小群

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

The results of three cladistic methods showed: the consanguinities of different genera in a same tribe were closer, such as Chalcis and Conura, Trigonurella, Megalocolus and Trigonura; the consanguinities of genera between different tribes were farther, such as Chalcis and Brachymeria, Dirhinus and Hallichella; Chalcis, Conura, Brachymeria and Epitranus were the most primitive relatively, Tainaniella and Oxycoryphe were the most evolutional, the consanguinities were the farthest between the former and the latter; the genera with the closest consanguinities were: Tainaniella and Oxycoryphe, Proconura and Nipponochalcidia, Chalcis and Conura, Megalocolus and Trigonura, they were regarded as 4 pairs of sister groups.

三种支序分析方法一致支持的结果为：同一族内成员之间亲缘关系较近，如小蜂属和卡诺小蜂属，微三角小蜂属、细尾小蜂属和三角小蜂属之间；不同族内成员相互之间的亲缘关系则较远，如小蜂属和大腿小蜂属之间，角头小蜂属和截胫小蜂属之间；小蜂属、卡诺小蜂属、大腿小蜂属和脊柄小蜂属相对最为原始，而泰内小蜂属和背突小蜂属最为进化，前者和后者之间的亲缘关系最远；亲缘关系最近的有：泰内小蜂属和背突小蜂属，泊卡小蜂属和日本小蜂属，小蜂属和卡诺小蜂属以及细尾小蜂属和三角小蜂属，它们各自之间都构成姊妹群关系。

Let F=LF be a s-closed local formation such that every minimal non-F-groups is solvable. It is proved that 1 If every cyclic subgroup of of order 4 and every minimal subgroup of G are contained in, then G is a F-group. 2 If there exists a normal subgroup N of G such that G/N∈F and every cyclic subgroup of N of order 4 is weakly c-normal in G and every element of N of prime order is contained in Z(superscript f subscript ∞), then G is a F-group.

设F=LF是一个子群闭的局部群系，满足每个极小非F-群是可解群，证明了：1如果G的任意极小子群和任意4阶循环子群都含于Z中，那么G是F-群；2如果存在G的正规子群，使得G/N∈F，且N的任一4阶循环子群在G中弱c-正规，N的任一素数阶元含于Z中，那么G是F-群。

Firstly, it's proved that the base of free monoid is unique, and that the equation of a base, a generating set and a irreducible generating set in the semigroup with length; Secondly, it's given the relation of a primitive word and a word of indecomposable--Let and is indecomposable, then is primitive ;And by using the length's method and chart,some properties of primitive word have been proved and the solutions of the equation , are discussed; Lastly, on the base of some proposition in Free monoids and Languages ,the proofs of some properties are improved by instruction. For example: Let be a primitive word over X, where .Then is a code. And let then if and only if {} is a code.

首先，讨论了含幺半群中基的基本性质及基与最小生成元集的联系，并给出了含幺半群中基、生成元集、不可约生成元集三者之间的关系；证明了在有唯一长度的半群S中，不可约生成元集、基、最小生成元集三者之间的等价关系；其次，讨论了字的组合与分解性，得出了字的本原性与不可分解性之间的关系---若为不可分解的，则一定是本原的，反之，不一定真；并运用图示法证明了字的可补性理论，讨论了方程，的可解性；在此基础上，用归纳法进一步证明了本原字与码的有关命题--若是X上的一个本原字，其中，则是一个码；若则当且仅当{}是一个码。

The results show that small world network model could explain the big change of intensiveness and connectedness in forming process. And individual selection value function could explain the stable intensiveness, connectedness in growing and mature process. Combined the both, the characteristics of the whole process could be reflected.

研究表明，小世界网络模型模拟的集群网络具有集群形成期网络整体密集性和连通性剧烈变化的特征，而个体选择价值函数模型可以解释集群网络的成长期、成熟期的密集性和连通性趋于稳定的特征，将2种演化规则相结合，则可以反映集群网络从形成期到成熟期的各生命周期特征。

Wear degree decreases, and the wear particle distribution curves become protrusive and precipitous gradually in the initial stage.

