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Equivalence of categories

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  • One of the major advances of science in the 20th century was the discovery of a mathematical formulation of quantum mechanics by Heisenberg in 1925 [94].1 From a mathematical point of view, this transition from classical mechanics to quantum mechanics amounts to, among other things, passing from the commutative algebra of classical observables to the noncommutative algebra of quantum mechanical observables. To understand this better we recall that in classical mechanics an observable of a system (e.g. energy, position, momentum, etc.

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  • This paper describes a method for recognizing coherence relations between clauses which are linked by te in Japanese - - a translational equivalent of English and. We consider that the coherence relations are categories each of which has a prototype structure as well as the relationships among them. By utilizing this organization of the relations, we can infer an appropriate relation from the semantic structures of the clauses between which that relation holds. We carried out an experiment and obtained the correct recognition ratio of 82% for the 280 sentences. ...

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  • [Mechanical Translation, vol.3, no.3, December 1956; pp. 81-88] † M. A. K. Halliday, Cambridge Language Research Unit, Cambridge, England The grammar and lexis of a language exhibit a high degree of internal determination, affecting all utterances whether or not these are translated from another language.

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  • After illustrating the benefits of this approach with several examples, we describe the algorithm for compiling zero morphemes into unary rules, which allows us to use zero morphemes more efficiently in natural language processing. 1 Then, we discuss the question of equivalence of a grammar with these unary rules to the original grammar. Lastly, we compare our approach to zero morphemes with possible alternatives. 1.

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  • In this work we constitute the category of coverings of the Lie fundamental groupoid associated with a connected smooth manifold. We show that this category is equivalent to the category of universal coverings of a connected smooth manifold. In addition, we prove the equivalence of the category of coverings of a Lie groupoid and the category of actions of this Lie groupoid on a connected smooth manifold.

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  • The purpose of this paper is to prove that the stable homotopy category of algebraic topology is ‘rigid’ in the sense that it admits essentially only one model: Rigidity Theorem. Let C be a stable model category. If the homotopy category of C and the homotopy category of spectra are equivalent as triangulated categories, then there exists a Quillen equivalence between C and the model category of spectra. Our reference model is the category of spectra in the sense of Bousfield and Friedlander [BF, §2] with the stable model structure. The point of the rigidity theorem is that its...

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  • We define and study sl2 -categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple reflection. We construct categorifications for blocks of symmetric groups and deduce that two blocks are splendidly Rickard equivalent whenever they have isomorphic defect groups and we show that this implies Brou´’s abelian defect group conjecture for symmetric groups. e We give similar results for general linear groups over finite fields. ...

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  • The NCRP has long recognized the need for a clear assessment of the magnitude of doses from various sources of radiation to which the population of the U.S. is exposed. In anticipation of the need to gather data for input into this process, five assessment committees, each addressing a different source category, were established. NCRP reports assessing exposures from natural background, consumer products, nuclear power generation, and diagnostic medical radiation have been published (NCRP, 1987a,b,c,d, NCRP, 1989)....

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  • Interaction of lexical and derivational semantics---for example substitution and lambda conversion--- is typically a part of the on-line interpretation process. Proof-nets are to categorial grammar what phrase markers are to phrase structure grammar: unique graphical structures underlying equivalence classes of sequential syntactic derivations; but the role of proof-nets is deeper since they integrate also semantics.

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  • Under categorial grammars that have powerful rules like composition, a simple n-word sentence can have exponentially many parses. Generating all parses is inefficient and obscures whatever true semantic ambiguities are in the input. This paper addresses the problem for a fairly general form of Combinatory Categorial Grammar, by means of an efficient, correct, and easy to implement normal-form parsing technique.

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  • Steedman (1985, 1987) and others have proposed that Categorial Grammar, a theory of syntax in which grammatical categories are viewed as functions, be augmented with operators such as functional composition and type raising in order to analyze • noncanonical" syntactic constructions such as wh- extraction and node raising. A consequence of these augmentations is an explosion of semantically equivalent derivations admitted by the grammar. The present work proposes a method for circumventing this spurious ambiguity problem.

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  • There has recendy been a revival of interest in Categorial Grammars (CG) among computational linguists. The various versions noted below which extend pure C G by including operations such as functional composition have been claimed to offer simple and uniform accounts of a wide range of natural language (NL) constructions involving bounded and unbounded "movement" and coordination "reduction" in a number of languages. Such grammars have obvious advantages for computational applications, provided that they can be parsed efficiently.

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  • This paper shows that a class of Combinatory Categorial Grammars (CCGs) augmented with a linguistically-motivated form of type raising involving variables is weakly equivalent to the standard CCGs not involving variables. The proof is based on the idea that any instance of such a grammar can be simulated by a standard CCG.

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  • This in-vitro study evaluates the antibacterial &antifungal action of aqueous & alcoholic extracts of new herbal vaginal formulation containing equal amounts of Symplocos racemosa Roxb. and Ficus glomerata Roxb. stem barks against gram positive and gram negative bacteria and candid fungus by using the methods of zone of inhibition and minimum inhibition concentration (MIC) to assess its efficacy in treating vaginitis. During phytochemical analysis, alkaloids, flavonoids, tannins and carbohydrates were found to be present in both extracts.

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  • Brian's Book Barn will concentrate its efforts on the buyers of "Pleasure" category books as discussed earlier. The educational category is not a target market as area schools order their textbooks and reading material through the Ministry of Education in Victoria. Other educational books are also available through satellite campuses of Northern Lights College and the University of Northern British Columbia. In the professional category, there is simply not enough demand in the area to stock these kinds of titles.

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  • The theory of Mackey functors has been developed during the last 25 years in a series of papers by various authors (J.a. Green [8], a. Dress [5], T. Yoshida [17], J. Th~venaz and P. Webb [13],[15],[14], G. Lewis [6]). It is an attempt to give a single framework for the different theories of representations of a finite group and its subgroups. The notion of Mackey functor for a group G can be essentially approached from three points of view: the first one ([8]), which I call "naive", relics on the poset of subgroups of G.

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  • Chapter 6 - Measurement. After reading this chapter, you should be able to: Understand that measurement is a process, explain the principle that numbers have no inherent meaning until the researcher assigns or imposes meaning, develop categories for nominal data that are mutually exclusive, exhaustive, and equivalent,...

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  • In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We also prove that the crossed modules and internal categories within topological groups with operations are equivalent.

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  • In this present work, we present the concept of a crossed module over generalized groups and we call it a “generalized crossed module”. We also define a generalized group-groupoid. Furthermore we show that the category of generalized crossed modules is equivalent to that of generalized group-groupoids whose object sets are abelian generalized group.

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  • We consider the categorical equivalence between crossed modules over groupoids and double groupoids with thin structures, and by this equivalence, we prove how normality and quotient concepts are related in these two categories and give some examples of these objects.

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