Joyce and Proust work from detail to generality; Kafka works from generality to detail, giving his fiction the feeling that something deeply significant is going on, if only we could grasp what precisely it is.
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I resist the impulse to pull a neat generality from it.
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Keynes's peers, while impressed by the book, weren't quite sure about its generality.
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He turns his specific detail of the workaday into a universal generality of jubilee.
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The system is specifically crafted for generality so that the end result will be emergent properties.
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"Wiretap" has often been used as a generality for surveillance, particularly among those of Trump's generation.
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The film is about a very complex relationship and I found that you can't play generality.
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We should all be cautious when universal truths are stated at a high level of generality.
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CS: I think the authorial intent that matters is not at a low level of generality.
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But it will gain you about zero incremental understanding of how to achieve generality in artificial intelligence.
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The one generality I'd like to offer is that it takes up a lot of our time and energy.
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This view has its detractors, but even its proponents insist that this generality hardly applies to all men and women.
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Yes, but: Technical standards may unite the industry, but given their intrinsic generality they are not sufficient for demonstrating safety.
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General intelligence can generate task-specific skills, but there is no path in reverse, from task-specific skill to generality.
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But I believe that the majority of my party members, as well as the generality of Zimbabweans, will share that vision.
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But because of the generality of neural networks, you can leverage this special-purpose hardware for a lot of other things.
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But even Nolde—who, incidentally, fell prey to Nazi sympathies, as Munch did not—tends toward generality in what he expresses.
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He filled his time by rising to a level of vapid generality that was utterly detached from the choices in the actual legislation.
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Of note: Considering the generality with which the term "millennial" is used, not everyone who identifies as a millennial may necessarily have this placement.
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"Republicans are strongest on these issues on the level of generality as opposed to the pragmatics," Mr. Miller, of the American Enterprise Institute, said.
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At the highest level of generality, there is some conceivable similarity between even the most extremely different cases or concepts, but this was a serious reach.
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Ben makes sure to compliment her morals, values, faith, commitment, and any other glittering generality that might possibly apply to both Becca and Viewers Like Her.
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The assumption seems to be that this A.I. could surpass the generality and flexibility of human intelligence while seamlessly retaining the speed, precision and programmability of a computer.
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At a high level of generality, FISA applications could contain investigative information obtained through a variety of sources, including sensitive technical (like wiretaps) and human sources, as examples.
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While acknowledging some truth to that generality, things are changing, said Emily Miller, director of the Association of American Universities' Undergraduate STEM (Science, Technology, Engineering and Mathematics) Education Initiative.
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Transfused into a sick person, that plasma would have a diluted generality—in fighting everything, it might not wage as intense an attack on the specific disease you're after.
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" Kelly Williams, a black American Microsoft office specialist in Houston did not find any fault in Trump's presidency when he said: "Trump is clearly misunderstood by the generality of Americans.
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In a theorem of stunning generality, Professor Arrow proved that no system of majority voting worked satisfactorily according to a carefully articulated definition of "satisfactory" (which social scientists generally accept).
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It's too early to know, but one generality that does seem to be emerging, and it's one that makes sense, is that closely related species tend to evolve the same way.
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"The generality of Zimbabwe, who have experienced brutalization, intimidation and violence, would be very skeptical if the role of the military is not properly defined," he told CNN's Christiane Amanpour on Thursday.
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Instead, they suggest bringing back a priority that's fallen out of fashion in many corners of political science: having specific and detailed knowledge of a particular context rather than striving for broad generality.
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While the lyrics describe sexual anxiety and coming out with empathetic generality, Lacy's hesitant singing often disappears beneath an oceanic expanse of high, wet, trebly rhythm guitar, the album's loudest and mildest ingredient.
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"She" could be anyone, which might be the point, but the generality robs the performance of the chance to add substance and depth to the engaging visual experience that Herbertson and Cobham have devised.
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At a high level of generality, it isn't unusual for presidential nominees to select running mates with whom they have long-standing substantive disagreements (though usually not as significant as the ones dividing Trump and Pence).
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"(The) French president for the second time in 24 hours met with me and he presented that plan to me, and I said that the generality of that plan from our point of view (is) acceptable," Rouhani said.
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Polkadot is all about extending the generality and efficiency of that by introducing new state-transition engines, and by allowing them to be securely interoperable without having to do all the usual faff of building a secure blockchain.
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Questions of generality—what effect that action might cause and for whom psychedelics could be helpful, given individual differences in genetics, microbial colonies, environment, and access to those treatments—as well as the legality surrounding psychedelic treatments remain.
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Each day you have to get up in the morning, get on the subway, perhaps deal with some gross man, and then sit down at your desk and think about it all over again on some dissociative level of generality.
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"You have this toxic dynamic where journalists and scientists enable each other in a way that massively inflates the certainty and generality of how scientific findings are communicated and the promises that are made to the public," writes Daniel Molden, an associate professor of psychology at Northwestern University.
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But CBO was unable to estimate the cost of the PTC mandate on freight railroads beyond a generality of "a few billion dollars," and the expansion of the mandate to commuter railroads happened on the Senate floor — not in committee — so CBO was not required to estimate its costs at all.
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Some comparisons made elsewhere, however, are less convincing because of their generality; it is curious, for example, to match Rodin's large scale erotically driven "The Kiss" (1882), its two figures entwined rising up from their plinth, with the reclining female figures L and M from the East pediment on the basis that their sensuously clinging drapery and arching headless bodies share an erotic charge.
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And I saw a recurring theme here, Sean, and that&aposs that most of the punditry that we heard over the last 48 hours, there was a lot of complaining about the generality of the agreement, about Trump not denouncing human right abuses in North Korea when we never heard anything about that with the Iran deal in Tehran and the way they treat their people in that country.
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Everything that keeps the Beatles sounding fresh and innovative after fifty years thanks to specificity of vision also applies to Prince after thirty years thanks to generality of vision; ignoring modern styles, which produce a contemporaneity that eventually dates, Prince instead targeted multiple past, present, and pseudo styles to produce a distance between musical subject (Prince) and object (the song, plus its genre, plus its timeframe) that remains permanently contemporary due to atemporality.
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Mr Casby shook his head, in Placid and benignant generality.
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Deleuze uses the introduction to clarify the term "repetition." Deleuze's repetition can be understood by contrasting it to generality. Both words describe events that have some underlying connections. Generality refers to events that are connected through cycles, equalities, and laws.
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In particular, this is true for . Since . Without loss of generality, assume that . Then .
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This points to the generality and intuitive appeal of effort as a heuristic for quality.
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Quasi-experiments occur when treatments are administered as-if randomly (e.g. U.S. Congressional districts where candidates win with slim-margins, weather patterns, natural disasters, etc.). Field experiments encompass a broad array of experimental designs, each with varying degrees of generality. Some criteria of generality (e.g.
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Lee, Witness. The Speciality, Generality, and Practicality of the Church Life. Anaheim: Living Stream Ministry (1984).
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The letter-frequency effect and the generality of familiarity effects on perception.Perception & Psychophysics, 30, 436 – 446.
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Saint-Sernin Basilica in Toulouse, displaying the typical pink brick architecture of Upper Languedoc. For administrative purposes, Languedoc was divided in two généralités, the généralité of Toulouse and the généralité of Montpellier, the combined territory of the two generalities exactly matching that of the gouvernement of Languedoc. At the head of a generality was an intendant, but in the case of Languedoc there was only one intendant responsible for both generalities, and he was often referred to as the intendant of Languedoc, even though technically speaking he was in fact the intendant of the generality of Toulouse and intendant of the generality of Montpellier. The generality of Toulouse is also referred to as Upper Languedoc (Haut-Languedoc), while the generality of Montpellier, down to the level of the sea, is referred to as Lower Languedoc (Bas-Languedoc).
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The French king was offered the Generality Lands and ten million guilders. Compared to the eventual outcome of the war, these conditions were very favourable to France. It would have made territorial gains not equalled until 1810. The Generality Lands included the fortresses of Breda, 's-Hertogenbosch and Maastricht.
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This extra generality is not used much as most decomposable measures that occur in practice are σ-finite.
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In more generality, the process can be applied independently to any collection of reguli in a regular spread, resulting in André planes.
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The Met Office have a climate station at Sidmouth in the generality of Bulverton that records the comparatively mild United Kingdom climate.
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Prove that . # If must divide and thus and . So, without loss of generality, assume that . # Let and rearrange and substitute to get .
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Additional instructions from Karol Stanisław also contained blackening of the opinions of the Generality and M. Krasiński, who attempted to persuade Turkey not to recognize Radziwiłł as the marshal (and even to assassinate him), which would enhance Radziwiłł to take up Krasiński's position. Under pressure from the Generality, Radziwiłł sent a letter to the Vizier recognizing the authority of M. Krasiński and ordering the return of Mr Horwatt. His efforts to raise 15,000 ducats for an unexpected conflict with the Generality was unsuccessful, though he searched for a loan from J. Mniszech and previously from his dear friend and close ally Jan Klemens Branicki. Eventually, in unknown circumstances, the control of the Generality was taken over by the Czartoryski family and Radziwiłł's position as envoy and diplomat was immediately terminated.
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But the principle may also be applied with even more generality (including even any selection from a matrix of beats of any size).
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Without loss of generality, suppose . Then by the lemma, the sum of is strictly less than and so is strictly less than , whereas the sum of is clearly at least . This contradicts the fact that and have the same sum, and we can conclude that either or must be empty. Now assume (again without loss of generality) that is empty.
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Additional laws have been suggested, but have not achieved the generality of the four accepted laws, and are generally not discussed in standard textbooks.
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On Specific Objectivity: An attempt at formalizing the request for generality and validity of scientific statements. The Danish Yearbook of Philosophy, 14, 58-93.
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Often elliptic curves in Edwards form are defined having c=1, without loss of generality. In the following sections, it is assumed that c=1.
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In methodology, the power of a method is inversely proportional to the generality of the method, i.e.: the more specific the method, the more powerful.
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This focus is without loss of generality since the climbing game is representative of problems with high miscoordination penalty and a single optimal joint action.
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The projection-slice theorem states that p(x) and s(kx) are 1-dimensional Fourier transform pairs. The projection-slice theorem is easily proven for the case of two dimensions. Without loss of generality, we can take the projection line to be the x-axis. There is no loss of generality because if we use a shifted and rotated line, the law still applies.
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Notice also that if T is a formalized axiomatic system, then the statement that T is consistent is itself finitary, formulable using a letter for generality.
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Gadaire, D.M.; Kelley, M.E. & DeRosa, N.M. (2010). Research Needed for Focusing on Additional Generality of Applied Behavior Analysis. The Behavior Analyst Today, 11(1), 49–58 BAO.
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Similarly, an arbitrary quantum operation can be implemented via introducing an ancilla and performing a suitable unitary evolution. Thus the no-cloning theorem holds in full generality.
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Sequent calculi and systems of natural deduction have been developed for several modal logics, but it has proven hard to combine generality with other features expected of good structural proof theories, such as purity (the proof theory does not introduce extra-logical notions such as labels) and analyticity (the logical rules support a clean notion of analytic proof). More complex calculi have been applied to modal logic to achieve generality.
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A glittering generality (also called glowing generality) is an emotionally appealing phrase so closely associated with highly valued concepts and beliefs that it carries conviction without supporting information or reason. Such highly valued concepts attract general approval and acclaim. Their appeal is to emotions such as love of country and home, and desire for peace, freedom, glory, and honor. They ask for approval without examination of the reason.
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Csikszentmihalyi, M., Finding Flow, 1997 Self-efficacy is made of dimensions like magnitude, strength, and generality to explain how one believes they will perform on a specific task.
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Modern developments have extended graphical models to non-parametric analysis, and thus achieved a generality and flexibility that has transformed causal analysis in computer science, epidemiology, and social science.
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Generality of these school sites is 38 acres located in the state assembly Peramu Jaya, Pekan Parliament, about 15 km from the city town and 35 km from Kuantan.
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93(5): p. 1351-1362.Thomsen, M.S. and T. Wernberg, On the generality of cascading habitat-formation. Proceedings of the Royal Society B: Biological Sciences, 2014. 281(1777):20131994.
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There is one proper noun for each singular event: Leibniz creates a logic of singularity, which Aristotle thought impossible (he considered that there could only be knowledge of generality).
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Otherwise, without loss of generality, g(x)>0. But g(-x)<0. Hence, by the IVT, there is a point y between x and -x at which g(y)=0.
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This surrender cut the town off from the rest of the duchy and the area was treated by the Republic as an occupation zone without political liberties (see also Generality Lands).
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Similar trends regarding lack of generality of proposed models is seen in the latest review by Fan and Qiao (2010).Fan, W., Qiao, P.Z., 2010. Vibration-based damage identification methods: a review and comparative study. Structural Health Monitoring. The lack of generality of damage models is addressed by proposing a ‘unified framework’ which is valid for self-adjoint systems using beam theories like Euler–Bernoulli beam theory, Timoshenko, plate theories like Kirchhoff and Mindlin and shell theories.
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It is observed by Forney that Viterbi's maximum likelihood decoding of convolutional codes also used algorithms of GDL-like generality. 2\. Forward-backward algorithm The forward backward algorithm helped as an algorithm for tracking the states in the markov chain. And this also was used the algorithm of GDL like generality 3\. Artificial intelligence The notion of junction trees has been used to solve many problems in AI. Also the concept of bucket elimination used many of the concepts.
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Sea otters and kelp forests in Alaska: generality and variation in a community ecological paradigm. Ecological Monographs 65: 75-100. sea otters (Enhydra lutris) control populations of herbivorous sea urchins through predation.
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In full generality, polyhedral spaces were first defined by Milka Milka, A. D. Multidimensional spaces with polyhedral metric of nonnegative curvature. I. (Russian) Ukrain. Geometr. Sb. Vyp. 5--6 1968 103–114.
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On the other hand, a modern view of the problem of multiple generality in traditional logic concludes that quantifiers cannot nest usefully if there are no polyadic predicates to relate the bound variables.
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Without loss of generality, we can choose, respectively, the - and -planes as these invariant planes. A rotation in 4D of a point through angles and is then simply expressed in Hopf coordinates as .
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In more generality, Weyl quantization is studied in cases where the phase space is a symplectic manifold, or possibly a Poisson manifold. Related structures include the Poisson–Lie groups and Kac–Moody algebras.
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To show that a non- trivial intersection of two spheres is a circle, assume (without loss of generality) that one sphere (with radius R) is centered at the origin. Points on this sphere satisfy :x^2 + y^2 + z^2 = R^2. Also without loss of generality, assume that the second sphere, with radius r, is centered at a point on the positive x-axis, at distance a from the origin. Its points satisfy :(x-a)^2 + y^2 + z^2 = r^2.
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This follows from the implication , which we will now prove. If , where G is some divisible group, and , then . Now fix some . Without loss of generality, we may assume that (otherwise, choose −x instead).
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But Article 15(2) nevertheless requires the forum court to consider adopting an approach that will preserve the overall validity of the trust insofar as that generality does not offend against the mandatory policy.
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Support for the generality of the rule is at best equivocal.Gaston, K. J., Blackburn, T. M. and Spicer, J. I. (1998). Rapoport's rule: time for an epitaph? Trends in Ecology and Evolution 13, 70–74.
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Ideally, each service operation maps to a single business function, although if a single operation can provide multiple functions without adding design complexity or increasing message sizes, this generality can reduce implementation and usage costs.
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"Generality" refers more to functional relationships than individual events. That responses occur to X about the same as to Z is irrelevant; rather, that distributed practice helps in learning nonsense syllables and in learning other tasks.
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Another reason for turning to C++, which Stepanov recognized early on, was the C/C++ model of computation that allows very flexible access to storage via pointers, which is crucial to achieving generality without losing efficiency.
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Second, in his view, the Act does not "change the law." To do so, a statute "must imply some measure of generality or preservation of an adjudicative role for the courts."Patchak, 138 S. Ct. at 920.
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In the history of mathematics, the generality of algebra was a phrase used by Augustin-Louis Cauchy to describe a method of argument that was used in the 18th century by mathematicians such as Leonhard Euler and Joseph-Louis Lagrange,. particularly in manipulating infinite series. According to Koetsier,. the generality of algebra principle assumed, roughly, that the algebraic rules that hold for a certain class of expressions can be extended to hold more generally on a larger class of objects, even if the rules are no longer obviously valid.
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Is loss-aversion magnitude- dependent? Measuring prospective affective judgments regarding gains and losses. Judgment and Decision Making, 12(1), 81–89. the other, is that the generality of the loss aversion pattern is lower than that thought previously.
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For example, consider to be the set of integers from to , and . Each player chooses an element of , and . Suppose player A plays and player B plays . Without loss of generality, assume player A chooses the larger number, so .
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J. 36 (1987), no. 1, 1–40. He later extended his formula to allow for general codimension and general positive solutions of the "backwards" heat equation; the monotonicity in this generality crucially uses Richard Hamilton's matrix Li-Yau estimate.Richard S. Hamilton.
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Universal Binary JSON (UBJSON) is a computer data interchange format. It is a binary form directly imitating JSON, but requiring fewer bytes of data. It aims to achieve the generality of JSON, combined with being much easier to process than JSON.
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The set of spectra of a theory is closed under union, intersection, addition, and multiplication. In full generality, it is not known if the set of spectra of a theory is closed by complementation; this is the so-called Asser's Problem.
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Prove that is a perfect square. # Fix some value that is a non-square positive integer. Assume there exist positive integers for which . # Let be positive integers for which and such that is minimized, and without loss of generality assume .
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The creativity conundrum. Philadelphia: Psychology Press With John Baer, he developed the Amusement Park Theoretical (APT) Model of Creativity.Baer, J., & Kaufman, J. C. (2005). Bridging generality and specificity: The Amusement Park Theoretical (APT) Model of creativity. Roeper Reviewer, 27, 158-163.
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With over 170 years of history, the association has a legacy of documenting the economic and social conditions of Catalan emigrants, and has received awards from the Institute of Catalan Studies, the Generality of Catalonia and the Cross of St.George 1993.
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This claim was rejected by the U.S. District Court in Abend v. Spielberg, 748 F.Supp.2d 200 (S.D.N.Y. 2010), on the basis that the original Woolrich short story and Disturbia are only similar at a high level of generality and abstraction.
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Government of the Kingdom of Spain, Gobierno del Reino de España), while those of the community of the Valencian Country and the Val d'Aran are known as the "Council of the Valencian Generality" (Consell de la Generalitat Valenciana) and the Síndic respectively.
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A number of numerical Poisson- Boltzmann equation solvers of varying generality and efficiency have been developed, including one application with a specialized computer hardware platform. However, performance from PB solvers does not yet equal that from the more commonly used generalized Born approximation.
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Some Protocol Independent Multicast routing protocols use rendezvous hashing to pick a rendezvous point. Given its simplicity and generality, rendezvous hashing has been applied in a wide variety of applications, including mobile caching, router design, secure key establishment, and sharding and distributed databases.
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See, e.g., Grant Gilmore, The Ages of American Law 81 (1977). Professor Grant Gilmore said of Wesley Sturges: > What did Wesley teach us?...He taught us forever to be on our guard against > the slippery generality, the received principle, the authoritative > proposition.
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Feurs with the Forez County is forfeited to the Constable of Bourbon along with his other possessions in 1523. It finally enters the royal domain in 1531. In 1542, the city is attached to the generality of Lyon, created by Henry II .
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Consequently, a force that tends to collapse the chain is exerted by the ideal chain between its two free ends. In this section, the mean of this force will be derived. The generality of the expression obtained at the thermodynamic limit will then be discussed.
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For simplicity, the above text describes a special case; Huygens's description has greater generality. This discovery gave Newton another reason to reject the wave theory: rays of light evidently had "sides".Newton, 1730, pp. 358–61. Corpuscles could have sidesNewton, 1730, pp. 373–4.
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In a uniform multicommodity flow problem, there is a commodity for every pair of nodes and the demand for every commodity is the same. (Without loss of generality, the demand for every commodity is set to one.) The underlying network and capacities are arbitrary.
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Donald Dewsbury reviewed the works of several psychologists and their definitions and concluded that the object of comparative psychology is to establish principles of generality focusing on both proximate and ultimate causation.Dewsbury, D. (1984). Comparative Psychology in the Twentieth Century. Hutchinson Ross Publishing Company.
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Smale conjectured that if M is an oriented smooth closed manifold, the identity component of the group of orientation-preserving diffeomorphisms is simple. This had first been proved for a product of circles by Michel Herman; it was proved in full generality by Thurston.
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In certain countries (viz. the Italian states pre-1860), armorial heraldry was not strictly regulated, while titles of nobility were. As a generality, most nobles, whether titled or not, have coats of arms, hence the widely held perception of heraldry as an aristocratic trapping.
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He investigated polymers and rubber. He showed that rubber consisted of repeating units. He established experimental procedures for ozonolysis, demonstrated the generality of the reaction of unsaturated compounds with ozone, and showed that ozone could be used for the synthesis of a variety of compounds.
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It was chartered on 31 December 1600. While membership was open to the public (known as 'the generality'), executive control was restricted to the merchant élite, and Leonard was not only one of the original 'committees' (i.e. directors) but also joint treasurer from 1600 until 1602.
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In behavioral psychology, the assumption of generality is the assumption that the results of experiments involving schedules of reinforcement, conducted on non-human subjects (often pigeons), can be generalized to apply to humans.Whaley, D.L & Mallott, R.W. (1971). Elementary Principles of Behavior. Englewood Cliffs, NJ: Prentice-Hall.
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Fergus Lowe has questioned the generality of schedule effects in cases of fixed-interval performance among humans and non-humans.Lowe, F.C. (1979) Determinants of human operant behavior. In M.D. Zeiler & P. Harzem (Eds), Reinforcement and the organization of behavior (pp. 159–192). New York: John Wiley.
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Sea otters and kelp forests in Alaska: Generality and variation in a community ecological paradigm. Ecological Monographs 65, 75-100. habitats. Foundation plant species can be replaced with other species or substratum completely lacking vegetation and insects can defoliate whole mangroves (Feller 2002).Feller, I. C. 2002.
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Perturbative forms of QCD have been tested to a few percent. Perturbative models assume relatively small changes from the ground state, i.e. relatively low temperatures and densities, which simplifies calculations at the cost of generality. In contrast, non- perturbative forms of QCD have barely been tested.
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He found that, agreeing with the beneficial acclimation hypothesis, colonies acclimated at 32 °C competed better at 32 °C. However, at 41.5 °C, colonies acclimated at 32 °C competed better as well. This led to the authors' rejection of the generality of beneficial acclimation. Huey et al.
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Still, there are other views as well. Some believe that democracy is part of the rule of law. The "formal" interpretation is more widespread than the "substantive" interpretation. Formalists hold that the law must be prospective, well-known, and have characteristics of generality, equality, and certainty.
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This gave a certain generality to those processes. They then showed how these processes related to the elimination of dominated strategies. This was shown to have implications for convergence in Cournot and Bertrand games.See also Gans, J.S. "Best Replies and Adaptive Learning," Mathematical Social Sciences, Vol.
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It takes a full parser to recognize such patterns in their full generality. A parser can push parentheses on a stack and then try to pop them off and see if the stack is empty at the end (see example in the Structure and Interpretation of Computer Programs book).
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Wilks continued to improve on the generality of the theorem throughout his life, with his most general proof published in 1962.Wilks, Samuel S. (1962), Mathematical Statistics, New York: John Wiley & Sons. . Reviews of the development of maximum likelihood estimation have been provided by a number of authors.
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In J. C. Kaufman & R. J. Sternberg (Eds.), Cambridge handbook of creativity (pp. 321-341). Cambridge University Press. He developed the Amusement Park Theory of creativity (with James C. Kaufman)Baer, J., & Kaufman, J. C. (2005). Bridging generality and specificity: The Amusement Park Theoretical (APT) Model of creativity.
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The naturalization of sunlight helps our bodies to stay awake and keep motivated. The darkness that comes with night tells our body to slow down for the day and get some rest. The ability to survive comes with generality. Experiments have been done to test inescapability and insolubility.
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Pietarinen and T. Tulenheimo, eds. Springer 2009, pages 249-350. criticizing it for lacking a convincing semantical justification the associated constructivistic claims, and for being incomplete as a result of "throwing out the baby with the bath water". Heyting's intuitionistic logic, in its full generality, has been shown to be soundG.
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The Derjaguin approximation is unique given its simplicity and generality. To improve this approximation, the surface element integration method as well as the surface integration approach were proposed to obtain more accurate expressions of the forces between two bodies. These procedures also considers the relative orientation of the approaching surfaces.
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This prevents the repetition of discovering the same rule as well as preserves the coverage accuracy and the generality of new rules. After that, the algorithm is repeated to select (conquer) another seed example until all the examples are covered. Hence, only one rule can be generated at each step.
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He was made under-engineer of the generality of Tours in 1751. Notably, it was he who conceived several bridges over the River Loire, along with the Pont des Arts over the Seine in Paris, the first dike project at Cherbourg, and several quays at ports in north-west France.
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Early examinations of the properties of equilibrium were based on an implicit definition as tangency, and convexity seems to have been implicitly assumed.Oscar Lange, ‘The Foundations of Welfare Economics’ (1942). There was no doubt that equilibrium would be reached: gradient ascent would lead to it. But the results lacked generality.
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Nial uses a generalized and expressive Array Theory in its Version 4, but sacrificed some of the generality of functional model, and modified the Array Theory in the Version 6. Only Version 6 is available now. Nial defines all its data types as nested rectangular arrays. ints, booleans, chars etc.
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Mathematical statements have their own moderately complex taxonomy, being divided into axioms, conjectures, propositions, theorems, lemmas and corollaries. And there are stock phrases in mathematics, used with specific meanings, such as "", "" and "without loss of generality". Such phrases are known as mathematical jargon. The vocabulary of mathematics also has visual elements.
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Budapest is the capital of Hungary. Below is a list of public place names of Budapest that refer to famous people, cities or historic events. Generality of Budapest's public place names relate to the Hungarian national history. In Budapest there are about 8,600 named public place (streets, squares, parks etc.).
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The generality of the theory of group testing lends it to many diverse applications, including clone screening, locating electrical shorts; high speed computer networks; medical examination, quantity searching, statistics; machine learning, DNA sequencing; cryptography; and data forensics. This section provides a brief overview of a small selection of these applications.
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26 (PDF p. 28) Lucy Mary Jane Garnett wrote in Turkish Life in Town and Country, published in 1904, that within Constantinople (Istanbul), "The generality of men, in official circles at least, speak French".Garnett, Lucy Mary Jane. Turkish Life in Town and Country. G.P. Putnam's Sons, 1904. p. 206.
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These usually involve fields in linear homogeneous media. This places considerable restrictions on the range and generality of problems suitable for boundary elements. Nonlinearities can be included in the formulation, although they generally introduce volume integrals which require the volume to be discretized before solution, removing an oft-cited advantage of BEM.
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Pures Appl. 9: 55 (1976) 269–296), and finally, in full generality, by Schoen ("Conformal Deformation of a Riemannian Metric to Constant Scalar Curvature," Journal of Differential Geometry 20 (1984) 478-495). Yamabe's visionary paper thereby became a cornerstone of modern Riemannnian geometry, and is thus largely responsible for his posthumous fame.
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The children studied are also atypical in that they are the offspring of researchers or their close colleagues, and so are from highly educated backgrounds. The child studied by Katherine Nelson, for example, was highly precocious in her language abilities, which raises questions about the generality of findings on that one child.
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Edward Elliott engaged in a discussion of Joseph Mede's Apostasy of the Last Times.Horae Apocalypticae Vol 2 p. 497 He considered the distinction between the Devil (in the singular) and demons (in their generality). The Devil or Satan, he said, meant "the Accuser" or prosecutor of mankind as used in a courtroom sense.
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To do this, Alpert asserted that the "hard science core" of the social sciences (i.e. Those social science studies that adopted quantitative research methods) could fall under the NSF mandate to support basic research which conforms to the highest standards of scientific inquiry and fulfills the basic conditions of objectivity, verifiability, and generality.
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Cox point processes exhibit a clustering of points, which can be shown mathematically to be larger than those of Poisson point processes. The generality and tractability of Cox processes has resulted in them being used as models in fields such as spatial statisticsJ. Møller and R. P. Waagepetersen. Modern statistics for spatial point processes.
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This common conception of communication simply views communication as a means of sending and receiving information. The strengths of this model are simplicity, generality, and quantifiability. Claude Shannon and Warren Weaver structured this model based on the following elements: # An information source, which produces a message. # A transmitter, which encodes the message into signals.
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The rings for which such a theorem exists are called Euclidean domains, but in this generality, uniqueness of the quotient and remainder is not guaranteed. Polynomial division leads to a result known as the polynomial remainder theorem: If a polynomial f(x) is divided by x − k, the remainder is the constant r = f(k).
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Doyle, 719 N.W.2d 408, 449 (Wis., 2006), ("Prior to the War Between the States all but three states had barred lotteries.") Their usage demonstrates the generality of the term's use. Roosevelt was born and raised in New York State, and Blackmun was born in southern Illinois but grew up in St. Paul, Minnesota.
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This question was answered negatively in the full generality, for which Conway et al. had hoped, by Costin, Friedman and Ehrlich in 2015. However, the analysis of Costin et al. shows that definite integrals do exist for a sufficiently broad class of surreal functions for which Kruskal's vision of asymptotic analysis, broadly conceived, goes through.
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The Bottleneck traveling salesman problem (bottleneck TSP) is a problem in discrete or combinatorial optimization. The problem is to find the Hamiltonian cycle in a weighted graph which minimizes the weight of the most weighty edge of the cycle.. It was first formulated by with some additional constraints, and in its full generality by ...
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The second defining property holds in more generality: for any -form ; more succinctly, . The third defining property implies as a special case that if is a function and a is -form, then because a function is a -form, and scalar multiplication and the exterior product are equivalent when one of the arguments is a scalar.
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Historical generalisations may be reduced to a set of laws of higher generality (i.e. one could say that history depends upon psychology). However, in order to form predictions from these generalisations we also need specific initial conditions. To the extent that conditions change or are changing, any ‘law’ may apply differently and trends may disappear.
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KIVA-4 is maintained and distributed through LANL. While KIVA-4 maintains the full generality of KIVA-3V, it adds the capability of computing with unstructured grids. Unstructured grids can be generated more easily than structured grids for complex geometries. The unstructured grids may be composed of a variety of elements including hexahedra, prisms, pyramids, and tetrahedra.
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In cognitive psychology, a basic category is a category at a particular level of the category inclusion hierarchy (i.e., a particular level of generality) that is preferred by humans in learning and memory tasks. The term is associated with the work of psychologist Eleanor Rosch, who demonstrated basic category preferences in a number of classic experiments.
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In mathematics, plurisubharmonic functions (sometimes abbreviated as psh, plsh, or plush functions) form an important class of functions used in complex analysis. On a Kähler manifold, plurisubharmonic functions form a subset of the subharmonic functions. However, unlike subharmonic functions (which are defined on a Riemannian manifold) plurisubharmonic functions can be defined in full generality on complex analytic spaces.
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In all examples below, there are two agents - Alice and George, and two goods - apples (x) and guavas (y). A. Unique equilibrium: the utility functions are: :u_A(x,y)=3x+2y, :u_G(x,y)=2x+3y. The total endowment is T=(6,6). Without loss of generality, we can normalize the price vector such that P_x=1.
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She uncovered new mechanisms by which integrins contribute to cancer, including the first tumour-associated integrin mutation. She also identified the first Wnt-inhibitory mutation that stimulates tumour formation. The generality of her observations has been confirmed in other solid tumours. In recent years she has become increasingly interested in the relationship between genetic variants and cellular behaviour.
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Unlike earlier turbulence models, k-ε model focuses on the mechanisms that affect the turbulent kinetic energy. The mixing length model lacks this kind of generality. The underlying assumption of this model is that the turbulent viscosity is isotropic, in other words, the ratio between Reynolds stress and mean rate of deformations is the same in all directions.
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Rasch Measurement Transactions, 19:3, 1032 that separate proponents of the Rasch model from the item response modeling tradition. A central aspect of this divide relates to the role of specific objectivity,Rasch, G. (1977). On Specific Objectivity: An attempt at formalizing the request for generality and validity of scientific statements. The Danish Yearbook of Philosophy, 14, 58-93.
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Whatever the cause of the risky shift phenomenon or the worries regarding the generality of the phenomenon, the point of interest is that individuals may be manipulated in their decision making. The mechanism causing the post- discussion group shift causes a change in the perception of the problem domain by some or all of the group members.
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They often reflect shades of sadness. His painting acquired greater generality, the drawing became more laconic. Composition of painting acquired more rigorous form and expressing the author's intent. All that was done by Dmitry Maevsky in landscape painting, it was extremely sincere and deeply felt, foreign to the slightest hint of external effects, the play, imitation.
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They can only provide conclusions based on deductive or inductive reasoning from their starting assumptions. Thought experiments invoke particulars that are irrelevant to the generality of their conclusions. It is the invocation of these particulars that give thought experiments their experiment-like appearance. A thought experiment can always be reconstructed as a straightforward argument, without the irrelevant particulars.
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This problem can be partially solved using an ortho methyl blocking group. Unfortunately, with ortho methyl groups both the rate and generality of the reaction are reduced. Substituents at the meta position influence regioselectivity. The reaction preferentially adds at the least sterically hindered ortho position, except when there is a meta group capable of coordinating with the Ru catalyst.
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The monograph Elements of Psychophysical Theory presents the mathematical foundation of psychophysics and includes an introduction to measurement theory and functional equations. Falmagne's work in philosophy of science concerns foundational issues in algebraic measurement and in probabilistic measurement. A distinctive feature of his research lies in the use of functional equations in order to achieve generality.
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Because of the generality of the tensor algebra, many other algebras of interest can be constructed by starting with the tensor algebra and then imposing certain relations on the generators, i.e. by constructing certain quotient algebras of T(V). Examples of this are the exterior algebra, the symmetric algebra, Clifford algebras, the Weyl algebra and universal enveloping algebras.
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Claude Gilliot, Creation of a fixed text, pg. 50. Taken from The Cambridge Companion to the Qur'an by Jane Dammen McAuliffe. Cambridge: Cambridge University Press, 2006. Together, their style is the most common form of Qur'anic recitation in the generality of African mosques outside of Egypt,Cyril Glasse, The New Encyclopedia of Islam, p. 268. Intr.
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The production of Diwas do not depend highly on exact measurements. This affects the generality of the music in indigenous tribes of the Philippines. Thus unlike the Western music which depends largely on musical notes in producing melody, indigenous music in the Philippines depends highly on rhythm. This is the very reason why sizes, length, radius, etc.
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Additional resolutions of the confederates, known as sanctia, would also be deposited with the court. Membership of the confederation was voluntary, and required an oath. The executive branch of a confederation was headed by a marshal, and a group of advisers, each known as konsyliarz konfederacji. A marshal and associated konsyliarze were known as a generality (generalność).
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Correspondingly there are types of tensors at work in many branches of abstract algebra, particularly in homological algebra and representation theory. Multilinear algebra can be developed in greater generality than for scalars coming from a field. For example, scalars can come from a ring. But the theory is then less geometric and computations more technical and less algorithmic.
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According to Vaisheshika school of philosophy Padārtha or all objects of experience can be primarily divided as "Bhāva" and "Abhāva". The bhāva padārthas are six types. These are: #Dravya (substance), #Guṇa (quality), #Karma (activity), #Sāmānya (generality), #Viśeṣa (particularity) #Samavāya (inherence). Later Vaiśeṣikas like, Śrīdhara and Udayana and Śivāditya added one more category abhava which means non- existence.
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A number of "special-purpose" systems have been designed, dedicated to a single problem. This allows the use of specially programmed FPGA chips or even custom ASICs, allowing better price/performance ratios by sacrificing generality. Examples of special-purpose supercomputers include Belle,Condon, J.H. and K.Thompson, "Belle Chess Hardware", In Advances in Computer Chess 3 (ed.M.R.B.Clarke), Pergamon Press, 1982.
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It has been suggested that since Article 9(1) of the Singapore Constitution is pitched at a high level of generality,. there is no limitation in the ordinary natural meaning of the phrase. Thus, there is no requirement in the Constitution for personal liberty to be construed narrowly to mean only freedom from physical restraint.Lee, p. 191.
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Twenty per cent of the new Republic's territory, known as the Generality Lands, was so under the direct rule of the Generality (). The Dutch East India Company and the Dutch West India Company were also under its general supervision; for this reason Staten Island in New York City (originally New Amsterdam) and Staten Island, Argentina (Discovered by Dutchman Jacob le Maire), are among places named after the . The "southern" States General after 1579 were a continuation of the States General as they had been under the Habsburg Netherlands. After the (re)conquest of most of the territory of the States of Brabant and of Flanders these States again sent representatives to these States General for the Southern Netherlands, together with the "obedient" provinces of the Union of Arras.
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The united provinces, with Drenthe and the Generality Lands The republic was a confederation of seven provinces, which had their own governments and were very independent, and a number of so-called Generality Lands. The latter were governed directly by the States General, the federal government. The States General were seated in The Hague and consisted of representatives of each of the seven provinces. The provinces of the republic were, in official feudal order: # Duchy of Guelders # County of Holland # County of Zeeland # Lordship of Utrecht # Lordship of Overijssel # Lordship of Frisia # Lordship of Groningen There was an eighth province, the County of Drenthe, but this area was so poor that it was exempt from paying federal taxes, and as a consequence, it was denied representation in the States General.
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In mathematics, the closed-subgroup theorem (sometimes referred to as Cartan's theorem) is a theorem in the theory of Lie groups. It states that if is a closed subgroup of a Lie group , then is an embedded Lie group with the smooth structure (and hence the group topology) agreeing with the embedding. Theorem 20.10. Lee states and proves this theorem in all generality.
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Pasinetti [1981], p. 54 The most important outcome of this analysis is that Pasinetti shows that, under such assumptions, it does not matter whether the analysis is carried out in macroeconomic terms or -in a more disaggregated way- in sectorial terms. As the system expands, while its proportions remain constant, the analysis does not lose any generality if carried out in aggregate terms.
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He was released shortly thereafter and returned to Eindhoven. However, he was re-arrested on 12 February 1788 (in Eindhoven this time), but managed to escape. In 1789 there was a failed, pro- French rebellion in the Southern Netherlands. Fearing that the insurrection would spread to the Generality Lands, the States-General posted a garrison in Eindhoven; Van Hooff left the town.
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Comparing groups gives the researcher the advantage of development of variety of categories. The main criterion is that the data collected should apply to a particular category or property, irrespective of the differences or similarities. The researcher's main focus is to keep the purpose of the research clear. As the researcher compares groups, he gains control over two scales of generality.
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Like Aristotle, Aquinas rejected Platonism.Aquinas. Commentary on Aristotle's Metaphysics, Bk. 1, lectio 10, n. 158. In his view, to speak of abstractions not only as existent, but as more perfect exemplars than fully designated particulars, is to put a premium on generality and vagueness. On this analysis, the abstract "good" in the first horn of the Euthyphro dilemma is an unnecessary obfuscation.
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Scratchpads are not used in mainstream desktop processors where generality is required for legacy software to run from generation to generation, in which the available on-chip memory size may change. They are better implemented in embedded systems, special-purpose processors and game consoles, where chips are often manufactured as MPSoC, and where software is often tuned to one hardware configuration.
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Psychological Record, 61(2), 313-322. This law applies fairly well when non-human subjects are exposed to concurrent variable interval schedules (but see below); its applicability in other situations is less clear, depending on the assumptions made and the details of the experimental situation. The generality of applicability of the matching law is subject of current debate.Simon, C., & Baum, W. M. (2017).
