A Remark on Weakly Compact Cardinals

We show that if κ is weakly compact, then κ → (stationary ,κ)³holds for treelike partitions. As an application we study model constructions.     

Geometry prediction of bridged zirconocene dichlorides by quantum chemical methods

The ab initio Hartree–Fock theory has been demonstrated to give accurate geometry predictions for bridged zirconocene dichlorides. Equilibrium geometries of crystallographically characterized bridged zirconocene dichlorides were optimized by Hartree–Fock, MP2, BLYP, and B3LYP methods, with basis sets ranging from 3‐21G* to 6‐311G**. Selected geometrical parameters were compared with experimental crystal structures. The least expensive HF/3‐21G* method proved to be notably accurate. The accuracy of HF/3‐21G* was verified by a comprehensive data set of 62 bridged zirconocene dichlorides. Furthermore, experimental corrections were applied to the optimized geometry parameters to eliminate systematic deviations. Corrections resulted in considerably improved accuracy for systematically overestimated metal–ligand distances, with maximum deviation falling from 0.081 to 0.039 Å, and absolute average deviations from 0.048 to 0.012 Å. Ligand–metal–ligand angles were predicted accurately with absolute average deviations of 0.7–1.3°. Zirconium–chlorine distances and chlorine–zirconium–chlorine angles are relatively constant in the studied molecules. Zirconium–cyclopentadienyl distances can be influenced mainly by modifying the ligand structure, whereas cyclopentadienyl–zirconium– cyclopentadienyl angles and cyclopentadienyl–cyclopentadienyl plane angles can be controlled by bridge modifications. The HF/3‐21G* method can be applied for the estimation of steric effects in zirconocene catalyzed polymerization reactions, therefore being suitable for the construction of structure–polymerization property correlations. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 51–64, 2001     

On Diophantine Approximations of Mock Theta Functions of Third Order

The paper gives bounds for the approximation of the values of Ramanujan's Mock Theta functions of third order and more generally of some q-hypergeometric functions by the elements of an algebraic number field. Simultaneous approximations for the values of q-exponential function are also obtained. All the results are given both in the archimedean and p-adic case.     

Theoretical investigations on Ziegler-Natta catalysis: Alkylation of the TiCl4 catalyst

Theoretical ab initio methods have been used to study the alkylation reaction of the MgCl₂-supported TiCl₄ catalyst. Investigation of the reaction path indicated that the Al(CH₃)₃ co-catalyst inserts into the coordination sphere of the titanium atom of the catalyst so that a methyl group of Al(CH₃)₃ interacts with the titanium. The methyl group migrates from Al(CH₃)₃ to the vacant coordination site of the catalyst. When the catalyst loses one of its chlorine atoms to the co-catalyst during this reaction, the catalyst maintains its vacant site, but the position of the vacant site changes. The presence of the external electron donor coordinated to the co-catalyst makes the alkylation reaction energetically more favourable.     

Stepwise 1D growth of luminescent Au(I)-Ag(I) phosphine-alkynyl clusters: synthesis, photophysical, and theoretical studies

Reactions between the diphosphino-gold cationic complexes [Au(2)(PPh(2)-C(2)-(C(6)H(4))(n)-C(2)-PPh(2))(2)](2+) (n = 0, 1, 2, 3) and polymeric acetylides (AuC(2)Ph)(n) and (AgC(2)Ph)(n) lead to the formation of a new family of heterometallic clusters with the general formula [Au(8+2n)Ag(6+2n)(C(2)Ph)(8+4n)(PPh(2)C(2)(C(6)H(4))(n)C(2)PPh(2))(2)](2+), n = 0 (1), 1 (2), 2 (3), 3 (4). Compounds 1-4 were characterized in detail by NMR and ESI-MS spectroscopy. Complex 1 (n = 0) crystallizes in two forms (orange (1a) and yellow (1b)), one of which (1a) has been analyzed by X-ray crystallography. The luminescence behavior of 1-4 has been studied. Compounds 2 and 3 exhibited orange-red phosphorescence with quantitative quantum efficiency in both aerated and degassed CH(2)Cl(2), implying O(2)-independent phosphorescence due to efficient protection of the emitting chromophore center by the organic ligands. Complex 3 exhibits reasonable two-photon absorption (TPA) property with a cross section of σ ≈ 45 GM (800 nm), which is comparable to the value of commercially available TPA dyes such as coumarin 151. Computational studies have been performed to correlate the structural and photophysical features of the complexes studied. The metal-centered triplet emission within the heterometallic core is suggested to play a key role in the observed phosphorescence. The luminescence spectrum of 1 in CH(2)Cl(2) shows dual phosphorescence maximized at 575 nm (the P(1) band) and 770 nm (the P(2) band). Both P(1) and P(2) bands possess identical excitation spectra, i.e., the same ground-state origin, and the same relaxation dynamics throughout the temperature range of 298-200 K. The dual emission of 1 arises from fast structural fluctuation upon excitation, perhaps forming two geometry isomers, which exhibit distinctly different P(1) and P(2) bands. The scrambling dynamics might require large-amplitude motion and, hence, is hampered in rigid media, as evidenced by the single emission for 1a (610 nm) and 1b (570 nm) observed in solid.     

Defibration mechanisms of autohydrolyzed Eucalyptus wood chips

The objective of this study was to evaluate the influence of autohydrolysis on mechanical defibration of Eucalyptus wood chips. The autohydrolysis process changed notably the mechanical properties of Eucalyptus chips. The removal of mainly hemicelluloses undoubtedly decreased the overall pulp yield. Hemicellulose losses cannot be solely accounted for the changes in the wood and pulp properties, because the autohydrolysis also caused changes in lignin. When comparing the mechanical pulp fibers of the original wood chips with the fibers resulting from the autohydrolyzed wood material, it was clear that the rupture point shifted from the secondary wall to the middle lamella, confirmed by X-ray photoelectron spectroscopy measurements. This study revealed the mechanical behavior of autohydrolyzed wood chips and can provide useful information for integration of mechanical pulp mills into the biorefinery concept in the future.     

Stability and General Logics

In this paper we make an attempt to study classes of models by using general logics. We do not believe that L_ww is always the best logic for analyzing a class of models. Let K be a class of models and L a logic. The main assumptions we make about K and C are that K has the L-amalgamation property and, later in the paper, that K does not omit L-types. We show that, if modified suitably, most of the results of stability theory hold in this context. The main difference is that existentially closed models of K play the role that arbitrary models play in traditional stability theory. We prove e. g. a structure theorem for the class of existentially closed models of K assuming that K is a trivial superstable class with ndop.     

Optical properties of thermally responsive amphiphilic gold nanoparticles protected with polymers

Amphiphilic thermally responsive gold nanoparticles have been prepared by protecting the particles with both polystyrene, PS, and poly(N-isopropylacrylamide), PNIPAM, chains. Particles form a monolayer on a water surface in a Langmuir trough, and according to in situ spectroscopic measurements, the surface plasmon resonance, SPR, band undergoes a blue-shift during the monolayer compression. The compression-induced blue-shift is related to a change in the conformation of tethered PNIPAM chains; the phenomenon is discussed on the basis of Mie-Drude theory. In contrast, a red-shift in the SPR of the multilayers of the same nanoparticles transferred at different temperatures has been observed with increasing the deposition cycle, attributed to the presence of a weak interparticle coupling in the multilayer.