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.     

Metal Complexes with Macrocyclic Ligands. Part XXIX.. Structural and kinetic studies of two isomeric Cu2+ complexes with 1,4-dimethyl-8-[2-(2-pyridyl)ethyl]-1,4,8,11-tetraazacyclotetradecane

The synthesis and complexation properties of 1,4-dimethyl-8-[2-(2-pyridyl)ethyl]-1,4,8,11-tetraazacyclotetra-decane ( 2 ) are described. This ligand forms with Cu²⁺ two complexes, one of which has been characterized by X-ray structure analysis. The structural, spectral, and kinetic studies indicate that the two Cu²⁺ complexes are isomers with the macrocycle in the trans-III and trans-I configuration. The rate of the interconversion of the trans-I isomer to the thermodynamically more stable trans-III species is proportional to [OH^?]. A mechanism for this reaction is proposed.     

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.     

Miniaturized sensor module for in-situ control of waters

A new sensor module is developed for the in-situ control of waters, especially surface waters. Complex miniaturized sensor technology is used for the determination of the parameters pO₂, pH, pNO₃, pCl, pPO₄, pNH₃ or pNH₄ and conductivity. Miniaturization of sensors results in small sample volumes and small volumes of calibration solution required. Results of testing this sensor module are described. The special features of this apparatus are its compact construction and its optimum functioning capability under flow conditions.     

Formation and dissociation mechanism of amide complexes III. Water substitution as the rate limiting factor for the interconversion of Cu2+ complexes with neutral and deprotonated amide groups

The protonation and deprotonation rates of the coordinated amide group in the Cu₂₊ complexes with N^α-(2-pyridyl-methyl)-glycinamide (I) and N^α-(2-pyridyl-methyl)-glycineethylamide (II) have been studied by stopped flow techniques. It is shown that the rate determining step of the formation of the complex with the deprotonated amide group is given by the rate of water dissociation from Cu₂₊. Weaker bases than OH^? or stronger acids than water can react by a different path, in which the proton transfer and/or the rotation from the O-co-ordinated into the N-co-ordinated form and vice versa is rate determining.     

Metal complexes with macrocyclic ligands. Part XXII. Synthesis two of bis-tetraaza-macrocycles and study of the structures,electrochemistry, VIS and EPR spectra of their binuclear Cu2+ and Ni2+ complexes

The two bis-macrocycles 4 and 5 in which the tetraaza units are separated by a chain of different length, have been synthesized using 1,4,7-tritosyl-1,4,7,11-tetraazacyclotetradecane as starting compound and bifunctional alkylating agents. The bis-macrocycles give binuclear complexes with Ni²⁺ and Cu²⁺, the properties of which have been studied to obtain information about the interaction of the two subunits as a function of the distance. The VIS spectra of the Ni²⁺ and Cu²⁺ complexes indicate that both metal ions are in a square-planar geometry as expected from the results of the analogous complexes with 1,4,7,11-tetraazacyclotetradecane 7 . Cyclic voltammetry and differential pulse polarography of the binuclear Ni²⁺complexes in CH₃CN show a single two-electron step for ligand 5 , whereas two distinct one-electron redox processes can be observed for ligand 4 , indicating that the two metal ions interact with each other when the chain length is shorter. Similarly, the EPR studies of frozen solutions of the binuclear Cu²⁺ complexes clearly show that a magnetic dipolar interaction between the two paramagnetic centers exists, and that the strength of it depends upon the length of the bridge. Finally, from the X-ray structures of the binuclear Ni²⁺ complexes with 4 and 5 , it is seen that the two rings are kept apart as far as possible, the distances between the two metal ions determined in the solid correlate well with the observations in solution.     

Formation and dissociation mechanism of amide complexes. V. Interconversion of dimeric and monomeric Cu2+-complexes with 1,8-diamino-3,6-diaza-2,7-octanedione: Comparison between the reactivity of terminal and internal amide groups

The protonation and deprotonation rates of the coordinated amide groups in the Cu²⁺-complexes of 1,8-diamino-3,6-diaza-2,7-octanedione (DED = L) have been studied by stopped-flow techniques. Starting at low pH from Cu²⁺ and DED the dimeric Cu₂L₂⁴⁺-complex, fully formed within the mixing time of the stopped-flow instrument, reacts in two consecutive steps to yield the final product CuLH_?2. The rate constants of the forward and backward reactions have been determined and are given in Table 1. The intermediate was identified as Cu₂L₂H_?2²⁺ by measuring its VIS.-absorption spectrum. The rate constants for the interconversion of the amide groups from the O- to the N-coordinated form in the Cu²⁺-complexes of DED, 2,10-dioxo-1, 4, 8, 11 tetraazaundecane (DANA) and triglycine (TRIGLY) are compared with each other. It is shown that these rate constants are similar, no matter whether the amide group is terminal or internal as long as the rotation is easily possible as is the case in the dimeric species Cu₂L₂⁴⁺ and Cu₂L₂H_?2²⁺. However, for CuLH_?2 the inter-conversion only takes place after opening of one of the chelate rings in a rapid protonation preequilibrium.