In-trees and plane embeddings of outerplanar graphs

A notion of anin-tree is introduced. It is then used to characterize and count plane embeddings of outerplanar graphs. In-trees have also been applied in the study of independent vertex covers of faces in outerplanar graphs.This research was partially supported by the grant RP.I.09, from the Institute of Informatics, University of Warsaw. Hospitality of the Institute of Datalogy, University of Copenhagen where this research has been completed is gratefully acknowledged.     

The dynamics of multidimensional cosmological models in the presence of quantum effects. I. The case FRW ×T D at high temperatures

The dynamical system approach is applied to the study of dynamics of multidimensional cosmological models with topology FRW ×T ^D (D-dimensional torus) in the presence of high-temperature quantum effects. The stability methods developed in the paper of Szydowski (Gen. Rel. Grav.,20, 221, 1988) are used in the analysis of typical states of the metric in the neighborhood of singularities and for large time values. The problems of dynamical dimensional reduction, structure of singularities, isotropization, etc., are discussed in this context.     

On an application of Hall's representatives theorem to a finite geometry problem

It is well-known thatn points not belonging to a hyperplane determine at leastn hyperplanes. The possible configurations of hyperplanes in the case when the number of hyperplanes is equal ton are known, too. In this paper we obtain these results by means of Hall's representatives theorem. The setting is that of a finite geometry.     

The group of local biholomorphisms of ℂ1 and conformal field theory in the operator formalism

Motivated by the operator formulation of conformal field theory on Riemann surfaces, we study the properties of the infinite dimensional group of local biholomorphic transformations (conformal reparametrizations) of ¹ and develop elements of its representation theory.     

A model of adsorption at liquid-solid interface involving association in the bulk phase

A model of monolayer adsorption of binary liquid mixtures on homogeneous and heterogeneous solid surfaces involving association of one component in the bulk phase is discussed. Suitable model calculations, illustrating association and heterogeneity effects, have been performed according to an equation derived for adsorption excess. This equation has been examined by using the experimental data of adsorption of alcohols from benzene andn-heptane on silica gel.

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Adsorptionsmodell für die Grenzfläche Feststoff-Flüssigkeit unter Berücksichtigung der Assoziation in der Flüssigkeitsphase

Zusammenfassung Es wird ein Adsorptionsmodell binärer, flüssiger Mischungen an homogenen und heterogenen Oberflächen von Feststoffen unter Beachtung der Assoziation eines der Bestandteile in der Flüssigkeitsphase diskutiert. Mit der aus dem Oberflächenüberschuß abgeleiteten Gleichung wurden entsprechende Modellberechnungen durchgeführt, die die mit Assoziation und Heterogenität verbundenen Effekte illustrieren. Die Gleichung wurde für die experimentellen Daten der Alkoholadsorption aus Benzol undn-Heptan an Kieselgel überprüft.

     

DTA determination of the anhydrite content in rock salts

The DTA method was used to determine the phase diagram of the NaCl-CaSO₄ system over the range 0.55 wt.% of CaSO₄ in air atmosphere. The effects of SiO₂, CaCO₃ and Fe₂O₃ on the melting temperatures of pure NaCl and the eutectic were determined. On the basis of the above temperatures, a method of quantitative determination of the anhydrite content in rock salts has been developed.

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Zusammenfassung DTA wurde benutzt, um in Luft im Bereich 0 bis 55,0 Gew.% CaSO₄ das Phasendiagramm des Systemes NaCl-CaSO₄ zu bestimmen. Es wurde auch der Einfluß von SiO₂, CaCO₃ und Fe₂O₃ auf die Schmelztemperatur von reinem NaCl bzw. des Eutektikums bestimmt. Auf der Grundlage obiger Temperaturen wurde eine Methode zur quantitativen Bestimmung des Anhydritgehaltes in Steinsalzen entwickelt.

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- 0–55,0 . , . , ( ) .

     

Protolytic reactions of 3,3'-dimethylnaphthidine and 3,3'-dimethoxybenzidine

The dissociation constants of diprotonated 3,3'-dimethylnaphthidine (DMN) and 3,3'-dimethoxybenzidine (DMB) have been determined spectrophotometrically. They are: pK(a1) = 2.62 +/- 0.03, pK(a2) = 3.33 +/- 0.09 for DMN: pK(a1) = 2.83 +/- 0.07, pK(a2) = 4.05 +/- 0.12 for DMB. The molar absorptivities (l.mole(-1).cm(-1)) of all forms of the indicators have been also determined: epsilon(B) = 1.68 x 10(4), epsilon(BH(+)) = 9.34 x 10(3), epsilon(BH(2+)(2)) = 1.80 x 10(3) at 300 nm for DMB; epsilon(B) = 7.33 x 10(3), epsilon(BH(+)) = 3.73 x 10(3), epsilon(BH(2+)(2)) = 0 at 330 nm for DMN.     

Use of SPE—TLC for Quality Control of Rhodiola rosea Extracts

SPE and TLC have been used for qualitative and quantitative analysis of salidroside, rosavin, rosarin, and rosin in commercially available dry extracts from Rhodiola rosea roots. The best separation of all the compounds was achieved on silica gel TLC plates with ethyl acetate—methanol—water, 77 + 13 + 10 (v/v), as mobile phase. UV detection was performed at λ = 215 nm for salidroside and at λ= 245 nm for the rosavins (rosavin, rosarin, and rosin). Detection limits for salidroside and the rosavins were 90 ng and 60 ng per spot, respectively. Results from quantitative analysis confirmed the manufacturer’s declaration of the amounts of salidroside and the rosavins in the extracts.

     

Retention Behavior of New Oral Antidiabetic Drugs in Reversed-Phase Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - The thin-layer chromatographic behavior of three of the newest oral antidiabetic agents, pioglitazone, rosiglitazone, and...