Extrapolation methods for approximating arc length and surface area

A well-known method of estimating the length of a parametric curve in is to sample some points from it and compute the length of the polygon passing through them. In this paper we show that for uniform sampling of regular smooth curves, Richardson extrapolation can be applied repeatedly giving a sequence of derivative-free length estimates of arbitrarily high orders of accuracy. A similar result is derived for the approximation of the area of parametric surfaces.      

Injectivity and adjoint extremals

The following investigation deals with injectivity results for general diffeomorphisms as well as for Haar's transformation. We apply these results to adjoint variational problems introduced by Haar [6]. In particular, we prove a generalization of Krust's theorem for two-dimensional adjoint extremals. Received March 20, 1998 / Accepted April 24, 1998     

Electrochemical measurements on clay minerals for possible sensor applications

Natural clays were characterized by XRD, TGA and SEM/EDX, then pressed to pellets and analyzed by impedance measurements under various defined gas compositions and temperatures. From the Nyquist plot, conductivity values were calculated for the different clay samples. A strong dependence of the conductivity on the water vapour concentration at low temperatures was found for all investigated clay samples. Partial substitution of water by methanol led to a decrease in conductivity at low temperatures, confirming the essential role water plays in the conductivity mechanism at these temperatures. Increasing the temperature resulted in a decrease in conductivity, until a turn-over point was reached. Beyond this temperature an Arrhenius behaviour was observed, suggesting a change in the conductivity mechanism. Paper presented at the 5th Euroconference on Solid State Ionics, Benamádena, Spain, Sept. 13–20, 1998.     

Polystyrene with Pendant Mixed Functional Ruthenium(II)‐Terpyridine Complexes

A vinyl substituted 2,2′:6′,2″‐terpyridine and a mixed, bifunctional ruthenium(II)‐terpyridine complex bearing a vinyl and a hydroxymethyl group are utilized as comonomers for radical copolymerization with styrene. The resulting polymers are characterized by means of UV‐vis spectroscopy and gel permeation chromatography, coupled with an in‐line diode array spectrophotometer.     

Calcium Thiolates and Selenolates: Synthesis and Structures

The synthesis and structural characterization of a family of calcium thiolates and selenolates is described. In the solid state the compounds adopt either contact pairs, as observed in Ca(THF)₄(SMes*)₂ ( 1 ), (Mes* 2,4,6‐tBu₃C₆H₂), and Ca(THF)₄(SeMes*)₂, ( 2 ), or separated ions as shown in [Ca(18‐crown‐6)(HMPA)₂][SeMes*]₂ ( 3 ). The two different ion association modes are induced by addition of specific donors. The compounds were prepared by metalation involving the reaction of elemental calcium dissolved in dry liquid ammonia with either HSMes* or Mes*SeSeMes*. All compounds were characterized by X‐ray crystallography, NMR and IR spectroscopy.