PP K-MEAN CLUSTERING

In this paper, we propose a dimension-reducing, K-mean clustering procedureby Projection Pursuit (PP) technique so as to explore the clustering structure of data inhigh-dimensional space in terms of low-dimensional projective points of data, and we obtainthe a.s. consistence of the estimates of the cluster centers and projection orientations.     

INTERPOLATED FINITE ELEMENT METHODS FOR SECOND ORDER HYPERBOLIC EQUATIONS AND THEIR GLOBAL SUPERCONVERGENCE

We develop the interpolated finite element method to solve second-order hy-perbolic equations. The standard linear finite element solution is used to generate a newsolution by quadratic interpolation over adjacent elements. We prove that this interpo-lated finite element solution has superconvergence. This method can easily be applied togenerating more accurate gradient either locally or globally, depending on the applications.This method is also completely vectorizable and parallelizable to take the advantages ofmodern computer structures. Several numerical examples are presented to confirm ourtheoretical analysis.     

刚性系统数字仿真算法

介绍刚性的本质,综述刚性算法、间断处理、实时算法、微分代数问题、稳定性、并行算法的一些结果,给出在这个领域的进一步研究的建议。     

一类微分代数系统并行仿真算法

利用对误差的预校正技术,本文提出一类微分代数系统的并行仿真算法,进行仿真误差估计。对于一个模型问题进行稳定性分析,画出稳定区域。计算实例表明算法是有效的。     

DEDS仿真模型优化算法的终止规则研究

终止规则在优化算法中起着十分重要的作用。本文首先对采用传统终止规则的优化算法在处理DEDS优化问题时遇到的问题进行分析,在此基础上针对DEDS优化问题及其算法的特点提出一个新的终止规则,文章最后通过实际例子对终止规则进行了仿真分析。     

A New Discipline of Science-The Study of Open Complex Giant System and Its Methodology

This paper introduces the conception of open complex giant system and the methodology for dealing with the system, with stress on its profound significance in development of science and technology. The authors conclude that the reductionism underlying the exact science is not suitable to open complex giant system, and the only feasible alternative is the meta-synthetic engineering from the qualitative to the quantitative.     

Discussion on Electromagnetic Missile

This paper presents the principle of electromagnetic missile from the mathematical point of view, and verifies rigorously that the radiating power over whole space is limited.     

Simulation Modeling by Fuzzy Nets

Fuzzy technology is a newly developed discipline based on fuzzy mathematics. In the recent years, it has been successfully applied into many areas, such as process control, diagnosis,evaluation, decision making and scheduling, especially in simulation where accurate mathematical models can not or very hard be established. In this paper, to meet the demands of fuzzy simulation, two fuzzy nets will first be presented, which are quite suitable for modeling the parallel or concurrent systems with fuzzy behavior. Then, a concept of active simulation will be introduced, in which the simulation model not only can show its fuzzy behavior, but also has a certain ability which can actively perform many very useful actions, such as automatic warning, realtime monitoring, simulation re-sult checking, simulation model self-adapting, error recovery, simulating path tracing, system states inspecting and exception handling, by a unified approach while some specified events occur. The simulation model described by this     

A FURTHER GENERALIZATION OF JUNG''''S THEOREM

Let G be a graph of order n. We define the distance between two vertices u andv in G, denoted by d(u, v), as the minimum value of the lengths of all u-v paths. We writeσ_k(G)=min{∑_i=1~k d(v_i)|{v_1, v_2,…, v_k} is an independent set in G} and NC2(G)=min {|N(u)∪N(v)| | d(u, v)=2}. We denote by ω(G) the number of components of agraph G. A graph G is called 1-tough if ω(G\S)≤|S| for every subset S of V(G) withω(G\S)>l. By c(G) we denote the length of the longest cycle in G; in particular, G iscalled a Hamiltonian graph if c(G)=n. H.A. Jung proved that every 1-tough graphwith order n≥11 and σ2≥n-4 is Hamiltonian. We generalize it further as follows: ifG is a 1-tough graph and σ3(G)≥n, then c(G)≥min {n,2NC2(G)+4}. Thus, theconjecture of D. Bauer, G. Fan and H.J. Veldman in [2] is completely solved.     

液体爆炸分散过程中界面破碎的实验研究

设计了一种有上下平面约束的液体爆炸分散装置, 通过阴影照相获得气液界面破碎形态变化的时间序列, 并应用平面激光诱导荧光(PLIF)得到了径向膨胀液体环内诱导的荧光照片. 采用二维图像处理、分形几何和数值模拟相结合的方法, 较系统地分析了实验结果. 最后, 讨论了液体环及其气液界面运动数学模型建立中的问题.