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His work contains a detailed description of the geometric dioptrics for uncentered systems. He provided a greater generality as previously found in the telescopic system treatments, with less emphasis on applications. In the second main sections, the results obtained are applied to optical instruments. The magnification, field of view, and the brightness of the instrument were dealt with in great detail.
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Projection construction is also affected by how the shape of the Earth or planetary body is approximated. In the following section on projection categories, the earth is taken as a sphere in order to simplify the discussion. However, the Earth's actual shape is closer to an oblate ellipsoid. Whether spherical or ellipsoidal, the principles discussed hold without loss of generality.
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Baron Augustin-Louis Cauchy (;"Cauchy". Random House Webster's Unabridged Dictionary. ; 21 August 178923 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors.
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The Adomian decomposition method, the Lyapunov artificial small parameter method, and his homotopy perturbation method are all special cases of the more general homotopy analysis method. These are series expansion methods, and except for the Lyapunov method, are independent of small physical parameters as compared to the well known perturbation theory, thus giving these methods greater flexibility and solution generality.
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However, the surface elevation is an extra unknown, for which an additional boundary condition is needed. This is provided by Bernoulli's equation for an unsteady potential flow. The pressure above the free surface is assumed to be constant. This constant pressure is taken equal to zero, without loss of generality, since the level of such a constant pressure does not alter the flow.
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In this generality, character varieties are only algebraic sets and are not actual varieties. To avoid technical issues, one often considers the associated reduced space by dividing by the radical of 0 (eliminating nilpotents). However, this does not necessarily yield an irreducible space either. Moreover, if we replace the complex group by a real group we may not even get an algebraic set.
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The error that many critics make is that they demand the false criterion of universality and infallibility to the practice of racial identification. Gordon argues that such a demand would not work for the identification of most social phenomena. What is required is not universality nor infallibility but generality. Gordon defends this claim by making the distinction between a law and a principle.
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Walls of the building are detached far from the mausoleum. Post stamp (2008) Peculiarities of architectural structure of the mausoleum indicate that masters of various architectural professions were involved in its construction. Despite a generality of the composition and architectural appearance of the portals, detailed representation of the arches’ archivolts is also original. There are patterns which aren’t met in other portals.
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It is also usually necessary to have a small magnet to bias the magnetostrictive material into its operating range. It is possible to dispense with the magnets if the biasing is taken care of on the electronic side by providing a d.c. current superimposed on the signal, but this approach would detract from the generality of the filter design.Carr, pp.170–172.
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If distinguishes points of and if denotes the range of the injection then is a vector subspace of the algebraic dual space of and the pairing becomes canonically identified with the canonical pairing (where is the natural evaluation map). In particular, in this situation we can assume without loss of generality that is a vector subspace of 's algebraic dual and is the evaluation map. :Convention: Often, whenever is injective (especially when forms a dual pair) then we will use the common practice of assuming without loss of generality that is a vector subspace of the algebraic dual space of , that is the natural evaluation map, and we may also denote by . In a completely analogous manner, if distinguishes points of then it is possible for to be identified as a vector subspace of 's algebraic dual space.
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The generality constraint, according to Evans, is intended to capture the structure that there is in thought. As Evans puts it, "The thought that John is happy has something in common with the thought that Harry is happy, and the thought that John is happy has something in common with the thought that John is sad" (1982, p. 100). The generality constraint requires that if one is to have a thought (that John is happy, for example) about an object (John), then one must be able to conceive of the object (John) as having different properties (such as being sad). He also defends a reading of Frege, derived in part from Michael Dummett's work, according to which Frege's notion of sense is not equivalent to a description, and indeed remains essential to a theory of reference that abandoned descriptivism (1982, §1.3).
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The ability to generalize information from one situation to another is a function of several factors: the reliability of the original information; the paradigm's validity; one's understanding of the paradigm, the true determinants of the behavior, and the relevant details of the situations in question; and the similarity between the original source of the data and the situation to which it is to be applied. There are both similarities and differences between the terms "stimulus generalization" and "generality of a functional relationship." Stimulus generalization is the description of the fact that an organism behaves in a similar way to similar stimuli, and that the more different the stimuli, the more different the behavior. The generality of a finding refers to the degree to which a functional relationship obtained in one situation is able to predict the obtained relationship in a new situation.
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Radziwiłł was extremely pleased when he found out about the new establishment of the Generality under the leadership of M. Pac and his secretary I. Bohusz, with whom Radziwiłł reconciled after an argument and later promised undying loyalty. Karol Stanisław considered (revealed in a letter to his stepmother from 20 December 1769) Pac a "reliable friend" and thought that he'd become independent from other conflicted leaders of the Confederation like Krasiński and Wessel who both disagreed with each other. His initiative also attributed the decision to move to the Generality from Bielsko to Presov, and Pac with Bohusz assured him that shortly after he would become "one of the leaders of free Europe." Radziwiłł's intellectual level, however, prevented him from playing the leading role in the league, and Pac with Bohusz, despite their alliance with him, were able to maintain their independent status.
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The Geneva-Brussels operational axiomatic approach to quantum theory is founded on very general notions, such as `yes-no experiment', 'property', 'state', 'measurement'. The generality of this approach aided very much in the identification and investigation of quantum structures in the non-microscopic realm. The interdisciplinary interest, together with this generality of the Geneva- Brussels quantum theory, made it possible to put forward a modeling of a simple opinion poll and prove that quantum structure was involved in the dynamics of the decision processes of the human participants of the survey. Two new PhD students, Sonja Smets and Liane Gabora, joined the center, and more signatures of the presence of quantum structure in the realm of cognitive science were investigated, a quantum model for the Liar paradox reasoning was elaborated, and the presence of entanglement, i.e.
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Most phenomena that can be directly described by science are generalities. Seemingly isolated events will occur in the same way over and over again because they are governed by the same laws. Water will flow downhill and sunlight will create warmth because of principles that apply broadly. In the human realm, behavior that accords with norms and laws counts as generality for similar reasons.
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"I am verily persuaded," he wrote, "the Generality of Preachers talk of an unknown, unfelt Christ. And the Reason why Congregations have been so dead, is because dead Men preach to them." Whitefield met Gilbert Tennent on Staten Island and asked him to preach in Boston to continue the revival there. Tennent accepted and in December began a three-month long preaching tour throughout New England.
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The restriction to formulas in prenex form containing only existential quantifiers does not limit the generality of the theorem, because formulas can be converted to prenex form and their universal quantifiers can be removed by Herbrandization. Conversion to prenex form can be avoided, if structural Herbrandization is performed. Herbrandization can be avoided by imposing additional restrictions on the variable dependencies allowed in the Herbrand disjunction.
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Continuity of functions is one of the core concepts of topology, which is treated in full generality below. The introductory portion of this article focuses on the special case where the inputs and outputs of functions are real numbers. A stronger form of continuity is uniform continuity. In addition, this article discusses the definition for the more general case of functions between two metric spaces.
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This provides the ability to capture the "memory" effect of devices like capacitors and inductors. It has been applied in the fields of medicine (biomedical engineering) and biology, especially neuroscience. It is also used in electrical engineering to model intermodulation distortion in many devices, including power amplifiers and frequency mixers. Its main advantage lies in its generality: it can represent a wide range of systems.
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Adviser at the Paris parliament 20 August 1758, then master of requests by provisions of 13 July 1761. Master fee requests in 1767, he resigned on 1 May 1773. Appointed steward assistant to the generality of Rouen in 1767, he replaced his father- in steward job in 1768. He was appointed first president of the Supreme Council created by the Maupeou reform in Rouen in 1771.
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Since the inequality is symmetric in x,y,z we may assume without loss of generality that x \geq y \geq z. Then the inequality : (x-y)[x^t(x-z)-y^t(y-z)]+z^t(x-z)(y-z) \geq 0 clearly holds, since every term on the left-hand side of the inequality is non-negative. This rearranges to Schur's inequality.
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He received the Premi d'Honor de les Lletres Catalanes ("Catalan Letters Award") (1975) and also, in the year 1983, the Medalla d’Or de la Generalitat de Catalunya ("Gold Medal of Catalonia's Generality"). In 1984 he was named doctor honoris causa by the University of Barcelona and by the Autonomous University of Barcelona. In 1986 he was appointed as professor of literature in the University of Valencia.
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Diffusion MRI relies on the mathematics and physical interpretations of the geometric quantities known as tensors. Only a special case of the general mathematical notion is relevant to imaging, which is based on the concept of a symmetric matrix.Several full mathematical treatments of general tensors exist, e.g. classical, component free, and so on, but the generality, which covers arrays of all sizes, may obscure rather than help.
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The handicap principle was proposed in 1975 by Israeli biologist Amotz Zahavi. The generality of the phenomenon is the matter of some debate and disagreement, and Zahavi's views on the scope and importance of handicaps in biology have not been accepted by the mainstream.Review by Nevertheless, the idea has been very influential,Maynard Smith, J. and Harper, D. (2003) Animal Signals. Oxford University Press. .
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If there is no ambient electric field, then the total energy of a state should remain unchanged under a charge reversal, i.e. under flipping all arrows. Thus one may assume without loss of generality that : \epsilon_1=\epsilon_2, \quad \epsilon_3=\epsilon_4, \quad \epsilon_5=\epsilon_6 This assumption is known as the zero field assumption, and holds for the ice model, the KDP model, and the Rys F model.
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An 1867 concert review remarks: "Mr Molloy's songs are (to use a common expression) 'for the drawing-room,' but there is more in them than in the generality of effusions written now-a-days for young lady amateurs, who cannot perceive the charm of a higher order of composition."Review headed "Mr. W. Bollen Harrison’s Concert", in: The Era, 22 Dec. 1867, p. 7.
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This demonstrated that spatial attention had been allocated to the target location. The use of multiple tasks simultaneously in an experiment can also demonstrate the generality of spatial attention, as allocation of attention to one task can influence performance in other tasks. For example, it was found that when attention was allocated to detecting a flickering dot (spatial probe), this increased the likelihood of identifying nearby letters.
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Begriffsschrift title page The original first-order, classical logic is found in Gottlob Frege's Begriffsschrift. It has a wider application than Aristotle's logic, and is capable of expressing Aristotle's logic as a special case. It explains the quantifiers in terms of mathematical functions. It was also the first logic capable of dealing with the problem of multiple generality, for which Aristotle's system was impotent.
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Members owe fiduciary duties to the close corporation. The Act gives an overview of the fiduciary duties and sets out to define some of them without prejudice to the generality of the expression "fiduciary relationship." Members must act honestly and in good faith, and exercise their powers to manage or represent the close corporation in its best interests and for its benefit.s 42(2).
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The title page of a textbook by Cauchy. In his book Cours d'Analyse Cauchy stressed the importance of rigor in analysis. Rigor in this case meant the rejection of the principle of Generality of algebra (of earlier authors such as Euler and Lagrange) and its replacement by geometry and infinitesimals. Judith Grabiner wrote Cauchy was "the man who taught rigorous analysis to all of Europe".
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Similarly, if then for all real , which implies that , as desired. Thus, we will henceforth assume that a positive real number and that (note, however, that we have not yet ruled out the possibility that is or ). Recall that just like , the function satisfies for all real . Since , if and only if so we may assume without loss of generality that and it remains to show that .
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Legendre predicted that it "will make itself conspicuous by the choice of methods, their generality, and the rigor of the demonstrations."Ivor Grattan-Guinness (1990) Convolutions in French Mathematics, 1800 — 1840, §2.5.4 Lacroix: scientific educator, pp 113,4, Science Networks: Historical Studies v. 2, Birkhäuser In hindsight Ivor Grattan-Guinness observed: :The Traite is by far the most comprehensive work of its kind for that time.
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The Mathematics Teacher, Vol. 59, No. 2 (1966), pp. 140–142. However, he acknowledged that the arithmetic problem of these cubics was still unsolved, adding that "possibly someone else will come to know it after us". This task remained open until the sixteenth century, where algebraic solution of the cubic equation was found in its generality by Cardano, Del Ferro, and Tartaglia in Renaissance Italy.
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However, having distinct random access iterators offers efficiency advantages. For example, a vector would have a random access iterator, but a list only a bidirectional iterator. Iterators are the major feature that allow the generality of the STL. For example, an algorithm to reverse a sequence can be implemented using bidirectional iterators, and then the same implementation can be used on lists, vectors and deques.
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A map of the Dutch Republic. The Dutch Republic was a confederation of seven provinces, which had their own governments and were very independent, and a number of so-called Generality Lands. These latter were governed directly by the States-General (Staten-Generaal in Dutch), the federal government. The States-General were seated in The Hague and consisted of representatives of each of the seven provinces.
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The phrase "hardworking families" or "working families" is an example of a glittering generality in contemporary political discourse. It is used in the politics of the United Kingdom and of the United States, and was heavily used by the political parties in the campaign of the 2005 United Kingdom general election and the 2007 Australian federal election where the Rudd Labor Party used the term extensively.
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Another difference between TSE measures concerns the issue of generality. This consideration is similar to the previous differentiation between-TSE as a broader concept and technology specific self-efficacy. Measurement attempts of the broader concept of technological self-efficacy will be considered first. McDonald and Siegall developed a five-item likert scale of technological self-efficacy based on the consideration of previous theoretical studies.
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Because each move typically changes only a small number of game features, the Zobrist value of the position after a move can be updated quickly from the value of the position before the move, without needing to loop over all of the features of the position. Tabulation hashing in greater generality, for arbitrary binary values, was later rediscovered by and studied in more detail by .
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The above definition of the characteristic polynomial of a matrix A \in M_n(F) with entries in a field F generalizes without any changes to the case when F is just a commutative ring. defines the characteristic polynomial for elements of an arbitrary finite-dimensional (associative, but not necessarily commutative) algebra over a field F and proves the standard properties of the characteristic polynomial in this generality.
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Radziwiłł strengthened the local garrison stationing in the town and ignored several threats from the authorities of Warsaw, that did not recognize the decision. Towards the end of June 1771, Karol Stanisław Radziwiłł returned to Sebeș, but on 1 September, together with the members and diplomats of the Generality, he went to Cieszyn, which was located on the border of the Polish–Lithuanian Commonwealth and the Habsburg Monarchy. He was convinced that through "proper alliances with former enemies" the Confederation would succeed (such topic was discussed in a letter dating from December 11 addressed to the Castellan of Bracław A. Czarnecki) and was assured that the maintained contacts with several county officials of the Grand Duchy of Lithuania could possibly interfere with the controversial political system of the government in Warsaw. Radziwiłł's support helped to rehabilitate the Generality headed by S. Kossakowski at the beginning of 1772.
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Biquadratic fields are all obtained by adjoining two square roots. Therefore in explicit terms they have the form :K = Q(,) for rational numbers a and b. There is no loss of generality in taking a and b to be non-zero and square-free integers. According to Galois theory, there must be three quadratic fields contained in K, since the Galois group has three subgroups of index 2.
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Suppose, to the contrary, there is an integer that has two distinct prime factorizations. Let n be the least such integer and write n = p1 p2 ... pj = q1 q2 ... qk, where each pi and qi is prime. (Note j and k are both at least 2.) We see p1 divides q1 q2 ... qk, so p1 divides some qi by Euclid's lemma. Without loss of generality, say p1 divides q1.
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She fits the pattern of education for leadership, rather than for the generality of women. When Johannes Sturm published Latin correspondence with Ascham centred on the achievements in humanist study of Elizabeth and other high- ranking English persons, in Konrad Heresbach's De laudibus Graecarum literarum oratio (1551), the emphasis was on the nobility of those tackling the classics, rather than gender.Lawrence V. Ryan, Roger Ascham (1963) p. 144.
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The basic data structure used by SciPy is a multidimensional array provided by the NumPy module. NumPy provides some functions for linear algebra, Fourier transforms, and random number generation, but not with the generality of the equivalent functions in SciPy. NumPy can also be used as an efficient multidimensional container of data with arbitrary datatypes. This allows NumPy to seamlessly and speedily integrate with a wide variety of databases.
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Para 51. The court decided, accordingly, that, when all the factors were weighed together, the scales came down firmly in favour of upholding the generality of the law in the face of the appellant's claim for a constitutionally compelled exemption. The appeal was dismissedPara 52. and the decision in the South Eastern Cape Local Division, in Christian Education South Africa v Minister of Education1999 (4) SA 1092. confirmed.
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Let r and s be two ultraparallel lines. From any two distinct points A and C on s draw AB and CB' perpendicular to r with B and B' on r. If it happens that AB = CB', then the desired common perpendicular joins the midpoints of AC and BB' (by the symmetry of the Saccheri quadrilateral ACB'B). If not, we may suppose AB < CB' without loss of generality.
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When a node x accepts a joining node y as its child and detects that the tree balance is violated, it initiates the restructuring process. Without loss of generality, suppose that this restructuring is towards the right. Assume that y joins as x's left child. To rebalance the system, x notifies y to replace its position, and notifies its right adjacent node z that x will replace z's position.
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This point A corresponds to the pen-hole in the inner disk of a real Spirograph. Without loss of generality it can be assumed that at the initial moment the point A was on the X axis. In order to find the trajectory created by a Spirograph, follow point A as the inner circle is set in motion. Now mark two points T on C_o and B on C_i.
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Uddayana divides Padārtha (Categories) into Bhava (existence) which is real, and Abhava (non-existence) which is not real. Dravya (substance), Guṇa (quality), Karma (action), Samanya (community or generality), Visesa (particularity or partimerity) and Samavaya (inherence) are the marks of existence. Abhava has not been categorically defined by the Vaisheshika School of Hindu philosophy but is of four kinds viz – 1) Pragabhava i.e. Prior non- existence, 2) Pradhvamsabhava i.e.
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In the category of sets, these are monoid actions, but monoid representations on vector spaces and other objects can be studied. More generally, one can relax the assumption that the category being represented has only one object. In full generality, this is simply the theory of functors between categories, and little can be said. One special case has had a significant impact on representation theory, namely the representation theory of quivers.
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Jacques Duchesneau de la Doussinière et d'Ambault, chevalier (died 1696, Ambrault, near Issoudun, Berry), was intendant of New France from 1675 to 1682. His other offices included counsellor to His Majesty, treasurer of France, commissary for the generality of Tours c. 1664 and general of the king’s finances in Touraine. He was the son of Guillaume Chesneau, chevalier, seigneur, cup-bearer to the king, and of Anne de Lalande.
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Chebyshev's inequality is important because of its applicability to any distribution. As a result of its generality it may not (and usually does not) provide as sharp a bound as alternative methods that can be used if the distribution of the random variable is known. To improve the sharpness of the bounds provided by Chebyshev's inequality a number of methods have been developed; for a review see eg.Savage, I. Richard.
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Because of its generality, abstract algebra is used in many fields of mathematics and science. For instance, algebraic topology uses algebraic objects to study topologies. The Poincaré conjecture, proved in 2003, asserts that the fundamental group of a manifold, which encodes information about connectedness, can be used to determine whether a manifold is a sphere or not. Algebraic number theory studies various number rings that generalize the set of integers.
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Chapel supports a multithreaded parallel programming model at a high level by supporting abstractions for data parallelism, task parallelism, and nested parallelism. It enables optimizations for the locality of data and computation in the program via abstractions for data distribution and data- driven placement of subcomputations. It allows for code reuse and generality through object-oriented concepts and generic programming features. For instance, Chapel allows for the declaration of locales.
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At a higher level of abstraction, Gerraint Wiggins has investigated general properties of music knowledge representations such as structural generality and expressive completeness. Although a great deal of cognitive musicology research features symbolic computation, notable contributions have been made from the biologically inspired computational paradigms. For example, Jamshed Bharucha and Peter Todd have modeled music perception in tonal music with neural networks.Bharucha, J. J., & Todd, P. M. (1989).
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Bastiaan Heeren, Daan Leijen, and Arjan van IJzendoorn in 2003 also observed some stumbling blocks for Haskell learners: "The subtle syntax and sophisticated type system of Haskell are a double edged sword – highly appreciated by experienced programmers but also a source of frustration among beginners, since the generality of Haskell often leads to cryptic error messages." To address these, researchers from Utrecht University developed an advanced interpreter called Helium, which improved the user- friendliness of error messages by limiting the generality of some Haskell features, and in particular removing support for type classes. Ben Lippmeier designed Disciple as a strict-by-default (lazy by explicit annotation) dialect of Haskell with a type-and-effect system, to address Haskell's difficulties in reasoning about lazy evaluation and in using traditional data structures such as mutable arrays.Ben Lippmeier, Type Inference and Optimisation for an Impure World, Australian National University (2010) PhD thesis, chapter 1 He argues (p.
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Images of Christ retain the long braided locks parted in the middle and flowing to the shoulders. Those of the Blessed Virgin still wear the veil which conceals a portion of the brow and confines the neck. The Orantes, which represent the generality of the faithful, have the hair covered by a full veil which falls to the shoulders. Byzantine iconography differs little as to head-dress from that of the catacombs.
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The generality of Nigerians dread any form of contact with law enforcement agents. This is largely borne out of ignorance of their rights under the law. Such ignorance is often exploited by police officers and others to intimidate and harass innocent persons. In taking up the challenge of educating Nigerians on their basic rights and providing legal support, Adeola started 'Know Your Constitution' now "Know Your Rights Nigeria" initiative on radio (UNILAG103.1FM) in 2008.
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The free-surface boundary conditions and apply at the yet unknown free-surface elevation . They can be transformed into boundary conditions at a fixed elevation by use of Taylor series expansions of the flow field around that elevation. Without loss of generality the mean surface elevation – around which the Taylor series are developed – can be taken at . This assures the expansion is around an elevation in the proximity of the actual free-surface elevation.
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The high level of training and specialized roles gave way to generality: the rifles were much faster and simpler to load, able to be reloaded while prone, and impossible to be double-loaded after a misfire. The term 'rifleman', once used solely as a mark of distinction and pride, became a commonplace description of all infantry, no matter what their actual status was. Nevertheless, the term retained a certain élan that is still found today.
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He returned to the Hague with the bleak message that capitulation was the only option. The States concurred, hoping to save the Republic proper, and the free exercise of the Reformed religion (Louis had already had the Utrecht cathedral reconsecrated to Catholic worship), but being prepared to sign away the Generality Lands.Israel (1995), pp. 798–799 But now the remarkable popular insurrection began that would save the Republic, and overturn the States-Party regime.
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Since then Atkins focused on aspects of the genetic decoding that are in defiance of the standard genetic code – phenomena collectively described as Recoding.Atkins, John F.; Gesteland, Raymond F.Recoding: Expansion of Decoding Rules Enriches Gene Expression. Springer. Recoding challenges the generality of the genetic decoding and encompasses phenomena such as programmed ribosomal frameshifting that violates triplet character of the genetic readout. Proteinogenic amino acids that are not part of the genetic code, e.g.
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Various definitions of compactness may apply, depending on the level of generality. A subset of Euclidean space in particular is called compact if it is closed and bounded. This implies, by the Bolzano–Weierstrass theorem, that any infinite sequence from the set has a subsequence that converges to a point in the set. Various equivalent notions of compactness, such as sequential compactness and limit point compactness, can be developed in general metric spaces.
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The spirit at once surrenders itself to this universal claim and appropriates it for itself."Alfred North Whitehead, Religion in the Making (New York: Fordham University Press, 1996), 60. In this way the individual and universal/social aspects of religion are mutually dependent. Whitehead also described religion more technically as "an ultimate craving to infuse into the insistent particularity of emotion that non-temporal generality which primarily belongs to conceptual thought alone.
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During the early Flanders Campaign, the exiles formed their own "Batavian Legion" that (like its Belgian equivalent) fought side by side with the armies of general Charles François Dumouriez under command of general Herman Willem Daendels. However, despite an incursion into North Brabant (then part of the non-selfgoverning Generality Lands), the attack on the Dutch Republic was unsuccessful in 1793 after the French defeat at Neerwinden.Schama, pp. 116, 131–135, 138–160.
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A standard method for getting lower bounds of complexity consists of reducing a problem to another problem. More precisely, suppose that one may encode a problem of size into a subproblem of size of a problem , and that the complexity of is \Omega(g(n)). Without loss of generality, one may suppose that the function increases with and has an inverse function . Then the complexity of the problem is \Omega(g(h(n))).
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The run time system selectively flattens call structures. This gives modest speedups in itself, but allows extensive caching of type information and multiple versions of code for different caller types. This removes the need to do many method lookups and permits conditional branch statements and hard-coded calls to be inserted- often giving C-like performance with no loss of generality at the language level, but on a fully garbage collected system.
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Just how well the RCC actually reflects patterns in natural systems is uncertain and its generality can be a handicap when applied to diverse and specific situations. The most noted criticisms of the RCC are: 1. It focuses mostly on macroinvertebrates, disregarding that plankton and fish diversity is highest in high orders; 2. It relies heavily on the fact that low ordered sites have high CPOM inputs, even though many streams lack riparian habitats; 3.
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By emphasizing the link between the war and the persecution of the Jews, the persecution could be construed as a justified response to an attack on Germany. Hitler always referenced the prophecy when discussing the extermination of the Jews. From late 1941, Nazi propagandists consistently avoided discussion of concrete anti-Jewish actions, such as deportations, instead relying on the prophecy's generality. Besides Nazi leaders, army propaganda and ordinary soldiers also referred to the prophecy.
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It is in this capacity that oversees the development ossuary of the Catacombs of Paris. It removes already closed cemeteries in the capital, eliminated the houses on the bridges of Paris, and participates with Louis Bénigne François Berthier de Sauvigny, intendant of the generality of Paris from 1744 to 1776, to the achievement of workshops to provide employment to the poor. He resigns in favor of Jean Sylvain Bailly (1736–1793), 17 July 1789.
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Kant said that the schema of a concept is the representation of a general procedure of the imagination by which an image can be supplied for a concept. Kant claimed that time is the only proper and appropriate transcendental schema because it shares the a priori category's generality and purity as well as any a posteriori phenomenon's manner of appearance. However, it may be true that time is not the only possible schema.
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Steiner's mathematical work was mainly confined to geometry. This he treated synthetically, to the total exclusion of analysis, which he hated, and he is said to have considered it a disgrace to synthetic geometry if equal or higher results were obtained by analytical geometry methods. In his own field he surpassed all his contemporaries. His investigations are distinguished by their great generality, by the fertility of his resources, and by the rigour in his proofs.
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The absorption neutron cross section of an isotope of a chemical element is the effective cross sectional area that an atom of that isotope presents to absorption, and is a measure of the probability of neutron capture. It is usually measured in barns (b). Absorption cross section is often highly dependent on neutron energy. As a generality, the likelihood of absorption is proportional to the time the neutron is in the vicinity of the nucleus.
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Lamberto Cesari (23 September 1910 – 12 March 1990) was an Italian mathematician naturalized in the United States, known for his work on the theory of surface area, the theory of functions of bounded variation, the theory of optimal control and on the stability theory of dynamical systems: in particular, by extending the concept of Tonelli plane variation, he succeeded in introducing the class of functions of bounded variation of several variables in its full generality.
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Letters patent of Louis XI, Les Ponts-de-Cé, July 1470 Louis Malet de Graville built a Market hall at the crossroads of the Paris to Étampes and Dourdan to Corbeil roads. In 1510 the monks, through the generosity of the Graville and Montagu families undertook major renovations of the church and in 1542 a sub-delegation of Chastres was attached to the Generality of Paris. In 1545 the lordship of Chastres became independent.
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James C. Kaufman, from the Neag School of Education at the University of Connecticut, and Ronald A. Beghetto, from the same university, investigated the possibility that everyone could have the potential for polymathy as well as the issue of the domain-generality or domain-specificity of creativity.Kaufman, J. C., Beghetto, R. A., Baer, J., & Ivcevic, Z. (2010). Creativity polymathy: What Benjamin Franklin can teach your kindergartener. Learning and Individual Differences, 20(4), 380-387.
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Chiral boronate Lewis acid derived from (1R)-(+)-camphor form a frustrated Lewis pair with tBu3P, which is isolable as a salt. This FLP catalyses the enantioselective hydrogenation of some aryl imines in high yield but modest ee (up to 83%). center Although conceptually interesting, the protocol suffers from lack of generality. It was found that increasing steric bulk of the imine substituents lead to decreased yield and ee of the amine product.
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The Astronomical Image Processing System (AIPS) is a software package to support the reduction and analysis of data taken with radio telescopes. Developed predominantly for use with the then under-construction VLA, the generality inherent in its design allowed it to become the standard data- reduction package for most radio interferometers, including VLBI. Limited single-dish capability is also featured. Although partially replaced by CASA, it continues to evolve and remains widely used.
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The software cases after Alice adopt its method of legal analysis, based on the decision of the Supreme Court in the Mayo case. This calls for a two-step analysis. First, the court determines whether the claimed invention is based on an abstract idea or principle of some sort, often expressed at a high level of generality, such as a computerized escrow or surety arrangement, as in the Bilski and Alice cases.See, e.g.
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In the statement of the theorem, two assumptions were made: the state to be copied is a pure state and the proposed copier acts via unitary time evolution. These assumptions cause no loss of generality. If the state to be copied is a mixed state, it can be purified. Alternately, a different proof can be given that works directly with mixed states; in this case, the theorem is often known as the no-broadcast theorem.
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Zeeland and usually Utrecht had the same stadtholder as Holland. There was a constant power struggle between the Orangists, who supported the stadtholders and specifically the princes of Orange, and the Republicans, who supported the States General and hoped to replace the semi-hereditary nature of the stadtholdership with a true republican structure. After the Peace of Westphalia, several border territories were assigned to the United Provinces. They were federally governed Generality Lands.
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An extensive meta-analysis of nearly 600 latitudinal gradients from published literature tested the generality of the latitudinal diversity gradient across different organismal, habitat and regional characteristics. The results showed that the latitudinal gradient occurs in marine, terrestrial, and freshwater ecosystems, in both hemispheres. The gradient is steeper and more pronounced in richer taxa (i.e. taxa with more species), larger organisms, in marine and terrestrial versus freshwater ecosystems, and at regional versus local scales.
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From this symmetry he inferred the characteristics of a fourth fundamental non-linear circuit element, linking magnetic flux and charge, which he called the memristor. In contrast to a linear (or non-linear) resistor the memristor has a dynamic relationship between current and voltage including a memory of past voltages or currents. Other scientists had proposed dynamic memory resistors such as the memistor of Bernard Widrow, but Chua introduced a mathematical generality.
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The failing wars intended to regain the 'heretical' northern Netherlands meant significant loss of (still mainly Catholic) territories in the north, which was consolidated in 1648 in the Peace of Westphalia, and given the peculiar inferior status of Generality Lands (jointly ruled by the United Republic, not admitted as member provinces): Zeelandic Flanders (south of the river Scheldt), the present Dutch province of Noord-Brabant and Maastricht (in the present-day Dutch province of Limburg).
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When elements of different degrees are multiplied, the degrees add like multiplication of polynomials. This means that the exterior algebra is a graded algebra. The definition of the exterior algebra makes sense for spaces not just of geometric vectors, but of other vector-like objects such as vector fields or functions. In full generality, the exterior algebra can be defined for modules over a commutative ring, and for other structures of interest in abstract algebra.
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Let π : P → X be a principal G-bundle and let ρ : G → Homeo(F) be a continuous left action of G on a space F (in the smooth category, we should have a smooth action on a smooth manifold). Without loss of generality, we can take this action to be effective. Define a right action of G on P × F viaHusemoller, Dale (1994), p. 45.Sharpe, R. W. (1997), p. 37.
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None of the 5 vertex- transitive graphs with no Hamiltonian cycles is a Cayley graph. This observation leads to a weaker version of the conjecture: : Every finite connected Cayley graph contains a Hamiltonian cycle. The advantage of the Cayley graph formulation is that such graphs correspond to a finite group G and a generating set S. Thus one can ask for which G and S the conjecture holds rather than attack it in full generality.
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By the pigeonhole principle, at least two of the three intervals were mapped to J because they have the same job class as J ', or because J ' is the interval with the earliest finishing time amongst all intervals in EFT(I) intersecting both intervals. Without loss of generality, assume that these two intervals are J1 and J2. :Case 1. Suppose J1 and J2 were mapped to J ' because they have the same job class as J '.
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The program includes a rich variety of courses at both undergraduate and graduate (MA) levels, such as: management, marketing, accounting and finance, business studies, operations management, business in action, etc. The principal defining feature of the program is teaching business in action. This ensures breadth and generality and encourages flexibility, creativity, and entrepreneurship. The Computer Science and Mathematics (MACS) program offers a bachelor's degree with two concentrations, one in mathematics and the other on computer science.
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These are not code words for future concepts, but refer to ancient concepts then in use. The authors cite Euclid, Elements, Book III, which concerns itself with circles, and maximum and minimum distances from interior points to the circumference. Without admitting to any specific generality they use terms such as “like” or “the analog of.” They are known for innovating the term “neusis-like.” A neusis construction was a method of fitting a given segment between two given curves.
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A policy is stationary if the action-distribution returned by it depends only on the last state visited (from the observation agent's history). The search can be further restricted to deterministic stationary policies. A deterministic stationary policy deterministically selects actions based on the current state. Since any such policy can be identified with a mapping from the set of states to the set of actions, these policies can be identified with such mappings with no loss of generality.
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Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty in a simple and elegant proof, such as Euclid's proof that there are infinitely many prime numbers, and in an elegant numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics.
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The term "algebra" denotes both a subject, namely the subject of algebra, and an object, namely an algebraic structure. Whereas the foregoing has addressed the subject of Boolean algebra, this section deals with mathematical objects called Boolean algebras, defined in full generality as any model of the Boolean laws. We begin with a special case of the notion definable without reference to the laws, namely concrete Boolean algebras, and then give the formal definition of the general notion.
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The Town don't like > it at all, but ... several excellent musicians think as I do." One of Handel's most loyal and enthusiastic supporters, Mary Delany, wrote to her sister Ann saying "Don't you remember our snug enjoyment of "Theodora?" Her sister replied "Surely "Theodora" will have justice at last, if it was to be again performed, but the generality of the world have ears and hear not". There are two surviving quotes of Handel about Theodora.
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Alexandra W. Logue attended Harvard University, receiving her A.B. in Psychology Magna Cum Laude in 1974, and her Ph.D. in Experimental Psychology in 1978. As a senior in college and in graduate school she interacted extensively with B. F. Skinner, as well as with other members of the Harvard University behavior analysis faculty. Her dissertation was entitled "Taste Aversion and the Generality of the Laws of Learning", a version of which was subsequently published in Psychological Bulletin.
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Annual Review of Ecology and Systematics 1: 1-18. and John Maynard-Smith and Eörs Szathmáry's co-authored book, The Major Transitions in Evolution. As a theoretical introduction to units of selection, Lewontin writes: > The generality of the principles of natural selection means that any > entities in nature that have variation, reproduction, and heritability may > evolve. ...the principles can be applied equally to genes, organisms, > populations, species, and at opposite ends of the scale, prebiotic molecules > and ecosystems.
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More generally, planar flavones and flavonols with a 7-hydroxyl group inhibit xanthine oxidase. An essential oil extracted from Cinnamomum osmophloeum inhibits xanthine oxidase in mice. The natural product propolis from selected sources inhibits xanthine oxidase in rats; the specific substance responsible for this inhibition has not been identified, and the generality of these findings is unknown. An extract of leaves of Pistacia integerrima also inhibits xanthine oxidase at a level that appears to merit further research.
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France saw the Rhine as its natural border and between France and the Rhine lay the Spanish Netherlands and the Dutch Generality Lands. The Dutch felt threatened by the French ambitions. According to the French ambassador, the Dutch acted from the motto: Gallicus amicus, non vicinus, or "The Frenchman is a good friend, but a bad neighbour". The Dutch again reinforced their fleet, but made insufficient preparations for their army because of a shortage of money.
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The functions of the Board as defined under the Act are: # To promote by such measures as it thinks fit the development of the rubber industry. # Without prejudice to the generality of the foregoing provision the measures referred to therein may provide for: ## undertaking, assisting or encouraging scientific, technological or economic research. ## training students in improved methods of planting, cultivation, manuring and spraying. ## the supply of technical advice to rubber growers ## improving the marketing of rubber.
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This was done at three levels of generality. First, overall monitoring of the DRV air defense network, SIGINT could maintain situational awareness of North Vietnamese tracking via radar and visual observers. Second, SIGINT detected the activation of specific weapons systems in the air defense network, such as SA-2 surface-to-air missiles (SAM), anti-aircraft artillery (AAA), and fighter interceptors. Finally, it could detect immediate threats, such as missile launches or impending attacks by fighters.
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In its full generality, partitioning cryptanalysis works by dividing the sets of possible plaintexts and ciphertexts into efficiently-computable partitions such that the distribution of ciphertexts is significantly non-uniform when the plaintexts are chosen uniformly from a given block of the partition. Partitioning cryptanalysis has been shown to be more effective than linear cryptanalysis against variants of DES and CRYPTON. A specific partitioning attack called mod n cryptanalysis uses the congruence classes modulo some integer for partitions.
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African-American Proverbs in Context. Jackson: University Press of Mississippi. Based on Persian proverbs, Zolfaghari and Ameri propose the following definition: "A proverb is a short sentence, which is well-known and at times rhythmic, including advice, sage themes and ethnic experiences, comprising simile, metaphor or irony which is well-known among people for its fluent wording, clarity of expression, simplicity, expansiveness and generality and is used either with or without change."p. 107, Hassan Zolfaghari & Hayat Ameri.
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In full generality, an algebraic structure may use any number of sets and any number of axioms in its definition. The most commonly studied structures, however, usually involve only one or two sets and one or two binary operations. The structures below are organized by how many sets are involved, and how many binary operations are used. Increased indentation is meant to indicate a more exotic structure, and the least indented levels are the most basic.
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This beautiful Castle situated about a mile to the north-east of Rosscarbery (Co. Cork), in the bosom of a secluded valley shut in by hills and at one time by a dense plantation of trees. It thus differed from the generality of the feudal strongholds which were either perched on a rocky eminence or surmounted the summit of some rising' ground. But the sheltered and isolated position of this castle probably protected it from external danger.
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In differential geometry, Yau's conjecture from 1982, is a mathematical conjecture which states that a closed Riemannian three-manifold has an infinite number of smooth closed immersed minimal surfaces. It is named after Shing-Tung Yau. It was the first problem in the Minimal submanifolds section in Yau's list of open problems. The conjecture has recently been claimed by Kei Irie, Fernando Codá Marques and André Neves in the generic case, and by Antoine Song in full generality.
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In geometry, collinearity of a set of points is the property of their lying on a single line.The concept applies in any geometry , but is often only defined within the discussion of a specific geometry , A set of points with this property is said to be collinear (sometimes spelled as colinearColinear (Merriam-Webster dictionary)). In greater generality, the term has been used for aligned objects, that is, things being "in a line" or "in a row".
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In general, a greedy algorithm is just an iterative process in which a locally best choice, usually an input of maximum weight, is chosen each round until all available choices have been exhausted. In order to describe a greedoid-based condition in which a greedy algorithm is optimal (i.e., obtains a basis of maximum value), we need some more common terminologies in greedoid theory. Without loss of generality, we consider a greedoid G = (F, E) with E finite.
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Reviewing Humphrey's show at Tibor de Nagy in 1960, Donald Judd said, of his monochromes, “They are large, subtle and single-colored. This is Purism of a sort, in which generality does not contain variables but excludes them, in which the basic diagram or color, the only continuity, is exposed, here the essence of a confused sequence of perceptions.” Donald Judd also likened these canvases to the work of Kazimir Malevich, Piet Mondrian, and Josef Albers.
