Elliptic equations with BMO coefficients in Reifenberg domains

The inhomogeneous Dirichlet problems concerning divergence form elliptic equations are studied. Optimal regularity requirements on the coefficients and domains for the W^1,p theory, 1 < p < ∞, are obtained. The principal coefficients are supposed to be in the John‐Nirenberg space with small BMO seminorms. The domain is a Reifenberg domain. These conditions for the W^1,p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains. In fact, these domains might have fractal dimensions. © 2004 Wiley Periodicals, Inc.     

Bounds to optimal burn‐in and optimal work size

Burn‐in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, we consider the problem of determining the optimal burn‐in time and optimal work size maximizing the long‐run average amount of work saved per time unit in the computer applications. Assuming that the underlying lifetime distribution of the computer has an initially decreasing or/and eventually increasing failure rate function, an upper bound for the optimal burn‐in time is derived for each fixed work size and a uniform (with respect to the burn‐in time) upper bound for the optimal work size is also obtained. Furthermore, it is shown that a non‐trivial lower bound for the optimal burn‐in time can be derived if the underlying lifetime distribution has a large initial failure rate. Copyright © 2005 John Wiley & Sons, Ltd.     

Enhanced ferromagnetic properties of diluted Fe doped ZnO with hydrogen treatment

The single-phase diluted magnetic Fe-ion (5%) doped ZnO powders were prepared by solid-state reaction method. The powders were annealed in Ar or Ar/H₂(5%) atmosphere at 1200 °C. The crystal structure, electric and magnetic properties for the Zn_0.95Fe_0.05O powders have been studied with X-ray diffraction (XRD) vibrating sample magnetometer, resistance and Hall measurement. All the peaks for the XRD pattern of samples belong to the hexagonal (P6₃mc) lattice of ZnO, and no indication of a secondary phase. The lattice parameters for the Zn_0.95Fe_0.05O with an annealing in Ar/H₂(5%) atmosphere were a₀=3.256 Å and c₀=5.206 Å at room temperature. The hysteresis curve for the Zn_0.95Fe_0.05O at room temperature was enhanced ferromagnetic behaviour with an annealing in Ar/H₂(5%) atmosphere. We give an explanation for enhanced ferromagnetic behaviour with H₂ treatment by electric properties.     

基于遗传算法构建巴耳末公式

基于遗传算法构建了巴耳末公式．通过建立合适的拟合数学模型，用计算机对数学模型进行优化，使之尽可能反映氢原子实际谱线分布，并求出经验常量和拟合公式，最后分析了所得结果．     

Mössbauer Studies and Magnetic Properties of Y3−x Ce x Fe5O12

It is shown that in-situ ^166mHo (I = 7) in a spherical single crystal of HoF₃ can be used as sensitive internal thermometer to thermally detect NMR (NMR-TDNO) from the 100% abundant stable ¹⁶⁵Ho (I = 7/2) nuclei. In addition, new ^166mHo NMRON results are reported. Both the ^166mHo NMRON and ¹⁶⁵Ho NMR-TDNO spectra show three distinct quadrupolar split sub-resonances, in zero applied field. The data is used to make estimates of the Ho magnetic moments and quadrupole parameters for the ^166mHo and ^166mHo sites.     

Restoration of catalytic activity by the preservation of ligand structure: Cu-catalysed asymmetric conjugate addition with 1,1-diborylmethane

Reported herein is a novel reaction engineering protocol to enhance the efficiency of a transition metal-catalysed process by strategically preventing ligand degradation. Based on spectroscopic investigations, a decomposition pathway of a chiral phosphoramidite ligand during a Cu-catalysed reaction was identified. The involvement of the destructive process could be minimized under the modified reaction conditions that control the amount of nucleophilic alkoxide base, which is the origin of ligand decomposition. Overall, the strategy has been successfully applied to a new class of asymmetric conjugate addition reactions with bis[(pinacolato)boryl]methane, in which α,β-unsaturated enones are utilised as substrates.

A novel Cu-catalysed asymmetric conjugate addition reaction with bis[(pinacolato)boryl]methane using α,β-unsaturated enones as substrates has been developed on the basis of strategic preservation of the supporting ligand.     

H2CCF自由基与HNCO反应机理的理论研究

采用密度泛函理论的B3LYP方法, 在6-311＋＋G(d,p)基组水平上研究了H₂CCF自由基与HNCO的微观反应机理, 优化了反应过程中的反应物、中间体、过渡态和产物, 为了获得更精确的能量信息, 还在QCISD(T)/6-311＋＋G(d,p)基组水平上计算了各物质的能量．振动分析结果和IRC分析结果证实了中间体和过渡态的真实性, 计算所得的成键临界点电荷密度的变化也确认了反应过程．对于H₂CCF自由基与HNCO反应, 我们找到了六条可行的反应通道, 结果分析表明通道H₂CCF＋HNCO→IM3→TS5→H₂CCFH＋NCO控制步骤活化能最低, 是该反应的主要通道, 在此反应过程中有稳定的氢键复合物IM3生成, 还表现出氢原子迁移的反应特征．