On the embedding problem with noncommutative kernel of order p4. VI

In the case of number fields the embedding problem of a p-extension with non-Abelian kernel of order p⁴ is studied. The two kernels of order 3⁴ with generators α, γ and relations α⁹ = 1, [α,α]³=1,[α,αγγ]==1,[αγγ]=α³,γ³=1 or γ³=α³ and the kernel of order 2⁴ with generators α, β, γ and relations α⁴=1 β²,[αγ]=1, [α,γ]=1,[βγ]=α² are considered. For kernels of odd order the embedding problem is always solvable. For the kernel of order 16 the solvability conditions are reduced to those for the associated problems at the Archimedean points, and to the compatibility condition. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 74–82.     

A note on dephasing and pair-breaking

It is shown that the dephasing which suppresses the weak localization correction to the conductivity has the same physical origin than pair-breaking in superconductors and thus-following de Gennes-may be expressed in terms of the correlation function of the operator for time reversal.     

A globally convergent multi-grid algorithm for moving boundary problems of two-phase Stefan type

In this paper we deal with the numerical solution of movingboundary problems of two-phase Stefan type. Based on an implicitdiscretization in time and the use of continuous, piecewiselinear finite elements in the space variables with respect tothe weak formulation of the problem, a globally convergent multi-gridalgorithm is developed. That algorithm strongly relies on thevariational characterization of the fully discretized problemas the unconstrained minimization of a subdifferentiable convexobjective functional. Numerical results indicate a significantimprovement in efficiency compared with previous multi-gridapproaches.     

Structure of thin block copolymer films studied by X-ray reflectivity

Summary X-ray reflectivity may be used to determine the internal structure of thin polymer films. An electron density difference of 10% for polystyrene and polyisoprene is sufficient to distinguish between a random distribution of lamellae, complete orientation parallel to the substrate surface and a surface induced formation of lamellae. The disappearance of the lamellar Bragg-peaks, with heating of the film, shows the transition into the disordered state.     

Liquid crystal properties of some substituted pyrazines

A number of biphenyl, terphenyl analogues and ethynes which contain a pyrazine ring have been made and their liquid crystal transition temperatures, together with examples of birefringence measurements, are reported. All the 2,5-disubstituted pyrazine systems are liquid crystalline showing high birefringence values for the biphenyl and terphenyl analogues, whereas the 1,5-disubstituted systems are not liquid crystalline. The pyrazine ethyne systems exhibit very high birefringence values. X-ray diffraction has been used to identify the liquid crystal phases of 2-n-nonyloxy-5-(4'-propylbiphenyl-4-yl)pyrazine.     

Novel optical techniques for the analysis of polymer surfaces and thin films

Summary We report on novel optical techniques, based on evanescent waves, for the characterization of polymer surfaces and thin films. We first describe photo-ablation studies with polysilane films investigated by surface plasmon microscopy, a technique which is particularly well-suited for ultrathin samples. Thicker films that are homogeneous enough to carry optical waveguide modes can be characterized with high lateral resolution by the recently developed waveguide microscopy. We demonstrate this for a thin film of a solid polyelectrolyte. Finally, we report on surface plasmon field-enhanced Raman-spectroscopic and -imaging investigations of ultrathin Langmuir-Blodgett-Kuhn-layers of cadmium arachidate.W. Hickel is now with HOECHST AG, Angewandte Physik, W-6230 Frankfurt 80     

Existence of solutions for the time-dependent thermistor equations

The equations describing the behaviour of temperature/flow microsensorsemploy-ing polysilicon thermistors form a degenerate nonlinearparabolic system. One special feature is that different equationsof this system are to be satisfied on different domains. Bymeans of supersolutions and subsolutions, the maximum principle,and fixed point arguments, the authors show the existence ofsolutions to the equations.