On an algorithm considered by Stieltjes

This paper studies an iterative algorithm of the type of Gauss's algorithm mentioned by Stieltjes in his correspondence with Hermite (lettre 323) and later investigated by Myrberg. In particular, what appears to be a false statement by Stieltjes is corrected. The same algorithm, apparently being unaware of his predecessors, has also been considered by Lehmer.     

Synthesis and characterisation of medium-sized ring systems by oxidative cleavage. Part 2: Insights from the study of ring expanded analogues

Variable temperature NMR analysis and computational methods have been used to develop a detailed understanding of the ¹H NMR spectra of a family of medium-sized ring containing compounds. The family consists of analogues containing 10-, 11- and 12-membered rings and in all cases the NMR spectra at room temperature showed a series of diastereotopic methylene signals despite the lack of a stereogenic centre in these systems. On repeating the NMR analysis at higher temperatures, all the signals coalesced for the 12-membered ring system consistent with full interconversion of ring conformers. This was not observed in the analogous 10- and 11-membered ring systems with the interchange of conformers remaining slow on the NMR timescale. However, 1D gs-NOESY/EXSY NMR experiments showed that in the smaller ring systems interconversion of diastereotopic protons did occur. Computational studies suggest that the dynamic process observed by NMR for the 10- and 11-membered rings systems is different from that observed in the 12-membered ring containing compound.     

On linear-fractional relations and images of angular operators

For plus-operators in a Banach indefinite space, we consider a linear-fractional relation. The classes of operators with the empty domain of definition for such a relation are described. The sufficient (and necessary, in some meaning) conditions for the chain rule to be valid are given.     

Eigenvalue estimates for Schrödinger operators on metric trees

We consider Schrödinger operators on radial metric trees and prove Lieb–Thirring and Cwikel–Lieb–Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit.     

Determination of Diaryliodonium Species by Reverse Iodometric Titration with Ascorbic Acid

Diaryliodonium salts are used in organic chemistry, materials science and pharmaceutical chemistry. For the quantitative analysis of diaryliodonium salts, only instrumentally demanding techniques requiring highly skilled operators are available. Surprisingly, no titration method taking advantage of the oxidising ability of diaryliodonium is available in the literature. In the present work, a titration method for the determination of diaryliodonium salts is presented. It is based on the reaction of diaryliodonium species with ascorbic acid, whose excess is subsequently determined by means of iodometric potentiometric titration. Application of the protocol to various diaryliodonium salts revealed the scope and limitations of the method.     

X-ray structure and UV spectroscopic studies of (adenmato-N9)triethylphosphinegold(I)

The preparation, characterization, and X-ray structure analysis of (adeninatoN9)triethylphosphinegold(I) is reported. The crystal structure consists of discrete molecules, the adeninate anion coordinates via the N(9) atom with a Au-N(9) bond distance of 2.057(5) Å and the linear geometry about the Au atom is completed by the P atom of a disordered Et₃P ligand; the Au-P(1) bond distance is 2.238(2) Å and the N(9)-Au-P(1) bond angle is 178.8(2)°. The crystals are orthorhombic, space groupPbca, with unit cell dimensionsa=8.528(1),b=17.797(3),c=18.526(2) Å andZ=8. The structure was refined by a full-matrix least-squares procedure to finalR=0.030 andR _w =0.033 for 1749 reflections withI>2.5a(I). The electronic spectrum of the complex dissolved in water in the near ultraviolet is consistent with essentially separate -electron systems of the adenine and phosphinegold moieties; a conclusion which corroborates the X-ray structural results.     

Thin SiC<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> layers prepared by hybrid laser–magnetron deposition

Thin SiC _x films were fabricated by hybrid laser–magnetron deposition system. KrF excimer laser was used for deposition of carbon and magnetron at the same time for sputtering of Si species. Films were fabricated in argon/hydrogen ambient with and without additional RF discharge. The substrate temperature was changed up to 700°C. Films topology, crystallinity, composition, chemical bonds and optical emission spectra were studied. Films were smooth and amorphous. Films of thickness 400–1000 nm were fabricated. Adhesion moved from 8 to 14 N, depending on deposition conditions.