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Multidimensional mechanism design for auctions with externalities. Journal of Economic Theory, 85(2), pp. 258–293. Moreover, Moldovanu and Jehiel have shown that multi-object auctions cannot be reduced to one-dimensional models without loss of generality because, in the presence of informational and allocative externalities, Bayes-Nash incentive compatible mechanisms exist only if private and social rates of information substitution are congruent, which in turn depends on whether signals are mono- or multi-dimensional.Jehiel, P., Moldovanu, B. (2001).
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With the exception of a few marked exceptions, only finite groups will be considered in this article. We will also restrict ourselves to vector spaces over fields of characteristic zero. Because the theory of algebraically closed fields of characteristic zero is complete, a theory valid for a special algebraically closed field of characteristic zero is also valid for every other algebraically closed field of characteristic zero. Thus, without loss of generality, we can study vector spaces over \Complex.
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According to the Vaisheshika school, all things that exist, that can be cognized and named are s (literal meaning: the meaning of a word), the objects of experience. All objects of experience can be classified into six categories, dravya (substance), (quality), karma (activity), (generality), (particularity) and (inherence). Later s ( and Udayana and ) added one more category abhava (non-existence). The first three categories are defined as artha (which can perceived) and they have real objective existence.
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The London Merchant is an early example of bourgeois tragedy. Tragedy, which had been a genre reserved for elite and royal subjects, has now been applied to the middle class. Lillo says in the dedication to the play that "tragedy is so far from losing its dignity by being accommodated to the circumstances of the generality of mankind.". What he refers to as "the end of tragedy" functions by "exciting the passions in order to the correcting of them".
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Parametric polymorphism implies that types themselves are passed as parameters as if they were proper values. Passed as arguments to a proper functions, but also into "type functions" as in the "parametric" type constants, leads to the question how to more properly type types themselves. Meta types are used to create an even more expressive type system. Unfortunately, only unification is not longer decidable in the presence of meta types, rendering type inference impossible in this extend of generality.
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Additionally, they appear to understand that adding or > subtracting one from a set will change the quantity of that set, though the > generality of this knowledge is difficult to assess without the ability to > label sets of arbitrary cardinality using number words. (emphasis > added)Michael C. Frank, Daniel L. Everett, Evelina Fedorenko and Edward > Gibson (2008), Number as a cognitive technology: Evidence from Pirahã > language and cognition. Cognition, Volume 108, Issue 3, September 2008, pp. > 819–824.
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Cambridge: Cambridge University Press. pp. 272–273 In the 1839 publication of his Journal and Remarks, Darwin said "This fox, more curious or more scientific, but less wise, than the generality of his brethren, is now mounted in the museum of the Zoological Society." He said it was "an undescribed species",Darwin, C. R. 1839. Narrative of the surveying voyages of His Majesty's Ships Adventure and Beagle between the years 1826 and 1836, Journal and Remarks 1832–1836.
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Extensible Markup Language (XML) is a markup language that defines a set of rules for encoding documents in a format that is both human-readable and machine-readable. The World Wide Web Consortium's XML 1.0 Specification of 1998 and several other related specifications—all of them free open standards—define XML. The design goals of XML emphasize simplicity, generality, and usability across the Internet. It is a textual data format with strong support via Unicode for different human languages.
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But that, of course, would be to read Congress's words of limitation as mere sham, and to read the presumption against pre-emption out of the law whenever Congress speaks to the matter with generality. That said, we have to recognize that our prior attempt to construe the phrase 'relate to' does not give us much help drawing the line here. 514 U.S. at 655. New York State Conference of Blue Cross & Blue Shield Plans v.
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The generality, however, are very poor, for they do not sow, nor do they harvest anything, save the dates upon which they subsist. They eat no meat but that of castrated camels, which are scarce and very dear." He also comments on the Jewish population: "There are many Jews, who lead a good life here, for they are under the protection of the several rulers, each of whom defends his own clients. Thus they enjoy very secure social standing.
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The French soldiers, and the remnants of the Legion of Salm and the "flying brigade" of Mappa were given safe conduct to the Generality Lands, and left on 7 October. The same day the Patriot members of the vroedschap stayed at home, and the members they had replaced in May occupied their seats again. On 9 October burgemeesters Dedel and Beels assumed their posts again, while Hooft stayed home. The situation before 21 April had been restored.
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The choices made in such a variant can be made without loss of generality. However, when a construction is being used to prove that something can be done, it is not necessary to describe all these various choices and, for the sake of clarity of exposition, only one variant will be given below. However, many constructions come in different forms depending on whether or not they use circle inversion and these alternatives will be given if possible.
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See Harris Corner Detector. Harris and Stephens improved upon Moravec's corner detector by considering the differential of the corner score with respect to direction directly, instead of using shifted patches. (This corner score is often referred to as autocorrelation, since the term is used in the paper in which this detector is described. However, the mathematics in the paper clearly indicate that the sum of squared differences is used.) Without loss of generality, we will assume a grayscale 2-dimensional image is used.
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The closure problem takes as input a directed acyclic graph with weights on its vertices and seeks the minimum (or maximum) weight of a closure, a set of vertices with no outgoing edges. (The problem may be formulated for directed graphs without the assumption of acyclicity, but with no greater generality, because in this case it is equivalent to the same problem on the condensation of the graph.) It may be solved in polynomial time using a reduction to the maximum flow problem..
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In settings where there is a generality-ordering on hypotheses, it is possible to represent the version space by two sets of hypotheses: (1) the most specific consistent hypotheses, and (2) the most general consistent hypotheses, where "consistent" indicates agreement with observed data. The most specific hypotheses (i.e., the specific boundary SB) cover the observed positive training examples, and as little of the remaining feature space as possible. These hypotheses, if reduced any further, exclude a positive training example, and hence become inconsistent.
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This quantity is nondimensional, adding to the prototype's generality. Generally, ZY is a complex quantity, ZY = U + iV\,\\! and as U and V are both, in general, functions of ω we should properly write, ZY = U(\omega) + iV(\omega)\,\\! With image filters, it is possible to obtain filters of different classes from the constant k filter prototype by means of a different kind of transformation (see composite image filter), constant k being those filters for which Z/Y is a constant.
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99 The States-General had only two direct sources of income: it taxed the Generality Lands directly, and the five Dutch admiralties set up under its authority, financed their activities nominally from the Convooien en Licenten levied on trade.De Vries and Van der Woude, p. 98 Otherwise, the provinces determined themselves how they would collect the revenues to finance their repartitie. Within the provinces there were other quota systems to determine the contributions of the cities and of the countryside.
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Minerals are classified by variety, species, series and group, in order of increasing generality. The basic level of definition is that of mineral species, each of which is distinguished from the others by unique chemical and physical properties. For example, quartz is defined by its formula, SiO2, and a specific crystalline structure that distinguishes it from other minerals with the same chemical formula (termed polymorphs). When there exists a range of composition between two minerals species, a mineral series is defined.
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Column generation leverages this idea to generate only the variables which have the potential to improve the objective function—that is, to find variables with negative reduced cost (assuming without loss of generality that the problem is a minimization problem). The problem being solved is split into two problems: the master problem and the subproblem. The master problem is the original problem with only a subset of variables being considered. The subproblem is a new problem created to identify a new variable.
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The constitutional conflict about the supremacy of the sovereignty of the Generality over provincial sovereignty, that seemed to be settled by the coup of William II, became "unsettled" again after his death. De Witt of course met opposition from other provinces from time to time, and sometimes Holland was even outvoted in the States General. This posed an unenviable dilemma for De Witt. Although decisions were supposed to be unanimous in the States General, this would in practice be unworkable.
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Fire behavior is different in every ecosystem and the organisms in those ecosystems have adapted accordingly. One sweeping generality is that in all ecosystems, fire creates a mosaic of different habitat patches, with areas ranging from those having just been burned to those that have been untouched by fire for many years. This is a form of ecological succession in which a freshly burned site will progress through continuous and directional phases of colonization following the destruction caused by the fire.Begon et al.
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It is known that any closed surface possesses infinitely many closed geodesics. The first problem in the minimal submanifolds section of Yau's list asks whether any closed three- manifold has infinitely many closed smooth immersed minimal surfaces. At the time it was known from Almgren–Pitts min-max theory the existence of at least one minimal surface. Kei Irie, Fernando Codá Marques, and André Neves solved this problem in the generic case and later Antoine Song claimed it in full generality.
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A sentence completion test form may be relatively short, such as those used to assess responses to advertisements, or much longer, such as those used to assess personality. A long sentence completion test is the Forer Sentence Completion Test, which has 100 stems. The tests are usually administered in booklet form where respondents complete the stems by writing words on paper. The structures of sentence completion tests vary according to the length and relative generality and wording of the sentence stems.
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In many cases, a phrase with an incorporated noun carries a different meaning with respect to the equivalent phrase where the noun is not incorporated into the verb. The difference seems to hang around the generality and definiteness of the statement. The incorporated phrase is usually generic and indefinite, while the non-incorporated one is more specific. In Yucatec Maya, for example, the phrase "I chopped a tree", when the word for "tree" is incorporated, changes its meaning to "I chopped wood".
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When electronic flash devices based on flashtube technology are used with most modern cameras (those with focal-plane shutters), shutter speed has no effect on guide numbers.A notable exception to this generality is when a flash device at full power is used in combination with cameras equipped with leaf shutters set to very brief exposure times. See also Shutter (photography). This is because even at the most powerful settings, flash durations seldom exceed a few milliseconds (thousandths of a second).
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There have been a number of occasions on which the ICJ has rejected claims that a customary rule existed because of a lack of consistency in the practice brought to its attention.Asylum Case (Colombia v Peru) [1950] ICJ Rep 266 at 277; Advisory Opinion on the Legality of the Threat or Use by a State of Nuclear Weapons in Armed Conflict [1996] ICJ Reports 226. Within the context of a specific dispute, however, it is not necessary to establish the generality of practice.
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The integrals along two paths from a to b are equal, since their difference is the integral along a closed loop. There is a relatively elementary proof of the theorem. One constructs an anti-derivative for f explicitly. Without loss of generality, it can be assumed that D is connected. Fix a point z0 in D, and for any z\in D, let \gamma: [0,1]\to D be a piecewise C1 curve such that \gamma(0)=z_0 and \gamma(1)=z.
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Mobile recommender systems make use of internet-accessing smart phones to offer personalized, context-sensitive recommendations. This is a particularly difficult area of research as mobile data is more complex than data that recommender systems often have to deal with. It is heterogeneous, noisy, requires spatial and temporal auto- correlation, and has validation and generality problems. There are three factors that could affect the mobile recommender systems and the accuracy of prediction results: the context, the recommendation method and privacy.
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It is reported that Mujahid said that "This verse was revealed about a man of the Helpers who had a black boy called Subayh whom he used to coerce to become Muslim".Al-Wahidi, Asbab Al-Nuzul, (2:256). In all cases, following the famous maxim (Consideration is granted to the Generality of the Language, not to the Specificity of the Reason [for Revelation])Ali Gomaa, al-Tariq ila al-Turath, p.207.Muhammad ash-Shawkani, Nayl al-Awtar, 8:112.
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Seus Olhos (Your Eyes) is a Brazilian soap opera produced and shown by the SBT from 18 May 2004 through 4 December 2004, with 173 chapters. Based on the original text from Inés Rodena "Seus Olhos" is an adaptation to the Portuguese language. The series writers were: Ecila Pedroso, Marine Noemi, Marcos Lazzarini, Aimar Labaki, Mário Viana and Fábio Torres. The series directors were: Jacques Lagoa, Luiz Antonio Piá and Henrique Martins, with David Grimberg as managing generality of teledramaturgia.
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1954), his nephew Moussa as-Sadr and another nephew Mohammad Sadeq al-Sadr. Haydar was considered a grand marja at-taqlid (supreme religious authority) of his time. A marja' at-taqlīd, literally, means "reference point for emulation", or one who through his learning and probity is qualified to be followed in all points of religious practice and Islamic law by the generality of Shi'is. He died in Kazimain, Iraq in 1937 leaving three children: Isma'il, Mohammad Baqir as-Sadr (d.
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This is an oversimplification for most materials and leads to restrictions on the types of materials that can be modeled. In particular, this assumption implies that any isotropic linear elastic solid is restricted to a Poisson ratio of 1/4. To address this lack of generality, the idea of "peridynamic states" was introduced. This allows the force density in each bond to depend on the stretches in all the bonds connected to its endpoints, in addition to its own stretch.
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This analogous structure is referred to as an n-qubit register. Measurements, drawn on a circuit diagram as stylized pointer dials, indicate where and how a result is obtained from the quantum computer after the steps of the computation are executed. Without loss of generality, one can work with the standard circuit model, in which the set of gates are single-qubit unitary transformations and controlled NOT gates on pairs of qubits, and all measurements are in the computational basis.
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Sometimes an economic hypothesis is only qualitative, not quantitative. Expositions of economic reasoning often use two-dimensional graphs to illustrate theoretical relationships. At a higher level of generality, Paul Samuelson's treatise Foundations of Economic Analysis (1947) used mathematical methods beyond graphs to represent the theory, particularly as to maximizing behavioural relations of agents reaching equilibrium. The book focused on examining the class of statements called operationally meaningful theorems in economics, which are theorems that can conceivably be refuted by empirical data.
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These usually involve fields in linear homogeneous media. This places considerable restrictions on the range and generality of problems to which boundary elements can usefully be applied. Nonlinearities can be included in the formulation, although they will generally introduce volume integrals which then require the volume to be discretised before solution can be attempted, removing one of the most often cited advantages of BEM. A useful technique for treating the volume integral without discretising the volume is the dual- reciprocity method.
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As an undergraduate at Princeton University, Swan was in 1952 one of five winners in the William Lowell Putnam Mathematical Competition. He earned his Ph.D. in 1957 from Princeton University under the supervision of John Coleman Moore. In 1969 he proved in full generality what is now known as the Stallings-Swan theorem. He is the Louis Block Professor Emeritus of Mathematics at the University of Chicago.. His doctoral students at Chicago include Charles Weibel, also known for his work in K-theory.
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Jamais Te Esquecerei (en:"I will never forget you") was a Brazilian telenovela shown by the SBT between April 14 and September 26 of 2003, at 10h30. Based on the original text of Caridad Bravo Adams, it was translated by Henrique Zambelli and adapted by Ecila Pedroso, that also the supervision of text signed, and Enéas Carlos. The soap opera was directed by Jacques Lagôa, Sacha and Henrique Martins, with David Grimberg as managing generality of teledramaturgia. It had 120 chapters.
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Shortly afterwards the finiteness of covolume was proven in full generality by Borel and Harish-Chandra. Meanwhile, there was progress on the general theory of lattices in Lie groups by Atle Selberg, Grigori Margulis, David Kazhdan, M. S. Raghunathan and others. The state of the art after this period was essentially fixed in Raghunathan's treatise, published in 1972. In the seventies Margulis revolutionised the topic by proving that in "most" cases the arithmetic constructions account for all lattices in a given Lie group.
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Rapoport's rule states that latitudinal ranges of species are generally smaller at low than at high latitudes. Thorson's rule contradicts this rule, because species disperse more widely at low than at high latitudes, supplementing much evidence against the generality of Rapoport's rule and for the fact that tropical species often have wider geographical ranges than high latitude species.Rohde, K., Heap M. and Heap, D. 1993. Rapoport's rule does not apply to marine teleosts and cannot explain latitudinal gradients in species richness.
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Conceptual models (models that are conceptual) range in type from the more concrete, such as the mental image of a familiar physical object, to the formal generality and abstractness of mathematical models which do not appear to the mind as an image. Conceptual models also range in terms of the scope of the subject matter that they are taken to represent. A model may, for instance, represent a single thing (e.g. the Statue of Liberty), whole classes of things (e.g.
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The inner nests contain (a) individuals (individual communication behaviors and effects) and (b) publics (groups of people sharing common interests and issues). The outer nests consist of (c) communities, (d) psychographics, lifestyles and subcultures, and social relationships, (e) geodemographics, (f) demographics/social categories and (g) mass audience. The nests display increasing specificity instead of generality as they move towards the inner center; more specificity provides more audience details and insights that allow communication campaigns to create more precise messages for the target audience.
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The Supreme Court calls the Sherman Antitrust Act a "charter of freedom", designed to protect free enterprise in America.Appalachian Coals, Inc. v. United States, "As a charter of freedom, the act has a generality and adaptability comparable to that found to be desirable in constitutional provisions.". One view of the statutory purpose, urged for example by Justice Douglas, was that the goal was not only to protect consumers, but at least as importantly to prohibit the use of power to control the marketplace.
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The greater generality of the method often allows for strong convergence of the solution over larger spatial and parameter domains. Third, the HAM gives excellent flexibility in the expression of the solution and how the solution is explicitly obtained. It provides great freedom to choose the basis functions of the desired solution and the corresponding auxiliary linear operator of the homotopy. Finally, unlike the other analytic approximation techniques, the HAM provides a simple way to ensure the convergence of the solution series.
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If the base of a circular cylinder has a radius and the cylinder has height , then its volume is given by :. This formula holds whether or not the cylinder is a right cylinder. This formula may be established by using Cavalieri's principle. A solid elliptic cylinder with the semi-axes and for the base ellipse and height In more generality, by the same principle, the volume of any cylinder is the product of the area of a base and the height.
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At the highest level of generality, a marginal cost is a marginal opportunity cost. In most contexts, marginal cost refers to marginal pecuniary cost, that is to say marginal cost measured by forgone money. A thorough-going marginalism sees marginal cost as increasing under the law of diminishing marginal utility, because applying resources to one application reduces their availability to other applications. Neoclassical economics tends to disregard this argument, but to see marginal costs as increasing in consequence of diminishing returns.
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The generality of the characterisation process is not and cannot be wholly scientific. It is always a matter of interpretation. For example, if A, who is a national of Arcadia, dies having made a valid local will and leaves land situated in Barsoom to C, who is domiciled in Catilage, how is the issue to be classified? One might say that any rights that C might have are vested by the will that was made in Arcadia, the lex loci actus.
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An Essay Concerning Human Understanding IV.5, 1-8. This view, known as psychologism, was taken to the extreme in the nineteenth century, and is generally held by modern logicians to signify a low point in the decline of logic before the twentieth century. Modern semantics is in some ways closer to the medieval view, in rejecting such psychological truth-conditions. However, the introduction of quantification, needed to solve the problem of multiple generality, rendered impossible the kind of subject- predicate analysis that underlies medieval semantics.
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SKOS semantic relations are intended to provide ways to declare relationships between concepts within a concept scheme. While there are no restrictions precluding their use with two concepts from separate schemes, this is discouraged because it is likely to overstate what can be known about the two schemes, and perhaps link them inappropriately. The property `related` simply makes an association relationship between two concepts; no hierarchy or generality relation is implied. The properties `broader` and `narrower` are used to assert a direct hierarchical link between two concepts.
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Her works explore the universality of language. However, later in her career lines lost association with the movement of her hand and gained the generality of concepts as she began to place them in ambiguous situations. She worked rapidly and in little over a year she had made the majority of approximately 2,000 drawings. In these works she also first combined multiple languages, using words and phrases from her principle spoken languages - Italian, German and Portuguese but also adding words in French, English, Croat and Czech.
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First, there must be a sovereign consisting of the whole population, which included women (in a way that was not practiced by almost all countries and so was quite revolutionary to suggest), that represents the general will and is the legislative power within the state. The second division is that of the government, being distinct from the sovereign. This division is necessary because the sovereign cannot deal with particular matters like applications of the law. Doing so would undermine its generality, and therefore damage its legitimacy.
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Vol II. p.508-527Dieudonne, J. History of Functional Analysis Chapter VIII. Section 2. A notable example of a result which had to wait for the development and dissemination of general locally convex spaces (amongst other notions and results, like nets, the product topology and Tychonoff's theorem) to be proven in its full generality, is the Banach–Alaoglu theorem which Stefan Banach first established in 1932 by an elementary diagonal argument for the case of separable normed spacesBanach, S. Theory of linear operations p.75.
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Without loss of generality, consider the marked points on the 3-ball boundary to lie on a great circle. The tangle can be arranged to be in general position with respect to the projection onto the flat disc bounded by the great circle. The projection then gives us a tangle diagram, where we make note of over and undercrossings as with knot diagrams. Tangles often show up as tangle diagrams in knot or link diagrams and can be used as building blocks for link diagrams, e.g.
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Advocates of CxG argue these kinds of idiosyncratic patterns are more common than is often recognized, and that they are best understood as multi-word, partially filled constructions. Construction grammar rejects the idea that there is a sharp dichotomy between lexical items, which are arbitrary and specific, and grammatical rules, which are completely general. Instead, CxG posits that there are linguistic patterns at every level of generality and specificity: from individual words, to partially filled constructions (e.g. drive X crazy), to fully abstract rules (e.g.
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Identify each such point θ on the circle with the corresponding point on the real line tan(θ/2). This function is undefined at the point π, since tan(π/2) is undefined; we will identify this point with our point ∞. Since tangents and inverse tangents are both continuous, our identification function is a homeomorphism between the real line and the unit circle without ∞. What we have constructed is called the Alexandroff one-point compactification of the real line, discussed in more generality below.
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In Boole the two parts run alongside one another, so that one is like the mirror image of the other, but for that very reason stands in no organic relation to it'BLC p. 14, quoted in Beaney p. 12 As well as providing a unified and comprehensive system of logic, Frege's calculus also resolved the ancient problem of multiple generality. The ambiguity of "every girl kissed a boy" is difficult to express in traditional logic, but Frege's logic resolves this through the different scope of the quantifiers.
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The plot of the short story "Fat and Thin" in its original version was based on an anecdote, and the conflict between the characters arose accidentally, due to the involuntary oversight of the "Thin". The 1886 edition, being in general textually close to the previous edition of 1883, changed the meaning of the story. The motive of official subordination was eliminated: the "Thin" now grovels before the "Fat" without any practical need, "reflexively". The story also received a much greater satirical sharpness and generality.
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Unhappy with the centralisation of political power to Habsburg Spain, seven northern provinces seceded into the Dutch Republic: Groningen, Frisia, Overijssel, Guelders, Utrecht, Holland and Zeeland. They kept parts of Limburg, Brabant and Flanders during and after the Eighty Years' War as Generality Lands. Military control was given to a stadtholder who in theory was elected by the States-General of the Netherlands of the now independent Dutch Republic. The function was de facto hereditary in Holland and Zeeland, and held by the Prince of Orange.
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Although the long-term population persistence of several species with low genetic variation has recently prompted debate on the generality of inbreeding depression, there are various empirical evidences for genetic Allee effects. One such case was observed in the endangered Florida panther (Puma concolor coryi). The Florida panther experienced a genetic bottleneck in the early 1990s where the population was reduced to ≈25 adult individuals. This reduction in genetic diversity was correlated with defects that include lower sperm quality, abnormal testosterone levels, cowlicks, and kinked tails.
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A diathermal wall is a physical connection between two bodies that allows the passage of heat between them. Bailyn is referring to diathermal walls that exclusively connect two bodies, especially conductive walls. This statement of the 'zeroth law' belongs to an idealized theoretical discourse, and actual physical walls may have peculiarities that do not conform to its generality. For example, the material of the wall must not undergo a phase transition, such as evaporation or fusion, at the temperature at which it must conduct heat.
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When designing and developing the software that provides the VNFs, vendors may structure that software into software components (implementation view of a software architecture) and package those components into one or more images (deployment view of a software architecture). These vendor-defined software components are called VNF Components (VNFCs). VNFs are implemented with one or more VNFCs and it is assumed, without loss of generality, that VNFC instances map 1:1 to VM Images. VNFCs should in general be able to scale up and/or scale out.
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Reign of the generality in fact meant nothing else than oppression and colonisation by the Protestants. There was no self-government and Catholicism was forbidden, which resulted in a flight of the Catholic clergy and occupation of the Catholic churches. Due to high taxes and oppression the bailiwick couldn't restore its old glory and became an intensely poor area without any importance. After the French war of 1795 and the proclamation of the Batavian Republic, the Meierij disappeared as s political unity and went up into Brabant.
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Philosophers (and other users of logic) spend a lot of time and effort searching for and removing (or intentionally adding) ambiguity in arguments because it can lead to incorrect conclusions and can be used to deliberately conceal bad arguments. For example, a politician might say, "I oppose taxes which hinder economic growth", an example of a glittering generality. Some will think he opposes taxes in general because they hinder economic growth. Others may think he opposes only those taxes that he believes will hinder economic growth.
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The induced EMF method is dependent on the assumption of a sinusoidal current distribution, delivering an accuracy better than about 10% as long as the wavelength to element diameter ratio is greater than about 60. However, for yet larger conductors numerical solutions are required which solve for the conductor's current distribution (rather than assuming a sinusoidal pattern). This can be based on approximating solutions for either Pocklington's integrodifferential equation or the Hallén integral equation. These approaches also have greater generality, not being limited to linear conductors.
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Initially Karol wanted his militia, who had arrived with General Bierzyński, to focus on the estate in Żmigród and further enlist around 600 men, but with the Russian army approaching he ordered them to withdraw to Muszynka where Józef Miączyński was named commander. To "friends" in the Grand Duchy of Lithuania he wrote letters calling for the establishment of the Confederation/Generality in those counties and provinces that have not done so. He later sent marshals and officials to break down any resistance that would have occurred.
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Holland and Zeeland acknowledged him perfunctorily, but mainly ignored him, and of the other members of the Union of Utrecht Overijssel, Gelderland and Utrecht never even recognised him.Israel (1995), p. 212 At the time of his sovereignty, Anjou replaced the Generality Lion by arms that he himself designed incorporating all the arms of the, at that time, nine Dutch rebellious provinces with France. Anjou himself was dissatisfied with his limited power, and decided to take the Flemish cities of Antwerp, Bruges, Dunkirk, and Ostend by force.
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The Bourbaki group holds regular private conferences for the purpose of drafting and expanding the Éléments. Topics are assigned to subcommittees, drafts are debated, and unanimous agreement is required before a text is deemed fit for publication. Although slow and labor-intensive, the process results in a work which meets the group's standards for rigour and generality. The group is also associated with the Séminaire Bourbaki, a regular series of lectures presented by members and non-members of the group, also published and disseminated as written documents.
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In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree p and q to form a composite cocycle of degree p + q. This defines an associative (and distributive) graded commutative product operation in cohomology, turning the cohomology of a space X into a graded ring, H∗(X), called the cohomology ring. The cup product was introduced in work of J. W. Alexander, Eduard Čech and Hassler Whitney from 1935–1938, and, in full generality, by Samuel Eilenberg in 1944.
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Reinforcement learning is an area of machine learning concerned with how software agents ought to take actions in an environment so as to maximize some notion of cumulative reward. Due to its generality, the field is studied in many other disciplines, such as game theory, control theory, operations research, information theory, simulation- based optimization, multi-agent systems, swarm intelligence, statistics and genetic algorithms. In machine learning, the environment is typically represented as a Markov decision process (MDP). Many reinforcement learning algorithms use dynamic programming techniques.
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The axiom of replacement allows one to form many unions, such as the union of two sets. However, in its full generality, the axiom of union is independent from the rest of the ZFC-axioms: Replacement does not prove the existence of the union of a set of sets if the result contains an unbounded number of cardinalities. Together with the axiom schema of replacement, the axiom of union implies that one can form the union of a family of sets indexed by a set.
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For example, the monster behavior in Bubble Bobble was not perfected until the code and data contained with the custom MCU was dumped through the decapping of the chip. This results in the ROM set requirements changing as the games are emulated to a more and more accurate degree, causing older versions of the ROM set becoming unusable in newer versions of MAME. Portability and generality are also important to MAME. Combined with the uncompromising stance on accuracy, this often results in high system requirements.
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In 1289, the Catalan 'Corts' or Parliament - considered as of the year 1300 as representing the totality or 'generality' (Generalitat) of Catalonia - formed a commission to collect the taxes that the Corts granted the King. The Corts - or 'General Assembly' of Catalonia, meeting at Cervera in 1359, formalised that commission or Deputation (Diputació) of the General. It consisted of deputies from the three estates: military or noble, ecclesiastical, and popular or royal (representatives of the guilds and citizens of towns directly subject to the King).
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Plant production models exist in varying levels of scope (cell, physiological, individual plant, crop, geographical region, global) and of generality: the model can be crop-specific or be more generally applicable. In this section the emphasis will be on crop-level based models as the crop is the main area of interest from an agronomical point of view. As of 2005, several crop production models are in use. The crop growth model SUCROS has been developed during more than 20 years and is based on earlier models.
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A network is a graph , where is a set of vertices and is a set of ’s edges – a subset of – together with a non-negative function , called the capacity function. Without loss of generality, we may assume that if then is also a member of , since if then we may add to E and then set . If two nodes in are distinguished, a source and a sink , then is called a flow network.A.V. Goldberg, É. Tardos and R.E. Tarjan, Network flow algorithms, Tech.
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The recast databases provide designed data access paths with data value commonality across databases. ; Simplicity of understanding : Answering queries with views arouses interest from a theoretical standpoint, but difficulties in understanding how to incorporate it as an "enterprise solution". ; Simplicity of deployment : Even if recognized as a solution to a problem, EII currently takes time to apply and offers complexities in deployment. Proposed schema-less solutions include "Lean Middleware", but ease-of-use and speed of employment appear inversely proportional to the generality of such systems.
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Feuerbach, who does not enter upon a > criticism of this real essence is hence obliged: :1. To abstract from the > historical process and to define the religious sentiment regarded by itself, > and to presuppose an abstract — isolated - human individual. :2. The essence > therefore can by him only be regarded as ‘species’, as an inner ‘dumb’ > generality which unites many individuals only in a natural way. Thus, Marx appears to say that human nature is no more than what is made by the 'social relations'.
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Single neurons are hypothesized to be simultaneously tuned to several modalities, such as visual, auditory, and olfactory. Neurons hypothesized to be tuned to different signals are often hypothesized to integrate information from the different sources. In computational models called neural networks, such integration is the major principle of operation. The best examples of neuronal tuning can be seen in the visual, auditory, olfactory, somatosensory, and memory systems, although due to the small number of stimuli tested the generality of neuronal tuning claims is still an open question.
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For greater accuracy but lower generality component testing is used. Each coupon or component test generates a point on the plot though in some cases there is a runout where the time to failure exceeds that available for the test (see censoring). Analysis of fatigue data requires techniques from statistics, especially survival analysis and linear regression. The progression of the S-N curve can be influenced by many factors such as stress ratio (mean stress), loading frequency, temperature, corrosion, residual stresses, and the presence of notches.
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As the laws of rational trigonometry give algebraic (and not transcendental) relations, they apply in generality to algebraic number fields beyond the rational numbers. Specifically, any finite field which does not have characteristic 2 reproduces a form of these laws, and thus a finite field geometry., page 1. Another version of this article is at Le Anh Vinh, Dang Phuong Dung (2008), "Explicit tough Ramsey Graphs ", Proceedings of International Conference on Relations, Orders and Graphs: Interaction with Computer Science 2008, Nouha Editions, 139–146.
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Under many circumstances, it is desirable to assign a limit to a series which fails to converge in the usual sense. A summability method is such an assignment of a limit to a subset of the set of divergent series which properly extends the classical notion of convergence. Summability methods include Cesàro summation, (C,k) summation, Abel summation, and Borel summation, in increasing order of generality (and hence applicable to increasingly divergent series). A variety of general results concerning possible summability methods are known.
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In 2014, a cross-chiral RNA polymerase ribozyme was demonstrated. It was hypothesized that it offers a new mode of recognition between an enzyme and substrates, which is based on the shape of the substrate, and allows avoiding the Watson-Crick pairing and, therefore, may provide greater sequence generality. Various other experiments have shown that, besides bearing polymerase properties, ribozymes could have developed other kinds of evolutionarily useful catalytic activity such as synthase, ligase, or aminoacylase activities. Ribozymal aminoacylators and ribozymes with the ability to form peptide bonds might have been crucial to inventing translation.
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M2001 is a modular educational mathematical programming language for developing and presenting mathematical algorithms, from the modern discrete to the classical continuous mathematics. M2001 is built on a semantic framework that is based in category theory and has a syntax similar to that of Pascal or Modula-2. It is designed purely for pedagogic use, so efficiency and ease of implementation have been far less important in its development than generality and range of application. It was created to play an important role in forming a formal algorithmic foundation for first-year college math students.
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The conclusions obtained from Pasinetti's Theorem led to a huge number of scientific works and papers, with the purpose of clarifying the nature of the Theorem and its more important implications. Specifically, in 1966, Paul A. Samuelson and Franco Modigliani, the MIT economists, wrote a detailed and widely quoted paper where they tried to minimize the consequences of the Pasinetti Theorem and to lessen the generality of its conclusions.Samuelson y Modigliani [1966], “The Pasinetti Paradox in Neoclassical and More General Models”, The Review of Economic Studies, pp. 269-301.
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Philip Gidley King (King) to Sir Joseph Banks (Banks), 20 Mar. 1799, ML Banks Papers, Series 39.043. He personally inspected the vessel on 8 October 1799, whilst it was being fitted-out at Deptford, and suggested that: > as few seamen know anything about the management of a cutter, her being > constructed into a brig would make her more manageable to the generality of > seamen. Schanck agreed with this change and the Commissioners of Transport were directed to rig the vessel as a brig, and not as a cutter like the Trial as had been intended.
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Some other principles were also required. Daniel Bernoulli The law of conservation of vis viva was championed by the father and son duo, Johann and Daniel Bernoulli. The former enunciated the principle of virtual work as used in statics in its full generality in 1715, while the latter based his Hydrodynamica, published in 1738, on this single conservation principle. Daniel's study of loss of vis viva of flowing water led him to formulate the Bernoulli's principle, which relates the loss to be proportional to the change in hydrodynamic pressure.
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Protests began in De Witt's hometown, Dordrecht, and soon spread to Rotterdam, Schiedam, Leiden and Amsterdam. In Rotterdam and Amsterdam the militias forced the vroedschap to vote against the capitulation. Nevertheless, on June 26 the States General voted four to three (Holland, and the three already occupied provinces Utrecht, Gelderland and Overijssel, against the rest) to send De Groot with a mandate to sign away the Generality Lands and offer a large war indemnity to Louis. Louis thought the offer insufficient, and sent De Groot back empty- handed.
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509 Buat, however, had the misfortune to be tried for treason by the Hof van Holland (the main court of the province of Holland). This in itself was controversial, as the asserted treason was against the Generality, so that the Hoge Raad van Holland en Zeeland (the federal supreme court) might have been more appropriate. Also, according to the opinion of many contemporaries and some later historians, the Executive in the form of the States of Holland exerted undue influence in the proceedings. (1901) Robert Fruin's verspreide geschriften, p. 279ff.
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From a wider perspective, without loss of generality, the similarities between the chaotic maps and the cryptographic systems is the main motivation for the design of chaos based cryptographic algorithms. One type of encryption, secret key or symmetric key, relies on diffusion and confusion, which is modeled well by chaos theory. Another type of computing, DNA computing, when paired with chaos theory, offers a way to encrypt images and other information. Many of the DNA-Chaos cryptographic algorithms are proven to be either not secure, or the technique applied is suggested to be not efficient.
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Thorngate's postulate of commensurate complexity, also referred to as Thorngate's impostulate of theoretical simplicity is the description of a phenomenon in social science theorizing. Karl E. Weick maintains that research in the field of social psychology can – at any one time – achieve only two of the three meta-theoretical virtues of "Generality", "Accuracy" and "Simplicity." One of these aspects therefore must always be subordinated to the others. The postulate is named for the Canadian social psychologist Warren Thorngate of the University of Alberta, whose work is quoted by Weick.
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The Zulu attitude towards firearms was that: "The generality of Zulu warriors, however, would not have firearms – the arms of a coward, as they said, for they enable the poltroon to kill the brave without awaiting his attack."Bourquin, S. Military History Journal, V.4, No.4, The Zulu military organization and the challenge of 1879, South African Military History Society, ISSN 0026-4016, Dec. 1978. Even though their fire was not accurate, it was responsible for five of the seventeen British deaths at Rorke's Drift.Bourquin, S. section 'War of 1879', subsection 'Weapons'Knight 1996, p.
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An example of a leptokurtic distribution is the Laplace distribution, which has tails that asymptotically approach zero more slowly than a Gaussian, and therefore produces more outliers than the normal distribution. It is also common practice to use an adjusted version of Pearson's kurtosis, the excess kurtosis, which is the kurtosis minus 3, to provide the comparison to the standard normal distribution. Some authors use "kurtosis" by itself to refer to the excess kurtosis. For clarity and generality, however, this article follows the non-excess convention and explicitly indicates where excess kurtosis is meant.
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A source or sender is one of the basic concepts of communication and information processing. Sources are objects which encode message data and transmit the information, via a channel, to one or more observers (or receivers). In the strictest sense of the word, particularly in information theory, a source is a process that generates message data that one would like to communicate, or reproduce as exactly as possible elsewhere in space or time. A source may be modelled as memoryless, ergodic, stationary, or stochastic, in order of increasing generality.
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1056 Lengths of lines in distributed-element circuits, for generality, are usually expressed in terms of the circuit's nominal operational wavelength, λ. Lines of the prescribed length in a commensurate line circuit are called unit elements (UEs). A particularly simple relationship pertains if the UEs are λ/8. Each element in the lumped circuit is transformed into a corresponding UE. However, Z0 of the lines must be set according to the component value in the analogous lumped circuit and this may result in values of Z0 that are not practical to implement.
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Later happiness and well-being development frameworks were similar to the proposal. For example the Bhutan GNH Index published in 2012 after 2 years of research was not dissimilar from the first secular GNH framework and Index of 2005. The main difference was the addition of spiritual elements such as Karma and prayers indicators to fit the local Bhutanese culture. The Bhutan GNH philosophy was initially dismissed due to its generality and was considered as touchy-feely concept, but later taken seriously after it published an econometric framework.
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Malebranche's theodicy is his solution to the problem of evil. Although he conceded that God had the power to create a more perfect world, free from all defects, such a world would have necessitated a greater complexity in divine ways. Thus, God produces the natural evils that follow from simple laws not because he wills those particular effects, but because he wills a world that best reflects his wisdom by achieving the best possible balance between the intrinsic perfection of the work and the simplicity and generality of its laws.
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Transportability: The performance and functional literacy studies both illustrated how g is transportable across life situations and it represents a set of largely generalizable reasoning and problem-solving skills. G appear to be linearly linked to performance in school, jobs and achievements. Generality: Studies show that IQ measured at the age of 11 predicted longevity, premature death, lung and stomach cancers, dementia, loss of functional independence, more than 60 years later. Research has shown that higher IQ at age 11 is significantly related to higher social class in midlife.
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The principle of virtual work had always been used in some form since antiquity in the study of statics. It was used by the Greeks, medieval Arabs and Latins, and Renaissance Italians as "the law of lever". The idea of virtual work was invoked by many notable physicists of the 17th century, such as Galileo, Descartes, Torricelli, Wallis, and Huygens, in varying degrees of generality, when solving problems in statics. Working with Leibnizian concepts, Johann Bernoulli systematized the virtual work principle and made explicit the concept of infinitesimal displacement.
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Some architectures such as PowerPC attempt to avoid the need for cacheline locking or scratchpads through the use of cache control instructions. Marking an area of memory with "Data Cache Block: Zero" (allocating a line but setting its contents to zero instead of loading from main memory) and discarding it after use ('Data Cache Block: Invalidate', signaling that main memory didn't receive any updated data) the cache is made to behave as a scratchpad. Generality is maintained in that these are hints and the underlying hardware will function correctly regardless of actual cache size.
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The border states, parts of Flanders, Brabant, and Limburg that were conquered by the Dutch in the final stages of the war, were to be federally governed by the States-General. These were the so-called Generality Lands (Generaliteitslanden), which consisted of Staats-Brabant (present North Brabant), Staats-Vlaanderen (present Zeelandic Flanders), and Staats-Limburg (around Maastricht). The peace would not be long-lived as the newly emerged world powers, the Republic of the Netherlands and the Commonwealth of England, would start their first war in 1652, only four years after the peace was signed.
