Cauchy boundary andb-incompleteness of space-time

It is shown that if a space-time (M, g) is time-orientable and its Levi-Civita connection [in the bundle of orthonormal frames over (M, g)] is reducible to anO(3) structure, one can naturally select a nonvanishing timelike vector field and a Riemann metricg ⁺ onM. The Cauchy boundary of the Riemann space (M, g ⁺) consists of endpoints ofb-incomplete curves in (M, g); we call it theCauchy singular boundary. We use the space-time of a cosmic string with a conic singularity to test our method. The Cauchy singular boundary of this space-time is explicitly constructed. It turns out to consist of what should be expected.     

A reanalysis of branching fractions of charmed mesonsD 0,D + andD s +

We combine highly complementary information on branching fractions of charmed mesonsD ⁰,D ⁺ andD _s ⁺ coming from two experiments both yielding doublecharm samples. The NA 32 experiment provided exclusive branching fractions for channels with at least two charged decay products while a recent Mark III paper provides results on inclusive charm decay properties. The knowledge of channels withK ⁰'s in the former is used to recalculate the charged multiplicity distribution in the latter. We obtain 〈n _ch〉=2.25±0.08 forD ⁰, 〈n _ch〉=1.96±0.08 forD ⁺ and 〈n _ch〉=2.41±0.38 forD _s ⁺ . In turn the knowledge of the charged multiplicity improves the overall normalization of exclusive branching fractions. This reanalysis yields model-independent results for charmed mesons. In particular we obtain branching fractions for 16D _s ⁺ decay channels including $$BF(D_s^ + \to \phi \pi ^ + ) = \left( {4.4\begin{array}{*{20}c} { + 2.3} \\ { - 1.8} \\ \end{array} } \right)\% .$$ .     

Gamow-Teller beta decay of the very neutron-deficientN=50 nuclide98Cd

For the first time, detailed decay-spectroscopic investigations were performed for the very neutron-deficientN=50 nuclide⁹⁸Cd. The⁹⁸Cd activity was produced in spallation reactions between 600 MeV protons and a natural tin target, yielding a⁹⁸Cd beam intensity of 10 to 60 atoms/s at the collector of the ISOLDE massseparator. By means of-ray and conversion-electron spectroscopy, 19 transitions were found to follow the ⁺/EC decay⁹⁸Cd⁹⁸Ag. The transitions at 61 and 107 keV were shown to beM1(+E2) andE2, respectively, and the⁹⁸Cd half-life was measured as 9.2±0.3 s. TheQ _EC value of⁹⁸Cd is determined semiempirically and is compared to model predictions together with the measuredQ _EC values of the neighbouring cadmium isotopes^100,102Cd and theN=50 isotones⁹²Mo,⁹⁴Ru, and⁹⁶Pd, taken from the literature. The newly established decay scheme of⁹⁸Cd includes 9 excited states of⁹⁸Ag. Four states at 1691, 1861, 2164, and 2544 keV are directly fed by 0⁺ 1⁺ Gamow-Teller beta transitions with a summed strength of 3.5 _–0.7 ^+0.8 . This value corresponds to 25±5% of the strength predicted for the GT transformation of a g_9/2 proton (in⁹⁸Cd) into a g_7/2 neutron (in⁹⁸Ag) by the extreme single-particle shell model. The GT-strength splitting and quenching, observed for⁹⁸Cd, are compared with the corresponding data for lighter even-even N=50 isotones, and are discussed with reference to the predictions of more sophisticated nuclear models. We find that only in some cases it is possible to explain qualitatively the observed GT strength distribution and its total magnitude without renormalizing the free-neutron value of the axial-vector coupling constant.Dedicated to Prof. P. Armbruster on the occasion of his 60th birthday     

Intermittency and the central limit theorem

Central limit theorem estimates of anomalous fractal dimensions of self-similar random cascades are studied. It is found that, in general, the normal approximation fails badly. A systematic series of approximations which converges to the exact result (both for the fractal dimensions and for the distribution itself) is derived for the -model. Consequences for the empty bin effect are indicated.Supported by the World Laboratory/HED and the CERN/LAA Projects     

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.     

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.

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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.

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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.

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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.     

Simultaneous determination of hydrogen as its iodine equivalent and of nitrogen by a volumetric method

Summary The method developed for simultaneous determination of hydrogen (by means of an equivalent amount of iodine) and of nitrogen by a volumetric method, is based on a flash combustion technique in a stream of CO₂ (100 ml/min) with controlled addition of O₂ (20%). Hydrogen is determined by conversion of water into hydrogen chloride on anhydrous magnesium chloride heated at 600–650° C, and reaction of the hydrogen chloride with Ag₂OI₂ at 220° C to yield iodine, which is collected on silver and weighed. The precision of the determination of hydrogen is excellent, the standard deviation being 0.008–0.017% abs., about a tenth of that obtained by the classical methods. The error in the determination of hydrogen was ±0.006% abs.

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Gleichzeitige Bestimmung von Wasserstoff als dessen Jodäquivalent und von Stickstoff auf volumetrischem Wege

Zusammenfassung Die entwickelte Methode zur gleichzeitigen Bestimmung von Wasserstoff in Form seines Jodäquivalents und von Stickstoff auf gasvolumetrischem Wege beruht auf der Entflammungsmineralisation im CO₂-Strom (100 cm³/min) mit kontrolliertem Zusatz von O₂ (20%). Der Gasstrom wird zusätzlich über P₂O₅ getrocknet. Die dem Wasserstoff äquivalente Jodmenge wird an metallischem Silber gebunden und gravimetrisch bestimmt, wobei Wasser bei 600–650° C mit Magnesiumchlorid in Chlorwasserstoff übergeführt wird, der nachfolgend bei 220° C mit Ag₂Oj₂ zu Jod umgesetzt wird. Für Verbindungen, die neben C, H, N und O auch Br, Cl, P und S enthalten, werden Wasserstoffresultate mit hoher Präzision erzielt:s _H beträgt 0,008 bis 0,017% absolut und ist etwa 10mal kleiner als bei den üblichen, klassischen Methoden. Die Genauigkeit der Wasserstoffbestimmung entspricht einem mittleren Fehler=±0,006% absolut. Die Resultate für den Wasserstoff und Stickstoff verlangen eine Blindwertkorrektur.