定义方程

The introduction of displacement operator, derivation operator, integral operator and the operator, such as differential calculus operator and the definition of the form of computing, will be applied to similar derivation formula gives Newton a Kete Si formula and Bernstein theorem Law said the operator, and form is derived; linear differential equations is the operator solution.

有没有高手可以帮我翻译下这段话啊？？？引入位移算子、求导算子、积分算子和差分算子等微积分算子的定义及其形式运算，将其应用于近似求导公式；给出牛顿一柯特斯公式和伯恩斯坦定理的算子法表示，并进行形式推导；给出线性常微分方程的算子解法。

By making use of eigenvalue problem of homogenerous equation, the finite Hankel transform is defind.

由相应的齐次方程的特征值问题，定义了有限Hankel变换。

So, the second section provides the definition of the equation of state of asymmetric nuclear matter.

在第二部分我们给出了非对称核物质状态方程定义。

Stochastic control system ; limited control ; exact controllability ; backward stochastic differential equation

本文组织如下，第二节引入主要定义，介绍倒向随机微分方程及彭有关随机精确能控性

An Extension on Differential Mean Value Theorem of Cauchy ;2. Infinitesimal in Cauchy ′s Cours d′ Analyse;3. This paper studies and analyzes the reasons and the background of Cauchy defined the residue concept,in which we have used the method of historic analysis and literature review.

采用历史分析和文献考证的方法，探讨和分析了柯西定义留数概念的原因及背景指明柯西从一些数学家的相关工作出发，在对C-R方程进行了讨论和分析之后，产生了他关于复积分问题的讨论。

While there has no control, the behavior of the system is discussed in Chapter 3. No defines in the point (0,0) of the system brings much difficulties in the research on the kinetic nature near (0, 0). By applying the series theories and methods in the literature on the singular point of nonlinear equations, we solve this problem satisfactorily and give the all possibility of the orbits of the system converging (0,0) as t→+∞ in the First Quadrant.

因为系统在(0，0)点处没有定义，这给研究其在(0，0)附近的动力学性质带来了困难，我们应用文献中关于研究非线性方程奇点的系列理论和方法，圆满解决了这一问题，给出了第一象限当t→4+∞时，在全参数状态下系统的轨线趋于(0，0)点的所有可能情况。

This paper gives a mathematical definition to that two open planar curves have the same shape based on curvature representation, therefore, a new kind of shape distance is proposed. It is concluded that the problem of computing the shape distance between two open planar curves can be changed to the problem of a functional extremum, and the differential equation is given, which can be used to figure out the shape distance.

本文为基于曲率表示的两条平面开曲线的等形下了严格的数学定义，从而找到了一种新的形状距离度量，并且证明了这种形状距离的计算问题可以转化为一个泛函的极值问题，同时给出了求解形状距离的微分方程。

By rolling out mathematical expression of G bubble physical process , space time structures of both information and information unit are fully exposed , therefore we have gotten strict definitions of these two physical quantities .

对G泡物理过程方程的数学展开使得信息和信息单位的时空形式完全暴露，进而得到了可以实证的关于信息和信息单位的物理学定义。

Then time-dependent invariant is introduced and a kind of method to solve the Schrodinger equation explicitly called Gauge transformation method.

稍后引入含时不变量的定义，以及精确求解薛定谔方程的含时规范变换方法，再次讨论了Aharonov-Bohm效应，Berry相位和绝热近似。

With the knowledge of linear algebra, general formula for arbitrary order Taylor finite difference has been derived. In this paper, the analysis of spectral property and computational error of arbitrary order TFD is presented in detail. Then it is applied into the numerical solution of Maxwell's equations. Stability condition and numerical dispersion relation are derived.

本文借助于采样定理，详细分析了不同阶Taylor中心差分格式的谱特性以及计算误差，并将任意阶Taylor中心差分格式用于数值求解麦克斯韦方程中，严格导出了稳定性条件和数值色散关系的表达式，引入了新的误差定义来衡量算法的好坏。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。