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Therefore, in order to offer reference to readers, the paper systematically expound and prove the eigenvalue of special matrix that base on idempotent matrix, antiidempotent matrix, involutory matrix, anntiinvolutory matrix, nilpotent matrix, orthogonal matrix, polynomial matrix, the shape of , matrix, diagonal matrix, invertidle matrix, adjoint matrix, similar matrix, transposed matrix, numerical matrix, companion matrix, and practicality and superiority of the achievement was showed by some examples.

为此本文系统地阐述幂等矩阵，反幂等矩阵，对合矩阵，反对合矩阵，幂零矩阵，正交矩阵，多项式矩阵，形为：，矩阵，对角矩阵，可逆矩阵，伴随矩阵，相似矩阵，转置矩阵，友矩阵一系列特殊矩阵的特征值问题并加以证明，并通过一些具体例子展示所得成果的实用性和优越性。

What is the probability that the intersectingof two lines belongs to K? Finally, in this paper, we introduce the concept of double chord-power integrals ofa convex body in R~3, and some properties of double chord-power integrals of a convex body in R~3 are got.

最后，本文通过弦幂积分的理论体系和已经得到的平面上双弦幂积分的概念和性质，把双弦幂积分的概念推广到R~3上，得到了R~3上双弦幂积分的一些性质和结论。

Based the new definition of double chord-power intergral which the pair of lines intersect the convex body in integral geometry, this paper studies the relationship of double chord-power intergral and chord-power intergral.

本文给出了积分几何中的最新定义：随机直线偶与凸体相交的双弦幂积分概念，利用积分几何的分析方法，研究了双弦幂积分的对称性，次可加性等性质及双弦幂积分与弦幂积分的相互关系。

We provide a substitution box, exponential permutation which has much measurable security, and give a enumerating result and a fast algorithm of calculating such permutation. An almost perfect nonlinear exponential permutation with high algebric degree is proposed. with some discussion on how to select the parameters of such permutation. The experimental result shows us a conjecture that there exists no such permutation over even dimensional space. As a way of generating substitution boxes, we briefly point out the cryptographic weakness of the exponential functions derived from such permutation. We also present two new cryptographic indexes, fixed point and cyclic structure, on which we investigate the performance of such permutation. Finally, we give a viewpoint about the application of correlation immune functions in designing substitution boxes.

提供了一种可度量安全强度的代换盒－幂置换；详细阐述了幂置换的实现和计数问题；给出了一种计算幂置换的快速算法；从几乎完善非线性幂置换角度讨论了幂置换参数的选取，并提出了一种高次几乎完善非线性置换；通过试验给出了关于偶数维空间上几乎完善非线性幂置换的一个猜想；简要给出了由幂置换派生出的幂函数的密码局限性；针对幂置换，提出了两个密码安全指标：不动点和循环结构；证明了幂置换在这两个指标下的密码性能；简要讨论了相关免疫函数与代换盒设计的关系。

By analyzing the compute results of the integral-exponent-function and the fractional exponent function, conclusion is obtained that the second will improve the precise for its superiority in avoiding "Romberg" phenomenon.

通过对比分析整数次幂和非整数次幂拟合的计算精度，得出了非整数次幂逼近拟合能消除龙格现象，使用非整数次幂进行拟合可使精度提高的结论。

This paper is generaly devided into three parts,The first prepare knowledge,introduceing some conceptions asssociated with the polynomial ring and ring of power series such as power-zero element,inverse element and primitive polynomia and so on,prepare to introduce characters of power series.

本文主要分为以下三部分：首先介绍与环、多项式环、幂级数环密切相关的一些概念，如幂零元、可逆元、本原多项式等，为接下来介绍幂级数环的定义及其性质做下铺垫；然后着重讨论了环的性质，加深对多项式环与幂级数环的理解；最后讨论了多项式的性质，并将这些性质推广到幂级数环中，这也是本文的重点所在。

Finally, we study the PLDP(n, 2) and strongly nilpotent Jacobian matrices, and we prove that if the nilpotency index of JH for a power-linear map H of degree 2 is less than 4, then JH is strongly nilpotent, and consequently the rows of JH are linearly dependent.

此外，我们特别对线性多项式2次幂映射的相关性问题进行了讨论，为此，对强幂零的Jacobi矩阵进行了研究，刻画了Gorni-Zampieri对的幂零指数之间的关系，并证明了Gorni-Zampieri对保持强幂零性。

By using Jordan-Hlder type theorem of table algebras, we prove that table algebras satisfying nilpotent extension condition are nilpotent, which does not correspond to extension problems of nilpotent groups exactly.

本文研究了幂零表代数的一个有趣的性质，利用表代数的Jorda-Hlder型定理，证明了表代数满足幂零被幂零扩张仍是幂零的，但有限幂零群没有这样的扩张。

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。

The matrix =( xi, xjp having the e-th power of the greatest common P-divisorp of xi and xj as its-entry is called the e-th power GCD matrix on S. The matrix = having the e-th power of the least common P-multiple p of xi and xj as its-entry is called the e-th power LCM matrix on 5. We obtained the following results:(1) is nonsingular for any set S;(2) If S is an FC set, then the determined of has formula Det =Jpe(x1)...Jpe, where the function Jpe is the generalized Jordan totient function;(3) A formula of the inverse of is given when S is an FC set;(4) If S is an FC set, then |.

以_P的e次方为第i行j列元素的矩阵称为定义在S上的e次幂GCD矩阵，记为；以_P的e次方为第i行j列元素的矩阵称为S上的e次幂LCM矩阵，记为，我们得到了如下结果：①定义在集合S上的e次幂GCD矩阵是非奇异的；②若S是R上的FC集，则S上的e次幂GCD矩阵的行列式Det=J_p~e(x_1)J_P~e(x_2)…，J_p~e，其中J_p~e为R上的Jordan函数；③当S为FC集时，得到了的逆矩阵~-1的表达式；④证明了当S是FC集时，整除，即等于与R上另一个矩阵的乘积。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。