On quartics with three-divisible sets of cusps

 We study the geometry and codes of quartic surfaces with many cusps. We apply Gr?bner bases to find examples of various configurations of cusps on quartics. Received: 10 May 2002 / Revised version: 11 November 2002 Published online: 3 March 2003 Permanent address: Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland. e-mail: rams@mi.uni-erlangen.de, rams@im.uj.edu.pl Research partially supported by the Schwerpunktprogramm ``Global methods in complex geometry' of the Deutsche Forschungsgemeinschaft, and by EAGER. Mathematics Subject Classification (2000): 14J25, 14J17     

Leggett-Williams norm-type theorems for coincidences

We study the existence of positive solutions to the operator equation Lx = Nx, where L is a linear Fredholm mapping of index zero and N is a nonlinear operator. Using the properties of cones in Banach spaces and Leray-Schauder degree for completely continuous operators, k-set contractions and condensing mappings, we obtain some refinements of the results established in [3] and [14]. Received: 9 July 2005; revised: 12 January 2006     

The measure of a translated ball in uniformly convex spaces

Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r ^q , whereq depends on the properties of the norm. We specify it in the case ofL spaces, >1.     

Structure of 18-cyanoprogesterone,C22H29O2N

The crystal structure of 18-cyanoprogesterone was determined by X-ray diffraction methods:P2₁2₁2₁ a=7.436(2),b=11.322(2),c=22.642(2) Å. The structure was solved usingShelx-86. Final conventionalR=0.054.R _w =0.051 for 1841 reflections. TheA ring has an intermediate sofa-half-chair conformation with asymmetry parameters C _s ^/1 =11.0, C ₂ ^3,4 =14.9. The steroid skeleton exhibits a flattening of theA ring relative to the rest of the molecule. The progesterone side chain has a typical conformation, and the C16-C17-C20-O20 torsion angle is –19.0(6)°.     

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.     

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.