Zu einigen mathematischen problemen in der theorie der transonischen strömung

The work deals with a definition of a weak solution of steady plane transonic flows past a thin profile, with the properties of the solution across a shock wave, and with a derivation of a conservative difference scheme suitable for numerical solution of the above mentioned problem by a finite difference method. The work presents several examples of numerical solution of transonic flows past a profile, through a plane cascade and some three-dimensional results. The numerical results presented are compared with experimental results or with numerical results by other authors.     

In situ vinylindole synthesis. Diels-alder reactions with maleimides to give tetrahydrocarbazoles

Tetrahydrocarbazoles have been prepared in one-flask syntheses from indoles, ketones or aldehydes, and maleimides, with acid catalysis. The reactions involve a condensation of the indole with the ketone or aldehyde, followed by an in situ trapping of the vinylindole in a Diels-Alder addition with a maleimide. Isomerization of the double bond into the indole nucleus gave the tetrahydrocarbazoles which were isolated ( 6, 9 , and 10 ). Variation of the indole, carbonyl compound, and maleimide has been explored. The predominant stereochemistry of the tetrahydro ring in the products is all-cis, although a second stereoisomer has been isolated. Two regioisomers were generated from all unsymmetrical 2-alkanones, except 2-butanone, which gave the single isomer 9a . Aromatization of tetrahydrocarbazoles 6 to carbazoles 7 was accomplished with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone.     

Modellierung und numerische Simulation der Thermoregulation von Früh- und Neugeborenen

Bei frühgeborenen S?uglingen spielt die Thermoregulation zur Aufrechterhaltung einer überlebenswichtigen K?rpertemperatur durch W?rmeproduktion, -abgabe bzw. -aufnahme eine entscheidende Rolle. Der Einsatz moderner Inkubatoren soll die k?rpereigenen Thermoregulatoren unterstützen, und es ist im Hinblick auf verschiedene medizinische Fragestellungen wünschenswert, diesen Prozess modellieren zu k?nnen. Wir stellen ein einfaches Modell auf der Basis von partiellen Differentialgleichungen vor und beschreiben detailliert die numerische Simulation mit Hilfe einer Finite-Volumen-Methode. Dazu wird ein zweidimensionales Modell eines Frühgeborenen trianguliert und das Modell diskretisiert. Zahlreiche numerische Resultate zeigen die Qualit?t unseres Modells.     

Laser Based Techniques for Ultra Trace Isotope Production, Spectroscopy and Detection

A variety of research activities in the field of fundamental and applied nuclear physics has evolved in the last years using resonantly tuned radiation from powerful lasers. The technique of resonance ionization spectroscopy has delivered outstanding results and found broad acceptance in the last years as a particularly efficient and highly selective method for rare and exotic radioisotope studies. It is used for production, spectroscopy and detection of these species and provides complete isobaric, high isotopic and even some isomeric selection, which altogether is needed for on-line investigation of short lived species far off stability as well as for ultra trace determination. Good overall efficiency pushes the experimental limits of detection in elemental trace analysis down to below 10⁶ atoms per sample, and additionally isotopic selectivity as high as 3 × 10¹² has been demonstrated. The widespread potential of resonance ionization techniques is discussed, focusing on the experimental arrangements for applications in selective on-line isotope production, spectroscopy of rare radioisotopes and ultra trace determination of radiotoxic isotopes like ²³⁸Pu to ²⁴⁴Pu, ^135,137Cs, ^89,90Sr or ⁴¹Ca in environmental, technical and biomedical samples.     

Modeling of stochastic forces in turbulent space plasmas

A model of a Langevin equation for electrons in turbulent, almost collisionfree magnetoactive plasmas is developed, which can form the starting point for particle simulations, especially in regions with reconnection of magnetic-field lines. The mean wave force is expressed by a friction force and a velocity derivative of the intensity of the stochastic force. The obtained expression for the Langevin force is consistent with the kinetic theory in a polarization approximation. The intensity of the stochastic force corresponds to the velocity diffusion tensor of the electrons, which is estimated for plasmas with ionacoustic turbulence using two different methods. One method is based on direct calculation of the space-time spectral density of the wave energy. The second method uses approximations of quasi-linear plasma theory. The estimates for the intensities of the stochastic forces found by the two methods differ by orders. A table of parameters of ion-acoustic waves, electron-wave collision frequencies, and intensities of stochastic-wave forces on electrons in solar flares, in the solar wind, as well as in different regions of the earth's magnetosphere is presented. Results are given for the entire ranges of available experimental data for the mean magnetic induction, mean plasma temperatures, and mean particle densities.Published from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 1, pp. 93–107, January, 1996.     

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.     

Stable solutions of some ill-posed problems

Stable solutions of equations of the first kind and equations of the second kind at a characteristic value are given. Iterative processes for solutions are constructed. Extension of operators is used to turn an ill-posed problem into a well-posed one.