环

Group, Subgoup, Permutation Group, Cyclic Group, Commutative Group, Normal Subgroup, Factor Group, Isomorphism, Ring, Ideal, Field, Polynomial Ring, Factor Ring.

课程内容：群，子群，置换群，循环群，交换群，正规子群，商群，群之同构，环，理想，体，多项式环，商环等。

As an application, we also describe the Jordan automorphisms of the algebra of upper triangular matrices over commutative rings, and give a sufficient and necessary condition for a commutative ring being connected.

作为应用，我们还刻划了交换环上的上三角矩阵代数的Jordan自同构，并给出了一个交换环是连通环的充要条件。

If R satisfies =0 for any elements x ,y in R then ⑴when k =1, R is commutative;⑵when R has the unity, R is commutative;⑶when R has at least one right regular element and f 2 (t 1,t2) has no terms with degree1 such that Fn= F then R iscommutative when R has at least one right regular element. Here we would like to point out that the above results generalized the results of Fu changlin ,moreover generalized some results of other references . This results enriched the commutative conditions of any ring.

若任取R 中元x， y均有=0 那么⑴k =1时R 为交换环；⑵R 有单位元时R 为交换环；⑶f_2 (t_1，t_2)中t_2的次数不小于k -1且R 中至少有一个右正则元时R 为交换环。

Then we introduce the concept of(n,0)-projective dimension for modules and rings.It measures how far away a finitely generated module is from being n-presented,and how far away a ring is from being Noetherian.

然后，我们介绍环与模的(n，0)-投射维数，它可以衡量一个有限生成模与n-表现模的差距，以及衡量一个环与Noether环的差距。

Every connected, compact Lie groups G contains a maximal torus T. This maximal torus is unique up to conjugation, and every element of G is conjugate to the element of the maximal torus.

每个连通紧李群具有极大环面子群，任二极大环面子群彼此共轭，且连通紧李群中每个元素共轭于极大环面的一个元素。

In this paper, the limit cycles in a nonlinear deterministic model in the continuous culture vessel with variable yield is studied.

用微分动力系统的定性理论研究了一个非线性连续微生物培养动力系统的极限环问题，探讨和估计了存在极限环的条件和极限环的周长。

A simplified PUMA robot force control model is given in this paper. The stability and rubustness is analysised by computer simulation. The step response of position loop and force loop in external alter mode is tested, and prove that the system posses critical damping ratio.

简化得出了PUMA机器人的力控制模型，利用计算机仿真的方法，分析了系统的稳定性及鲁棒性，给出了最佳参数的选择，测试了在外部修正方式下位置控制环及力控制环的阶跃响应，证明位控环具有临界阻尼的特性，并讨论了参数选择值不同时对系统性能的影响。

The integrability conditions and coefficient conditions for the appearance of 5 and 6 limit cycles from the neighborhood of the equator are obtained. An example of cubic system with 6 limit cycles bifurcating from the equator is given for the first time.

同时计算出系统的前6个赤道环量，得到了系统在赤道邻域的可积性条件及在赤道附近分支出5个和6个极限环的系数条件，从而首次给出了一个平面三次系统在赤道附近分支出6个极限环的计算实例。

Compared to NMR techniques, the fluorometric analysis method revealed that there are not only obvious interactions of quinoline or its derivates and cucurbit [ 7 ] uril, but also interactions of quinoline or its derivates and cucurbit[6]uril or cucurbit[8]uril which can not be observed by using ^1H NMR technique.

与核磁共振技术比较，荧光光谱分析方法具有高灵敏性的特点，不仅可观察到喹啉及其衍生物与七元瓜环相互作用而引起的荧光性质变化；还能观察到它们与六元瓜环或八元瓜环相互作用所产生的变化，这是通常的NMR方法所不能实现的。

By using these equtions, a vector control scheme of motor that is realized on EV under the d-q coordinates, and current loop and speed loop are included.

控制系统为电流环和速度环的双闭环系统。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。