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.     

Technological Opportunities for the Implementation of Anti-Microbial Activities into Dry-Wet Shaped Cellulose Fibres

Metal cations are valuable antimicrobial additives for controlling of bacteria growth on textile fibres. By means of multiple actions they are able to suppress the undesirable microbe action also during wound healing. Dry-wet shaping technology offers numerous opportunities for implementation of antimicrobial activities into textile structures (fibres, yarn, fabrics). The degree of load, insertion step as well as type of additive (Ag, Cu, Zn) presents a broad field of physical modification of dry-wet spun cellulose fibres. The investigation of antimicrobial activities of manufactured fibres and yarns exhibit bactericide or bacteriostatic effects against typical pathogenic germs. Ag contents higher than 30 ppm in fibres and 0.06 per cent in yarns as well as Cu contents higher than 100 ppm in fibres and about 0.5 per cent in yarns are fairly effective for a permanent antimicrobial effect. Fabrics based on the developed fibres and yarns could already been successfully commercialised by innovative small and medium sized enterprises (SME).     

Homogenous Carboxymethylation of Cellulose in the New Alkaline Solvent LiOH/Urea Aqueous Solution

In this work, the carboxymethylation of cellulose in a new alkaline cellulose solvent, LiOH/urea aqueous solution, was investigated. Carboxymethyl cellulose (CMC) samples were characterized with FT-IR, NMR, HPLC, and viscosity measurements. Water-soluble CMC with DS = 0.36∼0.65 was prepared, from both Avicel cellulose and cotton linters in the LiOH/urea system. The total DS of CMC could be controlled by varying the molar ratio of reagents and the reaction temperature. The results from structure analysis by HPLC after complete depolymerization showed that the mole fractions of the different carboxymethylated repeating units as well as those of unmodified glucose follow a simple statistic pattern. A distribution of the carboxymethyl groups of the AGU was determined to be in the order O-6 > O-2 > O-3 position at the level.     

Nonparametric Berkson regression under normal measurement error and bounded design

Regression data often suffer from the so-called Berkson measurement error which contaminates the design variables. Conventional nonparametric approaches to this errors-in-variables problem usually require rather strong conditions on the support of the design density and that of the contaminated regression function, which seem unrealistic in many cases. In the current note, we introduce a novel nonparametric regression estimator, which is able to identify the regression function on the whole real line under normal Berkson error although the location of the design variables is restricted to some bounded interval. The asymptotic properties of this estimator are investigated and some numerical simulations are provided.     

Das Taylor-Deansche Stabilitätsproblem für beliebige Spaltbreiten

Summary The stability of a viscous flow between two co-axial circular cylinders, produced by the simultaneous effect of rotation of the interior cylinder and by a constant pressure gradient in peripherical direction, has been examined. (The two single problems had been studied first byTaylor [1] resp.Dean [2].) The perturbations investigated are vortices of the Taylor-Görtler-type and are assumed to be small. It therefore becomes possible to operate on the basis of the linear differential equations for perturbations.The present stability problem had been treated under the same assumptions byDiPrima [5] for small gap-distances by using the series method ofTaylor. In this paper, however, arbitrary gap-distances are admitted, and the integral equation method ofGörtler [3] andHämmerlin [4] has been applied. The calculated dependences of the critical Reynolds number upon the pressure gradient are in good qualitative agreement with the results ofDiPrima. However, our computations performed by more exact methods yielded somewhat different results with regard to the dependence of the critical vortex number upon the pressure gradient.