On parabolic systems with variational structure

We prove global existence of strong solutions for two-dimensional parabolic systems of variational flow type subject to the one-sided condition.     

Glühdrahtexperimente mit den Systemen Pt/O2, Ir/O2, Pt/Cl2, Pt/Br und Rh/Br

Glowing Filament Experiments with the Systems Pt/O₂, Ir/O₂, Pt/Cl₂, Pt/Br, and Rh/Br Reactions of glowing filaments of platinum and iridium with oxygen confirmed the usefulness of the method for the determination of the formulae of the volatile compounds (PtO₂, IrO₃) under equilibrium conditions. The afterwards made experiments with glowing filaments of platinum with Cl₂ at 1300 K and with platinum and rhodium with Br at 1900 K under equilibrium conditions lead to the formation of PtCl₂, PtBr, and RhBr.     

Types of likelihood maxima in mixture models and their implication on the performance of tests

In two-component mixtures of exponential distributions, different strategies for starting the likelihood maximization algorithm converge to different types of maxima. The power of an LR test of homogeneity against such a mixture strongly depends on the considered strategy, and global maximization need not result in the largest power. An explanation is given on basis of a systematic investigation of the likelihood function in a large number of simulations, using a variety of diagnostic tools. Thereby, we also gain a deeper insight into the properties of the samples that generate particular types of solutions of the likelihood equation. In particular, “spurious solutions” often occur; these are mainly responsible for the fact that global maximization may not result in a statistically meaningful estimator. Removing the smallest elements of a sample may drastically increase the power of previously inferior strategies. This research has been supported by a grant from the Deutsche Forschungsgemeinschaft.     

Einstein and Cosmic Physics

The article gives an overview on Albert Einstein's activity in relation to geophysics. Various aspects of his fundamental investigations and their significance for geophysical research are discussed.     

Stereoselective glycosylation of Alcohols and Silyl Ethers Using Glycosyl Fluorides and Boron Trifluoride Etherate

The stereoselective glycosylation of alcohols and their silyl ethers has been achieved using O-alkyl-, O-acyl-, and acetal-protected glycosyl fluorides of the pyranose and furanose series and boron trifluoride etherate in CH₂Cl₂.     

An intuitionistic fixed point theory

In this article we prove that a certain intuitionistic version of the well-known fixed point theory is conservative over for almost negative formulas. Received October 24, 1995     

Fragments of arithmetic

We establish by elementary proof-theoretic means the conservativeness of two subsystems of analysis over primitive recursive arithmetic. The one subsystem was introduced by Friedman [6], the other is a strengthened version of a theory of Minc [14]; each has been shown to be of considerable interest for both mathematical practice and metamathematical investigations. The foundational significance of such conservation results is clear: they provide a direct finitist justification of the part of mathematical practice formalizable in these subsystems.The results are generalized to relate a hierarchy of subsystems, all contained in the theory of arithmetic properties, to a corresponding hierarchy of fragments of arithmetic. The proof theoretic tools employed there are used to re-establish in a uniform, elementary way relationships between various fragments of arithmetic due to Parsons, Paris and Kirby, and Friedman.