恒等式

Using the Green function of an anisotropic medium in free space and Green identity, we derive the equation of electric field in an anisotropic medium for TM polarized wave.

本文由各向异性介质无界空间Green函数和Green恒等式出发，推导了TM波入射时各向异性介质中电场满足的方程，由此得出总电场的积分公式。

Inspired by Chans double series representation formula of_∞~(10), the author constructs a new difference equation on quintuple products, which leads to clarification on the four symmetric differences that are equivalent in pairs.

受Chan得到的_∞~(10)的二重级数表示公式的启发，作者构造一个新的关于五重积的差分公式，并澄清迄今为止所出现的四个对称差恒等式之间成对等价的关系。

By means of two different methods, the author derives a general equation for expanding the product of two Jacobis triple products, which can be considered as the common generalization of the quintuple, sextuple and septuple product identities.

利用两种不同的方法，作者建立一个关于两个Jacobi三重积之乘积展开的广义公式，它可以看作是五重积，六重积和七重积恒等式的统一形式。

We further derive the recurrence formula of computing this series.

关于这类恒等式的研究一直是非常活跃的问题，并产生了许多证明方法（见文献[18，22-23，29，41，56，70-71，78]）。

According to the fine structures of reproducing kernels, the characterization of the image space in the wavelets transform and the isometric identities formulas are given by the perfect theory of reproducing kernel space.

根据再生核的这种较好的结构，利用较完善的再生核空间理论给出了小波变换像空间的描述及等距恒等式。

The author mainly studies the probabilistic representation of a special combinatorial number. Meanwhile, some special values of both kinds of Stirling numbers are obtained. Some new recurrence formulas and identities related to both kinds of Stirling numbers are found.

作者主要研究了一种特殊组合数的概率表示及其应用，得到了Stirling数的一个性质，推导出了其他有关Stirling数的递推公式并且发现了新的递推公式，并利用这些递推公式得到了几个恒等式，从而丰富发展了已有的一些结果。

In particular, we establish the weak spined product structure of the class of semigroups.

特别地，建立了一个wrpp半群满足置换恒等式的弱织积结构。

One of them contains a special case of q-Dougall summation formula,the other includes the famous Rogers-Ramanujan identities as special cases.

我们发现了两类新的基本超几何级数求和变换公式，其中一类的特殊情况包含在q-Dougall的求和公式中，另一类的特殊情况是著名的Rogers-Ramanujan恒等式。

A theorem for the summation of series expressed by function terms derived from function identities is established.

摘要建立了由函数恒等式所导出的函数项级数的求和定理，并给出了具体应用的实例。

In addition, new proofs are presented for two symmetric difference identities, as well as Ramanujans congruence modulo 11 on the partition function.

此外，作者重新证明其中另外两个对称差恒等式，并利用Chan的_∞~(10)的二重级数表示公式重新确认Ramanujan的关于分拆函数的模11同余性质。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。