设T=A 0 U B是三角矩阵环,其中A和B是环,U是(B,A)-双模.用环T上模张量的同构式作为桥梁,给出环T上的模是投射余可解的Gorenstein平坦模的等价条件:若fd(BU)<∞,fd(U A)<∞或id(U A)<∞,则左T-模M=M 1 M 2φM是投射余可解的Gore...设T=A 0 U B是三角矩阵环,其中A和B是环,U是(B,A)-双模.用环T上模张量的同构式作为桥梁,给出环T上的模是投射余可解的Gorenstein平坦模的等价条件:若fd(BU)<∞,fd(U A)<∞或id(U A)<∞,则左T-模M=M 1 M 2φM是投射余可解的Gorenstein平坦模当且仅当M 1是投射余可解的Gorenstein平坦左A-模,CokerφM=M 2/Im(φM)是投射余可解的Gorenstein平坦左B-模,且φM:U AM 1→M 2是单同态.展开更多
In this paper,the solution of a parallel redundant repairable system is investigated.by using the method of functional analysis.Especially,the linear semigroups of operator theory on Banach space,we prove the existenc...In this paper,the solution of a parallel redundant repairable system is investigated.by using the method of functional analysis.Especially,the linear semigroups of operator theory on Banach space,we prove the existence of the strictly dominant eigenvalue,and show the linear stability of solution.展开更多
We propose a method to determine the solvability of the diophantine equation x^2 - Dy^2 = n for the following two cases：the following two cases：（1） D = pq, where p, q ≡ 1 mod 4 are distinct primes with （q） = 1 ...We propose a method to determine the solvability of the diophantine equation x^2 - Dy^2 = n for the following two cases：the following two cases：（1） D = pq, where p, q ≡ 1 mod 4 are distinct primes with （q） = 1 and p q （p/q（q/p）4 = -1.（2） D = 2p1P2 ... Pro, where Pi ≡ 1 mod 8, 1 ≤ i ≤m are distinct primes and D = r2 ＋s2 with r, s ≡±3 mod 8.展开更多
A consistent tanh expansion(CTE) method is used to study the modified Boussinesq equation. It i proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a ...A consistent tanh expansion(CTE) method is used to study the modified Boussinesq equation. It i proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by th Painlev′e analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependen variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initia value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among soliton and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wav interaction behaviors are studied both in analytical and graphical ways.展开更多
Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This ...Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.展开更多
文摘设T=A 0 U B是三角矩阵环,其中A和B是环,U是(B,A)-双模.用环T上模张量的同构式作为桥梁,给出环T上的模是投射余可解的Gorenstein平坦模的等价条件:若fd(BU)<∞,fd(U A)<∞或id(U A)<∞,则左T-模M=M 1 M 2φM是投射余可解的Gorenstein平坦模当且仅当M 1是投射余可解的Gorenstein平坦左A-模,CokerφM=M 2/Im(φM)是投射余可解的Gorenstein平坦左B-模,且φM:U AM 1→M 2是单同态.
基金Supported by the Nature Science Foundation of Henan Education Committee(2008A110022)
文摘In this paper,the solution of a parallel redundant repairable system is investigated.by using the method of functional analysis.Especially,the linear semigroups of operator theory on Banach space,we prove the existence of the strictly dominant eigenvalue,and show the linear stability of solution.
基金supported by National Natural Science Foundation of China(Grant No.10901150)the Deutsche Forschungsgemeinschaft(Grant No.DE 1646/2-1)
文摘We propose a method to determine the solvability of the diophantine equation x^2 - Dy^2 = n for the following two cases：the following two cases：（1） D = pq, where p, q ≡ 1 mod 4 are distinct primes with （q） = 1 and p q （p/q（q/p）4 = -1.（2） D = 2p1P2 ... Pro, where Pi ≡ 1 mod 8, 1 ≤ i ≤m are distinct primes and D = r2 ＋s2 with r, s ≡±3 mod 8.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11305106 and 11505154
文摘A consistent tanh expansion(CTE) method is used to study the modified Boussinesq equation. It i proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by th Painlev′e analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependen variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initia value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among soliton and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wav interaction behaviors are studied both in analytical and graphical ways.
基金Supported by the Key Foundation of Anhui Education Bureau under Grant No.KJ2013A028the 211 Project of Anhhui University under Grant No.J18520104+2 种基金Scientific Training Project for University StudentsNational Natural Science Foundation of China under Grant Nos.11471015,11571016Natural Science Foundation of Anhui Province under Grant No.1408085MA02
文摘Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.
