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The stability of stationary interpolatory subdivision schemes for univariate data is investigated. If the subdivision scheme is linear, its stability follows from the convergence of the scheme, but for nonlinear subdivision schemes one needs stronger conditions and the stability analysis of nonlinear schemes is more involved. Apart from the fact that it is natural to demand that subdivision schemes are stable, it also has an advantage in a theoretical sense: is it shown that the approximation properties of stable schemes can very easily be determined.

In this paper analytical results are presented concerning the transient response of a composite superconducting wire in spatially periodical longitudinal ac magnetic fields. Locally solutions are positively, negatively or unsaturated in a region and the positions of the interfaces between different regions are calculated. One dominant time constant has to be included in the analysis due to the twist. Other time constants can be neglected, because the periodicity length of the field is assumed to be much larger than the radius of the wire. We focus on the influence of the dominant time constant on the interfaces.

In this paper the influence of stochastic contact resistances on coupling losses in cables is determined. The model consists of two parallel strands making contact with each other at several positions. The parallel resistances in the strands are constant. The interstrand contacts can have stochastic values. As time dependent electromagnetic fields induce currents, heat dissipation arizes. The dissipation due to the currents between the strands, defined as coupling losses, is investigated for constant contact resistances as well as for stochastic values. From the analysis, both analytical and numerical, it follows that, for spatially dependent time varying applied magnetic fields, the coupling losses increase when the parallel resistances decrease. Furthermore, it is shown that for smaller contact resistances the relative influence of the stochastic nature of the contact resistances on the coupling losses increases.