偏微商

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。

According to differentiable manifolds theory, the paper discusses tile Legendre transformation of the Pfaffian form, introdues the operator of the Legendre transformation, derives the relation between the Legendre transformation and the partial differentiation and proves three law s.

从微分流形理论出发，讨论了Pfaff形式的勒让德变换；引入了勒让德变换算子；给出了勒让德变换与偏微商的关系；证明了两个定理和一个引理。

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。

Named for Pierre-Simon Laplace, the equation states that the sum of the second partial derivatives (the Laplace operator, or Laplacian) of an unknown function is zero.

以法国数理学家拉普拉斯命名的这个方程式表述如下：一个未知函数的二级偏微商之和等于零。

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