The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the development of the parallel computers, but all the research work is limited in standard eigenproblems of ...The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the development of the parallel computers, but all the research work is limited in standard eigenproblems of symmetric tridiagonal matrix. The multisection method for solving the generalized eigenproblem applied significantly in many science and engineering domains has not been studied. The parallel region preserving multisection method (PRM for short) for solving generalized eigenproblems of large sparse and real symmetric matrix is presented in this paper. This method not only retains the advantages of the conventional determinant search method (DS for short), but also overcomes its disadvantages such as leaking roots and disconvergence. We have tested the method on the YH 1 vector computer, and compared it with the parallel region preserving determinant search method the parallel region preserving bisection method (PRB for short). The numerical results show that PRM has a higher speed up, for instance, it attains the speed up of 7.7 when the scale of the problem is 2 114 and the eigenpair found is 3, and PRM is superior to PRB when the scale of the problem is large.展开更多
We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the...We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.展开更多
In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is ...In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is a generalization of the decompostion theorem of coalgebra.展开更多
In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ ...In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ = M∨N） when nest M or N is a countable nest, or S belongs to algφ^-1 when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T = US where S ∈ DN^-1 and U is unitary as N be a countable nest.展开更多
Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equatio...Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results.展开更多
Let A and H be Hopf algebra, T-smash product AT H generalizes twisted smash product A ＊ H. This paper shows a necessary and sufficient condition for T-smash product moduie category AT HM to be braided monoidal category.
The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (...The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (A) is decompcoable, moreover, in the Hilbert algebras case the assumation that A is abelian and A has an identity can be released. Those results are partially answers to a question raised by K. B. Laursen and M. M. Neumann [5].展开更多
A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence nea...A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton＇s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.展开更多
文摘The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the development of the parallel computers, but all the research work is limited in standard eigenproblems of symmetric tridiagonal matrix. The multisection method for solving the generalized eigenproblem applied significantly in many science and engineering domains has not been studied. The parallel region preserving multisection method (PRM for short) for solving generalized eigenproblems of large sparse and real symmetric matrix is presented in this paper. This method not only retains the advantages of the conventional determinant search method (DS for short), but also overcomes its disadvantages such as leaking roots and disconvergence. We have tested the method on the YH 1 vector computer, and compared it with the parallel region preserving determinant search method the parallel region preserving bisection method (PRB for short). The numerical results show that PRM has a higher speed up, for instance, it attains the speed up of 7.7 when the scale of the problem is 2 114 and the eigenpair found is 3, and PRM is superior to PRB when the scale of the problem is large.
基金Supported by the National Natural Science Foundation of China(10371051)
文摘We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.
文摘In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is a generalization of the decompostion theorem of coalgebra.
基金Supported by the National Science Foundation of China(90205019)
文摘In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ = M∨N） when nest M or N is a countable nest, or S belongs to algφ^-1 when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T = US where S ∈ DN^-1 and U is unitary as N be a countable nest.
基金Supported by the National Natural Science Foundation of China（10471065） Supported by the Natural Science Foundation of Guangdong Province（04010474）
文摘Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results.
文摘Let A and H be Hopf algebra, T-smash product AT H generalizes twisted smash product A ＊ H. This paper shows a necessary and sufficient condition for T-smash product moduie category AT HM to be braided monoidal category.
文摘The author show that if A is a complex abelian Banach algebra with an identity, then the decomposability of T∈M(A),the set of all multipliers on A, implies that the corresponding multiplication operator T: M (A)→M (A) is decompcoable, moreover, in the Hilbert algebras case the assumation that A is abelian and A has an identity can be released. Those results are partially answers to a question raised by K. B. Laursen and M. M. Neumann [5].
基金Foundation item： Supported by the National Science Foundation of China（10701066）
文摘A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton＇s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.