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The matroid intersection problem becomes NP-hard when three matroids are involved, instead of only two. One proof of this hardness result uses a reduction from the Hamiltonian path problem in directed graphs. Given a directed graph G with n vertices, and specified nodes s and t, the Hamiltonian path problem is the problem of determining whether there exists a simple path of length n − 1 that starts at s and ends at t. It may be assumed without loss of generality that s has no incoming edges and t has no outgoing edges.
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In Nyaya (Generality or common features) school of Hinduism, there is extensive debate on what Guna means, and whether quality is innate, subjective or describable. Early scholars of this school identified 17 qualities, which later scholars expanded to 24 . Different scholars of this school list the 24 differently; for example, Bhasarvajna disallows 6 of the 24 commonly accepted by the ancient scholars. The most commonly accepted list is: color, taste, smell, touch, number, contact, disjunction, farness, nearness, dimension, separateness, knowledge, pleasure, frustration, desire, hatred, effort, weight, fluidity, viscosity, dispositional tendency, merit, demerit, and sound.
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An ideal chain (or freely-jointed chain) is the simplest model to describe polymers, such as nucleic acids and proteins. It only assumes a polymer as a random walk and neglects any kind of interactions among monomers. Although it is simple, its generality gives insight about the physics of polymers. In this model, monomers are rigid rods of a fixed length l, and their orientation is completely independent of the orientations and positions of neighbouring monomers, to the extent that two monomers can co-exist at the same place.
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Even though positive legal norms do commonly contain elements of generality, those elements are not central to the relation between a higher and a lower norm. This is a relation of legal 'validity' (not to be confused with logical validity), which is that the creation of the lower norm has been authorised by the higher norm. Since this moment of creation always involves extraneous considerations, Kelsen does not need to supplement his model with a concept of 'discretion'. What has to be consistent in a dynamic order of norms is only the process of authorising.
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If they do, they can be replaced by their combined convex hull without loss of generality. If after merging all overlapping hulls, a single barrier has resulted, then the more general algorithm need not be run; the coverage of a barrier is at most its convex hull, and we have just determined that its coverage is its convex hull. The merged hulls can be computed in O(nlog2n) time. Should more than one hull remain, the original algorithm can be run on the new simplified set of hulls, for a reduced running time.
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On a map of Guillaume Delisle, dating from the 18th century, there is a fort defending the west entrance of the bridge.Abbé Paul Decagny, L'Arrondissement de Péronne ou recherches sur les villes, bourgs, villages et hameaux qui le composent, 1844 - réédition partielle sous le titre, Péronne et son canton, Inval-Boiron, La Vague verte, 2010. Brie depended on the election and bailiwick of Péronne, the generality of Amiens and the diocese of Noyon. During the French Revolution, the hamlets of Pont-lès-Brie and Applaincourt were attached to the commune of Villers- Carbonnel.
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Châteauneuf was annexed and the lords resided at Maillebois until about the second half of the eighteenth century. The stronghold of Thymerais meanwhile gradually was dismantled so that by the late eighteenth century the barony of Châteauneuf-en-Thymerais was nowhere near the same extent as it was in the thirteenth century. In the late eighteenth century Châteauneuf was dependent on the election of Verneuil-sur-Avre and generality of Alençon. It was the chief town of the district from 1790 to 1795, and took the name of Puy-la- Montagne to the revolutionary era.
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In the theory of trespass, the plaintiff remained the owner of the chattel, with the possession or property rights interrupted or interfered with. In this case, the plaintiff must accept the chattel back when it was tendered. Recovery was limited to any damage to the chattel, or from the interruption of property rights. In the time of Bracton, despite the generality of the writ, the bailor of a chattel could only bring this action against the bailee of the chattel, or those who represent the bailee by testate or intestate succession.
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Charles Calvert's rule as governor was aggravated by growing economic problems. From the 1660s onwards, the price of tobacco, the staple crop of Maryland and its chief source of export income, began a long slide, causing economic hardship especially among the poor. In 1666, neighbouring Virginia proposed a "stint" on tobacco growing – a one-year moratorium that would lower supply and so drive up prices. Calvert initially agreed to this plan, but came to realize that the burden of the stint would fall chiefly upon his poorest subjects, who comprised "the generality of the province".
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However, the principles of estoppel and equity in the international context do not retain all the connotations they do under common law. The reference to the principles as "general" signify that, if rules were to be adapted from municipal law, they should be at a sufficient level of generality to encompass similar rules existing in many municipal systems. Principles of municipal law should be regarded as sources of inspiration rather than as sources of rules of direct application.International Status of South-West Africa (Advisory Opinion) [1950] ICJ Reports 128 at 148.
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Rudolf Halin (February 3, 1934 – November 14, 2014) was a German graph theorist, known for defining the ends of infinite graphs, for Halin's grid theorem,. for extending Menger's theorem to infinite graphs, and for his early research on treewidth and tree decomposition. He is also the namesake of Halin graphs, a class of planar graphs constructed from trees by adding a cycle through the leaves of the given tree; earlier researchers had studied the subclass of cubic Halin graphs but Halin was the first to study this class of graphs in full generality.
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One of them may have been is the correct accommodation of many elements whose atomic weights were thought to have wrong values but were later corrected. The debate on the position of the rare-earth metals helped spur the discussion about the table as well. In 1889, Mendeleev noted at the Faraday Lecture to the Royal Institution in London that he had not expected to live long enough "to mention their discovery to the Chemical Society of Great Britain as a confirmation of the exactitude and generality of the periodic law".
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The project began in 1991 in Berkeley when Don Maszle and Frederic Y. Bois translated in C and reorganized a program that Bois had developed at Harvard for his PhD thesis. The primary motivation for the work was to be able to quickly develop and easily maintain PBPK models. However, the syntax was defined with enough generality that many algebraic and first-order ordinary differential equations can be solved. The capability to perform efficient Monte Carlo simulations was added early on, for the research needs of the group.
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In algebraic geometry, the intersection of two sub-varieties of an algebraic variety is a finite union of irreducible varieties. To each component of such an intersection is attached an intersection multiplicity. This notion is local in the sense that it may be defined by looking at what occurs in a neighborhood of any generic point of this component. It follows that without loss of generality, we may consider, in order to define the intersection multiplicity, the intersection of two affines varieties (sub-varieties of an affine space).
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The development of the IUCN Red List of Ecosystems considered tradeoffs between generality, precision, realism and simplicity. Conceptual and operational weaknesses of the RLE approach, categories, and criteria have been discussed and debated. A fair evaluation of it effectiveness and importance needs to consider its real achievements in conservation and natural resource management, a balance between benefits and limitations and its performance against alternative methods. The Red List of Ecosystems is a relatively recent product, and it is still difficult to measure its medium and long-term impact.
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His 1939 work on "The Structure of Wholes" was seen as a precedent to systems theory in books in the 1960s–1980s edited by Fred Emery. Angyal's biospheric model of personality was found to have greater generality beyond the domain of personality, to a broader range of systems. > Angyal ... coined the word biosphere. The word refers to both the individual > and the environment, "not as interacting parts, not as constituents which > have independent existence, but as aspects of a single reality which can be > separated only by abstraction".
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Swietlicki here is cited by López-Baralt, Islam in Spanish Literature (1985, 1992) at 127-131, 134. The Catholic writings of Santa Teresa de Ávila, widely recognized and revered, may accordingly be understood to reflect as well a generality of shared values among the Judaic, Christian, and Islamic faiths during those blessed periods of convivencia in medieval Spain."Convivencia" signifies "living together" in Spanish, and may refer to an early medieval Golden Age ideal, in which the three faiths would share their cultures in peace. Prof. Asín contributed to the reification of the third pillar.
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More recent work has strongly challenged some of the basic presumptions of the "core knowledge" school, and revised ideas of domain generality—but from a newer dynamic systems approach, not from a revised Piagetian perspective. Dynamic systems approaches harken to modern neuroscientific research that was not available to Piaget when he was constructing his theory. One important finding is that domain-specific knowledge is constructed as children develop and integrate knowledge. This enables the domain to improve the accuracy of the knowledge as well as organization of memories.
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Improvement of models is an active area of research, with new models attempting to take factors such as life-history traits of species or processes such as migration into account when predicting distribution changes; though possible trade-offs between regional accuracy and generality are recognised. Climate change is also predicted to interact with other drivers of biodiversity change such as habitat destruction and fragmentation, or the introduction of foreign species. These threats may possibly act in synergy to increase extinction risk from that seen in periods of rapid climate change in the past.
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The antitrust laws came to be seen by the Supreme Court as a "charter of freedom", designed to protect free enterprise in America.Appalachian Coals, Inc. v. United States, 288 U.S. 344, 359-60 (1933) ("As a charter of freedom, the act has a generality and adaptability comparable to that found to be desirable in constitutional provisions."). One view of the statutory purpose, urged for example by Justice Douglas, was that the goal was not only to protect consumers, but at least as importantly to prohibit the use of power to control the marketplace.
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This second approach is sometimes called first order logic with equality, but many authors adopt it for the general study of first-order logic without comment. There are a few other reasons to restrict study of first-order logic to normal models. First, it is known that any first-order interpretation in which equality is interpreted by an equivalence relation and satisfies the substitution axioms for equality can be cut down to an elementarily equivalent interpretation on a subset of the original domain. Thus there is little additional generality in studying non-normal models.
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Cicynna or Kikynna () was a deme of ancient Attica of the phyle of Acamantis, sending two or three delegates to the Athenian Boule. It was the native deme of Strepsiades, the protagonist in Aristophanes' The Clouds. Representing the generality of the deme, Aristophanes depicts this character as a prosperous farmer and attentive to his lazy son. Probably Cicynna had his own diasia, the most important festival to Zeus in Attica, in which the god was honored as Zeus Meilichius: this is evident from a passage from the aforementioned comedy by Aristophanes.
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In a revisionist account, considers that Löwenheim's proof was complete. gave a (correct) proof using formulas in what would later be called Skolem normal form and relying on the axiom of choice: :Every countable theory which is satisfiable in a model M, is satisfiable in a countable substructure of M. also proved the following weaker version without the axiom of choice: : Every countable theory which is satisfiable in a model is also satisfiable in a countable model. simplified . Finally, Anatoly Ivanovich Maltsev (Анато́лий Ива́нович Ма́льцев, 1936) proved the Löwenheim–Skolem theorem in its full generality .
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The 80-year war came to an end on 15 May 1648 with the Peace of Munster. The peace between Spain and the Republic of the United Provinces led to a division of Brabant. The south of the duchy belonged to the Spanish Netherlands, while the north, Staats-Brabant, became part of the Republic of the United Netherlands. State Brabant was a so-called "Generality Country", unlike other areas, State Brabant was not recognized as an equivalent province of the Republic and therefore did not get its own government.
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Income distribution can describe a prospectively observable element of an economy. It has been used as an input for testing theories explaining the distribution of income, for example human capital theory and the theory of economic discrimination (Becker, 1993, 1971). In welfare economics, a level of feasible output possibilities is commonly distinguished from the distribution of income for those output possibilities. But in the formal theory of social welfare, rules for selection from feasible distributions of income and output are a way of representing normative economics at a high level of generality.
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By 1713 the public debt of the province of Holland had reached 310 million guilders; the debt of the Generality was 68 million; and the debts of the smaller provinces, and of the cities came on top of this. The debt service of Holland alone in that year required 14 million guilders, which exceeded its regular tax revenue.De Vries and Van der Woude, p. 119. Most of this humongous public debt was held by Dutch private citizens, so in a sense it merely engendered an internal money circuit in the Dutch economy.
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As a consequence, 18th century mathematicians believed that they could derive meaningful results by applying the usual rules of algebra and calculus that hold for finite expansions even when manipulating infinite expansions. In works such as Cours d'Analyse, Cauchy rejected the use of "generality of algebra" methods and sought a more rigorous foundation for mathematical analysis. An example is Euler's derivation of the series for 0. He first evaluated the identity at r=1 to obtain The infinite series on the right hand side of () diverges for all real x.
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Calvert's life as governor was aggravated by growing economic problems. From the 1660s onwards, the price of tobacco, the staple crop of Maryland and its chief source of export income, began a long slide, causing economic hardship especially among the poor. In 1666 neighbouring Virginia proposed a "stint" on tobacco growing, a one-year moratorium that would lower supply and so drive up prices. Calvert initially agreed to this plan but came to realize that the burden of the stint would fall chiefly upon his poorest subjects, who comprised "the generality of the province".
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The artistic education at Vkhutemas tended to be multidisciplinary, which stemmed from its origins as a merger of a fine arts college and a craft school. A further contributor to this was the generality of the basic course, which continued after students had specialised and was complemented by a versatile faculty. Vkhutemas cultivated polymath masters in the Renaissance mold, many with achievements in graphics, sculpture, product design, and architecture. ЛенДекор.Инфо, Взаимодействие архитектуры и левого изобразительного искусства Painters and sculptors often made projects related to architecture; examples include Tatlin's Tower, Malevich's Architektons, and Rodchenko's Spatial Constructions.
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The characteristic that persuaded a majority of the Court to approve the current federal sentencing scheme, consisting of sentencing guidelines ranges from which trial judges were permitted to depart, was the fact that all sentences were subject to appellate review for "reasonableness." All of these systems require trial judges to make factual findings on some level of generality. Under the Federal Sentencing Guidelines, these findings were somewhat specific; under the indeterminate sentencing scheme, they were not. Yet in both schemes the judge makes findings that allow them to impose an appropriate sentence.
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Martin noted in 1697 that the citizens seemed "happier than the generality of mankind as being almost the only people in the world who feel the sweetness of true liberty". In the 19th century, their good health and well being was contrasted favourably with conditions elsewhere in the Hebrides.See for example Steel (1988) page 71 quoting Macauley in 1756, MacCulloch in 1819 and Ross in 1887. Theirs was not a utopian society; the islanders had ingenious wooden locks for their property, and financial penalties were exacted for misdemeanours.
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A flurry of work in women's history led to a call for study of the male role (initially influenced by psychoanalysis) in society and emotional and interpersonal life. Connell wrote that these initial works were marked by a "high level of generality" in "broad surveys of cultural norms". The scholarship was aware of contemporary societal changes aiming to understand and evolve (or liberate) the male role in response to feminism.John Tosh calls for a return to this aim for the history of masculinity to be useful, academically and in the public sphere.
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Cauchy (1789–1857) started the project of formulating and proving the theorems of infinitesimal calculus in a rigorous manner, rejecting the heuristic principle of the generality of algebra exploited by earlier authors. In his 1821 work Cours d'Analyse he defines infinitely small quantities in terms of decreasing sequences that converge to 0, which he then used to define continuity. But he did not formalize his notion of convergence. The modern (ε, δ)-definition of limit and continuous functions was first developed by Bolzano in 1817, but remained relatively unknown.
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User-created containers only have to provide an iterator that implements one of the five standard iterator interfaces, and all the algorithms provided in the STL can be used on the container. This generality also comes at a price at times. For example, performing a search on an associative container such as a map or set can be much slower using iterators than by calling member functions offered by the container itself. This is because an associative container's methods can take advantage of knowledge of the internal structure, which is opaque to algorithms using iterators.
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Additionally, assuming a type of all types that includes itself as type leads into a paradox, as in the set of all sets, so one must proceed in steps of levels of abstraction. Research in second order lambda calculus, one step upwards, showed, that type inference is undecidable in this generality. Parts of one extra level has been introduced into Haskell named kind, where it is used helping to type monads. Kinds are left implicit, working behind the scenes in the inner mechanics of the extended type system.
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We give the more general definition of when a -valued function or multifunction defined on a subset of has a closed graph since this generality is needed in the study of closed linear operators that are defined on a dense subspace of a topological vector space (and not necessarily defined on all of ). This particular case is one of the main reasons why functions with closed graphs are studied in functional analysis. :Assumptions: Throughout, and are topological spaces, , and is a -valued function or multifunction on (i.e. or ).
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The longest primer extension performed by a ribozyme polymerase was 20 bases.Hani S. Zaher and Peter J. Unrau, Selection of an improved RNA polymerase ribozyme with superior extension and fidelity. RNA (2007), 13:1017-1026 In 2016, researchers reported the use of in vitro evolution to improve dramatically the activity and generality of an RNA polymerase ribozyme by selecting variants that can synthesize functional RNA molecules from an RNA template. Each RNA polymerase ribozyme was engineered to remain linked to its new, synthesized RNA strand, this allowed the team to isolate successful polymerases.
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A cylindric section in which the intersecting plane intersects and is perpendicular to all the elements of the cylinder is called a '. If a right section of a cylinder is a circle then the cylinder is a circular cylinder. In more generality, if a right section of a cylinder is a conic section (parabola, ellipse, hyperbola) then the solid cylinder is said to be parabolic, elliptic and hyperbolic respectively. Cylindric sections of a right circular cylinder For a right circular cylinder, there are several ways in which planes can meet a cylinder.
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For example, an email client may be known to handle messages with a simple structure without failure but not the full generality allowed by the standards. Transshipment can then be used to protect the mail client from attackers who can exploit weaknesses in its ability to handle the general case. The transshipment process extracts the business information in the email messages and creates a new message that conveys the same information but using simple structures. So the mail client is protected without knowing details of any weaknesses in its implementation.
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We have to prove that this leads to a contradiction. By Zorn's lemma, every linearly independent set is contained in a maximal linearly independent set . This maximality implies that spans and is therefore a basis (the maximality implies that every element of is linearly dependent from the elements of , and therefore is a linear combination of elements of ). As the cardinality of is greater than or equal to the cardinality of , one may replace with , that is, one may suppose, without loss of generality, that is a basis.
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In unquestioning idolization of the existing state of affairs, conservatives stress the preservation of order over all else. They fear the unknown – violent upheaval, tyranny, and death are often correlated with Enlightenment calls for liberty; the French Revolution of 1789 only further justified this claim. Conservatives find their roots, as a generality, having emerged from Anti-Enlightenment thinkers such as Rousseau and Burke. In recalling Rousseau's “stand against rationalism on the basis of the ‘reason of feeling’,” conservatives rejected the Enlightenments attempts to explain with the explicit intention of perceiving.
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The Baraki pretend descent from the Arab invaders, but this is a conceit of their conversion to Islam. They are a fine, tall and active people, with fairer complexions than the generality of Pashtuns, and are held in consideration as a respectable people. They have no place in the Pashtun genealogies by that name, being generally reckoned along with the Tajik population. Yet it is not altogether improbable that the present ruling tribe (Barakzai) of the Durrani/Abdali in Afghanistan and Pakistan is originally derived from the Baraki.
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Nevertheless, it was able to catalyse only a polymerization of a chain having the size of about 14 nucleotides, even though it was 200 nucleotides long. The most up-to-date version of this polymerase was shown in 2013. While it has an ability to catalyse polymerization of longer sequences, even of its own length, it cannot replicate itself due to a lack of sequence generality and its inability to transverse secondary structures of long RNA templates. However, it was recently shown that those limitations could in principle be overcome by the assembly of active polymerase ribozymes from several short RNA strands.
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First, if planar regions separated by the graph are not triangulated, i.e. do not have exactly three edges in their boundaries, we can add edges without introducing new vertices in order to make every region triangular, including the unbounded outer region. If this triangulated graph is colorable using four colors or fewer, so is the original graph since the same coloring is valid if edges are removed. So it suffices to prove the four color theorem for triangulated graphs to prove it for all planar graphs, and without loss of generality we assume the graph is triangulated.
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That dispersion of power, though seen by many, then and later, as a major weakness of the Republic, was actually the foundation stone of De Witt's political system, that he called de Ware Vrijheid (the "True Freedom"). We have already seen that De Witt primarily defended Oldenbarnevelt's and Grotius' claim to supremacy of (Holland's) provincial sovereignty over the sovereignty of the Generality under this moniker. But the doctrine went further. "True Freedom" implied the rejection of an "eminent head", not only of the federal state (where it would have conflicted with provincial sovereignty), but also of the provincial political system.
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The Union of Utrecht had guaranteed freedom of conscience,Israel (1995), p. 500 but this did not imply freedom of worship. Except for the Dutch Reformed Church, public worship by other denominations was usually restricted with more or less severity, and membership of the privileged church was supposed to be a prerequisite for holding public office (though this rule was often honored in the breach, even as far as Catholic office holders in the Generality Lands were concerned). This policy of supremacy of the Public Church was, however, never enforced consistently, either in the different parts of the country, or over time.
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In Holland, the city of Amsterdam was by far the largest contributor (though this was different from Habsburg times, when Delft made the relatively largest contribution), which explained the influence that city wielded, even at the national level. This system remained in place throughout the life of the Republic. Simon van Slingelandt made an attempt in 1716 to reform it by giving more power to the center. He convened the Groote Vergadering (a kind of constitutional convention) in that year, prompted by the fact that the Generality faced a liquidity crisis in 1715, when most provinces fell into arrears on their contributions.
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Austin: University of Texas at Austin, 1983. The advantage of communicating finite state machines is that they make it possible to decide many properties in communication protocols, beyond the level of just detecting such properties. This advantage rules out the need for human assistance or restriction in generality. Communicating finite state machines can be more powerful than finite state machines in situations where the propagation delay is not negligible (so that several messages can be in transit at one time) and in situations where it is natural to describe the protocol parties and the communication medium as separate entities.
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This allowed the fire to spread. He was convicted under the Criminal Damage Act 1971 for recklessly causing damage by omission. Lord Diplock said: :...I see no rational ground for excluding from conduct capable of giving rise to criminal liability, conduct which consists of failing to take measures that lie within one's power to counteract a danger that one has oneself created, if at the time of such conduct one's state of mind is such as constitutes a necessary ingredient of the offence. But although this may apply to the generality of offences, "constructive manslaughter" is different.
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In the Arrhenius theory, acids are defined as substances that dissociate in aqueous solution to give H+ (hydrogen ions), while bases are defined as substances that dissociate in aqueous solution to give OH− (hydroxide ions). In 1923 physical chemists Johannes Nicolaus Brønsted in Denmark and Thomas Martin Lowry in England both independently proposed the theory that carries their names. In the Brønsted–Lowry theory acids and bases are defined by the way they react with each other, which allows for greater generality. The definition is expressed in terms of an equilibrium expression : acid + base ⇌ conjugate base + conjugate acid.
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In 1987 Nuttin published his second study, describing experiments done in 1984 and 1985 with the help of Hilde Sas. Because of the far-reaching implications of the name-letter effect for psychological theories, Nuttin found it wise to first test the effect's generality and robustness, before setting off on a research program aimed at understanding the underlying affective and cognitive processes at work. He wondered whether the effect would be found in all cultural and linguistic communities, or whether the first study revealed an effect due to some unknown idiosyncratic aspect of the Dutch language in Belgium.
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The covering lemma can be used as intermediate step in the proof of the following basic form of the Vitali covering theorem. Actually, a little more is needed, namely the precised form of the covering lemma obtained in the "proof of the infinite version". :Theorem. For every subset E of Rd and every Vitali cover of E by a collection F of closed balls, there exists a disjoint subcollection G which covers E up to a Lebesgue-negligible set. Without loss of generality, one can assume that all balls in F are nondegenerate and have radius ≤ 1\.
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Although Dr Doddridge's congregation ‘highly respected Mr Clark, and thought themselves greatly obliged to him for his services during their pastor’s absence, he was not sufficiently popular and Calvinistical fully to satisfy the generality of them, so as to be chosen assistant to the Doctor’s successor in the ministerial part of his office.’Brief memoirs of the Rev Mr Samuel Clark', Monthly Repository, vol.I (London, 1806), 617-22. As a consequence, Clark moved to Daventry and continued as assistant tutor at the new academy, where he preached once a month.John Reynall Wreford, Sketch of Presbyterian nonconformity in Birmingham (Birmingham, 1832), p.37.
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Many of the English soldiers who fought during the siege would become prominent during the English Civil Wars. These were Thomas Fairfax, Jacob Astley, Philip Skippon, Thomas Glemham, George Monck as well as Henry Hexham, the historian of the Dutch wars. Fairfax, Skippon, and Monck, particularly, were Vere's pupils in the art of war.:s:Vere, Horace (DNB00) Although its population would remain predominantly Catholic, 's-Hertogenbosch would stay firmly in the hands of the Republic as part of the Generality Lands until French revolutionary forces captured it in 1794; only then would the Batavian Republic grant equality to Catholics.
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In waters <30 m deep it is not unreasonable to expect to collect the 170 SP images indicated in Figure 6 and produce a rough benthic classification map in a single field day. The categories may be based on sediment texture, overburden, specific detritus, biota, etc. Sampling effort can then be allocated to focus on the variability of communities among the gross habitat differences by using grabs as habitat replicates with varying lag. This type of approach produces a broader understanding of the system and permits more informed decisions by increasing the generality of the grab sample data.
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Also, one may consider classical groups over a unital associative algebra R over F; where R = H (an algebra over reals) represents an important case. For the sake of generality the article will refer to groups over R, where R may be the ground field F itself. Considering their abstract group theory, many linear groups have a "special" subgroup, usually consisting of the elements of determinant 1 over the ground field, and most of them have associated "projective" quotients, which are the quotients by the center of the group. For orthogonal groups in characteristic 2 "S" has a different meaning.
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63 But the verdict had constitutional consequences also. It recognizes the Union as the "injured party" in the trial and puts down the coalition of the eight "Arminian" cities that Oldenbarnevelt led, as a "rival faction" aimed at undermining the United Netherlands. Consequently, it derogates from all legitimacy Oldenbarnevelt's actions might have had and "construes" the "Generality" of all Provinces in the States General as the sole highest power (sovereign) legitimately exercising political power, and no longer the States of the several provinces. By acting as if this new constitutional construction was the positive law of the land, the constitution was materially changed.
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He defines a 'norm' as 'the meaning of an act of will'. Thus, for Kelsen a norm does not necessarily have any element of generality—hence not all norms are rules. Indeed, as the meaning of an act of will, a norm is not intrinsically rational; departing from Kant both back toward David Hume as well as in the direction of contemporary philosophical positivism, Kelsen denies the existence of practical reason. Legal science, as Kelsen would like it to be, has to describe a legal norm without either evaluating it or adopting it as an evaluation.
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Because it couples together the solution for both water levels at nodes and flow in conduits it can be applied to any general network layout, even those containing multiple downstream diversions and loops. It is the method of choice for systems subjected to significant backwater effects due to downstream flow restrictions and with flow regulation via weirs and orifices. This generality comes at a price of having to use much smaller time steps, on the order of a minute or less (SWMM can automatically reduce the user-defined maximum time step as needed to maintain numerical stability).
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Bohm maintained that relativity and quantum theories are in basic contradiction in these essential respects, and that a new concept of order should begin with that toward which both theories point: undivided wholeness. This should not be taken to mean that he advocated such powerful theories be discarded. He argued that each was relevant in a certain context—i.e., a set of interrelated conditions within the explicate order—rather than having unlimited scope, and that apparent contradictions stem from attempts to overgeneralize by superposing the theories on one another, implying greater generality or broader relevance than is ultimately warranted.
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In spite of the generality of Promise Theory, it was originally proposed by Burgess as a way of modelling the computer management software CFEngine and its autonomous behaviour. Existing theories based on obligation were unsuitable. CFEngine uses a model of autonomy both as a way of avoiding distributed inconsistency in policy and as a security principle against external attack: no agent can be forced to receive information or instructions from another agent, thus all cooperation is voluntary. For many users of the software, this property has been instrumental in both keeping their systems safe and adapting to the local requirements.
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Different ways of tracking and analyzing gestures exist, and some basic layout is given is in the diagram above. For example, volumetric models convey the necessary information required for an elaborate analysis, however they prove to be very intensive in terms of computational power and require further technological developments in order to be implemented for real-time analysis. On the other hand, appearance- based models are easier to process but usually lack the generality required for Human-Computer Interaction. Depending on the type of the input data, the approach for interpreting a gesture could be done in different ways.
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K-theory now appeared to be a homology theory for rings and a cohomology theory for varieties. However, many of its basic theorems carried the hypothesis that the ring or variety in question was regular. One of the basic expected relations was a long exact sequence (called the "localization sequence") relating the K-theory of a variety X and an open subset U. Quillen was unable to prove the existence of the localization sequence in full generality. He was, however, able to prove its existence for a related theory called G-theory (or sometimes K′-theory).
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As 's-Hertogenbosch was the main capital of the Meierij, the Protestants considered the bailiwick as their possession. However the Spanish kings refused to give it up, and thus one of the most difficult times started, the so-called "retorsie tijd" in which the population suffered from both Spanish and Dutch oppression. Finally in 1648 the whole bailiwick was given to the Dutch republic at the Peace of Westphalia. From now the former Brabant and Limburg areas were placed under the reign of the generality as well as Zeelandic Flanders which had been taken from Flanders.
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Illusie's construction of the cotangent complex generalizes that of Michel André and Daniel Quillen to morphisms of ringed topoi. The generality of the framework makes it possible to apply the formalism to various first- order deformation problems: schemes, morphisms of schemes, group schemes and torsors under group schemes. Results concerning commutative group schemes in particular were the key tool in Grothendieck's proof of his existence and structure theorem for infinitesimal deformations of Barsotti–Tate groups, an ingredient in Gerd Faltings' proof of the Mordell conjecture. In Chapter VIII of the second volume of the thesis, Illusie introduces and studies derived de Rham complexes.
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A book-length cricism of Virilio's work to 2004 was written by Steve Redhead.Steve Redhead (2004) Paul Virilio: Theorist for an Accelerated Culture, Edinburgh University Press He observed: :His scattergun writing style is not always easy to follow, often provoking disorientation and dislocation at the very least. Insights, personal memories, detailed histories, major theoretical leaps and banalities sit side by side. He also notes that Virilio does not pass the grade in academic studies: :Reading Virilio thoroughly does leave the reader with the feeling of many dislocated, undeveloped ideas swirling around often at the level of great generality.
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M. Kapovich and J. J. Millson (2002), Universality theorems for configguration spaces of planar linkages Topology, Pergamon Press.. This theorem has been popularized by describing it as saying, "One can design a linkage which will sign your name!"J. Malkevich, Feature Column, American Mathematical Society. Kempe recognized that his results demonstrate the existence of a drawing linkage but it would not be practical. He states > It is hardly necessary to add, that this method would not be practically > useful on account of the complexity of the linkwork employed, a necessary > consequence of the perfect generality of the demonstration.
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Another source of complexity is the generality of Kempe's application to all algebraic curves. By focusing on parameterized algebraic curves, dual quaternion algebra can be used to factor the motion polynomial and obtain a drawing linkage.G.Hegedus, Z. Li, J. Schicho, H. P. Schrocker (2015), From the Fundamental Theorem of Algebra to Kempe’s Universality Theorem This has been extended to provide movement of the end-effector, but again for parameterized curves. M. Gallet, C. Koutschan, Z. Li, G. Regensburger, J. Schicho, and N. Villamiza (2017), Planar Linkages Following a Prescribed Motion, Mathematics of Computation, 86(303), pages 473-506.
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Many historians would deny that the political upheavals in the Dutch Republic during the years 1785, 1786 and 1787 amounted to a civil war. It is true that compared to the French revolution the Patriot revolution was singularly bloodless and that widespread military maneuvering remained the exception. But there actually were military actions by regular forces on both sides, aimed at deciding the issue by military means, and blood was spilled in battle. To understand how this came about, it is important first to understand the way the forces on both sides were distributed in the seven provinces and the Generality Lands.
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Asín, Saint John of the Cross and Islam (1933; 1981) at 24-27 [in section III]. For further research which develops the work of Miguel Asín Palacios here, see Luce López-Baralt's book, San Juan de la Cruz y el Islam (1985, 1990). While not disputing these similarities as discussed by Asín, a subsequent scholar, José Nieto, remained critical of any implied linkage between the earlier teachings of the Sadili sufis and San Juan de la Cruz. To the contrary, the suggestion is that this 'shared mystical doctrine' functions at such a level of generality that it will arise spontaneously.
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The theory of data integration forms a subset of database theory and formalizes the underlying concepts of the problem in first-order logic. Applying the theories gives indications as to the feasibility and difficulty of data integration. While its definitions may appear abstract, they have sufficient generality to accommodate all manner of integration systems, including those that include nested relational / XML databases and those that treat databases as programs. Connections to particular databases systems such as Oracle or DB2 are provided by implementation-level technologies such as JDBC and are not studied at the theoretical level.
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Clearly, this means that n must have the value zero, and so a contradiction arises if one can show that in fact n is not zero. In many transcendence proofs, proving that n ≠ 0 is very difficult, and hence a lot of work has been done to develop methods that can be used to prove the non-vanishing of certain expressions. The sheer generality of the problem is what makes it difficult to prove general results or come up with general methods for attacking it. The number n that arises may involve integrals, limits, polynomials, other functions, and determinants of matrices.
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The U-resultant as defined by Macaulay requires the number of homogeneous polynomials in the system of equations to be n-1, where n is the number of indeterminates. In 1981, Daniel Lazard extended the notion to the case where the number of polynomials may differ from n-1, and the resulting computation can be performed via a specialized Gaussian elimination procedure followed by symbolic determinant computation. Let P_1, \ldots, P_k be homogeneous polynomials in x_1, \ldots, x_n, of degrees d_1, \ldots, d_k, over a field . Without loss of generality, one may suppose that d_1\ge d_2\ge \cdots \ge d_k.
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The algebraic description of Riemannian symmetric spaces enabled Élie Cartan to obtain a complete classification of them in 1926. For a given Riemannian symmetric space M let (G,K,σ,g) be the algebraic data associated to it. To classify the possible isometry classes of M, first note that the universal cover of a Riemannian symmetric space is again Riemannian symmetric, and the covering map is described by dividing the connected isometry group G of the covering by a subgroup of its center. Therefore, we may suppose without loss of generality that M is simply connected.
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Overfitting is addressed by estimating parameters on some of the experimental periods or experimental subjects and forecasting behavior in the remaining sample (if models are overfitting, these out-of-sample validation forecasts will be much less accurate than in-sample fits, which they generally are not). Generality in games is addressed by replacing fixed parameters with "self-tuning" functions of experience, allowing pseudo-parameters to change over the course of a game and to also vary systematically across games. Modern experimental economists have done much notable work recently. Roberto Weber has raised issues of learning without feedback.
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An example of a primitive recursive programming language is one that contains basic arithmetic operators (e.g. + and −, or ADD and SUBTRACT), conditionals and comparison (IF-THEN, EQUALS, LESS-THAN), and bounded loops, such as the basic for loop, where there is a known or calculable upper bound to all loops (FOR i FROM 1 TO n, with neither i nor n modifiable by the loop body). No control structures of greater generality, such as while loops or IF-THEN plus GOTO, are admitted in a primitive recursive language. Douglas Hofstadter's BlooP in Gödel, Escher, Bach is such a language.
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For applications to number theory, van der Waerden and Weil formulated algebraic geometry over any field, not necessarily algebraically closed. Weil was the first to define an abstract variety (not embedded in projective space), by gluing affine varieties along open subsets, on the model of manifolds in topology. He needed this generality for his construction of the Jacobian variety of a curve over any field. (Later, Jacobians were shown to be projective varieties by Weil, Chow and Matsusaka.) The algebraic geometers of the Italian school had often used the somewhat foggy concept of the generic point of an algebraic variety.
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S-algol was designed to differ from prior members of the ALGOL family by being designed according to semantic principles to provide power through simplicity, and simplicity through greater generality. (See Orthogonal.) Morrison describes three semantic principles that guided the design of S-algol: # Principle of correspondence – The rules governing names should be uniform and apply everywhere. This mostly applies to correspondence between declarations and procedure parameters, including consideration of all parameter passing modes. This principle was examined by R. D. Tennent in conjunction with Pascal, and has its roots in work by Peter Landin and Christopher Strachey.
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The first truly proprietary communities developed in the nineteenth century in the form of forerunners of the modern customer-service-oriented hotel. The twentieth century saw a veritable explosion of proprietary community types, and of ever-increasing generality and scale (for example, Disney World, The Venetian in Las Vegas, and Masdar City in the UAE). However, to date these proprietary communities have only existed within the framework of a larger nation-state—not as fully generalized independent sovereign jurisdictions. Since the 1960s, there have been various attempts to create such sovereign proprietary communities—unsuccessfully to date.
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It can refer to philosophical ethics or moral philosophy—a project that attempts to use reason to answer various kinds of ethical questions. As the English moral philosopher Bernard Williams writes, attempting to explain moral philosophy: "What makes an inquiry a philosophical one is reflective generality and a style of argument that claims to be rationally persuasive." Williams describes the content of this area of inquiry as addressing the very broad question, "how one should live". Ethics can also refer to a common human ability to think about ethical problems that is not particular to philosophy.
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The abstraction necessary for understandable models competes with accuracy. While generality, simplicity, and understandability are important to the application of models in human factors practice, many valuable human performance models are inaccessible to those without graduate, or postdoctoral training. For example, while Fitts's law is straightforward for even undergraduates, the lens model requires an intimate understanding of multiple regression, and construction of an ACT-R type model requires extensive programming skills and years of experience. While the successes of complex models are considerable, a practitioner of HPM must be aware of the trade-offs between accuracy and usability.
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His early work includes the classic texts Mental Acts and Reference and Generality, the latter defending an essentially modern conception of reference against medieval theories of supposition. His Catholic perspective was integral to his philosophy. He was perhaps the founder of analytical Thomism (though the current of thought running through his and Elizabeth Anscombe's work to the present day was only ostensibly so named forty years later by John Haldane), the aim of which is to synthesise Thomistic and analytic approaches. Geach was a student and an early follower of Ludwig Wittgenstein whilst at the University of Cambridge.
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But in other ways the poem disrupts the generality of pastoral convention by insisting on local particularities. In place of "purling streams" there are the "rine" and "moory sink" found in local place names. Again, the Somerset Levels, undrained as yet, were subject to severe inundations from the sea, of which those of 1696 and 1703 fell during Diaper's lifetime. These too, dressed in suitably mock- heroic garb, find their place in the poem, ::As when of late enraged Neptune sware, ::Brent was his own Part of his lawful Share; ::He said, and held his Trident o’er the Plain.
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In the Eighty Years' War, Zeeland was on the side of the Union of Utrecht, and became one of the United Provinces. The area now called ' (or Zeelandic Flanders) was not part of Zeeland, but a part of the county of Flanders (still under Habsburg control) that was conquered by the United Provinces, hence called ' (see: Generality Lands). After the French occupation (see ' Bouches- de-l'Escaut) and the formation of the United Kingdom of the Netherlands in 1815, the present province Zeeland was formed. During World War II, Zeeland was occupied by Nazi Germany between June 1940 and November 1944.
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Except for some formerly insular areas, the region now called Zeelandic Flanders was not part of the historical County of Zeeland, but a part of the County of Flanders initially ruled by the House of Habsburg. The region was front line in the Eighty Years' War and was conquered by the Dutch Republic in 1604. As such, it was the only part of Flanders, which took part in the insurgency, to become part of the new republic. Zeelandic Flanders was subsequently ruled directly by the Dutch States General (parliament) as one of the Generality Lands and called Flanders of the States (Staats-Vlaanderen).
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It would no doubt be better to say, in any case, that we are choosing not which process to say resulted in the belief, but instead how to describe the process, out of the many different levels of generality on which it can be accurately described. An objection in a similar line was formulated by Stephen Stich in The Fragmentation of Reason. Reliabilism usually considers that for generating justified beliefs a process needs to be reliable in a set of relevant possible scenarios. However, according to Stich, these scenarios are chosen in a culturally biased manner.
