Ranking fuzzy numbers with integral value

Ranking fuzzy numbers is important in decision making. Since very often the alternatives are evaluated by fuzzy numbers in a vague environment, a comparison between these fuzzy numbers is indeed a comparison between alternatives. This paper proposes a method of ranking fuzzy numbers with integral value. The method, which is independent of the type of membership functions used and the normality of the functions, can rank more than two fuzzy numbers simultaneously. It is relatively simple in computation, especially in ranking triangular and trapezoidal fuzzy numbers. Further, an index of optimism is used to reflect the decision maker's optimistic attitude. Discussion on comparative advantages is included.  

关于 Hilbert积分不等式(英)

本文通过引入一个适当的形如F（x，y）的正定二次型证明了Hilbert积分不等式可以得到改进．利用这一结果，Widder不等式得到了加强，并且建立了广义的Hardy－Littlewood不等式．  

一类奇异积分和Cauchy型积分关于积分曲线的稳定性

本文讨论了当任意给定的ｆ（т，ｔ）在某个区域Ｅ内属于Ｈ类时，奇异积分Ｉ（ｆ）（ｔ）＝１／πｉ∫Γｆ（т，ｔ）／т－ｔｄт（ｔ∈Г），在封闭或开口光滑曲线Г∪→Ｅ发生光滑扰动时的稳定性，并给出了相应的误差估计。作为应用，我们还讨论了当ψ（ｙ）在Ｅ内属于Ｈ类时，Ｃａｕｃｈｙ型积分Φ（ψ）（ｚ）＝１／２πｉ∫Γψ（ｔ）／ｔ－ｚｄｔ（ｚ不属于Γ），在封闭光滑曲线Γ∪→Ｅ发生光滑扰动时的稳定性及误差估计。  

天津市各区县经济发展水平评价

本文试用主成分分析方法，对天津市18个区县的经济发展情况做出综合评价，分析了各区县在天津的经济地位。并提出了利用聚类分析的方法来评价各区县经济地位等级的设想。  

关于积分中值定理的一个一般性结果

本文旨在研究积分中值定理中间点当区间长度趋于零时的渐近性质 ,得到一个具有一般性的新结果  

A Generalized Discrepancy and Quadrature Error Bound

An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case. This error bound takes the form of a product of two terms. One term, which depends only on the integrand, is defined as a generalized variation. The other term, which depends only on the quadrature rule, is defined as a generalized discrepancy. The generalized discrepancy is a figure of merit for quadrature rules and includes as special cases the -star discrepancy and that arises in the study of lattice rules.

  

关于变分学中逆问题的研究

本文研究了变分学中的逆问题。通过变积概念的引入，给出了系统地研究变分学中逆问题的一种新途径。将这种方法应用于线弹性动力学和粘性流体力学中，建立了各自的变分原理和广义变分原理。  

Boundedness of commutators on Hardy type spaces

Let [b, T] be the commutator of the function b ∈ Lipβ(Rn) (0 ＜β≤ 1) and the CalderónZygmund singular integral operator T. The authors study the boundedness properties of [b, T] on the classical Hardy spaces and the Herz-type Hardy spaces in non-extreme cases. For the boundedness of these commutators in extreme cases, some characterizations are also given. Moreover, the authors prove that these commutators are bounded from Hardy type spaces to the weak Lebesgue or Herz spaces in extreme cases.  

一种修正的求总极值的积分—水平集方法的实现算法收敛性

1978年，郑权等提出了一个积分型求总极值的概念性算法及Monte-Carlo随机投点的实现算法，给出了概念性算法的总极值存在的充分必要条件，但是其实现算法收敛性仍未解决，1986年，张连生等给出离散均值－水平集的实现算法，并证明了它的收敛性。本文给出修正的积分－水平集方法，用一致分布搂九值积分逼近水平集构造实现算法，并证明了算法的收敛性。  

一族可积Hamilton方程

本文利用屠规彰格式，导出了一族新的可积系，包含４个未知函数，具有双Ｈａｍｉｌｔｏｎ结构，且以ＴＣ族为特例。