通过分析铜合金销与碳钢盘在干摩擦条件下相互对磨所产生的磨粒群和销试样磨损量，发现磨粒的累积分布和微分分布特性随磨损时间的变化而变化：在磨损开始阶段，磨损程度逐渐减小，磨粒群分布曲线由平缓变得逐渐凸、陡；达到磨损平衡状态后，磨损率达到最小，磨粒群微分布曲线的幅值达到最大，横向宽度达到最小；随着销与盘间互适性变弱，磨损程度增大，磨粒分布曲线变得越来越平缓，横向宽度逐渐增大；磨粒分布曲线随磨损时间的变化规律与磨损率随磨损时间的变化规律有明显的对应关系，可为科学诊断和预测摩擦学系统状态提供有用信息。

Some important traits, i.e., oil and protein contents, 100-seed weight, and the resistance of soybean to Bean pyralid in F2 population, the resistance of soybean to soybean mosaic virus with strain Sa in the F2:3 population, and the number of branches, the number of main-stem nodes and plant height in the F2 and F2:3 populations, were measured.

主要结果如下： 1。连锁图总长度为1091.34cM，标记间平均距离为16.53cM。利用公共遗传图谱，将21个连锁群与大豆染色体相对应。每个连锁群上的标记数目在2-8个之间，连锁群长度在17.71-129.33cM之间。相邻标记间平均间距最大的连锁群为D1b，为43.55cM；最小平均间距的连锁群为M，为13.86cM；有20个区间长度大于20cM。

According to disadvantage of AS that the speed low of convergentiss and easily entering the stagnation,improving the AS in some aspect by the way that importing pheromone windows that the value of pheromone cannot exceed the window,only deposit the pheromone on the edge that belongs to the iteration shortest solution path,releasing additional pheromone to the edge belongs to the so-far shortest solution path,judging the situation of convergent and to reinitialize pheromone,optimizing the solutions by local search procedure at the end of every iteration,modifying the transition probability by add some problem specific parameters and so on.

本文主要运用蚁群优化算法(Ant Colony Optimization，ACO)来求解VRP。针对蚁群算法收敛性比较差，易于停滞的缺陷，通过使用信息素窗口限制、信息素的最大最小值，只更新信息素迭代中最好解，增加了精英的蚂蚁，信息素重新初始化之前先判断出汇聚情况，在每次迭代过程中加入局部的搜索进行优化，在对蚁群算法进行了优化时考虑选择概率当中加入与问题的相关参数等措施，从而使蚁群算法的收敛性得到大大提高，避免了算法的停滞现象。

By using properties of quasi-regular semigroups and left central idempotents, some statements are proved. Let S be a quasi-right semigroup, then (1) S is a quasi-completely regular semigroup;(2) RegS is a completely regular semigroup;(3) R(superscript *) is the smallest semilattice congruence on S;(4) Each R-class T(subscript α) on RegS is a right group;(5) T(subscript α)G(subscript α)×E(subscript α), where G(subscript α) is a group, E(subscript α) is a right zero semigroup.

利用拟正则半群和左中心幂等元的性质，证明了S为拟右半群时，(1) S为拟完全正则半群；(2) RegS为完全正则半群；(3) R为S上的最小半格同余；(4) RegS上的每个R-类T为右群；(5) TG×E，其中G为群，E为右零半群。

Five floral organ identity genes of Mussaenda pubescens were cloned and their expression patterns among different organs were detected by RT-PCR. The AP1 homologue, MupAP1, is expressed in enlarged and small sepals, petals and stamens, carpels and fruits; the SEP3 homologue, MupSEP is strongly expressed in all floral organs and weak in leaves as well. Two of the B class gene, AP3 homologue MupDEF and TM6 homologue MupTM6, were detected expressed in all floral organs, however, the other B class gene, MupGLO, homologous to PI, were detected expressed in small sepals, petals and stamens, carpels and fruits, but not in enlarged sepals.

本论文选殖出五个毛玉叶金花花器同源基因，其中A群基因AP1的同源基因MupAP1在两型花萼、花瓣及雄蕊、心皮、果实中有表现，E群基因SEP3的同源基因MupSEP则在所测部位均有表现，B群基因中，AP3的同源基因MupDEF及TM6的同源基因MupTM6在两型花萼、花瓣及雄蕊、心皮及果实中均有表现，另一个B群基因，PI的同源基因MupGLO则在花瓣及雄蕊、心皮、果实及小花萼中有表现，但在膨大花萼中并没有侦测到表现。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失