一类平面映射的解析不变曲线

研究了复合迭代函数方程所代表的一类不变曲线的解析解,通过构造辅助方程的幂级数解,从而获得原方程的解析解.     

具有最优代数免疫阶布尔函数的构造

给出了代数免疫阶,汉明重量,非线性度和相关免疫阶之间的关系,得出构造密码学综合性质较优的布尔函数的一种思想,给出构造方法,并给出了实例.     

共轭子群的几个性质

由于有限群子群的乘积不一定是子群,如何判断子群的乘积为子群是一个重要的问题.本文主要证明有限群的所有共轭子群的乘积是子群,并且给出了共轭子群的几个性质.     

一个有限环的零因子图性质

研究了二次代数整数环Z[u]={a＋bu｜a,b∈Z}（其中u=1/2＋√11/2 i）的模n剩余类环的零因子图的有关性质,讨论了当n不同情况时,它的直径、围长的取值情况．     

非对易空间马鞍势下二维量子谐振子能级差

我们在非对易空间中,利用不变本征算符（IEO）方法,对非耦合、动量耦合、坐标耦合以及坐标-动量交叉耦合四种情况马鞍势下的二维量子谐振子能谱进行了求解.计算结果表明IEO方法能较好地解决以上问题,并且在动量耦合、坐标耦合两种情况下指出能级差△E与耦合系数之和有关,不区分系数之间相等与否.     

基于支持向量机的栗属树种分类研究

形状特征是物体识别的重要依据。同时,分类算法的选择也将对识别的性能造成很大影响。围绕上述两个问题,以栗属树种的果实图像为例,在准确分割出目标图像的基础上,分别应用不变矩和边界矩提取其形状特征值,并使用支持向量机算法对栗属树种果实图像进行分类。实验结果表明:基于支持向量机的栗属树种果实图像分类识别准确率可达到87.5%,识别的结果较为理想。     

A novel texture clustering method based on shift invariant DWT and locality preserving projection

We propose a novel texture clustering method. A classical type of （approximate） shift invariant discrete wavelet transform （DWT）, dual tree DWT, is used to decompose texture images. Multiple signatures are generated from the obtained high-frequency bands. A locality preserving approach is applied subsequently to project data from high-dimensional space to low-dimensional space. Shift invariant DWT can represent image texture information efficiently in combination with a histogram signature, and the local geometrical structure of the dataset is preserved well during clustering. Experimental results show that the proposed method remarkably outperforms traditional ones.     

From arithmetical thought to algebraic thought: The role of the “variable”

The introduction of the concept of the variable represents a critical point in the arithmetic–algebraic transition. This concept is complex because it is used with different meanings in different situations. Its management depends on the particular way of using it in problem-solving. The aim of this paper was to analyse whether the notion of “unknown” interferes with the interpretation of the variable “in functional relation” and the kinds of languages used by the students in problem-solving. We also wanted to study the concept of the variable in the process of translation from algebraic language into natural language. We present two experimental studies. In the first one, we administered a questionnaire to 111 students aged 16–19 years. Drawing on the conclusions of this research we carried out the second study with two pairs of students aged 16–17 years.

定向量子余代数与其自身张量积上的定向量子余代数结构(英文)

定向量子代数(定向量子余代数)是拟三角Hopf代数(余拟三角Hopf代数)的推广并且可以得到定向1-1缠绕、定向扭结和连接的正则合痕不变量.令(H,σ,D,U)为域k上的定向量子余代数,则(H(×)H,ψ,D(×)D,U(×)U)为余代数H与其自身张量积上一个平凡的定向量子余代数结构,其中ψ(a(×)b,c(×)d)=ψ(a,c)ψ(b,d).本文给出余代数H H上的一种定向量子余代数结构(H(×)H,σ,D(×)D,U(×)U),其中σ(a b,c d)=σ-1(D1,a1)·σ(a2,c1)σ-1(d2,b1)σ(b2,c2).进一步得到定向量子余代数与其自身张量积上的一种非平凡的定向量子余代数结构,这一结果对偶于Radford发表于2007年的一文中的结论.理论上本文的结果对于构造定向扭结和连接不变量是非常重要的.     

λ-矩阵的最大公因式与不变因子间的关系及其性质

定义了λ-矩阵的最大公因式,讨论了其性质;证明了λ-矩阵的最大公因式与不变因子间的关系：d,（λ）=gcf（Ai（λ））．最后指出,利用这一关系可彻底解决λ-矩阵化标准形过程中存在的盲目性问题．