, then the proportion of the primes p congruent to a mod N is asymptotic to 1/n, where n=φ(N) is the Euler totient function. This is a special case of the Chebotarev density theorem for the Nth cyclotomic field K. Indeed, the Galois group of K/Q is abelian and can be canonically identified with the group of invertible residue classes mod N. The splitting invariant of a prime p not dividing N is simply its residue class because the number of distinct primes into which p splits is φ(N)/m, where m is multiplicative order of p modulo N; hence by the Chebotarev density theorem, primes are asymptotically uniformly distributed among different residue classes coprime to N.
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Since Cauchy sequences can also be defined in general topological groups, an alternative to relying on a metric structure for defining completeness and constructing the completion of a space is to use a group structure. This is most often seen in the context of topological vector spaces, but requires only the existence of a continuous "subtraction" operation. In this setting, the distance between two points x and y is gauged not by a real number ε via the metric d in the comparison d(x, y) < ε, but by an open neighbourhood N of 0 via subtraction in the comparison x − y ∈ N. A common generalisation of these definitions can be found in the context of a uniform space, where an entourage is a set of all pairs of points that are at no more than a particular "distance" from each other. It is also possible to replace Cauchy sequences in the definition of completeness by Cauchy nets or Cauchy filters.
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May it do good historical work, make good use of the comparative > method; may it collect documents and may it critique them; may it engage > itself in serious statistical enquiries, leaving aside a premature > generalisation, and an illusory assimilation of the social sciences with the > physical-chemical sciences. Mathematical systematisation will come, when it > is able, much later, without doubt very much later (Rey 1903: 199-199).“Nous > croyons en effet que les phénomènes psycho-sociologiques sont d’une telle > complexité qu’ils déjoueront tout effort d’analyse en ce sens. Et si jamais > nous arrivions à les réduire à les éléments assez simples pour les traiter > d’une façon toute mécanique, ce qui est peut-être possible, outre que cela > nous renvoie à un temps fort lointain, les lois qui les concerneraient se > formuleraient sans doute d’une façon bien plus compliquée, et aboutiraient à > des résultats tout à fait différents des résultats simplistes que nous > venons d’exposer.
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Accordingly, a key aspect of explanation is the emphasis on why things happen. In other words, one can think of explanation as an attempt to identify the cause of something. Fairhurst (1981) contextualized explanation in term of requiring something to be explained (the phenomenon that needs to be explained), an explainer (the provider of the explanation) and the explainee (the recipient of the explanation). In this context, Metcalf and Cruickshank (1991) argued that the role of an explanation is to make some concept, procedure or rule plain and comprehensible. Brown and Armstrong (1984) operationally defined explanation as an attempt to provide understanding of a problem to others. This definition strengthens the view of Perrott (1982) who argued that a clear explanation depends on (a) identification of the elements to be related to, for example objects, events, processes and generalisation, and (b), identifying the relationship between them, for example casual, justifying and interpreting.
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A generalisation to dimension 2 of the fundamental groupoid on a set of base was given by Brown and Higgins in 1978 as follows. Let (X,A,C) be a triple of spaces, i.e. C \subseteq A \subseteq X. Define \rho(X,A,C) to be the set of homotopy classes rel vertices of maps of a square into X which take the edges into A and the vertices into C. It is not entirely trivial to prove that the natural compositions of such squares in two directions are inherited by these homotopy classes to give a double groupoid, which also has an extra structure of so-called connections necessary to discuss the idea of commutative cube in a double groupoid. This double groupoid is used in an essential way to prove a two-dimensional Seifert-van Kampen theorem, which gives new information and computations on second relative homotopy groups as part of a crossed module.