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This property takes two different forms respectively for functions of one and several complex variables: for the n > 1 case, to express the chain rule in its full generality it is necessary to consider two domains \Omega'\subseteq\Complex^m and \Omega\subseteq\Complex^p and two maps g: \Omega'\to\Omega and f:\Omega \to \Omega having natural smoothness requirements.See and also : Gunning considers the general case of C^1 functions but only for p = 1\. References and , as already pointed out, consider only holomorphic maps with p = 1: however, the resulting formulas are formally very similar.
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Using Rogers' characterization of acceptable programming systems, Rice's Theorem may essentially be generalized from Turing machines to most computer programming languages: there exists no automatic method that decides with generality non-trivial questions on the behavior of computer programs. As an example, consider the following variant of the halting problem. Let P be the following property of partial functions F of one argument: P(F) means that F is defined for the argument '1'. It is obviously non-trivial, since there are partial functions that are defined at 1, and others that are undefined at 1.
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Communications of ACM, 1984 In this framework the input is a number of samples drawn from a distribution that belongs to a specific class of distributions. The goal is to find an efficient algorithm that, based on these samples, determines with high probability the distribution from which the samples have been drawn. Because of its generality, this framework has been used in a large variety of different fields like machine learning, approximation algorithms, applied probability and statistics. This article explains the basic definitions, tools and results in this framework from the theory of computation point of view.
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For example, if the particular deal turned out well, the Principal could adopt the transaction --if it turned out badly, the Principal could disavow it. If not for imputation, there would be a perverse incentive to conduct business through Agents rather than personally. Consequently, the Principal cannot exploit ignorance to advantage by instructing the Agent to withhold key information, or by appointing an Agent known to be secretive. This rule in favour of imputation relates to the generality of the duties an Agent owes to a Principal, in particular the Agent's duty to communicate material facts to the Principal.
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Each of the towns and cities in the seven provinces had its own differences and peculiarities. However, as a general rule, the government of the city of Amsterdam was fairly standard. Also, as noted above, in the 17th and 18th century, the wealth that Amsterdam generated from commerce made it the most powerful city in the province of Holland, accounting for half of Holland's revenues and taxes and through that a full quarter of the Generality's. Because of this economic weight, it was the most influential voice in the councils of the province and the Generality.
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Rorty views Proust, Nietzsche, and Heidegger each as different types of ironists. In Remembrance of Things Past, Proust almost perfectly exemplifies ironism by constantly recontextualizing and redefining the characters he meets along the way, thus preventing any particular final vocabulary from becoming especially salient. Nietzsche is an ironist because he believes all truths to be contingent, but he tends to slip back into metaphysics, especially when discussing his superman. Heidegger is an ironist because he has mostly rejected metaphysics, but his discussion of elementary words forces him to propose a generality that cannot be considered contingent or ironic.
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He was successively appointed an alternate member of the Third Estate of the generality of Paris and lieutenant of mayor in public institutions. In 1790 he published as such a Compte rendu concernant l’administration de Paris. In 1791 he was elected a member of the board of the Seine, and expelled from the position under the Reign of Terror for his moderate views, he was imprisoned for a time as a suspect. He reappeared in public life in 1800 only, when , the prefect of the Seine, appointed him head of the office of the civil hospitals of Paris.
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He contended that helicoidal striation is a general feature of muscles and that muscular conduction takes place along this helicoidal path, even though the evidence for this generality was against him, yet his cinematographic records supported his interpretation for arachnids and other arthropods. Between 1922 and 1934 Oscar Tiegs was almost entirely concerned with the physiology of nerve and muscle, apparently influenced by Brailsford Robertson. In 1925 he published the results of experiments regarding the importance of creatine. This line of research was inspired by the lactic acid hypotheses of muscular action at the time and before phosphagen was discovered.
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These include exploratory factor analysis, principal components analysis (PCA), and confirmatory factor analysis. Different factor-extraction methods produce highly consistent results, although PCA has sometimes been found to produce inflated estimates of the influence of g on test scores.Jensen 1998, 73 There is a broad contemporary consensus that cognitive variance between people can be conceptualized at three hierarchical levels, distinguished by their degree of generality. At the lowest, least general level there are many narrow first- order factors; at a higher level, there are a relatively small number – somewhere between five and ten – of broad (i.e.
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Assume without loss of generality that the support of the distribution of interest, F, is contained in [0,1]. Given a confidence envelope for F, it can be shown that the CDF within the envelope that minimizes the variance begins on the lower envelope, has a jump discontinuity to the upper envelope, and then continues along the upper envelope. Further, it can be shown that this variance-minimizing CDF, F', must satisfy the constraint that the jump discontinuity occurs at E[F']. The variance maximizing CDF begins on the upper envelope, horizontally transitions to the lower envelope, then continues along the lower envelope.
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The Life of W. S. Gilbert . The Gilbert and Sullivan Archive The Times wrote: "The chief care of Mr. Gilbert has been to make his dialogue as perfect a specimen as possible of smooth verse, and to stud it profusely with elaborate puns of unquestionable originality. ... Mr. Gilbert shows a power of detecting phonetic affinities ... in which perhaps he excels all his contemporaries. ... [S]eldom have mere verbal pleasantries provoked such frequent laughter and applause as those in La Vivandière ... an extravaganza more elegant in its tone than the generality of burlesques" The new piece ran for a total of 120 performances.
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Let X be a metric space, S a subset of X, R a complete metric space, and f: S \rightarrow R a continuous function. When can f be extended to a continuous function on all of X? If S is closed in X, the answer is given by the Tietze extension theorem: always. So it is necessary and sufficient to extend f to the closure of S in X: that is, we may assume without loss of generality that S is dense in X, and this has the further pleasant consequence that if the extension exists, it is unique.
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Dominican law has given a commercial nature to all acts, operations or activities carried out by business organizations. Therefore, in considering the applicable law in the generality of cases involving corporations in the Dominican Republic first priority is given the basic principles contained in the Dominican Commercial Code enacted on the July 4, 1882. Dominican Commercial Law, whose direct and main source is the Commercial Code, has as subsidiary sources, the Civil Code and the trade customs. Many consider that Article 18 of the Dominican Commercial Code is the text that legitimates the Civil Law as an important source of the Commercial Law.
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In this role he led the Cambridge efforts to develop the Titan Supervisor (a multi-programming operating system) and CPL (Combined Programming Language). The Titan Supervisor led in due course to the Cambridge Multiple-Access System which provided a pioneering time-sharing service to a large user community in Cambridge and was also later employed in the Cambridge-based Computer Aided Design Centre. The CPL project broke new ground in language design and application generality, and the resulting defining paper was written by the original development team. CPL was notable for leading to BCPL and hence B and then C programming language.
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An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities. introducing symbolic logic and the principles of what is now known as Boolean logic. In 1879, Gottlob Frege published Begriffsschrift, which inaugurated modern logic with the invention of quantifier notation, reconciling the Aristotelian and Stoic logics in a broader system, and solving such problems for which Aristotelian logic was impotent, such as the problem of multiple generality. From 1910 to 1913, Alfred North Whitehead and Bertrand Russell published Principia Mathematica on the foundations of mathematics, attempting to derive mathematical truths from axioms and inference rules in symbolic logic.
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As Consultant Editor and subsequently as Editor-in-Chief of Admap, he consolidated that publication's reputation for intellectual stringency and authority, which sets it aside from the generality of newsy, even gossipy, advertising periodicals. In 1983, he joined Mike Waterson in setting up a modest venture to launch the quarterly Food & Drink Forecast. This developed rapidly, and had grown by 1998 into Information Sciences Ltd and become one of the world's largest private sector suppliers of economic information through its operating arm NTC Research Ltd, and one of the world's major publisher of advertising and media knowledge via Admap, many other trade journals and books, and the World Advertising Research Center.
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Other explanations include the fact that Microsoft Excel was being offered as part of the Office bundle at marginal rates that were tiny in comparison, as well as several mis-steps during introduction, like the lack of a macro language or undo. Joel Spolsky blames it on the design itself, claiming it was too perfectly aimed at a specific market and lacked the generality that Excel featured.Joel Spolsky, "The best software writing", Apress, 2005, p. 25 Although Improv disappeared in the 1990s, the program is fondly recalled in the industryMichael O'Malley, "Moose's Greatest Products of All Time : Lotus Improv" , 4 February 2002 and continues to be mentioned in books on Excel.
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They even modeled the muscle response of the pilot, which led eventually to cybernetics. The unmanned V1's were particularly easy to model, and on a good day, American guns fitted with Wiener filters would shoot down 99 out of 100 V1's as they entered Britain from the English channel, on their way to London. What emerged was a mathematical theory of great generality--a theory for predicting the future as best one can on the basis of incomplete information about the past. It was a statistical theory that included applications that did not, strictly speaking, predict the future, but only tried to remove noise.
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De Witt now felt strengthened enough to start demanding recall of the Dutch plenipotentiaries in England if they could make no progress with the proposed English treaty. Downing, however, calculated that Friesland, and the land provinces, could be counted upon to keep the Dutch position weak, as he thought they would refuse to pay their share of the cost of a war with England. This was in itself not improbable, if only because the land provinces felt threatened by Bernhard von Galen, the Prince-Bishop of Münster, who made territorial demands on parts of Overijssel in the early 1660s. They, not unreasonably, demanded military protection against this aggressor from the Generality.
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The problem with using action-values is that they may need highly precise estimates of the competing action values that can be hard to obtain when the returns are noisy, though this problem is mitigated to some extent by temporal difference methods. Using the so-called compatible function approximation method compromises generality and efficiency. Another problem specific to TD comes from their reliance on the recursive Bellman equation. Most TD methods have a so-called \lambda parameter (0\le \lambda\le 1) that can continuously interpolate between Monte Carlo methods that do not rely on the Bellman equations and the basic TD methods that rely entirely on the Bellman equations.
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Depending on the setting, the process has several equivalent definitions as well as definitions of varying generality owing to its many applications and characterizations. The Poisson point process can be defined, studied and used in one dimension, for example, on the real line, where it can be interpreted as a counting process or part of a queueing model; in higher dimensions such as the plane where it plays a role in stochastic geometry and spatial statistics;A. Baddeley. A crash course in stochastic geometry. Stochastic Geometry: Likelihood and Computation Eds OE Barndorff-Nielsen, WS Kendall, HNN van Lieshout (London: Chapman and Hall), pages 1–35, 1999.
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Vegetation myths have structural resemblances to certain creation myths in which parts of a primordial being's body generate aspects of the cosmos, such as the Norse myth of Ymir.Stookey, Thematic Guide to World Mythology, p. 100. In mythography of the 19th and early 20th century, as for example in The Golden Bough of J.G. Frazer, the figure is related to the "corn spirit", "corn" in this sense meaning grain in general. That triviality is giving the concept its tendency to turn into a meaningless generality, as Walter Friedrich Otto remarked of trying to use a "name as futile and yet pretentious as 'Vegetation deity'".
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When an enumeration is used in an ordered list context, we impose some sort of ordering structure requirement on the index set. While we can make the requirements on the ordering quite lax in order to allow for great generality, the most natural and common prerequisite is that the index set be well-ordered. According to this characterization, an ordered enumeration is defined to be a surjection (an onto relationship) with a well-ordered domain. This definition is natural in the sense that a given well-ordering on the index set provides a unique way to list the next element given a partial enumeration.
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The abandoned building was demolished in the 1950s, its site is now used by a ball playing cage. For the inauguration of the monument Frederick William III chose the 30 March 1821, the seventh anniversary of the conquest of the Montmartre in the Battle of Paris.Michael Nungesser, Das Denkmal auf dem Kreuzberg von Karl Friedrich Schinkel, see references for bibliographical details, p. 41\. . The inauguration was attended by the royal family, the Prussian generality, the senior pastors of all Protestant congregations of Berlin, and as guests by Grand Duke Nicholas of Russia and his wife Alexandra Feodorovna (Charlotte of Prussia), as well as by thousands of other spectators.
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The MRI was first noticed in a non- astrophysical context by Evgeny Velikhov in 1959 when considering the stability of Couette flow of an ideal hydromagnetic fluid. His result was later generalized by S. Chandrasekhar in 1960. This mechanism was proposed by Acheson & Hide (1973) to perhaps play a role in the context of the Earth's geodynamo problem. Although there was some follow-up work in later decades (Fricke, 1969; Acheson and Hide 1972; Acheson and Gibbons 1978), the generality and power of the instability were not fully appreciated until 1991, when Balbus & Hawley gave a relatively simple elucidation and physical explanation of this important process.
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Setting out to compose atonal music may seem complicated because of both the vagueness and generality of the term. Additionally George Perle explains that, "the 'free' atonality that preceded dodecaphony precludes by definition the possibility of self-consistent, generally applicable compositional procedures" . However, he provides one example as a way to compose atonal pieces, a pre-twelve-tone technique piece by Anton Webern, which rigorously avoids anything that suggests tonality, to choose pitches that do not imply tonality. In other words, reverse the rules of the common practice period so that what was not allowed is required and what was required is not allowed.
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When a new problem can be shown to follow the laws of one of these algebraic structures, all the work that has been done on that category in the past can be applied to the new problem. In full generality, algebraic structures may involve an arbitrary collection of operations, including operations that combine more than two elements (higher arity operations) and operations that take only one argument (unary operations). The examples used here are by no means a complete list, but they are meant to be a representative list and include the most common structures. Longer lists of algebraic structures may be found in the external links and within :Category:Algebraic structures.
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The confederates were, however, of divergent goals and interests. The magnate oligarchy wanted to remove Stanisław August and replace him with a Wettin ruler. The Generality declared the King's dethronement in 1770, just as Stanisław August contemplated the feasibility of abandoning Catherine and reaching an understanding with the Bar Confederation movement. The middle nobility fought for national independence, but under conservative assumptions of inviolability of their own privileged position as well as of that of the Catholic Church, which limited the appeal of the entire undertaking (the army of the nobility-dominated uprising was mostly non-noble and the cities sympathized with the King).
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Despite its neutralist preferences the Republic had been dragged into the Alliance of Hanover of 1725. Though this alliance was formally intended to counter the alliance between Austria and Spain, the Republic hoped it would be a vehicle to manage the king of Prussia, who was trying to get his hands on the Duchy of Jülich that abutted Dutch territory, and threatened to engulf Dutch Generality Lands in Prussian territory.Israel, pp. 990-991 These are just examples of the intricate minuets European diplomats danced in this first third of the 18th century and in which Van Slingelandt tried his best to be the dance master.
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A federalist, he played a major role in gaining a provincial statute for Drenthe, previously only one of the Generality Lands. On 27 January 1796 he was elected deputy for Meppel in the first national Batavian assembly and appointed to the committee charged with writing a new constitution. He was president of the assembly from 6 to 20 February 1797 and re-elected as a deputy in August 1797. A unitarist coup d'État on 22 January 1798 ejected the Federalists from the assembly – De Vos van Steenwijk was imprisoned at Huis ten Bosch until 10 July, after another coup toppled the unitarists on 12 June.
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This process does not add any vertices to the subdivision (therefore, the size remains O(n)), and can be performed in O(n log n) time by plane sweep (it can also be performed in linear time, using polygon triangulation). Therefore, there is no loss of generality, if we restrict our data structure to the case of monotone subdivisions, as we do in this section. The weakness of the slab decomposition is that the vertical lines create additional segments in the decomposition, making it difficult to achieve O(n) storage space. Edelsbrunner, Guibas, and Stolfi discovered an optimal data structure that only uses the edges in a monotone subdivision.
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In mathematics, a group scheme is a type of algebro-geometric object equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field. This extra generality allows one to study richer infinitesimal structures, and this can help one to understand and answer questions of arithmetic significance. The category of group schemes is somewhat better behaved than that of group varieties, since all homomorphisms have kernels, and there is a well-behaved deformation theory.
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I, § 8. The Court explained that the right not to contribute money for the support of a religious establishment was "fundamentally unlike" whatever rights the plaintiffs may have under the Commerce Clause, and the comparison the plaintiffs attempted was "at such a high level of generality that almost any constitutional constraint on government power would 'specifically limit' a State's taxing and spending power for Flast purposes." The injury alleged in Flast was instead the specific extraction of money from the plaintiff to spend in aid of a religion, an injury that could be redressed by an injunction, in contrast to that alleged in this case.
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First local conversations are kept here and there by various actors in the course of their complementary activities. These will require the creation of ideal mutual obligations or transactions to stabilize the interdependencies between the actors involved in these negotiations and each bearing views and different values. These conversations and transactions they require are then translated into a discursive formation (a group of utterances) through an increase in generality (distancing) metacommunicationnal used to represent a plurality of voices and patterns like perspective and the will of one collective actor with its own identity. The discursive formation generated by metacommunicationnal distancing is then translated to give it an author, ie.
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Considering the rendering pipeline, the projection, the clipping, and the rasterization steps are handled differently by the following algorithms: ; Z-buffering: During rasterization the depth/Z value of each pixel (or sample in the case of anti-aliasing, but without loss of generality the term pixel is used) is checked against an existing depth value. If the current pixel is behind the pixel in the Z-buffer, the pixel is rejected, otherwise it is shaded, and its depth value replaces the one in the Z-buffer. Z-buffering supports dynamic scenes easily and is currently implemented efficiently in graphics hardware. This is the current standard.
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It was established when in 1957 Gérard de Berny left the city of Amiens his hôtel particulier, its surrounding buildings and his collection of art and Louis XV and Louis XVI furniture signed by François Foliot (le Jeune), Sené père and Pierre Roussel. He was a former senator for the Somme region. The hôtel is in the Louis XIII style in brick and stone, with a large main lodge and two pavilions behind it, built between 1633 and 1634 for the Treasurer of France for the generality of Picardy. In 1790 that office was suppressed and the hôtel sold off to become a private house.
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In contrast to the rules, laid out above, for calculating the geometrically defined stereoscopic depth rendition, the perceived depth involves factors — context, previous experience — that are individual and not specifiable with the same degree of generality. Chief among them is the distance at which the configuration appears to the viewer. This is by no means fixed: the subjective z is only vaguely related to the actual object distance, as is obvious in watching 3D film. Because apparent distance is the main source of judging object size (size or subjective constancy), observers' reports on the perceived depth/width ratio can deviate substantially from calculated values.
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Additionally, the chief of police can approve drone use for public safety or emergency situations. Critics such as the NYCLU argue that the generality of the term 'large scale events' allows for drones to be used in a broad range of applications, including the monitoring of protestors and activists. They also argue that although the drones themselves cannot perform facial recognition as per the policy, the footage collected from drones can still be used for such purposes. As with other video collected by the NYPD, drone footage is retained for a minimum of 30 days upwards to an indefinite period if needed for unspecified legal purposes.
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Sinusoidal plane-wave solutions are particular solutions to the electromagnetic wave equation. The general solution of the electromagnetic wave equation in homogeneous, linear, time-independent media can be written as a linear superposition of plane-waves of different frequencies and polarizations. The treatment in this article is classical but, because of the generality of Maxwell's equations for electrodynamics, the treatment can be converted into the quantum mechanical treatment with only a reinterpretation of classical quantities (aside from the quantum mechanical treatment needed for charge and current densities). The reinterpretation is based on the theories of Max Planck and the interpretations by Albert Einstein of those theories and of other experiments.
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In topology, a branch of mathematics, a first-countable space is a topological space satisfying the "first axiom of countability". Specifically, a space X is said to be first-countable if each point has a countable neighbourhood basis (local base). That is, for each point x in X there exists a sequence N1, N2, … of neighbourhoods of x such that for any neighbourhood N of x there exists an integer i with Ni contained in N. Since every neighborhood of any point contains an open neighborhood of that point the neighbourhood basis can be chosen without loss of generality to consist of open neighborhoods.
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Interest remains in Ni(II) precatalyst that are air and moisture stable, inexpensive to make, modular (in terms of compatibility with multiple ligand classes), and general (active in numerous reactions). The precatalysts listed above all contain phosphine ligands, limiting their generality for use in other reactions. Simultaneously, the Doyle group and a group at Pfizer speculated that use of N,N,N’,N’-tetramethylethylenediamine (TMEDA) as a dummy ligand would allow for in situ ligand exchange with the desired ligand for each particular reaction. The complex [(TMEDA)Ni(o-tolyl)Cl] had the desired properties, showing stability on the bench for at least 3 months.
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Otherwise it is permitted with the corresponding cost (0 being completely satisfactory). In WCSP, specific subclass of Valued CSP (VCSP), costs are combined with the specific operator \oplus defined as: \forall \alpha, \beta \in \langle 0,...,k \rangle, \alpha \oplus \beta = min(k,\alpha+\beta). The partial inverse of \oplus is \ominus defined by: if 0 \le \beta \le \alpha < k, \alpha \ominus \beta = \alpha - \beta and if 0 \le \beta , k \ominus \beta = k. Without any loss of generality, the existence of a nullary constraint c_\empty (a cost) as well as the presence of a unary constraint c_x for every variable x is assumed.
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Suppose we are given a PostBQP family of circuits to decide a language L. We assume without loss of generality (e.g. see the inessential properties of quantum computers) that all gates have transition matrices that are represented with real numbers, at the expense of adding one more qubit. Let denote the final quantum state of the circuit before the postselecting measurement is made. The overall goal of the proof is to construct a PP algorithm to decide L. More specifically it suffices to have L correctly compare the squared amplitude of in the states with to the squared amplitude of in the states with to determine which is bigger.
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The transverse field Ising model is a quantum version of the classical Ising model. It features a lattice with nearest neighbour interactions determined by the alignment or anti-alignment of spin projections along the z axis, as well as an external magnetic field perpendicular to the z axis (without loss of generality, along the x axis) which creates an energetic bias for one x-axis spin direction over the other. An important feature of this setup is that, in a quantum sense, the spin projection along the x axis and the spin projection along the z axis are not commuting observable quantities. That is, they cannot both be observed simultaneously.
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De Groot had been appointed Pensionary of his native city of Rotterdam in 1670. He now took up that function and represented his city in the States of Holland and the States-General. The latter body decided to use his expertise in diplomacy with the French court after the French armies under the personal command of king Louis XIV had made a whirlwind advance into Dutch territory, and captured the important city of Utrecht. It was felt that the defense of the Republic was about to collapse, and that the only way to avoid an unconditional surrender was to offer Louis the Generality Lands and a large war indemnity.
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As soon as those allegations and rumours reached Karol, he sharply reacted by declaring that he is not obliged to listen to anyone's orders and embarrass himself by performing such insane, purposeless and fruitless activities that would not benefit the Ottomans and the Poles, but the Russians instead. The Generality tried to appease him by sending additional money, jewelry and alcoholic beverages. On June 6, 1770 Radziwiłł returned to Presov, where he had a brief audience with Emperor Joseph II of Austria who was staying there for two days, however, the point of this audience and the topics discussed during his visit are unknown to modern historians and theologians.
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The mathematician Jerry P. King describes mathematics as an art, stating that "the keys to mathematics are beauty and elegance and not dullness and technicality", and that beauty is the motivating force for mathematical research. King cites the mathematician G. H. Hardy's 1940 essay A Mathematician's Apology. In it, Hardy discusses why he finds two theorems of classical times as first rate, namely Euclid's proof there are infinitely many prime numbers, and the proof that the square root of 2 is irrational. King evaluates this last against Hardy's criteria for mathematical elegance: "seriousness, depth, generality, unexpectedness, inevitability, and economy" (King's italics), and describes the proof as "aesthetically pleasing".
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Turian et al. (2003) point out that, "Any MT evaluation measure is less reliable on shorter translations", and show that increasing the amount of data improves the reliability of a metric. However, they add that "... reliability on shorter texts, as short as one sentence or even one phrase, is highly desirable because a reliable MT evaluation measure can greatly accelerate exploratory data analysis".Turian et al. (2003) Banerjee et al. (2005) highlight five attributes that a good automatic metric must possess; correlation, sensitivity, consistency, reliability and generality. Any good metric must correlate highly with human judgment, it must be consistent, giving similar results to the same MT system on similar text.
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A piecewise linear function over two dimensions (top) and the polygonal areas on which it is linear (bottom) In computational geometry, a polyhedral terrain in three-dimensional Euclidean space is a polyhedral surface that intersects every line parallel to some particular line in a connected set (i.e., a point or a line segment) or the empty set.Richard Cole, Micha Sharir, "Visibility problems for polyhedral terrains" 1989, Without loss of generality, we may assume that the line in question is the z-axis of the Cartesian coordinate system. Then a polyhedral terrain is the image of a piecewise-linear function in x and y variables.
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Microkernels trace their roots back to Danish computer pioneer Per Brinch Hansen and his tenure in Danish computer company Regnecentralen where he led software development efforts for the RC 4000 computer. In 1967, Regnecentralen was installing a RC 4000 prototype in a Polish fertilizer plant in Puławy. The computer used a small real-time operating system tailored for the needs of the plant. Brinch Hansen and his team became concerned with the lack of generality and reusability of the RC 4000 system. They feared that each installation would require a different operating system so they started to investigate novel and more general ways of creating software for the RC 4000.
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However, it was mostly concentrated in the hands of the rentier class, while the debt was serviced by mainly regressive taxes that weighed on the working population. Most importantly, these were taxes levied by the individual provinces, who serviced their own debt, and paid into the Generality coffers according to a repartition schedule last changed in 1616. Attempts to reform this structure during the 18th century were mainly fruitless. To ameliorate the situation the old Republic maintained a policy of severe austerity during the century, especially economizing on its defense outlays (which in large part explains why its military and political role declined so much).
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The modern approaches to algebraic geometry redefine and effectively extend the range of basic objects in various levels of generality to schemes, formal schemes, ind-schemes, algebraic spaces, algebraic stacks and so on. The need for this arises already from the useful ideas within theory of varieties, e.g. the formal functions of Zariski can be accommodated by introducing nilpotent elements in structure rings; considering spaces of loops and arcs, constructing quotients by group actions and developing formal grounds for natural intersection theory and deformation theory lead to some of the further extensions. Most remarkably, in late 1950s, algebraic varieties were subsumed into Alexander Grothendieck's concept of a scheme.
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Since Nevi'im as a whole is not covered in the liturgy, the melodies for certain rare cantillation notes which appear in the books of Nevi'im but not in the haftarot have been forgotten. For more on this, see Nevi'im. As a generality, although the Torah was chanted in a major key (ending in a minor key), the haftarah is chanted in a minor key (as is the blessing before the reading of the haftarah) and ends in a pentatonic mode (and the blessings following the haftarah reading are also pentatonic).Macy Nulman, "The Liturgical and Musical Development and Significance of the Haftarah", Journal of Jewish Music & Liturgy, vol.
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In twenty U.S. states, the term "village" refers to a specific form of incorporated municipal government, similar to a city but with less authority and geographic scope. However, this is a generality; in many states, there are villages that are an order of magnitude larger than the smallest cities in the state. The distinction is not necessarily based on population, but on the relative powers granted to the different types of municipalities and correspondingly, different obligations to provide specific services to residents. In some states such as New York and Michigan, a village is usually an incorporated municipality, within a single town or civil township.
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This point, missed by Hilbert, was first pointed out to him by Poincaré and later by Weyl in his 1927 comments on Hilbert's lecture: "For after all Hilbert, too, is not merely concerned with, say 0' or 0' ', but with any 0' ... ', with an arbitrarily concretely given numeral. One may here stress the "concretely given"; on the other hand, it is just as essential that the contentual arguments in proof theory be carried out in hypothetical generality, on any proof, on any numeral. ... It seems to me that Hilbert's proof theory shows Poincaré to have been completely right on this point."Weyl 1927, van Heijenoort p.
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Tellegen's theorem is extremely general; it is valid for any lumped network that contains any elements, linear or nonlinear, passive or active, time-varying or time-invariant. The generality is extended when W_{k} and F_{k} are linear operations on the set of potential differences and on the set of branch currents (respectively) since linear operations don't affect KVL and KCL. For instance, the linear operation may be the average or the Laplace transform. More generally, operators that preserve KVL are called Kirchhoff voltage operators, operators that preserve KCL are called Kirchhoff current operators, and operators that preserve both are simply called Kirchhoff operators.
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The post-war interest in several complex variables made it natural to pursue the idea of automorphic form in the cases where the forms are indeed complex-analytic. Much work was done, in particular by Ilya Piatetski-Shapiro, in the years around 1960, in creating such a theory. The theory of the Selberg trace formula, as applied by others, showed the considerable depth of the theory. Robert Langlands showed how (in generality, many particular cases being known) the Riemann–Roch theorem could be applied to the calculation of dimensions of automorphic forms; this is a kind of post hoc check on the validity of the notion.
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Johan de Witt, raadpensionaris of Holland 1653-1672 Most of the other provinces (except Friesland, whose government differed significantly) had their own pensionary. However, none of them had the ability to build up the power and influence of the Holland's given Holland's influence in the Generality. The office of Councillor Pensionary was a continuation of the office of Land's Advocate of Holland (landsadvocaat). That office shared many of the functions with the Councillor Pensionary, chairing meetings of the States of Holland, acting in committee for them, preparing business and agendas, acting a speaker for the nobility, and acting as their legal counselor and head of bureaucracy.
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The system was not immune to popular pressure, as events of the age showed, but it became tighter and more closed as time went on until the Republic fell. A son of family belonging to the regent class there opened up an equivalent of the Roman cursus honorum where he could show his talents and make the connections that would serve him and his city. As these same officials were appointed to provincial offices (e.g. delegate to the States of Holland, member of one of the admiralty boards) or offices under the Generality (ambassadors), the councils of local power perpetuated themselves into the regional and national levels.
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In 1878 Phillips wrote of an old woman who became convinced that "prayer is more efficacious than sacrifice" after her husband and her brother recovered from illness. On the other hand, Phillips reported that "the generality of our Lagos young men begin to think that polygamy is not opposed to the principles of Christianity". In the 1870s there were several outbreaks of smallpox. In July 1879, a Sango priest from out of town called on Phillips, and cynically described how he had accepted gifts to suppress the disease, which would not in fact happen until it had run its course and destroyed all the witches and charm-makers in the country.
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However, even the best systems often suffer from low ee's and a lack of generality. Certain pyrrolidine-derived enamines of aromatic ketones are amenable to asymmetrically hydrogenation with cationic rhodium(I) phosphonite systems, and I2 and acetic acid system with ee values usually above 90% and potentially as high as 99.9%. A similar system using iridium(I) and a very closely related phosphoramidite ligand is effective for the asymmetric hydrogenation of pyrrolidine-type enamines where the double bond was inside the ring: in other words, of dihydropyrroles. In both cases, the enantioselectivity dropped substantially when the ring size was increased from five to six.
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The field of compressive sensing is related to several topics in signal processing and computational mathematics, such as underdetermined linear-systems, group testing, heavy hitters, sparse coding, multiplexing, sparse sampling, and finite rate of innovation. Its broad scope and generality has enabled several innovative CS-enhanced approaches in signal processing and compression, solution of inverse problems, design of radiating systems, radar and through-the-wall imaging, and antenna characterization. Imaging techniques having a strong affinity with compressive sensing include coded aperture and computational photography. Conventional CS reconstruction uses sparse signals (usually sampled at a rate less than the Nyquist sampling rate) for reconstruction through constrained l_{1} minimization.
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A glittering generality has two qualities: it is vague and it has positive connotations. Words and phrases such as "common good", "reform", "courage", "democracy", "freedom", "hope", "patriotism", "strength", are terms with which people all over the world have powerful associations, and they may have trouble disagreeing with them. However, these words are highly abstract and ambiguous, and meaningful differences exist regarding what they actually mean or should mean in the real world. George Orwell described such words at length in his essay "Politics and the English Language" > The words democracy, socialism, freedom, patriotic, realistic, justice have > each of them several different meanings which cannot be reconciled with one > another.
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Textual entailment measures natural language understanding as it asks for a semantic interpretation of the text, and due to its generality remains an active area of research. Many approaches and refinements of approaches have been considered, such as word embedding, logical models, graphical models, rule systems, contextual focusing, and machine learning. Practical or large-scale solutions avoid these complex methods and instead use only surface syntax or lexical relationships, but are correspondingly less accurate. However, even state-of-the-art systems are still far from human performance; a study found humans to be in agreement on the dataset 95.25% of the time, while algorithms from 2016 had not yet achieved 90%.
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The laws of state responsibility are the principles governing when and how a state is held responsible for a breach of an international obligation. Rather than set forth any particular obligations, the rules of state responsibility determine, in general, when an obligation has been breached and the legal consequences of that violation. In this way they are "secondary" rules that address basic issues of responsibility and remedies available for breach of "primary" or substantive rules of international law, such as with respect to the use of armed force. Because of this generality, the rules can be studied independently of the primary rules of obligation.
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However, this required a level of technological innovation that apparently was no longer attainable. (In this respect it is remarkable that the number of patents granted in the Netherlands was remarkably lower in this period than in the first half of the 17th century.)De Vries and Van der Woude, pp. 345–48 Besides, this type of reorientation in investment was undercut by a third response: outsourcing of industrial production to areas with a lower wage level, like the Generality Lands, which solved the high-wage problem in a different way, but also contributed to deindustralization in the maritime provinces. The consequences of foreign protectionism were not all negative, however.
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It was a universal law, that was applying to the stars and the galaxies as much as to biological organisms, and to human social organisation as much as to the human mind. It differed from other scientific laws only by its greater generality, and the laws of the special sciences could be shown to be illustrations of this principle. The principles described by Herbert Spencer received different interpretations. Bertrand Russell stated in a letter to Beatrice Webb in 1923: 'I don't know whether [Spencer] was ever made to realize the implications of the second law of thermodynamics; if so, he may well be upset.
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Jeu de taquin slides generalize to skew semistandard (as opposed to skew standard) tableaux and retain most of their properties in that generality. The only change that has to be made to the definition of an inward slide, in order for it to generalize, is a rule on how to proceed when the (temporarily) empty cell has neighbours below and to its right, and these neighbours are filled with equal numbers. In this situation, the neighbour below (not the one to the right) has to be slid into the empty cell. A similar change is needed in the definition of an outward slide (where one has to choose the neighbor above).
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SHYSTER was tested in four different and disparate areas of case law. Four specifications were written, each representing an area of Australian law: an aspect of the law of trover; the meaning of “authorization [sic]” in Australian copyright law; the categorisation of employment contracts; and the implication of natural justice in administrative decision-making. SHYSTER was evaluated under five headings: its usefulness, its generality, the quality of its advice, its limitations, and possible enhancements that could be made to it. Despite its simple knowledge representation structure, it has shown itself capable of producing good advice, and its simple structure has facilitated the specification of different areas of law.
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Takurō Mochizuki Takurō Mochizuki (望月 拓郎, born 28 August 1972) of Kyoto University is a Japanese mathematician, whose research follows the Bourbaki style of generality and rigor. He was awarded the Japan Academy Prize in 2011 for his research on D-modules in algebraic analysis... In 2014 he was a plenary speaker at the International Congress of Mathematicians.. As a student at the University of Kyoto in 1994, Mochizuki left his undergraduate early to become a graduate student in mathematics at the same university. He completed his Ph.D. in 1999, and joined the faculty of Osaka City University, returning to Kyoto in 2004.
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Men differ because their pompous hairstyle, imitating apparently the horn of deer. Some of the women exhibit a type of hairstyle that reminds the one used by some feminine figures presented in Pajatén: composed by two oblique segments that the author has interpreted as symbolic wings. In the generality of the figures, the bodies and faces treatment is simple, with a tendency to the schematic. Men's face, in a special way the one that corresponds to that of the second couple counting from the left side, shows a high grade of improving speaking of its execution due to the realism and the expressiveness that he exhibits.
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1–3, 10–11 The purpose of scientific literature is to inform and persuade peers as to the validity of observations and conclusions and the forensic efficacy of methods. Popular science attempts to inform and convince scientific outsiders (sometimes along with scientists in other fields) of the significance of data and conclusions and to celebrate the results. Statements in scientific literature are often qualified and tentative, emphasizing that new observations and results are consistent with and similar to established knowledge wherein qualified scientists are assumed to recognize the relevance. By contrast, popular science emphasizes uniqueness and generality, taking a tone of factual authority absent from the scientific literature.
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Under the same assumptions as for a standard logit (model F), the probability for a ranking of the alternatives is a product of standard logits. The model is called "exploded logit" because the choice situation that is usually represented as one logit formula for the chosen alternative is expanded ("exploded") to have a separate logit formula for each ranked alternative. The exploded logit model is the product of standard logit models with the choice set decreasing as each alternative is ranked and leaves the set of available choices in the subsequent choice. Without loss of generality, the alternatives can be relabeled to represent the person's ranking, such that alternative 1 is the first choice, 2 the second choice, etc.
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The objective of any optimization for speed is to have the program run as swiftly as possible; the problem is that it is not possible for a compiler to correctly analyze a program and determine what it will do, much less what the programmer intended for it to do. By contrast, human programmers start at the other end with a purpose, and attempt to produce a program that will achieve it, preferably without expending a lot of thought in the process. For various reasons, including readability, programs are frequently broken up into a number of procedures, which handle a few general cases. However, the generality of each procedure may result in wasted effort in specific usages.
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The appeal was dismissed. Millin J held (and Maritz J concurred) that section 31(1)(a) was wide enough to cover all cases of reckless or negligent driving which would be civilly actionable if proved to be the proximate cause of damage sustained by the plaintiff. Its generality was not cut down by the provision made for special cases in the succeeding subsections. The appellant had correctly been convicted of a contravention of section 31(1)(a) by recklessly or negligently driving a motor car on a public road, inasmuch as his physical condition to his knowledge made it impossible for him to drive in a public road without probable danger to others.
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Some psychologists and logicians argue that fuzzy concepts are a necessary consequence of the reality that any kind of distinction we might like to draw has limits of application. At a certain level of generality, a distinction works fine. But if we pursued its application in a very exact and rigorous manner, or overextend its application, it appears that the distinction simply does not apply in some areas or contexts, or that we cannot fully specify how it should be drawn. An analogy might be, that zooming a telescope, camera, or microscope in and out, reveals that a pattern which is sharply focused at a certain distance becomes blurry at another distance, or disappears altogether.
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In the mid-18th century, it became apparent that certain progressions of mathematical reasoning recurred when similar ideas were studied on the number line, in two dimensions, and in three dimensions. Thus the general concept of a metric space was created so that the reasoning could be done in more generality, and then applied to special cases. This method of studying calculus- and analysis- related concepts came to be known as analysis situs, and later as topology. The important topics in this field were properties of more general figures, such as connectedness and boundaries, rather than properties like straightness, and precise equality of length and angle measurements, which had been the focus of Euclidean and non-Euclidean geometry.
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At around the same time physicist James P. Crutchfield and others used the phrase onset of chaos to describe more or less the same concept. In the sciences in general, the phrase has come to refer to a metaphor that some physical, biological, economic and social systems operate in a region between order and either complete randomness or chaos, where the complexity is maximal. The generality and significance of the idea, however, has since been called into question by Melanie Mitchell and others. The phrase has also been borrowed by the business community and is sometimes used inappropriately and in contexts that are far from the original scope of the meaning of the term.
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The isomorphism theorems were formulated in some generality for homomorphisms of modules by Emmy Noether in her paper Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern, which was published in 1927 in Mathematische Annalen. Less general versions of these theorems can be found in work of Richard Dedekind and previous papers by Noether. Three years later, B.L. van der Waerden published his influential Algebra, the first abstract algebra textbook that took the groups-rings-fields approach to the subject. Van der Waerden credited lectures by Noether on group theory and Emil Artin on algebra, as well as a seminar conducted by Artin, Wilhelm Blaschke, Otto Schreier, and van der Waerden himself on ideals as the main references.
