The Z-transform and linear multistep stability

^** Email: mapjjc{at}maths.bath.ac.uk^*** Corresponding author. Email: ath{at}maths.bath.ac.uk^**** Email: hl{at}maths.bath.ac.uk This paper makes systematic use of control-theoretic methodssuch as the -transform, small-gain theorems and frequency-domainstability criteria in the analysis of the stability behaviourof linear multistep methods. Some of the results in Nevanlinna'swork are recovered and a number of new boundedness and asymptoticproperties of solutions of numerical schemes are obtained. Inparticular, we give a careful and detailed analysis of the nonlinearstability properties of strictly zero-stable methods.     

Propagation of electrohydrodynamic flow fronts generated by bipolar injection in liquid anthracene

In liquid anthracene macroscopic motion of the fluid under the influence of an electric field is observed and in detail investigated by application of Schlieren optics. The sign of charge carriers and the electrohydrodynamical mobility are determined by this method.     

Theory and application of photoelectron spectroscopy : XXX. HgC hyperconjugation

Evidence for a hyperconjugative splitting due to the interacting HgC σ_u and ethylene π(b_1u) MOs in allylmercuric chloride is presented.     

Nonlinearity and disorder in fiber arrays

We experimentally investigate light propagation in a disordered two-dimensional array of mutually coupled optical fibers. In the linear case light either spreads in a diffusive manner or localizes at a few sites. For high excitation power diffusive spreading is arrested by the focusing nonlinearity, i.e., forming a discrete soliton. By contrast, fields, which are localized in the linear regime, can experience both spreading and contraction caused by the nonlinearity.