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.     

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.     

Structural and electronic trends among group 15 polyhedral fullerenes

We have investigated the structural and electronic characteristics of tetrahedral, octahedral, and icosahedral fullerenes composed of group 15 elements phosphorus, arsenic, antimony, and bismuth. Systematic quantum chemical studies at the DFT and MP2 levels of theory were performed to obtain periodic trends for the structural principles, stabilities, and electronic properties of the elemental nanostructures. Calibration calculations for polyhedral clusters with up to 20 atoms showed the applied theoretical approaches to be in good agreement with high-level CCSD(T)/cc-pVTZ results. By studying fullerenes up to P₈₈₈, As₅₄₀, Sb₆₂₀, and Bi₆₂₀, we found their structures and stabilities to converge smoothly toward their experimental bulk counterparts. The diameters of the largest studied cages were 4.8, 3.7, 4.8, and 5.1?nm for the P, As, Sb, and Bi fullerenes, respectively. Comparisons with the experimentally known allotropes of the studied elements suggest the predicted polyhedral cages to be thermodynamically stable. All studied group 15 polyhedral fullerenes were found to be semiconducting, and density of states analysis illustrated clear periodic trends in their electronic structure. Relativistic effects become increasingly important when moving from P to Bi and taking the spin?Corbit effects into account by using a two-component procedure had a significant positive effect on the relative stability of bismuth clusters.     

Molecular dynamics simulations of water droplets on polymer surfaces

Molecular dynamics simulations were used to study the wetting of polymer surfaces with water. Contact angles of water droplets on crystalline and two amorphous polyethylene (PE) and poly(vinyl chloride) (PVC) surfaces were extracted from atomistic simulations. Crystalline surfaces were produced by duplicating the unit cell of an experimental crystal structure, and amorphous surfaces by pressing the bulk polymer step by step at elevated temperature between two repulsive grid surfaces to a target density. Different-sized water droplets on the crystalline PE surface revealed a slightly positive line tension on the order of 10(-12)-10(-11) N, whereas droplets on crystalline PVC did not yield a definite line tension. Microscopic contact angles produced by the simple point charge (SPC) water model were mostly a few degrees smaller than those produced by the extended SPC model, which, as the model with lowest bulk energy, presents an upper boundary for contact angles. The macroscopic contact angle for the SPC model was 94 degrees on crystalline PVC and 113 degrees on crystalline PE. Amorphicity of the surface increased the water contact angle on PE but decreased it on PVC, for both water models. If the simulated contact angles on crystalline and amorphous surfaces are combined in proportion to the crystallinity of the polymer in question, simulated values in relatively good agreement with measured values are obtained.     

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.     

New irrationality measures for -logarithms

The three main methods used in diophantine analysis of -series are combined to obtain new upper bounds for irrationality measures of the values of the -logarithm function

when and .

     

Synthesis of nonanuclear heterometallic carbide clusters. Unexpected formation of the [Ru6(CO)16]2-[Pt2(CO)2(dppm)2]2+ ion pair on the way to [Ru6C(CO)16Pt3(dppm)2

A novel trimetallic cluster [Ru5CRh2Pt2(CO)16(dppm)2] was synthesized via coupling of two neutral clusters-[Ru5C(CO)15] and [Rh2Pt2(CO)6(dppm)2]. The structure of this mixed metal complex was established using X-ray crystallography and 31P NMR spectroscopy. It was found that the reaction between [Ru6C(CO)17] and [Pt2(CO)3(dppm)2] leads to spontaneous electron transfer between these polynuclear complexes and results in the formation of an unusually stable cluster "salt" {[Ru6(CO)16]2-[Pt2(CO)2(dppm)2]2+}, which was characterized by crystallographic and spectroscopic methods. Heating of the Ru6-Pt2 ion pair in an autoclave (145 degrees C, 15 atm N2) results in fusion of the metal frameworks to give a nonanuclear mixed metal [Ru6C(CO)16Pt3(dppm)2] cluster in a good yield. The latter complex was obtained earlier as a minor product of another thermal reaction and now has been additionally characterized by 31P NMR spectroscopy.