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.

     

On the isoperimetric inequality for the buckling of a clamped plate

In two dimensions, we prove the existence of a domain minimizing the buckling load of a clamped plate among all domains of given measure. In order to prove that the optimal set is the disk, we discuss possible ways of applying an idea of Willms and Weinberger if the regularity of the optimal set is not a priori assumed.     

Syntheses, structures and intermolecular interactions of tetraorganoammonium, -phosphonium and -stibonium dimethyl- and diphenyltetrahaloantimonates

The syntheses and spectroscopic (NMR, MS) investigations of the antimonates [Ph₄P]⁺[Me₂SbCl₄]⁻ (1), [Me₄Sb]⁺[Me₂SbCl₄]⁻ (2), [Et₄N]⁺[Ph₂SbCl₄]⁻ (3), [Bu₄N]⁺[Ph₂SbCl₄]⁻ (4), [Me₄Sb]⁺[Ph₂SbCl₄]⁻ (5), [Et₃MeSb]⁺[Ph₂SbCl₄]⁻ (6), [Et₄N]⁺[Ph₂SbF₄]⁻ (7) and [Et₄N]⁺[Ph₂SbBr₄]⁻ (8) are reported. Halogen scrambling reactions of Et₄NBr or Ph₄EBr (E = P, Sb) with R₂SbCl₃ (R = Me, Ph) produce mixtures of compounds from which crystals of [Et₄N]⁺[Ph₂SbBr_1.24Cl_2.76]⁻ (9), [Et₄N]⁺[Ph₂SbBr_2.92Cl_1.08]⁻ (10) or [Ph₄Sb]⁺[Me₂SbCl₄]⁻ (11) were isolated. The crystal and molecular structures of 1 and 3-11 are reported.     

Formation of Superoxo Species by Interaction of O2 with Na Atoms Deposited on MgO Powders: A Combined Continuous‐Wave EPR (CW‐EPR), Hyperfine Sublevel Correlation (HYSCORE) and DFT Study

The formation of O₂^? radical anions by contact of O₂ molecules with a Na pre‐covered MgO surface is studied by a combined EPR and quantum chemical approach. Na atoms deposited on polycrystalline MgO samples are brought into contact with O₂. The typical EPR signal of isolated Na atoms disappears when the reaction with O₂ takes place and new paramagnetic species are observed, which are attributed to different surface‐stabilised O₂^? radicals. Hyperfine sublevel correlation (HYSCORE) spectroscopy allows the superhyperfine interaction tensor of O₂^?Na⁺ species to be determined, demonstrating the direct coordination of the O₂^? adsorbate to surface Na⁺ cations. DFT calculations enable the structural details of the formed species to be determined. Matrix‐isolated alkali superoxides are used as a standard to enable comparison of the formed species, revealing important and unexpected contributions of the MgO matrix in determining the electronic structure of the surface‐stabilised Na⁺? O₂^? complexes.     

Viscoelastic materials with a double porosity structure

This paper in concerned with the linear theory of materials with memory that possess a double porosity structure. First, the formulation of the initial-boundary-value problem is presented. Then, a uniqueness result is established. The semigroup theory of linear operators is used to prove existence and continuous dependence of solutions. A minimum principle for the dynamical theory is also derived.     

The algebra of harmonic functions for a matrix-valued transfer operator

We analyze matrix-valued transfer operators. We prove that the fixed points of transfer operators form a finite-dimensional C^∗-algebra. For matrix weights satisfying a low-pass condition we identify the minimal projections in this algebra as correlations of scaling functions, i.e., limits of cascade algorithms.