- 更多网络例句与恒等式相关的网络例句 [注：此内容来源于网络，仅供参考]
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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。
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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。
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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。
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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。
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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。
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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。
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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。
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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。
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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。
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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。
- 更多网络解释与恒等式相关的网络解释 [注：此内容来源于网络，仅供参考]
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abel identity：阿贝耳恒等式
abel equation 阿贝耳方程 | abel identity 阿贝耳恒等式 | abel inequality 阿贝耳不等式
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euler identity：欧拉恒等式
euler formula 欧拉公式 | euler identity 欧拉恒等式 | euler number 欧拉数
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Euler's identity：欧拉恒等式
Euler 欧拉 | Euler's identity 欧拉恒等式 | Euler's theorem 欧拉定理
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fundamental identity：基本恒等式
fundamental homology class 基本同掂 | fundamental identity 基本恒等式 | fundamental invariant 基本不变量
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identical relation：恒等式
identical quantity 恒等量 | identical relation 恒等式 | identical substitution 恒等代换
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identities of kronecker：克罗内克恒等式
identification topology 同化拓扑 | identities of kronecker 克罗内克恒等式 | identity 恒等式
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ricci equatoin：李奇恒等式
riccati equation 黎卡提微分方程 | ricci equatoin 李奇恒等式 | ricci identity 李奇恒等式
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ricci identity：李奇恒等式
ricci equatoin 李奇恒等式 | ricci identity 李奇恒等式 | riemann function 黎曼函数
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Bianchi identity：毕安其恒等式
它涉及到协变导数:...给定流形某点的任一坐标表示,上述恒等式可以用黎曼曲率张量的分量形式表示为:另一个有用的恒等式可以由上面这些导出:...称为毕安其恒等式(bianchi identity),经常也叫第二毕安其恒等式(Second bianchi identity)或
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Bianchi identity：比安基恒等式
称为比安基恒等式(Bianchi identity),经常也叫第二比安基恒等式(Second Bianchi identity)或微分比安基恒等式(Differential Bianchi identity). 它涉及到协变导数: