查询词典 convolution theorem

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。

In addition, Koopmans' Theorem makes the assumption that upon the addition or subtraction of a single electron to or from the system, the Fock operators for all of the remaining electrons will not change at all.

Koopmans定理还假定如果体系增加或者减少一个电子，其余电子的Fock算子不发生变化。

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。

In additive prime number theory,a classical result of Hua states that,every suffi-ciently large odd number N can be represented as 〓,where 〓 is aninteger and 〓 are primes,which can be regarded as an extension of Goldbach-Vinogradov Theorem.

堆垒素数论中一个经典的结果是华罗庚教授证明的：任一个充分大的奇数N都可以表为N=〓+〓+〓，其中λ是一正整数，p1，p2，p3是素数，这一结果可以看作著名的Goldbach-Vinogradov定理的推广。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。