条件方程

Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier–Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack subjected to internal impulsive pressure are given by dynamic weight function method.

首先采用静态内压下的应力强度因子作为参考解，得到了带径向边裂纹厚壁圆筒的权函数；然后用振型函数方法推导无裂纹厚壁圆筒在冲击内压下的动应力响应，分析中将相应的弹性动力学方程解分为满足非齐次边界条件的准静态解和满足齐次边界条件的动态解的叠加，利用傅立叶-贝塞尔级数展开，推导出了厚壁圆筒内动应力的响应历程和分布规律；最后由动应力权函数方法导出带径向边裂纹厚壁筒在冲击内压下的动态应力强度因子计算公式。

According the connection between the solution of linear fractional differential equation and nonlinear fractional differential equation, the expression of the solution of the nonlinear fractional differential equation is formed.

在一定的条件下，建立了非线性分数阶微分方程在边值条件下有解存在。

Finally, based on the fundamental solutions of Biots consolidation of transversely isotropic saturated multi-layered soils, the Fredholm integral equation of second kind for the interaction between transversely isotropic saturated multi-layered soils and rectangular piles is established, the relevant numerical analysis is also carried out.

最后，基于横观各向同性层状饱和地基Biot固结问题的基本解答，建立了横观各向同性层状饱和地基与方形单桩、群桩共同作用问题的第二类Fredholm积分方程，并进行了数值分析与计算；通过将矩形刚性基础基底划分成若干个大小相等的矩形网格，用矩形均布荷载表示网格的基底反力，并利用已获得的横观各向同性层状饱和地基Biot固结问题的基本解来求解每个矩形网格的柔度系数，然后根据刚性基础与层状饱和地基的接触条件和其本身的静力平衡条件，求解分析了横观各向同性层状饱和地基与刚性矩形板的共同作用问题。

Concretely, firstly with Timoshenko beams, the fundamental formulae of solutions of dynamical equations, boundary conditions and initial conditions have been transformed by Laplace transformation. Secondly, in the Laplace regions , we gain the analytical solutions of impact forces at the impact contact points, shear and maximum inverse stress of beams. Then, by using Durbin numerical inverse method, we gain the numerical solutions of Timoshenko beams under various restriction conditions. Moreover, the graphs about impact forces at the impact contact points, shear and maximum inverse stress of beams can be obtained too.

把Timoshenko梁力学模型动力学方程的基本解形式、边界条件以及初始条件进行Laplace变换，在Laplace区域得到了冲击接触处的冲击力、整个梁的最大弯曲应力和剪力的解析解，然后利用Durbin数值反演的方法得到了各种约束条件下的Timoshenko梁模型时间-空间的数值解，得到了冲击接触处的冲击力、梁各处的最大弯曲应力和剪力的曲线图。

The boundary singular kernel method and the modified pen alty method are utilized to treat the essential boundary conditions and incompressibility constraint, respectively. The stiffness equation for analysis of metal forming using RKPM is derived and its key algorithms are given.

分别采用边界奇异权法和修正的罚函数法处理本质边界条件和体积不可压缩条件，推导了金属塑性成形过程无网格RKPM法数值模拟的刚度方程，给出了关键算法。

To inequality constraint s, a check procedure and a penalty function procedure are proposed, and equality constraints are dealt with by a procedure of solving equations in which tear equations may be converged by an iterating way or a penalty function way.

在无约束非线性规划问题全局优化的模拟退火算法基础上，进行有约束问题求解的进一步探讨，对不等式约束条件提出了检验法和罚函数法的处理方法，对等式约束条件开发了罚函数法和解方程法的求解步骤，并进行了分析比较，从而形成了完整的求取非线性规划问题全局优化的模拟退火算法。

The relationship between the inverse number density of particle of the laser transition levels and the discharge condition such as the discharge current, the He pressure and the temperature of Cd-reservior has been achieved. The discharge condition for obtaining maximum laser output was theoretically achieved.

分析了441.6nm谱线的激发机理及各种粒子的相互作用过程，导出了441.6nm谱线跃迁能级激励的理论模型及其粒子数密度速率方程，得到了粒子反转数密度与放电电流、氦气压强和镉炉温度等放电条件的关系，从理论上，定量得出了获得最大输出功率时的放电条件。

In the paper, with the characteristics of the line integral road, free surface condition and continuity condition, we gave the additional equations to close the equation group and overcame the difficulty, and successfully calculated and analysed the nonlinear ship wavemaking by the method.

文中根据自由面线积分路径的特点，自由面边界条件以及连续性条件来建立补充方程，而成功地解决这一难题，从而为非线性船波分析提供了一个有力的工具，并利用此方法分析非线性兴波取得了成功。

In the program, because of adopting local coordinate system, the condition of friction and displacement were easy to be introduced, and the general-strong equation kept symmetrical.

在程序中，由于采用了局部坐标系，使得摩擦条件和位移边界条件的引入非常方便，并且总刚度方程还是对称的。

A three solutions theorem of nonlinear operator equation in Hilbert space was given by Sun Jing-xian in 1983,in this paper,the theorem was expanded to general Banach space by using gradient method ,and some conditions was weakened,such as the local Lipschitz condition s transformation to the bounded character of F and so on.

依据H ilbert空间中非线性算子方程的一个三解定理，本文运用最速下降法将这个定理推广到了一般的Banach空间，并且减弱了原定理的某些条件，如将局部Lipschitz条件减弱为F的有界性等

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新