Deciding Frattini is NP-complete

We show that it is a NP-complete problem to decide whether a finite poset arises as the (Birkhoff) dual of the Frattini sublattice of some finite distributive lattice.This work was supported in part by Swiss NSF grant 20-32644.91.     

351 nm, 0.7 ns laser damage thresholds of monomeric liquid-crystalline systems

The 351 nm laser-damage thresholds (at 0.7 nm pulse length) of monomeric liquid crystals are reported and results from aromatic-core samples are compared with those from fully saturated systems. The role of π-electron conjugation is examined and identified as the key cause for laser damage. For UV laser compatibility of devices, the damage behaviour of an alignment-layer polymer (nylon 6/6) was also investigated.     

Numerical convergence study of the orthogonalized multi-channels approach to three-body Coulomb scattering below breakup threshold

The three-body Coulomb problem for nuclear clusters is solved numerically for a model below three-body breakup threshold. An orthogonalized multi-channels method is employed. The method allows to check for convergence by considering the norm square of the closed-channels part of the wave function. The numerical results show that convergence can well be achieved on present-day computers.     

Off-shell behaviour of theN-N interaction in a six-quark resonating group model of the deuteron

Two different 6-quark resonating group models of the deuteron are investigated to study the off-shell property of theN-N interaction. In the first model the quarks interact by a central one-gluon-exchange potential plus confinement potential. The meson-exchange contribution to then-p potential is simulated by a central GaussianN-N potential. In the second model the quarks interact by one-gluon-and one-pion-exchange potentials (central and noncentral) plus confinement potential. A small additional -exchange potential between neutron and proton binds the deuteron at the correct energy.Several off-shell variants of the two resonating group models are compared with each other by analyzing their elastic electron scattering cross sections. It is found that the standard renormalized version of the resonating group model yields potentials and wave functions that may be considered physical within the limitations of the model. Unitary off-shell transformations, which modify potentials and wave functions in any sizeable way, lead to a disagreement between the charge distribution predicted by the model via analysis of electron scattering and the charge distribution following from the microscopic quark distribution.Both of the 6-quark models support a soft repulsive core of the tripletn-p potential with a core height of around 900 MeV.     

Kinetik und stereochemischer Verlauf der thermischen Umlagerung der vier stereoisomeren Propenyl-(but-2′-enyl)-äther

The gas-phase rearrangement of (1Z, 2′E)-, (1Z, 2′Z)-, (1E, 2′E)-, and (1E, 2′Z)- propenyl but-2′-enyl ether (Z, E)-, (Z, Z)-, (E, E)-, and (E, Z)-1) into erythro- and threo-2, 3-dimethyl-pent-4-en-al (erythro- and threo-2) was investigated over a temperature range from 142,5° to 190,0° at 20–35 Torr (for kinetic data and activation parameters see table 2). All four stereoisomeric ethers 1 rearrange preferentially via a chair-like transition state C into the aldehydes 2 (ΔΔG^≠ (160°) = 2,5–2,7 kcal/mol for B – C (B = boat-like transition state). The relative rates (k_rel) for (Z, Z)-1, (Z, E)-1, (E,Z)-1, and (E,E)-1 at 160° are 1,0, 2,9, 4,3 and 9,0 respectively (see table 5). Taking into account the relative enthalpies of the ethers 1 and the steric interaction in the C transition state of the ethers 1 (see table 6), k_rel values can be estimated. They are in good agreement with those observed (see table 5).     

High-temperature synthesis, single-crystal X-ray structure determination and solid-state NMR investigations of Ba7[SiO4][BO3]3CN and Sr7[SiO4][BO3]3CN

The novel alkaline earth silicate borate cyanides Ba₇[SiO₄][BO₃]₃CN and Sr₇[SiO₄][BO₃]₃CN have been obtained by the reaction of the respective alkaline earth metals M=Sr, Ba, the carbonates M^IICO₃, BN, and SiO₂ using a radiofrequency furnace at a maximum reaction temperature of 1350°C and 1450°C, respectively. The crystal structures of the isotypic compounds M^II₇[SiO₄][BO₃]₃CN have been determined by single-crystal X-ray crystallography (P6₃mc (no. 186), Z=2, a=1129.9(1) pm, c=733.4(2) pm, R₁=0.0336, wR₂=0.0743 for M^II=Ba and a=1081.3(1) pm, c=695.2(1) pm, R₁=0.0457, wR₂=0.0838 for M^II=Sr). Both ionic compounds represent a new structure type, and they are the first examples of silicate borate cyanides. The cyanide ions are disordered and they are surrounded by Ba²⁺/Sr²⁺ octahedra, respectively. These octahedra share common faces building chains along [001]. The [BO₃]³⁻ ions are arranged around these chains. The [SiO₄]⁴⁻ units are surrounded by Ba²⁺/Sr²⁺ tetrahedra, respectively. The title compounds additionally have been investigated by ¹¹B, ¹³C, ²⁹Si, and ¹H MAS-NMR as well as IR and Raman spectroscopy confirming the presence of [SiO₄]⁴⁻, [BO₃]³⁻, and CN⁻ ions.