In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an ex...In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an exact solution of this equation through the Wronskian technique. In addition, we testify that this equation can be reduced to a Jacobi identity by considering its solution as a Grammian determinant by means of Pfaffian derivative formulae.展开更多
By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the inf...By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn＋r/（n＋rr）.展开更多
If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching s...If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching some crossings with the linking number：lk（L）=∑i=1^mεiC（EiL）＋n展开更多
基金The project supported by the Key Project of the Ministry of Education under Grant No.106033the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024+2 种基金National Natural Science Foundation of China under Grant Nos.60372095 and 60772023the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE07-001Beijing University of Aeronautics and Astronautics,and the National Basic Research Program of China(973 Program)under Grant No.2005CB321901
文摘In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an exact solution of this equation through the Wronskian technique. In addition, we testify that this equation can be reduced to a Jacobi identity by considering its solution as a Grammian determinant by means of Pfaffian derivative formulae.
基金Supported by the NNSF of China(10771093)Supported by the NSF of Henan Province(0511010300)
文摘By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn＋r/（n＋rr）.
文摘If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching some crossings with the linking number：lk（L）=∑i=1^mεiC（EiL）＋n