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In mathematics, the Laplacian of the indicator of the domain D is a generalisation of the derivative of the Dirac delta function to higher dimensions, and is non-zero only on the surface of D. It can be viewed as the surface delta prime function. It is analogous to the second derivative of the Heaviside step function in one dimension. It can be obtained by letting the Laplace operator work on the indicator function of some domain D. The Laplacian of the indicator can be thought of as having infinitely positive and negative values when evaluated very near the boundary of the domain D. From a mathematical viewpoint, it is not strictly a function but a generalized function or measure. Similarly to the derivative of the Dirac delta function in one dimension, the Laplacian of the indicator only makes sense as a mathematical object when it appears under an integral sign; i.e.
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Cox's later work produced after his move to Birmingham in 1841 was marked by simplification, abstraction and a stripping down of detail. His art of the period combined the breadth and weight characteristic of the earlier English watercolour school, together with a boldness and freedom of expression comparable to later impressionism. His concern with capturing the fleeting nature of weather, atmosphere and light was similar to that of John Constable, but Cox stood apart from the older painter's focus on capturing material detail, instead employing a high degree of generalisation and a focus on overall effect. The quest for character over precision in representing nature was an established characteristic of the Birmingham School of landscape artists with which Cox had been associated early in his life, and as early as 1810 Cox's work had been criticised for its "sketchiness of finish" and "cloudy confusion of objects", which were held to betray "the coarseness of scene-painting".
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German ambassador to India Michael Steiner responded to the incident with an open letter, excerpted below, addressed to Beck-Sickinger. :“Your oversimplifying and discriminating generalisation is an offence to women and men ardently committed to furthering women's empowerment in India; and is an offence to millions of law-abiding, tolerant, open-minded and hard-working Indians. Let's be clear: India is not a country of rapists,” :“The 2012 Nirbhaya rape case has refocused attention on the issue of violence against women. Rape is indeed a serious issue in India as in most countries, including Germany. In India, the Nirbhaya case has triggered lively, honest, sustained and very healthy public debate - a public debate of a quality that wouldn't be possible in many other countries,”. :“I would encourage you to learn more about the diverse, dynamic and fascinating country and the many welcoming and open-minded people of India so that you could correct a simplistic image, which – in my opinion – is particularly unsuitable for a professor and teacher.”.
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Related explorations go on in virtual realities (VR), which make extensive use of patchwork heuristics to crudely simulate immersive and convincing physical environments, albeit at a maximal speed of seventeen times slower than "real" time, limited by the optical crystal computing technology used at the time of the story. Larger VR environments, covering a greater internal volume in greater detail, are cost-prohibitive even though VR worlds are computed selectively for inhabitants, reducing redundancy and extraneous objects and places to the minimal details required to provide a convincing experience to those inhabitants; for example, a mirror not being looked at would be reduced to a reflection value, with details being "filled in" as necessary if its owner were to turn their model-of-a-head towards it. Within the story, "Copies" – digital renderings of human brains with complete subjective consciousness, the technical descendants of ever more comprehensive medical simulations – live within VR environments after a process of "scanning". Copies are the only objects within VR environments that are simulated in full detail, everything else being produced with varying levels of generalisation, lossy compression, and hashing at all times.
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The (apparent) paradox between the second law of thermodynamics and the high degree of order and complexity produced by living systems, according to Avery, has its resolution "in the information content of the Gibbs free energy that enters the biosphere from outside sources." Assuming evolution drives organisms towards higher information content, it is postulated by Gregory Chaitin that life has properties of high mutual information, and by Tamvakis that life can be quantified using mutual information density metrics, a generalisation of the concept of Biodiversity. In a study titled "Natural selection for least action" published in the Proceedings of the Royal Society A., Ville Kaila and Arto Annila of the University of Helsinki describe how the process of natural selection responsible for such local increase in order may be mathematically derived directly from the expression of the second law equation for connected non-equilibrium open systems. The second law of thermodynamics can be written as an equation of motion to describe evolution, showing how natural selection and the principle of least action can be connected by expressing natural selection in terms of chemical thermodynamics.
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