On Connected Transversals to Dihedral Subgroups of Order 2p n

Let G be a group with a dihedral subgroup H of order 2pⁿ, where p is an odd prime. We show that if there exist H-connected transversals in G, then G is a solvable group. We apply this result to the loop theory and show that if the inner mapping group of a finite loop Q is dihedral of order 2pⁿ, then Q is a solvable loop.1991 Mathematics Subject Classification: 20D10, 20N05     

cis-trans formic acid dimer: experimental observation and improved stability against proton tunneling

We prepared the first cis-trans dimer of formic acid and measured its vibrational spectrum in a low-temperature Ar matrix. This preparation was done by selective vibrational excitation of the trans-trans noncyclic dimer. It was found that the stability of the cis-trans dimer against proton tunneling is strongly improved compared to the monomer, especially at elevated temperatures (>30 K). This surprising phenomenon was explained by differences in dynamical, energetic, and vibrational properties of the dimer and monomer. The obtained results show that the proton tunneling reactions can be strongly modified in the hydrogen-bonded solid network compared to the monomeric species.     

Transport properties of heterogeneous materials. Combining computerised X-ray micro-tomography and direct numerical simulations

Feasibility of a method for finding flow permeability of porous materials, based on combining computerised X-ray micro-tomography and numerical simulations, is assessed. The permeability is found by solving fluid flow through the complex 3D pore structures obtained by tomography for actual material samples. We estimate overall accuracy of the method and compare numerical and experimental results. Factors contributing to uncertainty of the method include numerical error arising from the finite resolution of tomographic images and the rather small sample size available with the present tomographic techniques. The total uncertainty of computed values of permeability is, however, not essentially larger than that of experimental results. We conclude that the method provides a feasible alternative for finding fluid flow properties of the kind of materials studied. It can be used to estimate all components of permeability tensor and is useful in cases where direct measurements are not achievable. Analogous methods can be applied to other modes of transport, such as diffusion and heat conduction.     

Modified Engelmaier’s model taking account of different stress levels

In this paper, the solder fatigue model created by Werner Engelmaier is modified so that it takes better into account the different stress levels the solder material experiences. This is accomplished by replacing the fatigue ductility constant by a correction term that is temperature- excursion- range-dependent. In order to obtain the correction term, the effect of the temperature cycling profile on lifetime is studied. The correction term obtained is package type specific. More compliant plastic packages with a small coefficient of expansion mismatch with the organic printed wiring board are handled separately, and stiff ceramic packages assembled on an organic board – resulting in a large CTE mismatch – are considered as another entity.

Correction terms for both lead-free and tin–lead solder materials are given. This is necessary as the creep characteristics of the solders are different. Comparing solder material specific correction terms makes it possible to determine which solder material performs best in a certain environment and a given assembly type. In the case of ceramic packages, the transition where a eutectic tin–lead solder becomes superior to a SnAgCu solder is expected to take place when temperature excursions are smaller than ca. 70 °C. This indicates that although in a highly accelerated stress test, lead-free solders may be inferior compared to tin–lead solders, in the real field environment, the situation may be reversed.     

Infrared absorption spectrum of matrix-isolated noble-gas hydride molecules: fingerprints of specific interactions and hindered rotation

Noble-gas hydride molecules with the general formula HNgY (Ng denotes noble-gas atom and Y denotes electronegative fragment) are usually prepared in solid noble gases. In many cases, the matrix-isolated HNgY molecules show a characteristic structure of the H-Ng stretching absorption: A close doublet as the main spectral feature and a weaker satellite at higher energy. This characteristic band structure is studied here for matrix-isolated HXeBr and HKrCl molecules. Based on the experimental and theoretical results, we suggest a model explaining the common features of the band structure of the HNgY molecules in noble-gas matrices. In this model, the main doublet bands are attributed to matrix sites where the splitting is caused by specific interactions of the embedded molecule with noble-gas matrix atoms in certain local morphology. The weaker blueshifted band is probably a fingerprint of hindered rotation (libration) of the embedded molecule in the lattice. This librational band has a mirror counterpart at lower energies appearing at higher matrix temperatures. Our present ab initio calculations for the one-to-one Xe...HXeBr complexes and the simulation of hindered rotation in a matrix support this image.     

On a general associativity law in groupoids

In this paper we show that a division groupoid together with a general associativity law is in fact a group.     

Stable ammonium bisulfate clusters in the atmosphere

Liquid drop model based equilibrium thermodynamics predicts that in the presence of even small ammonia concentrations practically all the atmospheric sulfuric acid molecules are bound to tiny, stable ammonium-bisulfate clusters. Hitherto sulfuric acid has been believed to form hydrates with water. Thermodynamic theory predicts correctly the hydrate formation observed experimentally. Results from ab initio computer simulations contradict the thermodynamic results and also the experimental findings for cluster formation in both sulfuric acid-water and ammonia-sulfuric acid-water mixtures.     

Vibrational spectroscopy of cis- and trans-formic acid in solid argon

Absorption spectra of cis and trans conformers of formic acid (HCOOH) isolated in solid argon are analyzed in the mid-infrared (4000-) and near-infrared (7800-) regions. The HCOOH absorption spectrum reveals matrix-site splitting for the trapped molecule. Narrowband tunable infrared radiation is used to pump a suitable vibrational transition of the trans conformer in order to promote site-selectively the conversion to the cis conformer and separate the spectral features of each site group. Several anharmonic resonances are identified for both conformers. The results of anharmonic vibrational ab initio calculations (CC-VSCF) for the trans and cis conformers of formic acid are reported and compared with the experimental spectra.     

AC losses in high-temperature superconductors: revisiting the fundamentals of the loss modelling

The fundamentals of the electromagnetic modelling of high-temperature superconductors are discussed. Special attention is paid to intrinsic features of high-temperature superconductors different to those of low-temperature superconductors. Examples of those features are strong thermal fluctuations, which results in enhanced flux creep and slanted E(J)-characteristics, anisotropy of critical current density and material resistivity, and the granularity of the material. Having established the fundamental principles for the loss modelling, the influence of thermal fluctuations, anisotropy and granularity on the AC losses are considered.     

Preparation and structure determination of 1-benzyl-, 1-methyl- and 1H-5-[(2-nitro-2-phenyl)ethenyl]imidazoles

1-R-5-[(2-Nitro-2-phenyl)ethenyl]imidazoles (R = Bn, Me, H) 6a,b,c were synthesized by the Knoevenagel reaction of the corresponding aldehydes 4a,b,c with phenylnitromethane 5 . The E-isomers 6a,b,c were precipitated from the reaction mixture as crystalline compounds in 89, 81 and 60% yields, respectively. Traces of the Z-isomers 6a′b′,c′ were found in the reaction mixtures but could be obtained in a ratio of 4:3 from the E-form with UV irradiation. The E-forms were more stable and the Z-isomers changed again to the E-isomers in several weeks.