条件方程

The difference schema of the initial boundary value problem was converted to the step-by-step form,which was similar to the difference schema of the initial value problem.It is concluded that the difference schema satisfying the Von Neumann condition is a stable schema,and that,under the consistency condition,such stable schema is convergent.Moreover,with error estimate expression for the difference approximation to the classical solution,the linearity condition is unnecessary.

引入反投影算子将发展方程初边值问题的差分格式转化为与初值问题差分格式类似的逐步推进的形式，从而得出：满足Von Neumann条件的差分格式是稳定的格式；在相容条件下，差分格式若稳定(或满足VonNeumann条件)则格式收敛，且对古典解的差分逼近有误差估计式，不再需要线性的条件。

The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.

全文共分四章：第一章简要介绍了泛函偏微分方程的振动的背景和意义、对其研究的简单历史和现状，给出了本文的主要研究对象；第二章讨论了一类时滞抛物方程组解的振动性质，获得了判断其所有解振动的一个易于验证的充要条件；指出了这类具有时滞偏差变元的抛物方程组解的振动性质和不具有时滞偏差变元的抛物方程组解的振动性质的差异；并举例对主要结果进行阐明；第三章讨论了一类中立型抛物方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明；第四章讨论了一类中立型双曲方程组解的振动性质，获得了在给定的条件下其所有解振动或全振动的若干充分条件；并举例对主要结果进行阐明。

For a given Sturm-Liouville equation with positive leading coefficient function, by use of the monotonicity results of its natural loops, limit of boundary conditions and eigenvalues in the space of self-adjoint boundary conditions, a proof of the equalities among eigenvalues for coupled boundary conditions and those for separated boundary conditions is made.

内蒙古工业大学理学院副教授 2。对于给定的首相系数函数为正的 Sturm-Liouville方程，利用在自伴边界条件空间上自然圈、边界条件的极限和特征值的单调性的几个结果，给出了在偶合边界条件与分离边界条件下的特征值间的一些等式的证明。

The osculations are conducted on the two-dimensional hydrofoil section,based on a single-fluid model of the cavitation:the liquid/vapor mixture is considered as a homogeneous fluid whose eompsition is regulated by mass tranfer equation.The RNG k-ε turbulence model with modified eddy viscosity coefficient is used for computing,and the coefficient is related to the vapor and liquid densities in cavitated regions for simulating the cavitating flow.

实验采用高速录像技术观察了云状空化随时间的结构变化，应用 LDV 测量了云状空化条件下翼型周围的速度分布；采用 N-S 方程和基于空泡动力学方程的空化模型计算了绕水翼云状空化流场，湍流模型采用了 RNG k-ε方程，为了改善空化流动的计算精度，引入了一种与空化区域水汽相密度相关的系数，对湍流涡黏性系数进行了修正。

In this paper, by means of finding the solutions of Maxwells equitions which have a tensor dielectric permittivity,the wave equitions were obtained in rotation dielectric under the condition of longitudinal direct current magnetic field.

本文求解张量介质电常数条件下的麦克斯韦方程，导出了纵向场作用下旋光材料的波动方程。由于电场与磁场是互相耦合不能单独存在，因而引入了孪生标量波的概念，并证明了该标量波满足亥姆霍兹方程。

Finally, the wave equation of the electromagnetic field of this kind damper isderived from the Maxwells equation. The magnetic flux density at the boundary isassumed to be harmonic, so the analytical result of the wave equation is solved. When therotor rotates, eddy currents flowing inside the conducting material field are caused. Thetangential force acting on the rotor because of the action between eddy currents andmagnetic field is produced. The tangential force causes a retardation torque, which leadsto the increase of power and heating effects.

最后，应用Ahrens的电磁轴承简化模型，从Maxwell方程出发推导了应用于本文所述的被动式电磁阻尼器的波动方程，并用傅立叶级数把矩形磁场展开的谐变磁场作为磁场的边界条件，通过求解波动方程得到磁场的解析解，从而计算了阻尼器对转子的电磁力和由涡流引起的切向力产生的阻尼器附加功耗。

One of the most important measures that are used to make TWT work stably and reliably is to suppress all kinds of self-oscillations, including BWO. On the basis of the coupled mode theory, considering the effects of attenuator/sever, taper/step phase velocity, voltage gradient of electron beam, etc.

本论文基于耦合模理论，全面地考虑了衰减器/切断、相速渐变/跳变和电子注的电位梯度等的影响，建立了抑制返波振荡的统一的自洽线性工作方程组，包括线路方程、运动方程和电流连续性方程，并给出了相应的边界条件。

The problems of the heat transfer equation of cloud drop growth were analyzed from chemical potential and principle of phase equilibrium of multi-component system. It was pointed out that Clapeyron equation was the result gained under the condition of rigid phase equilibrium. It only shows the linear relation between steam press and temperature at saturation state, and does not show that there is any thermodynamic process which can meet this equation.

基于多元体系化学势和相平衡原理，分析了云滴长大热传导方程存在的问题，指出克拉伯龙方程是严格相平衡条件下推导出的结果，仅表示饱和状态下蒸汽压与温度之间的线性关系，并不表示存在满足克拉伯龙方程的热力学过程。

It is then proved that every equation in the hierarchy possesses the Hamiltonian structure if L has a skew-symmetric factorization and the first equation in the hierarchy satisfies some simple condition (K〓=θf〓 and f〓 is a gradient function).

然后在L具有反对称分解L=θJ，及等谱发展方程族中第一个方程满足简单条件（K〓=θf〓，f〓一个梯度函数）的假设下，获得了整个方程族的Hamilton结构。

Nonlinear partial differential dynamic equations of bending vibration of a tilting stepped drive shaft with two supports were built under non-inertia movement coordinate system by theorem of the motion of mass center and Heaviside function. According to the condition of equal displacement in an adjoining plane of the shaft, an equivalent shaft and its equation were obtained. A motion equation of the equivalent shaft was obtained by method of Galerkin. An approximate steady-state solution of the main resonance was obtained by method of multiple scales. The influence factors, motion stability, amplitude jump of main resonance of a stepped drive shaft and so on were analyzed.

用质心运动定理、Heaviside函数建立了非惯性系下倾料两端支承阶梯传动轴的非线性弯曲振动偏微分动力学方程，并根据相邻轴段的衔接面处位移相等的条件，得到阶梯轴的当量轴及其动力学方程；用Galerkin法得到当量轴的弯曲运动方程，用多尺度法求得稳态下当量轴的主共振的一次近似定常解，分析了影响阶梯传动轴主共振的因素、运动稳定性、振幅突变性等。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。