FINITE p-GROUPS WHICH CONTAIN A SELF-CENTRALIZING CYCLIC NORMAL SUBGROUP

For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.

Behavior of Pile Group with Elevated Cap Subjected to Cyclic Lateral Loads

The pile group with elevated cap is widely used as foundation of offshore structures such as turbines, power transmission towers and bridge piers, and understanding its behavior under cyclic lateral loads induced by waves, tide water and winds, is of great importance to designing. A large-scale model test on 3×3 pile group with elevated cap subjected to cyclic lateral loads was performed in saturated silts. The preparation and implementation of the test is presented. Steel pipes with the outer diameter of 114 mm, thickness of 4.5 mm, and length of 6 m were employed as model piles. The pile group was cyclic loaded in a multi-stage sequence with the lateral displacement controlled. In addition, a single pile test was also conducted at the same site for comparison. The displacement of the pile cap, the internal forces of individual piles, and the horizontal stiffness of the pile group are presented and discussed in detail. The results indicate that the lateral cyclic loads have a greater impact on pile group than that on a single pile, and give rise to the significant plastic strain in the soil around piles. The lateral loads carried by each row of piles within the group would be redistributed with loading cycles. The lateral stiffness of the pile group decreases gradually with cycles and broadly presents three different degradation patterns in the test. Significant axial forces were measured out in some piles within the group, owing to the strong restraint provided by the cap, and finally lead to a large settlement of the pile group. These findings can be referred for foundation designing of offshore structures.

Locally Transitive Graphs Admitting a Group with Cyclic Sylow Subgroups

All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.

Splitting Extensions of Abelian by Hyper-(cyclic or finite) Groups (Ⅱ)

Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained： if G∈F, f（ ∞ ） include f（p）, f（p） ≠φ for each p∈π, and A has no nonzero F central ZG- images, then any extension E of A by G splits conjugately over A, and A has no nonzero F central ZG-factors.

Vacuum Solutions of Classical Gravity on Cyclic Groups from Noncommutative Geometry

Based on the observation that the moduli of a link variable on a cyclic group modify Connes' distance on this group, we construct several action functionals for this link variable within the framework of noncommutative geometry. After solving the equations of motion, we find that one type of action gives nontrivial vacuum solution for gravity on this cyclic group in a broad range of coupling constants and that such a solution can be expressed with Chebyshev's polynomials.

F-Decomposition of Noetherian Modules over Hyper-(Cyclic or Finite) Groups

Let Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite, G∈F, f(∞)f(p), f(p)≠ for each p∈π. The following conclutions are obtained: (1) if there exists a maximal submodule B of A such that A/B is F-central in G and B has no nonzero F-central ZG-factors, then A has an F-decomposition; (2) if there exists an irreducible F-central submodule B of A such that all ZG-composition factors of A/B are F-ecentric, then A has an F-decomposition.

Toric Heaps, Cyclic Reducibility, and Conjugacy in Coxeter Groups

In 1986, G.X. Viennot introduced the theory of heaps of pieces as a visualization of Cartier and Foata’s “partially commutative monoids”. These are essentially labeled posets satisfying a few additional properties, and one natural setting where they arise is as models of reduced words in Coxeter groups. In this paper, we introduce a cyclic version of a heap, which loosely speaking, can be thought of as taking a heap and wrapping it into a cylinder. We call this object a toric heap, because we formalize it as a labeled toric poset, which is a cyclic version of an ordinary poset. Defining the category of toric heaps leads to the notion of certain morphisms such as toric extensions. We study toric heaps in Coxeter theory, because a cyclic shift of a reduced word is simply a conjugate by an initial or terminal generator. As such, we formalize and study a framework that we call cyclic reducibility in Coxeter theory, which is closely related to conjugacy. We introduce what it means for elements to be torically reduced, which is a stronger condition than simply being cyclically reduced. Along the way, we encounter a new class of elements that we call torically fully commutative (TFC), which are those that have a unique cyclic commutativity class, and comprise a strictly bigger class than the cyclically fully commutative (CFC) elements. We prove several cyclic analogues of results on fully commutative (FC) elements due to Stembridge. We conclude with how this framework fits into recent work in Coxeter groups, and we correct a minor flaw in a few recently published theorems.

