Sur un problème au sujet des homomorphismes

Sans résumé

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Dédié à Monsieur le Professeur Otto Haupt à l'occasion de son centenaire avec les meilleurs vœux.     

Graphical solution of axially symmetric problems of plastic flow

Résumé Une méthode graphique de solution des problèmes dans le cas de symétrie axiale a été proposée pour des corps rigides, parfaitement plastiques, obéissants au critère d'écoulement de Coulomb-Tresca et à l'hypothèse du potentiel plastique. Deux cas ont été considérés: d'une part des régimes de Haar-Kármán pour lesquels la contrainte circonférencielle est égale à l'une des contraintes principales contenues dans le plan axial, et d'autre part des régimes duor lesquels l'une des vitesses de déformation principales dans le plan axial est nulle.     

Synthesis of a cisplatin derivative from lithocholic acid

A new steroidal-platinum(II) hybrid compound was synthesized using a simple and efficient methodology. The synthesis was performed by a convergent approach with cross metathesis (CM) as a key step. An olefin derived from lithocholic acid and a vinyl substituted ethylenediamine derived from l-serine were used as chiral building blocks, which were combined in the CM step. The most important advantage of this method was the utilization of l-serine as a cheap, stereoisomerically pure substrate. A steroid with a diamino system in the side chain was subjected to reaction with potassium tetrachloroplatinate to obtain the target platinum(II) complex. Attempts to synthesize similar diamine systems using the asymmetric Strecker reaction were unsuccessful.     

Une généralisation d'un résultat de J. Aczél et M. Hosszú sur l'équation de translation

Résumé En généralisant un résultat de J. Aczél et M. Hosszú on donne des conditions nécessaires et suffisantes pour qu'une solution de l'équation de translationF(F(, x), y) = F(, xy), oùF: × G , est un ensemble arbitraire,G forme un groupe, soit de la formeF(, x) = f ^–1(f()·1(x)), oùf est une bijection de au groupeG ₁ isomorphe avecG et 1 est un homomorphisme deG àG ₁. On considère aussi le cas oùG forme un espace vectoriel sur le corps des nombres rationels.Si est un intervalle ayant plus qu'un point etG = R ^m avec l'addition comme l'opération on trouve des conditions pour que la fonction continueF soit de la formeF(, x ₁,, x _m ) =f ^–1(f() + c ₁ x ₁ + +c _m x _m ), oùf est une homéomorphie de àR et (c ₁,,c _m ) R ^m .

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Determination of traces of purine by cathodic stripping voltammetry at the hanging copper amalgam drop electrode

In the presence of purine, the copper(II)/copper(Hg) couple splits into copper(II)/copper(I) and copper(I)/copper(Hg) couples, which form two well-separated systems of peaks under voltammetric conditions. The copper(I)/purine complex adsorbs on the electrode surfacer and can be deposited on the electrode surface by electroreduction of copper(II) ions at the HMDE or by electro-oxidation of the hanging copper amalgam drop electrode (HCADE). The deposit can be stripped either cathodically or anodically over the pH range 2–9. The cathodic stripping variant at the HCADE, in solution with pH 2, offers the best results, with linear response for the range 5 × 10^?9–1.5 × 10^?7 mol dm^?3 purine after an accumulation time of 3 min. The detection limit found with the HMDE in the presence of copper(II) ions is higher.     

Effect of support and loading on oxidation of methane over platinum catalysts

Catalytic combustion of methane was carried out using platinum catalysts supported on low-and high-surface area alumina (denoted respectively as LSA and HSA) and platinum supported on silica. Methane conversion was the highest for platinum supported on LSA alumina, smaller for Pt/HSA alumina and the smallest for Pt/silica. However, the 3 wt.% Pt/HSA catalyst was found to show the highest selectivity.     

