条件方程

In order to probe the absorb coefficients of earth medium by the direct wave, reflected wave and transmied wave amplititude which are picked up from the radar wave racords yielded by finite element method,the paper gives out the attenuated radar wave equations in time domain and the attenuated radar wave differential equations while the motion changes simple harmonic with time and electric parametets change slowly with space.

摘 要 为了用有限元方法生成雷波正演记录，从而拾取直达波、反射波、透射波振幅信息，以确定介质吸收系数，文章在时间域给出了雷达波含衰减项的波动方程，及在运动随时间简谐变化以及电性参数随空间缓变的条件含衰减项的雷达波遵循的简化微分方程。

This paper deals with the singular perturbation of the boundary value problem of a class of third order nonlinear differential equations.

研究一类三阶非线性微分方程边值问题的奇摄动，由于退化问题是一阶微分方程，将失去两个初值条件，所以摄动解在x=0的某一邻域内将出现非一致性。

The difficuty of the dissertation is the nonlinear of the equations or the boundary conditions . When proving the existence of the solution to the singular integral equation , we must estimate the norm of the operators , the process of the estimation is a complicated process .

本文的难点是方程的非线性或边界条件的非线性，在证明奇异积分方程的解的存在性时，要进行模的估计，此估计过程是一个复杂的计算过程。

Through studying the singular points of the plane differential systems, the sufficient conditions of the nonexistence of limit cycle for the system are obtained by means of comparing theorem, analyzing divergence and change of variable.

通过对微分系统的奇点进行研究，借助比较定理，将该方程与其对称的方程进行比较，并通过分析散度和变量代换的定性分析，得到了其极限环不存在的充分条件。

Based on the limitation and tightness of computational time, it is concluded that the neighborhood of the equation solution is solvable under the condition of open solvable set.

研究了用差分法求解自治的发展方程时稳定性和收敛性这两个基本概念之间的联系，利用计算时间的有限性和紧致性，在可解集为开集的条件下，得出方程解的邻近也可解的结论。

The specific forms of charge transportation equation in a simple pipe for the two flow states were derived. The treatment method for boundary condition of the equation was studied.

分别推导出了两种流态下简单管道内电荷输运方程的表达式，并对方程的边界条件处理进行了研究。

By the expansion of a function in terms of spherical harmonics, solutions in form of separation about the asymmetry disturbance were studied. At last, by the theory of stability of differential equations, under the no limitation or less than 1 to the symmetry stationary radius, the asymmetry stability of stable and unstable conditions were obtained.

然后利用球调和函数展开，研究了有关扰动的偏微分方程的变量分离形式的解，最后根据微分方程稳定性定理，在肿瘤静止半径没有限制或肿瘤静止半径小于1的情况下，得到了非对称扰动的稳定和不稳定的条件。

In this paper, by using the notable Mountain Pass Lemma of critical point theory, some sufficient conditions for the existence and multiplicity of periodic and subharmonic solutions to a class of second order nonlinear functional difference equations with Jacobi operators are obtained.

论文研究了一类具有Jacobi算子类型的二阶非线性泛函差分方程(1)的周期解和次调和解的存在性与多重性。首先将方程（1）的解的存在性问题转化为某个泛函临界点的存在性问题，然后验证此泛函满足著名的山路引理的条件，从而得到论文的主要结论。

Based on the surjection of maximal monotone operators, we prove that some semilinear heat equations with weak Lipschitz nonlinear terms are exactly controllable by L〓 0, T: H〓(Ω control; Based on the critical point theorem of coercive convex functionals, we prove that some parabolic equations with Lipschitz nonlinear terms are globally approximately controllable and finite-dimensional exactly controllable by controls acting on mobile supports, and finally, we extend the results to parabolic equations in R〓.

首先利用极大单调算子的满射原理证明了半线性热方程在较弱Lipschitz条件下可通过L〓0.T；H〓(Ω控制实现精确能控。然后通过构造强制凸泛函并利用其临界点理论证明了带Lipschitz非线性项的抛物型方程可通过作用在在移动支集上的控制来实现整体近似能控与有限维精确能控，最后将整体近似能控与有限维精确能控结论推广到无界区域R〓上。

In this paper,by analyzing mathematically starting from physical concept,the relation between intensity of secondary nonlinear polarization and optico-electric field strength is presented under the condition of kleinman symmetrization,and the equation of amplitude coupling is deducted.

安徽大学物理系；四川激光，，编辑部邮箱 1983年 02期二次非线性；总电场；非线性极化率；极化场；振幅；耦合方程；极化强度；从物理概念出发，通过数学解析，在Kleinman对称性条件下，给出二次非线性极化强度与光电场强的关系，并推导出振幅耦合方程。

By the time of its fall, most of the prisoners were writers who had written against the corruptions of the government.

到它被攻陷的时候，里面多数的犯人是写了反对政府贪污文章的作家。

The most obvious variation to ovum morphological character was that the color was changed from light green to sepiaceous in embryonic development, and all the ovums were almost hatched after 96h.

在胚胎发育过程中卵的形态特征最明显的变化是颜色从淡绿到深褐色，卵在发育96h后卵基本全部孵化。