一类星色数为4的平面图

图的星色数的概念是Vince在1988年提出的,它是图的色数的一个推广.本文构造了一类星色数是4的平面图.     

Packing Densities and Simulated Tempering for Hard Core Gibbs Point Processes

Monotonicity and convergence properties of the intensity of hard core Gibbs point processes are investigated and compared to the closest packing density. For such processes simulated tempering is shown to be an efficient alternative to commonly used Markov chain Monte Carlo algorithms. Various spatial characteristics of the pure hard core process are studied based on samples obtained with the simulated tempering algorithm.     

Star coloring planar graphs from small lists

A star coloring of a graph is a proper vertex‐coloring such that no path on four vertices is 2‐colored. We prove that the vertices of every planar graph of girth 6 (respectively 7, 8) can be star colored from lists of size 8 (respectively 7, 6). We give an example of a planar graph of girth 5 that requires 6 colors to star color. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 324–337, 2010     

Some Inequalities for the General Radial Bo dies

Lutwak showed the radial bodies combining with the radial Minkowski linear combinations of star bodies. In this paper, the general radial bodies are introduced and its some properties and inequalities are established.     

Analyzing the Performance of Generalized Hill Climbing Algorithms

Generalized hill climbing algorithms provide a framework to describe and analyze metaheuristics for addressing intractable discrete optimization problems. The performance of such algorithms can be assessed asymptotically, either through convergence results or by comparison to other algorithms. This paper presents necessary and sufficient convergence conditions for generalized hill climbing algorithms. These conditions are shown to be equivalent to necessary and sufficient convergence conditions for simulated annealing when the generalized hill climbing algorithm is restricted to simulated annealing. Performance measures are also introduced that permit generalized hill climbing algorithms to be compared using random restart local search. These results identify a solution landscape parameter based on the basins of attraction for local optima that determines whether simulated annealing or random restart local search is more effective in visiting a global optimum. The implications and limitations of these results are discussed.     

三维水平井轨道设计模糊最优控制模型

建立了三维水平井井眼轨道设计模糊非线性多目标最优控制模型 ,利用模糊集理论把该模型转化为非线性规划问题 ,并把该模型应用到水平井的实际生产中 ,得到满意的结果 .     

含有等式约束非线性规划的全局优化算法

针对含有多个等式约束的非线性规划问题,提出一个全局优化算法.该方法基于可行集策略把改进的模拟退火方法与确定的局部算法方法相结合.对算法的收敛性进行了证明,数值结果表明算法的有效性及正确性.     

制造单元布局问题的双目标模型与算法研究

单元制造系统的布局对于提高系统的效率起着十分重要的作用。以最小化物料周转量和设施面积为目标,建立了一个单元制造系统布局的双目标优化模型,在该模型中不同制造单元的布局、单元内部不同设施的位置与方向这几个问题可以同时进行优化。基于模拟退火邻域解的变尺度生成机制和双目标抽样准则设计了模型的求解算法。算例表明本文算法所得Pareto解集优于经典的NSGA-Ⅱ算法。     

先天学关于太阳系定位原理

天上星星，繁而不乱。根据《易》“太极”2^k序列编出一个三角数表，可描测太阳系已知与未知行星的轨道参数。其中排行第七的一颗“女帛星”(合理存在)，按开普勒第三定律计算出公转速度与周期后，发现太阳系十大行星的动态组合就是一个“先天八卦模型”，进而可以解读太阳系平衡态运动的数学机理及其结构特征。