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Its practitioners were economists and historians > studying the histories of economies... The new economic history, or > cliometrics, formalized economic history in a manner similar to the > injection of mathematical models and statistics into the rest of economics. The relationship between economic history, economics and history has long been the subject of intense discussion, and the debates of recent years echo those of early contributors. There has long been a school of thought among economic historians that splits economic history—the study of how economic phenomena evolved in the past—from historical economics—testing the generality of economic theory using historical episodes. US economic historian Charles P. Kindleberger explained this position in his 1990 book Historical Economics: Art or Science?.
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Naghdi's work on continuum mechanics extended over a period of more than forty years and encompassed almost all aspects of the mechanical behavior of solids and fluids. A consummate theoretician, he was most strongly attracted by fundamental questions in mechanics, and always sought to treat these at the highest level of generality. His work is marked by a penetrating physical intuition combined with a methodical and mathematical line of thought. He is best known for his research in the areas of shell theory and plasticity, but is also recognized for his contributions to linear and nonlinear elasticity, viscoelasticity, the theory of deformable rods, the theories of fluid sheets and jets, thermomechanics, mixture theory, and general continuum mechanics.
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However the accuracy of the lunar theory was low, due to the perturbing effect of the Sun and planets on the motion of the Moon around the Earth. Jean le Rond d'Alembert and Alexis Clairaut, who developed a longstanding rivalry, both attempted to analyze the problem in some degree of generality; they submitted their competing first analyses to the Académie Royale des Sciences in 1747.The 1747 memoirs of both parties can be read in the volume of Histoires (including Mémoires) of the Académie Royale des Sciences for 1745 (belatedly published in Paris in 1749) (in French): : Clairaut: "On the System of the World, according to the principles of Universal Gravitation" (at pp.
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The first major language to provide such support was Ada, with its generic units feature. By 1987 Stepanov and Musser had developed and published an Ada library for list processing that embodied the results of much of their research on generic programming. However, Ada had not achieved much acceptance outside the defense industry and C++ seemed more likely to become widely used and provide good support for generic programming even though the language was relatively immature. Another reason for turning to C++, which Stepanov recognized early on, was that the C/C++ model of computation (which allows very flexible access to storage via pointers) is crucial to achieving generality without losing efficiency.
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Ivanov-Vano bore an animated film plan about the gifted master in Leskov's story about 30 years. Over time he arrived at idea that the originality of the narration of Leskov can be transferred, having created a graphic row with a support on an art system of the Russian popular print with "its characteristic generality of forms, specific expressiveness". For animation the idea to show evolution of character of the main character was innovative. Art directors at creation of the movie were inspired by ancient engravings (action in the imperial palace), English engravings (the foreign line), and the Tula episodes were solved in the stylistics of a popular print which is organically uniting all three lines.
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For example, any two vector spaces of the same dimension are isomorphic; if one of them is given an inner product and if we fix a particular isomorphism, then we may define an inner product on the other space by factoring through the isomorphism. ; without (any) loss of generality (WLOG, WOLOG, WALOG), we may assume (WMA): Sometimes a proposition can be more easily proved with additional assumptions on the objects it concerns. If the proposition as stated follows from this modified one with a simple and minimal explanation (for example, if the remaining special cases are identical but for notation), then the modified assumptions are introduced with this phrase and the altered proposition is proved.
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In mathematics, the G-function was introduced by as a very general function intended to include most of the known special functions as particular cases. This was not the only attempt of its kind: the generalized hypergeometric function and the MacRobert E-function had the same aim, but Meijer's G-function was able to include those as particular cases as well. The first definition was made by Meijer using a series; nowadays the accepted and more general definition is via a line integral in the complex plane, introduced in its full generality by Arthur Erdélyi in 1953. With the modern definition, the majority of the established special functions can be represented in terms of the Meijer G-function.
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The Traité du signe visuel (1992) (which Göran Sonesson said was to visual communication what Saussure's Cours de linguistique générale was to linguistics) sought to elaborate a general grammar of the image, independently of the type of corpus being considered. This semiotic of the visual contributed, in its turn, to semiotics in general: indeed, a question encountered by the group at this stage was that of the relationship between sensorial experience and signification, a question which certainly reveals something of this degree of generality since it comes up against the question of the origin of meaning itself. The group took its name from the metaphor, μ being the Greek initial for the term.
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If each of the bonding maps f_{i}^{j} is an embedding of TVSs onto proper vector subspaces and if the system is directed by with its natural ordering, then the resulting limit is called a strict (countable) direct limit. In such a situation we may assume without loss of generality that each is a vector subspace of and that the subspace topology induced on by is identical to the original topology on . In the category of locally convex topological vector spaces, the topology on a strict inductive limit of Fréchet spaces can be described by specifying that an absolutely convex subset is a neighborhood of if and only if is an absolutely convex neighborhood of in for every .
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De Witt demanded an oath from each Holland regent (city council member) to uphold the Edict; all but one complied. William saw all this as a defeat, but the arrangement was a compromise: De Witt would have preferred to ignore the prince completely, but now his eventual rise to the office of supreme army commander was implicit.Troost, 53–54 De Witt further conceded that William would be admitted as a member of the Raad van State, the Council of State, then the generality organ administering the defence budget.Troost, 59 William was introduced to the council on 31 May 1670 with full voting rights, despite De Witt's attempts to limit his role to that of an advisor.
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Although Louis took Maastricht and William's attack against Charleroi failed, Lieutenant-Admiral Michiel de Ruyter defeated the Anglo-French fleet three times, forcing Charles to end England's involvement by the Treaty of Westminster; after 1673, France slowly withdrew from Dutch territory (with the exception of Maastricht), while making gains elsewhere.Troost, 128–129 Fagel now proposed to treat the liberated provinces of Utrecht, Gelderland and Overijssel as conquered territory (Generality Lands), as punishment for their quick surrender to the enemy.Troost, 106–110 William refused but obtained a special mandate from the States General to appoint all delegates in the States of these provinces anew. William's followers in the States of Utrecht on 26 April 1674 appointed him hereditary stadtholder.
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Further evidence for domain general statistical learning was suggested in a study run through the University of Cornell Department of Psychology concerning visual statistical learning in infancy. Researchers in this study questioned whether domain generality of statistical learning in infancy would be seen using visual information. After first viewing images in statistically predictable patterns, infants were then exposed to the same familiar patterns in addition to novel sequences of the same identical stimulus components. Interest in the visuals was measured by the amount of time the child looked at the stimuli in which the researchers named “looking time.” All ages of infant participants showed more interest in the novel sequence relative to the familiar sequence.
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There are three important themes in the categorical approach to logic: ;Categorical semantics: Categorical logic introduces the notion of structure valued in a category C with the classical model theoretic notion of a structure appearing in the particular case where C is the category of sets and functions. This notion has proven useful when the set-theoretic notion of a model lacks generality and/or is inconvenient. R.A.G. Seely's modeling of various impredicative theories, such as system F is an example of the usefulness of categorical semantics. :It was found that the connectives of pre-categorical logic were more clearly understood using the concept of adjoint functor, and that the quantifiers were also best understood using adjoint functors.
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Montgomery (2001, Section 3.8: Discovering dispersion effects) There are no necessary assumptions for ANOVA in its full generality, but the F-test used for ANOVA hypothesis testing has assumptions and practical limitations which are of continuing interest. Problems which do not satisfy the assumptions of ANOVA can often be transformed to satisfy the assumptions. The property of unit-treatment additivity is not invariant under a "change of scale", so statisticians often use transformations to achieve unit-treatment additivity. If the response variable is expected to follow a parametric family of probability distributions, then the statistician may specify (in the protocol for the experiment or observational study) that the responses be transformed to stabilize the variance.
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If the state law is merely procedural, or relating merely to the form and mode of judicial operations, then the federal court does not have to apply the conflicting state law. However, the substance-procedure distinction is a generality as the Court rejected any test based upon "litmus paper criterion." Thus, a choice between state and federal law must be made with reference to the underlying policy of the Erie decision. The Court announced a modification of the "outcome- determinative" test in York, whereby the test must be applied in light of the twin aims of Erie, which are the discouragement of forum-shopping and avoidance of inequitable administration of the laws.
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The Duchy of Brabant was a State of the Holy Roman Empire established in 1183. It developed from the Landgraviate of Brabant and formed the heart of the historic Low Countries, part of the Burgundian Netherlands from 1430 and of the Habsburg Netherlands from 1482, until it was partitioned after the Dutch revolt. Present-day North Brabant (Staats-Brabant) was ceded to the Generality Lands of the Dutch Republic according to the 1648 Peace of Westphalia, while the reduced duchy remained part of the Southern Netherlands until it was conquered by French Revolutionary forces in 1794. Today all the duchy's former territories, apart from exclaves, are in Belgium except for the Dutch province of North Brabant.
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The search of the solution may be made dramatically faster by sieving. For this method, we suppose, without loss of generality, that 0\le a_i (if it were not the case, it would suffice to replace each a_i by the remainder of its division by n_i). This implies that the solution belongs to the arithmetic progression :a_1, a_1 + n_1, a_1+2n_1, \ldots By testing the values of these numbers modulo n_2, one eventually finds a solution x_2 of the two first congruences. Then the solution belongs to the arithmetic progression :x_2, x_2 + n_1n_2, x_2+2n_1n_2, \ldots Testing the values of these numbers modulo n_3,, and continuing until every modulus has been tested gives eventually the solution.
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If are the Cartesian coordinates of a point, then are the coordinates of its reflection across the second coordinate axis (the y-axis), as if that line were a mirror. Likewise, are the coordinates of its reflection across the first coordinate axis (the x-axis). In more generality, reflection across a line through the origin making an angle \theta with the x-axis, is equivalent to replacing every point with coordinates by the point with coordinates , where :x'=x \cos 2\theta + y \sin 2\theta :y'=x \sin 2\theta - y \cos 2\theta . Thus: (x',y') = ((x \cos 2\theta + y \sin 2\theta\,) , (x \sin 2\theta - y \cos 2\theta\,)) .
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The innovation here was that the corps would be organised on the level of the Generality, above the level of the five regional Admiralties. This brought him to attention of the stadtholder, with whom he discussed the proposal for the first time in the Spring of 1781. On 17 April 1781 the plan was formally approved by six of the seven provinces in the States General of the Netherlands, but Zeeland vetoed it "for lack of money." In 1782 the stadtholder appointed van Kinckel as one of the two Adjutants of the "corps de marine" he had proposedThough only after a conflict with his rival Lodewijk van Bylandt, who was originally appointed in the post.
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Silicon, in contrast, interacts with only a few other atoms, and the large silicon molecules are monotonous compared with the combinatorial universe of organic macromolecules. Indeed, it seems likely that the basic building blocks of life anywhere will be similar to those on Earth, in the generality if not in the detail. Although terrestrial life and life that might arise independently of Earth are expected to use many similar, if not identical, building blocks, they also are expected to have some biochemical qualities that are unique. If life has had a comparable impact elsewhere in the Solar System, the relative abundances of chemicals key for its survival—whatever they maybe—could betray its presence.
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Thus, logical formalization is important for thinking about existence, just as the issues of human existence are essential for understanding thinking and logic. This conception of philosophy owes the hardly unorthodox intersections that Cabrera did in his studies of logic, connecting Saul Kripke with Martin Heidegger, Immanuel Kant with John Austin, and Ludwig Wittgenstein with Jean- Paul Sartre. Cabrera's work has the expectation of allying the formal instruments to the existential contents of life. The critique to the alleged empty generality of logic goes in this direction as well as the proposal of a lexical logic of predicative connections, in an attempt to lend to lexical analysis a formal dimension, but loaded with content.
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A congruence subgroup is (roughly) a subgroup of an arithmetic group defined by taking all matrices satisfying certain equations modulo an integer, for example the group of 2 by 2 integer matrices with diagonal (respectively off-diagonal) coefficients congruent to 1 (respectively 0) modulo a positive integer. These are always finite-index subgroups and the congruence subgroup problem roughly asks whether all subgroups are obtained in this way. The conjecture (usually attributed to Jean-Pierre Serre) is that this is true for (irreducible) arithmetic lattices in higher-rank groups and false in rank-one groups. It is still open in this generality but there are many results establishing it for specific lattices (in both its positive and negative cases).
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Because Dutch trade, science, military, and art were among the most acclaimed in the world during much of the 17th century, this period became known in Dutch history as the Dutch Golden Age. The republic was a confederation of provinces each with a high degree of independence from the federal assembly, known as the States General. In the Treaty of Westphalia (1648) the republic gained approximately 20% more territory, located outside the member provinces, which was ruled directly by the States General as Generality Lands. Each province was led by an official known as the stadtholder (); this office was nominally open to anyone, but most provinces appointed a member of the House of Orange.
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His abelian category concept had at least partially been anticipated by others. David Buchsbaum in his doctoral thesis written under Eilenberg had introduced a notion of "exact category" close to the abelian category concept (needing only direct sums to be identical); and had formulated the idea of "enough injectives". The Tôhoku paper contains an argument to prove that a Grothendieck category (a particular type of abelian category, the name coming later) has enough injectives; the author indicated that the proof was of a standard type. In showing by this means that categories of sheaves of abelian groups admitted injective resolutions, Grothendieck went beyond the theory available in Cartan–Eilenberg, to prove the existence of a cohomology theory in generality.
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However, this modification has been criticized for being unrealistic, since a centered window cannot be applied to today's return without knowing the future. The increased accuracy has usually been deemed worth the loss of generality. Other generalizations to the model have been developed to do away with the fixed window constraint, such as models that employ Kalman filters to allow for more general time dilation. These methods still require assumed restrictions on the evolution of exposures, such as a return to normality assumption, or a fixed turnover parameter such as in Dynamic Style Analysis. These models are usually considered separate from classically defined ‘RBSA’, though they continue to analyze style based on returns.
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A review in The Times praised the book as a "powerful counter-blast against the monstrous regiment of 'useful idiots'" who have "contributed in recent decades to the murderous mess of modern times". On the other hand, columnist Oliver Kamm, writing for his Times blog, disputed the review, accusing Seymour of historiographical distortions. Seymour posted a lengthy reply to Kamm's criticisms on his own blog. A critical review in The Guardian by Philippe Sands contended that despite the book's "damning material" on the supporters of war, this "potentially important book" was weakened by "the generality" of its conclusions and the failure to concede that there are instances where the use of force is justified.
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Marvin Harris described Totem and Taboo as representative of what Boas's followers regarded as "the worst form of evolutionary speculation", criticizing "the grandiosity of its compass, the flimsiness of its evidence ... the generality of its conclusions" and its "anachronistic framework". In his view, nothing about the work prepared "orthodox Freudians" to deal with the variety of culturally determined personality structures revealed by the work of Bronisław Malinowski, Margaret Mead, and Ruth Benedict. Peter Farb wrote that Totem and Taboo "demonstrates the lengths to which a theorist will go to find an explanation" for totemism, adding that despite their disagreements on other issues, anthropologists by 1968 concurred that the work is "totally discredited".
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Although similar trigonometric series were previously used by Euler, d'Alembert, Daniel Bernoulli and Gauss, Fourier believed that such trigonometric series could represent any arbitrary function. In what sense that is actually true is a somewhat subtle issue and the attempts over many years to clarify this idea have led to important discoveries in the theories of convergence, function spaces, and harmonic analysis. When Fourier submitted a later competition essay in 1811, the committee (which included Lagrange, Laplace, Malus and Legendre, among others) concluded: ...the manner in which the author arrives at these equations is not exempt of difficulties and...his analysis to integrate them still leaves something to be desired on the score of generality and even rigour.
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In fact there was an eighth province, the lordship of Drenthe, but this area was so poor it was exempt from paying confederal taxes and, as a corollary, was denied representation in the States-General. The duchy of Brabant, the county of Flanders and the lordship of Mechelen were also among the rebelling provinces, but were later completely or largely reconquered by Spain. After the Peace of Westphalia, the parts of these provinces that remained in the Dutch Republic's hands, as well as several other border territories, became confederally governed Generality Lands (Generaliteitslanden). They were Staats-Brabant (present North Brabant), Staats-Vlaanderen (present Zeeuws-Vlaanderen), Staats-Overmaas (around Maastricht) and Staats-Opper-Gelre (around Venlo, after 1715).
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This was often why the Princes of Orange tended to favour a policy of war, against Spain or France (as was the case with Maurice and William II), rather than a policy of peace. However, this was not actually the power to command, but the power to influence, persuade the States, and have their decisions accepted as those of the States. As mentioned above, the ability of the 17th century House of Orange-Nassau Princes of Orange to influence and drive the States to a consensus lead to their leadership of the Generality. The inability of the Princes of Orange of the 18th Century to do so lead in great part to the fall of the Dutch Republic.
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The States Party at the height of the Republic in the First Stadholderless Period were led by such talented men as Johan de Witt, his brother Cornelis de Witt, Cornelis de Graeff, Andries de Graeff and Andries Bicker. During the Second Statholderless period, the States Party were again led by the Raadpensionaris of the time. As also noted above, the faction even thought through, at least during De Witt's time, an ideological justification of republicanism Ware Vrijheid (the "True Freedom") that went against the contemporary European trend of monarchical absolutism. De Witt and his allies primarily defended Van Oldenbarnevelt's and Grotius' claim to supremacy of (Holland's) provincial sovereignty over the sovereignty of the Generality.
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The bisection method consists roughly of starting from an interval containing all real roots of a polynomial, and divides it recursively into two parts until getting eventually intervals that contain either zero or one root. The starting interval may be of the form , where is an upper bound on the absolute values of the roots, such as those that are given in . For technical reasons (simpler changes of variable, simpler complexity analysis, possibility of taking advantage of the binary analysis of computers), the algorithms are generally presented as starting with the interval . There is no loss of generality, as the changes of variables and move respectively the positive and the negative roots in the interval .
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Assume without loss of generality that the support of the distribution is contained in [0,1]. Given a confidence envelope for the CDF of F it is easy to derive a corresponding confidence interval for the mean of F. It can be shown that the CDF that maximizes the mean is the one that runs along the lower confidence envelope, L(x), and the CDF that minimizes the mean is the one that runs along the upper envelope, U(x). Using the identity : E(X) = \int_0^1(1-F(x))\,dx, the confidence interval for the mean can be computed as : \left[\int_0^1(1-U(x))\,dx, \int_0^1(1-L(x))\,dx \right].
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In economics, the classic example of a situation in which a consumer X can be Dutch-booked is if they have intransitive preferences. Suppose that for this consumer, A is preferred to B, B is preferred to C, and C is preferred to A. Then suppose that someone else in the population, Y, has one of these goods. Without loss of generality, suppose Y has good A. Then Y can first sell A to X for B+ε; then sell B to X for C+ε; then sell C to X for A+ε, where ε is some small amount of the numeraire. After this sequence of trades, X has given 3·ε to Y for nothing in return.
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In Principles (1973), R. M. Hare accepts that rule utilitarianism collapses into act utilitarianism but claims that this is a result of allowing the rules to be "as specific and un-general as we please." He argues that one of the main reasons for introducing rule utilitarianism was to do justice to the general rules that people need for moral education and character development and he proposes that "a difference between act-utilitarianism and rule-utilitarianism can be introduced by limiting the specificity of the rules, i.e., by increasing their generality." This distinction between a "specific rule utilitarianism" (which collapses into act utilitarianism) and "general rule utilitarianism" forms the basis of Hare's two-level utilitarianism.
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A. In both Su's solution and Azrieli&Shmaya;'s solution, the preference relation of each partner is allowed (but not obliged) to depend on the entire price-vector. I.e, a partner may say "if room A costs 1000, then I prefer room B to room C, but if room A costs only 700, then I prefer room C to room B". There are several reasons such generality can be useful. # Future planning. Suppose the partner thinks that room A is best, then B, then C. If A is expensive, the partner settles on B. But if A is cheaper, the partner might buy C (which is the cheapest), and then save some money and switch to A. # Incomplete information.
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This led her to exaggerate the generality of ideogrammatic principles and to seem to hold that English was really rather like Chinese if only seen correctly, with its meaning atoms, highly ambiguous and virtually uninflected. It was a view that found little or no sympathy in the dominant linguistic or computational currents of the time. Her main creation in 1953, one which endured for twenty years, was the Cambridge Language Research Unit, which grew out of an informal discussion group with a very heterogeneous membership interested in language from philosophical and computational points of view. Subsequently, the attempt to build language processing programs which had a sound philosophical basis was a distinctive feature of the Unit's work.
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The new emphasis on Aragonese history led to the creation of the position of Chronicler or Historian of Aragon; its holders included Jerónimo Zurita y Castro, the De Argensola brothers, Bartolomé and Lupercio, Juan Costa and Jerónimo Martel. Much of the work produced by Aragonese writers challenged Philip II's version of events and were censored by the central government. In retaliation, the Generality of Aragon ordered the work of Castilian historian Antonio de Herrera y Tordesillas to be burned and commissioned Vicencio Blasco de Lanuza to write an alternative. His 'History of Aragon' was published in two volumes, 1616 and 1619 respectively; the urgency shows the importance placed on responding to Herrera.
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As with every universal property, the above definition describes a balanced state of generality: The limit object L has to be general enough to allow any other cone to factor through it; on the other hand, L has to be sufficiently specific, so that only one such factorization is possible for every cone. Limits may also be characterized as terminal objects in the category of cones to F. It is possible that a diagram does not have a limit at all. However, if a diagram does have a limit then this limit is essentially unique: it is unique up to a unique isomorphism. For this reason one often speaks of the limit of F.
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The study of computability came to be known as recursion theory or computability theory, because early formalizations by Gödel and Kleene relied on recursive definitions of functions.A detailed study of this terminology is given by Soare (1996). When these definitions were shown equivalent to Turing's formalization involving Turing machines, it became clear that a new concept - the computable function - had been discovered, and that this definition was robust enough to admit numerous independent characterizations. In his work on the incompleteness theorems in 1931, Gödel lacked a rigorous concept of an effective formal system; he immediately realized that the new definitions of computability could be used for this purpose, allowing him to state the incompleteness theorems in generality that could only be implied in the original paper.
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A hyper-heuristic usually aims at reducing the amount of domain knowledge in the search methodology. The resulting approach should be cheap and fast to implement, requiring less expertise in either the problem domain or heuristic methods, and (ideally) it would be robust enough to effectively handle a range of problem instances from a variety of domains. The goal is to raise the level of generality of decision support methodology perhaps at the expense of reduced - but still acceptable - solution quality when compared to tailor-made metaheuristic approaches.Burke E.K., Landa Silva J.D., Soubeiga E.: Multi-objective Hyper-heuristic Approaches for Space Allocation and Timetabling, In Meta-heuristics: Progress as Real Problem Solvers, Selected Papers from the 5th Metaheuristics International Conference (MIC 2003), pp 129-158, 2005.
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Again, we deal here with a generalization of what in queuing theory is sometimes referred to as Little's theorem that, and this is important, applies only to the whole system S (not to an arbitrary subsystem as in the mass-time equivalence); the mean sojourn time can in the Little's theorem be interpreted as mean transit time. As should be evident from the discussion of the figure above, there is a fundamental difference between the meaning of the two quantities sojourn time and transit time: the generality of the mass-time equivalence is very much due to the special meaning of the notion of sojourn time. When the whole system is considered (as in Littl's theorem) is it true that sojourn time always equals transit time.
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Despite the agreement to transfer the sovereignty of Macau to the People's Republic of China in 1999 and its designation as a special administrative region (SAR) of China, the position of the Baháʼí Faith in Macau - its administration, membership and communities - in the context of local laws has remained unchanged. The "National" Spiritual Assembly is now referred to as the “Spiritual Assembly” or “Main Spiritual Assembly” in Chinese and still retains jurisdiction over the Local Spiritual Assemblies in Macau. The Local Spiritual Assemblies of the Macau Peninsula, Taipa and Coloane are elected respectively once a year. The nine members of each Local Spiritual Assembly are elected from the generality of Baháʼí residents of the community through secret votes in a form of non-partisan democracy.
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An element of a commutative ring is said to be prime if it is not the zero element or a unit and whenever divides for some and in , then divides or divides . Equivalently, an element is prime if, and only if, the principal ideal generated by is a nonzero prime ideal., as indicated in the remark below the theorem and the proof, the result holds in full generality. (Note that in an integral domain, the ideal is a prime ideal, but is an exception in the definition of 'prime element'.) Interest in prime elements comes from the Fundamental theorem of arithmetic, which asserts that each nonzero integer can be written in essentially only one way as 1 or −1 multiplied by a product of positive prime numbers.
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Prussian National Monument for the Liberation Wars For the inauguration of the Prussian National Monument for the Liberation Wars Frederick William III chose the 30 March 1821, the seventh anniversary of the conquest of the Montmartre in the Battle of Paris.Michael Nungesser, Das Denkmal auf dem Kreuzberg von Karl Friedrich Schinkel, see references for bibliographical details, p. 41\. . The inauguration was attended by the royal family, the Prussian generality, the senior pastors of all Protestant congregations of Berlin, and as guests by Grand Duke Nicholas of Russia and his wife Alexandra Feodorovna (Charlotte of Prussia), as well as by thousands of other spectators. As the national monument is crowned by an Iron Cross the king renamed Götze'scher Berg into Kreuzberg (i.e.
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In mathematics, the Weyl–von Neumann theorem is a result in operator theory due to Hermann Weyl and John von Neumann. It states that, after the addition of a compact operator () or Hilbert–Schmidt operator () of arbitrarily small norm, a bounded self-adjoint operator or unitary operator on a Hilbert space is conjugate by a unitary operator to a diagonal operator. The results are subsumed in later generalizations for bounded normal operators due to David Berg (1971, compact perturbation) and Dan-Virgil Voiculescu (1979, Hilbert–Schmidt perturbation). The theorem and its generalizations were one of the starting points of operator K-homology, developed first by Lawrence G. Brown, Ronald Douglas and Peter Fillmore and, in greater generality, by Gennadi Kasparov.
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In these working groups, Cardinale and his colleagues have assembled extensive datasets of thousands of experiments and observational studies that have quantified how changes in biodiversity impact a wide variety of ecological processes and ecosystem services for organisms inhabiting 30 biomes on 5 continents. Their syntheses have led to publication of 15 formal meta- analyses. In 2012, Cardinale organized and led an invited review for a special issue of Nature dedicated to the 20th anniversary of the Rio Earth Summit in which his colleagues and he synthesized over 1,700 papers that have examined biodiversity's impact on 34 ecosystem goods and services. This synthesis revealed a remarkable level of generality in how biodiversity impacts the functioning of Earth's ecosystems and the services they provide to society.
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Signet of the Delegation of the Generality of the Principality of Catalonia in the late fifteenth century representing its patron bearing the shield of the Cross of St. George which were the arms of the Generalitat of Catalonia. On the caption: S(igillum): CORTIUM: ET: PARLAMENTORUM: GENERALIUM: PRINCIPATUS: CATHALONIE (Seal of the Courts and the Parliament of the Principality of Catalonia) In the Courts held in Monzón in 1289, Delegation of the General Court was appointed as a permanent council to collect the "service" or tribute that the arms granted to the king at his request. Later, this would give rise to the Generalitat of Catalonia, in the fourteenth century. Its regulation was also used to create in the fifteenth century the Valencian Generalitat.
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The Catalan and Valencian Generalitats were both abolished by the Nueva Planta decrees, signed by Philip V of Spain at the start of the eighteenth century, and only reinstated after the death of Franco in 1975, although in Catalonia it also had a few-years existence during the Second Spanish Republic (1931-1939). The Generalitat a l'Aran was legally created by the 2006 modification of the Statute of Autonomy of Catalonia, although the Val d'Aran had also enjoyed considerable autonomy within Catalonia under the 1979 Statute of Autonomy. Today, Generalitat refers to all three branches of government, not simply the executive. For example, the Catalan executive is, officially, the "Government of the Generality of Catalonia" (Govern de la Generalitat de Catalunya: cf.
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The stadtholders of the provinces were ex officio members, at least outside the First Stadtholderless Period and Second Stadtholderless Period. The executive powers of the Council were limited to military policy (both on land and sea); administering the Dutch States Army's financial aspects (naval affairs were administered by the five Admiralties, founded by Leicester); and formulating and executing tax policy for the Generality Lands. The Council usually played a self-effacing role, as laid down in its Instruction of 1651, at the beginning of the first Stadtholderless Period. However, the secretary of the Council, Simon van Slingelandt played a leading role in an attempt at constitutional reform (which would have greatly increased the executive powers of the Council, as intended in the time of Leicester) in 1717.
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In reaching the conclusion that Morse's claim 8 was too broad and thus not subject to patent protection, the Court considered not only the fact that Morse did not teach and enable other ways to communicate information at a great distance by using the electromagnetic force,See 35 U.S.C. sec. 112(a), which requires patentees to disclose their inventions in sufficient detail that others are enabled to practice the invention without undue experimentation. but also whether the claim was at such a high level of generality and abstraction that it claimed an "idea" rather than a practical application and implementation of an idea. In analyzing this aspect of the case, the Court looked to a recent English decision, Neilson v. Harford.
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After obtained the obligatory permissions on the part of the Headquarter of the Cultural Heritage, and of the Valencian Generality, began the works of excavation to the " Mas of Pepelillo-2 " on March 25, 2008, finishing them on April 29, of the same year. With an excavator machine was started withdrawing the vegetable existing land in the zone that had been marked it was doing a few months, which since have been indicated was where one was thinking that it could stay, the deposit Hispanic-Muslim of the Pepelillo 1. This vision changed, when immediately after one it would be of rains in the surface they appeared a great quantity of fragments of sílex. Also were observed some handmade, prehistoric ceramics.
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Compared to other parallel-processing models, Linda is more orthogonal in treating process coordination as a separate activity from computation, and it is more general in being able to subsume various levels of concurrency--uniprocessor, multi- threaded multiprocessor, or networked--under a single model. Its orthogonality allows processes computing in different languages and platforms to interoperate using the same primitives. Its generality allows a multi-threaded Linda system to be distributed across multiple computers without change. Whereas message-passing models require tightly-coupled processes sending messages to each other in some sequence or protocol, Linda processes are decoupled from other processes, communicating only through the tuplespace; a process need have no notion of other processes except for the kinds of tuples consumed or produced (data coupling).
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THE FEDERATION AND THE L.C3.84NDER and Article 25 states that 'general rules of international law shall be an integral part of federal law'. The latter article was included in deference to the post-war actions of the occupying Western powers; but had the unintended consequence that the Federal Constitutional Court tended to define 'rules of international law' as applicable to German federal law within Germany, that were nevertheless different from the generality of rules and principles of international law as they might operate between Germany and other nations. Hence, the Federal Constitutional Court could recognise East Germany as a sovereign state in international law in the second sense, while still asserting that it was not a 'sovereign state in international law' within Germany itself.
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He writes, > "I may here observe, that there cannot be a greater proof of the utility of > Dancing, than its being so universally adopted, as a material circumstance > in the education of the youth of both sexes, in every civilised country. Its > tendency to form their manners, and to render them agreeable, as well in > public as in private; the graceful and elegant ease which it gives to the > generality of those who practice it with attention, are apparent to everyone > of true discernment." He is particularly known for his eight-volume treatise on dance, Sketches Relative to the History and Theory, but More Especially to the Practice of Dancing (1805). This was one of the early works on the history of dance.
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It is extremely hard to develop suitable conditions for using alkyl halides and epoxides as electrophiles. Despite the broad scope, atom economy, and generality of the reaction, the slow rate of the Baylis-Hillman reaction (reaction times of a fortnight or even longer are not uncommon, even with 25 to 100 mol % catalyst) for hindered aliphatic aldehydes and electron-rich benzaldehydes often limits the synthetic utility of the process. For example, in the case of sterically hindered t-butyl acrylate, reaction with benzaldehyde with DABCO as catalyst in the absence of solvent requires 4 weeks to give moderate levels of conversion to the desired product. In the presence of aprotic solvents, the reaction rate is even slower, although protic additives (e.g.
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Simons, Martin (1962), "The morphological analysis of landforms: A new review of the work of Walther Penck (1888–1923)", Transactions and Papers (Institute of British Geographers) 31: 1–14. Both Davis and Penck were trying to place the study of the evolution of the Earth's surface on a more generalized, globally relevant footing than it had been previously. In the early 19th century, authors – especially in Europe – had tended to attribute the form of landscapes to local climate, and in particular to the specific effects of glaciation and periglacial processes. In contrast, both Davis and Penck were seeking to emphasize the importance of evolution of landscapes through time and the generality of the Earth's surface processes across different landscapes under different conditions.
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In mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold. Flag varieties are naturally projective varieties. Flag varieties can be defined in various degrees of generality. A prototype is the variety of complete flags in a vector space V over a field F, which is a flag variety for the special linear group over F. Other flag varieties arise by considering partial flags, or by restriction from the special linear group to subgroups such as the symplectic group.
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76; , p. 74. This may be seen from the connection, described above, between median graphs and 2-satisfiability: let G be the graph of solutions to a 2-satisfiability instance; without loss of generality this instance can be formulated in such a way that no two variables are always equal or always unequal in every solution. Then the space of all truth assignments to the variables of this instance forms a hypercube. For each clause, formed as the disjunction of two variables or their complements, in the 2-satisfiability instance, one can form a retraction of the hypercube in which truth assignments violating this clause are mapped to truth assignments in which both variables satisfy the clause, without changing the other variables in the truth assignment.
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That would be a misunderstanding, however, even though the court of the stadtholder took on a decidedly "princely" aspect (as it had done under William's grandfather Frederick Henry, Prince of Orange). If William was a monarch at all, it was a "constitutional" one, with still sharply limited powers, formally and politically. The States-General remained sovereign in the Republic, the entity with which other states concluded treaties and made war or peace. The pretensions to sovereign supremacy of the provinces, however, as under the De Witt regime, were again replaced with the constitutional theory of Maurice, Prince of Orange, after his overturning of the regime of Johan van Oldenbarnevelt in 1618, in which the provinces were at least in certain respects subservient to the "Generality".
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While bilingualism has repeatedly been shown to affect cognitive development, research has been less focused on which aspects of cognitive development, in particular, are affected. Bialystok and Barac, in a study about the generality of bilingual effects on development, compared three groups of bilinguals to one group of monolinguals in a series of linguistic tasks and one nonlinguistic, executive control task involving task-switching. The three bilingual groups differed according to three factors: similarity between languages spoken, cultural background, and language of educational experience. All three bilingual groups outperformed the monolingual group on the task-switching executive control task, however, even in excluding the monolingual group, neither of the three differentiating factors had a significant effect on the performance of the executive control task.
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In 2000, the Ruvkun lab reported the identification of second C. elegans microRNA, let-7, which like the first microRNA regulates translation of the target gene, in this case lin-41, via imperfect base pairing to the 3’ untranslated region of that mRNA. This was an indication that miRNA regulation via 3’ UTR complementarity may be a common feature, and that there were likely to be more microRNAs. The generality of microRNA regulation to other animals was established by the Ruvkun lab later in 2000, when they reported that the sequence and regulation of the let-7 microRNA is conserved across animal phylogeny, including in humans. Presently thousands of miRNAs have been discovered, pointing to a world of gene regulation at this size regime.
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Islington Council issued a ruling that the building be demolished in mid-2017 due to the error, which the council withdrew after an inquiry from a legal team employed by Taha. After rescinding the first order to demolish the structure, the council issued a second in February 2018, following "an investigation" that determined the building's final design differed from the approved design. This order cited the location of the fossils within the stone facade as "[...] deleterious to the conservation area and listed buildings" due to their "haphazard" placement. In August 2019, Taha's appeal was successful and the council's planning office granted planning permission, ruling that the building "accords with the generality of what had previously been approved" and removing the demolition order.
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A manifold is orientable if it has a consistent choice of orientation, and a connected orientable manifold has exactly two different possible orientations. In this setting, various equivalent formulations of orientability can be given, depending on the desired application and level of generality. Formulations applicable to general topological manifolds often employ methods of homology theory, whereas for differentiable manifolds more structure is present, allowing a formulation in terms of differential forms. An important generalization of the notion of orientability of a space is that of orientability of a family of spaces parameterized by some other space (a fiber bundle) for which an orientation must be selected in each of the spaces which varies continuously with respect to changes in the parameter values.
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Lagrange's four- square theorem is a special case of the Fermat polygonal number theorem and Waring's problem. Another possible generalization is the following problem: Given natural numbers a,b,c,d, can we solve :n=ax_1^2+bx_2^2+cx_3^2+dx_4^2 for all positive integers n in integers x_1,x_2,x_3,x_4? The case a=b=c=d=1 is answered in the positive by Lagrange's four-square theorem. The general solution was given by Ramanujan.. He proved that if we assume, without loss of generality, that a\leq b\leq c\leq d then there are exactly 54 possible choices for a,b,c,d such that the problem is solvable in integers x_1,x_2,x_3,x_4 for all n.
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Moreover, the Republic had come to occupy during the Eighty Years' War a number of so-called Generality Lands in Flanders, Brabant and Limburg. Their population was mainly Roman Catholic, and these areas did not have a governmental structure of their own, and were used as a buffer zone between the Republic and the Spanish-controlled Southern Netherlands. p. 66 Kampen by Hendrick Avercamp (1620s) Amsterdam's Dam Square in 1656 In the Dutch Golden Age, spanning much of the 17th century, the Dutch Empire grew to become one of the major seafaring and economic powers, alongside Portugal, Spain, France and England. Science, military, and art (especially painting) were among the most acclaimed in the world. By 1650, the Dutch owned 16,000 merchant ships.
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Without loss of generality, we describe Benson's algorithm for the Black player. Let X be the set of all Black chains and R be the set of all Black- enclosed regions of X. Then Benson's algorithm requires iteratively applying the following two steps until neither is able to remove any more chains or regions: # Remove from X all Black chains with less than two vital Black- enclosed regions in R, where a Black-enclosed region is vital to a Black chain in X if all its empty intersections are also liberties of the chain. # Remove from R all Black-enclosed regions with a surrounding stone in a chain not in X. The final set X is the set of all unconditionally alive Black chains.
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For proving bounds on this problem, it may be assumed without loss of generality that the inputs are strings over a two-letter alphabet. For, if two strings over a larger alphabet differ then there exists a string homomorphism that maps them to binary strings of the same length that also differ. Any automaton that distinguishes the binary strings can be translated into an automaton that distinguishes the original strings, without any increase in the number of states.. It may also be assumed that the two strings have equal length. For strings of unequal length, there always exists a prime number whose value is logarithmic in the smaller of the two input lengths, such that the two lengths are different modulo .
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Current AI systems can solve very simple and/or restricted versions of AI-complete problems, but never in their full generality. When AI researchers attempt to "scale up" their systems to handle more complicated, real-world situations, the programs tend to become excessively brittle without commonsense knowledge or a rudimentary understanding of the situation: they fail as unexpected circumstances outside of its original problem context begin to appear. When human beings are dealing with new situations in the world, they are helped immensely by the fact that they know what to expect: they know what all things around them are, why they are there, what they are likely to do and so on. They can recognize unusual situations and adjust accordingly.
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The CCCS design also address some concerns about the external validity or generality of findings of small-n single-case experimental design studies because it explicitly includes all cases encountered, regardless of outcome. By including all cases, any bias favoring a particular outcome in controlled for, resulting in stronger external validity relative to studies describing fewer cases that were not consecutively encountered. Moreover, when a large number of individuals are included in the series, this provides opportunities to identify variables that may predict treatment outcomes. Consecutive controlled case-series studies examining behavior analytic interventions of late have examined functional communication training.Rooker, G.W., Jessel, J., Kurtz, P.F. and Hagopian, L.P. (2013), "Functional Communication Training With And Without Alternative Reinforcement And Punishment: An Analysis Of 58 Applications".
