With the help of some reductions of the self-dual Yang Mills(briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of(2 + 1)-dimensional equations. Its first reductio...With the help of some reductions of the self-dual Yang Mills(briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of(2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation,the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new(2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of(2 + 1)-dimensional integrable couplings of a new(2 + 1)-dimensional integrable nonlinear equation.展开更多
This paper constructs a dual bialgebra for a multi-parameter FRT-bialgebra related to a Hayashi's R-matrix by using the skew-derivation method and proves that the pairing between them is non-degenerate.
In this paper, we introduce the signed weak gliding hump property in a dual pair with the structure of a system of sections and show that if a dual pair [E, F] has the signed weak gliding hump property, then the β-du...In this paper, we introduce the signed weak gliding hump property in a dual pair with the structure of a system of sections and show that if a dual pair [E, F] has the signed weak gliding hump property, then the β-dual space of E is a weak sequentially complete space if and only if for every n ∈N,(F[n] ,σ(F[n] ,E[n] )) is sequentially complete. Furthermore, we also prove that if [E,F] has the signed weak gliding hump property, then (E,τ(E,E<β> )) is an AK- space.展开更多
A module pair （C, T） over an Artin algebra A is called a tilting pair if both C and T are selforthogonal modules and the conditions T e ada C and C ∈ add T hold. The duality on a tilting pair is investigated to dis...A module pair （C, T） over an Artin algebra A is called a tilting pair if both C and T are selforthogonal modules and the conditions T e ada C and C ∈ add T hold. The duality on a tilting pair is investigated to discuss the condition under which the dual of a tilting pair is also a tilting pair. A necessary and sufficient condition of （D（7）, D（C） ） being an n-tilting pair over an Artin algebra for an n-tilting pair （ C, 7） is given. And, a necessary and sufficient condition of （ T^＊, C^＊ ） being an ntilting pair over a selfinjective Artin algebra for an n-tilting pair （C, 7） is also given.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities(2013XK03)the National Natural Science Foundation of China under Grant No.11371361
文摘With the help of some reductions of the self-dual Yang Mills(briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of(2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation,the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new(2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of(2 + 1)-dimensional integrable couplings of a new(2 + 1)-dimensional integrable nonlinear equation.
文摘This paper constructs a dual bialgebra for a multi-parameter FRT-bialgebra related to a Hayashi's R-matrix by using the skew-derivation method and proves that the pairing between them is non-degenerate.
基金Supported by Research Fund of Kumoh National Institute of Technology,Korea
文摘In this paper, we introduce the signed weak gliding hump property in a dual pair with the structure of a system of sections and show that if a dual pair [E, F] has the signed weak gliding hump property, then the β-dual space of E is a weak sequentially complete space if and only if for every n ∈N,(F[n] ,σ(F[n] ,E[n] )) is sequentially complete. Furthermore, we also prove that if [E,F] has the signed weak gliding hump property, then (E,τ(E,E<β> )) is an AK- space.
基金The National Natural Science Foundation of China (No.10971024)the Specialized Research Fund for the Doctoral Program of Higher Education ( No. 200802860024)+1 种基金the Natural Science Foundation of Jiangsu Province ( No. BK2010393 )Scientific Research Foundation of Guangxi University ( No. XJZ100246)
文摘A module pair （C, T） over an Artin algebra A is called a tilting pair if both C and T are selforthogonal modules and the conditions T e ada C and C ∈ add T hold. The duality on a tilting pair is investigated to discuss the condition under which the dual of a tilting pair is also a tilting pair. A necessary and sufficient condition of （D（7）, D（C） ） being an n-tilting pair over an Artin algebra for an n-tilting pair （ C, 7） is given. And, a necessary and sufficient condition of （ T^＊, C^＊ ） being an ntilting pair over a selfinjective Artin algebra for an n-tilting pair （C, 7） is also given.
