恒等式

The classical Abel identity as specific case and some significative combinatorial identities are obtained.

由此得到Abel恒等式的特殊情形和一些很有意义的组合恒等式。

By the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proof is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity.

恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

Moreover, by the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proofs is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity. Because of the 1-1 property of bijection, the identity is proved.

此外，恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

In the thesis some vital identities with binomial coefficient are given with their combinatorial proof, and the q-analogues of some identities are offered with corresponding combinatorial proofs on the subspace-lattice. Especially, one remarkable result is that a new q-analogue of the cube-sums identity is obtained with its combinatorial proof over the vector space.

本文给出了一些重要的二项式系数恒等式的组合证明或组合解释，并从向量空间角度给出了一些恒等式的q-模拟及组合证明，其中突出的成果是给出了立方和恒等式的一个新的q-模拟及组合证明。

In the thesis , we give combinatorial proof of some q-identities using integer partition.In the thesis some vital identities with binomial coefficient are given with their combinatorial proof, and the q-analogues of some identities are offered with corresponding combinatorial proof using integer partition.

本文给出了一些重要的二项式系数恒等式的组合证明或组合解释，并从分拆的角度给出了一些q-恒等式的组合证明，其中突出的成果是给出了平方和恒等式的一个直接的组合证明并给出了偶数平方和与奇数平方和的q-模拟及组合证明。

If the power series ∑anxn an ∑anxn and ∑bnxn satisfy the condition r =∑bn xn, we obtain the twin combinatorial identity theorem between the sequences {an} and bn}.We also obtain some specific twin combinatorial identities by using the expansion on the binomial expression formula, including two expansions of combinatorial number(rsn and ...

如果幂级数∑anxn与∑bnxn满足条件r＝∑bnxn 时，获得数列｛an｝与｛bn｝之间孪生组合恒等式的定理，应用在二项式定理等展开式上得出具体的多组孪生组合恒等式，其中包含组合数的两种展开法，Bernoulli数直接表达式的新证等结果。

At last, in Section 3, we calculate the Pohozaev identity for p-harmonic equation under Navier or Dirichlet boundary condition from which we obtain the corresponding nonexistence of nontrivial solutions for p-harmonic equations with critical growth.

最后在第三节中，我们分别对带Navier边值条件和Dirichlet边值条件的p-调和方程的Pohozaev恒等式作了演算，并利用这些恒等式得到了相应的p-调和方程临界增长问题的非平凡解的非存在性结果。

In the last chapter we derive new identities frominversion and famous hypergeometric series identities.

在最后一章里，我们利用-反演和一些著名的超几何级数恒等式，得到了一些形式比较漂亮的新的恒等式。

Liouville"s Theorem on entire functions is proposed as a proving method for theta function identities. Several identities are exemplified, such as the quintuple and septuple product identities; four symmetric difference identities related to the Ramanujan"s congruence modulo 11 on the partition function; as well as two theta function identities on the Rogers-Ramanujan functions G and H.

作者提出利用Liouville定理作为证明theta函数恒等式的基本方法，并以Watson五重积，Hirschhorn七重积恒等式，四个与分拆函数中Ramanujan的模11同余有关的对称差恒等式，以及两个与Rogers-Ramanujan函数G，H有关的theta函数恒等式为范例，论证这种方法的有效性。

Especially, we derive the Pohozaev identity for p-harmonic equation from which we obtain the corresponding nonexistence of nontrivial solution for p-harmonic equation with critical growth.

本文考虑了几类椭圆方程的Pohozaev恒等式，特别是对p-调和方程在两种边界条件下的恒等式作了详细的演算，并利用这些恒等式得到了一些解的非存在性结果。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了