The F-Decomposition of Artinian Modules over Hyper-(Cyclic or Finite)Groups

Let (?) be a formation locally defined by f(P), G ∈ (?) and A a ZG-module, where p ∈ π = { all primes and symbol ∞}. Then a p-main-factor U/V of G is said to be (?)-central in G if G/CG(U/V) ∈f(p). In this paper, we have proved that: let (?) be a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A an artinian ZG-module with all irreducible ZG-factors of A being finite; if G ∈ (?), f(∞) ≡ f(p) . f(p)≠φ for each p ∈ π, A has an (?)-decomposition.

Average Probability of an Element Being a Generator in the Cyclic Group

All elements in the cyclic group are generated by a generator g. The number of generators of of , namely is known to be Euler’s totient function;however, the average probability of an element being a generator has not been discussed before. Several analytic properties of have been investigated for a long time. However, it seems that some issues still remain unresolved. In this study, we derive the average probability of an element being a generator using previous classical studies.

Surface functional groups and redox property of modified activated carbons

A series of activated carbons（ACs） were prepared using HNO_3,H_2O_2 and steam as activation agents with the aim to introduce functional groups to carbon surface in the ACs preparation process.The effects of concentration of activation agent,activation time on the surface functional groups and redox property of ACs were characterized by Temperature Program Desorption（TPD） and Cyclic Voltammetry（CV）.Results showed that lactone groups of ACs activated by HNO_3 increase with activation time,and the carboxyl groups increase with the concentration of HNO_3.Carbonyl/quinine groups of ACs activated by H_2O_2 increase with the activation time and the concentration of H_2O_2,although the acidic groups decrease with the concentration of H_2O_2.The redox property reflected by CV at 0 and 0.5 V is different with any kinds of oxygen functional groups characterized by TPD,but it is consistent with the SO_2 catalytic oxidization /oxidation properties indicated by TPR.

General Cyclic Orthogonal Double Covers of Finite Regular Circulant Graphs

An orthogonal double cover (ODC) of a graph H is a collection of subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC G of H is cyclic (CODC) if the cyclic group of order is a subgroup of the automorphism group of G. In this paper, we introduce a general orthogonal labelling for CODC of circulant graphs and construct CODC by certain classes of graphs such as complete bipartite graph, the union of the co-cycles graph with a star, the center vertex of which, belongs to the co-cycles graph and graphs that are connected by a one vertex.

Quantum Group Symmetry in Hofstadter Problem

We show that there is a quantum Sl_q(2) group symmetry in Hofstadter problem on square lattice.The cyclic representation of the quantum group is discussed and its application for computing the degeneracy density of the model is shown.

On Some Embedment of Groups into Wreath Products

In this paper, we showed how groups are embedded into wreath products, we gave a simpler proof of the theorem by Audu (1991) (see [1]), also proved that a group can be embedded into the wreath product of a factor group by a normal subgroup and also proved that a factor group can be embedded inside a wreath product and the wreath product of a factor group by a factor group can be embedded into a group. We further showed that when the abstract group in the Universal Embedding Theorem is a p-group, cyclic and simple, the embedding becomes an isomorphism. Examples were given to justify the results.

基于差异阈值循环分组的密钥生成算法

针对无线通信中通信双方提取的信道特征存在明显差异,导致双方的密钥生成速率和一致率较低的问题,提出差异阈值循环分组的密钥生成算法(TGKG)。首先,对信道状态信息(CSI)进行差异阈值分组,使任意组内元素间的间隔均大于该值,提高组内数据的差异,减小量化误差以降低密钥不一致率;循环分组只需一方进行,防止因数据误差导致的分组不一致。同时,提取信道系数的实部和虚部量化,增加量化比特数目,提高了密钥生成速率。通过概率论及信息论公式证明了所提算法在密钥不一致率、密钥可达速率和安全性3方面的优势。实验结果表明,所提算法在5 dB信噪比(SNR)条件下,通信双方的密钥不一致率约为2%,密钥生成速率约为142%。

