Die Kristallstruktur der Verbindung Cd2Ge7O16

The crystal structure of Cd₂Ge₇O₁₆ has been determined by means of three-dimensional single-crystal data. A finalR-value of 6.3% was obtained by least squares refinement based on 230 observed reflexions. The tetragonal unit cell with the lattice parametersa=11.31 andc=4.63 Å contains two formula units Cd₂Ge₇O₁₆. The compound is built up by [GeO₄]-tetrahedra and [GeO₆]-octahedra forming a three-dimensional framework with the Cd atoms located in the cavities. The average interatomic distances are found to be: Ge–O=1.74 (tetrahedra), 1.89 (octahedra) and Cd–O=2.36 Å.

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Mit 1 Abbildung     

Metal benzoylpivaloylmethanates. Part III. Manganese(III) and iron(III) chelates

Summary The synthesis and principle properties of several novel tris[1-(4-X-phenyl)-4,4-dimethylpenta-1, 3-dionato]-iron(III) and manganese(III) complexes, where X=MeO, Me, H, F, Cl and NO₂, are described. Magnetic susceptibility measurements in the 4.2–295 K range show a near Curie behaviour and a constant magnetic moment for manganese(III) complexes and for iron complexes, with X=F, Cl or NO₂. Iron complexes with ligands having substituents: X=MeO, Me and H, show weak antiferromagnetic interaction (J=ca.–8 cm^–1 for the two former compounds) and a decrease in magnetic moment with decreasing temperature. In both manganese(III) and iron(III) complexes the diketonate ligand can be easily replaced by chlorine. Equilibrium constants could be evaluated only for substitution of the third diketonate ligand by chloride in the iron complexes on the basis of spectrophotometric measurements. For manganese chelates, the replacement of the second diketonate by chloride is accompanied by reduction of manganese(III) manganese(II) and free organic radical formation is observed.     

Obtaining the key set of typical vectors by factor analysis and subsequent isolation of component spectra

The key set of typical rows (or typical columns), used to reproduce a data matrix, are obtained by finding the set of rows (or set of columns) most orthogonal to each other. If the data matrix consists of the spectra of a series of related mixtures, and there exists at least one data point unique to each of the components, the spectra of the pure components can be isolated. The method is applied to problems in nuclear magnetic resonance, gas—liquid chromatography and mass spectrometry.     

Biomineralization of unicellular organisms: an unusual membrane biochemistry for the production of inorganic nano- and microstructures

With evolution, Nature has ingeniously succeeded in giving rise to an impressive variety of inorganic structures. Every organism that synthesizes biogenic minerals does so in a form that is unique to that species. This biomineralization is apparently biologically controlled. It is thus expected that both the synthesis and the form of every specific biogenic mineral is genetically determined and controlled. An investigation of the mechanism of biomineralization has only become possible with the development of modern methods in molecular biology. Unicellular organisms such as magnetic bacteria, calcareous algae, and diatoms, all of which are amongst the simplest forms of life, are particularly suited to be investigated by these methods. Crystals and composites of proteins and amorphous inorganic polymers are formed as complex structures within these organisms; these structures are not known in conventional inorganic chemistry.     

Ein Satz über Riemannsche Integrale

Ohne Zusammenfassung     

Über die Zetafunktion und die Hadamardsche Theorie der ganzen Funktionen

Ohne Zusammenfassung     

A graph-based hyper-heuristic for educational timetabling problems

This paper presents an investigation of a simple generic hyper-heuristic approach upon a set of widely used constructive heuristics (graph coloring heuristics) in timetabling. Within the hyper-heuristic framework, a tabu search approach is employed to search for permutations of graph heuristics which are used for constructing timetables in exam and course timetabling problems. This underpins a multi-stage hyper-heuristic where the tabu search employs permutations upon a different number of graph heuristics in two stages. We study this graph-based hyper-heuristic approach within the context of exploring fundamental issues concerning the search space of the hyper-heuristic (the heuristic space) and the solution space. Such issues have not been addressed in other hyper-heuristic research. These approaches are tested on both exam and course benchmark timetabling problems and are compared with the fine-tuned bespoke state-of-the-art approaches. The results are within the range of the best results reported in the literature. The approach described here represents a significantly more generally applicable approach than the current state of the art in the literature. Future work will extend this hyper-heuristic framework by employing methodologies which are applicable on a wider range of timetabling and scheduling problems.     

Beiträge zur Theorie der Riemannschen Zetafunktion

Ohne Zusammenfassung