恒等式

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

In this thesis, by employing generating function technique, some new combinatorial identities have been established.

本文利用发生函数理论建立了一系列新的组合恒等式，并且利用发生函数方法讨论了一些级数的取整值问题以及某些多项式在有理点的取值问题。

Furthermore, some new Rogers-ramanujan type identities are obtained by a transformation of basic hypergeometric series.

接着，由一个级数变换出发，获得了若干个新的Rogers-Ramanujan类型恒等式。

In the thesis, the basic knowledge of the basic hypergeometric series, some results of the Rogers-Ramanujan type identities and its applications in number theory are studied.

本文主要介绍了基本超几何级数的基本内容，关于Rogers-Ramanujan类型恒等式的一些结果以及基本超几何级数在数论中的若干应用。

A transformation formula containing four independent bases is found and applied to derive a few summation formulas for basic hypergeometric series.

由此说明我们又找到了一个新的证明和发现Rogers-Ramanujan型恒等式的有效方法。

In Chapter 3, by means of Carlitz inversion formulas and a transformation of basic hypergeometric series obtained by Chu, we give new proofs for several Rogers-Ramanujan type identities.

第三章：在第二章内容的基础上，使用Carlitz-反演公式和初文昌获得的一个级数变换公式再次证明了许多Rogers-Ramanujan类型恒等式。

We Introduce produce elements factor of tendency result coefficient, turn structure production function model into identity that come into existence to every group of sample.

引入生产要素的势效系数，将结构生产函数模型转化为对任意一组样本成立的恒等式。

Starting with diagrammatic methods in linear algebra,this paper reviews the mathematical basis for spin network s,proves again loop operator and binor identity,and computes some formulas about spin network s.

从线形代数的图解方法出发，对自旋接网圈的数学基础做出回顾，并重新推证了圈算符和双元恒等式，计算了关于自旋接网圈的一些计算公式。

Further,we findalso that groups in Saito's results may be replaced by right groups;secondly we mainly investigatethe semidirect products and wreath products of P-regular semigroups;Finally we shallcharacterize the sandwich matrice of completely simple P-regular semigroups,and investigate thestructure of P-regular semigroup whose C-set satisfies a permutation identity.

在这一章中，首先指出Saito在研究半群的半直积和圈积时，对S的限制是不必要的，证明了Saito结果中群可换为右群；其次，研究P—正则半群的半直积和圈积；最后刻划了完全单P—正则半群的夹心阵和C—集满足置换恒等式的P—正则半群的结构。

In this paper,a new structural method of supplementary function is introduced, and the method is used to prove differential identical equation or integral inequality.

本文给出辅助函数新的构造方法，并将它运用于微分恒等式和积分不等式的证

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。