Singular measures with smalH(p, q)-projections

We construct a singular probability measure μ on the complex sphere such that the Poisson integral of μ is a pluriharmonic function in the ball and the Fourier transform of μ is asp→∞. Supported by the Centre de Recerca Matemàtica (Institut d’Estudis Catalans, Barcelona) under a grant from DGICYT (Spain); partially supported by the RFFI grant 96-01-00693.     

New estimates of continuity in $$M/GI/1/ \infty$$ queues

The paper deals with an estimation of the total variation distance between stationary distributions of waiting time in two queueing systems with equal Poisson inputs and different distributions B and $\widetilde B$ of service time. Assuming equality of two first moments of B and $\widetilde B$ the continuity inequalities are derived in terms of difference pseudomoments of B and $\widetilde B$ . When in addition the third moments of B and $\widetilde B$ coincide then the constant involved in the corresponding inequality has the asymptotics ${\text{O}}\left[ {\left( {1 - \rho } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} } \right]$ in the heavy traffic limit $\rho \to 1$ .     

Conjugation enhancement of intramolecular exciton migration in poly(p-phenylene ethynylene)s

Efficient energy migration in conjugated polymers is critical to their performance in photovoltaic, display, and sensor devices. The ability to precisely control the polymer conformation is a key issue for the experimental investigations and deeper understanding of the nature of this process. We make use of specially designed iptycene-containing poly(p-phenylene ethynylene)s that display chain-extended conformations when dissolved in nematic liquid crystalline solvents. In these solutions, the polymers show a substantial enhancement in the intrachain exciton migration rate, which is attributed to their increased conjugation length and better alignment. The organizational enhancement of the energy transfer efficiency, as determined by site-selective emission from lower energy traps at the polymer termini, is accompanied by a significant increase of the fluorescence quantum yield. The liquid crystalline phase is a necessary requirement for these phenomena to occur, and when the temperature was increased above the nematic-isotropic transition, we observed a dramatic reduction of the energy transfer efficiency and fluorescence quantum yield. The ability to improve the exciton migration efficiency through precise control of the polymer structure with liquid crystalline solutions demonstrates the importance of a polymer's conformation for energy transfer, and provides a way to improve the energy transporting performance of conjugated polymers.     

Side chain functionalized liquid crystalline polymers and blends, 1. Reentrant nematic phase formation in hydrogen-bonded blends of liquid crystalline functionalized copolymers with a low molecular weight non-mesogeic dopant

Hydrogen-bonded blends based on smectic comb-shaped functionalized LC copolymers containing alkyloxy-4-hydroxybenzoic acid fragments (proton donor) and the low molecular weight dopant 4-(4-pyridyloyl)cyanobenzoate (proton acceptor) were obtained. It was observed that blends containing 10–25 mol-% of low molecular weight dopants form a reentrant nematic phase (SmA-RN-SmA-I). The blend behavior in the magnetic field was studied, and the orientational elastic constants of the RN phase were determined.     

Separation of Variables in the Elliptic Gaudin Model

For the elliptic Gaudin model (a degenerate case of the XYZ integrable spin chain) a separation of variables is constructed in the classical case. The corresponding separated coordinates are obtained as the poles of a suitably normalized Baker-Akhiezer function. The classical results are generalized to the quantum case where the kernel of the separating integral operator is constructed. The simplest one-degree-of-freedom case is studied in detail. Received: 21 August 1998 / Accepted: 12 January 1999     

Generic pairs of SU-rank 1 structures

For a supersimple SU-rank 1 theory T we introduce the notion of a generic elementary pair of models of T (generic T-pair). We show that the theory T^* of all generic T-pairs is complete and supersimple. In the strongly minimal case, T^* coincides with the theory of infinite dimensional pairs, which was used in (S. Buechler, Pseudoprojective strongly minimal sets are locally projective, J. Symbolic Logic 56(4) (1991) 1184–1194) to study the geometric properties of T. In our SU-rank 1 setting, we use T^* for the same purpose. In particular, we obtain a characterization of linearity for SU-rank 1 structures by giving several equivalent conditions on T^*, find a “weak” version of local modularity which is equivalent to linearity, show that linearity coincides with 1-basedness, and use the generic pairs to “recover” projective geometries over division rings from non-trivial linear SU-rank 1 structures.     

