Capillary zone electrophoresis in the analysis of dyes and other compounds employed in the dye-manufacturing and dye-using industries

High resolution separation of several dyes and related intermediates, as well as other compounds employed in the dye-manufacturing and dye-using industries, has been achieved using capillary zone electrophoresis (CZE).

The analysis of anionic dyes and some non-coloured anionic intermediates has been achieved using 10 mM Na₂B₄O₇−40 mM sodium dodecyl sulphate (SDS) buffer; high-resolution separations of water soluble anionic, neutral and cationic intermediates were also achieved using this micellar buffer. Micellar electrokinetic capillary chromatography (MECC) has also been developed for the analysis of aqueous insoluble, electrically neutral compounds by incorporating a co-solvent, acetonitrile, into a micellar buffer. In addition, MECC has been used successfully for following all the major steps involved in the synthesis of a disperse dye.     

Multiplication and Compact-friendly Operators

During the last few years the authors have studied extensively the invariant subspace problem of positive operators; see [6] for a survey of this investigation. In [4] the authors introduced the class of compact-friendly operators and proved for them a general theorem on the existence of invariant subspaces. It was then asked if every positive operator is compact-friendly. In this note, we present an example of a positive operator which is not compact-friendly but which, nevertheless, has a non-trivial closed invariant subspace.In the process of presenting this example, we also characterize the multiplication operators that commute with non-zero finite-rank operators. We show, among other things, that a multiplication operator M commutes with a non-zero finite-rank operator if and only the multiplier function is constant on some non-empty open set.     

Positive operators on Krein spaces

A Krein operator is a positive operator, acting on a partially ordered Banach space, that carries positive elements to strong units. The purpose of this paper is to present a survey of the remarkable spectral properties (most of which were established by M.G. Krein) of these operators. The proofs presented here seem to be simpler than the ones existing in the literature. Some new results are also obtained. For instance, it is shown that every positive operator on a Krein space which is not a multiple of the identity operator has a nontrivial hyperinvariant subspace. Dedicated to the memory of M.G. Krein (1907–1989)     

The contribution of nuclear activation techniques to medical science

Activation techniques have been used since their inception to analyse body fluids and tissues in medical research. In recent years they have also been adapted to analyse tissues in vivo. Their wider application is restricted by their complexity and relative inaccessibility, and inter-laboratory comparisons of analyses of reference materials continue to show serious discrepancies for some elements. Activation techniques contribute most to medical science when they are applied to important medical problems which cannot be solved in other ways and when they are used as reference techniques to evaluate simpler, more accessible methods.