Obituary

With the death of Brian Kuttner on 2 January 1992, near Birmingham,England, summability theory has lost one of its leading exponents.During the period 1934–1991 he published over 100 researchpapers, including work on Fourier series, strong summability,Riesz means, Nörlund methods and Tauberian theory. Sincehis death, further papers with joint authorship have continuedto appear; his influence persists.     

13C-NMR. Spectroscopy of Naturally Occurring Substances. XXXV. Labdanic diterpenes

A total carbon shift analysis of several representatives of the labdane diterpene family of natural products is presented. The shift assignment is based on the prior shift designation of some synthetic trans-decalin derivatives.     

Dehydration-induced water disordering in a synthetic potassium gallosilicate natrolite

A new potassium gallosilicate zeolite with a natrolite topology (approximate formula K8.2Ga8.2Si11.8O40.11.5H2O) was synthesized under hydrothermal conditions and characterized as a function of temperature using monochromatic synchrotron X-ray powder diffraction and Rietveld analyses. Unlike the previously known tetragonal K8Ga8Si12O40.6H2O phase, the as-synthesized material contains twice the amount of water molecules in an ordered arrangement throughout the channels in an orthorhombic (I212121) symmetry. The ordered configuration of water molecules is stabilized below 300 K, whereas heating above 300 K results in a selective dehydration and subsequent disordering of water molecules in a tetragonal (I2d) symmetry. Above 400 K, the material transforms to a fully dehydrated tetragonal phase with a concomitant volume reduction of ca. 15%. The fully dehydrated material transforms back to its original state when rehydrated over a period of up to 2 weeks. The distribution of potassium cations within the channels remains largely unperturbed during the water rearrangements and their order-disorder transition within the channels.     

Crystal and molecular structures of tris (p-methoxyphenyl)- and tris(2,4, 6-trimethylphenyl)tin(IV) acetates

The crystal and molecular structures of tris(p-anisyl)tin acetate (1) (p-anisyl = p-methoxyphenyl) and trimesityltin acetate (2) (mesityl = 2,4,6-trimethylphenyl) have been determined. Both have monomeric structures with the acetate group acting as an asymmetric bidentate ligand. Bond valence analysis of (1) and (2) and other Ph₃SnO₂CR suggest however that the carboxylate ligand effectively occupies a single bonding position at tin. Thus in (1) and (2) the tin atom is in a chemical environment equivalent to that found in four-coordinate R₃Sn-X systems based on tetrahedral geometry.     

Absence of Absolutely Continuous Spectra for Multidimensional SchrOdinger Operators with High Barriers

We prove absence of absolutely continuous spectra for multidimensionalSchrödinger operators with high barriers. The result isformulated in terms of a geometric condition on the barrierswhich entails singular spectrum. The proof combines probabilisticand functional analytic techniques.     

Integrable optical geometry

It is shown that a Lorentzian 4-manifold admitting a congruence of optical (null) geodesics without shear and twist defines an optical geometry which is integrable (locally flat) in the sense of the theory of G-structures. The existence of a symmetric linear connection compatible with the optical geometry is another condition equivalent to the integrability of the optical G-structure.