We discuss two-stage iterative methods for the solution of linear systemAx = b, and give a new proof of the comparison theorems of two-stage iterative methodfor an Hermitian positive definite matrix. Meanwhile, we put...We discuss two-stage iterative methods for the solution of linear systemAx = b, and give a new proof of the comparison theorems of two-stage iterative methodfor an Hermitian positive definite matrix. Meanwhile, we put forward two new versionsof well known comparison theorem and apply them to some examples.展开更多
This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic...This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates.展开更多
In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking ...In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.展开更多
In this paper, by introducing isometrically Pc0 property a separation form of convergence theorem is presented and the results generalize and unify several interesting conclusions in recent years.
As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the ...As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.展开更多
Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with...Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.展开更多
基金This work is supported by NSF of Shanxi province,20011041.
文摘We discuss two-stage iterative methods for the solution of linear systemAx = b, and give a new proof of the comparison theorems of two-stage iterative methodfor an Hermitian positive definite matrix. Meanwhile, we put forward two new versionsof well known comparison theorem and apply them to some examples.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10962004and11061019)'Chunhui Program' Ministry of Education(Grant No.Z2009-1-01010)+3 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20070126002)the Doctoral Foundation of Inner Mongolia(Grant No.2009BS0101)the Natural Science Foundation of Inner Mongolia(Grant No.2010MS0110)the Cultivation of Innovative Talent of '211Project'of Inner Mongolia University
文摘This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates.
文摘In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.
文摘In this paper, by introducing isometrically Pc0 property a separation form of convergence theorem is presented and the results generalize and unify several interesting conclusions in recent years.
文摘As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.
文摘Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.
