Minimal surfaces with prescribed topological type on a Schwarzian chain inMc3

Similar to the investigations of unstable polygonal minimal surfaces by Courant [1] we introduce here a variational principle for the free boundary problem with prescribed topological type which produces minimal surfaces in Riemannian manifolds with constant curvature. For special boundary configurations the surfaces have no branch points. The approach can be applied to numerical algorithms since it is constructive.     

Abels Unmöglichkeitsbeweis im Spiegel der modernen Galoistheorie

Ohne Zusammenfassung Eingegangen am 14.07.1997 / Angenommen am 02.10.1997     

Perturbed hard-sphere equations of state of real fluids. II. Effective hard-sphere diameters and residual properties

Effective hard-sphere diameters for argon, krypton and xenon have been calculated from the currently most accurate perturbation theories using accurate pair-potential models. Based on the theoretical diameters and on pressure—volumes—temperature data for the real fluids, the van der Waals parameter a_p is examined and two conjectures generalizing the behavior of a_p are formulated. These conjectures make it possible to evaluate the effective hard-sphere diameters of simple liquids at the triple-point temperature from data for a few low-temperature pressure—volume isotherms. This fact, together with a corresponding-states principle that emerges from results for the theoretical diameters, forms the basis of a simple method which we propose for evaluating temperature-dependent effective hard-sphere diameters of a perturbed hard-sphere equation of state, independently of any pair-potential model and any perturbation theory. The applicability of the method is demonstrated for methane and its extension to nonsimple liquids is discussed. It is also shown that the use of an approximate theory and/or approximate pair-potential model may often result in a qualitatively misleading picture of a_p behavior.     

Potenzsummenformeln im 17. Jahrhundert

Interest in power series of natural numbers is to be seen not only against the background of their application to the quadrature-problem of parabolas and hyperbolas, as with Fermat, but it is fueled as well by purely number-theoretic interests, which were accompanied by number-mystical speculations, as with Johannes Faulhaber. On another level the seventeenth-century works on power series of natural numbers show quite clearly how long heuristic methods were regarded as powerful in proofs, and how much the introduction of rigorous methods of proof depended on the communications system of mathematicians.     

Phase Equilibria in the Ni–Al–W System at 900°C

Summary. Multicomponent Ni-base alloys exhibit good mechanical properties even at elevated temperatures and they are widely used for industrial production of exertion-resistive parts of engines. These properties are mainly determined by the coexistence of a disordered γ matrix with a face centred cubic lattice and cuboidal domains of its ordered γ′ structure. Therefore it is useful to study phase equilibria in Ni-base systems, namely in the regions involving both mentioned phases. One of the conclusions of our recent work on Ni–Al–Cr–W system was a necessity of modification of selected thermodynamic parameters of the ternary Ni–Al–W subsystem in order to achieve a better agreement of our experimental observations with theoretical modelling. This involves new measurements of the microstructure of selected samples of the Ni–Al–W system at 900°C and the comparison of the results with existing literature data in order to confirm our conclusions on higher order system investigated before. It is a first step on the way to an assessment of the Ni–Al–W system, which has not been done before.     

Photoinduced switch of a DNA/RNA inactive molecule into a classical intercalator

Spectroscopic titrations and thermal denaturation experiments show that "acyclic" analogue 1 does not bind to ds-DNA, but under same conditions "cyclic" 2 strongly interacts with ds-DNA and ds-RNA by intercalation into the double helix. Besides, 2 is significantly more effective in inhibition of the tumor cell growth in vitro than 1. We have shown that it is possible to efficiently and irreversibly convert "DNA inactive" compound 1 into "DNA active" compound 2 by light irradiation of the aqueous solutions of the former. This strategy offers a new and attractive approach to photoinduced anticancer therapy.     

Energy spectrum of α particles emitted from sources of different thicknesses

The shape of the energy distribution of all particles emitted by sources of different thicknesses was investigated. The energy distribution N(E) dE found can be expressed by a semi-empirical formula, which on the whole agrees with experiment. The source of particles was uranium oxide U ₃ 0 ₈.The energy distribution was measured with AGFA K2 nuclear emulsions 200 thick. Altogether 3,602 trajectories of particles in the nuclear emulsions of five plates were measured.The author would like to thank Prof. Dr. V. Petrílka, M. Rozko and L. Drka for remarks and their interest in this paper. He also thanks R. Krejí, J. Lejnarová and H. Koutová for carefully and promptly measuring the trajectories and for help in realizing the experiments.     

The Reaction of 3-Formylchromone with ortho-Substituted Anilines. Preparation of a Tetraaza [14]annulene

The reactions of 3-formylchromone ( 1 ) with 1, 2-phenylenediamine, 2-amino-diphenylamine and 2-aminophenol were reinvestigated and shown to yield 1, 8-dihydro-6, 13-di (2-hydroxybenzoyl)-dibenzo [b, i]-l, 4, 8, 11-tetraazacyclotetradeca- 4, 6, 11,13-tetraene ( 7 ), 3-[2-(1-phenyl)benzimidazolyl]chromone ( 10b ) and 3-(2-hydroxyphenyl)iminomethylchromone ( 4 ), respectively at variance with earlier reports. Compound 4 reacts with ethanol to give 2-ethoxy-3-[(2-hydroxyphenyl)-aminomethylidene]chroman-4-one ( 5b ). Dehydrogenation of 7 produces 3-(2-benz-imidazolyl)chromone ( 10a ), also at variance with earlier reports. The structures have been elucidated with the aid of NMR. and mass spectra. The reaction mechanism is discussed.     

Condensed phases in flame spectrometry: an equilibrium model of the acetylene flame

An equilibrium model for a wet acetylene flame has been used for the calculation of the distribution of carbon, aluminium and silicon between gaseous and condensed phases. Calculated values of free atom vapour fractions are in agreement with published experimental data. It is thermodynamically probable that the formation of condensed phases limits atom vapour formation. There is a relationship between the position of an element in the Periodic Table and the nature of the condensed phase.