Polynuclear manganese grids and clusters—A magnetic perspective

High nuclearity paramagnetic, spin-coupled transition metal clusters and grids are fascinating chemists and physicists partly because of their structural beauty, and the challenge of creating them, but also because of their novel physical properties. Magnetic interactions between the spin centers are a primary focus. This review will examine a selection of Mn(II) polynuclear grids and clusters, with nuclearities in the range Mn₄ to Mn₉. Theoretical treatments of the magnetic properties are discussed, and approaches to solving the exchange problem for ‘large’ spin systems related to computational difficulties. A freely available software package (MAGMUN4.1) is presented as a means of dealing simply with spin-coupled clusters in general, and symmetry reduction methods are discussed briefly as a means of dealing with ‘large’ spin systems.     

分子手性的温度效应：D-丙氨酸的变温X衍射和中子衍射研究

利用X衍射（300, 270, 250 K）和中子衍射（300, 260, 250, 240 K）研究D-氨酸单晶在静态的和动力学的变温过程中的结构特征以及考证Salam预言的由D到L构型转变的可能性. 实验发现丙氨酸晶体的空间群P212121对称性没有改变. 实验结果否定了构型相变的可能，但是发现在~250 K有一个微小的、连续的对称性破缺发生. 晶体分子振动产生的环电流模型可以用来解释D-和L-丙氨酸单晶直流磁化率和天然旋光角相反的现象， 与之相关的中子衍射数据进一步揭示了变温过程中αC－H(2), N－H(1), N－H(4), N－H(6) 键长的不同变化. 中子衍射还显示了质子移动所导致的动力学无序，来源于分子内氨基和羧基形成的氢键和分子间αC－H和氨基形成的氢键，从而产生的晶格扭曲和NH³⁺的扭转. 实验结果表明Salam预言相变不是传统意义的结构相变，而是由于温度效应导致了在相变点附近分子的宇称破缺能差（PVED）增大，然后通过氨基酸分子的隧道效应扩大了宇称破缺能差的影响，这一研究为生命现象中快速的均一手性形成提供了非线性机理的合理解释.     

The European Eco-Management and Audit Scheme Accreditation – an overview

 Environmental quality is still deteriorating in the EU and worldwide despite all the Directives and Regulations in this field over the past 20 years. The European Community has devised a new approach to this problem with the introduction of the Eco-Management and Audit Scheme Regulation. This Regulation provides industry with an opportunity to demonstrate that it can achieve continuous improvement in its environmental performance through a voluntary scheme which is not based on the traditional command and control mechanisms of Directives. This paper gives an overview of the steps involved in implementing the European Eco-Management and Audit Scheme and the role of accreditation in supporting the scheme.     

A High-Order Finite Difference Scheme for 3D Unsteady Convection Diffusion Reaction Equations北大核心CSCD

针对三维非稳态对流扩散反应方程,构造了一种高精度紧致有限差分格式,对空间的离散采用四阶紧致差分方法,对时间的离散采用Taylor级数展开和余项修正技术,所提格式在时间上的精度为二阶、在空间上的精度为四阶。利用Fourier稳定性分析法证明了该格式是无条件稳定的。最后给出数值算例验证了理论结果。     

带五次项的非线性Schrödinger方程的守恒差分格式

本文研究带有五次项的非线性Schrödinger方程初边值问题的有限差分法,其中方程中二阶偏导数项的系数、五次项的系数及初值满足下面的条件（1.6）.针对此问题,我们研究了一个守恒差分格式,在条件（1.6）下,差分解的$L^{\infty}$模先验估计被得到.在此基础上,我们得到了差分解最优$L^2$模的误差估计.     

求解二维Fisher-KPP方程的一类保正保界差分格式及其Richardson外推法

本文研究求解二维Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP)方程的一类保正保界差分格式.运用能量分析法证明了当网格比满足$R_{x}+R_{y}+[b\tau (p-1)]/2\leq\frac{1}{2}$时差分解具有一系列数学性质,包括保正性、保界性和单调性,且在无穷范数意义下有$O (\tau+h_{x}^{2}+h_{y}^{2})$的收敛阶.然后通过发展Richardson外推法得到收敛阶为$O (\tau^{2}+h_{x}^{4}+h_{y}^{4})$的外推解.最后数值实验表明数值结果与理论结果相吻合.值得提及的是在运用本文构造的Richardson外推法时对时空网格比没有增加更严格的条件.     

An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems

A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives, the coefficients, and source terms all can have finite jumps across one or several arbitrary smooth interfaces. The method is based on the 2D finite element-finite difference (FE-FD) method but with substantial differences in method derivation, implementation, and convergence analysis. One of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions. A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface; and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts through. We aim to get a sharp interface method that can have second order accuracy in the point-wise norm. We show the convergence analysis by splitting errors into several parts. Nontrivial numerical examples are presented to confirm the convergence analysis.     

性别差异对研发投资决策影响的实验研究

基于Z-Tree实验平台利用研发投资自然博弈实验研究发现风险规避导致女性的研发投入强度低于男性,但女性在研发投资过程中愿意投入的研发努力程度高于男性。随着时间推移,男性的研发努力程度明显下降,但女性的研发努力程度反而上升。男性和女性在决策中均表现出心理账户效应,女性更加愿意通过努力来提高业绩。男性在投资中更多体现期权思想,而女性更多表现出长期倾向下的持续努力。文章在揭示性别因素影响研发投资机理基础上,为董事会性别多样性、分级董事会以及递延薪酬等治理机制发挥作用机理提供了新解释。研究结论可以为企业职位的性别配置、分级董事会以及激励契约设计提供借鉴。关键词:性别差异;研发投资;实验研究;心理账户;风险规避;长期倾向     

On Two-point Boundary Value Problems for Second-order Difference Equation

In this paper, we aim to investigate the difference equation \begin{align*} \Delta^{2}y(t-1)+|y(t)|=0, \ \ \ \ \ t\in[1,T]_{\mathbb{Z}} \end{align*} with different boundary conditions $y(0)=0$ or $\Delta y(0)=0$ and $y(T+1)=B$ or $\Delta y(T)=B$,\ where\ $T\geq 1$ is an integer and $B\in\mathbb{R}$. We will show that how the values of $T$ and $B$ influence the existence and uniqueness of the solutions to the about problem. In details, for the different problems, the $TB$-plane explicitly divided into different parts according to the number of the solutions to the above problems. These parts of $TB$-plane for the value of $T$ and $B$ guarantee the uniqueness, the existence and the nonexistence of solutions respectively.     

Certain bilateral generating relations for generalized hypergeometric functions

Recently, we introduced a class of generalized hypergeometric functionsI n:(b _q)/α:(a _p) (x, w) by using a difference operator Δ _x,w , where . In this paper an attempt has been made to obtain some bilateral generating relations associated withI _n ^ga (x, w). Each result is followed by its applications to the classical orthogonal polynomials.