A new wavelet multigrid method

The standard multigrid procedure performs poorly or may break down when used to solve certain problems, such as elliptic problems with discontinuous or highly oscillatory coefficients. The method discussed in this paper solves this problem by using a wavelet transform and Schur complements to obtain the necessary coarse grid, interpolation, and restriction operators. A factorized sparse approximate inverse is used to improve the efficiency of the resulting method. Numerical examples are presented to demonstrate the versatility of the method.     

Conditional expectation values in quantum mechanics

The general question of defining the expectation value of an operator for a fixed value of another noncommuting observable is considered and explicit expressions are derived. Due to the noncommutivity of operators a unique definition is not possible, and we consider different possible expressions. Special cases which have previously been considered in the literature are shown to be derivable from the methods presented.In honor of Ilya Prigogine on the occasion of his 70th birthday.     

Bemerkung über einen verzerrungssatz bei topologischen Abbildungen in der Hydromechanik

Ohne Zusammenfassung     

Untersuchungen über die Gestalt der Himmelskörper

Ohne Zusammenfassung     

Untersuchungen über zweidimensionale reguläre Variationsprobleme

Ohne Zusammenfassung     

Single-vendor multi-buyer inventory coordination under private information

This paper considers the problem of coordinating a single-vendor multi-buyer inventory system when there are privacy restrictions in the information required to solve the problem. The objective function and cost parameters of each facility are regarded as private information that no other facilities in the system have access to. Moreover, each facility is responsible to specify its own replenishment policy. The objective is to minimize the total average setup/ordering and inventory-related cost. Solution methodologies under private and global information are developed to find two types of nested power-of-two stationary policies. The first policy assumes all the buyers must replenish simultaneously. The second policy is a more general case where the common replenishment assumption is relaxed. A simple form of information exchange is uncovered that allows the solution methodologies for private and global information yield the same results. The experimental results suggest that the performance of the proposed heuristics is comparable or better than an existing method.     

Neue Grundlagen der Logik und Mathematik

Ohne Zusammenfassung     

On the risk-based steam generator lifetime optimisation

A probabilistic fracture mechanics model is employed to estimate the failure probability of axially cracked steam generator tubes. The model estimates the failure probability from the random changes of the influencing parameters such as tube and crack geometry, material properties and non-destructive examination results, reliability and sizing accuracy and stable crack propagation. The performance of the model is illustrated by a numerical example. A steam generator tubing severely affected by the stress corrosion cracking is studied during most unfavourable accidental conditions. Two different plugging approaches are analyzed and the quality is compared, showing the superior performance of crack length oriented approach over tube wall thickness reduction both in terms of SG failure probability and extent of plugging. Thus, apart from setting the acceptable SG failure probability, all elements for the risk-based SG lifetime optimisation are provided on the example of stress corrosion cracking in the tube expansion transition zone.