水平循环荷载作用下群桩基础累积变形三维数值模拟

为进一步研究群桩基础水平累积变形特性,以及桩体自身因素、荷载因素、桩周土体因素等影响下的变化规律,结合USDFLD子程序的实现过程与ABAQUS三维建模过程,采用有限元计算结果对群桩累积变形特性进行研究。通过改变桩距、桩数、荷载入射角度、加载频率、土体初始弹性模量、桩-土界面摩擦系数等参数,进一步对群桩水平累积变形特性,及其在桩体自身因素、荷载因素、桩周土体因素等影响下的变化规律进行研究。数值模拟中经常忽略桩周土体弱化对群桩基础累积变形特性的影响,因此对如何在数值模型中实现土体软化也进行了研究。最终得到群桩水平累积变形特性,以及在各种影响因素下的变化规律,如在桩体自身因素的影响下,群桩承台水平累积变形随桩距与桩数的增加不断减小,荷载-位移滞回圈随桩数的减少越饱满,土体非线性越明显等变化规律。

关于一道抽象代数题的推广

用初等的方法证明了:设G是有限群,p是G的最小素因子,若对任意n∣|G|都有|{x∈G∣x^(n)=1}|≤(p-1)n,则G是循环群.推广了教材[1]第1.4节的习题3.

非对称循环温度荷载下2×2能源群桩倾斜性状离心机试验研究

在能源桩地源热泵系统运行过程中,能源群桩基础可能产生非对称温度分布,导致基础倾斜,对其正常使用构成不利影响因素。研究通过离心机试验,量化了砂土中2×2能源群桩在非对称循环温度荷载下的倾斜变形,试验在恒定竖向荷载下施加15个幅值为10℃的双向循环温度荷载,共开展10个试验,研究了群桩基础中能源桩非对称布置形式、竖向荷载大小以及筏板-土体相互作用对基础倾斜的影响。结果表明:非对称循环温度荷载导致基础倾斜不断累积并逐渐趋于稳定,在正常竖向荷载作用下(安全系数2.0),基础累积倾斜约1.8‰,小于规范限值2.5‰,群桩发生轴力重分布,最大轴力增加约40%初始值;随着竖向荷载的增加,基础累积倾斜有可能超过2.5‰。非对称循环温度荷载所导致群桩基础倾斜在设计中应予以考虑。

循环荷载作用下斜坡段桥梁群桩受力与变形特性试验研究

斜坡段桥梁群桩基与普通的平地桩基相比,受力环境更加复杂,动荷载对其造成的动力响应更加显著。为研究循环荷载和斜坡坡度对桥梁群桩受力与变形的影响,完成了一系列斜坡群桩水平循环加载室内模型试验,根据试验现象及监测数据对桩基变形、弯矩分布进行分析,并通过数值模拟和试验对比验证,探讨了动荷载作用下斜坡桩基的受力与变形特性。试验发现:当斜坡坡度为0°时,基桩前后土体所受扰动的范围基本相同,桩周土体出现圆形塌陷;当斜坡坡度≥20°时,桩前土体的破坏表现为明显隆起,桩后土体表现为滑坡开裂,桩周土体所受扰动的范围随坡度的增加而增大。斜坡段桥梁桩基的水平承载力会随循环加载次数和加载等级的增大而减小;坡度越大,群桩的正向水平承载能力减弱,负向水平承载能力增强。对于平地或斜坡群桩进行正向加载时,前排桩弯矩最大值均大于后排桩;随着循环加载次数增加,前排桩弯矩值随之增大,后排桩弯矩值随之减小。由于群桩效应对前后排桩受力分配的影响,前排桩最大土抗力值显著大于后排桩,且随着坡度增加桩侧土抗力显著降低,斜坡效应对桩基p-y曲线的影响较大。随着坡度由0°增大到30°,荷载-位移滞回曲线圈斜率降低,水平割线刚度减小。

具有指数p的子群的双循环群

研究了当有限群G是具有指数p的子群(即极大子群)的双循环群时的另一种结构,利用群G的2阶子群对循环子群的共轭作用导出了24阶双循环群的结构。

循环码的一种构造方法研究

运用循环码生成多项式的性质与定义,对循环码新的构造方法进行研究,确定了构造出的循环码的重量分布、重量谱、最小距离和自同构群。新的构造方法在一定条件下比现有文献中的构造方法更易得出循环码的自同构群等性质。