Darstellung und Molekülstrukturen von oligofunktionalen Dirheniumcarbonylderivaten aus Dirheniumnonacarbonylphosphan

Preparation and Molecular Structures of Oligofunctional Dirhenium Carbonyl Derivatives from Dirhenium Nonacarbonylphosphane Starting with dirheniumdecacarbonyl, one CO-Ligand was eliminated oxidatively and substituted by the labile acetonitrile ligand. As an intermediate eq-Re₂(CO)₉NCCH₃ was received. The reaction of this labilised carbonyl with tris(trimethylsilyl)phosphine and subsequent methanolysis gave ax-Re₂(CO)₉PH₃, which was isolated and characterized for the first time. Photochemical and thermal reaction of ax-Re₂(CO)₉PH₃ led to the new bi- and trinuclear complexes Re₂(μ-H)(μ₃-PHRe(CO)₅)(CO)₈, Re₂(μ-PH₂)₂(CO)₈ and Re₂(μ-H) · (μ-PH₂)(CO)₈, which were characterized by IR-, ¹H- and ³¹P-NMR spectroscopy. The structures of ax-Re₂(CO)₉PH₃, Re₂(μ-H)(μ₃-PHRe(CO)₅)(CO)₈ and Re₂(μ-PH₂)₂(CO)₈ were confirmed by single-crystal X-ray analysis. ax-Re₂(CO)₉PH₃ has a very short Re? P bond length of 228(2) pm.     

Ultrafiltration of a polymer-electrolyte mixture

We present a mathematical model to describe the ultrafiltration behaviour of polymer-electrolyte mixtures. The model combines the proper thermodynamic forces (pressure, chemical potential and electrical potential differences) with multicomponent diffusion theory. The model is verified with experimental data on the ultrafiltration of aqueous solutions of PEG-4000 and potassium phosphate. The single solute rejection of PEG-4000 goes through a maximum as also found by others. The single solute rejection of potassium phosphate depends on the ionic strength of the solution. At low ionic strength rejections are found of 50%. Solutions containing a high concentration of PEG-4000 and potassium phosphate show a negative rejection for potassium phosphate. This is caused by the strongly non-ideal behaviour of these aqueous solutions. The model predicts the behaviour of single solute experiments quite well, but some deviations are found with the mixed solute experiments. However, negative rejections found in the mixed solute experiments are predicted by the model.     

Finding nonnormal bent functions

The question if there exist nonnormal bent functions was an open question for several years. A Boolean function in n variables is called normal if there exists an affine subspace of dimension n/2 on which the function is constant. In this paper we give the first nonnormal bent function and even an example for a nonweakly normal bent function. These examples belong to a class of bent functions found in [J.F. Dillon, H. Dobbertin, New cyclic difference sets with Singer parameters, in: Finite Fields and Applications, to appear], namely the Kasami functions. We furthermore give a construction which extends these examples to higher dimensions. Additionally, we present a very efficient algorithm that was used to verify the nonnormality of these functions.     

Pricing and distributed QoS control for elastic network traffic

We study a processor-sharing model in which users choose between a high- and a low-priority service, based on their utility functions and prices charged by the service provider. The latter aims at revenue maximization. The model is motivated by file transmissions in data networks with distributed congestion control.