快速造P(n,k)大表的左肩法则和斜线法则

设Ｐ（ｎ,ｋ）为整数ｎ分为ｋ部的无序分拆的个数,每个分部≥１,它为大师欧拉所建立（１７０７－１７８３）．它是组合图论和数论里最重要的数据之一．然而,它却十分难于计数和造表．本文,由公式Ｐ（ｎ,ｋ）＝Ｐ（ｎ－１,ｋ－１）＋Ｐ（ｎ－ｋ,ｋ）定义了Ｐ（ｎ,ｋ）的左肩数和锐角数,并由此得到求Ｐ（ｎ,ｋ）的左肩法则（第一法则）．还根据本文作者［５］的一些重要定理得到求 Ｐ（ｎ,ｋ）的斜线法则（第二法则）．使用这些法则得到造Ｐ（ｎ,ｋ）大表的有趣原理．为方便计,我们仅用第一法则设计了计算机程序,用此程序即可快速造出任意大的Ｐ（ｎ,ｋ）表．     

修正积分水平集算法的一个实现算法及其收敛性证明

郑权等（1978）在“一个求总极值的方法”一文中给出了一个积分水平集求总极值的概念性算法及Monte-Carlo随机投点的实现算法,其收敛性一直未得以解决,本文在张连生,邬冬华等提出的修正算法的基础上,利用数论中一致分布佳点集列,给出了一个实现算法及全局收敛性的证明,为了提高算法的计算效率,文中对算法进行了并行化处理。     

Commutator-Finite D-Lattices

Commutator-finite D-lattices as a generalization of commutator-finite orthomodular lattices are defined and their properties studied. A necessary and sufficient condition is found under which a D-lattice can be uniquely decomposed into a direct product of an MV-algebra and finitely many irreducible D-lattices which are not MV-algebras. This condition is satisfied if the D-lattice is orthocomplete or if all commutators are sharp. A condition under which a block-finite D-lattice is commutator-finite is found. Some necessary and sufficient conditions for the existence of states and valuations are proved, and some examples are given. Mathematics Subject Classifications (2000) Primary 06F05; Secondary 03G25, 81P10.This research is supported by grant VEGA 2/3163/23.     

The construction of orthodox super rpp semigroups

We define orthodox super rpp semigroups and study their semilattice decompositions. Standard representation theorem of orthodox super rpp semigroups whose sub-band of idempotents is in the varieties of bands described by an identity with at most three variables are obtained.     

Nests with the partial factorization property

It is proved that a nest on a separable complex Hilbert space has the left (resp. right) partial factorization property, which means that for every invertible operator from onto a Hilbert space there exists an isometry (resp. a coisometry) from into such that both and are in the associated nest algebra if and only if it is atomic (resp. countable).

     

基于RAGA的模糊层次分析方法在爆破方案优选中的应用

探讨了应用实码加速遗传算法,直接检验和修正模糊优先关系矩阵的爆破方案模糊层次分析改进优选方法。实例应用表明,该法可合理确定指标权重,能提高评价结果的精度和优度值的离散度。     

结构能度可靠性方法研究

结构系统可靠性研究分随机模型、模糊模型和非概率模型.本文分析了传统随机模型的局限性,利用蒙特卡诺的基本思想.提出了一种新的基于区间分析的模糊可靠性度量体系及分析方法.从物理、几何等方面解释了文中理论的合理性.该方法确定的失效可能度综合了更多的结构有用信息,能够反映结构的实际可靠状态.最后还提出了基于本文可靠性度量方法的结构优化设计模型,通过实例介绍了该方法的具体应用.     

基于粗集—模糊理论的柴油机磨损模式识别

在总结柴油机磨损模式的磨粒分析基础上,首次提出在柴油机磨损模式识别中采用基于粗集和模糊理论相结合的模式识别方法。在建立磨损形式标准样本库的基础上,利用粗集理论对标准样本知识库进行简化和权重集计算,然后利用模糊理论确定隶属函数,最后给出结论。     

弱交换富足序半群(Ⅰ)

本文将序半群上的 Ｇｒｅｅｎ’ｓ－关系推广为 Ｇｒｅｅｎ’ｓ＊一关系．给出主序（左、右）＊－理想、主序＊－滤特征描述和弱交换富足序半群的特征．用这些特征证明了一类弱交换富足序半群的结构定理：若序半群Ｓ满足 ,则Ｓ是弱交换富足序半群当且仅当Ｓ是左（右）单序半群｛（ｅ）（Ｓ）｝的半格．