Über Anzahl und Verteilung der Scheitel ebener Bogen

Zusammenfassung Seit der Entdeckung des 4-Scheitel-Satzes durch S. Mukhopadhaya (1909) und A. Kneser (1912) hat sich eine umfangreiche Literatur über Scheitel- und verwandte Sätze entwickelt. Unter anderem wurden ebene Bogen auf Scheitel hin untersucht bzgl. Charakteristiken, welche von k 1 Parametern stetig abhängen. Wir legen für die wichtigsten Sätze aus diesem Teil der Theorie überarbeitete Definitionen und Beweise unter vereinfachten Voraussetzungen vor.

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A constructive approach to the foundations of quantum mechanics

An axiomatic theory is formulated which describes a class of yes-no experiments, involving a fixed basic source, a fixed basic detector, and various filters. It is assumed that all filters considered can be constructed from a setP of primitive filters by composition and stochastic selection. Two physically plausible axioms are formulated which allow us to define the concept of asystem in the present context (cf. Definition2.4). To each system we can attach anorder unit module ( ) (cf. Definition5.1) whereby ( ) is acomplete, separable order unit space. Two additional axioms are proposed which have the effect that the space ( ) becomes isomorphic to the order unit space underlying a JB-algebra, at least in the case where isfinite dimensional (cf. Corollary7.9).     

Intramolecular hydrogen bonds and hydrogen-bonded systems in di-Schiff bases of 4-methyl-isophthalaldehyde with 4-substituted anilines

Three di-Schiff bases of 2-hydroxy-5-methyl-isophthalaldehyde with 4-R-anilines (R=H, CH₃, OCH₃) and their 1:1 complexes with HClO₄ were studied by FT-IR, ¹H, and ¹³C NMR spectroscopy in acetonitrile and [²H₃]acetonitrile solutions, respectively. In di-Schiff bases intramolecular OH…N hydrogen bonds have been detected; however, they show no proton polarizability. Hydrogen-bonded systems with fast proton fluctuation and large proton polarizability have been found in the 1:1 complexes of di-Schiff bases with HClO₄.     

Ab initio calculations of vibronic activity in phosphorescence microwave double resonance spectra of p-dichlorobenzene

The phosphorescence spectrum of p-dichlorobenzene has been calculated using multiconfiguration self-consistent-field wave functions and the quadratic response technique. Attention has been paid to the intensity distribution of the singlet–triplet (³B_1u¹A_g) transition through a number of vibronic subbands. The second order spin–orbit coupling (SOC) contribution to the spin splitting of the ³B_1u (^3*) state is found to be almost negligible, and the calculations therefore provide a good estimate for the zero-field splitting (ZFS) parameters based only on the electron spin–spin coupling expectation values. Nuclear quadrupole resonance constants for the different Cl isotopes are also calculated to accomplish the ZFS assignment. The electric dipole activity of the spin sublevels in the triplet–singlet transitions to the ground-state vibrational levels is estimated by calculations of derivatives using distorted geometries which are shifted from the equilibrium position along different vibrational modes. A vibrational analysis of the phosphorescence spectrum, based on the SOC-induced mixing of the singlet and triplet states calculated along different vibrational modes, provides reasonable agreement with experimental data.Acknowledgment O. R.-P. would like to thank the European MOLPROP network for support. The authors thank Alexander Baev for fruitful discussions. This work was supported by the Swedish Royal Academy of Science (KVA).     

Development of a capillary electrophoretic method for the separation of diastereoisomers of a new human immunodeficiency virus protease inhibitor

A capillary electrophoretic (CE) method was developed for the separation of diastereoisomers of a new human immunodeficiency virus (HIV) protease inhibitor TMC114. In total 16 isomers of this drug have been synthesized (eight pairs of enantiomers). We succeeded in the separation of the eight diastereoisomers, but no enantiomers could be separated. Because of the high similarity and water-insolubility of these isomers, the separation is a real challenge. Different CE modes were tried out: capillary zone electrophoresis (CZE), nonaqueous capillary electrophoresis (NACE), micellar electrokinetic capillary chromatography (MEKC), and microemulsion electrokinetic capillary chromatography (MEEKC). Only MEEKC offered resolution of these compounds.     

