Recently,Andrews and Paule established the generating functions for the k-elongated plane partition function d_(k)(n)and proved a large number of results on d_(k)(n)with k=2,3.In particular,they posed some conjectures...Recently,Andrews and Paule established the generating functions for the k-elongated plane partition function d_(k)(n)and proved a large number of results on d_(k)(n)with k=2,3.In particular,they posed some conjectures on congruences modulo powers of 3 for d_(2)(n).Their work has attracted the attention of da Silva,Hirschhorn,Sellers and Smoot.Very recently,Smoot proved a congruence family for d_(2)(n)which implies one conjecture due to Andrews and Paule by using the localization method.In this paper,we prove the rest two conjectures given by Andrews and Paule.展开更多
At present, chaotic communications have been widely studied. However, these researches mainly focus on the binary systems while the researches of M-ary chaotic communications are not extensive. To change the situation...At present, chaotic communications have been widely studied. However, these researches mainly focus on the binary systems while the researches of M-ary chaotic communications are not extensive. To change the situation, a chaos M-ary modulation method based on phase plane partition of Hamilton map is proposed. Firstly, the chaotic model of Hamilton map and its phase plane features are described, and then the way of creating the chaos M-ary modulation is discussed. Next, to evaluate the proposed method, the system simulation results and analysis are given. Finally, the chaos M-ary modulation method is applied to communications.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12371334)the Natural Science Foundation of Jiangsu Province(Grant No.BK20221383)。
文摘Recently,Andrews and Paule established the generating functions for the k-elongated plane partition function d_(k)(n)and proved a large number of results on d_(k)(n)with k=2,3.In particular,they posed some conjectures on congruences modulo powers of 3 for d_(2)(n).Their work has attracted the attention of da Silva,Hirschhorn,Sellers and Smoot.Very recently,Smoot proved a congruence family for d_(2)(n)which implies one conjecture due to Andrews and Paule by using the localization method.In this paper,we prove the rest two conjectures given by Andrews and Paule.
基金supported by the National Natural Science Foundation of China (60772025)the Science Research Fund of Harbin Engineering University (HEUF0507)
文摘At present, chaotic communications have been widely studied. However, these researches mainly focus on the binary systems while the researches of M-ary chaotic communications are not extensive. To change the situation, a chaos M-ary modulation method based on phase plane partition of Hamilton map is proposed. Firstly, the chaotic model of Hamilton map and its phase plane features are described, and then the way of creating the chaos M-ary modulation is discussed. Next, to evaluate the proposed method, the system simulation results and analysis are given. Finally, the chaos M-ary modulation method is applied to communications.
