定义方程

The concept and definition of linear process with independent increments were presented. Then the regression model and analysis method for linear process with independent increments were established. Furthermore, the regression equation and confidence limit curves were given.

提出了线性独立增量随机过程的概念和定义，建立了线性独立增量过程回归模型及其分析方法，给出了回归方程和高置信度、高可靠度的置信上、下限曲线。

The computational methods of line element conic curve s tangent point decided by any line on projective plane is presented on the basis of this study.

从实际计算的角度出发，使用N矢量表示视平面上的点和直线，并由线素二次曲线的射影定义推导出线素二次曲线的N矢量方程；在此基础上，给出了射影平面上任意一条直线所确定的线素二次曲线切点的N矢量的计算方法。

Chapter 1 discusses multiple parameters simultaneous estimation of a two-dimensional distributed parameter system; First, the distributed parameter system is transformed by applying a Laplace transform; Then by defining the objective function combined with the principle of optimal control, the problem of parameter estimate is converted into the problem of optimal control.

第一章讨论了一类二维分布参数系统的多参数同步辨识问题。首先利用Laplace变换对原系统方程进行了转换；然后结合最优控制原理定义目标泛函，将参数辨识问题转化为最优控制问题。

Various forms of wave equations, definitions of wave number and frequency, derivations of phase speed and group velocity, and a quick discussion on dispersion relationships.

各种形式的波动方程，波数和频率的定义，相速度和群速度的引入，以及一个关於色散关系的小讨论。

The beginning of this article gives the definition of elliptic curve, ellipse standard equation, and the long axis of oval, short, with an area of the formula of a binary quadratic equation of the circumstances under which the judge said to provide the basis of an oval, as well as the conditions in this the long axis of the ellipse, short, with an area of what is the formula?

本文开始给出了椭圆曲线的定义，椭圆的标准方程，及椭圆的长轴，短轴，面积公式，对一个二元二次方程在什么情况下表示椭圆提供了判断依据，以及在此条件下的椭圆的长轴，短轴，面积公式是什么？

Based on definition of strain energy function,increment formula of stationary potential energy of finite displacement theory were derived in terms of Kirchhoff stress tensor and Green strain tensor.

基于有限位移理论应变能密度函数的定义，利用Kirchhoff 应力张量和Green应变张量，推出了非线性分析中增量形式的势能驻值公式，并证明了由势能增量驻值原理得到的增量平衡方程形式与由虚位移原理所得的结果完全一致。

This article mainly simulates gradually damage destruction process of rock, major in determinationg the definition of rock three-dimensional damage tensor, simplify to the damage tensor and obtain its engineering calculation method, and obtains the basic expression form of equivalent stress by equivalent stress assumption, symmetrization to the actual stress, thus obtains construction relation of the festival principle of three-dimensional damage rock mass, finally couples elasticity- plasticity with damage in the finite element equation, with reference to elasticity-plasticity gradually degenerated method thought, simulates rock damage to advance gradually the destruction process in finite element method, draws up elasticity - plasticity and damage coupling two-dimension finite element procedure with the C language in the VC contact surface, by simulating experiment destroyed process, acquires destruction image and the axial load distortion curve of model, agreement with the experimental result.

本文主要模拟岩石渐进损伤破坏过程，确定岩石三维损伤张量的定义，对损伤张量进行简化计算并得出其工程计算方法，采用等效应力假设得出有效应力的基本表达形式，对有效应力进行对称化，得出节理损伤岩体的三维本构关系，在有限元方程中实现弹塑性和损伤耦合；借鉴弹塑性渐进退化方法的思想，采用有限元的方法模拟岩石损伤渐进破坏过程，用C++语言在VC界面编制了弹塑性和损伤耦合的二维有限元程序，通过模拟已有的实验破坏过程，得出模型的破坏图像和轴向荷载变形曲线，与实验结果基本一致。

Finally, combining PDE with Differential Geometry, parametrically representing the surface, tensor based image processing techniques have been proposed, such as edge detection , morphological operation? implicitly representing the surface as the level-set of the higher dimensional function, the variational problems and partial differential equations that define maps onto the given generic surface have been discussed.

本文结合微分几何学，基于曲线坐标系下的微分算子将平面上的图像处理框架推广到曲面上，得到了参数化曲面上的图像处理框架，并给出了边缘检测和形态学运算的算例；在已知给定曲面的隐式表达时，探讨了定义在任意曲面上的偏微分方程，解决了任意曲面上数据场的扩散问题。

A thermal equilibrium equation is established by analyzing the production of temperature and the transmission of heat in the foil rolling.

通过分析箔材轧制过程中温度的产生和热量的交换情况，建立热平衡方程；由板形的定义和轧制前后体积不变原理建立板形值和热凸度的关系；在此基础上，确定板形值和冷却液流量控制的关系

Sell,we discuss theproblems of topological dynamics system of the equation form as x'=g+hby using Kurzweil-Henstock integrals.

借助于G.R.Sell定义的局部动力系统理论，利用Kurzweil-Henstock积分，讨论了形如〓型方程的拓扑动力系统问题。

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。