代数化

As advantage of this method, at the same time of diagonalization, one can know the algebraic structure in the Hamiltonian and get the eigenstates that are revealed to be an algebraic coherent state as well as some other possible information of the corresponding physical system.

这种方法的优点是，在用代数法将哈密顿量对角化的同时，不但得出了该系统哈密顿量的代数形式，并且可以得知对应的本征态与代数相干态的关系及对应的物理系统的其他物理信息。

In this paper,we propose a concept called interval implicitization of rational bézier surfaces,that is ,finding an interval algebraic surface with lower degree which bounds a given parametric rational bézier surface such that some objective function involving the width and the tention term of the interval algebraic surface is minimized.

本文提出有理Bézier曲面的区间隐式化的概念，即找到一条较低次的区间代数曲面使得给出的有理Bézier曲面落在该区间代数曲面内，并使得一包含区间代数曲面的宽度和张量项的目标函数达到最小。

We investigate the centralizer of an arbitrary element of a Lie algebra of type L and obtain a sufficient condition for a Lie algebra of type L being semisimple.

在李代数方面，我们研究了L-型李代数中任一元素的中心化子，给出了L-型代数为半单代数的充分条件。

We prove every linear and local centralizer on J -subspace lattice algebras is a centralizer.

第三章研究J -子空间格代数的局部中心化子，证明J -子空间格代数的线性局部中心化子是中心化子。

Yu introduced in 1997 the localization Roe algebras , and shown that, to attack the Coarse Baum-Connes Conjecture, it suffices to prove that the local index map is an isomorphism from the coarse K-homology to the K-theory of the localization Roe algebras.

Yu受热方程方法的启发，引入局部化Roe代数，把粗Baum-Connes猜测的证明归结为证明从粗化K-同调群到局部化Roe代数的K-理论群的局部指标映射为同构。

This paper proves that it is impossible for all the theorems in classical propositional calculus to be tautologies in the field of fuzzy propositional calculus, then a quasi formal deductive system is established for fuzzy propositional calculus based on a kind of type algebra.

引入了一种代数，称为模糊公式代数。在这种代数上建立了一个准形式演绎系统，证明了相应的可靠性定理与相容性定理，提出了程度化的ModusPonens规则和HypotheticalSylogism规则

In this paper, we mainly study representations of strong semisimple n-Lie algebras, prove that a representation of a strong semisimple n-Lie algebra is a representation of the reductive Lie algebra LP, and the relative properties.

本文主要研究了强半单的n-李代数的表示，证明了强半单的n-李代数的表示可转化为一个约化李代数Lρ的表示，并证明了不变线性形等其它相关性质。

Throughout the present paper, the author mainly discuss the complexification of n-Lie algebras and the classification of real simple n-Lie algebras.

就李代数而言，单李代数的复化和复李代数的实形是一个非常重要的问题，同时其分类也是人们关注的焦点，本文将这两个结论放在n-李代数中进行深入的研究。

Further picosecond PL studies on dendronized PFs show that the fluorene-based emission in dilute solution follows a single exponential decay, whereas those in thin film decayed in a multi-phase manner and the lifetime prolongs with the generation of dendronization. These observations are discussed in terms of dispersive transport happening between adjacent chains in film. The dispersive relaxation can be controlled by site isolation of bulky dendrons. Our results prove that dendronization is highly effective in controlling the inter-chain interactions of fluorene-based polymers.

不同代数树枝化聚芴的时间分辨荧光动力学研究结果表明，溶液状态下的发光为单指数衰减行为，而薄膜状态下的发光为多指数衰减行为，且其发光寿命随树枝化代数增加而增长，表明树枝化基团抑制了邻近的聚芴分子之间能量传递所致的激发态能量耗散。

Secondly, in a more generalized framestructrue--lattice-ordered monoids,the notion of lattice-valued Mealy-type automata is introduced,we traverse some algebraic properties of this automata and investigate the congruences and homomorphisms of this type automata.Our main results indicate that the algebraic properties of lattice-valued Mealy-type automata have Close links to the algebraic properties of lattice-ordered monoids which automata take values in.Futhermore we study the minimization of lattice-valued Mealy-type automata and provide an algorithm to achieve the minimal lattice-valued Mealy-type automata within finite steps.

其次，在更一般的框架—格半群意义下，提出具有输入和输出字符的自动机——格值Mealy自动机的概念，从代数角度出发较详细地研究了此类自动机具有的性质，同时研究了此类自动机的同余和同态，揭示了此类自动机的代数性质和格半群的紧密联系，最终研究了格值Mealy自动机的极小化问题，并给出了在有限步可实现此极小化的算法。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