幂

Next we obtain some group theoretic conditions for the existence of p-blocks with defect 0 in some special groups, for instance, in an extension group of a nilpotent group by a abelian group, in a p-nilpotent group, in a group with all subgroups of order p are conjugate, and so on.

其次我们给出了一些特殊群的亏零块存在的群论条件，如幂零群被交换群扩张的群，p—幂零群，p—阶子群均共轭的群等。

When fitness satisfies the bimodal distribution, the connectivity distribution of the network satisfies a generalized power-law form.

当Fitness服从一个双模分布时，网络的度分布是一个广义的幂律形式；当Fitness服从均匀分布时，网络的度分布是一个带有对数修正的广义的幂律形式。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

The results showed that there was power function relationship between the capillary water rise height and groundwater supply quantity and the time. There was linear function relationship between capillary water rise height and groundwater supply quantity and a power function between them and the time. There was linear function relationship between the capillary water rise velocity and the groundwater supply rate. Parameters could be calculated by measured data, which showed that it is possible to simulate capillary water rise process of homogeneous soil by Green-Ampt model.

结果表明：均质土毛管水上升高度和地下水补给量均与时间之间为幂函数关系，毛管水上升速度和地下水补给速率也均与时间呈幂函数关系，毛管水上升高度与地下水补给量之间呈明显的线性关系，毛管水上升速度与地下水补给速率也呈线性关系；通过试验资料可以推求有关参数；说明入渗条件下的Green-Ampt模型用于模拟均质土的毛管水上升过程是可行的。

Results of analysis show that Generalized Paris Law can consider the complex crack propagation in the material of the pavement structure. The fatigue life of the pavement increases with increasing thickness of surface layer in a power function. Use of a thicker surface layer may extend the service life of the asphalt pavement. The fatigue life increases with decreasing modulus of surface layer in a power function with a negative exponent. However, since reduced modulus would scarify the structural strength and might cause rutting-related distress, caution should be taken when using low modulus materials for improving fatigue performance of asphalt pavements. The fatigue life increases with increasing modulus of base material in a power function. However, the fatigue life can not infinitely increases with increasing modulus of the base.

计算与分析表明：广义Paris公式可以考虑沥青路面结构内材料复杂的裂缝扩展：沥青面层的疲劳寿命随着面层厚度的增加以幂函数的形式增加，适当增加沥青面层厚度可以提高路面的使用寿命；沥青面层的疲劳寿命随着面层材料模量的降低以负指数的幂函数形式增加；由于材料模量的降低将牺牲路面的整体强度并可能引起路面车辙类损坏，以此提高疲劳寿命的方法应慎重对待；沥青面层的疲劳寿命随着基层材料模量的增加呈幂函数的形式增加，但由疲劳方程可以看出，寿命并不是随基层材料模量的增加而无限的增加，疲劳曲线在经过一个上升段后，逐渐趋于一个常数值，这说明，这时基层模量对寿命已不作关键性贡献；随着底基层厚度的增加，面层的疲劳寿命近似地呈线性函数增加，但效果并不很明显。

So,the massive data acquired in the period from January to December in 2006 and authorized by CAIDA Skitter project were used to analyze the searched topological data at CAIDA(cooperative association for Internet data analysis) router level,thus describing the characteristics of the distribution of the degree s of nodes at router level.

针对目前对路由层面的Internet拓扑研究较少的问题，基于2006年1月至2006年12月采集的CAIDA Skitter项目授权的海量数据，对CAIDA路由层面拓扑探测数据进行了分析，描述了路由级节点度分布的幂率性。在此基础上计算出了更能体现网络拓扑层次性的各节点的核数，描述了节点核的幂率分布性质，进一步分析了节点核数与度之间的关系。研究表明，对低核节点，其度分布存在着幂率性质

By introducing the concepts of semiideal and regular semiideal with respect to a given subring, the general power rings and regular power rings are constructed and a number of examples of non-regular HX rings and non-regular power rings are cited.

通过引入了关于一个子环的半理想与正则半理想概念，构造出一般幂环与正则幂环，并具体给出了若干非正则HX环与非正则幂环的例子。

For this purpose, from 2004 to 2006 Professor Zhang create uniform limit power function space and strong limit power function space that are large, nice spaces.

Sarason在1984年提出了遥远概周期函数和缓慢振动函数并提出了一个公开问题，本文对这两个函数主要做了以下工作第一，将在一维空间中定义的遥远概周期函数和缓慢振动函数推广到高维空间，并指出其与一致极限幂函数和强极限幂函数等新的极限幂函数的关系。

After power-law being represented,some network topology models emerge.But these models do not involve any reference to underlying geometry.In order to solve this problem,this paper proposes an improved network topology model based on heuristically optimized trade-offs,which generates topology with the power of law,and has an appropriate amount of leaf nodes.It is closer to the real characteristics of the Internet.

幂法则提出以后，出现了一些符合幂法则的网络拓扑模型，但是这些模型没有充分考虑到底层节点的几何排列，针对这种情况，提出了一种改进的&启发式最优化平衡&网络拓扑模型，生成的拓扑图符合幂法则规律，且具有适当数量的叶子节点，更加接近互联网真实特征。

The spin-1/2 dimerized antiferromagnetic system is related to spin-Peierls tran-sition.There are still some discrepancy on the behavior of the ground energy densityand energy gap,such as pure power-law,logarithmic correction to the pure power-law in the uniform,integer powers in the dimerized limit,etc.

自旋S-1/2的二聚化反铁磁链与spin-Peierls相变有关，在对其基态能和激发能隙的临界行为描述上仍存在一些不完全一致的观点：如均匀极限的纯幂级数律，纯幂级数律的对数修正；二聚化极限的整数幂级数行为等。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。