上微分

In addition to calculus with linear algebra, I had two semesters of mathematical analysis, partial differential equations, abstract algebra was also a senior this semester in the measurement theory.

除了微积分跟线性代数，我还上了两个学期的数学分析，偏微分方程，抽象代数还有在大四这个学期上的测量理论。

To use symbolic and algebraic computation techniques for studying the computational properties of procedure schemes, some convergent procedure schemes are investigated in algebraically closed field and real closed field.

过程模式在代数闭域和实闭域上的应用：本文在代数闭域和实闭域上研究了收敛过程模式，设计了用于自动推理的过程模式，并且用其解决微分动力系统研究中的中心-焦点问题。

The basic idea is to set a continuous solution of the region with a finite number of discrete points instead of a grid consisting of, these discrete points called grid nodes the solution of a continuous area on a given function of continuous variables used in the definition of discrete grid variable function approximation the original equation and boundary conditions in the micro-business operators to approximate differential, integral with the points and to approximate, so the original differential equations and boundary conditions are replaced by algebraic equations near Side, that is, finite difference equations , solve this equation group can get the original problem in discrete points on the approximate solution.

基本思想是把连续的定解区域用有限个离散点构成的网格来代替，这些离散点称作网格的节点；把连续定解区域上的连续变量的函数用在网格上定义的离散变量函数来近似；把原方程和定解条件中的微商用差商来近似，积分用积分和来近似，于是原微分方程和定解条件就近似地代之以代数方程组，即有限差分方程组，解此方程组就可以得到原问题在离散点上的近似解。

The exact form of exterior boundary value problems for plane potential problem is established with variational principle.

使用变分法确立平面 Laplace外问题的确切形式；在此基础上，为了避免使用无限区域上的 Green公式，通过构造紧支集上的无穷可微函数，获得满足非齐次控制微分方程的特解的重要结果。

It takesthe weighted average of the L2 norm of the difference of the observation and thesolution of the system and the L2 norm of the difference of conormal derivativeat the different sides of the interface for every subdomain as cost functional andthe smooth coefficients of the subproblem and the value of solution of the originalproblem at interface as identification parameters;Using the property of continu-ous functional defined on compact set,the existence of the optimal solution of theidentification problem is proved;The necessary conditions of optimality charac-terized by the system equation,the adjoit equation and the variational inequalitysimultaneously are given by introducing the conception ofdifferential andadjoit variable;An algorithm is devised and its flow graph is given.

其次，针对分片光滑动力系统的特征，结合正演过程的区域分解算法，建立了分片光滑系统的分解区域参数辨识模型，该模型以子区域上解的实测值与计算值之差的L2范数和界面两侧的通量差的L2范数的加权平均作目标泛函，各子问题的光滑系数及界面上真解的值为待辨识参量；利用紧致集上连续泛函的性质，证明了子区域上参数辨识问题最优辨识参量的存在性；引入微分的概念，借助伴随变量，给出了由系统方程，伴随方程和变分不等式共同表征的最优性必要条件；根据此必要条件设计了算法，给出了算法的程序框图。

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

Based on this, to avoid using the Green′s formula on infinite domain, an infinitely differentiable function with compact subset is constructed and some important results to a especial solution of the inhomogeneous field equation are obtained.

在此基础上，为了避免使用无限区域上的 Green公式，通过构造紧支集上的无穷可微函数，获得满足非齐次控制微分方程的特解的重要结果。

Any function on an interval will be expanded as the sum of finite items of the scaling functions and wavelets. It plays an important role for numerical analysis of partial differential equations, signal processes, and other similar problems.

于是，任何有限区间上的函数皆可表示为该区间上的尺度函数和小波函数的有限和，即小波级数，这克服了用无穷区间上的小波进行有限信号处理时，在边界上误差较大的不足，同时将该小波用于偏微分方程具有同样重要的意义。

In the base of above research, establish movement model of hyperboloid clutch with rollers and find the relation between force of outer race and moment of inner race. I establish mechanics model of hyperboloid clutch with rollers with differential geometry.

在上述研究的基础上利用运动转化原理建立了内外环与滚柱之间的运动模型，并利用微分几何的相关知识通过对施加在外环上的主动轴向力的分解及合成，求的其在内环上所产生的力学反应，建立双曲面滚柱加载器力学模型。

It gives a decent example for the angular value distribution theory and value distribution theory on p-adic field, n-dimensional complex Euclidian space, and even on general manifold.

值分布论为复微分方程的研究提供了重要的方法，为多维复欧氏空间空间上，p-adic域上以及一般的复流形上的值分布理论提供了模板。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。