Fully ordered groups in partially ordered linear algebras

No abstract. Received September 2, 1999; accepted in final form October 23, 2000.     

基于集值统计的模糊神经网络专家系统及其应用

建立基于集值统计的模糊神经网络专家评审系统,并应用于科研项目评审工作,实际应用表明该系统是可行的。     

Relative polars in ordered sets

In the paper, the notion of relative polarity in ordered sets is introduced and the lattices of R-polars are studied. Connections between R-polars and prime ideals, especially in distributive sets, are found.     

Compatible weighting method with rank order centroid: Maximum entropy ordered weighted averaging approach

In a situation where imprecise attribute weights such as a rank order are captured, various approximate weighting methods have been proposed to aid multiattribute decision analysis. Among others, it is well known that the rank order centroid (ROC) weights result in the highest performance in terms of the identification of the best alternative under the ranked attribute weights. In this paper, we aim to reinterpret the meaning of the ROC weights and to develop a compatible weighting method that is based on other well-established academic disciplines. The ordered weighted averaging (OWA) method is a nonlinear aggregation method in that the weights are associated with the objects reordered according to their magnitudes in the aggregation process. Some interesting semantics can be attached to the approximate weights in view of the measure developed in the OWA method. Furthermore, the weights generated by the maximum entropy method show equally compatible performance with the ROC weights under some condition, which is demonstrated by theoretical and simulation analysis.     

环上的模糊理想幂格及其强截集诱导的格

给出了环上模糊理想幂格的概念,得到相关性质。进而由环上模糊理想强截集诱导出格,讨论了它不是分配格,但为模格。同时,将环上升为主理想环,得到了模糊理想乘积的强截集等于强截集的乘积,且都为环的理想。最后,讨论了Boolean环的模糊子集为模糊理想与其伴随构成交半格的关系。     

Geometric control of hybrid systems

In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched linear systems. We reformulate the invariance of a set as an inequality for its support function that is valid for any convex set. This produces novel algebraic conditions for the invariance of sets with polynomial or piecewise quadratic support functions.     

序半群的阿基米德半群的半格分解

本文通过一个序半群S上的一些二元关系以及它的理想的根集的性质该序半群是阿基米德半群的半格,特别地是阿基米德半群的链的刻划,证明了S是阿基米德链当且仅当S是准素的.通过序半群的m-系的概念,证明了S的任意半素理想是含它的所有素理想的交,并通过该结论,证明了S是阿基米德半群的链当且仅当S是阿基米德半群的半格且S的所有素理想关于集包含关系构成链.作为应用,该结论在一般的半群（没有序）[1]中也成立.     

A viability theorem for set-valued states in a Hilbert space

Applications in robust control problems and shape evolution motivate the mathematical interest in control problems whose states are compact (possibly non-convex) sets rather than vectors. This leads to evolutions in a basic set which can be supplied with a metric (like the well-established Pompeiu–Hausdorff distance), but it does not have an obvious linear structure. This article extends differential inclusions with state constraints to compact-valued states in a separable Hilbert space H. The focus is on sufficient conditions such that a given constraint set (of compact subsets) is viable a.k.a. weakly invariant. Our main result extends the tangential criterion in the well-known viability theorem (usually for differential inclusions in a vector space) to the metric space of non-empty compact subsets of H.     

有序介孔碳材料的软模板合成、结构改性与功能化

有序介孔碳材料在吸附、分离、催化以及能量存储/转化等方面具有广阔的应用前景。相较于复杂的硬模板路线,基于两亲性嵌段共聚物和聚合物前驱体间（如酚醛树脂）自组装的软模板路线是合成有序介孔碳材料更为有效的方法。本文讨论比较了溶剂挥发诱导自组装法、水相协同自组装法和无溶剂法等三种典型软模板路线的基本过程和特点,并介绍了近年来在新型碳前驱体应用、介孔碳的结构改性和功能化等方面的一些重要进展,最后总结了介孔碳的合成研究中所需解决的关键问题。     

Computing the dimension ofN-free ordered sets is NP-complete

We show that the problem of deciding whether anN-free ordered set has dimension at most 3 is NP-complete.Both authors supported by Office of Naval Research contract N00014-85K-0494.