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This paper studies the invariant, which is the linear preserving problem based on generalized inverse of matrices. The generalized inverse of matrices and the research status of preserving problems of generalized inverse are outlined. In the basis of deeply understanding the basic knowledge of linear maps, the definition, characteristics of generalized inverse and decomposition of matrix, the author analyzes the decomposition form of preserving idempotence and preserving tripotence in the PID, then studies on the linear maps form of preserving group inverses of symmetric matrices.

本文研究的不变量是矩阵广义逆线性算子的保持问题，概述了广义逆矩阵，广义逆保持问题的研究现状，在对线性映射的基础知识，广义逆矩阵的定义、性质和矩阵的分解深入理解的基础上，深入分析了保幂等、保立方幂等矩阵在主理想整环上的分解形式，继而研究了保对称矩阵群逆的线性算子形式。

In this paper the different methods ti find general term formulas of power series sum functions,by means of which coefficients are higher arithmetical of geometrical sequence .

利用差分法导出了求幂级数和函数的一个通项公式，用它能求出系数为高阶等差数列和高阶等比数列的幂级数∑∞n=0 anxn的和函数

Basing on the computing model of liquid viscous resistance of the sucker rod string, damping coefficient of power law flow for sucker rod string is created, using the condition of equivalent merit. Mathematics model and emulate model of the vibration of sucker rod sting are established.

以幂律流抽油杆柱液体粘滞阻力的计算模型为基础，并应用等功条件提出了幂律流条件下抽油杆柱阻尼系数的计算方法，并依此建立了聚驱抽油杆柱轴向振动的数学模型和仿真模型。

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。

Furthermore, there exists a minimum congestion with adaptive greed extent. Proposing the concept of congestion flexibility to represent what extent the congestion could be reduced, we also find that congestion in assortative network is less flexible than its disasss...

我们提出采用拥塞弹性的概念来表征网络拥塞可以降低的程度，进而发现相比于同配网络，异配网络更具拥塞弹性，而就幂率网络而言，幂率系数约为2.4时呈现拥塞弹性最大值。

In this paper, I first give two methods with which we can determine all the power integral bases in maximal real subfields of cyclotomic fields. Then I determine all the power integral bases for ?

本文首先给出了确定分圆域的极大实子域的幂元整基的两种方法；然后利用这两种方法找出了Qζ_m+ζ_m~(-1(m=5，7，8，9，12，16，20，24)的所有幂元整基。

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 allomatric scaling for the wet clonal plants including Phalaris arundinacea Scirpus planiculmis Phragmites australis and Phragmites Jeholensis did not show "1/4-power Rule". The variation of the allometric exponents between vegetative and reproductive ramets was mainly due to the different regulation mechanisms in different development stages. Moreover, the variation of the allometric exponents between plantsin wet or drought environments was the result of the long-time divergent response for ramets to moisture environments.

虉草、紧穗三棱草、芦苇和热河芦苇4种湿地根茎植物分株异速生长规律并不表现为&1／4或1／4整倍数&规律，营养株和生殖株异速生长幂值的差异是不同发育类型的分株生长调节机制不同的结果，水生生境和旱生生境分株异速生长幂值的差异则是分株对生境水因子差异长期趋异响应的结果。

In Chapter 2, starting from a generalization of Hensel's Lemma to non-commutative case, we introduce the Brauer characters and the generalized decomposition numbers, and construct a kind of maximal semisimple algebras; then, similarly to Puig's methods, we prove Brauer's Second Main Theorem over arbitrary fields; applying it to blocks with nilpotent coefficient extensions, a formula on characters of such blocks is given; the formula of characters of nilpotent blocks is just an easy consequence of the fomula.

在第二章中，我们将Hensel的引理推广到非交换的情况，以此为起点，定义了Brauer特征标和广义分解数，构造了一类极大的半单的代数，类似于Puig的方法，给出了任意域上Brauer的第二主要定理；作为该定理的应用，我们给出了具有幂零系数扩张的块的特征标公式，幂零块的特征标公式只是它的一个简单的推论。

The neutron emission intensities of spent fuel for different initial enrichment and different burnup and different cooling time were calculated, the power function relationship between burnup and neutron emission intensity was decided and verified after analysis, and the factors that affected the power function relationship were studied.

计算了不同初始富集度、不同燃耗、不同冷却时间的乏燃料的中子发射强度，经分析，证实了燃耗与中子发射强度间存在的幂函数关系，并对影响幂函数关系的各种因素进行了研究。

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。