Electrochemistry of the system Cu(II)Cu(I)Cu(0) in acidified thiocyanate solutions

The system Cu(II)Cu(I)Cu(0) in acidified thiocyanate medium was investigated at carbon, mercury, and copper amalgam electrodes using cyclic voltammetry, normal, differential and reverse pulse voltammetry, double potential step chronocoulometry, and exhaustive coulometry. Reduction of Cu(II) to Cu(I) on carbon electrodes proceeds quasireversibly. At moderate concentrations of Cu(II) and SCN^? the reduction of Cu(II) leads to three-dimensional precipitation of CuSCN which can be deposited at the electrode surface. At high concentration of SCN^? complexation dominates over precipitation and only soluble species are formed. At mercury and copper amalgam electrodes the situation is more complicated. The three- dimensional precipitation is preceded by strong thiocyanate-induced adsorption of Cu(I) which results in formation of a mono layer at potential well-separated from those where diffusing product is formed.     

Comparison of the utility of several tensammetric techniques for the determination of traces of surfactants after preconcentration at the hanging mercury drop electrode

After preconcentration of surfactants at the HMDE, four tensammetric signals were examined to establish the optimum conditions for the determination of ultratraces of surfactants in alkaline, neutral and acidic media. The signals studied were: (1) the depth of the depression occuring on the curves obtained in a.c. fundamental tensammetry; and (2–4) the height of the peaks on the curves obtained in a.c. fundamental tensammetry, a.c. second-harmonic tensammetry and differential pulse tensammetry, respectively. The lowest detection limits found for Triton X-100 and a polyethylene glycol (PEG-4000) were 10 and 2 μg dm^-3, respectively. Traces of surfactants found in supporting electrolytes (ca. 25 μg dm^-3) gave desorption peaks at potentials around ?1 V. These contaminants had no significant effect on the peaks on Triton X-100 and PEG-4000 and they affected the SDS peak markedly. The reproducibility of the results obtained for SDS was poorer than for Triton or PEG.     

Direct determination of pKa values of cationic acids conjugated to heterocyclic amine N-oxides in polar aprotic and amphiprotic solvents

The applicability of the direct method of pK_a determination in the case of protonated heterocyclic amine N-oxides in a series of polar non-aqueous (aprotic and amphiprotic) solvents has been tested. The method is based on the pH determination of the non-aqueous solution of complex salt (the semiperchlorate in this case) formed by the N-oxides studied. The direct method not only provides for quick (one data point per each pK_a determined), but also relatively accurate estimates of acidic dissociation constants. It has been experimentally shown on the example of substituted pyridine N-oxides that this method is precise enough in all studied non-aqueous solvents when applied to compounds of not too low basicity (the pK_a being of the order of 5 or higher). To prove this, the pK_a values of protonated monocyclic N-oxides obtained by the direct method have been compared with those resulting from the potentiometric titration curve. The agreement between the results found by using both methods is very good in most cases, the differences being within standard deviations. Based upon this observation it can be inferred that the pK_a values of protonated bicyclic N-oxides in solvents studied determined by using the direct method can be also considered reliable, especially in the case of polar aprotic solvents.     

Silver based mercury film electrode: Part II. The influence of aging of electrode on the electrode processes of various metal ions

The cyclic voltammetric behaviour of 8 metal ions at solid silver amalgam electrodes prepared by aging of a thin silver based mercury film electrode (SBMFE) and by deposition of silver and mercury on platinum were investigated. It was established that such electrodes behave in relation to some metals (Pb, Bi, Sn) similarly as silver electrodes i.e. the cyclic curves obtained with these electrodes at concentration 10^?3M range show a prepeak-postpeak system corresponding to deposition and dissolution of the monolayer of deposit. On the other hand under the same conditions no prepeaks were observed for cadmium, zinc and thallium. In all cases investigated the heights of anodic stripping peaks were lower on curves obtained with aged SBMFE than on those obtained with fresh SBMFE having a mercury layer 1 μm thick.