Divisible Effect Algebras

Divisible effect algebras and their relations to convex effect algebras and MV-algebras are studied. A categorical equivalence between divisible effect algebras and rational vector spaces is proved. Infinitesimal, sharp and extremal elements in divisible effect algebras are studied and their relations to properties of the state space are shown.     

Tensor Products of Quantum Structures and Their Applications in Quantum Measurements

Tensor products of quantum logics and effect algebras with some known problems are reviewed. It is noticed that although tensor products of effect algebras having at least one state exist, in the category of complex Hilbert space effect algebras similar problems as with tensor products of projection lattices occur. Nevertheless, if one of the two coupled physical systems is classical, tensor product exists and can be considered as a Boolean power. Some applications of tensor products (in the form of Boolean powers) to quantum measurements are reviewed.     

Lattice animals: Supplementation of perimeter polynomial data by graph-theoretic methods

Application of graph-theoretic methods to new perimeter polynomials for connected clusters on a lattice yields extra data on the total number of clusters and for the coefficients in the series expansion for the mean size of clusters at low densities. The lattices studied are the square, the square with next nearest neighbors, the triangular, and the simple cubic.     

Thrombinwirkung und Fibrinolyse in gereinigten Gerinnungs-systemen

Ohne ZusammenfassungD 21.Die vorstehende Arbeit wurde auf Anregung und unter Leitung von Herrn Professor Dr. Wöhlisch ausgeführt.     

Finitely additive states and completeness of inner product spaces

For any unit vector in an inner product space S, we define a mapping on the system of all -closed subspaces of S, F(S), whose restriction on the system of all splitting subspaces of S, E(S), is always a finitely additive state. We show that S is complete iff at least one such mapping is a finitely additive state on F(S). Moreover, we give a completeness criterion via the existence of a regular finitely additive state on appropriate systems of subspaces. Finally, the result will be generalized to general inner product spaces.     

Mechanical properties of single motor molecules studied by three-dimensional thermal force probing in optical tweezers.

A new method combining three-dimensional (3D) force measurements in an optical trap with the analysis of thermally induced (Brownian) position fluctuations of a trapped probe was used to investigate the mechanical properties of a single molecule, the molecular motor kinesin. One kinesin molecule attached to the probe was bound in a rigorlike state to one microtubule. The optical trap was kept weak to measure the thermal forces acting on the probe, which were mainly counterbalanced by the kinesin tether. The stiffness of kinesin during stretching and compression with respect to its backbone axis were measured. Our results indicate that a section of kinesin close to the motor domain is the dominating element in the flexibility of the motor structure. The experiments demonstrate the power of 3D thermal fluctuation analysis to characterize mechanical properties of individual motor proteins and indicate its usefulness to study single molecule in general     

Synthese und Kristallstruktur von [Ba(18-Krone-6)(DMF)4][Cd(Se4)2]

Synthesis and Crystal Structure of [Ba(18-Crown-6)(DMF)₄][Cd(Se₄)₂] The title compound has been prepared by the reaction of a DMF-solution of lithium polyselenide with BaSe₂ and cadmium acetate in the presence of 18-crown-6, forming black crystals. The compound was characterized by IR spectroscopy and by an X-ray structure determination. Space group P2/a, Z = 4, 5392 observed unique reflections, R = 0.048. Lattice dimensions at ?90°C: a = 2021.9(12); b = 1019.8(6); c= 2270.8(14)pm, ß = 106.98(4)°. The structure consists of [Ba(18-crown-6)(DMF)₄]²⁺ ions, in which the barium ions are coordinated by the six oxygen atoms of the crown ether molecule and by four oxygen atoms of the DMF molecules, and of [Cd(Se₄)₂]^2? ions. The cadmium atoms are coordinated by two tetraselenide ions in a chelating fashion.     

Continuous flow hydroformylation of alkenes in supercritical fluid-ionic liquid biphasic systems

A process for the hydroformylation of relatively low volatility alkenes (demonstrated for 1-dodecene) in a continuous flow system is described. The catalyst is dissolved in an ionic liquid while the substrate and gaseous reagents are transported into the reactor dissolved in supercritical CO(2), which simultaneously acts as a transport vector for aldehyde products. Decompression of the fluid mixture downstream yields products which are free of both reaction solvent and catalyst. The use of rhodium complexes of triaryl phosphites leads to ligand degradation through reaction of the ionic liquid with water and subsequent attack of the released HF on the phosphite. Sodium salts of sulfonated phosphines are insufficiently soluble in the ionic liquids to obtain acceptable rates, but replacing the sodium by a cation similar to that derived from the ionic liquid, allows good solubility and activity to be obtained. The nature of the ionic liquid is very important in achieving high rates, with 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amides giving the best activity if the alkyl chain is at least C(8). Catalyst turnover frequencies as high as 500 h(-1) have been observed, with the better rates at higher substrate flow rates. Rhodium leaching into the product stream can be as low as 0.012 ppm, except at low partial pressures of CO/H(2), when it is significantly higher. Oxygen impurities in the CO(2) feed can lead to oxidation of the phosphine giving higher rates, lower selectivities to the linear aldehyde, increased alkene isomerization and greater leaching of rhodium. However, it is found that under certain process conditions, the supercritical fluid-ionic liquid (SCF-IL) system can be operated continuously for several weeks without any visible sign of catalyst degradation. Comparisons with commercial hydroformylation processes are provided.     

Adsorption voltammetric techniques for the determination of uranium(VI) with 2,5-dichloro-3,6-dihydroxy-1,4-benzoquinone as complex forming reagent

Uranium (VI) can be determined by adsorptive voltammetric techniques, as its chloranilic acid complex, over a wide concentration range. Differential pulse polarography is useful for quantification of uranium between 0.1 and 1.5 mg/l; for the range from 10 to 500 g/l differential pulse voltammetry and for ultra-trace analysis between 0.024 and 40 g/l adsorptive stripping voltammetry are preferred. The standard deviation for the 3-detection limit of 24 ng/l uranium was found to be 8%. In the trace analysis of metals in aquatic environmental systems by adsorptive stripping voltammetry it is normally necessary to decompose polluted water samples by UV irradiation or microwave digestion. The advantage of the developed method is the fact that no sample pretreatment is necessary.Dedicated to Professor R. Geyer on the occasion of his 80th birthday