设N 是Hilbert空间H 上的一个非平凡套，f 是套代数 A lg N 上的一个连续广义零点Lie-可导映射，d 是套代数 A lg N 上的一个连续Lie-导子。证明了，如果"A，B ? A lg N 且 AB=0有 f ([A，B])=f (A)B-f (B)A+Ad(B)-Bd(A)，则 f ([A，B])=f (A)B-f (B)A+Ad(B)-Bd(A)，"A，B?AlgN。

Let N be a non-trivial nest on Hilbert space H, f be a continuous generalized Lie derivable mapping at zero point on nest algebra A lg N and d be a continuous Lie derivation on nest algebra A lg N. In this paper, It is shown that if f satisfies f ([A,B])=f (A)B-f (B)A+Ad(B)-Bd(A) for all A,B?AlgN with AB=0,then f ([A,B])=f (A)B-f (B)A+Ad(B)-Bd(A) for all A,B?AlgN.

给定域K 的单代数扩域K (?)上可解多项式代数A=K (?)[a 1,…,a n ],设A 的子代数A 0=K [a 1,…,a n ]是K 上可解多项式代数。通过考察A 与多项式代数A 0[x ]之间的结构关系,给出将A 中左Gr?bner基的计算转换为A 0[x]中左Gr?bner基计算的有效方法。

Let A=K (?)[a 1 ,…,a n ]be a solvable polynomial algebra on a simple algebraic extension K (?)of the field K ,and the subalgebra A0=K [a 1 ,…,a n ]of A be a solvable polynomial algebra on K .The structural relation between A and the polynomial algebra A0 [x]shows the computation of left Gr?bner bases in A is effectively converted to the computation of left Gr?bner bases in A0 [x].

给出了 WGP-内射环的等价定义，研究了 WGP-内射环的一些性质，证明了：若 R 是左非奇异的左 WGP-内射环，且对 R 中任意无限序列 a1，a2，a3…，升链 l（a1）彻l（a1 a2）彻l（a1 a2 a3）彻…是平稳的，则 R 是半单环。

Some equivalent definitions of WGP-injective rings are introduced.And the properties of WGP-injective rings are studied.It is proved that if R is a left nonsingular left WGP-injective ring, and the ascending chain l(a1 )∈l(a1 a2 )∈l(a1 a2 a3 ∈terminates for every infinite sequence a1 ,a2 ,a3…, then R is semisimple.

设A是Jordan代数,如果线性映射d：A→A满足任给a,b∈A都有d（a。b）=d（a）。b＋a。d（b）,则称d是Jordan导子。本文给出了自伴算子构成的Jordan代数和Spin因子上的Jordan导子的具体表达形式,并且证明了Spin因子上的局部Jordan导子和2-局部Jordan导子是Jordan导子。

Let A be a unital Jordan algebra.A linear map d： A→A is called a Jordan derivation on A if it satisfies that d（a 。b）=d（a） 。b＋a 。d（b） for all a,b∈A.Expressions of the Jordan derivations of Jordan algebras of all self-adjoint operators and Spin factors are given.It is proved that all local Jordan derivations and 2-local Jordan derivations on Spin factors are Jordan derivations.

以Cl-为示踪剂,采用停留时间分布法(RTD)研究A/A/O反应器和填料A/A/O反应器,在清水和有污泥稳定运行条件下,采用不同水力停留时间对A/A/O反应器和填料A/A/O反应器水力特性的影响,并进行了对比分析。结果表明,在反应器内没有污泥时,停留时间分布只与反应器结构有关;随着水力停留时间的增加,反应器的扩散作用有增强趋势;填料A/A/O反应器的实际平均水力停留时间比A/A/O反应器更接近理论水力停留时间;填料A/A/O反应器的容积利用率比A/A/O反应器高;当HRT为6 h时,填料A/A/O反应器的死水区容积率最小,即此时反应器的容积利用率最高。

Taking Chlorides (Cl-) as the tracer, the residence time distribution (RTD) was adopted to study the effect of different HRT conditions on the hydraulic characteristic of A/A/O reactor and A/A/O filler reactor under the conditions of stable operation in water and sludge, and the results were compared and analyzed. The results show that the residence time distribution is only related with the reactor structure when there is no sludge in reactor;the diffusion of reactor is enhanced with the increasing hydraulic retention time;the actual average HRT of filler A/A/O reactor is more close to the theoretical HRT than that of A/A/O reactor;the volume utilization ratio of filler A/A/O reactor is higher than that of A/A/O reactor;when the HRT is 6 h, the dead zone volume rate of A/A/O filler reactor is minimum, that is to say the volume utilization ratio is highest.