Solutions for a Mode Ⅲ Growing Crack in a Piezoelectric Plane Under Two Kinds of Electric Boundary Conditions ＊

The solutions for a mode Ⅲ crack growing along an arbitrary propagation path in a piezoelectric plane are studied under the impermeable surface condition and the electrical contact surface condition respectively. According to the two kinds of electric boundary conditions, the Hilbert and Riemann boundary value problems in a half-plane including opening smooth arc are obtained from the theoretical analysis. Moreover, the equipollence of the solution formed under these two electric boundaries is proved, and unified solutions for the stress and electric displacement distribution in the crack-tipfield of the piezoelectric plane are achieved.     

高聚物固体电解质聚氧化乙烯－溴化铜复阻抗谱及介电常数的静水压效应

采用分子量５００万的聚氧化乙烯和无水溴化铜，通过混溶蒸发法制备成高聚物固体电解质Ｐ（ＥＯ）ｎ－ＣｕＢｒ２薄膜，并在０．１～３００ＭＰａ范围不同的流体静水压下详细测量其复平面阻抗谱，分别得到在不同压力下离子电导率和介电常数与测量频率的关系．进一步解谱准确地求出Ｐ（ＥＯ）ｎ－ＣｕＢｒ２（ｎ＝１２、１６）薄膜离子电导率和介电常数的静水压效应，并结合Ｘ－光物相分析，根据离子迁移通道的物理图象和高聚物的极化机构进行了初步的讨论．添加２０％的增塑剂碳酸丙烯酯，较大改进了压力下的导电性．１２０～３００ＭＰａ的离子电导率提高一个数量级     

锌的平面三配位[Bu_4N][Zn(SC_6H_2Pr_3~i-2,4,6)_3]·Pr~iOH配合物的合成与晶体结构

在许多重要的金属蛋白中,都存在ⅡB金属与半胱氨酸残基配位的活性中心M(Cys-S)_n.锌、镉、汞与含硫配体的配位化学作为M(Cys-S)_n中心的化学基础,三配位的[M(SR)_3]被认为是金属蛋白中ⅡB金属的一种配位形式.而近年来,Koch报道了平面三配位的锌、镉、汞的硫酚配合物[(n-Pr)_4N][Zn(SC_6HMe_4-2,3,5,6)_3]和[PPh_4][Cd(SC_6H_2Pr_3~i-2,3,6)_3]及[(n-Pr)_4N][Hg(SC_6H_2Pr_3~i-2,4,6)_3]的晶体结构.他们在实验中由于晶体迅速失去溶剂而未能测定以2,4,6-三异丙基硫酚为配体的锌配合物的晶体结构.最近我们合成了这个配合物,并测定了其晶体结构.     

1,2-聚丁二烯介电松弛的复平面分析

本文对1,2-聚丁二烯的介电松弛进行了复平面分析.结果表明,在1,2-聚丁二烯的玻璃化转变过程中,ε″(ω)与ε＇(ω)的关系满足Havriliak-Negami方程.由复平面图求出了样品的静态和光频下的介电系数,平均松弛时间和松弛时间分布参数.利用所得数据讨论了1,2-聚丁二烯在玻璃化转变过程中的构象变化、松弛时间分布和平均偶极矩等问题.     

对两道平面向量最值题的探究

本文以2020年高考中的两道平面向量最值题为例,分析试题的解法,并对背后隐藏的本质进行思考、探究,总结出一般性规律.     

三种版本教材中“平面向量基本定理”的比较及教学启示

平面向量基本定理是平面向量的核心内容,是深入学习向量知识的基础,本文研究不同版本教材中的这一内容,通过定理形成过程的比较,领悟编者的编写意图,体悟情境设置在定理形成过程中的作用,通过定理表述方法以及位置次序的区别,理解教材编排的逻辑关系,以进一步指导教学.     

巧思维切入,妙视角拓展——一道向量题的探究

破解平面向量问题的两个主要基本思路是:函数法与基底法,借助自身同时兼备“形”与“数”的双重身份,可以进行多层面、多角度的问题创设,融入其他相关的数学知识,吻合高考在知识交汇点处命题的指导精神.结合一道模拟题,从两个基本思路视角切入,多思维解决,多方向拓展,多规律总结,引领并指导数学教学与解题研究.     

共振光散射成像检测5,10,15,20-四(对三甲基氨基苯)卟吩诱导的DNA超螺旋聚集体

A resonance light scattering （RLS） imaging method was proposed based on imaging and measuring the RLS features of single suprahelical species of DNA, and its appfication to DNA assay was also investigated. In acidic medium, porphine-5,10,15,20-tetrakis（p-phenyltlimethylaminium） （PTPTMA）, could stack along the molecular surface of DNA with the mode of long-range assembly to induce the formation of suprahelical species of DNA, resulting in strong RLS signals in the range of 450-510 nm. Under the excitation of 488 nm fight beam of argon ion laser source, single suprahelical species could be observed with the aid of a common microscope due to the strong scattered fight emitted by the suprahelical species. By capturing the RLS images of the single suprahelical species with a cooled charge coupled device （CCD） camera, and analyzing the RLS data, herein an RLS imaging method of DNA was proposed based on the linear relationship between the counts of suprahelical species in the detection focus plane and the concentration of DNA in nanograms. When 1.8 μmol/L PTPTMA was employed, both calf thymus DNA （ct DNA） and fish sperm DNA （fs DNA） in the range of 25-1100 ng/mL could be detected with the limits of detection lower than 25 ng/mL （3a）. Four synthetic samples were detected satisfactorily with relative standard deviations less than 5.1%.