单代数

Without using Lie derivative and Lie bracket operation of differential geometry , we only use the algebra method to give a sufficient condition of single input exact feedback linearizable bilinear systems.

摘 要 研究了单输入的双线性系统的精确线性化及其鲁棒控制器设计问题，避免了用微分几何的李导数、李括号的复杂运算，只用纯代数的方法给出了一般单输入双线性系统精确线性化的充分条件。

In this paper, we continue thestudy of Jordan multiplicative maps, Jordan triple multiplicative maps, elementarymaps, Jordan-triple elementary maps, Lie-skew multiplicative maps, Lie and Jordanderivation, 2-local isomorphism, local derivation and 2-local derivation on some operatoralgebrac.

这些算子代数包括一类非常重要的非自伴非半单非素的算子代数，即套代数。

It introduces partial fractions of meromorphic functions, product developments of entire functions, Hadamard's theorem, Riemann Zeta functions, Poisson-Jensen's formula; elliptic functions, including simply periodic functions and doubly periodic functions; algebraic functions and algebroid functions, Riemann surface, Nevanlinna theory, including characteristic functions, the first and second fundamental theorems, growth orders, etc; complex differential equations and complex functional equations, etc.

具体为：亚纯函数的部分分式、整函数的无穷乘积展开、Hadamard定理、Riemann Zeta函数、Poisson-Jensen公式；椭圆函数，包括单周期函数、双周期函数；代数函数和代数体函数、Riemann曲面简介；Nevanlinna理论简介，包括特征函数、第一和第二基本定理、增长级等；复微分方程和复函数方程，等等。在教学内容上充分体现基础性、新颖性。

It is proved that the set which all atoms of a BCH algebra are made up is a p semisimple BCI algebra.

证明了一个 BCH-代数的所有原子做成的集合是一个 p-半单 BCI-代数。

This result is a generalization of the Chevalley basis in case a simply-laced complex simple Lie algebra. Meanwhile, it generalizes also the corresponding Chevalley forms in case affine Lie algebras and 2- extended affine Lie algebras.

该结果是simply-laced复半单李代数情形下Chevalley基的推广，同时也是仿射李代数和2-扩大仿射李代数的相应Chevalley结构形式的推广。

In section 2.2,we prove that if the set of arrows in a quiver is not empty,then NQ is not semisimple.We construct the nonsovable subalgebra of NQ when there is no less than one circle whose length is bigger than one ,and there is no loop in quiver Q,thus leads to a conclusion that NQ is nonsovable .

我们还对只有一个单循环和一个单循环及若干单箭头的箭图，给出了其项链李代数的某些中心元素的具体形式，在2.2节中，我们对非平凡图，即当箭图中有箭头时，利用H中的元素证明了N_Q不是半单纯李代数。

Over a field of arbitrary characteristic, we construct a class of associative superalgebras of Weyl type and a class of Lie superalgebras of Weyl type from ∧(2, 2) and the polynomial algebra of the special deravation subalgebra of it. In addition, we prove that the sufficient and necessary conditions of the simplicity of the associative and the Lie superalgebras.

在任意特征域上，从∧(2，2)和它的特殊导子的子空间的多项式代数出发，构造了一类Weyl型结合超代数和一类Weyl型李超代数，进而给出并证明了它们为单的充要条件。

Let 〓 be a finite-dimensional Z-graded Lie superalgebra.Weprove that if L has a non-degenerate trace form then s=r.Using the result,weobtain that the Killing forms of Lie superalgebras of Cartan type are degenerate.

本文得出如果有限维单Z-阶化李超代数L=〓具有非退化迹型〓，则s=r，由此可推出Cartan型李超代数的killing型是退化的。

The derived group series of p - semisimple BCI - algebras and the derived semigroup series of generalized a - associative BCI - algebras are given.

并给出了p-半单BCI-代数的一个导群列和广义a-结合BCI-代数的导半群列。

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。

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