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In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $. 相似文献
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We introduce the notion of n-nuanced MV-algebra by performing a Łukasiewicz–Moisil nuancing construction on top of MV-algebras. These structures extend both MV-algebras and Łukasiewicz–Moisil algebras, thus unifying two important types of structures in the algebra of logic. On a logical level, n-nuanced MV-algebras amalgamate two distinct approaches to many valuedness: that of the infinitely valued Łukasiewicz logic, more related in spirit to the fuzzy approach, and that of Moisil n-nuanced logic, which is more concerned with nuances of truth rather than truth degree. We study n-nuanced MV-algebras mainly from the algebraic and categorical points of view, and also consider some basic model-theoretic aspects. The relationship with a suitable notion of n-nuanced ordered group via an extension of the Γ construction is also analyzed. 相似文献
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Summary A separated filtered ring has a maximally complete immediate extension. This is an analogue of Krull Theorem from valuation
ring theory in the frame of filtered rings.
Riassunto Un anello separato filtrato ha una immediata estensione massimale completa. Questo risultato è un analogo del teorema di Krull della teoria degli anelli di valutazione nell’ambito degli anelli filtrati.相似文献
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JPC – Journal of Planar Chromatography – Modern TLC - Separations of eight methyl esters of higher fatty acids on RP-18 stationary phase with methanol—water and... 相似文献
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Alina Constantinescu 《Applications of Mathematics》2007,52(4):321-326
In one if his paper Luo transformed the problem of sum-fuzzy rationality into artificial learning procedure and gave an algorithm
which used the learning rule of perception. This paper extends the Luo method for finding a sum-fuzzy implementation of a
choice function and offers an algorithm based on the artificial learning procedure with fixed fraction. We also present a
concrete example which uses this algorithm. 相似文献
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Szklarzewicz Janusz Samotus Alina Nowicka Beata Burgess John Fawcett John Russell David R. 《Transition Metal Chemistry》1999,24(2):177-182
The X-ray crystal structure of (bpyH2)2[W(CN)8]·4H2 O (bpyH2=2,2-bipyridinium) is described. The [W(CN)8]4– anion has an approximately square antiprismatic (D4d) conformation, seemingly imposed by strong anion–water–cation hydrogen-bonding interactions. Bond distances in the anion are: WC 2.150(5), 2.163(5); CN 1.128(6), 1.145(6)Å and the angles WCN are 177.6(5), 178.3(5)°. The dihydrate and the anhydrous salt are both intensely black solids, exhibiting ion-pair charge-transfer interaction between cation and anion. E.s.r. spectra indicate that 30% of the tungsten is present as WV in the solid state, but that in solution only the WIV complex is present. The electron withdrawing effect of the cation is discussed and compared with that in a series of salts with different bipyridinium cations. 相似文献