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Partitioned chain grammars
(1979)

This paper introduces a new class of grammars, the partitioned chain grammars, for which efficient parsers can be automatically generated. Besides being efficiently parsable these grammars possess a number of other properties, which make them very attractive for the use in parser-generators. They for instance form a large grammarclass and describe all deterministic context-free languages. Main advantage of the partitioned chain grammars however is, that given a language it is usually easier to describe it by a partitioned chain grammar than to construct a grammar of some other type commonly used in parser-generators for it.

Fast reconstruction formulae in x-ray computerized tomography demand the directions, in which the measurements are taken, to be equally distributed over the whole circle. In many applications data can only be provided in a restricted range. Here the intrinsic difficulties are studied by giving a singular value decomposition of the Radon transform in a restricted range. Practical limitations are deduced.

The Trippstadt Problem
(1984)

Close to Kaiserslautern is the town of Trippstadt, which, together with five other small towns forms a local administration unit (Verbandsgemeinde) called Kaiserslautern-Süd. Trippstadt has its own beautiful public swimming pool, which causes problems though; the cost for the upkeep of the pool is higher than the income and thus has to be divided among the towns belonging to the Verbandsgemeinde. Because of this problem the administration wanted to find out which fraction of the total number of pool visitors came from the different towns. They planned to ask each pool guest where he came from. They did this for only three days though because the waiting lines at the cashiers became unbearably long and they could see that because of this the total number of guests would decrease. Then they wondered how to find a better method to get the same data and that was when I was asked to help with the solution of the problem.

We report on the exchange bias effect as a function of the in-plane direction of the applied field in two-fold symmetric, epitaxial Ni80Fe20/Fe50Mn50 bilayers grown on Cu(110) single crystal substrates. An enhancement of the exchange bias field, Heb, up to a factor of two is observed if the external field is nearly, but not fully aligned perpendicular to the symmetry direction of the exchange bias field. From the measurement of the ex-change bias field as a function of the in-plane angle of the applied field, the unidirectional, uniaxial and four-fold anisotropy contributions are determined with high precision. The symmetry direction of the unidirec-tional anisotropy switches with increasing NiFe thickness from [110] to [001].

In these notes we will discuss some aspects of a problem arising in carindustry. For the sake of clarity we will set the problem into an extremely simplified scheme. Suppose that we have a body which is emitting sound, and that the sound is measured at a finite number of points around the body. We wish to determine the intensity of the sound at an observation point which is moving.