Contributions of restructuring and oxidation to the aging of the surface of plasma polymers containing heteroatoms

The properties and composition of plasma polymer surfaces stored in air can change considerably over time, especially as a result of oxidative reactions. When plasma polymers contain an element other than O, it is possible to probe for mechanisms in addition to oxidation that contribute to the aging of the surface. Plasma polymers containing N were fabricated from either 1,3-diaminopropane (DAP),n-heptylamine (nHA), or allylamine (AA), and studied by X-ray photo-electron spectroscopy (XPS) and air/water contact angles (CA). For each of the plasma polymers, a multiexponential increase in the O/C ratio was observed over time using XPS. The N/C ratios remained constant (AA) or decreased somewhat (nHA and DAP). In contrast, the trends in CA values differed, declining for the nHA surfaces, rising for the AA, and changing little for the DAP. Surface roughness, assessed by scanning tunnelling or atomic force microscopy, did not change over time. The diverse adjustments in the polarity of each surface and the similar compositional changes between them are reconcilable if the aging of the plasma polymer surface is a manifestation of the superposition of concurrent oxidative reactions and partial surface reorientation; the former introduce polar groups and the latter transports then from the surface to deeper regions beyond the CA probe depth but within the XPS analysis depth. These processes vary between different plasma polymers. Data for the alkylamine plasma polymers is also compared with that for two plasma polymers fabricated from methanol. The change in composition, but not polarity, of the DAP surface after 4 days of storage demonstrates the importance of using multiple techniques to characterize the aging of plasma polymer surfaces.     

Anomalies in the Structural Chemistry of Silicon

In contrast to carbon, silicon fails to form multiple bonds that are stable at room temperature. Consequently molecules in which silicon exhibits coordination numbers (CN) of 1, 2, and 3 may only be obtained at very high or low temperatures. Under these conditions their structural features, including multiple bonds, resemble those of carbon. On the other hand, silicon is capable of forming various hexacoordinated compounds making use of its d orbitals. Nitrogen and oxygen bonded to silicon develop an unusual stereochemistry: planar nitrogen, nearly or completely linear oxygen, and considerable shortening of SiN, SiO, and SiF bonds are specific examples. N(SiR₃)₂ and CH₂SiR₃ ligands permit stabilization of unusually low CNs of many metals and give rise to amino and alkyl derivatives of unexpectedly high stability due to the particular electronic, the R₃Si group.     

15N-NMR spectroscopy. III. Neighboring residue effects in sequence polymers containing glycylglycine units

The tripeptides Phe-Gly-Gly, β-Ala-Gly-Gly, and ?-Aca-Gly-Gly as well as the peptide derivatives δ-isothiocyanatovaleroyl-Gly-Gly and ?-isothiocyanatocaproyl-Gly-Gly were synthesized by using known methods so that the peptide nitrogen between the two glycyl residues was isotopically enriched in ¹⁵N to a level of 0.8–0.9%. These monomer units were then used to produce the sequence polymers (Phe-Gly-Gly)_n, (β-Ala-Gly-Gly)_n, (δ-Ava-Gly-Gly)_n, and (?-Aca-Gly-Gly)_n. The 18.24 MHz ¹⁵N-NMR spectra of the oligo- and polypeptides were obtained by using trifluoroacetic acid as solvent, since the solutions have relatively low viscosity and exhibit a strong negative nuclear Overhauser enhancement of the ¹⁵N signals. For comparison, ¹⁵N-NMR spectra of the homopolymers (Gly)_n, (β-Ala)_n, (γ-Abu)_n, (δ-Ava)_n, and (?-Aca)_n were also recorded. The ¹⁵N signals from the ω-aminoacyl residues in the sequence polymers appear up to 11 ppm upfield of the signals observed for the homopolyamides. The ¹⁵N signals from the two glycyl residues are separated by 3–7 ppm. Comparison with the ¹³C-NMR spectra of the same polymers indicates that ¹⁵N-NMR is better suited for the characterization and sequence analysis of these types of polymers.