Congruences,equational theories and lattice representations

We survey results concerning the representations of lattices as lattices of congruences and as lattices of equational theories. Recent results and open problems will be mentioned.To László Fuchs on the occasion of his 70th birthday     

The light-cone expansion and the parton model in polarized muon-production

The relation between the light-cone expansion and the QCD improved parton model formalism for polarized deep inelastic muon-production is discussed in detail. The regulator dependence of the relevant quantities is explicity studied at the two-loop level for the first moment ofg ₁ ^P . It is shown that the anomalous gluon component is well defined if the quark term is specified as a conserved quantity that does not evolve inQ ². The behaviour of the first moment ofg ₁ ^P at the threshold for heavy quark production is also discussed.     

Über basische Aluminiumsalze und ihre Lösungen. XI. Vergleichende 27Al-NMR-Untersuchungen am Mineral Zunyit und basischen Aluminium-Salzen mit tridekameren Al-oxo-hydroxo-aquo-Kationen

Basic Aluminium Salts and their Solutions. XI. ²⁷Al-NMR Studies Comparing the Mineral Zunyite and Basic Aluminium Salts of Tridecameric Al-oxo-hydroxo-aquo-Cations Solid-state high resolution ²⁷Al NMR studies of basic aluminum sulphate and the mineral zunyite, both containing tridecameric Al-oxo-hydroxo groups, show different ²⁷Al spectra. While for zunyite both AlO₆ octahedra (0 ppm) and the central AlO₄ tetrahedron (69 ppm) are observed in the spectrum, in the case of the basic aluminum sulphate only the tetrahedrally coordinated Al (59 ppm) is detected by NMR. This behaviour is explained by structural data, which indicate stronger distortions of the AlO₆ octahedra in the case of the basic aluminum sulphate. The increased shielding of the fourcoordinated Al of the basic sulphate is attributed to an increased ionic character of the Al? O bond in this compound.     

O(G μ 2 m t 4 ) electroweak radiative corrections to theZb \bar b vertex

The leading heavy-top two-loop corrections to theZb \(\bar b\) vertex are determined from a direct evaluation of the corresponding Feynman diagrams in the largem _t limit. The leading one-loop top-mass effect is enhanced by \([{{1 + G_\mu m_t^2 ({{9 - \pi ^2 } \mathord{\left/ {\vphantom {{9 - \pi ^2 } 3}} \right. \kern-0em} 3})} \mathord{\left/ {\vphantom {{1 + G_\mu m_t^2 ({{9 - \pi ^2 } \mathord{\left/ {\vphantom {{9 - \pi ^2 } 3}} \right. \kern-0em} 3})} {(8\pi ^2 \sqrt 2 )}}} \right. \kern-0em} {(8\pi ^2 \sqrt 2 )}}]\) . Our calculation confirms a recent result of Barbieri et al..     

Longitudinal jet cross sections in order α s 2

We calculate the cross section fore ⁺ e ^–3 jets for longitudinally polarized virtual photons up to order _s ² in the quark-gluon coupling.Dedicated to the memory of Kurt Symanzik     

Solid-state high-resolution 29Si NMR in zunyite

High-resolution ²⁹Si NMR spectra of zunyite Si₅Al₁₃O₂₀ (OH,F)₁₈Cl have been studied by magic-angle sample spinning in combination with high-power proton decouplina and polarization transfer. The isotropic ²⁹Si chemical shift depends mainly on the number of Si-O-Si bridges and the bond angles in these bridges connecting the different SiO₄ tetrahedra.     

SiH+5 and the proton affinity of monosilane

Tandem mass spectrometric studies show that SiH⁺₅ is formed in bimolecular reactions of SiH₄ and NH⁺₂, C₂H⁺₃, C₂H⁺₆ and C₃H⁺₈ ions. The dependence of the reaction cross sections on ion energy indicates the formation of SiH⁺₅ from NH⁺₂, C₂H⁺₃, and C₂H⁺₆ to be exothermic reactions, while formation from C₃H⁺₈ is endothermic. Using known thermochemical data, these facts permit the assignment of 150 and 156 kcal/mole to the lower and upper limits of the proton affinity of monosilane.     

Jet production rates at LEP and the scale of αs

We discuss the scale dependence of _s in connection with jet multiplicities on theZ pole in the framework of perturbative QCD. Several scale defining procedures are applied to jet fractions and compared to recent measurements at LEP.Dedicated to Prof. Dr. H.J. Mang on the occasion of his 60th birthday     

One-Loop QCD Corrections to the Inclusive Production Cross-Section for Heavy Quarks in p Collisions at High Transverse Energies

We calculate one-loop QCD corrections to the production cross-section for heavy quarks in protonantiproton collisions. We are interested in the behaviour of the cross-section at high transverse energies. At high P_T the quark mass should become an irrelevant parameter. Therefore we work in the framework of massless QCD and absorb all mass singularities in a redefinition of the parton densities and fragmentation functions. Numerical results of the cross-section at √S = 0.63, 1.8 and 10 TeV are presented and the dependence of these results on the factorization scheme is examined.     

Comparison of electron spin resonance probe and dielectric relaxation in physically and chemically crosslinked polymers

Dielectric relaxation spectroscopy in the frequency range from 10⁻² Hz to 10⁶ Hz and electron spin resonance (ESR) experiments are employed to study the dynamics in chemically and physically crosslinked networks. As examples for physically crosslinked networks ortho- and para-cresol novolacs were investigated. Dielectrically these materials show low-temperature β- and high-temperature α-relaxation. Both relaxation regions differ for both types of novolacs. This is also reflected by the ESR measurements and is discussed in terms of different hydrogen bonds found to be stronger in para-cresol novolac. For the chemically crosslinked poly(triallyl isocyanurate) only a β-peak is found by the dielectric measurements. Also in the ESR experiment the slow motion regime is characterized up to high temperatures. This means that the segmental motion is strongly suppressed by chemical crosslinking. Nevertheless the obtained change in the formal T_50G value can be used to characterize the glass transition in highly crosslinked systems by the ESR method.