基于粗糙集与层次分析法的组合预测方法

本文在改进的属性约简启发式算法 ,即应用加权平均的属性重要度对属性进行约简的基础上 ,将粗糙集理论和层次分析相结合 ,给出了一种全新的组合预测方法 .     

多人合作投资多元化中的层次分析法

本文利用层次分析法对企业中存在的多人合作投资多元化问题进行探讨与研究 ,将定性分析与定量计算结合起来 ,求解多元化投资规划中的权系数 .     

Adiabatic multi-step separation method and its application to coupled oscillators

Extension of the adiabatic approach to a multi-step separation method is presented. This method step by step reduces the multi-dimensional Schrödinger equation to the effective equations of lower dimensions. The reduction procedure allows to take advantage of multi-level hierarchy of various physical systems. The multi-step separation method is applied in the calculation of vibrational energies of coupled oscillators. The new method is found to be very effective and accurate.     

Hierarchical Discrete Models of Competition for a Resource

A coupled pair of first order nonlinear discrete hierarchical age-structured models are applied to study two modes of intraspecific competitions; scramble and contest. The study focuses on several comparisons of the dynamical outcomes of the two competitions. For a constant resource, it is shown, using analytical and numerical approaches, that solutions of the contest model monotonically equilibrate, while solutions of the scramble model oscillate and become chaotic. It is also shown that the inherent net reproductive number of each population affects the comparison of equilibrium points in the two populations. By considering cases on the resource and model parameters, the local as well as the global stability of nontrivial equilibrium points are studied. The impact of a contest and a scramble consumer on a time dependent resource is considered numerically.     

The rank-size scaling law and entropy-maximizing principle

The rank-size regularity known as Zipf’s law is one of the scaling laws and is frequently observed in the natural living world and social institutions. Many scientists have tried to derive the rank-size scaling relation through entropy-maximizing methods, but they have not been entirely successful. By introducing a pivotal constraint condition, I present here a set of new derivations based on the self-similar hierarchy of cities. First, I derive a pair of exponent laws by postulating local entropy maximizing. From the two exponential laws follows a general hierarchical scaling law, which implies the general form of Zipf’s law. Second, I derive a special hierarchical scaling law with the exponent equal to 1 by postulating global entropy maximizing, and this implies the pure form of Zipf’s law. The rank-size scaling law has proven to be one of the special cases of the hierarchical scaling law, and the derivation suggests a certain scaling range with the first or the last data point as an outlier. The entropy maximization of social systems differs from the notion of entropy increase in thermodynamics. For urban systems, entropy maximizing suggests the greatest equilibrium between equity for parts/individuals and efficiency of the whole.     

未确知有理数在投标方案择优中的应用

评标是工程项目招投标的中心环节,许多评价因素易于定性分析而难于定量分析.根据评标中的主要评价因素,建立起量化评价指标体系,以各量化指标为变量,根据评标实践条件,构建出考虑招标单位相对收益的评标择优决策模型,利用未确知有理数理论,给出对投标方案的综合情况进行量化并进行选择的一个数学模型方法.     

周期环境中年龄等级结构种群模型分析

本文提出并分析一类基于个体年龄的等级结构种群模型,其生命参数随时间作周期性振荡.运用不动点方法证明了周期解的存在唯一性和非负有界性.推广了一些现有结果.     

The polynomial hierarchy and a simple model for competitive analysis

The multi-level linear programs of Candler, Norton and Townsley are a simple class of sequenced-move games, in which players are restricted in their moves only by common linear constraints, and each seeks to optimize a fixed linear criterion function in his/her own continuous variables and those of other players. All data of the game and earlier moves are known to a player when he/she is to move. The one-player case is just linear programming.We show that questions concerning only the value of these games exhibit complexity which goes up all levels of the polynomial hierarchy and appears to increase with the number of players.For three players, the games allow reduction of the ₂ and ₂ levels of the hierarchy. These levels essentially include computations done with branch-and-bound, in which one is given an oracle which can instantaneously solve NP-complete problems (e.g., integer linear programs). More generally, games with (p + 1) players allow reductions of _p and _p in the hierarchy.An easy corollary of these results is that value questions for two-player (bi-level) games of this type is NP-hard.The author's work has been supported by the Alexander von Humboldt Foundation and the Institut fur Okonometrie und Operations Research of the University of Bonn, Federal Republic of Germany; grant ECS8001763 of the National Science Foundation, USA; and a grant from the Georgia Tech Foundation.     

Lattice-driven cellular automata implementing local semantics

We propose a model based on Elementary Cellular Automata (ECA) where each cell has its own semantics defined by a lattice. Semantics play the following two roles: (1) a state space for computation and (2) a mediator generating and negotiating the discrepancy between the rule and the state. We call semantics playing such roles ‘local semantics’. A lattice is a mathematical structure with certain limits. Weakening the limits reveals local semantics. Firstly, we implement local semantics for ECA and call the result ‘Lattice-Driven Cellular Automata’ (LDCA). In ECA rules are common and invariant for all cells, and uniquely determine the state changes, whereas in LDCA rules and states interplay with each other dynamically and directly in each cell. Secondly, we compare the space-time patterns of LDCA with those of ECA with respect to the relationship between the mean value and variance of the ‘input-entropy’. The comparison reveals that LDCA generate complex patterns more universally than ECA. Lastly, we discuss the observation that the direct interplay between levels yields wholeness dynamically.