查询词典 addition theorem

In addition also introduced the differential theorem of mean in the proof equality and the inequality, the certificate equation root existence, asks the limit, to ask the approximate value, as well as aspect and so on research function condition should thus deepen to the differential theorem of mean understanding.

此外还介绍了微分中值定理在证明等式和不等式、证明方程根的存在性、求极限、求近似值，以及研究函数性态等方面的应用，从而加深对微分中值定理的理解。

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。"

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。

this article discusses the integral theorem of mean the promoted question, mainly has two aspects: On the one hand in analyzes in the teaching material under the first integral theorem of mean condition, had proven lies between the value spot to have to be possible to obtain in the open-interval, further discusses this knot promotes to the generalized Riemann integral, and further proved the conclusion also establishes to the promoted first integral theorem of mean; Promotes on the one hand in addition the integral theorem of mean to in the curve and the curved surface, and has proven the curvilinear integral theorem of mean and the surface integral theorem of mean.

本文讨论积分中值定理的推广问题，主要有二个方面：一方面在分析教材中第一积分中值定理的条件下，证明了介值点必可在开区间内取得，进一步将这个结论推广到广义Riemann积分，并进一步证明结论对推广的第一积分中值定理也成立；另一方面，将积分中值定理推广到曲线和曲面中，并证明了曲线积分中值定理和曲面积分中值定理。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

In addition, when the nonlinearities have the properties of mixed-monotonicity, the existence of a positive solution for difference equations is ob-tainded by using fixed point theorem in a cone or fixed point theorem of conic expansion and compression.

在最后一部分讨论了带有特征值的非线性二阶差分方程正解存在性问题，利用锥压缩与拉伸不动点定理及逼近性理论，在一定的假设条件下，得到了差分方程正解存在性。

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。