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.     

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.     

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.     

Zur Theorie der ebenen,instationären Unterschallströmung um ein schwingendes Profil im Kanal

Summary The mixed boundary value problem for the determination of the velocity potential of an unsteady perturbation flow past an oscillating thin profile in an inviscid compressible gas at subsonic speeds is treated. After the separation of the wave-like terms in the Fourier expansions of the reduced potential, satisfying the Helmholtz wave equation, the boundary value problem for the remaining potential is transformed into a functional equation of the generalized Wiener-Hopf type by means of the Laplace transform. The familiar Wiener-Hopf technique leads to a linear system of infinitely many unknowns which can be solved by iteration for not too small profile lengths. Finally, two analytic expressions for the reduced potential in terms of different kernel functions and formulae for the lift and moment acting on the profile are written down.

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Diese Arbeit enthält einen Teil der von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität des Saarlandes am 30. Oktober 1963 angenommenen Habilitationsschrift des Verfassers.     

Weak norms of random sums

Let denote a sequence of measurable functions on , and let denote the weak norm. It is shown that

where is a sequence of independent random variables taking on values and with equal probability. Moreover, it is shown that

The paper concludes by providing an example indicating that, if , then the estimate

is the best possible.