In this paper, we give some characteristic properties of star-shaped sets which include a subset of a convex metric space. Using the characteristic properties, we discuss the existence problems of fixed points of none...In this paper, we give some characteristic properties of star-shaped sets which include a subset of a convex metric space. Using the characteristic properties, we discuss the existence problems of fixed points of nonexpansive type mappings on star-shaped subsets of convex metric spaces, which generalize the recent results obtained by Ding Xie-ping, Beg and Azam. Finally, we give an example which shows that our generalizations are essential.展开更多
Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defin...Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.展开更多
由导航星表构造导航星匹配模式是星图匹配、识别的最关键步骤。为了从根本上能保证星图识别模式的完备性,提出了构造导航星视场的方法。从导航星表中任一颗星开始,依次找到两两角距小于FOV的星,构成1颗星、2颗星…m颗星的全部子集(子集P...由导航星表构造导航星匹配模式是星图匹配、识别的最关键步骤。为了从根本上能保证星图识别模式的完备性,提出了构造导航星视场的方法。从导航星表中任一颗星开始,依次找到两两角距小于FOV的星,构成1颗星、2颗星…m颗星的全部子集(子集P)。以子集P中心的视轴为基准,取两倍于视场的导航星子集Q(Q包含P)。把Q中的每一颗星投影到星敏感器像平面,形成点列子集Q。视场的构造就可以表述为平面上点集的几何覆盖问题。对每一个子集P来说,先计算其最小覆盖圆,若其半径小于视场在像平面的投影值(R),则计算点列子集Q删除P后的Voronoi图,这样就可求出包含点列子集P的最大空圆;若其半径大于R,则点列子集P为一个导航星视场。给出了由20颗导航星生成的124个视场,并与Monte Carlo 20万次随机生成的视场作了比较。结果证明了该算法是有效的、实用的。展开更多
文摘In this paper, we give some characteristic properties of star-shaped sets which include a subset of a convex metric space. Using the characteristic properties, we discuss the existence problems of fixed points of nonexpansive type mappings on star-shaped subsets of convex metric spaces, which generalize the recent results obtained by Ding Xie-ping, Beg and Azam. Finally, we give an example which shows that our generalizations are essential.
文摘Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.
文摘由导航星表构造导航星匹配模式是星图匹配、识别的最关键步骤。为了从根本上能保证星图识别模式的完备性,提出了构造导航星视场的方法。从导航星表中任一颗星开始,依次找到两两角距小于FOV的星,构成1颗星、2颗星…m颗星的全部子集(子集P)。以子集P中心的视轴为基准,取两倍于视场的导航星子集Q(Q包含P)。把Q中的每一颗星投影到星敏感器像平面,形成点列子集Q。视场的构造就可以表述为平面上点集的几何覆盖问题。对每一个子集P来说,先计算其最小覆盖圆,若其半径小于视场在像平面的投影值(R),则计算点列子集Q删除P后的Voronoi图,这样就可求出包含点列子集P的最大空圆;若其半径大于R,则点列子集P为一个导航星视场。给出了由20颗导航星生成的124个视场,并与Monte Carlo 20万次随机生成的视场作了比较。结果证明了该算法是有效的、实用的。
