恒等式

Because of the 1-1 property of bijection, the identity is proved. This thesis just applies this method to give identities their combinatorial proof.

本文也正是采用了这种方法对恒等式进行组合证明，从而揭示组合证明的一般方法。

In this thesis, we mainly discuss the applications of matrix representation of inverse relations to the WZ theory and to the hypergeometric series identities.

本文主要讨论反演关系的矩阵表示在WZ理论中的一些应用及由-反演和著名的超几何级数恒等式推出形式比较漂亮的新的恒等式。

By using this method we obtain two gen-eralized transformation formulae of q-integral form,two identities of basic hypergeometric series,as well as formal extensions for q-Pfaff-Saalschütz formula,q-Chu-Vandermonde identity and a three-term transformation formula of _3φ_2-series.

我们推广了两个q-积分形式的变换公式和两个有关基本超几何级数的恒等式，还得到q-Pfaff-Saalschütz公式、q-Chu-Vandermonde恒等式和基本超几何级数中一个有关_3φ_(2~-)级数的三项变换公式等的形式推广。

It is proved that a wrpp semigroup satisfies a permutation identity if and only if it satisfies the identity xyzw= xzyw.

证明了wrpp半群满足置换恒等式当且仅当它满足恒等式xyzw=xzyw。

Variational identity play a important role to prove nonexistence and get prior estimate of solution, In this thesis, we study following parts on the relationship of symmetry group of partial differential equations with variational structure and the variational identity.

变分恒等式在证明具有变分结构偏微分方程解的不存在性以及得到方程解的先验估计时有着非常重要的作用，本文研究了一些具有变分结构偏微分方程的对称群与其变分恒等式的关系。

Besides giving new proofs of known identities, the author establishes several interesting product identities, and discusses briefly applications to combinatorial computations as well as analytic theory of numbers.

在对已有恒等式提供新的证明的基础上，作者发现许多新的有趣的乘积恒等式，并详细讨论它们在组合计算，解析数论等方面的应用。

With the help of a transformation formula of basic hypergeometric functions, known identities, and Jacobi triple, we have established some new Rogers-Ramanujan type identities.

2我们对Agarwal与Singh（见文献[1]）推导出的一个新的Rogers--Ramanujan型恒等式〓给出了一个新的、更为简单的证法，并得出一系列新的Rogers-Ramanujan型恒等式。

Was introduced to extend Pascal functional matrices to Pascal operator matrices by using polynomial of binomials type.

本文给出了Tepper 恒等式的一个算子形式的推广，并且由此导出一些组合恒等式。

Based on the phase-space generating functional for a system with a singular higher-order Lagrangian,the quantal canonical Noether identities under the local and non-local transformation in phase space for such system have been derived.

基于高阶微商奇异拉氏量系统的相空间生成泛函，导出了定域和非定域变换下的量子正则Noether恒等式；对高阶微商规范不变系统，导出了位形空间中定域和非定域变换下的量子Noether恒等式。

We investigate this kind of numbers in Chapter 4 and give the following results:(1) By generating functions theory, we have established a number of identities involving the powers of generalized Fibonacci and Lucas numbers. From these identities, we can obtain some new congruences.

第四章：利用发生函数理论以及一些运算技巧，讨论与广义Fi-bonacci，Lucas数有关的问题：(1)利用发生函数原理，建立了一系列涉及广义Fibonacci，Lucas数的幂的恒等式，并由这些恒等式得到了新的同余关系。

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。