Unavoidable Traces Of Set Systems

Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set system consisting of sufficiently many sets contains at least one of these structures with many sets.     

Analysis and prediction of primary structures of proteins using a computer

On the basis of a computer analysis of four classes of toxic polypeptides, generalized primary structures of each class have been obtained which can be used for planning the synthesis of biologically active compounds.     

Numerical differentiation of photomechanical data using smoothing spline functions with generalized boundary conditions

The smoothing spline function has been used for differentiation of photomechanical data in experimental stress analysis. However, since the available software packages use the algorithm with the so-called natural boundary conditions which are not necessarily suitable in many circumstances, errors tend to occur in both the first and second derivatives. In this paper we have modified the algorithm so that the user can have more freedom in selecting boundary conditions which suit the problem best and therefore, as a result, improve the accuracy of the analysis. Two examples are given to show the improvement achievable using the new scheme.     

A classical no-interaction theorem for bosonic strings and its quantum significance

We show that, in dimensions equal or greater than three, classical strings do not join or split. This is part of a no-interaction theorem that is also proved. The quantum theory is considered.     

Neural networks and chip design

I present an abstraction of the Hopfield-model for neural networks which is suitable for physical chip design using commerically available two-dimensional gate arrays. It can be shown that ±1-bonds combined with a dilution of about 80–90% of the original Hopfield-connections still lead to a comparable performance of the network. Furthermore the learning capability of the chips is discussed. Future extensions concerning programmable designs are outlined. The impact on aspects of brain research is discussed.     

Investigation of multicomponent fluoride optical materials in the UV spectral region: I. Single crystals of Ca1−x R xF2+x (R = Sc, Y, La, Yb, Lu) solid solutions

Crystalline materials that are transparent in the vacuum UV spectral region and currently used have been reviewed. Transmission of crystals of solid solutions with the fluorite structure Ca_1?x R _xF_2+x (R = Sc, Y, La, Yb, Lu) in the UV and vacuum UV spectral regions has been investigated. It is shown that application of different methods of purification of fluorides from some impurities can significantly improve the optical quality of fluoride multicomponent crystals in the short-wavelength spectral region.     

Coset extensions of <Emphasis Type=”Italic”>S</Emphasis>-sets

Summary Three weak variants of compactness which lie strictly between compactness and quasicompactness, are introduced. Their basic properties are studied. The interplay with mapping and their direct and inverse preservation under mappings are investigated. In the process three decompositions of compactness are observed.