Sedimentationsanalyse

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Über einen neuen Typus linearer Differentialgleichungen

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Die Einwirkung von Organomagnesiumverbindungen aufo-Phthalonitril

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Über den Existenzbeweis algebraischer Funktionen zu einer gegebenen Riemannschen Fläche

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Weitere Beiträge zum Infinitesimalkalkul der Matrizen

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Minimax problems of discrete optimization invariant under majority operators

A special class of discrete optimization problems that are stated as a minimax modification of the constraint satisfaction problem is studied. The minimax formulation of the problem generalizes the classical problem to realistic situations where the constraints order the elements of the set by the degree of their feasibility, rather than defining a dichotomy between feasible and infeasible subsets. The invariance of this ordering under an operator is defined, and the discrete minimization of functions invariant under majority operators is proved to have polynomial complexity. A particular algorithm for this minimization is described.     

Stability Concepts in Topological Dynamics by Nonstandard Methods

It is known that it is not possible to introduce C⁰ -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rⁿ. Classically these amount to considering the space of all systems on a given subset of Rⁿ as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.     

Laboratoriumsapparate

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Direct Imaging of Octahedral Distortion in a Complex Molybdenum Vanadium Mixed Oxide

Complex Mo,V‐based mixed oxides that crystallize in the orthorhombic M1‐type structure are promising candidates for the selective oxidation of small alkanes. The oxygen sublattice of such a complex oxide has been studied by annular bright field scanning transmission electron microscopy. The recorded micrographs directly display the local distortion in the metal oxygen octahedra. From the degree of distortion we are able to draw conclusions on the distribution of oxidation states in the cation columns at different sites. The results are supported by X‐ray diffraction and electron paramagnetic resonance measurements that provide integral details about the crystal structure and spin coupling, respectively.