Short-range order and F ion diffusion inside the Pb1 − xAlxF2 + x solid solution Part II: Al NMR investigation and proposal of clustering process

A ²⁷Al nuclear magnetic resonance (NMR) investigation at room temperature of the Pb_{1 − x}Al_xF_{2 + x} (0 ≤ x ≤ 0.12) solid solution and of the ordered Pb₉Al₂F₂₄ phase is carried out. Two different types of aluminium ions are identified and their ratio is determined as a function of x. A clustering process based on the formation of column clusters, more and more extended when x increases, is proposed on the basis of results issued from the ¹⁹F (Part I) and ²⁷Al NMR investigations.     

On Subspaces and Quotients of Banach Spaces C(K, X)

 We study the relation of to the subspaces and quotients of Banach spaces of continuous vector-valued functions , where K is an arbitrary dispersed compact set. More precisely, we prove that every infinite dimensional closed subspace of totally incomparable to X contains a copy of complemented in . This is a natural continuation of results of Cembranos-Freniche and Lotz-Peck-Porta. We also improve our result when K is homeomorphic to an interval of ordinals. Next we show that complemented subspaces (resp., quotients) of which contain no copy of are isomorphic to complemented subspaces (resp., quotients) of some finite sum of X. As a consequence, we prove that every infinite dimensional quotient of which is quotient incomparable to X, contains a complemented copy of . Finally we present some more geometric properties of spaces. Received 8 November 2000; in revised form 7 December 2001     

A new class of Ornstein transformations with singular spectrum

It is shown that for any family of probability measures in Ornstein type constructions, the corresponding transformation has almost surely a singular spectrum. This is a new generalization of Bourgain's theorem [J. Bourgain, On the spectral type of Ornstein class one transformations, Israel J. Math. 84 (1993) 53–63], same result is proved for Rudolph's construction [D. Rudolph, An example of a measure-preserving map with minimal self-joining and applications, J. Anal. Math. 35 (1979) 97–122].     

Quadratic spline interpolation on uniform meshes

The interpolation problem at uniform mesh points of a quadratic splines(x _i)=f _i,i=0, 1,...,N ands(x ₀)=f₀ is considered. It is known that s–f=O(h ³) and s–f=O(h ²), whereh is the step size, and that these orders cannot be improved. Contrary to recently published results we prove that superconvergence cannot occur for any particular point independent off other than mesh points wheres=f by assumption. Best error bounds for some compound formulae approximatingf _i andf _i ⁽³⁾ are also derived.     

Numerical methods for reaction-diffusion problems with non-differentiable kinetics

Summary We consider a class of steady-state semilinear reaction-diffusion problems with non-differentiable kinetics. The analytical properties of these problems have received considerable attention in the literature. We take a first step in analyzing their numerical approximation. We present a finite element method and establish error bounds which are optimal for some of the problems. In addition, we also discuss a finite difference approach. Numerical experiments for one- and two-dimensional problems are reported.Dedicated to Ivo Babuka on his sixtieth birthdayResearch partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under Grant Number AFOSR 85-0322     

Properties of RF sputtered ZnxCd1−xS thin films

Zn _x Cd_1–x S thin films (0x0.20) were prepared using rf sputtering in argon atmosphere and characterized using X-ray diffraction, optical transmission, electrical resistivity and photoconductive decay measurements. The films were found to possess hexagonal structure. The crystallite size and degree of preferential orientation were found to decrease with the increase ofx and to improve upon annealing in vacuum at 250 °C. The transmission edge shifted towards shorter wavelengths with the increase ofx in agreement with the expected shift in the energy band gap. The films were found to exhibit room temperature resistivity in the range 100–1000 cm. The obtained values of long wavelength transmission (70–80%) and minority carrier diffusion length (30 m) are high enough for the application of these films in the field of solar cells.     

Studies on the liquid-liquid extraction and ion and precipitate flotation of Co(II) with decanoic acid

The liquid-liquid extraction, ion and precipitate flotation of Co(II) from chloride media of 1·10^–4M initial Co(II) concentration and =0.1 have been investigated using decanoic acid and the results are compared. Organic solvents used were chloroform in the case of liquid-liquid extraction and ethanol (used as a solvent for the collector and a frother) in the case of flotation. From the results it appears that liquid-liquid extraction takes place through the formation of the complex: (CoR₂)₂(HR)₂ but flotation occurs through the formation of a surface active product which has the empirical formula CoR₂. The effects of pH and of decanoic acid concentration on the three separation processes were also investigated and the results discussed. Good agreement was observed between the experimental precipitate flotation curves and the theoretical curve calculated from the data published for Co(II) hydrolysis.