Zur Berechnung Stekloffscher Eigenwerte-numerische Beispiele

Zusammenfassung Es werden Ergebnisse numerischer Experimente bei der Berechnung des ersten nichttrivialen Stekloff Eigenwertes angegeben.Alle Beispiele zeigen eine Monotonieeigenschaft des Eigenwertes und stützen eine Vermutung über Eigenwerte konvexer Außengebiete.

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Results of numerical experiments are given for the evaluation of the first nontrivial Stekloff eigenvalue.All examples show a monotonicity property of the eigenvalues and support a conjecture of eigenvalues for convex exterior domains.

     

Evolution on a smooth landscape

We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population is governed by correlation functions that although being formally down by powers ofN (the population size), nonetheless control the evolution process after a very short transient. The long-time behavior can be found analytically since only one of these higher order correlators (the two-point function) is relevant. We compare and contrast the exact findings derived herein with a previously proposed phenomenological treatment employing mean-field theory supplemented with a cutoff at small population density. Finally, we relate our results to the recently studied case of mutation on a totally flat landscape.     

Dissolution and forming of cellulose with ionic liquids

The dissolution of cellulose in different ionic liquids will be described as a very recent subject for a direct dissolving process, which was used to prepare regenerated cellulose fibres. The preparation of the dopes was arranged starting from slurry of cellulose in the aqueous ionic liquid by removing the water at elevated temperature, vacuum and high shearing rates. As ionic liquids, the 1-N-Butyl-3-methylimidazolium chloride, the 1-Ethyl-3-methylimidazolium chloride, the 1-N-Butyl-2,3-dimethylimidazolium chloride, the 1-N-Butyl-3-methylimidazolium acetate and the 1-Ethyl-3-methylimidazolium acetate were investigated. The cellulose solutions in ionic liquids were characterised by means of light microscopy, cone-plate rheometry and particle analysis. In addition these results were compared with cellulose solutions in N-methyl-morpholine-N-oxide monohydrate. Finally the cellulose dopes were shaped by a dry-wet spinning process to manufacture cellulose fibres. The properties of the resulted fibre had been determined and will be discussed.     

Note on the theory of solutions of strong electrolytes

Summary In the general case, assumptions of an increase in the average diameter of ions and hydration numbers with temperature contradict experiment. To explain the positive deviations of experimental heats of dilution from the Debye-Hückel theory, it is necessary to consider the existence of ionic pairs in solution and changes in the solution structure with concentration.