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.

     

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.     

The enthalpy of mixing of liquid NaF and NaMgF3 from drop calorimetry

The enthalpy of mixing of three liquid mixtures of NaF and NaMgF₃ has been measured by drop calorimetry and was found to be negative. This energy release is attributed to a change in the equilibrium

Mg_1/4[MgF²⁻₄]_3/4+f⁻ å MgF²⁻₄ to the formation of complex MgF²⁻₄-ions. A ΔH^M diagram for the system NaF-MgF₂ up to 50 mol % MgF₂ has been constructed.     

Isonitrile trapping reactions under thermolysis of alkoxyamines for the synthesis of quinolines

[reaction: see text] An efficient tandem radical process comprising a thermal alkoxyamine homolysis, an isonitrile trapping reaction, a 5-exo-trig cyclization, and a homolytic aromatic substitution leads to substituted dihydroquinolines. Depending on the substituent R(1), oxidation to dihydro-1H-cyclopenta[b]quinolines (for R(1) = aryl) or tautomerization to tetrahydro-1H-cyclopenta[b]quinolines (for R(1) = CO(2)Me, CN) occurs. The heterocycles are obtained in moderate to good yields. Upon using microwave-induced heating, the reaction time can be shortened from 3 days to 30 min.     

Perturbations of positive semigroups on AM-spaces

We consider positive perturbations of positive semigroups on AM-spaces and prove a result which is the dual counterpart of a famous perturbation result of Desch in AL-spaces. As an application we present unbounded perturbations of the shift semigroup.