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.

     

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.     

Vanadium Doped Sol-Gel TiO2 Coatings

A study of the experimental conditions required to obtain vanadium doped sol-gel TiO2 coatings is presented. Tetraethyl orthotitanate was employed as the TiO2 source and VCl3, VOSO4 · H2O and VOSO4 dissolved H2SO4 where employed as vanadium sources.Dip coating has been used to produce coatings on silicon wafers, spectral carbon electrodes and titanium electrodes. Both supported and unsupported films have been studied by UV-Vis spectra, IR spectroscopy and X-ray diffraction (XRD). The measurements have been made on samples as prepared and treated thermally at temperatures between 100°C and 300°C. The thermal treatment temperatures have been established from DTA/TGA measurements.The vanadium doped sol-gel TiO2 coatings have been tested as sensors for redox potential measurements in electrochemical processes. The influence of both the thickness of films and the nature of substrate has been investigated.     

Einwirkung von p-Nitroso-dimethylanilin auf Brenztraubensäure und ihre Derivate, 6. Mitt.: Kondensation der Phenylbrenztraubensäure mit primären aromatischen Aminen

Phenylpyruvic acid reacts with p-nitroaniline to yield the 3-hydroxypyrrolinone2a, and with anilines bearing+M substituents in the p-position to yield the 3-enaminopyrrolinones1b-1e.

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Mit 1 Abbildung

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5. Mitt.:M. Ruse, E. Hamburg undM. Petri, Chem. Ber.103, 3727 (1970).     

Kobalt(III)ammin-derivate einiger Reineckesalz-Analoga mit Xylidinen

Zusammenfassung Es wurden 34 neue Komplexsalze durch doppelte Umsetzung aus wäßr.-alkohol. Lösungen der folgenden Reineckeat-Analoga: [Cr(NCS)₄(m-xylidin)₂]^–, [Cr(NCS)₄(p-xyl)₂]^– und Hexammin-, Monoacido-pentammin- und Diacido-tetramminkobalt(III)-komplexsalze erhalten. Es wurden in einigen Fällen Unterschiede in physiko-chemischen Eigenschaften, wie Farbtönung, Kristallform, Löslichkeit und papierchromatographischeR _f-Werte, bei den stellungsisomeren Salzen vom Typus: Kation · [Cr(NCS)₄(xyl)₂] und auch bei den Koordinationsisomerpaaren: [Co(DH)₂(m-xyl)₂] [Cr(NCS)₄(p-xyl)₂] und [Co(DH)₂(p-xyl)₂] [Cr(NCS)₄(m-xyl)₂] usw. beobachtet.

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Cobalt(III)ammine derivatives of some reineckate analogues with xylidines

34 new complex salts were prepared by double conversion of the reineckate analogues [Cr(NCS)₄(m-xylidine)₂]^–, [Cr(NCS)₄(p-xyl)₂]^–, with the hexammine-, monoacido-pentammine- and diacidotetrammine-complexes of Co(III). In some of the position and coordination isomeres differences of the standard physico-chemical properties, i.e. color, crystal form, solubility and paper chromatographyR _f-values were observed.