恒等式

When q=1, this Gaussian coefficient identity changes the corresponding binomial coefficient identity.

当q=1时得到对应的普通二项式系数恒等式。

In Chapter 2, by means of the integral theory, a number of reciprocal series involving binomial coefficients have been established and some results related to binomial coefficients have been extended.

本章利用定积分的方法和常见的发生函数，结合一些运算技巧，建立了一些与二项式系数的倒数有关的恒等式。

Based on the phase-space generating functional of Green function, the canonical Ward identities for non-local transformation have been derived.

黄永畅 ，唐太明，李子平基于相空间Green函数的生成泛函，导出了非定域变换下正则形式的Ward恒等式。

Based on the phase-space generating functional of Green function, the canonical Noether identities under the local transformation at the quantum level have been derived.

基于Green函数的相空间生成泛函，导出了定域变换下的量子正则Noether恒等式

And get the closed form of general 〓W〓 and 〓V〓.

得到了一些新的Rogers-Ramanujan型恒等式。

It shows the effectiveness and practicability of the approach to prove algebraic identies with combinatorial analysis .

说明了用组合分析方法证明代数恒等式的有效性和实用性。

By using the lattice path model to combinatorial identity,it can be made very flexible to prove.

将格路模型应用在证明组合恒等式中，使证明方法十分灵活。

The main purpose of this paper is to study some properties of Fibonacci numbers and give some new identities and interesting congruence expressions.

研究了Fibonacci数的一些性质，并给出了一类新的恒等式和一些有趣的同余式。

Furthermore, we define a convolution multiplication between characteristic functions of constructible subsets by using push-forward functor from the category of algebraic varieties over C to the category of spaces of constructible functions. We construct geometric model for "intrinsic symmetry" of the octahedral axiom in a triangulated category. Using it, we deduce the multiplication satisfies the Jacobi identity of Lie algebra and then realize infinite dimensional Lie algebras.

进一步，我们使用复代数簇范畴到可构函数空间范畴的pushforward函子，给出了可构集上特征函数的卷积乘法，并构造了三角范畴八面体公理的内蕴对称性的几何模型，最终证明了对于不可分解支撑有界可构集的特征函数，乘法满足李代数定义的Jacobi恒等式，从而给出了无限维李代数的实现。

The inconsistencies of dimensional reduction and naive dimensional regularization in dealing withChern-Simons-matter theory are analyzed.The consistent dimensional regularization combiningwith higher covariant derivative regularization is adopted to consider Chern-Simons field theorycoupled to complex scalar and spinor field.All the local parts of one-loop two-point functionsand three-point functions are computed.Slavnov-Taylor identity is combined with these explicitcalculation results to give the one-loop local effective action.The finite gauge invariant quantumcorrection is shown and finite wave function renormalization constant for each field is defined.Thelocal part of one-loop three gauge field vertex is especially evaluated and it is verified that thereexists a renormalization choice compatible with BRST symmetry.

然后计算了所有的两点函数和三点函数单圈修正的定域部分，利用S-T恒等式给出了单圈定域有效作用量，定义了场的重正化常数，发现物质场和规范场都存在有限的规范不变的量子修正，并讨论了这些有限的规范不变的量子修正的物理意义，进而通过考察单圈三规范场顶角，表明存在与BRST对称性相容的重正化选择。5、在背景场方法的框架下，选择高阶协变导数正规化与维数正规化的杂化正规化方案计算了背景场两点函数的两圈量子修正，结果表明，标志紫外发散的极点项恰好抵消；进一步利用背景场方法中明显的规范对称性，证明背景场三点函数的两圈图贡献也是有限的。

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。