数幂

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。

In 2000, F. LUCA proved that Fermat number are anti-sociable numbers, and in 2005, M. H. LE proved all powers of 2 are anti-sociable numbers. We have used the method of M. H. LE to obtain some new results of the anti-sociable numbers. For every integer n containing prime divisors that are 1 mod 4, let p mod 4 be an arbitrary prime divisor of n. There is at least one anti-sociable number in n^2, p^2n^2, p^4n^2, and p^6n^2. Therefore we can prove that anti-sociable numbers have positive density in perfect square numbers. We also give a method to find the exact anti-sociable numbers.

LUCA证明了Fermat数都是孤立数；2005年，乐茂华教授证明了2的方幂都是孤立数，用乐茂华教授的方法给出孤立数的一些新的结果：对于任意含有4w+1型素因子的正整数n，设p为n的任意一个4w+1型素因子，则在n^2，p^2n^2，p^4n^2，p^6n^2里至少有一个是孤立数，因此可以证明孤立数在完全平方数里有正密度，另外也给出求解确定孤立数的方法。

The results showed that the pressure and pressure derivative of non-newtonian fluid is higher than newtonian one;The power index is more smaller,the pressure and pressure derivative is more higher;The effect of skin factor on transient was different from that of power index;The storativity ratio and inter-porosity flow factor is just same as the newtonian fluid,and the effect of outer-boundary on transient pressure is different from that of newtonian fluid.

结果表明，非牛顿流体的压力及压力导数都明显高于牛顿流体；幂律流指数越小则压力和压力导数越大；表皮系数和非牛顿流体幂律流指数对压力响应的影响有着明显的不同；而弹性储容比和窜流系数的影响和普通三重介质相同，只是由于非牛顿流体的影响其"凹陷"的位置升高；外边界的影响也和牛顿流体的情况明显不同。

In this paper employing periodic function of complex function, a power function and a logarithmic function were constructed to obtain Principle Quantum Number , Angular Quantum Number , Magnetic Quantum Number , Spin Quantum Number and the relations between them.

利用复变函数中周期函数结构，构造了一个幂函数和一个对数函数。给出了电子的主量子数、角量子数、磁量子数和自旋量子数，以及它们之间的关系。

127 Chapter 1 The History and Future of Computers 3.1.2 Positional Notation The exponential powers of the positions are critical for understanding numbers in other numbering systems.

位的指数幂在理解其他计数制中的数时是个关键。基数小数位的指数幂在理解其他计数制中的数时是个关键。

8 Chapter 3 Number Systems and Boolean Algebra 3.1.2 Positional Notation The exponential powers of the positions are critical for understanding numbers in other numbering systems.

位的指数幂在理解其他计数制中的数时是个关键。基数小数位的指数幂在理解其他计数制中的数时是个关键。

In order to solve the derivation of power exponent function,this paper has studied the derivation regulations on power function from the perspective of the differentiation of multi-variable function and in accordance with the derivation laws on multi-variable complex function.

为解决幂指函数的求导问题，从多元函数微分法的角度出发，根据多元复合函数的求导法则，探索幂指函数求导的规律，并揭示了幂指函数与幂函数及指数函数导数间的关系，给出了幂指函数求导的另一种方法。

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

On the basis of the definition of matrix traces , this paper discusses their characteristics at first and then according to the norm of the F of square matrix and Cauchy-Schwarz inequality gives how to prove the zero matrix, unsimilar matrix, number cloth matrix, column matrix idempotent matrix and non-equality matrix.

根据矩阵迹的定义，首先给出了矩阵迹的性质，然后依据方阵的F—范数定义Cauchy—Schwarz不等式，给出了零矩阵，不相似矩阵，数幂矩阵，列矩阵，幂等矩阵及矩阵不等式的证法。

It is important that you understand the difference between positive and negative exponents.

懂得正幂数和负幂数的区别是很重要的。

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。