本文将完全刻划出无零因子环的所有幂自同态。
In this paper, we will completely characterize all power endomorphisms of rings without zero divisor.
哲学家与暴君，之间的差别刻划出，两种非常不同的哲学概念。
The difference between the philosopher and the tyrant illustrate two very different conceptions of philosophy.
变形而刻划出来的。纹样衬托出一种狰狞、神秘、威严的气氛。
The animal figures are portrayed with artistic exaggeration and create a ferocious, mysterious and dignified mood.
在晷面的正反两面刻划出12个大格，每个大格代表两个小时。
Both sides of the dial are divided into 12 parts, each part representing two hours.
刻划花是指用工具在陶瓷坯体上刻划出纹样，经施釉入窑烧制而成的一种陶瓷装饰方法。
Established in ceramic tool refers to carve, after blowing glaze kiln firing a ceramic decoration.
双牛用墨浓淡适宜，传神地刻划出斗牛的肌肉张力、逃者喘息躲避的憨态、击者蛮不可挡的气势。
The exact lines and appropriate saturation vividly display the muscle tensions and the irresistibility of the attacking bull, the pants and naughtiness of the escaping one.
在这个假定下，我们进一步根据商有向图及核K为C（G，S）的自同构群刻划出了一系列特性。
Under this assumption, the present paper further gives a characterization for the automorphism group of C( G, S) in terms of the quotient di-graph and the kernel K.
力求创造具有诗意的建筑形象，诉说世事的繁荣岁月的辉煌，刻划出气派的外观与尽善尽美的细节。
It strives to create a poetic architectural image, narrate earthly prosperity and time's glory, and portray a magnificent appearance and perfect details.
通过对一类相当复杂的变分方程问题的研究并利用其有关结论，我们证明了新模型最佳控制的存在性并刻划出其结构。
From studying some kind of quite complex variational equation problems and applying the conclusion, we prove that the optimal control of new model is existent and characterize its structure.
通过对一类相当复杂的变分方程问题的研究并利用其有关结论，我们证明了新模型最佳控制的存在性并刻划出其结构。
From studying some kind of quite complex variational equation problems and applying the conclusion, we prove that the optimal control of new model is existent and characterize its structure.
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