Groupwise density and related cardinals

We prove several theorems about the cardinal associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps from to, all families of size are below all unbounded families. With respect to a natural ordering of filters on, all filters generated by sets are below all non-feeble filters. If then and . (The definitions of these cardinals are recalled in the introduction.) Finally, some consequences deduced from by Laflamme are shown to be equivalent to .     

An instanton-invariant for 3-manifolds

To an oriented closed 3-dimensional manifoldM withH ₁(M, )=0, we assign a ₈-graded homology groupI _*(M) whose Euler characteristic is twice Casson's invariant. The definition uses a construction on the space of instantons onM×.     

WKB properties of the time-dependent Schrödinger system

It is shown that the time-dependent WKB expansion highlights some of the hidden properties of the Schrödinger equation and forms a natural bridge between that equation and the functional integral formulation of quantum mechanics. In particular it is shown that the leading (zero- and first-order in ) terms in the WKB expansion are essentially classical, and the relationship of this result to the classical nature of the WKB partition function, and of the anomalies in quantum field theory, is discussed.     

Chiral recognition in the resolution of enantiomers by GLC

Summary Chiral recognition of many enantiomeric solutes by a chiral amide stationary phase is based mainly on hydrogen bonding. A chiral-recognition-factor CHI is proposed, given by the difference of the enthalpy change in the enantiomer discrimination, standardized with respect to the specific interaction of the solutes with the diamide core of the stationary phase. The r?le of the entropy part is also discussed. By extrapolation of the retention behaviour to elevated temperature, peak inversion of enantiomers is predicted. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

Energetic ion bombardment of Ag surfaces by C<Stack><Subscript>60</Subscript><Superscript>+</Superscript></Stack> and Ga<Superscript>+</Superscript> projectiles

The ion bombardment-induced release of particles from a metal surface is investigated using energetic fullerene cluster ions as projectiles. The total sputter yield as well as partial yields of neutral and charged monomers and clusters leaving the surface are measured and compared with corresponding data obtained with atomic projectile ions of similar impact kinetic energy. It is found that all yields are enhanced by about one order of magnitude under bombardment with the C60+ cluster projectiles compared with Ga+ ions. In contrast, the electronic excitation processes determining the secondary ion formation probability are unaffected. The kinetic energy spectra of sputtered particles exhibit characteristic differences which reflect the largely different nature of the sputtering process for both types of projectiles. In particular, it is found that under C60+ impact (1) the energy spectrum of sputtered atoms peaks at significantly lower kinetic energies than for Ga+ bombardment and (2) the velocity spectra of monomers and dimers are virtually identical, a finding which is in pronounced contrast to all published data obtained for atomic projectiles. The experimental findings are in reasonable agreement with recent molecular dynamics simulations.     

On-line coupling of ion chromatography and atomic spectrometry for ultra trace analysis in high purity molybdenum- and tungsten-silicide

The well-established technique of on-line coupling ion chromatography and atomic spectrometry for ultra trace analysis in high purity molybdenum and tungsten is extended to include the silicides MoSi(x) and WSi(x). An additionally included matrix elimination step allows an almost interference-free trace analysis in the silicide matrices. Reproducibility and accuracy of the on-line method were checked by comparison with several other methods, such as isotope dilution, radiochemical neutron activation analysis, direct determination by atomic absorption analysis and not at least with glow discharge mass spectrometry. The results show the high potential of the on-line method for reaching detection limits in the pg g(-1) range, but they show also remaining problems with contamination and system calibration.     

How electrons guard the space: shape optimization with probability distribution criteria

Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume ³ for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue     

Chemical Reactions in the Manufacture of Waveguides for Long Distance Optical Data Transmission

One of the modern high technologies which has advanced enormously in the last few years is glass fiber technology. This is used in the manufacture of glass fibers for lighting purposes and for the optical transfer of analog and digital data with a high transfer density. The technical demands made on the glass fibers required for data transfer, the optical waveguides, are extremely high and are already fulfilled to a large extent by industry. At present about four million kilometers of fiber, worth ca. 800 million DM are produced worldwide (10% in the Federal Republic of Germany). Numerous chemical processes take place during the manufacture of optical waveguides. However, in contrast both to the high and constantly growing demands on the quality and to the increasing production volume of such fibers, little is in fact known about the reactions involved. The present article will attempt to develop a picture of the multifarious reactions occurring in the course of this technical process on the basis of literature data and our own studies.     

Conductive polyethylene-carbon black composites by elongational-flow injection molding Part 3. Study of the structure and morphology

The morphology and structure of high molecular weight linear polyethylene (M _w 450000) filled with carbon black and processed using molds that introduce an elongational flow component during injection molding has been examined using electron microscopy and x-ray diffraction techniques. The study of fracture surfaces reveals the display of shish-kebabs oriented along the injection direction with segregated longitudinal channels of carbon black particles. Molecular and lamellar changes in orientation are, furthermore, studied across the thickness of the moldings. It is shown that addition of carbon black particles to injection-molded polyethylene induces significant changes in lamellar orientation. Thus, while lamellar overgrowth proceeds perpendicular to the fiber axes within carbon free channels, lamellae grow randomly within carbon-enriched regions where flow is less pronounced.