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The newspaper described it as: > "A beautiful example of etching on steel, the production of a Sheffield > mechanic. It is a copy of Stothard's Vintage, and the execution holds out > great promise from its producer, Mr Thomas Skinner ... The piece possesses > some claim to novelty, as well as merit, from being much larger in size than > the generality of specimens of etching in steel, and is framed, for the > purpose of hanging in a room." Before his trip to America in the 1860s, Skinner attempted to profit from his invention by leaving paid employment and going into partnership. Coulson and Branson paid him £600 for right to his invention, and they went into partnership as Skinner, Coulson and Branson, working out of Sycamore Street.
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Many advantages are to be found when moving crowdsourcing applications to the cloud: focus on project development rather than on the infrastructure that supports this process, foster the collaboration between geographically distributed teams, scale resources to the size of the projects, work in a virtualized, distributed, and collaborative environment. Reference Architecture for Software Crowdsourcing The demands on software crowdsourcing systems are ever evolving as new development philosophies and technologies gain favor. The reference architecture presented above is designed to encompass generality in many dimensions including, for example different software development methodologies, incentive schemes, and competitive/collaborative approaches. There are several clear research directions that could be investigated to enhance the architecture such as data analytics, service based delivery, and framework generalization.
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Hi-Octane is a racing and vehicular combat video game released in 1995 for the MS-DOS, PlayStation and Sega Saturn, developed by Bullfrog, and based upon their earlier Magic Carpet game code. It is notable amongst racing games for its wide and open tracks, and the resulting freedom offered to the player, and also for its excessive speed. It suffered in the marketplace due to thematic similarities with the better received Wipeout by Psygnosis and the generality of its graphics engine made for a very short depth of view compared to contemporary racing games. Bullfrog later released an addon pack for Hi-Octane which included additional features made for the Saturn and DOS, including 3 new tracks and new game modes.
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Underlying these hallmarks are genome instability, which generates the genetic diversity that expedites their acquisition, and inflammation, which fosters multiple hallmark functions. Conceptual progress in the last decade has added two emerging hallmarks of potential generality to this list—reprogramming of energy metabolism and evading immune destruction. In addition to cancer cells, tumors exhibit another dimension of complexity: they contain a repertoire of recruited, ostensibly normal cells that contribute to the acquisition of hallmark traits by creating the “tumor microenvironment.” Recognition of the widespread applicability of these concepts will increasingly affect the development of new means to treat human cancer. By November 2010, the paper had been referenced over 15,000 times by other research papers, and was downloaded 20,000 times a year between 2004 and 2007.
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Gromov showed that certain moduli spaces of pseudoholomorphic curves (satisfying additional specified conditions) are compact, and described the way in which pseudoholomorphic curves can degenerate when only finite energy is assumed. (The finite energy condition holds most notably for curves with a fixed homology class in a symplectic manifold where J is \omega-tame or \omega-compatible). This Gromov compactness theorem, now greatly generalized using stable maps, makes possible the definition of Gromov–Witten invariants, which count pseudoholomorphic curves in symplectic manifolds. Compact moduli spaces of pseudoholomorphic curves are also used to construct Floer homology, which Andreas Floer (and later authors, in greater generality) used to prove the famous conjecture of Vladimir Arnol'd concerning the number of fixed points of Hamiltonian flows.
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Another of the most common objections to reliabilism, made first to Goldman's reliable process theory of knowledge and later to other reliabilist theories, is the so-called generality problem. For any given justified belief (or instance of knowledge), one can easily identify many different (concurrently operating) "processes" from which the belief results. My belief that there is a bird in the tree outside my window might be accorded a result of the process of forming beliefs on the basis of sense- perception, of visual sense-perception, of visual sense-perception through non-opaque surfaces in daylight, and so forth, down to a variety of different very specifically described processes. Some of these processes might be statistically reliable, while others might not.
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It follows that every sheaf E has an injective resolution: :0\to E\to I_0\to I_1\to I_2\to \cdots. Then the sheaf cohomology groups Hi(X,E) are the cohomology groups (the kernel of one homomorphism modulo the image of the previous one) of the complex of abelian groups: : 0\to I_0(X) \to I_1(X) \to I_2(X)\to \cdots. Standard arguments in homological algebra imply that these cohomology groups are independent of the choice of injective resolution of E. The definition is rarely used directly to compute sheaf cohomology. It is nonetheless powerful, because it works in great generality (any sheaf on any topological space), and it easily implies the formal properties of sheaf cohomology, such as the long exact sequence above.
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Just as the delegates to the States-General of the Generality could not make any decisions without consulting back with their principals at the States of the provinces, so the delegates to the states of the provinces could not make major decisions without consulting back with their principals in the various cities and towns. As noted above, this lack of delegation of sovereignty led to a fair degree of inertia and would have been unworkable in a larger country less well connected with transport (albeit waterborne canals and shipping) links. It did, however, give the cities and towns a large amount of freedom. Also, the sovereignty of the provincial states was in practice dependent for its exercise on the magistrates of the cities.
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This reduced damping again meant that their tops could vibrate more freely, contributing to the characteristic "humming" sound of viols; yet the absence of a sound post also resulted in a quieter and softer voice overall. It is commonly believed that C-holes (a type and shape of pierced sound port visible on the top face or belly of string instruments) are a definitive feature of viols, a feature used to distinguish viols from instruments in the violin family, which typically had F-shaped holes. This generality, however, renders an incomplete picture. The earliest viols had either large, open, round, sound holes (or even round pierced rosettes like those found on lutes and vihuelas), or they had some kind of C-holes.
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In computer graphics, a silhouette edge on a 3D body projected onto a 2D plane (display plane) is the collection of points whose outwards surface normal is perpendicular to the view vector. Due to discontinuities in the surface normal, a silhouette edge is also an edge which separates a front facing face from a back facing face. Without loss of generality, this edge is usually chosen to be the closest one on a face, so that in parallel view this edge corresponds to the same one in a perspective view. Hence, if there is an edge between a front facing face and a side facing face, and another edge between a side facing face and back facing face, the closer one is chosen.
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The rational maps play a role analogous to the meromorphic functions of complex analysis, and indeed in the case of compact Riemann surfaces the two concepts coincide. If V is now taken to be of dimension 1, we get a picture of a typical algebraic curve C presented 'over' P1(K). Assuming C is non-singular (which is no loss of generality starting with K(C)), it can be shown that such a rational map from C to P1(K) will in fact be everywhere defined. (That is not the case if there are singularities, since for example a double point where a curve crosses itself may give an indeterminate result after a rational map.) This gives a picture in which the main geometric feature is ramification.
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Lyotard's work is characterised by a persistent opposition to universals, métarécits (meta-narratives), and generality. He is fiercely critical of many of the 'universalist' claims of the Enlightenment, and several of his works serve to undermine the fundamental principles that generate these broad claims. In his writings of the early 1970s, he rejects what he regards as theological underpinnings of both Karl Marx and Sigmund Freud: "In Freud, it is judaical, critical sombre (forgetful of the political); in Marx it is catholic. Hegelian, reconciliatory (...) in the one and in the other the relationship of the economic with meaning is blocked in the category of representation (...) Here a politics, there a therapeutics, in both cases a laical theology, on top of the arbitrariness and the roaming of forces".
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A common characteristic of these pre-CSIEA events was that they were organized and managed by a relatively small number of people (in some instances only one person) and as a result, they lacked the generality in purpose and the continuity that a real association should demonstrate. Another weakness was the relatively small target audience of these events, which were mostly limited to friends and acquaintances. With these shortfalls in mind, different groups of people were talking about the possibility of organizing these individual efforts into a more systematic form. In summer of 2004 some of these networking pioneers finally got together and undertook a full-fledged feasibility study on the eventual establishment of a society for Iranian engineers and architects in Ottawa.
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Most legal theorists believe that the rule of law has purely formal characteristics. For instance, such theorists claim that law requires generality (general rules that apply to classes of persons and behaviors as opposed to individuals), publicity (no secret laws), prospective application (little or no retroactive laws), consistency (no contradictory laws), equality (applied equally throughout all society), and certainty (certainty of application for a given situation), but formalists contend that there are no requirements with regard to the content of the law. Others, including a few legal theorists, believe that the rule of law necessarily entails protection of individual rights. Within legal theory, these two approaches to the rule of law are seen as the two basic alternatives, respectively labelled the formal and substantive approaches.
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The Early Modern Age was marked by increasing tension between the power of the Spanish Monarchy and those of the regions. The appointment of a Castilian as Viceroy in 1590, contrary to the agreement all Royal officials be Aragonese caused widespread unrest; when the Madrid authorities attempted to arrest the Aragonese writer and politician Antonio Perez in May 1591, it caused street violence in Zaragossa and a revolt known as the Alterations of Aragon. The unrest was largely confined to Zaragossa and quickly suppressed, with Perez going into exile. Philip then ordered a reduction in the proportion of taxes retained by the Generality of Aragon to lessen their capacity to raise an army against him. Blaeu based on that of João Baptista Lavanha published circa 1640.
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The Mattarella law was technically the accidental result of the combination of different historic events. After WW2, PR was restored for the election of the Chamber of Deputies as it was before the fascist era. The Senate instead was at its first democratic election, so a FPTP was proposed, but the supermajority clause, which was introduced to win a direct mandate, vanished that aim, and the generality of the Senate seats was itself assigned by PR. Constituencies for the Senate effectively were a ”pro forma” in this mechanism of localized lists, so they were not changed when in 1963 a constitutional reform expanded the Parliament with a 33% more seats. In the early 1990s, the Italian political system was largely discredited, and PR was seen as a font of corruption.
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Not every tiling by congruent cubes has this property: for instance, three-dimensional space may be tiled by two- dimensional sheets of cubes that are twisted at arbitrary angles with respect to each other. instead defines a cube tiling to be any tiling of space by congruent hypercubes, and states without proof that the assumption that cubes are axis-parallel can be added without loss of generality. An n-dimensional hypercube has 2n faces of dimension n − 1, that are themselves hypercubes; for instance, a square has four edges, and a three-dimensional cube has six square faces. Two tiles in a cube tiling (defined in either of the above ways) meet face-to-face if there is an (n − 1)-dimensional hypercube that is a face of both of them.
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Generalitat (, literally in English 'Generality') is the name of medieval and early modern political institutions of the ancient Principality of Catalonia and the Kingdom of Valencia as well as, today, the systems of self-government of the Catalonia and the Valencian Spanish autonomous communities. The term is also used for the government of the semi-autonomous comarca of Val d'Aran, the Generalitat a l'Aran. The institution of the Generalitat dates back to the 13th century when the medieval courts of the ancient Principality of Catalonia and the Kingdom of Valencia respectively were created. The term originally referred to a delegation of members of the Corts, who oversaw the implementation of the decisions of the Corts between sessions, and is derived from the Catalan Diputació del General (de Catalunya).
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New valid vanilla sequences can be generated by swapping adjacent elements from another valid vanilla siteswap sequence, adding 1 to the number being swapped to the right and subtracting 1 from the number being swapped to the left. Without loss of generality, the swap property will convert the valid sequence a_0a_1a_2...a_ia_{i+1}...a_{n-1} with arbitrary value i, to generate the new valid sequence a_0a_1a_2...(a_{i+1}+1)(a_i-1)...a_{n-1}. For example, the swap property performed on the inner two throws of the sequence 4413 would move the 4 to the right subtracting 1 from it to become 3 and move the 1 to the left adding 1 to it to become 2. This produces the new valid siteswap pattern 4233.
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How then can we differentiate between regularities or hypotheses that construe law-like statements from those that are contingent or based upon accidental generality? Hempel's confirmation theory argued that the solution is to differentiate between hypotheses, which apply to all things of a certain class, and evidence statements, which apply to only one thing. Goodman's famous counterargument was to introduce the predicate grue, which applies to all things examined before a certain time t just in case they are green, but also to other things just in case they are blue and not examined before time t. If we examine emeralds before time t and find that emerald a is green, emerald b is green, and so forth, each will confirm the hypothesis that all emeralds are green.
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Peter Kropotkin argued in his 1902 book Mutual Aid: A Factor of Evolution that Darwin did not define the fittest as the strongest, or most clever, but recognized that the fittest could be those who cooperated with each other. In many animal societies, "struggle is replaced by co-operation". > It may be that at the outset Darwin himself was not fully aware of the > generality of the factor which he first invoked for explaining one series > only of facts relative to the accumulation of individual variations in > incipient species. But he foresaw that the term [evolution] which he was > introducing into science would lose its philosophical and its only true > meaning if it were to be used in its narrow sense only—that of a struggle > between separate individuals for the sheer means of existence.
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In the Tenth Elucidation, for instance, Malebranche introduced his theory of "intelligible extension", a single, archetypal idea of extension into which the ideas of all particular kinds of bodies could be jointly resolved. In others, Malebranche placed a greater emphasis than he had previously done on his occasionalist account of causation, and particularly on his contention that God acted for the most part through "general volitions" and only rarely, as in the case of miracles, through "particular volitions". Malebranche expanded on this last point in 1680 when he published Treatise on Nature and Grace. Here, he made it explicit that the generality of the laws whereby God regulated His behaviour extended not only to His activity in the natural world but also applied to His gift of grace to human beings.
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Of these " the positive alone is real, the negative is only an abstraction of the other, and in the highest generality even an abstraction of thought itself." A study of the few sentences under this head might have obviated the trifling criticism of Hamilton's objection which has been set afloat recently, that the denial of a knowledge of the absolute or infinite implies a foregone knowledge of it. How can you deny the reality of that which you do not know? The answer to this is that in the case of contradictory statements—A and not A—the latter is a mere negation of the former, and posits nothing; and the negation of a notion with positive attributes, as the finite, does not extend beyond abolishing the given attributes as an object of thought.
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"In Canada the legal definition of a hate crime can be found in sections 318 and 319 of the Criminal Code". In 1996 the federal government amended a section of the Criminal Code that pertains to sentencing. Specifically, section 718.2. The section states (with regard to the hate crime): A court that imposes a sentence shall also take into consideration the following principles: (a) a sentence should be increased or reduced to account for any relevant aggravating or mitigating circumstances relating to the offence or the offender, and, without limiting the generality of the foregoing, (i) evidence that the offence was motivated by bias, prejudice or hate based on race, national or ethnic origin, language, colour, religion, sex, age, mental or physical disability, sexual orientation, or any other similar factor, . . .
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In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure. Non-simply connected 5-manifolds are impossible to classify, as this is harder than solving the word problem for groups.. Simply connected compact 5-manifolds were first classified by Stephen Smale and then in full generality by Dennis Barden, while another proof was later given by Aleksey V. Zhubr. Rather surprisingly, this turns out to be easier than the 3- or 4-dimensional case: the 3-dimensional case is the Thurston geometrisation conjecture, and the 4-dimensional case was solved by Michael Freedman (1982) in the topological case, but is a very hard unsolved problem in the smooth case. In dimension 5, the smooth classification of manifolds is governed by classical algebraic topology.
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In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not quite the same as, powers of prime ideals). The theorem was first proven by for the special case of polynomial rings and convergent power series rings, and was proven in its full generality by . The Lasker–Noether theorem is an extension of the fundamental theorem of arithmetic, and more generally the fundamental theorem of finitely generated abelian groups to all Noetherian rings. The Lasker–Noether theorem plays an important role in algebraic geometry, by asserting that every algebraic set may be uniquely decomposed into a finite union of irreducible components.
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In mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that the Euler-Poincaré characteristic (a topological invariant defined as the alternating sum of the Betti numbers of a topological space) of a closed even- dimensional Riemannian manifold is equal to the integral of a certain polynomial (the Euler class) of its curvature form (an analytical invariant). It is a highly non-trivial generalization of the classic Gauss–Bonnet theorem (for 2-dimensional manifolds / surfaces) to higher even-dimensional Riemannian manifolds. In 1943, Carl B. Allendoerfer and André Weil proved a special case for extrinsic manifolds. In a classic paper published in 1944, Shiing-Shen Chern proved the theorem in full generality connecting global topology with local geometry.
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Lagrange's lectures on the differential calculus at École Polytechnique form the basis of his treatise Théorie des fonctions analytiques, which was published in 1797. This work is the extension of an idea contained in a paper he had sent to the Berlin papers in 1772, and its object is to substitute for the differential calculus a group of theorems based on the development of algebraic functions in series, relying in particular on the principle of the generality of algebra. A somewhat similar method had been previously used by John Landen in the Residual Analysis, published in London in 1758. Lagrange believed that he could thus get rid of those difficulties, connected with the use of infinitely large and infinitely small quantities, to which philosophers objected in the usual treatment of the differential calculus.
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According to historian and author Antonia Fraser, a study of the earliest sermons preached demonstrates an anti-Catholic concentration "mystical in its fervour". Delivering one of five 5 November sermons printed in A Mappe of Rome in 1612, Thomas Taylor spoke of the "generality of his [a papist's] cruelty", which had been "almost without bounds". Such messages were also spread in printed works like Francis Herring's Pietas Pontifica (republished in 1610 as Popish Piety), and John Rhode's A Brief Summe of the Treason intended against the King & State, which in 1606 sought to educate "the simple and ignorant ... that they be not seduced any longer by papists". By the 1620s the Fifth was honoured in market towns and villages across the country, though it was some years before it was commemorated throughout England.
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Suppose two cycles are represented by points [x], [y] ∈ Q. Then x · y = 0 if and only if the corresponding cycles "kiss", that is they meet each other with oriented first order contact. If [x] ∈ S ≅ R2 ∪ {∞}, then this just means that [x] lies on the circle corresponding to [y]; this case is immediate from the definition of this circle (if [y] corresponds to a point circle then x · y = 0 if and only if [x] = [y]). It therefore remains to consider the case that neither [x] nor [y] are in S. Without loss of generality, we can then take x= (1,0,0,0,0) + v and y = (1,0,0,0,0) + w, where v and w are spacelike unit vectors in (1,0,0,0,0)⊥. Thus v⊥ ∩ (1,0,0,0,0)⊥ and w⊥ ∩ (1,0,0,0,0)⊥ are signature (2,1) subspaces of (1,0,0,0,0)⊥.
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A wide range of organisms benefit from organic farming, but it is unclear whether organic methods confer greater benefits than conventional integrated agri- environmental programs. Organic farming is often presented as a more biodiversity-friendly practice, but the generality of the beneficial effects of organic farming is debated as the effects appear often species- and context-dependent, and current research has highlighted the need to quantify the relative effects of local- and landscape-scale management on farmland biodiversity. There are four key issues when comparing the impacts on biodiversity of organic and conventional farming: (1) It remains unclear whether a holistic whole-farm approach (i.e. organic) provides greater benefits to biodiversity than carefully targeted prescriptions applied to relatively small areas of cropped and/or non-cropped habitats within conventional agriculture (i.e.
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Siegel's theorem on integral points occurs in Chapter 28. Mordell's theorem on the finite generation of the group of rational points on an elliptic curve is in Chapter 16, and integer points on the Mordell curve in Chapter 26. In a hostile review of Lang's book, Mordell wrote He notes that the content of the book is largely versions of the Mordell–Weil theorem, Thue–Siegel–Roth theorem, Siegel's theorem, with a treatment of Hilbert's irreducibility theorem and applications (in the style of Siegel). Leaving aside issues of generality, and a completely different style, the major mathematical difference between the two books is that Lang used abelian varieties and offered a proof of Siegel's theorem, while Mordell noted that the proof "is of a very advanced character" (p. 263).
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Radziwiłł's costly visit in Sebeș, where he kept the exceptionally well- trained dragoons as bodyguards, that have personally accompanied him to Ottoman Turkey and joined the Confederate in the spring of 1771, lavish lifestyle and hosting or supporting many wealthy, but demanding members of the Generality forced him into ever greater debt, however, Radziwiłł successfully defended himself from selling any personal assets. He rather preferred to increase the debt instead. Upon receiving the news about his stepmother's rapidly deteriorating health, he left in March 1771 for Dresden. Because of the vivid support of the commander of the Prussian army, occupying the Pomeranian provinces in the northern part of the Polish–Lithuanian Commonwealth, Radziwiłł was able to keep the city of Człuchów following his stepmother's sudden death on March 19, 1771.
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Until the 1990s, simple adaptive models, such as Cournot competition or fictitious play, were generally used. In the mid-1990s, Alvin E. Roth and Ido Erev demonstrated that reinforcement learning can make useful predictions in experimental games.Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria,Ido Erev, Alvin E Roth,American economic review,1998/9/1,848-881 In 1999, Colin Camerer and Teck-Hua Ho introduced Experience Weighted Attraction (EWA), a general model that incorporated reinforcement and belief learning, and shows that fictitious play is mathematically equivalent to generalized reinforcement, provided weights are placed on past history. Criticisms of EWA include overfitting due to many parameters, lack of generality over games, and the possibility that the interpretation of EWA parameters may be difficult.
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Flags of the provinces near the Hofvijver in The Hague Nearly all Dutch provinces can trace their origin to a medieval county or duchy, as can the provinces of regions in Belgium. Their status changed when they came under a single ruler who centralised their administration, reducing their powers. There were 17 in total: from these unified Netherlands, seven northern provinces from 1588 formed the Republic of the Seven United Provinces, namely Holland, Zeeland, Gelderland, Utrecht, Friesland, Overijssel and Groningen. The Republic's lands also included Drenthe (one of the 17, but without the autonomous status of the others), and parts of the Duchy of Brabant, Duchy of Limburg and County of Flanders, which were considered to be "conquered lands" and were governed directly by the States General, hence their name Generality Lands.
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He compared him to Andreas Lubitz, the pilot who shortly before the report's release had deliberately crashed a Germanwings flight into the side of a French mountain, killing 149 passengers and crew in addition to himself, and was later found to have been suffering from depression severe enough that he feared losing his commercial pilot's license. "As I write with tears about my friend, John," Bateman wrote, "I recognize that mental depression must just completely overwhelm a person's normal judgment." Although he had agreed with Sheridan about the failings of the state medical examiner system, Weedn defended Lilavois' conclusion. Based on reviewing the autopsy reports, he found the couple's injuries "more consistent as a generality with a murder-suicide", although he qualified that by saying he had not seen the photos.
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Historically this equation arose as a variant on the Prony equation; this variant was developed by Henry Darcy of France, and further refined into the form used today by Julius Weisbach of Saxony in 1845. Initially, data on the variation of with velocity was lacking, so the Darcy–Weisbach equation was outperformed at first by the empirical Prony equation in many cases. In later years it was eschewed in many special-case situations in favor of a variety of empirical equations valid only for certain flow regimes, notably the Hazen–Williams equation or the Manning equation, most of which were significantly easier to use in calculations. However, since the advent of the calculator, ease of calculation is no longer a major issue, and so the Darcy–Weisbach equation's generality has made it the preferred one.
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Evolutionarily speaking, offspring have a greater bond to mothers than fathers; women are universally known to be the direct caregivers in a parent- offspring relationship, whereas males are seen as material resource providers or involved only with their own reproductive success. Women have the "maternal instinct" to aid, assist, embrace and invest in their offspring. Males are evolutionarily known to invest less due to paternal uncertainty and therefore seek as many sexual partners and seek for an increase of their genes amongst society.Gilding, Michael, "Paternity uncertainty and evolutionary psychology: How a seemingly capricious occurrence fails to follow laws of greater generality", Sociology, pages 140-157 However, males also have a role in securing a connection with the offspring by taking part in making an offspring's decisions when involved in a household.
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In 1736 he published at Dublin Sixteen Irish Sermons, in an easy and familiar stile, on useful and necessary subjects, in English characters, as being the more familiar to the generality of our Irish clergy. In his preface the author mentioned that he had composed those discourses principally for the use of his fellow-labourers, to be preached to their respective flocks, as his repeated troubles debarred him "of the comfort of delivering them in person". He added: > I have made them in an easy and familiar style, and of purpose omitted cramp > expressions which be obscure to both the preacher and hearer. Nay, instead > of such, I have sometimes made use of words borrowed from the English which > practice and daily conversation have intermixed with our language.
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In 1978, the autonomy process was initiated in Morella, culminating in the Statute of Autonomy of the Valencian Community. The President of the Valencian Generality, Josep Lluís Albinyana, convened a meeting of the Council of the Valencian Country on December 29, 1978, which was prevented by a heavy snowfall, and finally held on January 9, 1979. In that cold fifteenth-century Gothic hall of the Morella City Council, the proposal of President Albinyana was agreed upon, and by unanimous agreement of the parties PSOE, UCD, PCE, PSP and AP, the autonomy process, of the then officially named "Valencian Country", was initiated, in accordance with Article 151 of the Spanish Constitution, "in order to achieve the most perfect institutionalization of the Valencian community, for obtaining the maximum possible powers of self-government".
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Its service covers Urumqi, the capital of Xinjiang, and many regions under the XPCC, and several other provinces in China. On July 1, 2008, Bingtuan Television was rendered meliorative, with the generality modified by concentrating on music programs, in an effort to become the top youth music channel in China. However, after the July 5 Urumqi riots, State Administration of Radio, Film, and Television demanded for BTTV to rectify its contents;82频道节目调整公告 ，杭州华数在线 BTTV had to cancel the previously planned entertainment-centered projects made by the specialized program production company based in Urumqi and Beijing, routinely rebroadcasting CCTV-1, the primary channel of China Central Television. BTTV only keep some of its original programs, sucu as the Bingtuan News and soap operas.
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Formalist accounts collapse because they depend upon a theory of plain meaning that can only be accepted if one accepts the doctrine of intelligible essences, which liberalism must reject. A purposive account of legal justice, which holds that judges must consider the purposes and policies of laws they apply, in order to apply them correctly and uniformly, results in judges applying their own subjective preferences, and there is no method of choice among the many policies that may compete for the judge's attention in finding a rationale for decision. Ultimately, purposive adjudication results in the exercise of instrumental rationality, which cannot pretend to have stability or generality, thus it is fatal to the aims of legal justice. Substantive justice does not offer hope for the liberal seeking a basis for a coherent theory of adjudication.
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Milgrom and Roberts build on their work in supermodular games to understand the processes by which strategic agents reach equilibrium in a normal-form game. In Milgrom and Roberts (1991), they proposed two learning processes each with a degree of generality so as to not model learning but learning processes. They considered a sequence of plays over time which, for a player n, is denoted {xn(t)} where for each possible time, t, xn(t) is a pure strategy. Given this, an observed sequence, {xn(t)}, is consistent with adaptive learning if a player n eventually chooses only strategies that are nearly best-replies to some probability distribution over the joint strategies of other players (with near zero probability being assigned to strategies that have not been played for a sufficiently long time).
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Justice Stevens, J. wrote, in partial dissent: :The basic premise underlying the Court’s ruling is its iteration, and constant reiteration, of the proposition that the First Amendment bars regulatory distinctions based on a speaker’s identity, including its "identity" as a corporation. While that glittering generality has rhetorical appeal, it is not a correct statement of the law. Nor does it tell us when a corporation may engage in electioneering that some of its shareholders oppose. It does not even resolve the specific question whether Citizens United may be required to finance some of its messages with the money in its PAC. The conceit that corporations must be treated identically to natural persons in the political sphere is not only inaccurate but also inadequate to justify the Court’s disposition of this case.
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A tight lower bound is not known on the number of required additions, although lower bounds have been proved under some restrictive assumptions on the algorithms. In 1973, Morgenstern proved an Ω(N log N) lower bound on the addition count for algorithms where the multiplicative constants have bounded magnitudes (which is true for most but not all FFT algorithms). This result, however, applies only to the unnormalized Fourier transform (which is a scaling of a unitary matrix by a factor of \sqrt N), and does not explain why the Fourier matrix is harder to compute than any other unitary matrix (including the identity matrix) under the same scaling. Pan (1986) proved an Ω(N log N) lower bound assuming a bound on a measure of the FFT algorithm's "asynchronicity", but the generality of this assumption is unclear.
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At other times the ladies associated with the cup and the oratory performed baptisms and weddings though without the labels of being priests or priestesses. Meanwhile Pole went on to meet with ʻAbdu'l-Bahá again in late 1910 in Egypt and sent a letter to Scotland with second had reports from ʻAbdu'l-Bahá of a prediction of a World War in light of the anticipated Armageddon of the Book of Revelation and beyond to the generality of the 20th century. Writer Patrick Benham related Pole learning of ʻAbdu'l-Bahá only in 1910 through Archdeacon Wilberforce. Pole felt a healing presence and a confirmation of ʻAbdu'l-Bahá "as a world teacher" (in the words of writer Patrick Benham.) Pole went on to then have his own visions of the same ideas of this foretold conflict after returning home.
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On this view, infants and children are essentially proto-scientists because they regularly use a kind of scientific method, developing hypotheses, performing experiments via play, and updating models about the world based on their results. For Gopnik, this use of scientific thinking and categorization in development and everyday life can be formalized as models of Bayesian inference. An application of this view is the "sampling hypothesis," or the view that individual variation in children's causal and probabilistic inferences is an artifact of random sampling from a diverse set of hypotheses, and flexible generalizations based on sampling behavior and context. These views, particularly those advocating general Bayesian updating from specialized theories, are considered successors to Piaget’s theory rather than wholesale refutations because they maintain its domain-generality, viewing children as randomly and unsystematically considering a range of models before selecting a probable conclusion.
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Open form is a term coined by Heinrich Wölfflin in 1915 to describe a characteristic of Baroque art opposed to the "closed form" of the Renaissance . Wölfflin tentatively offered several alternative pairs of terms, in particular "a-tectonic" and "tectonic" (also free/strict and irregular/regular), but settled on open/closed because, despite their undesirable ambiguity, they make a better distinction between the two styles precisely because of their generality. In an open form, which is characteristic of 17th-century painting, the style "everywhere points out beyond itself and purposely looks limitless", in contrast to the self- contained entity of a closed form, in which everything is "pointing everywhere back to itself" . In general, the closed compositions of the 16th century are dominated by the vertical and horizontal, and by the opposition of these two dimensions.
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Casimir Pulaski fought in the Confederation of Bar uprising and in the American War of Independence The szlachta challenges in the meantime picked up steam, as new confederations were being established in the western Crown provinces and in the Grand Duchy of Lithuania. A rebellion in Kraków, which took place soon after the fall of Bar, ended in capitulation after a month-long siege, but it was apparent that the fighting would go on. The outbreak of the Russo-Turkish War in October 1768 gave rise to new hopes for the confederates. France, in whose interest was the weakening of Russia, incited the Ottoman Empire to fight Russia and supported the confederate insurgents with money, arms and professional military cadres, while Austria provided asylum for the confederate supreme authority (the so-called Generality) that had been formed in 1769 in Biała.
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Inspired by both Darwinian principles of natural evolution and Dawkins' notion of a meme, the term “Memetic Algorithm” (MA) was introduced by Pablo Moscato in his technical report in 1989 where he viewed MA as being close to a form of population-based hybrid genetic algorithm (GA) coupled with an individual learning procedure capable of performing local refinements. The metaphorical parallels, on the one hand, to Darwinian evolution and, on the other hand, between memes and domain specific (local search) heuristics are captured within memetic algorithms thus rendering a methodology that balances well between generality and problem specificity. This two-stage nature makes them a special case of Dual-phase evolution. In a more diverse context, memetic algorithms are now used under various names including Hybrid Evolutionary Algorithms, Baldwinian Evolutionary Algorithms, Lamarckian Evolutionary Algorithms, Cultural Algorithms, or Genetic Local Search.
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While their educational programs tend to include a diverse array of Muslim academic texts, few adherents of the movement ascribe themselves to one school of Muslim jurisprudence, placing a greater emphasis on personal responsibility to derive judgments and ritual practice. While the movement's figureheads have ascribed to the Zahirite legal school, with a great number of them preferring the works of Yemeni scholar Shawkani, the generality of the movement is described as respecting all Sunni schools of Islamic law while preferring to take directly from the Qur'an, prophetic tradition and consensus of the early generations of Muslims. While the movement has been compared to Salafist movement in Arab nations and been branded as Wahhabist by the opposing Barelwi movement, the Ahl-i Hadith remain similar to yet distinct from Salafists.Mathieu Guidère, Historical Dictionary of Islamic Fundamentalism, pg. 177.
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The seven northern provinces gained their independence as a republic called the Seven United Provinces. They were: # the Lordship of Groningen and of the Ommelanden # the Lordship of Friesland # the Lordship of Overijssel # the Duchy of Guelders (except its upper quarter) and the county of Zutphen # the prince-bishopric, later lordship of Utrecht # the county of Holland # the county of Zeeland The southern provinces – Flanders, Brabant, Namur, Hainaut, Luxembourg and so forth – were restored to Spanish rule thanks to the military and political talent of the Duke of Parma, especially at the siege of Antwerp (1584-1585). Hence, these Provinces became known as the Spanish Netherlands or the Southern Netherlands. The northern Seven United Provinces kept parts of Limburg, Brabant and Flanders during and after the Eighty Years' War (see Generality Lands), which ended with the Treaty of Westphalia in 1648.
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In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of "exponential family", or the older term Koopman–Darmois family. The terms "distribution" and "family" are often used loosely: properly, an exponential family is a set of distributions, where the specific distribution varies with the parameter; however, a parametric family of distributions is often referred to as "a distribution" (like "the normal distribution", meaning "the family of normal distributions"), and the set of all exponential families is sometimes loosely referred to as "the" exponential family.
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Evolutionary psychologists generally presume that, like the body, the mind is made up of many evolved modular adaptations, although there is some disagreement within the discipline regarding the degree of general plasticity, or "generality," of some modules. It has been suggested that modularity evolves because, compared to non-modular networks, it would have conferred an advantage in terms of fitness and because connection costs are lower. In contrast, some academics argue that it is unnecessary to posit the existence of highly domain specific modules, and, suggest that the neural anatomy of the brain supports a model based on more domain general faculties and processes. Moreover, empirical support for the domain-specific theory stems almost entirely from performance on variations of the Wason selection task which is extremely limited in scope as it only tests one subtype of deductive reasoning.
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This article assumes that the rotation is also stable, such that no torque is required to keep it going. The kinematics and dynamics of rotation around a fixed axis of a rigid body are mathematically much simpler than those for free rotation of a rigid body; they are entirely analogous to those of linear motion along a single fixed direction, which is not true for free rotation of a rigid body. The expressions for the kinetic energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than for general rotational motion. For these reasons, rotation around a fixed axis is typically taught in introductory physics courses after students have mastered linear motion; the full generality of rotational motion is not usually taught in introductory physics classes.
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From 1237 the Count of Auxonne was replaced in the chain of vassalage by the Duke of Burgundy following an exchange of lands between Hugh IV, Duke of Burgundy and John, Count of Chalon. From 1366 to the French Revolution the Lordship of Athée was held by co-lords who were canons of Sainte-Chapelle de Dijon on the one hand and Lay Lords (the Laverne, Senevoy, Moussier families) on the other. In 1516 the lordship became subject to the Kingdom of France and depended on the bailiwick of Auxonne and the Généralité de Bourgogne (Generality of Burgundy).An administrative division created in 1542 with its seat in Dijon Between 1790 and 1794 Athée, separately from Poncey and Magny, became a French commune depending on the Canton of Auxonne, the district of Saint-Jean-de-Losne, and the department of Côte-d'Or.
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Bishop Josif was born in 1743 in Irig to reverend father Andrija Jovanović, the younger brother of Patriarch Arsenije IV Jovanović Šakabenta and Peško Jovanović Šakabenta. Priest Andrija died in 1759. The brothers, Arsenije, Andrija, and Peško and their family members, were granted Hungarian nobility on 11 September 1746."Српски сион", Сремски Карловци 30. мај 1899. Josif was ordained a presbyter and later elevated once again in 1774 by the Metropolitan Vićentije Jovanović Vidak to archimandrite. On 31 July 1781, Metropolitan Mojsije Putnik consecrated him to the Bishop of Pakrac- Slavonian and the entire Generality of Varaždin. One of the first and most important jobs that the new Bishop of Pakrac had to do was suppress the union because it was at this time that it started a new and very lively action in the General Staff of Varaždin.
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Article XIII of the Union of Utrecht stipulated that the regulation of religion was a matter of policy for the individual provinces (so not of the "Generality"). It first reaffirmed the provision in the Pacification of Ghent, which gave the States of Holland and the States of Zeeland full discretion in religious matters in their jurisdictions, while the other provinces were constrained by the provisions of the "religious peace" previously promulgated by Archduke MatthiasAt the time the treaty was concluded (January 1579) the signatories were still formally members of the Union of Brussels who accepted Matthias as governor-general of the Habsburg Netherlands. Matthias had promulgated the "religious peace" (on the advice of William the Silent) in 1578. The article also provided that no province would be authorized to intervene in religious matters in another province.
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Back to My Mac was a feature introduced with Mac OS X Leopard (10.5) that uses Wide-Area Bonjour to securely discover services across the Internet and automatically configure ad hoc, on-demand, point-to-point encrypted connections between computers using IPsec. The current version of the feature requires users to have iCloud set up, as well as an Apple ID. Due to its generality, Back to My Mac can work for many Bonjour-enabled services, not just Screen Sharing (similar to Apple Remote Desktop) and File Sharing. Users must have a router that supports either Universal Plug and Play (UPnP) or NAT Port Mapping Protocol (NAT-PMP) with either of those features enabled in their connected router. It uses UDP port 4500 for point-to-point IPsec connections (which may be mapped to different UDP ports on the public side of a NAT router).
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Though disapproving of Cromwell's action in dissolving the Rump Parliament in April 1653, Ludlow maintained his employment. However, when Cromwell was declared Lord Protector after the failure of Barebone's Parliament he declined to acknowledge his authority. According to his Memoirs he believed that Cromwell "had not appeared that he ever approved on any persons farther than he might make them subservient to his own ambitious designs; ...and that the generality of the people that had engaged with us having acted upon no higher principles than those of civil liberty, and that they might be governed by their own consent, it could not be just to treat them in another manner upon any pretenses whatsoever."The Memoirs of Edmund Ludlow, Lieutenant-General of the Horse in the Army of the Commonwealth of England 1625–1672 Edited with Appendices of Letters and Illustrative Documents by C. A. Firth, M.A., in two volumes. v.
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In addition to facilitating applied tariff reductions, the early GATT's contribution to trade liberalization "include binding the negotiated tariff reductions for an extended period (made more permanent in 1955), establishing the generality of nondiscrimination through most-favored nation (MFN) treatment and national treatment status, ensuring increased transparency of trade policy measures, and providing a forum for future negotiations and for the peaceful resolution of bilateral disputes. All of these elements contributed to the rationalization of trade policy and the reduction of trade barriers and policy uncertainty." According to Dartmouth economic historian Douglas Irwin, > The prosperity of the world economy over the past half century owes a great > deal to the growth of world trade which, in turn, is partly the result of > farsighted officials who created the GATT. They established a set of > procedures giving stability to the trade-policy environment and thereby > facilitating the rapid growth of world trade.
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Sometimes, grammatical number will not represent the actual quantity. For example, in Ancient Greek neuter plurals took a singular verb.“Learn Ancient Greek: 11_Unit 2 Agreement Infinitives Questions”, video tutorial by Leonard Muellner and Belisi Gillespie at Center for Hellenic Studies at Harvard University, published January 25, 2018; retrieved May 30, 2018 The plural form of a pronoun may also be applied to a single individual as a sign of importance, respect or generality, as in the pluralis majestatis, the T-V distinction, and the generic "you", found in many languages, or, in English, when using the singular "they" for gender- neutrality. In Arabic, the plural of a non-human noun (one that refers to an animal or to an inanimate entity regardless of whether the noun is grammatically masculine or feminine in the singular) is treated as feminine singular—this is called the inanimate plural.
