循环群

In section 4,we research the solvable groups of finite rank,and provethat the union set of all quasi-cyclic subgroups of G is a characteristic subgroup andthe Hirsch number hdoes not exceed n if G is a solvable group of rank n.Inparticular,for an arbitrary solvable torsion-free group G of rank n,we give theupper bound fof the derived length of G.

在第4节里，我们研究了有限秩的可解群，证明了这类群的所有拟循环子群构成它的一个特征子群，且对秩n的可解群G来说，其Hirsch数h≤n，另外，我们给出了秩n的无挠可解群的导出长度的一个上界。

In chapter 1 ,on one hand ,we give some sufficient conditions for a finite group to be supersolvable and nilipotent by using the properties of π-supplemented subgroups;For example: Theorem 3 Let G be a group, 2 ∈π, if every subgroup of G of prime order is contained in SE, every cyclic subgroup of G of order 4 is π-supplemented in G, then G will be supersolvable.

在第一章中，一方面我们利用π-可补子群的性质给出了有限群为超可解群及幂零群的若干充分条件；例如：定理3设G是群，2∈π，如果G的每个素数阶子群包含在SE中，G的每个4阶循环子群在G中π-可补，则G为超可解群。

Theorem 7 Let G be a group, if every subgroup of G of prime order is contained in Z_∞,2 ∈π, every cyclic subgroup of G of order 4 is π-supplemented in G,then G will be nilpotent.

定理7设G是群，G的素数阶子群包含在Z_∞中，2∈π，如果G的每个4阶循环子群在G中π-可补，则G为幂零群。

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。

In this paper, the author introduces the theory of cycylic group into integer linear programming problem.

本文将抽象代数中循环群的理论引入至整数线性规划问题。

Then G∈U.③ If every subgroup of prime order or of order 4 of a group G has a U-s-supplement or be S-quasinormal in G. then G is supersoluble.

若群G的每个素数阶子群和4阶循环子群在G中或有U-s-补充，或为S-拟正规，则G为超可解群。

According to the property that all states of a certain cellular automata can build a permutation group, we can design block cipher based on this property.5. One simple cellular automata and one simple linear feedback shift register have been implemented.

根据有些细胞自动机的所有状态可以构成一个循环群这一特点，指出了利用细胞自动机构造分组密码的方式。

Seven grapevine cultivars originated from different regions, i. e.'Carbernet Sauvignon' and'Queen of Vineyard'(two members of the Western Europe Cultivars Group),'Rizamat'(a member of the East Cultivars Group),'Red Double Taste'(a hybridized cultivar from Vitis vinifera L. and V. labrusca L.),'1103Paulsen','Red Globe'and 'Autumn Royal'(two new hybridized cultivars between cultivars groups which were warmly planted in recent years) were selected. After different drought stress, a combined measurement of gas exchange and chlorophyll fluorescence was conducted to evaluate the effects of drought stress to photoinhibition, as well as the role of photorespiration and xanthophyll cycle in photoprotective mechanism. After photorespiration and xanthophyll cycle were separately inhibited, the complementary effect of these two photoprotective pathways was discussed. Detached leaves of different grapevine cultivars, i. e.'Cabernet Sauvignon','Cabernet Franc','Merlot', and a rootstock,'1103Paulsen'were selected as materials, and photoinhibition degree, photorespiration activity as well as its photoprotective function under drought stress were studied. The results are as follows: 1. Under the same drought stress treatment, different photoinhibition degrees formed in different grapevine cultivars.

本研究选择不同起源地的葡萄品种－－包括西欧品种群的赤霞珠和葡萄园皇后、东方品种群的里扎马特、欧美杂种红双味、美洲种砧木1103Paulsen，以及近年来发展较快的品种群间杂交新品种红地球和皇家秋天等七个品种盆栽苗，在进行不同程度的干旱胁迫处理后，利用气体交换参数和叶绿素荧光参数同步测定的方法，研究干旱对其光抑制程度的影响，以及光呼吸和叶黄素循环组分在其光保护中的作用；并在分别抑制光呼吸和叶黄素循环的基础上，探讨了赤霞珠葡萄两种光保护机制的互补效应；同时选择不同的酿酒葡萄品种赤霞珠、品丽珠、梅鹿辄和砧木1103Paulsen的叶片，研究其离体干旱条件下光抑制程度、光呼吸活性及其光保护作用，结果发现： 1。

Otto Holder once worked over the structure of metacyclic group; G.

lder曾研究并给出了有限亚循环群的构造；G。

The effect of iner- tia weight factor on performance of PSO is discussed.The results show that the particle swarm optimiza- tion algorithm with nonlinear inertia weight factor is suitable to solve multivariahle optimum design prob- lem...

结果表明，带动态非线性惯性因子的微粒群算法对求解多变量的干燥优化设计问题具有方法简单、所需微粒群规模小、收敛速度快等特点；采用部分废气循环并进行优化设计对干燥系统的节能具有十分重要的意义，对湿空气出口温度和废气循环比进行优化设计，其年总费用比无废气循环的常规设计节省18.2%，比循环比为0.2时的常规设计节省12.6%。

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