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.     

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.     

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.     

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     

Difference posets,effects, and quantum measurements

Difference posets as generalizations of quantum logics, orthoalgebras, and effects are studied. Observables and measures generalizing normalized POV-measures and generalized measures on sets of effects are introduced. Characterization of orthomodularity of subsets of a difference poset in terms of triangle closedness and regularity of these subsets enables us to characterize observables with a Boolean range. Boolean powers of difference posets are investigated; they have similar properties to that of tensor products, and their connection with quantum measurements is studied.     

Synthese und Charakterisierung von Pr2InF und [K(15-Krone-5)2][Pr2InCl2]. Die Kristallstrukturen von [Pr2InCl] ∞ und [K(15-Krone-5)2][Pr2InCl2] Bernhard Neumüller

The reaction of ⁱPr₂InCl (1) with KF and 15-crown-5 in acetonitrile at room temperature leads to the toluene-soluble crown ether salt [K(15-crown-5)₂][ⁱPr₂InCl₂] (2) and to the MeCN-soluble diorganoindium fluoride ⁱPr₂InF (3). Pure 3 can be isolated, when the reaction is carried out with KF but without crown ether at −15°C. Crystals of 1 und 2, suitable for X-ray structure determinations, were obtained when 1 and 2 were recrystallized from toluene. 1 exists as infinite chains of the monomeric unit ⁱPr₂InCl, while the unit cell of 2 contains separate ions.     

Die Zusammensetzung der Neutrallipide aus normalen Hirnen alter Menschen

The chemical composition of lipids from six human brains (60–73 years) is reported. The total lipids out of cortex, white matter, diencephalon and cerebellum, pons, and medulla oblongata have been isolated and the neutral lipids have been separated in cerebrosides, sphingomyelines, and lecithins. The highest amount of pure lipids is found in the white matter, the lowest in the cortex. The relation of neutral lipids to acid lipids as well as the amount of cholesterol are about equal for all regions. The white matter shows more cerebrosides and sphingomyelines than the cortex, the opposite being the case for lecithins. The differences are strongly significant. The fatty acids out of the different pure lipid fractions have been analysed as esters by gas chromatography. Stearic and lignoceric acid, and cerebronic and hydroxy nervonic acid respectively are main components of cerebrosides, with only little differences for the different brain regions. The fatty acids of sphingomyelines consist mainly of stearic and nervonic acid; in the white matter these two acids are present about in the same quantity, whereas stearic acid dominates in the cortex and the other sections. Lecithins contain above all palmitic and oleic acid. The amount of the latter in the white matter is higher than that of palmitic acid.