On the Strong Law of Large Numbers and the Law of the Logarithm for Weighted Sums of Independent Random Variables with Multidimensional Indices

Let (X, X ; ^d} be a field of independent identically distributed real random variables, 0 < p < 2, and {a _, ; ( , ) ^d × ^d, ≤ } a triangular array of real numbers, where ^d is the d-dimensional lattice. Under the minimal condition that sup _, |a _, | < ∞, we show that | |^{− 1/p} ∑ _≤ a _, X → 0 a.s. as | | → ∞ if and only if E(|X|^p(L|X|)^{d − 1}) < ∞ provided d ≥ 2. In the above, if 1 ≤ p < 2, the random variables are needed to be centered at the mean. By establishing a certain law of the logarithm, we show that the Law of the Iterated Logarithm fails for the weighted sums ∑ _≤ a _, X under the conditions that EX = 0, EX² < ∞, and E(X²(L|X|)^{d − 1}/L₂|X|) < ∞ for almost all bounded families {a _, ; ( , ) ^d × ^d, ≤ of numbers.     

Existence of weak solution and semiclassical limit for quantum drift-diffusion model

The existence and semiclassical limit of the solution to one-dimensional transient quantum drift-diffusion model in semiconductor simulation are discussed. Besides the proof of existence of the weak solution, it is also obtained that the semiclassical limit of this solution solves the classical drift-diffusion model. The key estimates rest on the entropy inequalities derived from separation of quantum quasi-Fermi level.     

Monte Carlo simulations on magnetic behavior of a spin-chain system in triangular lattice doped with antiferromagnetic bonds

A three-dimensional Ising-like model doped with anti-ferromagnetic (AFM) bonds is proposed to investigate the magnetic properties of a doped triangular spin-chain system by using a Monte-Carlo simulation. The simulated results indicate that a steplike magnetization behavior is very sensitive to the concentration of AFM bonds. A low concentration of AFM bonds can suppress the stepwise behavior considerably, in accordance with doping experiments on Ca₃Co₂O₆. The analysis of spin snapshots demonstrates that the AFM bond doping not only breaks the ferromagnetic ordered linear spin chains along the hexagonal c-axis but also has a great influence upon the spin configuration in the ab-plane.      

具有突变结构开放腔的矩阵分析

利用模式展开与场匹配原理，建立了突变波导的散射矩阵(S参数矩阵)，在此基础上分析研究了具有突变结构的波导开放式谐振腔，并由矩阵级联建立了开放腔总的S参数矩阵.通过Matlab编制计算程序对具有多级突变结构的开放式输出腔进行了数值计算和分析，并通过与实验数据和软件模拟的结果比较对该方法得到的数据结果进行了验证. 关键词： 回旋管 开放式谐振腔 突变结构 S参数矩阵     

First Total Synthesis of 12-Hydroxy-13-methylpodocarpa-9, 11, 13-trien-3-one

12-Hydroxy-13-methylpodocarpa-9, 11, 13-trien-3-one 9 was isolated from the twigs ofCroton salutaris1. Many diterpenes exhibit significant bioactivities, such as antibac-terial and antitumour and 9 has a rare structure. In order to study the relationshipb…     

二元合金微观偏析的相场法数值模拟

使用耦合溶质场的相场模拟研究了Ni-Cu二元合金枝晶生长过程中固相溶质扩散系数D_s 对枝晶形貌和微观偏析等的影响.计算结果表明，随着D_s的减少，固液界 面前沿溶质扩散层越薄，枝晶生长越有利，枝晶尖端生长的速度越大，侧向分支越发达；D< sub>s越小，固相中溶质成分的波动越强烈，随着D_s的增大，固相中溶质 成分的波动相应减小；溶质微观偏析程度随D_s的增大而减小. 关键词： 相场方法 微观偏析 固相扩散系数 数值模拟     

An Improved Extra-Gradient Method for Minimizing a Sum of p-norms—A Variational Inequality Approach

This paper presents a variational inequality (VI) approach to the problem of minimizing a sum of p-norms. First the original problem is reformulated as an equivalent linear VI. Then an improved extra-gradient method is presented to solve the linear VI. Applications to the problem of p-norm Steiner Minimum Trees (SMT) shows that the proposed method is effective. Comparison with the general extra-gradient method is also provided to show the improvements of the new method.     

A high-resolution MAS NMR study on the potential catalysts Mo/HBeta for olefin metathesis: The interaction of Mo species with HBeta zeolite

The interfacial interaction of Mo species with the HBeta zeolite was studied by multinuclear MAS NMR, XRD and N₂ adsorption. As proved by the quantitative ²⁷Al MAS NMR, this interaction is so strong as to dealuminate the framework of HBeta, and leads to a new peak appearing at −14 ppm, which indicates the formation of crystalline Al₂(MoO₄)₃. This can also be detected by XRD measurements when the Mo loading is as high as 9.0 wt.%. The corresponding quantitative ²⁹Si and ¹H MAS NMR spectra show that the amount of silanols and Brønsted acidic sites decrease obviously with increasing Mo loading. This also reveals an interaction between Mo species and HBeta support through an oxygen bridge resulting from condensation with the hydroxyls on the support. At higher Mo loadings, the interaction is so strong that it results in an extraction of aluminum from the zeolite framework, and subsequently appearance of Al₂(MoO₄)₃ and loss of Brønsted acidic sites. These can be correlated to the low catalytic activity of Mo/HBeta in metathesis of ethylene and 2-butylene to propylene.     

Ethylene–propylene copolymerization with bis(β‐enaminoketonato) titanium complexes activated with modified methylaluminoxane

Ethylene–propylene copolymerization, using [(Ph)NC(R₂)CHC(R₁)O]₂TiCl₂ (R₁ = CF₃, Ph, or t‐Bu; R₂ = CH₃ or CF₃) titanium complexes activated with modified methylaluminoxane as a cocatalyst, was investigated. High‐molecular‐weight ethylene–propylene copolymers with relatively narrow molecular weight distributions and a broad range of chemical compositions were obtained. Substituents R₁ and R₂ influenced the copolymerization behavior, including the copolymerization activity, methylene sequence distribution, molecular weight, and polydispersity. With small steric hindrance at R₁ and R₂, one complex (R₁ = CF₃; R₂ = CH₃) displayed high catalytic activity and produced copolymers with high propylene incorporation but low molecular weight. The microstructures of the copolymers were analyzed with ¹³C NMR to determine the methylene sequence distribution and number‐average sequence lengths of uninterrupted methylene carbons. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5846–5854, 2006