特征微分方程

Part Two. The approximation theory of distributed parameter systems.

偏微分方程的特征函数理论是研究分布参数系统的一个有效方法，但分布参数系统的特征函数的求取十分困难。

Based on the study of characteristic equation,we obtain some new oscillationcriteria for higher order neutral differential equations.

本文利用特征方程，建立了高阶中立型泛函微分方程新的振动准则，推广了文[1][2]中的工作，改进了文[3]中的结果

By means of the eigenvalue theory of partial differential equation, the crosswind and vertical sub-Green functions corresponding to the boundary types are derived.

引用Green函数的概念，提出了公路机动车多源扩散方程的求解思路，利用微分方程的特征理论，求得了Green函数的横风和垂直向分量。

In this paper,by using the characteristic equation,some forced oscillation of certain delay hyperbolic differential equation s are obtained.

借助其特征方程，获得了一类时滞双曲型微分方程解的强迫振动的若干充分条

So we can analyse the stability of lattice structure as solid web beam without change its geometry dimension. The out-of-plane stability of bending beam, which is made up with 2 beams and loaded by non-directional force, is studied.

对两节梁组成的弯曲梁在非保向力作用下的平面外失稳问题进行了研究，通过建立每节梁临界状态下弯曲和扭转变形微分方程，根据杆件变形的边界条件以及杆件之间的变形协调关系，得出了一端固定一端悬臂的弯曲梁在非保向力作用下平面外失稳的特征方程。

The essence idea of restoration based on Total Variation is that translate the problem into minimum of energy functional with TV regularization, then the Partial Differential Equations are got from the principle of variation, finally after discretization the optimal resolution with the numerical methods is obtained.

基于整体变分的图像恢复概括的说就是把图像恢复问题形式化为带有整体变分正则化项的图像能量泛函极值问题，采用变分原理将其中的最小化问题转为所要求解的偏微分方程，即Euler-Lagrange方程，利用数字图像本身的离散特征使用适当的数值方法来求它的最优解，最后达到逼近原始图像的目的。

If the step of the linear system question is not very high, direct solving method is better; if coefficient matrix of the linear system question is not regular and large-sparse matrix , direct solving method does not settle the storage question.

而在求解线性方程组的许多实际问题中，尤其在偏微分方程的差分方法与有限元方法求解问题之中，方程具有重要的特征，一是多为大型稀疏矩阵；二是满足一些条件如对称正定、对角占优等，这使迭代法得到广泛的应用。

It introduces partial fractions of meromorphic functions, product developments of entire functions, Hadamard's theorem, Riemann Zeta functions, Poisson-Jensen's formula; elliptic functions, including simply periodic functions and doubly periodic functions; algebraic functions and algebroid functions, Riemann surface, Nevanlinna theory, including characteristic functions, the first and second fundamental theorems, growth orders, etc; complex differential equations and complex functional equations, etc.

具体为：亚纯函数的部分分式、整函数的无穷乘积展开、Hadamard定理、Riemann Zeta函数、Poisson-Jensen公式；椭圆函数，包括单周期函数、双周期函数；代数函数和代数体函数、Riemann曲面简介；Nevanlinna理论简介，包括特征函数、第一和第二基本定理、增长级等；复微分方程和复函数方程，等等。在教学内容上充分体现基础性、新颖性。

The distribution of gear's contact stress, root stress, and contact engagement line in the engagement situation of gear pairs, were obtained on the base of explicit integration method. 3. Adopting the method of system matrix, the torsional vibration differential equation of general shafting was gained. The simple harmonic forms of excitation torque under the normal combustion or piston flameout of in-line engine and v-type engine were analysed. The decoupled algorithm of free vibration and forced vibration and the solution to the vibration damper's energy of resistance and the off-resonance calculation were studied. The sensitivity formulations of the natural frequency and vibration mode to physical parameters of system were derived by solving the eigenvalue problem. These sensitivity formulations provided the theoretical base for the dynamic modification of structure.

运用系统矩阵法建立了轴系的扭振微分方程，并对直列和V型发动机在正常发火和气缸熄火工况下的激振力矩进行了详细的简谐分析；基于精确方法推导了自由振动和强迫振动的解耦算法，给出了能量法计算中的减振器阻尼功求解和非共振计算方法；并研究了曲轴系扭振非线性分析中的变惯量问题，得到了单缸转动惯量的精确求解公式以及变惯量和固有频率的关系式；最后，从特征方程和振型正交性出发，推导了固有频率和振型对轴系转动惯量和刚度等物理参数的灵敏度，为扭振系统的结构动力学修改提供了理论基础。

The research result cannot satisfy the need of engineering design.In this paper, according to practical liquid differential equation ,allowing for moving rule and characteristic of moving field of vertical vortex , simplifying N-S equation, I have studied the discipline of condition, velocity and pressure of vertical vortex and analyzed some theory solutions such as plain vortex solution and solution in axial direction.

本文从实际流体运动微分方程出发，结合立轴旋涡运动规律和流场特征，采用对称恒定性假设，简化N—S方程，研究了立轴旋涡的水流流态、速度与压力的分布规律，分析了若干理论解，如平面螺旋流解、轴向流解等。

In this paper, the requirement analysis, design and implementation of the system are introduced in detail.

此论文详细介绍了系统的需求分析，系统设计和具体实现。

In the context of economic globalization is increasingly deepening, China's economy can not be spared.

在经济全球化日益加深的背景下，中国经济不可能做到独善其身。