Endomorphism rings and automorphism groups of almost completely decomposable groups

To every non-cuspidal K-rational point on the modular curve X_l(n) a non-commutative Noetherian domain of global dimension 3 can be associated : the Sklyanin algebra. In this paper we give the defining equations of the Sklyanin algebras and their centers when X_l(n) is rational, i.e. n <= 10 or n = 12.     

Single cell green algae reference materials with managed levels of heavy metals

Three batches of single cell green algal biomass have been produced as model substances for green biomass reference materials with the aim of arriving at three different concentration levels for selected heavy metals in the same matrix. The green algal biomass is produced in a water based culture medium in open and closed bioreactors. An outdoor open bioreactor technology was used to produce a batch of “natural level” algae as well as a batch with elevated levels of As, Cd, Cr, Hg, Ni, and Pb. A photoreactor constructed without metal parts and employing artificial light sources was used in a clean air environment with high purity chemicals to reduce heavy metal concentrations in the third batch of algal biomass. For the above elements, the depleted level material, with exception of Hg, showed about one order of magnitude lower concentration than the natural level, while concentrations in the enriched material were up to four orders of magnitude higher. Analysts can use these materials to sustain verification of calibration and analytical quality over the entire operational range of the analytical work.     

Proficiency tests using four batches of green alga with controlled levels of cadmium

A set of test materials of the green alga Chlorella vulgaris with different levels of naturally bound Cd and about the same levels of other 13 essential or trace elements (BIOMA 1–4) was produced for proficiency testing of laboratories involved in elemental analysis of food. Criteria of the laboratories’ performance, such as the z-score and combination scores RSZ and SSZ were evaluated and discussed in terms of their suitability for proficiency testing using a set of test materials with the same matrix. The use of the test materials as a set of internal reference materials has also been suggested. Received: 23 May 1997 / Revised: 1 August 1997 / Accepted: 11 August 1997     

Connectivity keeping trees in k‐connected graphs

We show that one can choose the minimum degree of a k‐connected graph G large enough (independent of the vertex number of G) such that G contains a copy T of a prescribed tree with the property that G ? V(T) remains k‐connected. This was conjectured in [W. Mader, J Graph Theory 65 (2010), 61–69]. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory 69: 324–329, 2012     

Indecomposable (1,3)-Groups and a matrix problem

Almost completely decomposable groups with a critical typeset of type (1, 3) and a p-primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient p ^k , either no indecomposables if k ? 2; only six near isomorphism types of indecomposables if k = 3; and indecomposables of arbitrary large rank if k ? 4.     

Room-temperature ferromagnetic Mn-alloyed ZnO films obtained by pulsed laser deposition

Ferromagnetic, semi-insulating Mn-alloyed ZnO films with a Curie temperature above 375 K have been grown by pulsed laser deposition on c-plane sapphire substrates. Antiferromagnetic coupling is revealed by temperature-dependent magnetization measurements. The antiferromagnetic coupling would be compatible with the observed weak ferromagnetism by assuming that the magnetic moments order antiferromagnetically but nonparallel (canted). We find a clear correlation between coercivity and mosaicity of the ferromagnetic Mn-alloyed ZnO films and explain it on the basis of a coercivity mechanism known from soft magnetic materials.     

Openly disjoint circuits through a vertex in regular digraphs

In 1985, Thomassen [14] constructed for every positive integer r, finite digraphs D of minimum degree δ(D)=r which do not contain a vertex x lying on three openly disjoint circuits, i.e. circuits which have pairwise exactly x in common. In 2005, Seymour [11] posed the question, whether an r-regular digraph contains a vertex x such that there are r openly disjoint circuits through x. This is true for r≤3, but does not hold for r≥8. But perhaps, in contrast to the minimum degree, a high regularity degree suffices for the existence of a vertex lying on r openly disjoint circuits also for r≥4. After a survey of these problems, we will show that every r-regular digraph with r≥7 has a vertex which lies on 4 openly disjoint circuits.     

über minimaln-fach zusammenhängende,unendliche Graphen und ein Extremalproblem

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Ecken vom Gradn in minimalenn-fach zusammenhängenden Graphen

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