基于区间数度量的区间值模糊集合的归一化距离、相似度、模糊度和包含度的关系研究

区间值模糊集合的距离、相似度、模糊度和包含度及其关系研究是区间值模糊集合的一个研究热点.考虑到区间值模糊集合所表示信息的丰富性,本文使用区间数而非实数来刻画区间值模糊集合的距离,首先给出基于区间数度量的区间值模糊集合的归一化距离的公理化定义,然后通过五个定理详细研究了基于公理化定义的区间值模糊集合的归一化距离、相似度、模糊度和包含度之间的相互转换关系,最后,给出了若干公式来计算基于区间数度量的区间值模糊集合的相似度、模糊度和包含度.这些结论,一方面丰富了区间值模糊集合的信息测度(距离、相似度、模糊度和包含度)的内容,另一方面也为区间值模糊集合的近似推理、决策分析、模式识别等领域的应用提供了新方法和新理论.     

λ-矩阵的若干性质及应用

本文主要从数字矩阵具有的合同关系和相似关系等性质入手,定义并讨论λ-矩阵的合同关系和相似关系,并讨论它们的性质．     

Generalized CR Equation with a Singularity

This article deals with the solvability of the CR equation rw = (A₀(θ) ? O(r^α))w ? (B₀(θ) ? O(r^α)), where z = r e^iθ and where A₀, B₀ are continuous and 2π-periodic. The solutions of this equation are shown to be similar to those of the model equation rw = A₀(θ)w ? B₀(θ). The solutions of the model equation are completely characterized by using dynamical systems and Fourier techniques.     

一类带核的平行机排序问题

研究了一类工件具有相似加工时间的带核的平行机排序问题,运用ＬＰＴ算法求解,得到ＬＰＴ算法界的精确估计并对问题的某些情形,给出了界紧的例子。     

X衍射指纹图谱及相似度分析用于鉴别野生和栽培天麻

用X射线粉末衍射法建立了野生和栽培天麻及伪品羊角天麻的指纹图谱。通过数字信号处理技术提取天麻样品的特征信息,按2θ进行相似度计算和分析。天麻的XRD指纹图谱呈多峰重叠的弥散性峰,识别图谱的整体轮廓能区分真伪天麻。野生与栽培天麻的差异主要是2θ在5～10°和30～50°间,通过数字信号处理技术提取低频信号,能有效鉴别野生和栽培天麻。相似度的计算结果进一步表明方法的可行性。     

本质正规算子的模小紧相似

本文证明了一类本质正规算子Ａ＇（Ω＇;１）（Ｔ∈Ａ＇（Ω＇;１）,如果Ｔ满足（１）Ｔ,Ｔ｜Ｈ（Ｔ）分别是本质正规算子;（２）σ（Ｔ）＝Ω,ρＦ（Ｔ）∩σ（Ｔ）＝Ω;（３）ｉｎｄ（Ｔ－λ）＝－１,ｎｕｌ（Ｔ－λ）＝０,λ∈Ω＇;（４）σ（Ｔ｜Ｈ（Ｔ））是一完全集,这里Ω＇是一连通的解析Ｃａｕｃｈｙ域, Ｈｌ（Ｔ）＝ Ｖ｛ｋｅｒ（Ｔ－λ）＊：λ∈ρｒｓ－Ｆ（Ｔ）｝是模小紧相似的．     

Laminar free-convective heat transfer from a vertical isothermal plate to water at low temperatures with variable physical properties

All studies concerning laminar free convection along a vertical isothermal plate in water at low temperatures have been conducted assuming constant dynamic viscosity and thermal conductivity both taken at ambient or film temperature. In this study the problem has been treated taking into account the temperature dependence of all water physical properties. The results are obtained with the numerical solution of the boundary layer equations. The variation of μ and k with temperature has a small influence on wall heat transfer but a strong influence on wall shear stress. These quantities show a significant reduction at density extremum.     

基于模糊聚类分析和曲线拟合的FTIR不同产地鸡骨草、毛鸡骨草鉴别分析

利用傅里叶变换红外光谱技术结合模糊聚类分析法和曲线拟合对鸡骨草、毛鸡骨草进行产地鉴别。选用曼哈顿距离单位计算的相异度聚类分析结果最优,5个产地鸡骨草都可完全区分开来,毛鸡骨草则只能鉴别出3个产地,南宁和钦州2个产地发生重叠;为了进一步鉴别不同产地鸡骨草和毛鸡骨草,对鸡骨草和毛鸡骨草平均红外谱图中1 034 cm-1吸收峰进行曲线拟合,野生鸡骨草拟合出11个子峰,其他各产地鸡骨草均只能拟合出9个子峰,上林产毛鸡骨草拟合出9个子峰,其他各产地毛鸡骨草均只能拟合出8个子峰,而且不同产地鸡骨草和毛鸡骨草拟合出的子峰位置和归一化强度都不完全相同;模糊聚类分析法和曲线拟合法有机结合能够使产地鉴别结果更加准确。     

关于集合的粗相似度量的注记

举例说明文献"集合的粗相似度量"中定理3.1(2)的结论是不严谨的,从而给出一个严谨的结论。     

A study of the similarities between topics

This paper presents a new methodology whereby the relationships among points of interest appearing in Internet Web pages may be graphically represented. This is done by quantifying the various points and representing them graphically using an intuitive interpretation of the similarity of sets. The similarity or interrelationships existing among various lines of research may be studied based on information taken from the Web pages using function taken from Learning Theory. A visual analysis of those interrelationships has been applied to the field of machine learning during the time interval May 2003–May 2004.