Rulers and slaves in a random social group

LetD(n, d) be a digraph chosen at random from a family of alld-out-regular digraphs onn points. LetK(n, p) be a simple graph onn points in which each edge appears independently with probabilityp. A relationship between the properties of extreme in-degrees ofD(n,d) and extreme degrees ofK(n, p) in the case whend = (n – 1)p = o(n) is presented. A sociological interpretation is also provided.     

Bemerkungen zur colorimetrischen Bestimmung von Vanadium mit Phosphorwolframs?ure

Zusammenfassung Die colorimetrische Bestimmungsmethode von Vanadium mit Phosphorwolframsäure wurde in bezug auf den Einfluß der Reagenskonzentrationen untersucht. Außerdem wurde die Bestimmungsmöglichkeit in Gegenwart von Eisen geprüft. Es zeigte sich, daß die Konzentrationen an Phosphorsäure und Wolframat in weiten Grenzen geändert werden können, ohne die Bestimmungsgenauigkeit zu beeinflussen. Zu große Mengen Salpetersäure bewirken negative Fehler, indem die Extinktionen mit zunehmender HNO₃-Konzentration linear abnehmen. Nach der angegebenen Vorschrift kann Vanadium in Gegenwart von bis zu 150 mg Eisen(III)-ionen in einem Volumen von 25 ml bestimmt werden.     

Quecksilber(II)-Titrationen mit Variaminblau als Redoxindicator

Zusammenfassung Es wird eine volumetrische Methode zur Bestimmung von Cyanid- und Quecksilber(II)-ionen mit titrierter Quecksilber(II)-nitratlösung gegen Variaminblau als Indicator beschrieben. Das Verfahren liefert genaue, wenig streuende Werte.Vorgetragen auf der III. Arbeitstagung für analytische Chemie in Prag am 1. September 1959.     

Development in the area of UV-crosslinkable solvent-based pressure-sensitive adhesives with excellent shrinkage resistance

Solvent-based UV-crosslinkable pressure-sensitive adhesives (PSA) present a new class of products that offers the potential to produce a novel generation of ultraviolet cured self-adhesive products with excellent shrinkage resistance. A variety of solvent-based pressure-sensitive adhesives were prepared by synthesis in ethyl acetate with solid content on 50 wt.% with 2-ethylhexyl acrylate, methyl acrylate, acrylic acid, N-vinyl caprolactam and unsaturated photoinitiators: 4-acryloyloxy benzophenone, allyl benzoine and phenyl-(1-acryloyloxy)-cyclohexyl ketone. The main emphasis is given to the influence of viscosity and molecular mass of synthesized adhesive on their shrinkage. Further trials show the effect of the UV-crosslinking process with UV-lamp and comparison with acrylics PSA crosslinked with metal chelates aluminium acetylacetonate and titanium acetylacetonate on shrinkage. Further examinations describe the influence of various factors such as UV exposure time and UV dose on very relevant PSA performance such as shrinkage on coated PVC carrier.     

The application of triphenylmethane dyes to visualization of selected aliphatic compounds in thin-layer chromatography

Selected triphenylmethane dyes were used as new visualizing agents in thin-layer chromatography of higher fatty acids, higher fatty alcohols, and higher aliphatic amines.     

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.     

Dünnschicht-Chromatographie höherer Fettsäuren

Zusammenfassung Die Dünnschichtchromatographie von Fettsäuren wurde mit der Papierchromatographie solcher Säuren hinsichtlich ihrer Trennwirkung verglichen. Ein Verfahren zur quantitativen Bestimmung auf Dünn-schichten getrennter Fettsäuren wurde ausgearbeitet.

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Summary The thin layer chromatography of fatty acids was compared with the paper chromatography of such acids with respect to their separation. A method was worked out for the quantitative determination of fatty acids separated on thin layers.

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Résumé On compare la chromatographie en couche mince des acides gras avec celle sur papier, du point de vue de leur pouvoir de séparation. On a mis au point un procédé de dosage quantitatif des acides gras séparés sur couches minces.

     

On bifurcation points of a complex polynomial

Let be a polynomial of degree . Assume that the set there is a sequence s.t. and is finite. We prove that the set of generalized critical values of (hence in particular the set of bifurcation points of ) has at most points. Moreover, We also compute the set effectively.

     

The Polyakov path integral over bordered surfaces

Following the general scheme of the convariant path integral quantization of gauge systems, two alternative formulations of the first quantized closed bosonic string in a position representation are presented. In both approaches the covariant path integral representations of the propagator and of the higher order off-shell amplitudes are constructed. For a wide class of gauges the explicit formulae for off-shell amplitudes are obtained. This paper is the continuation of our previous work where the corresponding problems in the open string case were considered [20].