数幂

Throush the interlace series type linear differential equation,coefficient containing three negative number of times,power function and arrangement number can be changed into the linear differential equation of successive integral.

通过把系数含有负三次幂函数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程，找出了求这类方程通解的方法与理论，把所得定理给出了严格的证明，并将其推广，同时通过实例介绍了它的应用。

Calculation formulae for real number order derivative and integral of logarithmic functions and power functions have been obtained which are the important references to calculate real number order calculus of any other functions.

计算得出了对数函数、幂函数的任意实数阶导数及积分的完整计算公式，它们是推导其它函数任意实数阶微积分公式的重要参照式。

Limit, derivative, integral power series expansion, differential equation solving certain other.

求极限、导数、积分，幂级数展开，求解某些微分方程等。

In chapter 6, we study the dimension of a code associated with a difference set and we also study how to construct Ramanujan graph by using difference sets, we obtain:(1) let q≡1 (mod 4) be a prime power, p be a prime such that p｜〓, then the p-rank of the quadratic residue partial difference set in the finite field GF is 〓.

在第六章中，我们研究差集对应的码的维数及用差集构造Ramanuian图，得到了：（1）设q≡1（mod 4）是素数幂，素数p｜〓，则GF中的二次剩余部分差集的p-秩是〓。

That calculated the result of raising a given number to a given power to use appropriate using declarations rather than accessing library names through a std:: prefix.

用适当的 using声明，而不用 std：：，访问标准库中名字的方法，重新编写第 2.3节的程序，计算一给定数的给定次幂的结果。

This dissertation involves the study of the growth dynamics of colloidal particles under unequilibrium and irreversibility condition. Firstly, it is of interest to investigate whether the ideal diffusion or reaction-limited aggregation universal behavior can be observed for the initially polydisperse practical system of basic yttrium carbonate as well. The fractal structure of basic yttrium carbonate aggregate cluster was observed using transmission eletron microscopy. The aggregation kinetics of basic yttrium carbonate colloids was studed using dynamic 1ight-scattering techniques. At 1.00mol/l NaCl solution the fast diffusion-limited aggregation behavior was observed with an increase in the aggregate size over time described by a power law. The aggregates are characterized by a fractal dimension D=1.82. The disordered and ramified cluster is consisted of primary colloidal particles and tenuous and more open. These are in good agreement with those observed for other colloidal system such as colloidal gold (1.86), silica (1.85) and polystyrene latex (1.82) in diffusion-limited aggregation from the static and dynamic light scattering by Lin. Therefore ideal diffusion-limited aggregation behavior can be observed in practical polydisperse system as well. Smoluchwski and fractal theories were used to obtain the aggregation rate constant for initially polydisperse system for the first time.

本论文研究胶粒的非平衡不可逆聚集动态学，分为两个部分，第一部分是通过实验研究一个新的初始多分散的碱式碳酸钇胶粒实际体系中，聚集标度性质的普适性，即使用透射电子显微技术观测聚集粒子簇的分形结构，使用动态激光光散射研究碱式碳酸钇胶粒的聚集动力学，胶粒带电而产生静电排斥作用使得碱式碳酸钇胶粒处于稳定状态，当加入电解质NaCl溶液时，碱式碳酸钇胶粒间的Debye-Hückel屏蔽距离缩短，从而降低静电排斥能垒，引起胶粒发生不可逆聚集，加入电解质NaCl的浓度为1.00mol/l时，碱式碳酸钇胶粒进行快速聚集，经历扩散控制聚集机理，形成结构疏松、更为开放的分形聚集粒子簇，其分形维数为1.82，碱式碳酸钇胶粒聚集增长动力学遵循幂函数增长规律，与Lin等使用静态激光光散射和动态激光光散射测量硅胶(1.85)、金胶(1.86)和聚苯乙烯胶乳(1.82)在扩散控制聚集状态形成聚集粒子簇的分形维数值以及粒子簇聚集增长的动力学规律相一致，表明胶粒聚集标度性质的普适性质在初始多分散的实际体系中也是存在的，首次由动态激光光散射的实验数据得到初始多分散胶粒分形粒子簇的聚集速率常数，并且其值与Smoluchowski聚集速率理论预期相符。

In the fifth chapter,we study dipolarizations in some quadratic Lie algebras.Inthe first section,we obtain some results on the classification of dipolarizations in gen-eral quadratic Lie algebras,and prove that there exist dipolarizations in the solvablequadratic Lie algebras whose Cartan subalgebras consist of semisimple elements.

第五章讨论了某些二次李代数的双极化，在第一节中，我们给出了二次李代数的双极化的一些分类结果；特别证明Cartan子代数是由半单元组成的二次李代数上存在双极化，第二节确定了四维扩张Heisenberg代数的所有双极化，在第三节中，我们构造了2n+2维扩张Heisenberg代数的六类双极化，我们发现两个不同于半单李代数情形的有趣事实：（1）在扩张Heisenberg代数上同时存在对称和非对称双极化；（2）对应于扩张Heisenberg代数的双极化的特征元有的是半单的有的是幂零的。

In the second place, we introduce some relativeconceptions of topos and weak topos, including category, topos, middleobject, weak topos, power object and pullback lemma.

第二部分是预备知识，首先介绍了区间数的概念及其运算，在此基础上引入了区间值模糊集的概念、运算以及它与直觉模糊集之间的关系；然后介绍了topos和弱topos的相关概念，包括范畴、topos、中间元、弱topos、幂对象和拉回引理。

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。