Highly stereoselective reductions of α-alkoxy-β-keto esters. Aspects of the mechanism of sodium borohydride reduction of ketones in 2-propanol

Reduction of α-alkoxy-β-keto esters with sodium borohydride in 2-propanol proceeds with high stereoselectivity via a five-membered ring chelated sodium ion.     

An array model for the field adsorption of helium on tungsten (111)

A theory of field adsorption has been developed, using a charged-surface model comprising an infinite regular array of superimposed monopoles and dipoles, together with a distant array of monopoles of the opposite polarity. Previous theoretical treatments are shown to be oversimplified, and the effects of various corrections to the present treatment are explored. For helium on tungsten (111) in an external field of 56 V/nm, the conventionally-defined field-induced contribution to the short-range binding energy is estimated to probably lie between 40 and 75 meV, and the total differential short-range binding energy is estimated to probably lie between 30 and 50 meV. As far as is known, this is the first detailed theoretical discussion of field adsorption on a specific crystal face, and a paradigm situation has been chosen for investigation.     

A class of multidimensional periodic splines

Periodic spline functions are introduced by use of reproducing kernel structure in Hilbert spaces. Minimum properties are described in interpolation and best approximation problems. A numerical method for determining interpolating splines and best approximations is proposed.Dedicated to Prof. Dr. F. Reutter on the occasion of his 70th birthday     

Die Automorphismen der isotropen Bewegungsgruppe

Ohne ZusammenfassungHerrn Professor K.Strubecker zum 60. Geburtstag     

Conjugate function theory in weak1 Dirichlet algebras

The fundamental theorems on conjugate functions are shown to be valid for weak¹ Dirichlet algebras. In particular the conjugation operator is shown to be a continuous map of L^p to L^p for 1 < p < ∞, to be a continuous map of L¹ to L^p, 0 < p < 1, and to map functions in L^∞ to exponentially integrable functions. These results allow a number of results for Dirichlet algebras to be extended to weak¹ Dirichlet algebras.     

Gauge fields,BRS symmetry and the Casimir effect

The canonical quantization of the photon field in covariant gauge is studied in the presence of static boundaries, on which the field satisfies either “bag” or superconductor boundary conditions. The inclusion of the Fadeev-Popov ghost fields is found to be essential for agreement with Coulomb gauge calculations of the Casimir energy.