模数

The injective rings play an important role in the study of rings and categories of modules . First , we introduce the notion of ann-injective rings and CT-injective modules .Second,we make an inquiry into a series of their properties.Third,we give the definition of homological dimension of CT-injective modules.At last,we give the definition of FGT rings which is the extension of cogenerator rings.

本文对环与模范畴中一重要的模类—内射模进行了延拓，引入了ann -自内射环以及CT -内射模的概念，探讨了它们一系列的性质，并定义了CT -内射模的同调维数，最后对余生成子环进行推广得到了FGT -环，讨论了它与CT -内射环的关系以及它的一些性质。

Since the modes of foundation are dense,by taking the criterion of energy response as mode truncation index,the energy norm and criterion are established to calculate the mode truncated order of dynamic compaction response.

由于地基模态密集，提出以能量响应信息的收敛作为模态截断的判断指标，建立能量范数和能量判据，计算强夯动力响应的模态截断阶数。

Moreover,using Ito differential formul a to the constructed Lyapunov function along solutions of lto stochastic differential systems,Lyapunov method is adopted to set up the fundamental theory of dissipativity in the module corresponding to the theory on the dissipativity of deterministic ordinary dif- fere.

提出了有关Ito型随机微分系统耗散性理论的新概念：按模耗散、按模等度耗散和按模一致耗散，并利用Lyapunov方法，借助于Ito 微分公式沿着Ito型随机微分系统的解对所构造的Lyapunov函数求导数，给出了Ito型随机微分系统有关按模耗散理论的一些代数判据，获得了与确定性常微分系统耗散性理论相对应的结论，最后的算例证明了该方法的有效性和可行性。

It is often seen that only lower order modes of the beam without large overallmotions are chosen to reduce the number of the generalized coordinates,the simulation,however,is able to reach certain accuracy.

本章对不同转速和中心刚体半径下模态截断法和有限元法的仿真结果进行比较，根据两种方法的振动基频的相对误差确定了模态截断的阶数与转速、中心刚体半径的关系，提出了模态截断的准则，解决了模态截断法的精度问题。

The existence of global weak solution for a class of generalized Ginzburg-Landau equations with an inhomogeneous boundary condition was studied. Some integral indentities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained.

研究具非线性边界条件的一类广义Ginzburg＿Landau方程解的整体存在性·推导了Ginzburg＿Landau方程的非齐次初边值问题光滑解的几个积分恒等式，由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计；通过逼近技巧、先验估计和取极限方法证明了Ginzburg＿Landau方程的非齐次初边值问题整体弱解的存在性

The structure of prime submodules of free modules is depicted and a calculable formula about prime dimensions of free modules is given.

对自由模的素子模是进行了刻画，给出了自由模的素子模的结构为(PF，u1，u2，…，us)，且给出了自由模的素维数的计算公式D=dimA+rankF-1。

II, Polynomial rings on a general field( on contrast of those over a number field): concepts of ring, ideals, field and several special rings as domains, principal ideal domains and unique factorization domains, the unique factorization theory of polynomial rings.

二、一般域上的多项式理论（是数域上多项式理论的推广）：学习环、域和几类特殊结构的环（整环、主理想环，唯一分解环等）的概念，多项式环的唯一分解定理；三、线性代数：讲述一般数域上的向量空间理论（是数域上向量空间理论的继续和推广），模的概念，主理想环上的模的结构及其线性变换的若当标准型等；四、一元多项式的解及域论：学习域扩张及其相关概念，伽罗瓦理论，用伽罗瓦定理判断根式解的存在性。

In chapter 4, we define the projective dimension of flat modules, use it to characterize many rings, and the relations between cotorsion modules and the projective dimension of flat modules are also given.

在第四章中，我们定义了平坦模的投射维数，用它刻划了一些环，并讨论了Cotorsion模和严坦模的投射维数的关系。

Some new conceptions are presented about the dissipativity theory of Ito stochastic differential systems as follows:dissipativity in module,equi-dissipativity in module and uniform dissipativity in module.

提出了有关Ito型随机微分系统耗散性理论的新概念：按模耗散、按模等度耗散和按模一致耗散，并利用Lyapunov方法，借助于Ito微分公式沿着Ito型随机微分系统的解对所构造的Lyapunov函数求导数，给出了Ito型随机微分系统有关按模耗散理论的一些代数判据，获得了与确定性常微分系统耗散性理论相对应的结论，最后的算例证明了该方法的有效性和可行性。

The study results show that the dispersion of travelling wave is mainly caused by earth mode; Compared with aerial mode earth mode is greatly influenced by the factors such as ground conductivity, line average height above ground, bundle config...

研究结果表明：行波色散主要由地模引起；行波中地模受大地电阻率、线路高度、分裂导线数、分段地线、连续地线等因素的影响较大，而线模受到的影响较小，因此将线模作为故障定位用行波传播模式比较适宜。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。