In the present paper, an attempt is made to obtain the degree of approximation of conjugate of functions (signals) belonging to the generalized weighted W(LP, ξ(t)), (p ≥ 1)-class, by using lower triangular matrix o...In the present paper, an attempt is made to obtain the degree of approximation of conjugate of functions (signals) belonging to the generalized weighted W(LP, ξ(t)), (p ≥ 1)-class, by using lower triangular matrix operator of conjugate series of its Fourier series.展开更多
This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problem...This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.展开更多
The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice ...The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of Lie algebra is an important step towards constructing integrable systems.展开更多
Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomp...Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomposed into a product of involutive, inner and diagonal automorphisms.展开更多
In [Perturbation of Spectrums of 2 × 2 Operator Matrices, Proceedings of the American Mathematical Society, Vol. 121, 1994], the authors asked whether there was an operator ?such that ?for a given pair?(A,B)?of o...In [Perturbation of Spectrums of 2 × 2 Operator Matrices, Proceedings of the American Mathematical Society, Vol. 121, 1994], the authors asked whether there was an operator ?such that ?for a given pair?(A,B)?of operators, where the operator ?was defined by . In this note, a partial answer for the question is given.展开更多
Property(R)holds for an operator when the complement in the approximate point spectrum of the Browder essential approximate point spectrum coincides with the isolated points of the spectrum which are eigenvalues of fi...Property(R)holds for an operator when the complement in the approximate point spectrum of the Browder essential approximate point spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity.Let A∈B(H)and B∈B(K),where H and K are complex infinite dimensional separable Hilbert spaces.We denote by M_(C)the operator acting on H⊕K of the form M_(C)=(AC0B).In this paper,we give a sufficient and necessary condition for M_(C)∈(R)for all C∈B(K,H).展开更多
Let R be a commutative ring with identity, Tn （R） the R-algebra of all upper triangular n by n matrices over R. In this paper, it is proved that every local Jordan derivation of Tn （R） is an inner derivation and t...Let R be a commutative ring with identity, Tn （R） the R-algebra of all upper triangular n by n matrices over R. In this paper, it is proved that every local Jordan derivation of Tn （R） is an inner derivation and that every local Jordan automorphism of Tn（R） is a Jordan automorphism. As applications, we show that local derivations and local automorphisms of Tn （R） are inner.展开更多
引入拟正则Armendariz环并研究其性质。证明弱Armendariz环是拟正则Armendariz环,直积∏i∈I R i是拟正则Armendariz环当且仅当每个环R i(i∈I)是拟正则Armendariz环,同时证明R是拟正则Armendariz环当且仅当上三角矩阵环T n(R)(n≥2)是...引入拟正则Armendariz环并研究其性质。证明弱Armendariz环是拟正则Armendariz环,直积∏i∈I R i是拟正则Armendariz环当且仅当每个环R i(i∈I)是拟正则Armendariz环,同时证明R是拟正则Armendariz环当且仅当上三角矩阵环T n(R)(n≥2)是拟正则Armendariz环,并通过例子说明任意环R上的全矩阵环M n(R)(n≥2)不是拟正则Armendariz环。展开更多
文摘In the present paper, an attempt is made to obtain the degree of approximation of conjugate of functions (signals) belonging to the generalized weighted W(LP, ξ(t)), (p ≥ 1)-class, by using lower triangular matrix operator of conjugate series of its Fourier series.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)the National Natural Science Foundation of China (No. 10962004)
文摘This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.
基金＊The project supported by the National Key Basic Research Development of China under Grant No. N1998030600 and National Natural Science Foundation of China under Grant No. 10072013
文摘The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of Lie algebra is an important step towards constructing integrable systems.
文摘Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomposed into a product of involutive, inner and diagonal automorphisms.
文摘In [Perturbation of Spectrums of 2 × 2 Operator Matrices, Proceedings of the American Mathematical Society, Vol. 121, 1994], the authors asked whether there was an operator ?such that ?for a given pair?(A,B)?of operators, where the operator ?was defined by . In this note, a partial answer for the question is given.
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.GK 202007002)Nature Science Basic Research Plan in Shaanxi Province of China(Grant No.2021JM-189,2021JM-519)。
文摘Property(R)holds for an operator when the complement in the approximate point spectrum of the Browder essential approximate point spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity.Let A∈B(H)and B∈B(K),where H and K are complex infinite dimensional separable Hilbert spaces.We denote by M_(C)the operator acting on H⊕K of the form M_(C)=(AC0B).In this paper,we give a sufficient and necessary condition for M_(C)∈(R)for all C∈B(K,H).
基金Supported by the Doctor Foundation of Henan Polytechnic University (Grant No. B2010-93)
文摘Let R be a commutative ring with identity, Tn （R） the R-algebra of all upper triangular n by n matrices over R. In this paper, it is proved that every local Jordan derivation of Tn （R） is an inner derivation and that every local Jordan automorphism of Tn（R） is a Jordan automorphism. As applications, we show that local derivations and local automorphisms of Tn （R） are inner.
