查询词典 normalization theorem

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。

First the theorem is verified for the smallest admissible value of the integer.

归纳法：证明涉及到正整数变量的定理所运用的两部法。

This paper first analyses the stress acting on the cable by means of tiny segment analytical methods, establishes cable's stress equation, and finds out the relation between the tethered aerostat's position and its stress acting by cable; then, based on the momentum and moment of momentum theorem, the longitudinal nonlinear dynamic equation is established; Finally a numerical simulation of dynamic responses of the balloon and cable to gust are carried out.

本文首先通过微段分析法对缆绳进行受力分析，建立缆绳的受力方程，找出了系留气球在空中的位置同系留气球所受缆绳拉力的关系；然后根据动量和动量矩定理建立了球体的纵向非线性运动方程；最后通过数值仿真计算，对系留气球的纵向动态响应特性进行了分析。

We found that our proposed theorem is far better than the affine map in dealing the transformation problems of coordinate systems.

本研究发现用座标系统整合理论比Affine Map理论更能准确的处理座标的转换问题。

We also get a representation theorem for Bi-difference sets.2. Ideal and filter are two important concepts in quantum logic. From the order structure and algebraic structures of effect algebra, there are many definitions of ideals and filters.

理想和滤子是量子逻辑中的两个重要概念，由于量子逻辑有自身的代数结构和序结构，因此有多种意义下的理想和滤子概念。

Applying multivariate spline theory which was established by Wang RenHong in ( [1] , [2] ), the Nother theorem of algebraic curve [71] is generalized to the piecewise algebraic curve.

1：利用王仁宏在文献（[1]，[2]）中关于多元样条函数的基本理论，本文将代数曲线的Nother定理（[71]）推广到分片代数曲线上，给出了剖分为〓，和星形剖分上的C〓分片Nother型定理。

Don not attempt to do something which you can not to do.

不要企图做那些办不到的事情。

The expression of CTGF and TNF-αweredetected by immunochemistry and the number of Clara Cells was calculated.

光镜下观察肺组织的病理变化，采用免疫组化染色观察肺组织中结缔组织生长因子和肿瘤坏死因子-α的表达和Clara细胞的数量。