精确解

In this paper, the reciprocal theorem is applied to research on the bending problem of rectangular plates with opposite simple supported and clamped edges under distributed bending moment and a concentrated bending moment acting at any of its points, the accurate solution of the problem are given.

应用功的互等定理研究了在分布弯矩与任一点集中弯矩共同作用下对边简支另一对边固定的矩形板的弯曲问题，给出了该问题的精确解。

In Chapter 2, we study exact solutions of the separated parts of Klein-Gordon field equation on some stationary and axisymmetry black hole backgrounds. We demonstrate that the radial and angular parts of a massive scalar field equation in the Kerr-Newman and Kerr-Sen black hole space-times satisfies the generalized spheroidal wave equation which is, in fact, a confluent Heun equation.

在第二章中我们研究了稳态轴对称黑洞背景几何中Klein-Gordon场方程分离变量部分的精确解，表明了Kerr-Newman黑洞及Kerr-Sen黑洞中有质量复标量场方程的径向部分和角向部分均满足广义椭球波方程，而后者实际上就是合流的Heun方程。

The structure of exact solution set of multi pantograph delay differential equation is studied and existence and uniqueness of an exact solution is proved.

研究了多比例延迟微分方程y=ay+by(q1t)+cy(q2t)的精确解的结构，探讨了初值问题解的唯一性和存在性。

It is verified that if max-min (or max-product) fuzzy relation equation is solvable, the FDA algorithm will converge to the maximum solution, and a conclusion for the perfect association of stored pairs is achieved.

证明了如果最大-最小模糊关系方程有精确解，则FDA算法必定收敛到它的最大解。

In spherical polar coordinates, DRSC potential have supersymmetry and shape invariance for θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrodinger equation with double ring-shaped Coulomb potential are presented. The normalized angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.

本文研究了双环形Coulomb势Schrdinger方程的束缚态精确解，所采用的方法是首先对双环形Coulomb势的Schrdinger方程在球坐标系中进行分离变量，得到相应的角向方程和径向方程；证明双环形Coulomb势在角向和径向具有超对称性和形不变性；根据超对称性和形不变性的性质，获得了角动量量子化条件和束缚态的能谱方程，并将归一化角向波函数用Jacobi多项式表示，将归一化径向波函数用Laguerre多项式函数表示。

Several important nonlinear equations of mathematical physics such as φ4 equation, Klein-Gordon equation, the approximate equations of sine-Gordon equation and sinhGordon equation, Landau-Ginzburg-Higgs equation, Duffing equation, nonlinear telegraph equation are the special cases of the nonlinear wave equation presented in this paper.

几个有重要应用的非线性数学物理方程，如矿方程，Klein-Gordon方程，Sine-Gordon方程，及Sinh-Gordon方程的近似，Landau-Ginzburg-Higgs方程，Duffing方程，非线性电报方程等都可作为该方程的特殊情形得到相应的显式精确解，这里方法也可推广到n+1维空间情形。

The properties of torsional vibration wave in a 200 MW of turbogenerator shaft system are calculated.

计算了一台200 MW机组转子轴系扭振波动特性的精确解，并与离散系统计算结果做了比较。

The motion of two charged quasiparticle s on an infinite Chain in a uniform electric field is presented.

本文研究了在均匀电场中位于一维长链上的两带电准粒子的运动，给出了一般情况下的精确解，并讨论了两准粒子运动的动态定域性和复合、分离等问题。

The three-dimensional exact solution methods for dynamic problems of a finitely long piezoelectric composite laminates are studied .

有限长压电层合板结构动态问题的三维精确解研究。

The one is Pagano method which has been proven effective to static problems, but it is very complicate for the three-dimension dynamic problems of finitely long piezoelectric laminated plates.

同时，指出Pagano方法求解动态问题所遇到的困难，为克服这些困难，提出了一种求解压电层合板动态问题三维精确解的幂级数展开方法。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。