特征方程

The basic concept in these sections is replacing backward Euler's method by modified backward Eulers's method to approximate the characteristic differential equation and discretizing the convection-diffusion equation at the middle point of the approximate characteristic curve, which will make the convective term get up to second order accuracy.

这三节的基本离散方法是用改进的Euler公式代替向后Euler公式来近似特征微分方程，并且将近似特征线的中点作为离散节点，使得对流项的离散精度提高到二阶，对于扩散项，将其转移到待求时间层进行离散。

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。

In this paper perturbation of eigenvalue and eigenfunction for higher order ordinary differential equation in the case of boundary perturbation combined with operator perturbation we considered.

本文研究了在边界和算子摄动相结合的情况下高阶常微分方程特征值与特征函数的摄动，把摄动问题A_6，μ的特征值λ_ε，μ和特征函数y_6，μ按两参数ε、μ的次幂展开，并且证明这些展开式当ε、μ充分小时是收敛的。

The rule about water flow in unsaturated soil and the soil-water characteristic curve are described in this papsr, and it respectively regards moisture content and capillarity head as basic variable to deduce unsaturated seepage control equation.

本文阐述了非饱和土中的流动规律和土—水特征曲线的特征及其应用，分别以含水量和毛细水头为未知量推导了非饱和渗流的控制方程。

Based on the theories of rheology, Non-Newtonian Fluid Mechanics, petroleum chemistry, crystallography and pipeline technology etc. and sampling Huabei crudes, experimental indexes and programmes are drew out, integrating the oil properties and parameter analysis; in terms of the macro analysis of continuum mechanics, substantial experiments are conducted with HAAKE RS600 rotational rheometer and the rheological equation as well as the viscosity-temperature equation are further developed with tested rhrogramme and viscosity-temperature curve, respectively. Beased on the researches on thixotropic mechanism and thixotropy fluid property, hysteresis loop curve, structure failure and viscosity build-up curve as well as shear stress decrement curve for one type oil are first present in this paper. According to the theoretical researches and testing results, a novel thixotropy equationwith τ=τ_∞e~ pattern, which is of hi-accuracy, few parameter and simplicity, is developed.Considering the influence of various parameters on rheological behaviour, depressant adding condition is optimized and experimental evaluation on BEM-5P is conducted, which further unrip its mechanism on the Huabei crude. A corresponding viable pipe transportion programmel is also recommended.

本文基于原油流变学、非牛顿流体力学、石油化学、结晶学、原油管输工艺学等理论，以华北原油为研究对象，结合原油物性及实验影响因素分析，制定出实验研究的评价指标及实验方案；从连续介质力学宏观分析的角度，利用HAAKE RS600高端旋转流变仪开展了大量的室内实验，并运用微观研究方法，测定了油样的流变曲线和粘温曲线，建立了流变方程和粘温方程；通过对触变性机理和触变性流体特征的研究，首次对华北原油测定出滞回环曲线、结构破坏与恢复粘时曲线、剪切应力裂降过程曲线，并在理论研究和实验结果的基础之上，建立了能定量描述含蜡原油剪切应力裂降过程的新型三参数触变模式τ=τ_∞e~b/(t+c，该模型具有精度高、参数少、实验简便且适用性强的特点；通过对含蜡原油流变性的影响因素理论研究，开展了加剂条件优选及BEM-5P降凝剂室内评价实验，进一步揭示了降凝剂对华北原油作用机理，在此基础之上，提出了华北原油管输的可行性方案。

The results show that the maximum CLA content is 15.4 g CLA per 100 g isomerized rapeseed oil and the characteristic peaks of CLA in CLA standard as well as isomerized rapeseed oil are found at 234 nm at 25 ℃. A linear regression equation is obtained.

4g，利用紫外分光光度法测定的共轭亚油酸标准品和异构化菜油在25℃条件下的最大特征吸收峰波长为234nm，并建立了线性回归方程，因此，只要测定油样在234nm的吸光度再依此方程可算得油样中共轭亚油酸的浓度。

By field and indoor test, the paper measures soil physical property, soilmoisture constant and soil water movement parameter, provides the soil specificgravity , the soil apparent density, the soil fraction, the soil field moisturecapacity, the soil saturated moisture capacity, the soil percent moisture content ofcom germination and seedlings emergence, the corn wilting point, and alsoestablishes the equation of soil water retention curves, the equation of soil waterdispersion coefficient and the relationship between pressure and soil apparentdensity, and so those provides the parameter for numerical simulation.

通过田间和室内试验，测定了供试土壤的物理性质、土壤水分常数和土壤水分运动参数，得到了该土样的比重、容重、机械组成、田间持水率、饱和含水率、玉米种子发芽出苗土壤含水率、玉米凋萎系数，给出了土壤水分特征曲线方程、土壤水分扩散系数方程及土壤容重与土壤压紧力的关系，提供了数值模拟过程中所需的参数。

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。

Initially, assuming that the contact between cam and tappet is"dry contart", a dynamics model of Hertzin contact stiffness and impact damping is established. Next, with dynamic load on cam—tappet pair from the model, an analysis is made both to unsteady EHD oil film in cam—tappet pair under condition of full and partial lubrtication and to wear characteristics of cam profile. then, according to the fact that the lubrication in cam—tappet contact surface is EHD lubrication, taking the interaction between stiffness and damping of unsteady EHD oil film and rigidity of solid object contact into account, a dynamics equation of valve train relating to the dynamic effect of EHD oil film is built up and solved. Consequently, a further study is made on the dynamic characteristics of valve train under interaction of EHD oil film dynamic behavior and the problem of EHD lubrication in cam—tappet pair. Finally, the dynamic effect of full and partial EHD oil film is studied accordingly.

首先，通过对凸轮—挺杆接触为&干接触&的假设，建立了考虑赫兹&接触刚度&和冲击&阻尼&的配气机构动力学模型，用由此求得的凸轮—挺杆表面动载荷对凸轮—挺杆进行了全膜状态和部分膜状态非稳态弹流润滑分析，并研究了凸轮轮廓的磨损规律；然后，是在凸轮挺杆表面存在弹流动压油膜这一事实的基础上，相当于在动力学方程中考虑非稳态弹流油膜的&刚度&、&阻尼&和固体接触&刚度&的耦合作用，建立并求解了考虑弹流润滑行为动力学效应的配气机构的动力学方程，从而深入地研究了弹流润滑行为与动力学行为耦合作用下的配气机构动力学特征以及凸轮挺杆弹流润滑问题；作为前面工作的对应部分，考虑弹流油膜动力学效应的研究工作也同样分为全膜状态和部分膜状态进行。

Considerable progresses are made in terms of theoretical,experimental and numerical studies by using the shallow-water equation s.

滚波具有浅水长波的特征，因而利用一维浅水方程开展滚波问题的研究，取得了丰富的成果：如判定自由面稳定性的临界弗劳德数、演化方程的理论解及试验、数值研究等。

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