Nevanlinna functions as quotients

Let be a holomorphic function in the unit ball. Then is a Nevanlinna function if and only if there exist Smirnov functions , such that and has no zeros in the ball.

     

Nanosized Au4Pd32(CO)28(PMe3)14 Containing a Highly Distorted Encapsulated Au4 Tetrahedron: Proposed Multi-Twinned Growth-Pattern from Two Deformed Au-Centered Double Icosahedral-Based Fragments*

As part of an extensive effort to synthesize a variety of nanosized gold–palladium carbonyl phosphine clusters, the neutral Au₄Pd₃₂(CO)₂₈(PMe₃)₁₄ (1) was isolated and unambiguously characterized by low-temperature CCD X-ray diffraction and IR measurements. This nanosized Au₄Pd₃₂ cluster was prepared in low yields (<5%) from the room-temperature reaction of Pd₁₀(CO)₁₂(PMe₃)₆ (2) with Au(SMe₂)Cl in THF/acetone. The heretofore unknown molecular geometry of 1 of pseudo-D₂ (222) symmetry (without methyl substituents) may be viewed to arise from a relatively strong (Au–Au)-bonded linkage (2.64 Å (av)) of two pentagonal-bipyramidal (μ₅-Au)(μ₅-Pd)Pd₅ polyhedra; this generated 14-atom Au₂Pd₁₂ unit may be considered as a markedly deformed part of a 19-atom Au-centered double icosahedron without the inner pentagon (corresponding to five missing inner atoms). In turn, two Au₂Pd₁₂ units form a central composite-twinned Au₄Pd₂₂ kernel via vertex-fusion of two common Pd atoms along with additional formation of four Pd–Pd bonding, four Au–Pd bonding, and two weaker secondary Au–Au bonding interactions at 2.90 Å (av) (versus the other two diagonal Au–Au nonbonding ones at 3.51 Å (av)); this resulting Au₄Pd₂₂P₈ kernel is augmented by the addition of two triangular Pd₃P core-fragments and four exopolyhedral PdP groups to give the Au₄Pd₃₂P₁₄ framework of 1. This cluster is stabilized by 28 bridging COs, of which 20 are doubly bridging and 8 triply bridging. The largest metal-core diameter of 1 along one pseudo C₂ axis is 1.1 nm. This new type of multi-twinned metal cluster has direct relevance to both ligated and non-ligated (naked) non-crystalline metal nanoparticles, many of which possess multiple twinning and/or disorder.^*Dedicated to Professor F. A. Cotton on the occasion of his 75th birthday in recognition of numerous seminal contributions to modern Inorganic Chemistry. Professor Cotton has a truly unparalleled scientific career in Inorganic Chemistry in terms of the overall composite effects of his highly prolific research productivity, his tremendous impact on former graduate students, postdoctoral associates, and collaborators, and his matchless textbooks/monographs.     

Generalized scheme of chemisorption,electrooxidation and electroreduction of simple organic compounds on platinum group metals

A generalized scheme of successive stages for chemisorption, electrooxidation and electroreduction of simple organic compounds from methane to CO₂ on platinum group metals has been developed on the basis of experimental data. The actual pathway of electrooxidation or electroreduction of an organic compound and the yield of the reaction products depend on the ratio between the rates of individual steps which, in their turn, are determined by various factors (potential, temperature, coverage of the surface with H_ads and OH_ads, with reacting and intermediate organic particles, as well as with foreign particles). The accumulation of chemisorbed compounds on the electrode surface depends on the relationship between the rates of their formation and subsequent transformation.