Let H(Bd) denote the space of holomorphic functions on the unit ball Bd 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 Bd, 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. 相似文献
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. 相似文献
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. 相似文献
In continuing our research on solid-state organic photochemistry, we have been investigating the phenomenon of reactivity in stages. In this study we present new examples where the photochemical reactivity changes discontinuously at some point in the conversion. In these instances, the reaction course of the solid differs from that in solution. One example is the reaction of 2-methyl-4,4-diphenylcyclohexenone, where an unusual reaction course was encountered in the solid state; and, of two possible mechanisms, one was established by isotopic labeling. A second case is that of 4,5,5-triphenylcyclohexenone. The solid-state reaction of this enone was found to give a new photochemical transformation, the Type C rearrangement, a process that involves a delta to alpha aryl migration. In the case of 3-tert-butyl-5,5-diphenylcyclohexenone the Type C rearrangement occurred even in solution. The stage behavior was investigated using X-ray analysis and Quantum Mechanics/Molecular Mechanics computations. This permitted us to determine the sources and details of the stage phenomenon. The analysis revealed how a product molecule as a neighbor affects reactivity. The computations were employed to follow the course of a solid-state reaction from reactant through the succeeding stages. Additionally, the Delta-Density Analysis was utilized to ascertain the electronic nature of molecular changes. Besides product composition changing with extent of conversion, the reaction quantum yield was found to change as one stage gave way to a succeeding one. 相似文献
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. 相似文献
Let μ be a measure on the complex sphere. Denote by μpq the projection of μ on H(p, q), the space of complex spherical harmonics. Assume that μpq = 0 if (p − 1)q ≠ 0, and ∥μ1q∥∞ → 0 as q → ∞. Then μ is absolutely continuous with respect to Lebesgue measure on the sphere. 相似文献
A series of in situ-prepared catalytic systems incorporating RuII 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. 相似文献