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The potential functions of incident and scattered waves were expanded into Fourier-Bessel series, and the coefficients of scattering waves field were determined by imposing continuity conditions of stress and displacement at the soil-pile interfaces with the help of a set of cylindrical coordinate systems and in accordance with the Graff's addition theorem.

将倾斜入射波和散射坡的势函数展开成Fourier-Bessel函数的无穷级数的形式，利用一组圆柱坐标系统和Graff加法转换定理，通过施加桩土界面处的应力和位移连续的边界条件，求解出散射波势函数的待定系数，进而得到饱和土体中任意点的位移和应力。

As for mixed problem with integral boundary conditions for a certain nonlinear pseudo-parabolic partial equation, the existence and uniqueness of a strong solution to the corresponding linear problem is established and so the nonlinear problem can be solved by using addition theorem.

对于一类非线性伪抛物型方程的带积分边值条件的混合问题，本文通过相应的线性方程利用迭加原理来解决。

In order to expand half space Green's functions with addition theorem, a high order approximation method is proposed for evaluation of reflection term of half-space Green's functions with far interactions.

采用高阶拟合方法将远区相互作用单元的半空间空域格林函数用级数表示，对高阶拟合项作加法定理展开，进而应用多层快速多极子算法。

Using the exterior expression for the Graf′s addition theorem, the closed form solution for scattering of plane SH waves by circular inclusion in half-space is given in the paper. The effect of the inclusion on the surface ground motion is ellustrated and the effect region of the scattering field from the inclusion is analyzed.

文中利用Graf加法公式的内域型表达给出了半空间内含圆形夹塞区出平面散射的封闭级数解答，讨论了夹塞区散射场对附近地表运动的作用，并特别分析了这一作用在地面上的影响范围。

Considering "addition theorem of probabilities", the above idea can be expressed as follows: Assum that a beam passes through a partition with two slit and arrives a screen. The probability of the event that an indivedual particle falls on somewhere of the screen under the condition that two slit open simultaneously, is equal to the sum of two probabilities of the same event under that two slit open in turn.

考虑到"概率的加法定理"，这种看法可表成："当一个拉子束通过一个带有两条缝的隔板到达一个屏上时，在两条缝同时打开的条件下单个粒子落在屏土某处的概率，等于在两条缝轮流打开的条件下该拉子落在该处的两个概率之和。"

From the theory, the algorithm for determination of the degree of implicit polynomials is followed: detecting the stationary points in the object boundary based on its features, and then calculating the minimum degree according to the formula derived from the theorem. In addition, the theory can be extended to three-dimensional object.

该方法首先由给定物体边界的轮廓检测出其驻点数，然后根据驻点数得到拟合隐含多项式曲线方程次数的下界，进而推广到三维物体的隐含多项式曲面拟合次数的确定。

The main idea behind these methods is to take advantage of the known state variables and the theorem of addition for linear system without building up a new Jacobian matrix again. But the equivalent computation of algebraic equation must be performed to get state variables corrections. Accordingly, the speed required to model the contingencies is not fast enough to meet the demand of fast contingency analysis under emergency condition, which is proved by several well-known blackouts caused by flow transferring.

但是，这些算法中的大多数是在实时潮流计算的基础上，利用其中间结果和线性系统的叠加原理，直接求解出事故后的状态变量，都需要通过网络方程求解整个网络状态变量的增量，计算量较大，难于满足紧急状态下快速安全性评估的实时性要求，国内外一系列因静态潮流问题引起的大停电事故就是例证。

The scattering coefficients of a single charged sphere are deduced. And with spherical vector wave functions and addition theorem, the scattering coefficients of multiple charged and uncharged spheres are derived. The sampling method of simulating a Gaussian beam in use of MC is provided.

详细推导了单个带电球粒子的散射系数；并采用矢量波函数展开方法结合矢量波函数的加法定理导出了高斯波束入射多个带电/不带电球粒子的散射系数；提出了用MC模拟高斯波束的抽样方法。

Basing on the Graf′s addition theorem, two expessions, interior and exterior expression, are deduced and the suitable problems for them are discussed. It has been found that the interior expression is the main point for sovling the scattering problem of circular inclusion in half-space. It also has been found that the exterior expression is the key for the scattering problem of circular arc canyon and circular arc alluvial valley, and is one of the main points for scattering problem of circular arc hill as well.

从Graf原有加法公式出发，本文给出了其内域型和外域型两种表达形式并讨论了这两种表达的适用范围，同时指出：内域型表达是求解半空间内含夹塞区出平面散射问题的要点，而外域型表达是解决任意圆弧型凹陷地形和任意圆弧型沉积盆地出平面散射问题中求解难点的关键，同时也是克服任意圆弧型凸起地形出平面散射问题求解困难的要点之一。

Also using the exterior expression for the Graf′s addition theorem, the exact solution for scattering of plane SH waves by circular arc alluvial valley is presented in the paper. From the numerical results the complex effect of the depth-to-width ratio of the alluvial valley on the surface ground motion is found.

利用Graf加法公式的外域型表达，本文还给出了任意圆弧型沉积盆地出平面散射的精确级数解答，提供了大量数值结果并指出了盆地深宽比对地面运动的复杂影响作用。

And discuss some key point of integrated management system design, include hazard identification and risk assessment and risk control in the occupational health and safety management, the measure of satisfaction target of customer, the flawlessness of law system, the integration of the integrated management system and enterprise standardization system, unify lead institution and work orgnization, integreted internal audit and integrated management review.

同时，论述了一体化管理体系构建中的几个主要问题，包括职业健康安全管理中的危险源辨识、风险评价和风险控制、顾客满意度的科学监测、法律、法规体系的完善、一体化管理体系与企业标准化体系的有机结合、统一的领导机构和工作机构、一体化的内部审核和管理评审。

Deepwater Taranaki is investigated for its petroleum potential, using all available seismic data tied to shallow-water wells.

运用与浅水井相关的现有全部震波探测数据考察了深海区塔拉纳基盆地的油藏前景。