微商

Based on the second- and fourth-order compact difference formulas for second-order derivatives and the idea of weighted average, two classes of the alternating direction implicit method are proposed for solving two-dimensional wave equation. The methods are of accuracy O (T^2+h^4) and O (T^4+h^4) respectively. Stability conditions are obtained by Fourier analysis method.

基于二阶微商的四阶紧致差商逼近公式及加权平均思想，提出了数值求解二维波动方程的2种精度分别为O(т^2+h^4)和O(т^4+h^4)的交替方向隐式格式，以及与其相匹配的第一个时间层的同阶离散格式，并且通过Foulier方法分析了格式的稳定性。

Limit theorems, asymptotic methods, asymptotic efficiency and efficiency bounds for estimation, maximum likelihood estimation, Bayes methods, asymptotics via derivatives of functionals, sample-based estimates of variability:; robustness; estimation for dependent data, nonparametric estimation and testing.

高级统计推断理论：极限理论，渐进方法，渐进有效和估计的效率，加大似然估计，贝叶斯方法，泛函数的微商渐进性，基于样本的估计：(bootstrap 和 jackknife方法)；稳健性；独立数据的估计，非参数估计和经验。

Now we study the properties of four multi-layer potentials and their high deriva-tives of biharmonic equation in the plane when they approach the boundary of adomain.

我们研究了重调和方程四种多层位势及其高阶微商在边界附近的性质，得到了这些微商新的表达式，从而将重调和方程的自由边值问题归化为新的边界积分-微分方程组。

The paper expounded internal difference between 0/0 of the derivative and of algebra, and discussed in detail the dual nature of 0/0 about algebraic substance of derivative on the basis of the philosophical thought about the concept of the differential quotient of Marx and Engels, and thus answered how derivative itself is converted to differential quotient logically.Then the discussion was extended to the Concept of the partial derivative, and proved that the form of differential quotient converted f...

本文依据马克思、恩格斯关于微商概念的哲学思想，阐述了代数的0/0与导数的0/0的内在差异，并详细讨论了导数的代数实体0/0的双重性质，从而回答了导数本身是如何合平逻辑地转化为微商的问题；其次，把这一讨论推广到偏导数的概念中去，论证了偏导数转化为微商形式的合理性，以及偏微商表述的意义，文中还就微商所牵涉到的形式逻辑与辩证逻辑的问题做了具体分析。

The paper expounded internal difference between 0/0 of the derivative and of algebra, and discussed in detail the dual nature of 0/0 about algebraic substance of derivative on the basis of the philosophical thought about the concept of the differential quotient of Marx and Engels, and thus answered how derivative itself is converted to differential quotient logically.Then the discussion was extended to the Concept of the partial derivative, and proved that the form of differential quotient converted from pa...

本文依据马克思、恩格斯关于微商概念的哲学思想，阐述了代数的0/0与导数的0/0的内在差异，并详细讨论了导数的代数实体0/0的双重性质，从而回答了导数本身是如何合平逻辑地转化为微商的问题；其次，把这一讨论推广到偏导数的概念中去，论证了偏导数转化为微商形式的合理性，以及偏微商表述的意义，文中还就微商所牵涉到的形式逻辑与辩证逻辑的问题做了具体分析。

In the PFD, both the differentials and non-differential terms in the differential equation are discretized, and the coefficients of the power series are determined by means of eliminating the truncation error of the corresponding modified scheme, then the high accurate difference scheme is obtained.

摄动有限差分方法在微分方程的差分近似中，离散微商项的同时，也离散非微商项，把非微商项摄动展开成网格步长△x的幂级数，并通过提高差分格式相应修正微分方程误差阶的方法求出摄动幂级数系数，从而获得高精度差分格式。

In the path integral formalism, we represent the generating functional and Green functions of Φ〓 theory by taking account of that the partial and the functional derivatives commute. Also we discuss the effective action for noncommutative scalar fields, and show how the noncommutative phase factors appear in path integral formalism. We realize that the two approaches (path integral and canonical quantizations) are completely equivalent each other.

在用路径积分方法对非对易标量场进行研究时，我们利用偏微商和泛函微商的可交换性，给出了Φ〓场格林函数和格林函数生成泛函的具体表达形式，得出了非对易相因子在路径积分方法中的具体表现形式，并对连通格林函数和有效作用量等问题做了讨论。

A method for the determination of water soluble chloride content in iron ore by potentiometric titration was studied.

以2g/L硫酸钾为溶解试剂，硝酸银为滴定剂，电位滴定法测定铁矿石中的水溶氯，通过电极电位-浓度二次微商滴定曲线，计算二次微商等于零时对应的V为滴定终点，可省去绘制E-V曲线或ΔE/ΔV-V一次微商曲线作图带来的麻烦。

Based on the phase-space generating functional for a system with a singular higher-order Lagrangian,the quantal canonical Noether identities under the local and non-local transformation in phase space for such system have been derived.

基于高阶微商奇异拉氏量系统的相空间生成泛函，导出了定域和非定域变换下的量子正则Noether恒等式；对高阶微商规范不变系统，导出了位形空间中定域和非定域变换下的量子Noether恒等式。

The 2 g/L solution of potassium sulfate was employed for the dissolving of sample, and silver nitrate was used as titrant.

以2g/L 硫酸钾为溶解试剂，硝酸银为滴定剂，电位滴定法测定铁矿石中的水溶氯，通过电极电位-浓度二次微商滴定曲线，计算二次微商等于零时对应的V为滴定终点，可省去绘制E-V曲线或ΔE/ΔV-V一次微商曲线作图带来的麻烦。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