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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Thermal conductivity and specific heat of amorphous Zr0.67Ni0.33 after structural relaxation

Low-temperature measurements of the thermal conductivity (0.3KT5K) and of the specific heatC (0.07KT3.5K) of splat-cooled amorphous superconducting Zr_0.67Ni_0.33(T _c 2.7K) after different annealing stages are reported. increases progressively (up to 55%) after annealing. An analysis of with the help of normal-state measurements belowT _c in an overcritical field shows that the phonon-electron scattering remains unaltered after annealing. Hence the increase in must be entirely attributed to structure-induced (intrinsic) scattering, i.e. by two-level tunneling states (TLS) at low temperatures (T1K). The specific heat shows a small decrease aboveT _c (by 8%) which is attributed to a small diminution of the electronic density of states at the Fermi level and to a small increase in the Debye temperature. ForTT _c where TLS dominate, the specific heatC decreases less upon annealing than expected from the increase of in the standard tunneling model. This points to a change in the TLS relaxation time spectrum upon annealing, as observed previously for Zr _x Cu_1–x glasses.     

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.     

Rotational-diffusion anomalies in dye solutions from transient-dichroism experiments

Subnanosecond transient-dichroism experiments have been performed to investigate the rotational diffusion of dyes in solution. Dyes and solvents were chosen in a way to obtain information on the influence of size, shape and hydrogen-bonding abilities either of the solute or the solvent molecules. One finds slow orientational relaxation of di-anionic xanthene dyes in alcohols, while oblate cationic dyes rotate faster in spite of their comparable size. The rotational diffusion times for alcohol solutions exceed the theoretical values predicted by the Debye-Einstein model except for prolate molecules. For a solute molecule with internal mobility the rotational diffusion exhibits a partial slip behaviour. It is shown that the deviations from the Debye-Einstein model are restricted to alcohols since for other solvents either with or without strong hydrogen-bonding abilities the experimental values agree with the hydrodynamic model including the stick-boundary condition. Experiments on erythrosine B reveal the influence of size and shape of the attached solvent molecules.     

Direct measurement of gas solubility and diffusivity in poly(vinylidene fluoride) with a high-pressure microbalance

We present solubility and diffusion data for the gases methane and carbon dioxide in the polymer poly(vinylidene fluoride). The polymer was cut from extruded piping intended for use in offshore oil and gas applications. Measurements were carried out using a purpose-built high-pressure microbalance. These properties were determined in the temperature range 80-120 °C and in the pressure range 50-150 bar for methane and 20-40 bar for carbon dioxide. In general, good agreement was obtained for similar measurements reported in the literature. Solubility follows a Henry’s law (linear) dependence with pressure. Diffusion coefficients for each of the gases in the polymer were also measured using the balance. Activation energies for diffusion and heats of solution for the two gases in the polymer were also determined.     

On-line coupling of packed capillary electrochromatography with coordination ion spray-mass spectrometry for the separation of enantiomers

Pressure-supported packed capillary electrochromatography (CEC) and packed capillary high-performance liquid chromatography (pHPLC) have been coupled on-line to electrospray ionization-mass spectrometry (ESI-MS) and coordination ion spray-mass spectrometry (CIS-MS). Separation of enantiomers of barbiturates and chlorinated alkyl phenoxypropanoates were performed on a permethylated beta-cyclodextrin stationary phase by pressure-supported CEC. For on-line detection with ESI- and CIS-MS, a modified sheath-liquid interface was used. CIS-MS is a universal, novel ionization technique which improves the selectivity as well as the sensitivity. Charged complexes were formed through the addition of central complexing ions such as silver(I), cobalt(II), copper(II), and lithium(I) to the sheath flow. Advantages of CIS-MS detection compared to the ESI-MS mode are discussed. In the CIS-MS mode, increased sensitivity and high selectivity was attained through different possibilities of complexation. The superiority of pressure-supported CEC compared to pHPLC in the hyphenation with CIS-MS is demonstrated.     

Fluorescence excitation spectroscopy of Xenon doped Neon clusters: size and site effects,and cluster melting

Electronic excitations of Xe atoms and Xe₂ molecules embedded in free Ne clusters are studied with time resolved fluorescence excitation spectroscopy. Several distinct absorption bands blueshifted relativ to the first atomic resonance line of Xe are observed and are attributed to Xe or Xe₂ located in different sites. For Ne clusters containing less than 300 atoms only interior sites are observed indicating that small Ne clusters are liquid-like.     

Sigma-aromaticity and sigma-antiaromaticity in saturated inorganic rings

The magnetic properties of a series of inorganic saturated rings, (SiH2)n, (GeH2)n, (NH)n, (PH)n, (AsH)n, On, Sn, and Sen (n = 3-6), exhibit zigzag behavior with ring size resembling that of aromatic and antiaromatic Hückel pi-systems and (CH2)n rings. Computed GIAO-SCF nucleus-independent chemical shifts (NICS) and localized (LMO) NICS analysis indicate that the sigma-ring electrons are chiefly responsible for this zigzag behavior. This evidence for sigma-aromaticity is further supported by theoretical strain energy (TSE). The Hückel 4n + 2/4n aromaticity/antiaromaticity rule for pi-electron systems applies well to the smaller saturated rings.