On the spectral norm of algebraic numbers

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}}} $.     

A common generalization for MV-algebras and Łukasiewicz–Moisil algebras

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.     

Immediate extensions of filtered rings

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.

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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.

     

Intact size-selected Au(n) clusters on a TiO2(110)-(1 x 1) surface at room temperature

Experiments in which mass-selected gold clusters were deposited on a surface have found that the catalytic properties depend strongly on cluster size. However, these experiments have not established definitively that the clusters maintain their size after deposition. We report here work in which we deposit low kinetic energy, mass-selected Aun+ (n = 1-8) clusters on a rutile TiO2(1 x 1) surface and use ultrahigh vacuum scanning tunneling microscopy (UHV-STM) to determine their size and shape.     

Electron impact mass spectral interpretation for some thiophosphoryl-p-acetylaminobenzenesulfonamides

This work discusses the synthesis and the fragmentation patterns for 2-(p-acetylaminosulfonamido)-2-thiono-(5,5-dimethyl-1,3,2-dioxaphosphorinane)(1) and for the p-acetylaminosulfonylamides of O,O-diethylthiophosphoric acid (2), O,O-diphenylthiophosphoric acid (3), dimethylaminocyclohexylthiophosphoric acid (4), and diethylaminophenylthiophosphoric acid (5). A thionamidic-thiolimidic structure was attributed to compounds 1-5, consistent with their IR and NMR spectra. EI mass spectra at 70 eV, high resolution (HR) mass measurements and metastable ion spectra were used to elucidate the fragmentation processes and to determine the kinetic energy release values associated with the metastable ion dissociations. HR accurate mass measurements were used to confirm the compositions of the more abundant ions.     

The use of polarized light scattering for the study of the dynamics of the spinodal decomposition

Due to the fact that in a system undergoing spinodal decomposition the long wavelength fluctuations are enhanced, we expect that multiple events can be observed when the passage of light through the sample is measured. We study here the intensity of double scattering for both polarized and depolarized measurements, as a function of time and angle of detection. The time dependence is nonexponential and the dependence on the scattering wave vector is less pronounced than in the case of single scattering. For systems with spherical molecules it is possible to separate double and single scattering contributions if both polarized and depolarized measurements are made. This increases the amount and quality of information about the dynamics of the spinodal decomposition that can be obtained from light scattering experiments.