A fast algorithm for determining the minimal polynomial and linear complexity of a upn-periodic sequence over a finite field Fq is given.Let p,q,and u be distinct primes,q a primitive root modulo p2,m the smallest pos...A fast algorithm for determining the minimal polynomial and linear complexity of a upn-periodic sequence over a finite field Fq is given.Let p,q,and u be distinct primes,q a primitive root modulo p2,m the smallest positive integer such that qm≡1 mod u,and gcd（m,p（p-1））=1.An algorithm is used to reduce a periodic upn sequence over Fq to several pn-periodic sequences over Fq（ζ）,where ζ is a u-th primitive root of unity,and an algorithm proposed by Xiao et al.is employed to obtain the minimal polynomial of each pn-periodic sequence.展开更多
By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph（the Theorem 1）, a first class hi-cycle graph and a second class bicycle graph...By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph（the Theorem 1）, a first class hi-cycle graph and a second class bicycle graph（the Theorem 2）, respectively.展开更多
In the present letter, we get the appropriate bilinear forms of （2 ＋ 1）-dimensional KdV equation, extended （2 ＋ 1）-dimensional shallow water wave equation and （2 ＋ 1）-dimensional Sawada -Kotera equation in a ...In the present letter, we get the appropriate bilinear forms of （2 ＋ 1）-dimensional KdV equation, extended （2 ＋ 1）-dimensional shallow water wave equation and （2 ＋ 1）-dimensional Sawada -Kotera equation in a quick and natural manner, namely by appling the binary Bell polynomials. Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations. And the corresponding figures of the periodic wave solutions are given. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.展开更多
By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system....By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riecati equation that the symmetrical Lucas functions satisfy. From the variable separation sohition and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated.展开更多
We prove here the smoothness and the irreducibility of the periodic dynatomic curves(c,z)∈C2such that z is n-periodic for zd+c,where d 2.We use the method provided by Buff and Lei where they proved the conclusion for...We prove here the smoothness and the irreducibility of the periodic dynatomic curves(c,z)∈C2such that z is n-periodic for zd+c,where d 2.We use the method provided by Buff and Lei where they proved the conclusion for d=2.The proof for smoothness is based on elementary calculations on the pushforwards of specific quadratic differentials,following Thurston and Epstein,while the proof for irreducibility is a simplified version of Lau-Schleicher’s proof by using elementary arithmetic properties of kneading sequence instead of internal addresses.展开更多
基金The National Natural Science Foundation of China (No.10971250,11171150)
文摘A fast algorithm for determining the minimal polynomial and linear complexity of a upn-periodic sequence over a finite field Fq is given.Let p,q,and u be distinct primes,q a primitive root modulo p2,m the smallest positive integer such that qm≡1 mod u,and gcd（m,p（p-1））=1.An algorithm is used to reduce a periodic upn sequence over Fq to several pn-periodic sequences over Fq（ζ）,where ζ is a u-th primitive root of unity,and an algorithm proposed by Xiao et al.is employed to obtain the minimal polynomial of each pn-periodic sequence.
基金Supported by the NNSF of China(10861009)Supported by the Ministry of Education Science and Technology Item of China(206156)
文摘By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph（the Theorem 1）, a first class hi-cycle graph and a second class bicycle graph（the Theorem 2）, respectively.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075055,61021004,10735030Shanghai Leading Academic Discipline Project under Grant No.B412Program for Changjiang Scholars and Innovative Research Team in University(IRT0734)
文摘In the present letter, we get the appropriate bilinear forms of （2 ＋ 1）-dimensional KdV equation, extended （2 ＋ 1）-dimensional shallow water wave equation and （2 ＋ 1）-dimensional Sawada -Kotera equation in a quick and natural manner, namely by appling the binary Bell polynomials. Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations. And the corresponding figures of the periodic wave solutions are given. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.
文摘By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riecati equation that the symmetrical Lucas functions satisfy. From the variable separation sohition and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated.
基金supported by National Natural Science Foundation of China (Grant No. 11101402)
文摘We prove here the smoothness and the irreducibility of the periodic dynatomic curves(c,z)∈C2such that z is n-periodic for zd+c,where d 2.We use the method provided by Buff and Lei where they proved the conclusion for d=2.The proof for smoothness is based on elementary calculations on the pushforwards of specific quadratic differentials,following Thurston and Epstein,while the proof for irreducibility is a simplified version of Lau-Schleicher’s proof by using elementary arithmetic properties of kneading sequence instead of internal addresses.
