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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.
In this thesis, I investigated the factors influencing the growth and vertical distribution of planktonic algae in extremely acidic mining lakes (pH 2-3). In the focal study site, Lake 111 (pH 2.7; Lusatia, Germany), the chrysophyte, Ochromonas sp., dominates in the upper water strata and the chlorophyte, Chlamydomonas sp., in the deeper strata, forming a pronounced deep chlorophyll maximum (DCM). Inorganic carbon (IC) limitation influenced the phototrophic growth of Chlamydomonas sp. in the upper water strata. Conversely, in deeper strata, light limited its phototrophic growth. When compared with published data for algae from neutral lakes, Chlamydomonas sp. from Lake 111 exhibited a lower maximum growth rate, an enhanced compensation point and higher dark respiration rates, suggesting higher metabolic costs due to the extreme physico-chemical conditions. The photosynthetic performance of Chlamydomonas sp. decreased in high-light-adapted cells when IC limited. In addition, the minimal phosphorus (P) cell quota was suggestive of a higher P requirement under IC limitation. Subsequently, it was shown that Chlamydomonas sp. was a mixotroph, able to enhance its growth rate by taking up dissolved organic carbon (DOC) via osmotrophy. Therefore, it could survive in deeper water strata where DOC concentrations were higher and light limited. However, neither IC limitation, P availability nor in situ DOC concentrations (bottom-up control) could fully explain the vertical distribution of Chlamydomonas sp. in Lake 111. Conversely, when a novel approach was adopted, the grazing influence of the phagotrophic phototroph, Ochromonas sp., was found to exert top-down control on its prey (Chlamydomonas sp.) reducing prey abundance in the upper water strata. This, coupled with the fact that Chlamydomonas sp. uses DOC for growth, leads to a pronounced accumulation of Chlamydomonas sp. cells at depth; an apparent DCM. Therefore, grazing appears to be the main factor influencing the vertical distribution of algae observed in Lake 111. The knowledge gained from this thesis provides information essential for predicting the effect of strategies to neutralize the acidic mining lakes on the food-web.
Der Begriff der religiösen Erfahrung bei William James und seine Weiterentwicklung nach Wittgenstein
(2003)
Das Placebo-Argument
(2003)