On a Family of Thue Equations Over Function Fields

Many families of parametrized Thue equations over number fields have been solved recently. In this paper we consider for the first time a family of Thue equations over a polynomial ring. In particular, we calculate all solutions of X(X-Y)(X-(T+x)Y)+Y³=1+xT(1-T)X(X-Y)(X-(T+\xi)Y)+Y^3=1+\xi T(1-T) over \Bbb C[T]{\Bbb C}[T] for all x ? \Bbb C\xi\in{\Bbb C} .     

Application of glow discharge optical emission spectroscopy (GDOES) to the analysis of PVD- and CVD-layers

Summary PVD- and CVD-layers were analysed by GDOES using a homemade laboratory device and the commercial Spectrumat 1000. The presented examples demonstrate the many possibilities of GDOES and give information about the further development of this analytical technique.     

Stability of isooctane mixtures with 3-pentanone or biacetyl as fluorescence tracers in combustion experiments

Evidence is presented in the literature that common fluorescence tracer/fuel mixtures used in engine experiments, 3-pentanone/isooctane and biacetyl/isooctane, may decompose during extended use and storage. Investigations presented here show that preferential evaporation of the tracer and not chemical decomposition is responsible for observed decreases in fluorescence signal strength in these experiments.     

Synthesis of tungsten carbide nanopowder via submerged discharge method

Tungsten carbide nanopowder was prepared via pulsed discharge of bulk tungsten and graphite rods immersed in pure ethanol. The effect of discharge parameters on the characteristics of final products was investigated. Structural and morphological characterization of nanopowder was performed by means of X-ray diffraction analysis and transmission electron microscopy. In order to determine the feasibility of using synthesized material as an electrocatalyst, tungsten carbide nanopowder was tested for hydrogen evolution. A correlation was found between morphology of nanoparticles, their phase composition and electrocatalytic activity.     

On the cycling operation in braid groups

The cycling operation is a special kind of conjugation that can be applied to elements in Artin’s braid groups, in order to reduce their length. It is a key ingredient of the usual solutions to the conjugacy problem in braid groups. In their seminal paper on braid-cryptography, Ko, Lee et al. proposed the cycling problem as a hard problem in braid groups that could be interesting for cryptography. In this paper we give a polynomial solution to that problem, mainly by showing that cycling is surjective, and using a result by Maffre which shows that pre-images under cycling can be computed fast. This result also holds in every Artin-Tits group of spherical type, endowed with the Artin Garside structure.On the other hand, the conjugacy search problem in braid groups is usually solved by computing some finite sets called (left) ultra summit sets (left-USSs), using left normal forms of braids. But one can equally use right normal forms and compute right-USSs. Hard instances of the conjugacy search problem correspond to elements having big (left and right) USSs. One may think that even if some element has a big left-USS, it could possibly have a small right-USS. We show that this is not the case in the important particular case of rigid braids. More precisely, we show that the left-USS and the right-USS of a given rigid braid determine isomorphic graphs, with the arrows reversed, the isomorphism being defined using iterated cycling. We conjecture that the same is true for every element, not necessarily rigid, in braid groups and Artin-Tits groups of spherical type.     

Das Wachstumsnetz,ein graphisches Hilfsmittel für Entwicklungsprognosen

Zusammenfassung Zur Prognose über das Anwachsen von Verbraucheranzahlen (Fernsprechteilnehmer, Verbraucher von Konsumgütern usw.) wird vielfach mit Erfolg ein Wachstumsmodell benutzt, das sich durch die sogenannte logistische Kurve, d. h. eine durch den Tangens hyperbolicus ausdrückbare Funktion darstellen läßt. Im folgenden wird ein Wachstumsnetz angegeben, in dem sich die Kurven dieser Klasse nach ihrer Normierung (Sättigungswert bei 100%) zu Geraden strecken. So erhält man ein (in der Handhabung dem bekannten Wahrscheinlichkeitsnetz vergleichbares) Prognosehilfsmittel, dessen Gebrauch erläutert wird. Insbesondere ist das Wachstumsnetz geeignet, systematische zeitliche Änderungen der Wachstumsgesetzmäßigkeiten erkennen zu lassen und besser fundierte Approximationen zu liefern, als sie bisher mit graphischen oder numerischen Mitteln erreicht wurden.Ein besonderer Vorteil des Wachstumsnetzes liegt darin, daß es ein einfaches Kriterium dafür liefert, ob ein beobachteter Wachstumsprozeß ganz oder zeitweise einer logistischen Kurve folgt und deshalb eine entsprechende Prognose sinnvoll ist.

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Summary For the purpose of predicting the increase in consumer numbers (telephone subscribers, consumers of various goods) a growth model is often successfully used which can be represented by means of the so-called logistic curve, i. e. a curve that can be expressed in terms of a hyperbolic tangens. In the following, a growth paper is specified where curves in this category become straight lines after normalization (saturation value at 100%). A prediction device, comparable in operation to the well-known probability paper, is thereby obtained and its use is explained. The growth paper permits in particular systematic time variations of growth laws to be recognized and more exact approximations to be obtained than was possible up to now by graphical or numerical means.The growth paper offers the particular advantage of providing a simple criterion for deciding whether a certain observed growth process follows the pattern of a logistic curve closely or partially, and hence whether a prediction based on such a curve is reasonable.

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Vorgel. v.:J. Heinhold.     

Zur Erweiterung von Mengenkörpern

Ohne Zusammenfassung