级数的

In chapter 2, we studied the type of two kinds of general random Dirichlet series, and obtained the type in whole plane of these two kinds of random Dirichlet series is almost surely equal to the in whole plane of the corresponding Dirichlet series, as well as the type in horizontal line and in horizontal zone is almost surely equal to the type of the corresponding Dirichlet series in whole plane respectively.

几乎必然等于相应的Dirichlet级数在全平面上的型，以及在水平直线上和水平带形上的型也a.s。等于相应的Dirichlet级数在全平面上的型。

In this thesis, we define the notions of μ-semirings, A-semirings,*-μ-semirings and *-λ-semirings which extend the notions of inductive *-semirings. we also study the basic properties of these semirings and discuss the interrelation between them. Also, we discuss whether these semirings are closed for the construction of formal power series via a fixed point-theoretical viewpoint.

本文给出了归纳术*-半环及弱归纳*-半环概念的推广，即μ-半环、λ-半环、*-μ-半环以及*-λ-半环的定义；研究了这些半环的一些基本性质以及它们之间的相互关系；同时结合形式幂级数及不动点理论，讨论了这些半环关于形式幂级数构造的封闭性问题。

By means of traditional criterions of generalized integral's convergence and divergence, this paper, from the analysis of integrated function's nature, discovers a series of new criterions, which are briefer and more suitable: on the aspect of generalized integral for functions of a single variable, through the investigation of integrated function, together with the inner relationship between positive series and generalized integral in infinite interval under the condition of positive function, it gives several criterions of generalized integral's convergence and divergence, which are similar to positive series' criterions of convergence and divergence.

本文从分析被积函数本身所具的性质出发，借助传统的广义积分敛散性判别方法，发现1系列更简捷适用的新判别方法：单变量函数广义积分方面，通过考察被积函数，结合正项级数与正函数情形下无穷区间上广义积分的内在联系，给出了几个与正项级数敛散性判别法相类似的广义积分敛散性判别方法；多变量函数广义积分方面，着重讨论了广义2重积分和广义3重积分，结合被积函数的特点，运用比较判别法和柯西判别法，本文给出了判别广义2重积分收敛的1种新方法。

It is also the base of structure optimization.According to main object characteristics of structural dynamics design,structuraleigenveetor sensitivity computation is,first,be studied.A Neumann series expansionmethod is proposed in accordance with the modal method and is developed to agreewith the structure with rigid body modes.A rapid Neumann series expansion methodfor eigenvector sensitivity is formed;it may greatly improve the efficiency ofcomputing eigenvector derivation.

本文根据结构动力学设计的主要目标特性，首先进行了结构特征向量灵敏度分析研究：形成了计算特征向量灵敏度的Neumann级数展开法，并将其扩展到适用于具有刚体模态的结构特征向量灵敏度分析；研究出计算特征向量灵敏度的快速Neumann级数展开法，该方法大大提高了特征向量灵敏度分析的效率；建立了无需K-1运算的结构特征向量灵敏度分析的共轭梯度迭代法。

Firstly, a two-dimension tensor product space is constructed, in which reproducing kernel exists. Secondly a multiresolution analysis is constructed in the reproducing kernel space. Then an orthonormal basis in is obtained. Thus,the reproducing kernel space can be expressed by wavelets spaces. Wavelets approximation formula and sampling formula can also be obtained in the space. Besides, the wavelets approximation formula is simple and easy for calculation. That completes the theory of multiresolution analysis in finite interval fully and provides theoretical base and algorithm for application.

首先，构造二维张量积空间，并证明该空间具有再生核；其次在再生核空间中，建立多尺度分析，获得该空间的一个标准正交基，使得再生核空间可以由小波空间来刻画，进而得到小波级数和相应的采样公式，而且给出的小波级数形式简单易于数值分析，进一步完善了有限区间上的多尺度分析方法，也为实际应用提供了良好的理论基础和算法。

Based on the power series expansion of the general flexible matrix of the sub-system, a general expression of the dynamic stiffness matrix of the reduced model was derived from the exact expression of the reduced model for the direct substitution dynamic condensation methods. The general expression was also expressed as a power series of the unknown eigenvalues. After that, the validity and error of the Guyan condensation method were analyzed.

对于动力缩聚直接代入法，本文从降阶模型的精确表达式出发，利用子系统广义柔度矩阵的幂级数展开式，导出了降阶模型动刚度矩阵的一般表达，并把它表示为未知特征值的幂级数形式，在此基础上对 Guyan缩聚法的适用范围和误差进行了一般分析。

So using theory of power series to define and study function is an effective method of deal with question of function.

因此，用幂级数定义和研究函数是处理函数问题的一种有效的手段，并能给问题的解决带来一些方便，但是，幂级数只是函数的一种表示形式，只有与函数的其他表示形式相互协调和补充，才能真正简洁有效地处理函数问题。

In this paper,fuzzy complex numbers,limits of the sequence of fuzzy complex numbers,the metrical convergence and levelwise convergence,the continuity offuzzy complex functions,the calculus of fuzzy complex functions,theseries whose terms are fuzzy complex numbers,the series whose terms arefuzzy complex functions,the fuzzy complex measure and fuzzy differentialequation are investigated in details.All this may be a foundation forfurther researching fuzzy complex analysis.

本文对模糊复数、模糊复数列的极限、度量收敛与水平收敛、模糊复函数的连续性、模糊复函数的微积分、模糊复数项级数、模糊复函数项级数、模糊复测度及模糊微分方程理论进行了详细的研究，为模糊复分析的进一步研究打下一定基础。

By measuring the vapor-liquid equilibrium of ethanol- hexamethylene -NaI and verifying the data by means of ternary Gibbs-Duhem equation,the data of the vapor-liquid equilibrium of ethanol- hexamethylene -NaI were in agreement with both criterions.

假定NaI的平均活度系数可表示为盐浓度平方根(m1/2)的幂级数，采用全部合格的汽液平衡数据拟合出幂级数中的各项参数，从而获得在双液比固定条件下盐在非水混合体系中的活度系数。

The results show that the reactive characters of macro-kinetics are different from that of intrinsic kinetics under the same experimental conditions. The isobutene dimeric reaction follows 1.5 order reaction because of the effect of inner diffusion, and isooctane dimeric reaction follows zero order reaction.

结果表明，在相同的实验条件下，反应的宏观动力学行为与本征动力学行为有较大的不同，异丁烯的反应级数受内扩散影响由2级变为1.5级，异辛烯的反应级数则为0级。

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。