The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs

In this article we consider partitioned Runge-Kutta (PRK) methods for Hamiltonian partial differential equations (PDEs) and present some sufficient conditions for multi-symplecticity of PRK methods of Hamiltonian PDEs.

     

醇体系中合成CuGaS2纳米晶及其形貌演变

以CuCl2·2H2O,自制的GaCl3和(NH2)2CS为原料,在乙二醇体系中合成了花状结构的CuGaS2纳米晶．产物分别用X射线粉末衍射仪、透射电子显微镜、场发射扫描电子显微镜、高分辩透射电子显微镜和X射线光电子能谱仪进行了表征．实验结果表明,220℃反应24 h得到均匀的花状纳米结构CuGaS2,它是由厚度80-100 nm的片晶组成．同时,通过反应时间的控制,可以清楚的看到由纳米颗粒到纳米球以及花状纳米结构的演变过程．另外,研究了反应温度、反应时间、溶剂等对产物和形貌的影响．此外,对花状结构纳米晶的生长机理进行了初步的探讨．室温荧光光谱表明,随粒径的降低,发光位发生了部分蓝移．     

AN ESTIMATE ON THE DISTRIBUTION AND MOMENTS OF THE LAST EXIT TIME OF AN ELLIPTIC DIFFUSION PROCESS

Let LB be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of LB is obtained, and the sufficient and necessary condition for Ex(LBk)<∞is proved.     

分离变量法与等腰直角三角形波导的边值问题

根据叠加原理，讨论等腰直角三角形波导边值问题的IE波解和TM波解，纠正有关文献中的错误解法，指出分离变量法的适用条件。     

A remark on the mild solutions of non-local evolution equations

We provide a counterexample to some recent publications concerning the existence of the mild solutions of the non-local evolution equations, and indicate that in the study of the non-local evolution equations, the operators from which the mild solutions may be derived are in general not compact, thus those fixed point theorems requiring the compactness of the operators are not applicable.     

Pd (II)‐catalyzed vinyl addition polymerization of novel functionalized norbornene bearing dimethyl carboxylate groups

Three novel functionalized polynorbornenes (PNB) with pendant dimethyl carboxylate group (carboxylates—acetate, propionate, and butyrate) are synthesized as a vinyl‐type with a palladium (II) catalyst in high yield. The effects of size of substitutents, molar ratio of monomer to catalyst, solvent polarity, reaction time, and temperature on the polymerization of exo‐norbornene dimethyl propionate were systematically investigated. The low molar ratio and temperature, as well as high polarity of solvent, and long reaction time, are favorable for the enhancement of the monomer conversion, especially, the solvent have an obvious effect on the catalyst activity. The resulting poly(cis‐norbornene‐exo‐2,3‐dimethyl carboxylates) (PNB‐dimethyl carboxylates) show good solubility in common organic solvent and high thermal stability up to 360 °C. The glass transition temperature was detected by DMA at 331, 324, and 318 °C for acetate, propionate, and butyrate, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3391–3399, 2007     

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.      

Structure for a graph with average genus

In [2], Chen et al. showed that the average genus for a graph of maximum degree at most 3 is at least 1/2 its maximum genus. In this paper, the structure for a graph of maximum degree at most 3 with average genus equal to 1/2 its maximum genus is described. Furthermore, LetH be a subgraph ofG and γ_avg(G) = γ_avg(H). It’s shown thatG can be obtained by a series operations of type I and II onH.     

ATP与Mg2+、Ca2+生成配合物反应的热力学研究

The formation constant (K) and thermodynamic parameters (ΔC.ΔH.ΔS) in reactions in which complexes of adenosine triphosphate with magnesium ion and calcium ion are formed have been obtained by a microcalorimetric method. All experimentes were made at 30 ℃, pH=8.0 and at ionic strength μ=0.2 mol L~(-1). Measured experimental values indicate that complex formation reactions are driven by the entropic factor.     

A functional modulus of continuity for Brownian motion

In this paper, we prove a sharpening of large deviation for increments of Brownian motion in (p,r)-capacity and Hölder norm case. As an application, we obtain a functional modulus of continuity for (p,r)-capacity in the stronger topology.