In this paper we investigate and compare four variants of the double-pushout approach to graph transformation. As well as the traditional approach with arbitrary matching and injective right-hand morphisms, we consider three variations by employing injective matching and/or arbitrary right-hand morphisms in rules. We show that injective matching provides additional expressiveness in two respects: for generating graph languages by grammars without non-terminals and for computing graph functions by convergent graph transformation systems. Then we clarify for each of the three variations whether the well-known commutativity, parallelism and concurrency theorems are still valid and – where this is not the case – give modified results. In particular, for the most general approach with injective matching and arbitrary right-hand morphisms, we establish sequential and parallel commutativity by appropriately strengthening sequential and parallel independence.

We describe a new condensation method for computing the submodule lattice of a module for a finite dimensional algebra over a finite field, which exploits the idea of condensation and extends it to the case of primitive idempotents. The method has been implemented in the new C version of the Meat-Axe developed at Aachen, and we give several examples which have been analysed with our method.1991 Mathematics Subject Classification. 06C05, 15-04, 16G10, 20C40.

In this article we consider functions 4 which are holomorphic exactly on a domain S1 C @ and whose power series are universal with respect to overconvergence. Our main purpose is to solve a problem of Nestoridis. In addition some properties of universal power series are proved.

We prove that certain universality properties of the partial sums force a power series to have Ostrowski-gaps. This has interesting consequences for some classes of universal functions.

We determine the Green vertices and sources of many of the simple modular representations of the finite symmetric group being parametrized by hook partitions. Mathematics Subject Classification (2000). 20C30, 20C20.

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A stagnation point cold-wall reactor was used for the CVD of corundum alumina (a-Al 2 O 3 ) on metallic substrates. Depositions were carried out under low pressure using the thermally induced pyrolytic oxidation of aluminum tri-isopropoxide (ATI). The effects of the substrate temperature (300±1080 C) and the total pressure (50±250 mbar) on the growth rate and morphology of the deposits were investigated. An excess of oxygen facilitates the formation of dense alumina films. Precursor depletion was prevented using high gas velocity, low ATI concentration, and a high temperature gradient. X-ray diffraction (XRD) analysis provided evidence of corundum alumina deposition at substrate temperatures above 1000 C.

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