特征方程

This paper, firstly, after a deep study of image mathematical models, sets up two kinds of image models namely Laplace partial differential equation model and biharmonic equation model and then obtains the eigenvectors of image by the methods of eigenfunction expansion and boundary recurrence.

本文首先较深入地研究了图象的数学描述，提出图象的Laplace偏微分方程和双调和方程两种模型，继而采用特征函数展开法和边界递推法分别求得图象的特征矢量。

And then the influence of two of the damage models, the Kachanov and the gradient dependent constitutive equations, on the well posed properties of the fundamental equations in continuum damage mechanics is studied according to th.

首先从非局部理论出发，推导了应变梯度损伤本构方程；然后利用一阶拟线性偏微分方程组的特征理论，在一维弹性损伤情况下分析了两种不同的本构模型，即 Kachanov损伤本构方程与应变梯度损伤本构方程，对连续介质损伤力学基本方程适定性的影响。

In the numericalstudy, three-dimensional elastodynamics equations and Morison equation are applied tosimulate the time histories of dynamic response of submarine pipelines suspended over flatbeds sucessfully. The three-dimensional interaction of pipeline and internal flow isnumerically simulated by applying the iterative computation to the fluid-structure interfacesand using the elastodynamic equation and the incompressible fluid N-S equation andcontinuity equation.

在数值研究方面，本文利用三维弹性动力学方程，结合莫里森方程，较好地模拟了规则波浪作用下近壁悬跨弹性海底管线动力响应过程，结合不可压缩流体N-S方程和连续方程，进行管线及其内部流体的三维流固耦合数值计算，基于数值计算结果探讨内流管线系统的动力特性和管内流体特征。

The optimum models were obtained by non-linear fitting to describe the kinetic processes of adsorption of Cd on four types of soils in Northeast, China. According to the results, exponential equation and exponential function equation were more appropriate to fit the kinetic process than other equations.

通过非线性拟合的方法获取了适宜描述Cd在东北地区土壤上吸附动力学特征的最优化模型，综合来看，指数方程和指数函数方程比较适宜于描4种土壤对Cd的吸附动力学特征。

After analyzing the characteristics of gas behavior, a general PVT gas equation of state is developed.

根据热力学普遍特征和推断性特征，对状态方程（式（4.16））提出了确定其常系数的方法，使式（4 16）发展成为通用型气体状态方程。

Combined with the new process and new products, we have developed their characteristic equations and models, especially for hollow; heteromorphism and composite fibers.

结合新工艺和新产品的开发，本文推导了高速纺丝、热管纺丝、热辊纺丝等工艺的特征单元方程及中空、异形、复合纺丝等新品种的特征单元方程，着重推导了圆形纤维、中空纤维、三叶异形纤维、皮芯复合纺丝的分层结构模型及分块模型，并对高速纺丝及中空纤维的不对称冷却结构进行了系统的数学模拟。

In Chapter 4,we consider the problem of totally characteristic type equation,whose indicial exponent takes positive integers.

在第四章中，我们对全特征型微分方程也讨论了一类不满足第二、三章中定理条件的问题，即对全特征型偏微分方程也考虑了Yamane在文[11]中考虑的问题。

First, the algrithm classify the measurement characteristics as point, line and surface which can be classified to conicoid and free surface. Then, this algorithm establishes the parametric equation according to various features. After that this paper brings forward the characteristic parameters utilising least square method with several characteristic points. Finally high precision probe radius compensation is carried out according to the features.

该算法首先把测量特征分为点、线、面3种基本特征（其中面特征又分为二次曲面和自由曲面），然后建立各种特征的参数方程，利用测量得到的少量特征点，采用最小二乘法拟合得到被测特征的参数，最后根据被测特征参数进行高精度半径补偿。

Neutral differential equations with variable sign coefficients are separatedinto neutral differential equations with positive and negative coefficients bytransformation.According to the characteristic of these equations,a real number setwith supremum is constructed,and sufficient conditions for oscillation of all solutionsto neutral equations with variable sign coefficients are obtained.

通过变换将具有变号系数的中立型微分方程分解为具有正负系数的中立型微分方程；分析具有正负系数中立型微分方程的特征，构造存在上确界的实数集；并对中立型微分方程的解作细致分析，得到了具有变号系数中立型微分方程所有解振动的充分条件。

The results showed that both of Michaelis-Menten equation and Dagneli equation primely simulated response of photosynthesis rate to light intensity, and their effect was consilient. But the parameters of maximum photosynthesis, initial quantum efficiency and dark respiration by Michaelis-Menten equation was very distinctly bigger than them by Dagneli equation.

结果表明，两种方程均能很好地描述大豆和玉米叶片光合速率对光强的响应特征，两种方程的模拟效果是一致的，但两种方程得到的参数存在极显著差异，用Michaelis-Menten方程模拟得到的表观初始量子效率、表观最大光合速率、表观暗呼吸速率极显著大于用Dagneli方程得到的参数。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失