Instability of nonlinear bound states

We establish a sharp instability theorem for the bound states of lowest energy of the nonlinear Klein-Gordon equation,u _tt–u+f(u)=0, and the nonlinear Schrödinger equation, –iu _t–u+f(u)=0.Supported in part by NSF Grants MCS 81-21487 and MCS 82-01599     

A Simple proof of the generalized electrostatic Israel theorem

A simple proof of a generalization of the theorem of Israel concerning the uniqueness of the Reissner-Nordström black holes is presented. The present method is also applied to show, in the bosonic sector ofN=4-supergravity, the uniqueness of a static black hole solution found by Gibbons.Work supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. 4961.     

Gravitational field strength and generalized Komar integral

We define a gravitational field strength in theories of the Einstein-Cartan type admitting a Killing vector. This field strength is a second rank, antisymmetric, divergence-free tensor, whose (Komar) integral over a closed 2-surface gives a physically meaningful quantity. We find conditions on the Lagrange density of the theory which ensure the existence of such a tensor, and show that they are satisfied forN=2-supergravity and for a special case of the bosonic sector ofN=4-supergravity. We discuss a possible application of the generalized Komar integral in the theory of stationary black holes. We also consider the field strength problem in Kaluza-Klein theory, where the application to black holes is particularly interesting.     

Synthesis of the methanesulfonates of α-(4-chlorophenyl)-α-[1-(2-chlorophenyl)emenyl]-1H-1,2,4-triazole-1-ethanol and α-[1-(2-chlorophenyl)ethenyl]-α-(2,4-difluorophenyl)-1H-1,2,4-triazole-1-ethanol,alpha styryl carbinol antifungal agents

The methanesulfonates of (α-(4-chlorophenyl)-α-[1-(2-chlorophenyl)ethenyl]-1H-1,2,4-triazole-1-ethanol and α-[1-(2-chlorophenyl)ethenyl]-α-(2,4-difluorophenyl)-1H-1,2,4-triazole-1-ethanol ( 1a, b ) are orally effective α-styryl carbinol derivatives developed for the treatment and prevention of systemic fungal infections. Practical new processes amenable for the large-scale production of these compounds are described. Of note is the selection of dichlorostyrene as a convenient precursor of the styryl portion, modification of a sensitive Grignard addition into a realistic preparative reaction and the use of 1,2,4-triazole simultaneously as a base transfer agent and nucleophile.     

Microdetermination of aliphatic amines and polyamines with cupric ion: Relationship between pK1 and half-complexation potential

The first equilibrium constant for the combination of ligand with cupric ion, K₁, is related to the half-complexation potential, E_HC, by log K₁ = a + b[E_HC]. The coefficients differ for n ? 2 and n ? 2, where n is the number of nitrogen atoms in the molecule. The correlation coefficients, r, based on data available from the literature were ?0.98. The equations can be used for estimating log K₁ of aliphatic amines. Successful titration of aliphatic amines vs cupric ion requires log K₁ ? 4 and an initial pH of a 10^?3M solution of ?9.     

Zur Chemie der Pyrrolpigmente, 56. Mitt.

From an investigation of the ICD of bilatrienes-abc and 2,3-dihydrobilatrienes-abc induced by mixtures of CCl₄ with (+)-cis-Pinane, (–)-lactic and (+)-tartaric acid esters it is concluded that specific interactions between chromophore and the chiral reagents afford a partial resolution of the labile racemate of helices. Attaching chiral residues covalently to the chromophore induces very low resolution of the same kind in case of apolar ligands like a cholesteryl-residue. However, with polar ligands as in the case ofBoc-lysyl derivatives enantiomeric excesses up to 90% are achieved depending on the solvent used.

Herrn Prof. Dr.Karl Schlögl zu seinem 60. Geburtstag gewidmet.