从Bragg方程的Ewald图建立倒易点阵概念

倒易点阵是化学、物理、地质学、矿物学、材料学等专业相关课程中重要的教学内容,也是通识化本科教学过程中的难点之一。目前,大多数本科教材仅给出了其中的教学内容点,各部分间缺乏逻辑关系,这给教师课堂教学以及学生自学带来了困难。从Bragg方程的Ewald图解法入手,建立倒易点阵概念,给出了构建时的2个关键问题,倒易基矢如何定义和倒易矢量结点指数如何确定,并用数理推导证明如果大小为1/d（hkl）的倒易矢量g垂直于对应正空间中一组晶面间距为d（hkl）、密勒指数为（hkl）的平行晶面,则它在倒易点阵中的结点指数为hkl,该倒易矢量可记为ghkl。从Ewald图解法构建倒易点阵概念的思路,将使倒易点阵更形象化、具体化及逻辑化,为师生理解和深化倒易点阵概念提供了一条新途径。     

电压反馈倒数示波计时电位滴定法

用电压反馈的(dE/dt)~(-1)-E示波图上去极剂峰的出现或消失指示滴定终点的方法称为电压反馈倒数示波计时电位滴定法。电压反馈的(dE/dt)~(-1)-E曲线使峰形更加尖锐,峰高大大增加,从而提高了分析测试的灵敏度,对所得曲线再进行一次微分和二次微分处理,则终点时去极剂峰形变化更加敏锐。     

On non-explosion for the solution of a stochastic differential equation

In the present work we give general sufficient conditions in terms of Lyapunov functions which ensure existence of a weak solution for a stochastic differential equation for which conditions of existence hold in every bounded region.     

衡量互反矩阵一致性的一种新指标

本文针对ＡＨＰ中利用几何平均值来估计各因素权向量的方法提出了与之匹配的一种新的衡量互反矩阵一致性的指标，并且制定了相应的衡量标准，同时将其与利用最大特征值所建立的指标入标准进行了比较与讨论。     

关于修正的功的互等定理的讨论

以线弹性直梁系统为例,对Betti-Maxwell功的互等定理与修正的功的互等定理进行了比较研究.研究发现处于真实状态的两个不同的直梁系统均可等效地转化为同一直梁受两组不同外力作用的系统,进而揭示了修正的功的互等定理中"两个不相同的线弹性体"即为位移和力的边界条件相互等效的同一个结构.所以,"修正的功的互等定理"实际上仍是Betti-Maxwell功的互等定理的另一种表现形式.     

一对超标准互反关系及应用

The method of non-standard analysis(NSA) is used to construct a pair of hyperstandard reciprocal formulas involving certain non-standard difference operators with realnumber orders.Our main result consists of some extensions of earlier results appearing previously [5].An essential meaning of the paper is to indicate the fact that only the basic idea of NSA is applicable to the construction of a unified pattern that may have certain applications to both the analysis and the number theory.     

Generalizing the Reciprocal Logarithm Numbers by Adapting the Partition Method for a Power Series Expansion

Recently, a novel method based on the coding of partitions was used to determine a power series expansion for the reciprocal of the logarithmic function, viz. z/ln (1+z). Here we explain how this method can be adapted to obtain power series expansions for other intractable functions. First, the method is adapted to evaluate the Bernoulli numbers and polynomials. As a result, new integral representations and properties are determined for the former. Then via another adaptation of the method we derive a power series expansion for the function z ^s /ln  ^s (1+z), whose polynomial coefficients A _k (s) are referred to as the generalized reciprocal logarithm numbers because they reduce to the reciprocal logarithm numbers when s=1. In addition to presenting a general formula for their evaluation, this paper presents various properties of the generalized reciprocal logarithm numbers including general formulas for specific values of s, a recursion relation and a finite sum identity. Other representations in terms of special polynomials are also derived for the A _k (s), which yield general formulas for the highest order coefficients. The paper concludes by deriving new results involving infinite series of the A _k (s) for the Riemann zeta and gamma functions and other mathematical quantities.     

Abel’s lemma on summation by parts and partial <Emphasis Type="Italic">q</Emphasis>-series transformations

The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q-series are established. This work was partially supported by National Natural Science Foundation for the Youth (Grant No. 10801026)