Kirkman covering designs with even-sized holes

A Kirkman holey covering design, denoted by KHCD(g^u), is a resolvable group-divisible covering design of type g^u. Each of its parallel class contains one block of size δ, while other blocks have size 3. Here δ is equal to 2, 3 and 4 when gu≡2, 3 and 4 (mod 3) in turn. In this paper, we study the existence problem of a KHCD(g^u) which has minimum possible number of parallel classes, and give a solution for most values of even g and u.     

Intersecting invariant manifolds in spatial restricted three-body problems: Design and optimization of Earth-to-halo transfers in the Sun-Earth-Moon scenario

This work deals with the design of transfers connecting LEOs with halo orbits around libration points of the Earth-Moon CRTBP using impulsive maneuvers. Exploiting the coupled circular restricted three-body problem approximation, suitable first guess trajectories are derived detecting intersections between stable manifolds related to halo orbits of EM spatial CRTBP and Earth-escaping trajectories integrated in planar Sun-Earth CRTBP. The accuracy of the intersections in configuration space and the discontinuities in terms of Δv are controlled through the box covering structure implemented in the software GAIO. Finally first guess solutions are optimized in the bicircular four-body problem and single-impulse and two-impulse transfers are presented.     

粗糙面分形计算理论研究进展

为提出一种工程上适用可靠的粗糙面分形维数计算方法,在分形曲线的维数计算方法(码尺法,盒维法)基础上,先后提出了星积分形曲面的维数计算方法、三角形棱柱表面积法、投影覆盖法、立方体覆盖法、改进的立方体覆盖法、分形的增变量描述法等曲面分形维数理论.鉴于上述方法的共有缺陷——获取三维坐标的激光表面仪器的扫描尺度限制,研究者提出了粗糙面图像维数计算理论,包括二值化图像维数、灰度图像维数、RGB图像维数计算理论.最后,本文展望了分形维数计算理论领域内亟待解决的三大问题.     

基于改进遗传算法的集合覆盖问题

集合覆盖问题是组合优化中的典型问题,在日常生活中有着广泛的应用.提出了一种改进遗传算法来解决集合覆盖问题.算法对标准遗传算法的改进主要表现在:1)结合启发式算法和随机生成,设计了新的产生初始种群的方法;2)引入修补操作处理不可行解使其转换成可行解;3)对重复个体进行处理再利用;4)对多点交叉进行推广,提出了新的交叉算子;5)针对可行解和不可行解,采取两种自适应多位变异操作.数值实验结果表明该算法对于解决规模较大的集合覆盖问题是有效的.     

交换环的M-赋值与序的相容性

在有单位元的交换环上,引入了M-赋值与序之间的相容性,由此获得一些有关M-赋值与序相容的结果.结果可看作Manis赋值和形式有限V-赋值的相关结果的推广.