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.     

Biosensors based on highly sensitive acetylcholinesterases for enhanced carbamate insecticides detection

This paper presents the construction of amperometric biosensors for the highly sensitive detection of carbamate insecticides based on the inhibition of acetylcholinesterase (AChE). This enzyme was immobilised by entrapment in an optimised sol-gel matrix on TCNQ-modified screen-printed electrodes. The enzyme activity was estimated by measuring the thiocholine produced by the enzymatic hydrolysis of the acetylthiocholine using TCNQ as mediator. Wild and genetically engineered AChEs from Drosophila melanogaster (Dm) were chosen for their high sensitivity towards insecticides, which substantially improves the LOD compared with cholinesterases from other sources. The wild type and three mutant enzymes were tested against three carbamate insecticides: carbaryl, carbofuran and pirimicard. The best LOD were obtained with the Y370A mutant for carbaryl (1 × 10⁻⁸ M), the E69W mutant for pirimicarb (2 × 10⁻⁸ M) and the I161V mutant for carbofuran (8 × 10⁻¹⁰ M). The biosensors were applied to the analysis of two potable water samples.     

Sur un théorème de Choquet

Résumé Le but de ce travail est de caractériser les éspaces topologiques qui possèdent la propriété suivant: pour toute famille(f _t ) _{t I} de fonctions numériques définies dansX il existe une partie dénombrableI ₀ de l'ensemble d'indicesI telle que les fonctions inf _tI f _i et inf _tI0 f _i ont la meme régularisation inférieurement semi-continue.On démontre que l'espace topologiqueX possède cette propriété si et seulement si pour tout sous-ensembleA deX il existe une sous-ensemble dénombrableA ₀,A ₀ A tel queA ₀.On généralise un résultat topologique de G. Choquet.

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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.     

Orthonormal bases generated by Cuntz algebras

We show how some orthonormal bases can be generated by representations of the Cuntz algebra; these include Fourier bases on fractal measures, generalized Walsh bases on the unit interval and piecewise exponential bases on the middle third Cantor set.