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Many sufficient and necessary conditions for a finite group to be solvable are given, which generalize some known results.

另一方面，我们研究了Sylow-子群的某些特殊子群的半覆盖远离性对有限群结构的影响，给出了一些有限群为p-幂零和超可解的充分条件。

Many scholars have studied these respects and given many important results, for example, the Hupperts famous theorem, namely, a finite group G is supersolvable if and only if every maximal subgroup of G has prime index; a finite group G is nilpotent if and only if every maximal subgroup of G is normal in G; a finite group G is solvable if and only if every maximal subgroup of G is c-normal in G (See it in [70]); etc.

很多学者都在这些方面进行了研究，得到了很多重要的结果，如：著名的Huppert定理，即有限群为超可解当且仅当它的所有极大子群的指数为素数；有限群为幂零当且仅当每个极大子群都正规；有限群为可解当且仅当它的极大子群均c-正规(见[70])；等等。

A combinatorial identity is obtained:=:~z 2r扟32-rn-iJ As main result of this paper, in section two, the convolution梩ype identities emerge from our discussion about Lagrange formula whom in author 憇 view can be taken as the inherent characteristic of Lagrange formula but have been ignored fOi so long time.

第一章对拉格朗日反演在Riordan群理论中的应用进行了介绍，证明了一个组合等式：第二章通过对拉格朗日反演定理本身的分析，得到一个对任意的形式幂级数都适用的三个拟卷积公式，这些公式体现了任意能在零点解析的函数的内在性质。

The process of replacing polynomials by formal power series is an example of a general device known as completion.

用形式幂级数来代替多项式的过程是被称之为完备化的这种一般手段的一个例子。

In chapter 4, we define the notions of μ-semirings and λ-semirings and also study the primary properties of them. Moreover, we discuss the interrelation between them and the formal power series semirings of them.

第四章给出了μ-半环和λ-半环的定义和基本性质，讨论了两者的一些内在关系并研究了它们的形式幂级数半环。

The third chapter introduces the notion of inductive *-semirings and weak inductive *-semirings. We give some basic properties of them and discuss the formal power series semirings.

第三章以归纳*-半环为重点，介绍了归纳*-半环及弱归纳*-半环的概念及基本性质，并讨论了归纳*-半环的形式幂级数半环。

In chapter 5, we define the notions of *-μ-semirings as well as *-λ-semirings and also study the primary properties of them. We discuss the interrelation between *-μ-semirings and *-λ-semirings, and their relation with those semirings introduced above. In the end, we study the formal power series semirings of *-λ-semirings as well as weak inductive *-semirings.

第五章给出了*-μ-半环和*-λ-半环的定义和基本性质，讨论了这两类半环之间以及它们与归纳*-半环、弱归纳*-半环之间的一些内在关系并研究了它们的形式幂级数半环。

The kinetics data were fitted with formate mechanism and power-law models, and the parameters in the models were estimated.

用甲酸盐机理模型和幂函数模型拟合实验数据，确定了本征动力学模型参数。

A relatively direct method is expounded in this paper to prove the termwise differentiation of power series, and a simple method is expressed to calculate the Fourier coefficient.

文摘：用比较直接的方法证明幂级数的和函数在收敛域内可以逐项微分的公式；并得到了计算傅立叶系数的一种简便方法。

Application of fractional power polynomial kernel function to kernel direct discriminant analysis.

分数次幂多项式核函数在核直接判别式分析中的应用

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。