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It is a commonly held fallacy that the main functions of the nave and aisles of a church are to seat as many people as possible. That had certainly not been the case in medieval times, when the nave and aisles were regarded not as an auditorium filled with a static body of people in fixed seats, but as a liturgical space in which there was movement and drama (for example the festal processions on high days and holy days, and the penitential processions in Lent). Though benches were not uncommon in medieval times, fixed seating as a generality came about only after the Reformation, and the arrangements in early nineteenth-century Catholic chapels were little different from those of Nonconformist ones, with seating often running right across the width of the building, and with galleries to provide extra accommodation. Pugin would have no such "protestantisms" at Cheadle.
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In March 2012, Motley Rice was ordered to pay ITT Educational Services almost $400,000 in legal fees for pursuing a "frivolous" lawsuit the judge said was "based on a completely false story."Daniel Fisher, Judge Slaps Motley Rice With Fees Over "Frivolous" Lawsuit, Forbes, 28 March 2012Martha Neil, Federal Judge: Motley Rice, 2 Other Law Firms Must Pay $395K in Legal Fees re ‘Frivolous’ Suit, ABA Journal, 28 March 2012 On review, the 7th US Circuit Court of Appeals reversed the order and reinstated the lawsuit against ITT.Molly McDonough, 7th Circuit erases $400K sanction against Motley Rice, revives whistleblower case, ABA Journal, 10 July 2013 The Court of Appeals was critical of the lower court's dismissal, writing, "[W]e believe that Leveski's case is yet another instance of a district court dismissing an [False Claims Act] suit after viewing the allegations at too high a level of generality." Leveski v.
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This consideration of alternatives was the first major instance of underdetermination in the history of science (where the same observational evidence equally supports two, logically different hypotheses), although the historical agents were unaware of the epistemological generality of that problem. It resulted in new kinds of controversies and raised unprecedented questions about weighting the criteria for adjudicating among different hypotheses, including ancient authority, scriptural compatibility, simplicity, explanatory breadth, predictive accuracy and physical coherence. 7\. The second generation followers of Copernicus (Michael Maestlin [1550-1631], Thomas Digges [1546-1595], Giordano Bruno [1548-1600], Christopher Rothmann [ca. 1550-1600]) did not constitute a socially- and intellectually-unified movement. And the failure of the high-profile third- generation proponents Johannes Kepler (1571-1630) and Galileo Galilei (1564-1638) to forge a cooperative and productive alliance around their defense of the Copernican theory is a particularly notable instance of this larger pattern of disunity. 8\.
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Her book Tracking Truth presents a unified treatment of knowledge, evidence, and epistemological realism and anti-realism about science, based on the idea that knowing is responsiveness to the way the world is, and that this is an ability to follow the truth through time and changing circumstances. Responsiveness is defined for empirical knowledge by a reformulation of Robert Nozick’s tracking conditions—for example: if p were false, then S wouldn't believe p—using conditional probability instead of counterfactuals. Roush argues that the new tracking view is superior to other externalist views of knowledge, including process reliabilism. Of particular interest are the new view's fallibilist account of knowledge of logical truth, its treatment of reflective knowledge and lottery propositions, its solutions to the value problem and the generality problem, its implications about skepticism, and its explanation of why knowledge is power in the Baconian sense.
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This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality. Diophantine geometry in general is the study of algebraic varieties V over fields K that are finitely generated over their prime fields—including as of special interest number fields and finite fields—and over local fields. Of those, only the complex numbers are algebraically closed; over any other K the existence of points of V with coordinates in K is something to be proved and studied as an extra topic, even knowing the geometry of V. Arithmetic geometry can be more generally defined as the study of schemes of finite type over the spectrum of the ring of integers.
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He eventually divided (philosophical) logic, or formal semiotics, into (1) speculative grammar, or stechiology on the elements of semiosis (sign, object, interpretant), how signs can signify and, in relation to that, what kinds of signs, objects, and interpretants there are, how signs combine, and how some signs embody or incorporate others; (2) logical critic, or logic proper, on the modes of inference; and (3) speculative rhetoric, or methodeutic, the philosophical theory of inquiry, including his form of pragmatism. His speculative grammar, or stechiology, is this article's subject. Peirce conceives of and discusses things like representations, interpretations, and assertions broadly and in terms of philosophical logic, rather than in terms of psychology, linguistics, or social studies. He places philosophy at a level of generality between mathematics and the special sciences of nature and mind, such that it draws principles from mathematics and supplies principles to special sciences.
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Quantum tunneling was first noticed in 1927 by Friedrich Hund when he was calculating the ground state of the double-well potential and independently in the same year by Leonid Mandelstam and Mikhail Leontovich in their analysis of the implications of the then new Schrödinger wave equation for the motion of a particle in a confining potential of a limited spatial extent. Its first application was a mathematical explanation for alpha decay, which was done in 1928 by George Gamow (who was aware of the findings of Mandelstam and Leontovich) and independently by Ronald Gurney and Edward Condon. The two researchers simultaneously solved the Schrödinger equation for a model nuclear potential and derived a relationship between the half-life of the particle and the energy of emission that depended directly on the mathematical probability of tunnelling. After attending a seminar by Gamow, Max Born recognised the generality of tunnelling.
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Members of the Council are also the Trustees of the Association. 36\. In 1962 Article 5(b) of the Royal Charter was amended to give the objects that we would recognise today: “To promote the Welfare by charitable means of those serving or have served in Our Air Forces, their wives and dependants and the widows and dependants of those who died either while serving in Our Air Forces or thereafter and, without prejudice to the generality of the foregoing:- (i) To preserve the memory and honour by charitable means, of comrades or members, of the Association who have died in Our Service. (ii) To advise members of the Association, persons eligible for membership and their wives, widows and dependants regarding service and other pensions, disability awards and civilian employment and to assist by charitable means such members and persons when sick or in need of assistance.
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The argument centered on the inequality shown above, crucial to the solution of the Cambridge equation, namely on: Samuelson and Modigliani proposed that the following inequality (which they called anti- Pasinetti's inequality) was also reasonable, and claimed that it would endow the model with greater generality: Such inequality, however, requires that the workers' propensity to save becomes so high as to allow them to accumulate capital at a greater speed than capitalists. If this were to happen, in the end the total capital of the economy would entirely be owned by the workers, while the capitalists would disappear. The formulation of the anti-Pasinetti range and all theoretical justification (and some empirical exercises) proposed by Samuelson and Modigliani was challenged by PasinettiPasinetti [1974], essay 6. and in a much more critical way by KaldorKaldor, N. [1966], “Marginal Productivity and the Macroeconomic Theories of Distribution: Comment on Samuelson and Modigliani”, Review of Economic Studies, XXXIII, October, pp. 309-19.
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It implies that the optimal win probability is always at least 1/e (where e is the base of the natural logarithm), and that the latter holds even in a much greater generality (2003). The optimal stopping rule prescribes always rejecting the first \sim n/e applicants that are interviewed and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs). Sometimes this strategy is called the 1/e stopping rule, because the probability of stopping at the best applicant with this strategy is about 1/e already for moderate values of n. One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.
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The problem of multiple generality names a failure in traditional logic to describe certain intuitively valid inferences. For example, it is intuitively clear that if: :Some cat is feared by every mouse then it follows logically that: :All mice are afraid of at least one cat The syntax of traditional logic (TL) permits exactly four sentence types: "All As are Bs", "No As are Bs", "Some As are Bs" and "Some As are not Bs". Each type is a quantified sentence containing exactly one quantifier. Since the sentences above each contain two quantifiers ('some' and 'every' in the first sentence and 'all' and 'at least one' in the second sentence), they cannot be adequately represented in TL. The best TL can do is to incorporate the second quantifier from each sentence into the second term, thus rendering the artificial-sounding terms 'feared-by- every-mouse' and 'afraid-of-at-least-one-cat'.
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Nonetheless, some physicists continued to doubt whether radiation would be produced by a binary star system, where the world lines of the centers of mass of the two stars should, according to the EIH approximation (dating from 1938 and due to Einstein, Infeld, and Banesh Hoffmann), follow timelike geodesics. Inspired by conversations by Felix Pirani, Hermann Bondi took up the study of gravitational radiation, in particular the question of quantifying the energy and momentum carried off 'to infinity' by a radiating system. During the next few years, Bondi developed the Bondi radiating chart and the notion of Bondi energy to rigorously study this question in maximal generality. In 1957, at a conference at Chapel Hill, North Carolina, appealing to various mathematical tools developed by John Lighton Synge, A. Z. Petrov and André Lichnerowicz, Pirani explained more clearly than had previously been possible the central role played by the Riemann tensor and in particular the tidal tensor in general relativity.
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The highest observed neutron star mass is two solar masses, with a conservative upper limit for the mass of a stable neutron star of three solar masses, so that a pair of neutron stars would not have had sufficient mass to account for the merger (unless exotic alternatives exist, for example, boson stars), while a black hole-neutron star pair would have merged sooner, resulting in a final orbital frequency that was not so high. The decay of the waveform after it peaked was consistent with the damped oscillations of a black hole as it relaxed to a final merged configuration. Although the inspiral motion of compact binaries can be described well from post-Newtonian calculations, the strong gravitational field merger stage can only be solved in full generality by large-scale numerical relativity simulations. In the improved model and analysis, the post-merger object is found to be a rotating Kerr black hole with a spin parameter of , i.e.
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Raid on the Medway of 9–14 June 1667 By early-1667, the financial position of the English crown had become desperate. The kingdom lacked sufficient funds to maintain their fleet's seaworthiness, so it was decided in February that the heavy ships were to remain laid up at Chatham, with only a small Flying Fleet manned to attack Dutch merchant shipping, which lowered morale in the fleet and prevented merchant ship from sailing and colliers from reaching London without fear of Dutch interception. Clarendon informed Charles as to his only two options: to make very substantial concessions to Parliament, or to initiate peace talks with the Dutch under their conditions, which began in March. Charles had wished for peace talks to be held in England or, failing that, at the Hague, but the Dutch offered three other cities where support for the House of Orange was less and Charles selected Breda, in the southern Generality Lands.
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His socio-economic contribution in the state is to date a point of reference to the generality of the people and many aspiring leaders. Some of his major achievements during his brief first term of office include the establishment of three different housing schemes for public officers consisting of over 1,500 housing units in Lokoja, the transformation of Lokoja township with asphalt roads, street lights, aesthetic roundabouts, the construction of inter-township and rural roads, over 75 electrification schemes and 50 water projects. Others include the founding of Kogi State Polytechnic, the establishment of a television station, radio station (both AM and FM), a state newspaper (The Graphic) and the transformation of the colonial residence of Lord Lugard into an ultra modern government house complex, the construction of office blocks for ministries as the new state had no office accommodation, the construction of shopping arcade complex to enhance commercial activities, among others.
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The House of Commons Voting on the Family of Action Plan in Budapest, Hungary. This would be an example of the general will espoused by Rousseau. According to Thompson, the general will has three rules that have to be obeyed in order for the general will to function as intended: (1) the rule of equality—no unequal duties are to be placed upon any other community member for one's personal benefit or for that of the community; (2) the rule of generality—the general will's end must be applicable to the likewise needs of citizens, and all the members' interests are to be accounted for; (3) the rule of non-servitude—no one has to relinquish themselves to any other member of the community, corporation, or individual, nor do they have to be subordinate to the mentioned community's, corporation's, or individuals' interests or wills. Nonetheless, there are ways in which the general will can fail, as Rousseau mentioned in The Social Contract.
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But if one did not make that assumption, then the simplest definition might not be the right one for the most useful concept; in any case, it would destroy the (transitive) entailment of Ti by Tj, allowing (for example) non-Hausdorff regular spaces. Topologists working on the metrisation problem generally did assume T1; after all, all metric spaces are T1. Thus, they used the simplest definitions for the Ti. Then, for those occasions when they did not assume T1, they used words ("regular" and "normal") for the more complicated definitions, in order to contrast them with the simpler ones. This approach was used as late as 1970 with the publication of Counterexamples in Topology by Lynn A. Steen and J. Arthur Seebach, Jr. In contrast, general topologists, led by John L. Kelley in 1955, usually did not assume T1, so they studied the separation axioms in the greatest generality from the beginning.
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His result says that if the hypersurface is sufficiently convex relative to the geometry of the Riemannian manifold, then the mean curvature flow will contract it to a point, and that a normalization of surface area in geodesic normal coordinates will give a smooth deformation to a sphere in Euclidean space (as represented by the coordinates). This shows that such hypersurfaces are diffeomorphic to the sphere, and that they are the boundary of a region in the Riemannian manifold which is diffeomorphic to a ball. In this generality, there is not a simple proof using the Gauss map. Following work of Yoshikazu Giga and Robert Kohn which made extensive use of the Dirichlet energy as weighted by exponentials, Huisken proved in 1990 an integral identity, known as Huisken's monotonicity formula, which shows that, under the mean curvature flow, the integral of the "backwards" Euclidean heat kernel over the evolving hypersurface is always nonincreasing.
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After the American example, he advised that the seven regions of the Netherlands and the Generality Lands be forced to give up their sovereignty and administrations, to be replaced by a whole new constitution in which the people's influence on the election of the regents would be hugely increased. The Van Staphorst brothers, along with Wilhelm Willink and Rutger Jan Schimmelpenninck, were in 1789 shareholders in the Holland Land Company, a society that invested in the north of the state of New York, not far from Ontario, Pennsylvania and some canals: the Patowmack Canal, James River and Kanawha Canal and Santee Canal. He supported Gerrit Boon, his brother-in-law, winning maple syrup from the ahorn. Nicolaas and the secret political societies which were formed were of the opinion that this issue had to be resolved at all costs, and that Johan Valckenaer and his friends were the most appropriate people to draw up a Dutch-language constitution.
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There is a historical reference to Dewar in the 'Ragman Rolls', which is described as '..the Submission and Fealty sworne by the Generality of all the Scots Nation to King Edward I between the years 1292 to 1298’. It records a Thomas de Dewere and Piers de Dewere, both of the place Dewar in the parish of Heriot, Midlothian in the county of Edinburgh, 'did render true and rightful homage to King Edward I of England' at Berwick-on-Tweed on the 28th day of August in the year 1296. In the ‘Scottorum Historiae’ (1527) Hector Boece suggests that Thomas de Dewere and Piers de Dewere were descendants of a Malcolm Robert Dewere, formerly of Ewich near Strathfillan and Glen Dochart, who received land in Heriot as a reward for slaying a marauding wolf 'muckle feart' in the district. Malcolm named this land as Dewere, now Dewar, and was known thereafter as Malcolm de Dewere or 'Dewer the Wolf'.
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In 1758, with the aid of his pupils (mainly with Daviet), Lagrange established a society, which was subsequently incorporated as the Turin Academy of Sciences, and most of his early writings are to be found in the five volumes of its transactions, usually known as the Miscellanea Taurinensia. Many of these are elaborate papers. The first volume contains a paper on the theory of the propagation of sound; in this he indicates a mistake made by Newton, obtains the general differential equation for the motion, and integrates it for motion in a straight line. This volume also contains the complete solution of the problem of a string vibrating transversely; in this paper he points out a lack of generality in the solutions previously given by Brook Taylor, D'Alembert, and Euler, and arrives at the conclusion that the form of the curve at any time t is given by the equation y = a \sin (mx) \sin (nt)\,.
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The FonF (focus on form) model of practice introduced by Bahari (2019a) was prepared and contextualized based on the effectiveness of FonF-based instruction for its potential for incidental and preplanned L2 learning (Bahari, 2018a; Fredricks, Blumenfeld, & Paris, 2004; Nassaji, 1999, 2016; Nassaji & Fotos, 2007, 2011; Williams, 2005). The FonF practice model has proved effective in catering for learners’ nonlinear and dynamic motivational factors at individual level and taking advantage of the CALL affordances towards developing listening and speaking skills (Bahari, 2019a). In keeping with Nassaji and Fotos (2011) the FonF is considered as an optimal approach for learning which aims at mixing the best features of classroom L2 learning with computer-assisted L2 learning by using CALL tools and applications to facilitate L2 learning process. In contrast to previous L2 learning practice models sharing the feature of generality at group level, the FonF practice model addresses the nonlinearity and dynamicity of individual differences during learning process (Bahari, 2018a).
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In late July, he again decided to continue his journey to Ottoman Turkey. He requested, however, that this diplomatic mission was to be short, not because he wished to stay away from the Generality and the dangerous or risky politics, but fearing that A. Krasiński might attract the adherents of the Czartoryski family. On September 20 Radziwiłł sent one of his private diplomats from Czernihów province to the Grand Vizier of the Ottomans in order to arrange an anti-Russian coalition - an alliance between the Polish–Lithuanian Commonwealth and the Ottoman Empire to repel the Russian aggressors and halt the numerous threats that haunted the inhabitants of the Eastern Borderlands (Kresy) of the Commonwealth and the northern territories of Turkey. Radziwiłł's second goal was to convince Sultan and Caliph of Islam, Mustafa III, to recognize the Czartoryski clan as enemies and to ensure that the upcoming war or conflict would be profitable for both Poland and Turkey.
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In other cities similar revolutions took place in which the Patriots took over the government. During the spring of 1795, the French government and the new revolutionary Batavian administration negotiated which regions would be annexed by France: Paris agitated for the Waal as the border between the two republics, but the Bavatians found this too high a price for the population which had largely liberated itself, and wanted to retain friendly ties with the French. The resulting Treaty of The Hague (16 May 1795) stipulated that only the Generality Lands of Staats-Vlaanderen, Staats- Overmaas and Staats-Opper-Gelre would become French territory, while Staats- Brabant and the parts of Duchy of Guelders and the County of Holland below the river Waal would remain in Batavian control. Nijmegen thus became part of the new Batavian Republic, but the division of Guelders caused the city to be reassigned to the Department of the Dommel and to lose its status as capital to 's-Hertogenbosch.
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Anglicans adhere to a range of views although the teaching in the Articles of Religion holds that the body of Christ is received by the faithful only in a heavenly and spiritual manner. Some Christians do not believe in the concept of the real presence, believing that the Eucharist is only a ceremonial remembrance or memorial of the death of Christ. The Baptism, Eucharist and Ministry document of the World Council of Churches, attempting to present the common understanding of the Eucharist on the part of the generality of Christians, describes it as "essentially the sacrament of the gift which God makes to us in Christ through the power of the Holy Spirit", "Thanksgiving to the Father", "Anamnesis or Memorial of Christ", "the sacrament of the unique sacrifice of Christ, who ever lives to make intercession for us", "the sacrament of the body and blood of Christ, the sacrament of his real presence", "Invocation of the Spirit", "Communion of the Faithful", and "Meal of the Kingdom".
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In a series of papers between 2004 and 2009, David Ginzburg, Dihua Jiang, and Stephen Rallis showed the (1) implies (2) direction of the global Gan–Gross–Prasad conjecture for all quasisplit classical groups. In the Bessel case of the global Gan–Gross–Prasad conjecture for unitary groups, Wei Zhang used the theory of the relative trace formula by Hervé Jacquet and the work on the fundamental lemma by Zhiwei Yun to prove that the conjecture is true subject to certain local conditions in 2014. In the Fourier–Jacobi case of the global Gan–Gross–Prasad conjecture for unitary groups, Yifeng Liu and Hang Xue showed that the conjecture holds in the skew-Hermitian case, subject to certain local conditions. In the Bessel case of the global Gan–Gross–Prasad conjecture for special orthogonal groups and unitary groups, Dihua Jiang and Lei Zhang used the theory of twisted automorphic descents to prove that (1) implies (2) in its full generality, i.e.
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In their 1974 book, Lloyd Shapley and Robert Aumann extended the concept of the Shapley value to infinite games (defined with respect to a non-atomic measure), creating the diagonal formula. This was later extended by Jean-François Mertens and Abraham Neyman. As seen above, the value of an n-person game associates to each player the expectation of his contribution to the worth or the coalition or players before him in a random ordering of all the players. When there are many players and each individual plays only a minor role, the set of all players preceding a given one is heuristically thought as a good sample of the players so that the value of a given infinitesimal player around as "his" contribution to the worth of a "perfect" sample of the population of all players. Symbolically, if is the coalitional worth function associating to each coalition measured subset of a measurable set that can be thought as I=[0,1] without loss of generality.
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Carl Friedrich Gauss's Disquisitiones Arithmeticae, first edition Joseph-Louis Lagrange (1736–1813) was the first to give full proofs of some of Fermat's and Euler's work and observations—for instance, the four-square theorem and the basic theory of the misnamed "Pell's equation" (for which an algorithmic solution was found by Fermat and his contemporaries, and also by Jayadeva and Bhaskara II before them.) He also studied quadratic forms in full generality (as opposed to m X^2 + n Y^2)—defining their equivalence relation, showing how to put them in reduced form, etc. Adrien-Marie Legendre (1752–1833) was the first to state the law of quadratic reciprocity. He also conjectured what amounts to the prime number theorem and Dirichlet's theorem on arithmetic progressions. He gave a full treatment of the equation a x^2 + b y^2 + c z^2 = 0 and worked on quadratic forms along the lines later developed fully by Gauss.
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Three subfields of the complex numbers C have been suggested as encoding the notion of a "closed-form number"; in increasing order of generality, these are the Liouville numbers (not to be confused with Liouville numbers in the sense of rational approximation), EL numbers and elementary numbers. The Liouville numbers, denoted L, form the smallest algebraically closed subfield of C closed under exponentiation and logarithm (formally, intersection of all such subfields)—that is, numbers which involve explicit exponentiation and logarithms, but allow explicit and implicit polynomials (roots of polynomials); this is defined in . L was originally referred to as elementary numbers, but this term is now used more broadly to refer to numbers defined explicitly or implicitly in terms of algebraic operations, exponentials, and logarithms. A narrower definition proposed in , denoted E, and referred to as EL numbers, is the smallest subfield of C closed under exponentiation and logarithm—this need not be algebraically closed, and correspond to explicit algebraic, exponential, and logarithmic operations.
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If a "specific intent" in either sense is required and there is clear evidence that the accused was too intoxicated to form the element subjectively, this fact is recognised as a defense unless the loss of control was part of the plan. But this is of little value to defendants since there are almost always offenses of basic intent that can be charged and/or the basic intent offenses are usually lesser included offenses and an alternative verdict can be delivered by judge or jury without the need for a separate charge. In English law, note the controversial Jaggard v Dickinson [1980] 3 All ER 716 which held that, for the purposes of the statutory defense of lawful excuse under s5 Criminal Damage Act 1971, a drunken belief will found the defense even though this allows drunkenness to negate basic intent. This is limited authority and does not affect the generality of the defense.
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Even without knowledge that we are working in the multiplicative group of integers modulo n, we can show that a actually has an order by noting that the powers of a can only take a finite number of different values modulo n, so according to the pigeonhole principle there must be two powers, say s and t and without loss of generality s > t, such that as ≡ at (mod n). Since a and n are coprime, this implies that a has an inverse element a−1 and we can multiply both sides of the congruence with a−t, yielding as−t ≡ 1 (mod n). The concept of multiplicative order is a special case of the order of group elements. The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n.
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During the 1960s, various philosophers such as Donald Davidson, Hilary Putnam, and Fodor tried to resolve the puzzle of developing a way to preserve the explanatory efficacy of mental causation and so-called "folk psychology" while adhering to a materialist vision of the world which did not violate the "generality of physics". Their proposal was, first of all, to reject the then-dominant theories in philosophy of mind: behaviorism and the type identity theory. The problem with logical behaviorism was that it failed to account for causation between mental states and such causation seems to be essential to psychological explanation, especially if one considers that behavior is not an effect of a single mental event/cause but is rather the effect of a chain of mental events/causes. The type-identity theory, on the other hand, failed to explain the fact that radically different physical systems can find themselves in the identical mental state.
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Regardless of the actual date that contacts with France began, it would end with the formation of a Catalan-French alliance that confronted the Spanish Crown and gave rise to the so-called Reapers' War or Catalan Revolt. Although it remains a controversial issue among historians, it seems that they could have already started in the month of May 1640. Pau Claris had summoned the general court on September 10, 1640, but simultaneously and without consulting the cities, would have begun the contacts with the French. On September 7 of 1640, the representatives of the Generality of Catalonia, Francesc de Tamarit, Ramon de Guimerà, and Francesc de Vilaplana, nephew of Claris, signed the first Pact of Céret with Bernard Du Plessis-Besançon, delegated by Armand Jean du Plessis de Richelieu, Cardinal- Duc de Richelieu on behalf of Louis XIII of France, for which Catalonia had received military support aimed at facing the Castilian offensive commanded by the Count-Duke of Olivares, who had already decided to intervene in Catalonia.
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Radziwiłł, reluctant like the other leaders residing in Radom to Repnin's decision of moving the generality seat and headquarters to Warsaw, tried to dissuade him (On July 21 he even a letter to Rzewuski in this matter), pointing out the alleged danger lurking on the Confederation from the furious and aggressive Czartoryski clan in the capital, as most of the residences and palaces in Warsaw belonged to Czartoryski and the family possessed the largest army reserves in all of Europe. The fear of the "Czartoryski army and influence" has gone so far that Colonel Karr stated that he prefers to leave everything and flee abroad, rather fight alongside Radziwiłł and declare himself the detainee. Repnin persuaded Karr that under the protection of Catherine II, he is secure in the Commonwealth, and that the allied army of Russia, Prussia and Austria would make Czartoryski "crawl" on the floor. Additionally, Radziwiłł specifically requested that the Russian infantry would guard his Warsaw residence, rather than the Polish Royal Guard forces of the King.
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As Henry Casimir was unmarried, and did not have children, William Frederick inherited his titles. However, as the office of stadtholder was not yet hereditary, William Frederick only managed to be appointed in Friesland. The stadtholdership in Groningen and DrentheDrenthe was a self-governing territory that was not represented in the States-General of the Netherlands, but was not one of the Generality Lands either, and usually appointed the same stadtholder as Groningen. went to Frederick Henry, not without a struggle with William Frederick, however. (1995), The Dutch Republic: Its Rise, Greatness and Fall, 1477–1806, Oxford University Press, hardback, paperback, pp. 538–539 After Frederick Henry's death in 1647 William II succeeded his father also in these two provinces as stadtholder. Only when William II died in 1650, just a week before his son William III was born, did William Frederick obtain the stadtholdership in the other two provinces also. At that time he might have obtained the stadtholdership in the five other provinces (Holland, Zeeland, Utrecht, Gelderland and Overijssel) also.
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Although Algorithmic Combinatorics on Partial Words is primarily aimed at the graduate level, reviewer Miklós Bóna writes that it is for the most part "remarkably easy to read" and suggests that it could also be read by advanced undergraduates. However, Bóna criticizes the book as being too focused on the combinatorics on words as an end in itself, with no discussion of how to translate mathematical structures of other types into partial words so that the methods of this book can be applied to them. Because of this lack of generality and application, he suggests that the audience for the book is likely to consist only of other researchers specializing in this area. Similarly, although Patrice Séébold notes that this area can be motivated by applications to gene comparison, he criticizes the book as being largely a catalog of its author's own research results in partial words, without the broader thematic overview or identification of the fundamental topics and theorems that one would expect of a textbook, and suggests that a textbook that accomplishes these goals is still waiting to be written.
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An example of such coalition happened during the Versailles Peace Conference in 1919 when the Allied powers attempted to reach a peace agreement. Examples of military coalitions include the Coalition of the Gulf War, when George H. W. Bush ended Saddam Hussein's aggression in the Middle East by enlisting and leading a military coalition in the 1991 Gulf War's Operation Desert Storm as well as his son George W. Bush's efforts in the "Coalition of the Willing", a phrase employed during the 2003 campaign for the war in Iraq led by the United States and its allies. A contemporary example is the United Nations coalition that intervened in the 2011 Libyan Civil War against Muammar Gaddafi. For coalitions to be effective in principle, let alone in action, participating nations have tended to require a single overpowering threat—perhaps to freedom or a way of life or a crucial national interest—or the presence of a single despotic figure or regime whose continued existence is considered not only abhorrent to the generality of nations but also destabilizing to the region or world order.
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Marxism and the Oppression of Women received mixed reviews from the sociologist Johanna Brenner in Contemporary Sociology, Gilda Zwerman in the American Journal of Sociology, Bonnie J. Fox in the Canadian Journal of Sociology, and Scarlet Pollock in the Canadian Review of Sociology & Anthropology. The book was also reviewed by Hester Eisenstein in Science & Society, Carol A. Brown in Qualitative Sociology, and Mary Margaret Fonow in Signs, and in Choice. Brenner credited Vogel with providing a "clear and lively presentation" which demonstrated that "classical marxist theory grappled with key questions for today's feminists". However, she wrote that Vogel's analysis "remains at such a high level of abstraction and generality that it never quite addresses the central issues that socialist-feminist theory has been engaging for more than a decade", and criticized Vogel for failing to explain "why the outcome of this class struggle seems to be almost universally a family system in which men exercise power over women", and for her neglect of the work of the anarchist Emma Goldman and the Bolshevik Alexandra Kollontai.
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The AST is written to the precompiled header file in such a way that the compiler can read it in using random-access I/O, in particular not reading in the parts of the precompiled AST that subsequent code does not in fact reference, which is a common occurrence with headers that provide large template libraries. This eliminates the problem of reading the cache file scaling linearly with the size of the precompiled input. The downside is, however, the loss of generality compared to the pretokenization mechanism. The precompiled header has to store information about the language dialect being used, down to the level of whether things like C++-style `//` comments are enabled in non-C++ languages, the target architecture, the compiler version (more specifically, the version of the internal AST data structure that the compiler is using), and the list of predefined pre-processor macros; so that upon re-reading the precompiled header file the compiler can ensure that it is using a precompiled header that is valid for the compilation at hand.
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According to Boris Golubov, BV functions of a single variable were first introduced by Camille Jordan, in the paper dealing with the convergence of Fourier series. The first successful step in the generalization of this concept to functions of several variables was due to Leonida Tonelli,Tonelli introduced what is now called after him Tonelli plane variation: for an analysis of this concept and its relations to other generalizations, see the entry "Total variation". who introduced a class of continuous BV functions in 1926 , to extend his direct method for finding solutions to problems in the calculus of variations in more than one variable. Ten years after, in , Lamberto Cesari changed the continuity requirement in Tonelli's definition to a less restrictive integrability requirement, obtaining for the first time the class of functions of bounded variation of several variables in its full generality: as Jordan did before him, he applied the concept to resolve of a problem concerning the convergence of Fourier series, but for functions of two variables.
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On appeal, the court held (per Lewis AJA), that the surrounding circumstances—what passed between the parties, their negotiations and their conduct—did not show that the words "no warranty whatsoever" had included the implied warranty against eviction. Although the phrase had to be regarded at first blush as a complete catch-all, saving the seller from any liability that might have arisen by operation of law, or by virtue of representations or warranties, it could not, given its generality, and the absence of any evidence that the question of title had been considered or in contemplation, have excluded the most fundamental obligation of the seller: to give undisturbed possession of the merx to the buyer. The only inference to be drawn from the circumstances was that Arnold had not intended or even contemplated that he might be deprived of possession by the true owner, and yet have no recourse to Van der Westhuizen. The evidence did not show that Van der Westhuizen had any such liability in mind either.
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Article 16(1) of the Constitution prohibits discrimination against citizens of Singapore on the ground only of religion, race, descent or place of birth in the administration of public educational institutions (and, in particular, as regards the admission of students or the payment of fees), and in providing financial aid from public funds for the maintenance or education of students in any educational institution. This provision is stated to be "[w]ithout prejudice to the generality of Article 12". Article 16(2) declares that religious groups have the right to establish and maintain institutions for the education of children and to provide them religious instruction in those institutions, but there must not be any discrimination on the ground only of religion in laws relating to such institutions or the administration of such laws. Article 154 states that all persons who are in the same Government service grade must be treated impartially regardless of their race, subject to the terms and conditions of their employment and to other provisions of the Constitution.
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In Milgrom (1981), Milgrom introduced into economics a new notion of "favorableness" for information; namely, that one observation x is more favorable than another observation y, if, for all prior beliefs about the variable of interest, the posterior belief conditional on x first-order stochastically dominates the posterior conditional on y. Milgrom and others have used this notion of favorableness and the associated "monotone likelihood ratio property" of information structures to derive a range of important results in information economics, from properties of the optimal incentive contract in a principal-agent problem, to the notion of the winner's curse in auction theory. In the same paper, Milgrom introduced a novel "persuasion game", in which a salesperson has private information about a product, which he can, if he chooses, verifiably report to a potential buyer. (That is, the salesperson can, if he wishes, conceal his information, but he cannot misreport it if he reveals it.) Milgrom demonstrates that, with substantial generality, at every sequential equilibrium of the sales encounter game, the salesperson employs a strategy of full disclosure.
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William (though a lax Calvinist himself, like his father) keenly supported the Calvinist die-hards in their attempts to force the Protestant religion on the Catholic inhabitants of the recently acquired Generality Lands (though his father had been far more tolerant of Catholic freedom of conscience). William managed to gain much popularity by this hard-line policy among the more orthodox lower classes in the Republic-proper, but especially the Holland regents thwarted the policy, because they were aware of the needless resentment it caused.Israel (1995), pp. 598–602 This was, however, just political posturing on William's part, cynically exploiting certain prejudices in an attempt to gain ascendancy over the regents. More important as a matter of principle was the conflict over the reduction of the standing army that arose during 1649 and 1650. The regents understandably did not quite see the need for an expensive, large, mercenary standing army in peacetime. Holland demanded a reduction of the army to 26,000 (from a level of 35,000 in 1648), whereas William argued that the personnel needs were now appreciably larger, because the territory to be protected by garrisoned fortresses was now a great deal larger.
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De Groote Peel National Park The Duchy of Brabant was a state of the Holy Roman Empire established in 1183 or 1190. It developed from the Landgraviate of Brabant and formed the heart of the historic Low Countries, part of the Burgundian Netherlands from 1430 and of the Habsburg Netherlands from 1482, until it was split up after the Dutch revolt. After the War of Independence, Catholics in the Southern Netherlands were systematically and officially discriminated against by the Northern Protestant government until the second half of the 19th century, which had a major influence on the economic and cultural development of the southern part of the Netherlands. Present-day North Brabant (Staats-Brabant) was adjudicated to the Generality Lands of the Dutch Republic according to the 1648 Peace of Westphalia, while the reduced duchy remained in existence with the Southern Netherlands until it was conquered by French Revolutionary forces in 1794. Until the 17th century, the area that now makes up the province of North Brabant was mostly part of the Duchy of Brabant, of which the southern part is now in Belgium.
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Although the description sitting-on (graph 1) is more abstract than the graphic image of a cat sitting on a mat (picture 1), the delineation of abstract things from concrete things is somewhat ambiguous; this ambiguity or vagueness is characteristic of abstraction. Thus something as simple as a newspaper might be specified to six levels, as in Douglas Hofstadter's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach (1979):Douglas Hofstadter (1979) Gödel, Escher, Bach > :(1) a publication ::(2) a newspaper :::(3) The San Francisco Chronicle > ::::(4) the May 18 edition of The San Francisco Chronicle :::::(5) my copy > of the May 18 edition of The San Francisco Chronicle ::::::(6) my copy of > the May 18 edition of The San Francisco Chronicle as it was when I first > picked it up (as contrasted with my copy as it was a few days later: in my > fireplace, burning) An abstraction can thus encapsulate each of these levels of detail with no loss of generality. But perhaps a detective or philosopher/scientist/engineer might seek to learn about something, at progressively deeper levels of detail, to solve a crime or a puzzle.
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The fund set up by the mayor of Merthyr Tydfil grew rapidly, and within a few months nearly 88,000 contributions had been received, totalling £1,606,929; the final total raised was £1.75 million. No specific aims for the fund had been outlined by the mayor until it was put on a firm legal footing under the auspices of a permanent committee with clear local representation. They drew up a deed that outlined the purposes of the fund as: > # For the relief of all persons who have suffered as a result of the said > disaster and are thereby in need. # Subject as aforesaid for any charitable > purpose for the benefit of persons who were inhabitants of Aberfan and its > immediate neighbourhood (hereinafter called "the area of benefit") on the > 21st day of October 1966 or now are or hereafter become inhabitants of the > area of benefit and in particular (but without prejudice to the generality > of the last foregoing trust) for any charitable purpose for the benefit of > children who were on the 21st day of October 1966 or who now are or > hereafter may become resident in the area of benefit.
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In mathematics, an unfoldable cardinal is a certain kind of large cardinal number. Formally, a cardinal number κ is λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model with the critical point of j being κ and j(κ) ≥ λ. A cardinal is unfoldable if and only if it is an λ-unfoldable for all ordinals λ. A cardinal number κ is strongly λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus- power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model "N" with the critical point of j being κ, j(κ) ≥ λ, and V(λ) is a subset of N. Without loss of generality, we can demand also that N contains all its sequences of length λ.
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The halved cube graph of order 4, obtained as the bipartite half of an order-4 hypercube graph In graph theory, the bipartite half or half-square of a bipartite graph G = (U,V,E) is a graph whose vertex set is one of the two sides of the bipartition (without loss of generality, U) and in which there is an edge uiuj for each two vertices ui and uj in U that are at distance two from each other in G.. That is, in a more compact notation, the bipartite half is G2[U] where the superscript 2 denotes the square of a graph and the square brackets denote an induced subgraph. For instance, the bipartite half of the complete bipartite graph Kn,n is the complete graph Kn and the bipartite half of the hypercube graph is the halved cube graph. When G is a distance-regular graph, its two bipartite halves are both distance-regular.. For instance, the halved Foster graph is one of finitely many degree-6 distance-regular locally linear graphs. The map graphs, that is, the intersection graphs of interior- disjoint simply-connected regions in the plane, are exactly the bipartite halves of bipartite planar graphs..
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The Gelfand–Naimark theorem implied that there is a correspondence between commutative and geometric objects: Every commutative is of the form C_0(X) for some locally compact Hausdorff space X. Consequently it is possible to study locally compact Hausdorff spaces purely in terms of commutative Non- commutative geometry takes this as inspiration for the study of non- commutative If there were such a thing as a "non-commutative space X," then its C_0(X) would be a non-commutative ; if in addition the Gelfand–Naimark theorem applied to these non-existent objects, then spaces (commutative or not) would be the same as so, for lack of a direct approach to the definition of a non-commutative space, a non-commutative space is defined to be a non- commutative Many standard geometric tools can be restated in terms of and this gives geometrically-inspired techniques for studying non-commutative . Both of these examples are now cases of a field called non-commutative geometry. The specific examples of von Neumann algebras and are known as non-commutative measure theory and non-commutative topology, respectively. Non-commutative geometry is not merely a pursuit of generality for its own sake and is not just a curiosity.
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Case A for n = 5 can be proven immediately by Sophie Germain's theorem if the auxiliary prime θ = 11\. A more methodical proof is as follows. By Fermat's little theorem, : x5 ≡ x (mod 5) : y5 ≡ y (mod 5) : z5 ≡ z (mod 5) and therefore : x + y + z ≡ 0 (mod 5) This equation forces two of the three numbers x, y, and z to be equivalent modulo 5, which can be seen as follows: Since they are indivisible by 5, x, y and z cannot equal 0 modulo 5, and must equal one of four possibilities: ±1 or ±2. If they were all different, two would be opposites and their sum modulo 5 would be zero (implying contrary to the assumption of this case that the other one would be 0 modulo 5). Without loss of generality, x and y can be designated as the two equivalent numbers modulo 5. That equivalence implies that : x5 ≡ y5 (mod 25) (note change in modulo) : −z5 ≡ x5 \+ y5 ≡ 2 x5 (mod 25) However, the equation x ≡ y (mod 5) also implies that : −z ≡ x + y ≡ 2 x (mod 5) : −z5 ≡ 25 x5 ≡ 32 x5 (mod 25) Combining the two results and dividing both sides by x5 yields a contradiction : 2 ≡ 32 (mod 25) Thus, case A for n = 5 has been proven.
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