Some Hardy type inequalities on the ball and its complementary set in the Euclidean space are established by using the Picone type identity and constructing suitable auxiliary functions.
The addressing and routing algorithm on hexagonal networks is still an open problem so far.Although many related works have been done to resolve this problem to some extent,the properties of hexagonal networks are sti...The addressing and routing algorithm on hexagonal networks is still an open problem so far.Although many related works have been done to resolve this problem to some extent,the properties of hexagonal networks are still not explored adequately.In this paper,we first create an oblique coordinate system and redefine the Euclidean space to address the hexagonal nodes.Then an optimal routing algorithm using vectors and angles of the redefined Euclidean space is developed.Compared with the traditional 3-directions scheme and the Cayley graph method,the proposed routing algorithm is more efficient and totally independent of the scale of networks with two-tuples addresses.We also prove that the path(s) obtained by this algorithm is always the shortest one(s).展开更多
基金Supported by the National Nature Science Foundation of China( 1037099)
文摘Some Hardy type inequalities on the ball and its complementary set in the Euclidean space are established by using the Picone type identity and constructing suitable auxiliary functions.
基金supported in part by International Researcher Exchange Project of National Science Foundation of China and Centre national de la recherche scientifique de France(NSFC-CNRS)under Grant No.61211130104national information security project 242 under Grant No.2014A104National Science Foundation of China under Grants No.60932003,61271220,61202266,61172053
文摘The addressing and routing algorithm on hexagonal networks is still an open problem so far.Although many related works have been done to resolve this problem to some extent,the properties of hexagonal networks are still not explored adequately.In this paper,we first create an oblique coordinate system and redefine the Euclidean space to address the hexagonal nodes.Then an optimal routing algorithm using vectors and angles of the redefined Euclidean space is developed.Compared with the traditional 3-directions scheme and the Cayley graph method,the proposed routing algorithm is more efficient and totally independent of the scale of networks with two-tuples addresses.We also prove that the path(s) obtained by this algorithm is always the shortest one(s).
