A short proof of a theorem of Juhász

We give a simple proof of the increasing strengthening of Arhangel?skii Theorem. Our proof naturally leads to a refinement of this result of Juhász.     

Réduction semi-active du battement de volume généré par une cavité profonde soumise à un écoulement aérodynamiqueSemi-active reduction of the sound generated by a deep cavity under an airflow

We present experimental results obtained with a deep cavity, such as a Helmholtz resonator, excited by an airflow. The resonance under the action of the vortices generated in the shear layer is well described and quantified. The mounting of actuators, based on a few piezo-electric elements, allows us to generate a series of two-dimensional vortices forced at a frequency which is different than the natural resonance frequency. The sound level in the cavity is strongly decreased and only the broadband noise of the turbulence remains. To cite this article: X. Amandolese et al., C. R. Mecanique 330 (2002) 101–106.     

Nonlinear finite element analysis of no-tension masonry structures

A numerical approach for structural analysis of masonry walls in plane stress conditions is presented. The assumption of a perfectly no-tension material (NTM) constitutive model, whose relevant equations are in the form of classical rate-independent associated flow laws of elastoplastic material, allows one to adopt numerical procedures commonly used in computational plasticity. An accuracy analysis on the integration algorithm employed in the solution of constitutive relations has been carried out. The results obtained for some relevant case-studies and their comparison with data, available in the literature show the effectiveness of the proposed method.

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Sommario Si presenta un approccio numerico per l'analisi strutturale di pareti in muratura in stato piano di tensione. L'assunzione di un modello costitutivo per materiale perfettamente non resistente a trazione (NTM), le cui equazioni sono esprimibili nella classica forma incrementale delle leggi dello scorrimento plastico di tipo associato per materiali elastoplastici, consente di adottare procedure numeriche comunemente utilizzate in plasticità computazionale. Si conduce un'analisi di accuratezza dell'algoritmo utilizzato nell'integrazione delle equazioni costitutive del modello esaminato. I risultati ottenuti per alcuni casi analizzati ed il confronto effettuato con esempi riportati in letteratura mostrano l'efficienza dell'approccio proposto.

     

Noetherian type in topological products

The cardinal invariant Noetherian type Nt(X) of a topological space X was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces. We prove in Section 2:

1. There are spaces X and Y such that Nt(X×Y)< min{Nt(X), Nt(Y)}.
2. In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace.

The Noetherian type of the Cantor Cube of weight \({\aleph _\omega }\) with the countable box topology, \({({2^{{\aleph _\omega }}})_\delta }\) , is shown in Section 3 to be closely related to the combinatorics of covering collections of countable subsets of \({\aleph _\omega }\) . We discuss the influence of principles like \({\square _{{\aleph _\omega }}}\) and Chang’s conjecture for \({\aleph _\omega }\) on this number and prove that it is not decidable in ZFC (relative to the consistency of ZFC with large cardinal axioms). Within PCF theory we establish the existence of an (?₄, ?₁)-sparse covering family of countable subsets of \({\aleph _\omega }\) (Theorem 3.20). From this follows an absolute upper bound of ?₄ on the Noetherian type of \({({2^{{\aleph _\omega }}})_\delta }\) . The proof uses a method that was introduced by Shelah in 1993 [33].     

Asymmetric Syntheses Promoted by Organoselenium Reagents

Using chiral nonracemic electrophilic-organoselenium-reagents-asymmetric alkoxy-, hydroxy-, azido- and amido-selenenylation of alkenes were effected with high diastereoselectivity. These reagents have also been employed in catalytic amounts to promote one-pot selenenylation-deselenenylation processes. The asymmetric cyclization of properly substituted alkenes diastereoselectively afforded lactons, tetrahydrofurans oxazolines, thiazolines, pyrrolidines, isoxazolidines, 1,2-oxazines, and cyclic nitrones. Enantiopure dioxane, morpholine, tetrahydrofuran, oxazolidin-2-one and aziridine derivatives were prepared from alkenes, PhSeX, and optically active nucleophiles or substrates.     

A New Alkaliphilic Cold-Active Esterase from the Psychrophilic Marine Bacterium Rhodococcus sp.: Functional and Structural Studies and Biotechnological Potential

The special features of cold-adapted lipolytic biocatalysts have made their use possible in several industrial applications. In fact, cold-active enzymes are known to be able to catalyze reactions at low temperatures, avoiding side reactions taking place at higher temperatures and preserving the integrity of products. A lipolytic gene was isolated from the Arctic marine bacterium Rhodococcus sp. AW25M09 and expressed in Escherichia coli as inclusion bodies. The recombinant enzyme (hereafter called RhLip) showed interesting cold-active esterase activity. The refolded purified enzyme displayed optimal activity at 30 °C and was cold-active with retention of 50 % activity at 10 °C. It is worth noting that the optimal pH was 11, and the low relative activity below pH 10 revealed that RhLip was an alkaliphilic esterase. The enzyme was active toward short-chain p-nitrophenyl esters (C2–C6), displaying optimal activity with the butyrate (C4) ester. In addition, the enzyme revealed a good organic solvent and salt tolerance. These features make this an interesting enzyme for exploitation in some industrial applications.     

Naphthoxazole‐Based Singlet Oxygen Fluorescent Probes

In this study, we report the synthesis and photochemical behavior of a new family of photoactive compounds to assess its potential as singlet oxygen (¹O₂) probes. The candidate dyads are composed by a ¹O₂ trap plus a naphthoxazole moiety linked directly or through an unsaturated bond to the oxazole ring. In the native state, the inherent great fluorescence of the naphthoxazole moiety is quenched; but in the presence of ¹O₂, generated by the addition and appropriate irradiation of an external photosensitizer, a photooxidation reaction occurs leading to the formation of a new chemical entity whose fluorescence is two orders of magnitude higher than that of the initial compound, at the optimal selected wavelength. The presented dyads outperform the commonly used indirect fluorescent ¹O₂ probes in terms of fluorescence enhancement maintaining the required specificity for ¹O₂ detection in solution.     

Spectrofluorimetric determination of pharmaceutical compounds with the cerium(IV)—cerium(III) system

The compounds to be determined are oxidised by cerium(IV). The concentration of cerium(III) formed is measured spectrofluorimetrically. The method has been used both in solution and, by fluorodensitometry, on t.l.c. plates. Detection limits of some substances are 15 ng ml^-1 for the solution method and 5 ng per spot for the t.l.c. method.