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.     

Stereochemie von Metallocenen, 40. Mitt.

Starting from optically active methylferrocene-- and--carboxylic acids (1 a and1 b) of known absolute configuration and enantiomeric purity about 15 chiral ferrocenes (of each isomeric series— and ) were obtained by suitable ligand transformations. Thereby (almost) all possible chiral combinations of the ligands CH₃, COOH (COO^–), COOCH₃, CN and NH₂ (NH₃ ⁺) were accessible which are necessary for a potential test of approximations of chirality functions for compounds with basic symmetry C_5v. The chiroptical properties of these disubstituted ferrocenes are recorded.Preliminary tests using a shortened Ansatz revealed large discrepancies between calculated () and found [M]_D-values. Possible reasons for this failure are discussed.

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61. Mitt. über Ferrocenderivate

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39. Mitt.:A. Meyer, H. Neudeck undK. Schlögl, Chem. Ber.110, 1403 (1977).

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60. Mitt.:V. Rapi, K. Schlögl undB. Steinitz, J. Organometal. Chem.94, 87 (1975).     

The magnetic hyperfine field of bromine in iron by NMR/ON

Nuclear magnetic resonance of⁸²Br oriented at low temperature in iron has been observed with a sample prepared by ion implantation atT<0.2 K. The asymmetric resonance signal can be decomposed in a broad background signal and a narrow line of FWHM=1.8 (4) MHz which can be attributed to⁸²Br in undisturbed substitutional sites of Fe. From the center frequency of this narrow line (B _ext=0)=201.86(13) MHz we derive the magnetic hyperfine field asB _hf(BrFe)=81.38(6) T. This value is considerably larger than the result of theoretical calculations.     

Ferrocenasymmetrie, 4. Mitt.: Die Absolutkonfiguration von (β- und γ-Phenyl-α-ketotetramethylen)-ferrocen

Zusammenfassung Ringschluß von -bzw. -Phenyl--ferrocenyl-buttersäure liefert die homoannular überbrückten Ketone (- bzw. -Phenyl--ketotetramethylen)-ferrocen (VI, VII, XIV). Die Ermittlung der Absolutkonfiguration dieser Ketone gelang durch Korrelation des Asymmetriezentrums der optisch aktiven -Phenyl--ferrocenyl-buttersäure (deren Absolutkonfiguration primär bestimmt wurde) mit der Konfiguration des planar asymmetrischen Anteils in den optisch aktiven Ketonen.Die erhaltenen Ergebnisse waren auch mit der früher für (+)-1,2-(-Ketotetramethylen)-ferrocen (I) auf unabhängigem Weg ermittelten Konfiguration in Einklang, wie durch Messung des optischen Circulardichroismus erwiesen werden konnte: die rechtsdrehenden Enantiomeren besitzen die (R), die linksdrehenden (S)-Konfiguration.

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Ring closure of - and -phenyl--ferrocenylbutyric acid yielded the corresponding homoannularily bridged ketones, (- and -phenyl--ketotetramethylene)-ferrocene (VI, VII, XIV), respectively. The absolute configuration of these ketones could be established by correlation of the asymmetric center of the optically active -phenyl--ferrocenylbutyric acid (whose absolute configuration was determined previously) with the configuration of the planar asymmetric part in the optically active ketones.The results obtained support the configuration reported earlier for (+)-1,2-(-ketotetramethylene)-ferrocene (I) and established by an independent route. The configurations could also be supported by use of optical circular dichroism, i. e., the dextrorotatory enantiomers have the (R)-configuration, the laevorotatory the (S)-configuration.

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Mit 1 Abbildung

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Über die Verwendung des Ausdruckes Ferrocen-Chiralität (bzw. Chiralitäts-Zentrum und Planar-Chiralität) vgl., Fußnote S. 266.

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Vgl. hierzu die Fußnote auf S. 1066

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3. Mitt. über Ferrocenasymmetrie, zugleich 24. Mitt. über Ferrocenderivate:H. Falk undK. Schlögl, Mh. Chem.96, 266 (1965).     

Stereochemie von Metallocenen, 13. Mitt.: Optisch aktive Derivate des Methylcymantrens: Darstellung,Rotationsdispersion und konfigurative Korrelation

Zusammenfassung Optisch aktive Methylcymantren-- und--carbonsäuren wurden durch Racematspaltung ihrer Phenäthylaminsalze erhalten. Bei der Umwandlung in die entsprechenden Acetyl- bzw. Vinyl-methylcymantrene treten charakteristische Drehwertänderungen auf. Aus diesen, vor allem aber aus der Rotationsdispersion, ließ sich auf Grund von Konformationsanalysen und Vergleichen zwischen offenkettigen und cyclischen Verbindungen sowie mit analogen Methylferrocenderivaten für die -substituierten Produkte mit großer Sicherheit die absolute Konfiguration ableiten: (1S) für (+)-Methylcymantren--carbonsäure und ihre Folgeprodukte. Dieser Befund wurde durch kinetische Racematspaltung des Anhydrides der racem. Säure mit (–)--Phenäthylamin gestützt.

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Optically active methylcymantrene-- and--carboxylic acids were obtained by resolution of their salts with -phenethylamine. Upon transformation into the corresponding acetyl and vinyl methylcymantrenes, characteristic shifts of the optical rotation are observed. From these data, and especially from the rotatory dispersions, on the basis of conformational analyses and comparisons between open chain and cyclic compounds as well as with analogous methylferrocene derivatives, the absolute configurations of the -substituted products could be deduced with reasonable probability: (1S) for (+)-methylcymantrenecarboxylic acid and its subsequent products. This result was supported by kinetic resolution of the anhydride of the racemic carboxylic acid with (–)--phenethylamine.

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Mit 3 Abbildungen     

Ferrocenderivate LX. Rationelle synthesen der ferrocen-1,1′-dicarbonsäure sowie von isomeren methyl-, phenyl-ferrocen- und [3]ferrocenophan-mono- und -1,1′-di-carbonsäuren

Mono- or 1,1′-bis-acylation of ferrocene, its mono and 1,1′-dimethyl and phenyl derivatives and of [3]ferrocenophane with o-chlorobenzoyl chloride/AlCl₃ affords the corresponding (isomeric) chlorobenzoyl ferrocenes in high yields which can be separated by column, layer or high pressure liquid chromatography and in the case of the monomethylferrocene monoketones also by crystallization. The cleavage of the (o-chlorobenzoyl)ferrocenes by potassium-t-butoxide (and traces of water) yields the corresponding ferrocene carboxylic acids except for the α-phenyl derivatives in almost quantitative yields, thus offering a very convenient access to these acids. In all cases the isomer distribution and thereby the relative site reactivities were determined.