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Algebra und Diskrete Mathematik gehören zu den wesentlichen Grundlagen der Informatik. Sie sind unverzichtbare Werkzeuge eines jeden Informatikers und spielen daher auch im Studium eine zentrale Rolle. Das Lehrbuch vermittelt anschaulich und leicht nachvollziehbar die wichtigsten algebraischen Grundlagen der Informatik bis hin zur Gleichungstheorie der Universellen Algebra. Zahlreiche Übungsaufgaben und ihre Lösungen helfen dem Leser, den Stoff zu verstehen
Clones of n-ary algebras
(2003)
Valuations of Terms
(2003)
Let tau be a type of algebras. There are several commonly used measurements of the complexity of terms of type tau, including the depth or height of a term and the number of variable symbols appearing in a term. In this paper we formalize these various measurements, by defining a complexity or valuation mapping on terms. A valuation of terms is thus a mapping from the absolutely free term algebra of type tau into another algebra of the same type on which an order relation is defined. We develop the interconnections between such term valuations and the equational theory of Universal Algebra. The collection of all varieties of a given type forms a complete lattice which is very complex and difficult to study; valuations of terms offer a new method to study complete sublattices of this lattice
Integral-field spectrophotometry of the quadruple QSO HE 0435-1223 : Evidence for microlensing
(2003)
We present the first spatially resolved spectroscopic observations of the recently discovered quadruple QSO and gravitational lens HE 0435-1223. Using the Potsdam Multi-Aperture Spectrophotometer (PMAS), we show that all four QSO components have very similar but not identical spectra. In particular, the spectral slopes of components A, B, and D are indistinguishable, implying that extinction due to dust plays no major role in the lensing galaxy. While also the emission line profiles are identical within the error bars, as expected from lensing, the equivalent widths show significant differences between components. Most likely, microlensing is responsible for this phenomenon. This is also consistent with the fact that component D, which shows the highest relative continuum level, has brightened by 0.07 mag since Dec. 2001. We find that the emission line flux ratios between the components are in better agreement with simple lens models than broad band or continuum measurements, but that the discrepancies between model and data are still unacceptably large. Finally, we present a detection of the lensing galaxy, although this is close to the limits of the data. Comparing with a model galaxy spectrum, we obtain a redshift estimate of zlens=0.44+/- 0.02.
sent observations of the Type Ia supernova SN 2002er during the brightening phase. The observations were performed with the Potsdam Multi Aperture Spectrophotometer (PMAS) integral field instrument. Due to the 8arcsecx8 arcsec field of view of the spectrograph an accurate background subtraction was possible. Results from analyses of the evolution of absorption features in comparisons with other SNe show that SN 2002er is a fairly bright Type Ia supernova with a peak brightness of MB=-19.6+/-0.1.
Der Begriff der religiösen Erfahrung bei William James und seine Weiterentwicklung nach Wittgenstein
(2003)
Das Placebo-Argument
(2003)
Our aim in this paper is to explicate some unexpected and striking similarities and equally important differences, which have not been discussed in the literature, between Wittgenstein's methodology and the approach of Chinese Chan or Japanese Zen Buddhism. We say 'unexpected' similarities because it is not a common practice, especially in the analytic tradition, to invest very much in comparative philosophy. The peculiarity of this study will be further accentuated in the view of those of the 'old school' who see Wittgenstein as a logical positivist, and Zen as a religious excuse for militarism or sadomasochism. If the second claim were true, the following investigation would not only be futile but also impossible. That the first claim, concerning the 'old school' perspective on Wittgenstein, si incorrect, we will demonstrate in the ensuing discussion. By now more experts have come to accept hits claim and we hope that our comparative perspective will add even more momentum