Kreisverwandtschaften in der hyperbolischen Geometrie

Ohne Zusammenfassung     

The effect of molecular topology on π-molecular-orbital energies

Three models for constructing topologically related pairs of molecular isomers are discussed at length. The topological-effect-on-molecular-orbitals (TEMO) theorem is presented in detail and illustrated with experimental data; this theorem demonstrates that molecular topology imposes constraints in the form of general interlacing rules on the MO energy patterns of topologically related molecules. Further, non-empirical SCF MO calculations have been performed for topologically related o- and p-divinylbenzenes, difluorobenzenes, benzoquinones, and benzoquinodimethanes in standard and optimized geometries using various basis sets. In most cases, the SCF -MO eigenvalue patterns of topological related isomers are in complete agreement with the TEMO theorem, thus demonstrating the dominant influence of topology on the -MO energies. A modified version of the generalized perturbationalvariational Rayleigh-Ritz (PV-RR) procedure is described which is used to study the occasional observed deviations from the TEMO predictions; this procedure had been combined with the concept of critical (i.e. the threshold value of the perturbation parameter at which the TEMO order of a pair of MO eigenvalues starts to invert), thus enabling us to analyze in quantitative detail the physical factors which compete with molecular topology in conditioning the ab initio MO energy patterns.Part 10 of the TEMO series; for Part 9, see Ref. [9b].Dedicated to Prof. Dr. Günther Wilke on the occasion of his 60th birthday     

Voice quality after carbon dioxide laser and conventional surgery for T1A glottic carcinoma

The different types of small vocal fold tumor therapy allow the preservation of respiration and deglutition; the quality of phonation is the most important criterion for the patient. The aim of the study is to compare vocal function after treatment of T1a tumors by conventional and laser cordectomy. Fifty-seven male patients were included in the study: 27 underwent conventional cordectomy using an external approach, and 30 underwent an endoscopic microscopic laser cordectomy. Videolaryngoscopy was performed for each subject, and the maximal phonation time was measured. Spectrograms were recorded, and a perturbation analysis was performed if a clear harmonic structure was visible. Voices were perceptually rated by two experienced phoniatricians using the GRBAS scale. Even though a slightly better voice was found after conventional surgery throughout the data, no statistically significant difference was measured in the two groups. The data on voice outcome per se do not indicate the selection of one surgical approach over another.     

Über einen neuen Aufbau der hyperbolischen Geometrie und eine Ungleichung

Ohne Zusammenfassung     

On the construction of the matching polynomial for unbranched catacondensed benzenoids

An algorithm for obtaining the matching polynomial of an arbitrary catacondensed unbranched benzenoid molecule is presented. It is based on multiplication of only three 5 x 5 transfer matrices I, J, K, and an appropriate terminal vector. The choice of the matrices is dictated by the history of the growth of the hexagonal “animals” (i.e., by the pattern of the successive fusions of the benzene rings). The approach also gives the number of Kekule valance structures, the count of conjugated circuits, the values of the topological index Z, and the characteristic polynomials.     

Terpyridine Based Metallo-Supramolecular Initiators: Towards Novel Self-Organizing Materials

[Fe(II){5,5- bis(bromomethyl)-terpyridin}₂](PF₂6)₂2 complexes were used as metallo-supramolecular initiators for the living polymerization of 2-ethyl-2-oxazolines yielding defined hydrophilic polymers with a central supramolecular building unit and star-like architectures. The living character of the polymerization allows an exact control of the molecular weight as well as the incorporation of additional (complexing) units at the polymer chain ends.