Abstract: Generalized Möbius-Listing surfaces and bodies generalize Möbius bands, and this research was motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin

Abstract: We present a Ginzburg-Landau theory for a two-band superconductor with emphasis on MgB2. We propose experiments which lead to identification of the possible scenarios: whether both sigma- and pi-bands superconduct or sigma-alone. According to the second scenario a microscopic theory of superconducting MgB2 is proposed based on the strongly interacting or-electrons and non-correlated pi-electrons of boron ions. The kinematic and Coulomb interactions of sigma-electrons provide the superconducting state with an anisotropic gap of s(*)-wave symmetry. The critical temperature T-c has a non-monotonic dependence on the distance r between the centers of gravity of sigma- and pi-bands. The position of MgB2 on a bell-shaped curve T-c (r) is identified in the overdoped region. The derived superconducting density of electronic states is in agreement with available experimental and theoretical data. It is argued that the effects of pressure are crucial to identify the microscopic origin of superconductivity in MgB2. Possibilities for increase of T, are discussed.

Abstract: In the past years, and also within the framework of this CRP, we have used a combination of several nuclear and non-nuclear techniques in fundamental research and especially in various applications. Most work has been done with energy-dispersive X ray fluorescence in combination with electron probe X ray microanalysis, but several other more common analysis techniques have been used as well. The applications have included mostly preventive conservation (e.g. characterisation of damaging atmospheric particles in many museums) and environmental monitoring (e.g. for atmospheric particles in relation to their health effects in outdoor and especially indoor environments). Fundamental aspects have been in the optimising of interfaced electron microprobe and Raman microprobe analysis and the evaluation of the potential of such an instrument for atmospheric aerosols; quite a few unexpected and unpredicted problems have appeared in the latter study.