The twoscale asymptotic error analysis for piezoelectric problems in the quasi-periodic structure

Applications for piezoelectric efect have grown rapidly,and piezoelectric materials play important roles in countless areas of modern life.By means of twoscale method and coupled boundary layer,some new kinds of twoscale asymptotic expansions for solutions to the electrical potential and the displacement in quasi-periodic structure under coupled piezoelectric efect are derived,and the homogenization constants of piezoelectric materials are presented.The coupled twoscale relation between the electrical potential and the displacement is set up,and some improved asymptotic error estimates are analyzed.     

n次单位根在代数问题中的应用

主要论述n次单位根在一些组合数求和、多项式的整除、因式分解中的应用,说明了n次单位根法可拓宽解题思路,是一种方便、快捷的数学解题方法.     

Chemoselective and enantioselective transfer hydrogenation of β,β-disubstituted nitroalkenes catalyzed by a water-insoluble chiral diamine–rhodium complex in water

Asymmetric transfer hydrogenation of β,β-disubstituted nitroalkenes catalyzed by a chiral diamine–rhodium complex in combination with HCO₂Na–HCO₂H as a hydrogen source in water was successfully realized with high reactivity, excellent chemoselectivity and good enantioselectivity. The metal precursor and pH value of the aqueous solution have a large influence on the reactivity and chemoselectivity. The substituents on the benzene rings and the sulfonyl groups of TsDPEN have significant effects on the enantioselectivity. This catalytic asymmetric transformation is one of the most practical pathways to obtain optically active nitroalkanes.     

微波消解-火焰原子吸收光谱法测定三七中的微量元素

采用微波消解处理三七,用火焰原子吸收光谱法测定Mn、Zn、Cu、Fe4种微量元素的含量.三七中Mn、Zn、Cu、Fe含量分别为9.30、19.54、178.45、3.05μg· g-1.该方法加标回收率在98.1％-102.8％之间,方法简单、快捷、准确,可为三七的现代研究提供依据.     

Invariant (α, β)-metrics on homogeneous manifolds

In this paper we study invariant (α, β)-metrics on homogeneous spaces. We first give a method to construct invariant (α, β)-metrics on homogeneous spaces. Then we obtain some conditions for some special type of (α, β)-metrics to be of Berwald type and Douglas type. At last, we give a rigidity result concerning the Randers metrics and Matsumoto metrics of Berwald type on homogeneous spaces. Members of LPMC and supported by NSFC (no. 10671096) and NCET of China. Second author was corresponding author. Authors’ address: Huihui An and Shaoqiang Deng, School of Mathematical Sciences, Nankai University, Tianjin, 300071, People’s Republic of China     

GA-BP嵌套算法的理论及应用

分析了BP算法、遗传算法以及GA-BP-APARTING算法的特点,提出了GA-BP-NESTING算法.在人工神经网络的在线学习和离线学习方式下,分别对BP算法、GA算法、GA-BP-APARTING算法和GA-BP-NESTING算法进行了比较研究,研究发现:第一,网络初始权值的赋值对人工神经网络训练影响很大;第二,离线学习方式下GA-BP-NESTING算法效果最佳.     

内陷在C_(60)中的氢原子的性质

在短程球形势阱的模型下 ,运用线性变分法并采用B 样条作为展开基函数计算了内陷于C60 几何中心的氢原子能谱和波函数 ,并计算了势阱深度对能谱的影响 ,详细讨论了内陷氢原子表现出的一系列特殊性质 ,从而对低维半导体材料性能的研究提供了有效的数据 ;同时这一工作也表明 ,用线性变分法结合B 样条函数在处理这类问题时是非常有效的。