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In chapter 3,we will consider the automorphisms of triangular matrix algebras over commutative semirings.

利用矩阵的一些性质，克服了环上可逆矩阵在半环中未必可逆的难点，证明交换半环R上的n阶三角矩阵代数Tn的自同构都是内自同构。

This paper gives the definition of the trivial solution to the high degree congruence x^ n = a, presents one sufficient and necessary condition for the congruence to have solutions, derives and proves one new judgment condition complementarily.

这篇文章给出了高阶同余方程 x^ n = a平凡解的定义，介绍了高阶同余方程有解的一个充要条件，补充推导和证明了另一个充要条件。

I find it easy to make friends with most people, but I just can't get on with Tyrone.

我觉得我很容易同大多数人友好相处，但我就是不能同蒂龙友好相处。

With the brave act for a just cause as an act in law, the actor will suerly be of unaccountability, justice and legal characteristics of immediately-faced dangers of giant personal harm, fighting against breach of law and rescue and relief work.

见义勇为是一种在法律上有正当理由的行为，其行为人一般具有非义务性、正义性、合法性的特点，面临有人遭受重大损害的危险时实施了同违法犯罪作斗争或抢险救灾的行为（金山词霸例句翻译：见义勇为作为一种法律行为，其行为人应具有非义务性、正义性、直接面临本人遭受重大损害的危险和实施了同违法犯罪作斗争或抢险救灾的行为的法律特征）。

Their love for man, their zeal for God's service -- these holy impulses may or may not coexist in their hearts with the evil inmates to which their guilt has unbarred the door, and which must needs propagate a hellish breed within them.

他们对人类的爱，他们为上帝服务的热忱——这种种神圣的冲动在他们的内心中，或者可以或者无法同邪恶的伙伴同处共存，然而这些邪恶的伙伴既是他们的罪孽开门放进来的，就必然会在他们心中繁衍起一个魔鬼的种籽。

In competition initial stage for journalism, homogeneity is favorable to the improvement of the quality of the newspaper, but that homogeneity develops into certain stage will aggravate the fierce degree of the competition , result in propagandizing maliciously , sell such unfair competition phenomena as the newspaper , and present newspaper unboundedly ,etc. at a low price.

在报业竞争初期，同质化有利于报纸质量的提高，但同质化发展到一定阶段，会加剧竞争的激烈程度，导致恶意炒作、低价售报、无节制赠报等不公平竞争现象。

The good detective story writer competes not only with all the unburied dead but with all the hosts of the living as well.

优秀的侦探小说作家则不仅要同所有没有埋葬的死者，还要同所有大批大批的活着的人竞争。

At each level along the way they give rise to causes which are clear and pure and undefiled.

前边这个无尽功德藏回向，说这一位的菩萨，他这个地同佛地，「於同佛地」：在这个佛的地位中。

China will unflinchingly follow an independent diplomatic policy for peace, continue strengthening the solidarity and cooperation with developing countries, and work together with them to safeguard their justifiable rights and benefits.

中国将坚定不移的奉行独立自主的和平外交政策，继续加强同发展中国家的团结合作，同它们一道维护发展中国家正当合理的权益。

During the early uninucleate stage, the POD activity on area A、area B and area C with CHAs of treatment 2、3 was obviousely lower than the control. But in these areas POD activity with CHAs of treatment 4、5 was obviousely higher than the control.

在单核早期，处理2和3的A、B和C区POD 同工酶活性均明显低于对照；处理4和5上述各区POD同工酶活性却明显高于对照。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。