The line cartographic symbol located on the boundary and the point cartographic symbol located by single point are the main body and stress of the map. The cartographic symbols are divided into point, line and area sy...The line cartographic symbol located on the boundary and the point cartographic symbol located by single point are the main body and stress of the map. The cartographic symbols are divided into point, line and area symbol in cartography and traditional educational books, but up to now there is only qualitative description about the three kinds of symbols, there are not the mathematical definitions of point, line and area symbols. This paper tries to solve the problem. The authors propose the mathematical definition about point, line and area cartographic symbol according to the theory of topology and expound their dependence relation.展开更多
Polarization singularities,which emerge from the incoherent superposition of two vector electric fields with the same frequency,and their evolution in free space are studied analytically and illustrated by numerical e...Polarization singularities,which emerge from the incoherent superposition of two vector electric fields with the same frequency,and their evolution in free space are studied analytically and illustrated by numerical examples.It is shown that there exist C-points,L-lines,in particular,C-lines in incoherently superimposed two-dimensional wavefields.Usually,the C-lines are unstable and disappear during the free-space propagation.The motion,pair creation-annihilation process of the emergent C-points,as well as the distortion of the L-lines may take place,and the degree of polarization of the emergent C-points varies upon propagation and may be less than 1.展开更多
文摘The line cartographic symbol located on the boundary and the point cartographic symbol located by single point are the main body and stress of the map. The cartographic symbols are divided into point, line and area symbol in cartography and traditional educational books, but up to now there is only qualitative description about the three kinds of symbols, there are not the mathematical definitions of point, line and area symbols. This paper tries to solve the problem. The authors propose the mathematical definition about point, line and area cartographic symbol according to the theory of topology and expound their dependence relation.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10874125)
文摘Polarization singularities,which emerge from the incoherent superposition of two vector electric fields with the same frequency,and their evolution in free space are studied analytically and illustrated by numerical examples.It is shown that there exist C-points,L-lines,in particular,C-lines in incoherently superimposed two-dimensional wavefields.Usually,the C-lines are unstable and disappear during the free-space propagation.The motion,pair creation-annihilation process of the emergent C-points,as well as the distortion of the L-lines may take place,and the degree of polarization of the emergent C-points varies upon propagation and may be less than 1.
