The bestL 2-approximation by finite sums of functions with separable variables

Summary We consider the problem of the best approximation of a given functionh L ² (X × Y) by sums _k=1 ⁿ f _k f _k, with a prescribed numbern of products of arbitrary functionsf _k L ² (X) andg _k L ² (Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL ² (X × Y).     

Blaschke-Süss type theorems for closed plane curves

A C¹-class of plane closed curves is considered, which contains all ovals and rosettes. This class is divided into some subclasses for which greatest lower bounds of numbers of antipodal and arc-antipodal sets are determined.     

Adams methods for neutral functional differential equations

Summary In this paper Adams type methods for the special case of neutral functional differential equations are examined. It is shown thatk-step methods maintain orderk+1 for sufficiently small step size in a sufficiently smooth situation. However, when these methods are applied to an equation with a non-smooth solution the order of convergence is only one. Some computational considerations are given and numerical experiments are presented.     

Kinetics of the hydrogen electrode reactions of platinum in the NaHSO4 + KHSO4 eutectic melt

The kinetics of the hydrogen electrode reactions on Pt in the NaHSO₄ + KHSO₄ melt at ca. 185°C is studied. Under potentiodynamic conditions both the anodic and cathodic processes can be interpreted with the hydrogen electrode reaction mechanism already known. At potentials more negative than 0.1 V (vs. Ag/Ag⁺ (0.06 M)) the mechanism of the cathodic reaction changes because of a sulphide species formed on the electrode which is produced by a reduction of the melt components.     

A new Ba(OH)2 catalyst for synthesis of diacetone alcohol

The application of new Ba(OH)₂ catalysts for the preparation of diacetone alcohol is described. No loss of activity is observed when they are stored in a dessiccator over NaOH. The same yield as that described in the literature is obtained, but in a much shorter reaction time (9.5 h against 72–120 h)

---

Ba(OH)₂ . NaOH . , , (9,5 72–120 ).

     

Thermal analysis of binary and ternary systems of salicylic acid,sodium salicylate and sodium hydrogen carbonate

The thermal decompositions of binary and ternary systems of salicylic acid, monosodium salicylate, disodium salicylate and sodium hydrogen carbonate were studied by thermogravimetry and differential thermal analysis. The possibility was shown of analyzing systems involving components which react with each other upon heat treatment. Use can be made of results of this work to follow the course and extent of the reaction employed in the commercial method of manufacturing sodium salicylate and to check declared compositions of salicylate mixtures.

---

Zusammenfassung Die thermische Zersetzung binärer und ternärer Systeme, die Salicylsäure, Mononatriumsalicylat, Dinatriumsalicylat und Natriumhydrocarbonat enthalten, wurde untersucht. Die Möglichkeit der Analyse von Systemen, deren Komponenten bei Hitzebehandlung miteinander reagieren, wurde gezeigt. Die Ergebnisse dieser Arbeit gestatten den Verlauf und das Ausmaß der Reaktionen zu untersuchen, welche bei dem Herstellungsverfahren von handelsüblichen Natriumsalicylat ablaufen und die deklarierte Zusammensetzung von Salicylatmischungen zu prüfen.

---

Résumé Etude par thermogravimétrie et analyse thermique différentielle de la décomposition thermique de systèmes binaires et ternaires constitués d' acide salicylique salicylate monosodique, de salicylate disodique et d'hydrogénocarbonate de sodium. On montre la possibilité d'analyser des systèmes dont les composants réagissent entre eux lors du traitement thermique. Les résultats de cette étude permettent de suivre le déroulement et le degré d'avancement de la réaction utilisée dans le procédé commercial de fabrication du salicylate de sodium et de contrôler la composition déclarée des mélanges de salicylates.

---

, , , , . , . , - .

     

Kinetics of particle deposition in the oblique impinging jet cell

A new oblique impinging-jet (OBIJ) cell was developed, suitable for colloid deposition studies at various interfaces. In contrast to previously used orthogonal cells, the OBIJ construction makes possible direct microscope observations of particle deposition on nontransparent substrates. The cell performance was tested by studying kinetics of polystyrene latex particle deposition on mica. Two limiting cell configuration were used in the experiments: (i) the lower position (inverted microscope observation of substrate surface through air) and (ii) the upper position (observation of the substrate surface with adsorbed particles through the suspension layer). The dependence of local mass transfer rate (particle flux) on the position over the substrate surface was studied for various flow Reynolds numbers. It was demonstrated that deposition rate attained maximum at the flow stagnation point whose position was dependent on Re number. Moreover, it was shown that the local flux decreased at much slower rate when moving in the downstream direction, than for previously used impinging-jet cells. Consequently, the area of uniform transport conditions was larger, enabling more precise determination of the limiting particle flux at the stagnation-point. The dependence of the flux on Re number was systematically studied for various ionic strength of the suspension. It was demonstrated, in accordance with previous results for the ordinary impinging-jet, that the flux increased significantly for low ionic strength and high Re number. This phenomenon, referred to as the inverse salt effect, was interpreted in terms of the convective diffusion theory. The governing transport equation originating from this theory was solved numerically, for the region near the stagnation point, using the finite-difference method. These numerical solutions were used for nonlinear fitting of the flow intensity parameter dependence on the Re number. In this way the flow field in the vicinity of the stagnation point was fully characterized. It was concluded that the new cell can be exploited as an effective experimental tool for colloid deposition studies on various substrates.     

Contribution to the mechanism of liquid membrane oscillators involving cationic surfactant

It is shown that liquid membrane oscillators with cationic surfactants have more complex oscillation patterns than observed previously. The actual details of the oscillations depend strongly on the nature of the membrane material, disclosing even the presence of parallel molecular events. It appears that sampling topology also has a great influence on the observed oscillatory behavior. Variation of oscillation patterns with diffusion path length in the membrane demonstrated the decisive role played by the actual timing of molecular events. The new evidences produced complete usefully the actual views concerning the mechanism of oscillations.     

Potential energy surface for the CCl4 + H --> CCl3 + ClH reaction: kinetics and dynamics study

An analytical potential energy surface for the gas-phase CCl4 + H --> CCl3 + ClH reaction was constructed with suitable functional forms to represent vibrational modes. This surface is completely symmetric with respect to the permutation of the four chlorine atoms and is calibrated with respect to experimental thermal rate constants available over the temperature range 297-904 K. On this surface, the thermal rate constants were calculated using variational transition-state theory with semiclassical transmission coefficients over a wider temperature range 300-2500 K, therefore obtaining kinetics information at higher temperatures than are experimentally available. This surface was also used to analyze dynamical features, such as tunneling and reaction-path curvature. In the first case, the influence of the tunneling factor is very small since a heavy chlorine atom has to pass through the barrier. In the second, it was found that vibrational excitation of the Cl-H stretching mode can be expected in the exit channel.     

The reactions of 2-benzoylpyridine with [RuHCl(CO)(PPh3)3] and [(C6H6)RuCl2]2

The reactions of [RuHCl(CO)(PPh₃)₃] and [(C₆H₆)RuCl₂]₂ with 2-benzoylpyridine have been examined, and two novel ruthenium(II) complexes – [RuCl(CO)(PPh₃)₂(C₅H₄NCOO)] and [RuCl₂(C₁₂H₉NO)₂] – have been obtained. The compounds have been studied by IR and UV–Vis spectroscopy, and X-ray crystallography. The molecular orbital diagrams of the complexes have been calculated with the density functional theory (DFT) method. The spin-allowed singlet–singlet electronic transitions of the compounds have been calculated with the time-dependent DFT method, and the UV–Vis spectra of the compounds have been discussed on this basis.