Solutions in the Grammian form for a variable-coefficient Kadomtsev-Petviashvili （KP） equation which has the Wronskian solutions are derived by means of Pfaffian derivative formulae.
In this paper we discuss the global optimality of vector lengths for lattice bases. By introducing a partial order on lattice bases and the concept of successive minimal basis （SMB for short）, we show that any of it...In this paper we discuss the global optimality of vector lengths for lattice bases. By introducing a partial order on lattice bases and the concept of successive minimal basis （SMB for short）, we show that any of its minimal elements is a general greedy-reduced basis, and its least element （if exists） is an SMB. Furthermore, we prove the existence of SMB for lattices of dimension up to 6.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 10771196, and the Natural Science Foundation of Zhejiang Province under Grant No Y605044. The authors would like to thank-Dr Kui-Hua Yan for his discussion.
文摘Solutions in the Grammian form for a variable-coefficient Kadomtsev-Petviashvili （KP） equation which has the Wronskian solutions are derived by means of Pfaffian derivative formulae.
文摘In this paper we discuss the global optimality of vector lengths for lattice bases. By introducing a partial order on lattice bases and the concept of successive minimal basis （SMB for short）, we show that any of its minimal elements is a general greedy-reduced basis, and its least element （if exists） is an SMB. Furthermore, we prove the existence of SMB for lattices of dimension up to 6.
