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.     

Comparison of the Hartree-Fock,Møller-Plesset,and Hartree-Fock-Slater method with respect to electrostatic properties of small molecules

Summary The results of various quantum chemical calculations, the Hartree-Fock (HF) method, the Møller-Plesset perturbation theory (MP2), and the Hartree-Fock-Slater (HFS) method are compared. Atomic charges, dipole moments, topological properties of the electron density distribution and polarizabilities, and first hyperpolarizabilities are calculated. Atomic charges obtained with the HFS method are found to be very close to those calculated with the MP2 method, from which we conclude that the HFS method describes to some extent electron correlation effects. Performing an MP2 calculation after an HF calculation improves the molecular dipole moments considerably, yielding values close to the experimental ones. HFS calculations are computationally less demanding than MP2 and yield comparable results for the electron density distributions, dipole moments and polarizabilities.     

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.