Reverse estimates in growth spaces

Let H(B _d ) denote the space of holomorphic functions on the unit ball B _d of ${{\mathbb{C}}^d}$ . Given a radial doubling weight w, we construct functions ${f, g\in H(B_1)}$ such that |f| + |g| is comparable to w. Also, we obtain similar results for B _d , d ≥ 2, and for circular, strictly convex domains with smooth boundary. As an application, we study weighted composition operators and related integral operators on growth spaces of holomorphic functions.     

Low‐Temperature FT‐NIR Spectroscopy of Strain‐Induced Orientation and Crystallization in a Poly(dimethylsiloxane) Network

Summary: The mechanical properties, morphology, and orientation of a poly(dimethylsiloxane) (PDMS) network have been studied during cyclic elongation and recovery by simultaneous Fourier‐transform near‐infrared polarization spectroscopy at temperatures ranging from room temperature to −40 °C. Completely different orientation/recovery mechanisms and changes in the state of order of PDMS were detected as a consequence of cyclic loading/unloading with decreasing temperature. The differences observed at −20 °C compared to room temperature are explained in terms of conformationally regular chain segments, whereas the cooling to −40 °C leads to the formation of lamellar crystals.

Stress/strain diagrams of the elongation/recovery‐cycles of the PDMS films.     

Electronic absorption spectra of CCS and CCS in neon matrices

Mass selected C₂S⁻ ions have been co-deposited with neon to grow a matrix at 6 K. The and electronic absorption spectra of the linear CCS⁻ anion have been identified with origin band at 10 606 and 22 273 cm⁻¹, respectively. After exposure to UV radiation a new electronic transition of CCS is observed (origin band at 30 563 cm⁻¹) in addition to its known band system. Ab initio calculations provide support for the symmetry assignment of the upper electronic states of CCS⁻, CCS and of the vibrational structure in the spectra.     

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.     

Heterogeneous oxidation of ethanol over Cu(OH)2/-α-Fe2O3 under visible light

A Cu(OH)₂/α-Fe₂O₃ photocatalyst is shown to be active in the gas phase oxidation of ethanol under visible light. The calculated initial quantum efficiency of the ethanol photooxidation is 0.1-1%. However, ethanol is oxidized only into acetic acid, which deactivates the catalyst. This revised version was published online in August 2006 with corrections to the Cover Date.     

An F. and M. Riesz Theorem on the Complex Sphere

Let μ be a measure on the complex sphere. Denote by μ_pq the projection of μ on H(p, q), the space of complex spherical harmonics. Assume that μ_pq = 0 if (p − 1)q ≠ 0, and ∥μ_1q∥_∞ → 0 as q → ∞. Then μ is absolutely continuous with respect to Lebesgue measure on the sphere.     

Ruthenium-Catalyzed Coupling Reactions of CO2 with C2H4 and Hydrosilanes towards Silyl Esters

A series of in situ-prepared catalytic systems incorporating Ru^II precursors and bidentate phosphine ligands has been probed in the reductive carboxylation of ethylene in the presence of triethylsilane as reductant. The catalytic production of propionate and acrylate silyl esters was evidenced by high-throughput screening (HTS) and implemented in batch reactor techniques. The most promising catalyst systems identified were made of Ru(H)(Cl)(CO)(PPh₃)₃ and 1,4-bis(dicyclohexylphosphino)butane (DCPB) or 1,1’-ferrocene-diyl-bis(cyclohexylphosphine) (DCPF). A marked influence of water on the acrylate/propionate selectivity was noted. Turnover numbers [mol mol(Ru)⁻¹] up to 16 for acrylate and up to 68 for propionate were reached under relatively mild conditions (20 bar, 100 °C, 0.5 mol % Ru, 40 mol % H₂O vs. HSiEt₃). Possible mechanisms are discussed.     

The IR spectra of Mg5C(CO) complexes on the (0 0 1) surfaces of polycrystalline and single crystal MgO

The FTIR spectroscopy of carbon monoxide adsorbed on polycrystalline MgO smoke has been investigated as a function of the CO equilibrium pressure at constant temperature (60 K) (optical isotherm) and of the temperature (in the 300–60 K range) at constant CO pressure (optical isobar). In both cases the spectra fully reproduce those of CO adsorbed on the (0 0 1) surface of UHV cleaved single crystals [Heidberg et al., Surf. Sci. 331–333 (1995) 1467]. This result, never attained in previous investigations on dispersed MgO, contribute to bridging the gap which is commonly supposed to exist between surface science and the study of “real” (defective) systems. Depending on the surface coverage θ the main spectral features due to the CO/MgO smoke interaction are a single band shifting from 2157.5 (at θ→0) to 2150.2 cm⁻¹ (at θ=1/4) or a triplet, at 2151.5, 2137.2 and 2132.4 cm⁻¹ (at θ>1/4). These manifestations are due to the ν(CO) modes of Mg_5C²⁺· · · CO adducts formed on the (0 0 1) terminations of the cubic MgO smoke microcrystals. The formation of the CO monolayer is occurring in two different phases: (i) a first phase with CO oscillators perpendicularly oriented to the surface (2157–2150 cm⁻¹) and (ii) a second phase constituted by an array of coexisting perpendicular and tilted species (triplet at 2151.5, 2137.2 and 2132.4 cm⁻¹). A much weaker feature at 2167.5–2164 cm⁻¹ is assigned to Mg_4C²⁺· · · CO adducts at the edges of the microcrystals. The heat of adsorption of the perpendicular Mg_5C²⁺· · · CO complex in the first phase has been estimated from the optical isobar and results to be 11 kJ mol⁻¹.