Abstract： At first one of g-inverses of A （×） In＋Im（×） BT is given out, then the explicit solution to matrix equation AX ＋ XB = C is gained by using the method of matrix decomposition, finally, a nume...Abstract： At first one of g-inverses of A （×） In＋Im（×） BT is given out, then the explicit solution to matrix equation AX ＋ XB = C is gained by using the method of matrix decomposition, finally, a numerical example is obtained.展开更多
In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system...In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.展开更多
Let ARDkCS（v） denote an almost resolvable directed k-cycle system of order v. It is clear that a necessary condition for the existence of an ARDkCS（v） is v=1（mod k）. For k：3,4,5 and 6, the existence of an ARDk...Let ARDkCS（v） denote an almost resolvable directed k-cycle system of order v. It is clear that a necessary condition for the existence of an ARDkCS（v） is v=1（mod k）. For k：3,4,5 and 6, the existence of an ARDkCS （v） had been completely solved. This paper shows that there exists an ARD7CS（v） if and only if v≡1 （rood 7） and v≥8.展开更多
A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational iden...A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.展开更多
We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix...We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system and the matrix equation when thesolvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of thispaper. We also mention the other applications of the equivalence canonical form, for instance, for the compressionof color images.展开更多
Electrical property is an important problem in the field of natural science and physics, which usually involves potential, current and resistance in the electric circuit. We investigate the electrical properties of an...Electrical property is an important problem in the field of natural science and physics, which usually involves potential, current and resistance in the electric circuit. We investigate the electrical properties of an arbitrary hammock network, which has not been resolved before, and propose the exact potential formula of an arbitrary m × n hammock network by means of the Recursion-Transform method with current parameters(RT-I) pioneered by one of us [Z. Z. Tan, Phys. Rev. E 91(2015) 052122], and the branch currents and equivalent resistance of the network are derived naturally. Our key technique is to setting up matrix equations and making matrix transformation, the potential formula derived is a meaningful discovery, which deduces many novel applications. The discovery of potential formula of the hammock network provides new theoretical tools and techniques for related scientific research.展开更多
文摘Abstract： At first one of g-inverses of A （×） In＋Im（×） BT is given out, then the explicit solution to matrix equation AX ＋ XB = C is gained by using the method of matrix decomposition, finally, a numerical example is obtained.
基金Foundation item： Supported by the Science Foundation of Liuzhou Vocational Institute of Technology（2007C03）
文摘In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.
基金Natural Science Research Leading Item ofJiangsu (No.04 DJ110144) Natural Out-standing Younger Science Foundation(No.60225007)and Postdoctoral ScienceFoundation of China(No.20020248024)
文摘Let ARDkCS（v） denote an almost resolvable directed k-cycle system of order v. It is clear that a necessary condition for the existence of an ARDkCS（v） is v=1（mod k）. For k：3,4,5 and 6, the existence of an ARDkCS （v） had been completely solved. This paper shows that there exists an ARD7CS（v） if and only if v≡1 （rood 7） and v≥8.
基金Project supported by the State Administration of Foreign Experts Affairs of Chinathe National Natural Science Foundation of China (Nos.10971136,10831003,61072147,11071159)+3 种基金the Chunhui Plan of the Ministry of Education of Chinathe Innovation Project of Zhejiang Province (No.T200905)the Natural Science Foundation of Shanghai (No.09ZR1410800)the Shanghai Leading Academic Discipline Project (No.J50101)
文摘A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.
基金supported by National Natural Science Foundation of China (GrantNo. 60672160)the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20093108110001)+3 种基金the Scientific Research Innovation Foundation of Shanghai Municipal Education Commission (Grant No. 09YZ13)the Netherlands Organization for Scientific Research (NWO)Singapore MoE Tier 1 Research Grant RG60/07Shanghai Leading Academic Discipline Project (Grant No. J50101)
文摘We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system and the matrix equation when thesolvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of thispaper. We also mention the other applications of the equivalence canonical form, for instance, for the compressionof color images.
基金Supported by the Natural Science Foundation of Jiangsu Province under Grant No.BK20161278
文摘Electrical property is an important problem in the field of natural science and physics, which usually involves potential, current and resistance in the electric circuit. We investigate the electrical properties of an arbitrary hammock network, which has not been resolved before, and propose the exact potential formula of an arbitrary m × n hammock network by means of the Recursion-Transform method with current parameters(RT-I) pioneered by one of us [Z. Z. Tan, Phys. Rev. E 91(2015) 052122], and the branch currents and equivalent resistance of the network are derived naturally. Our key technique is to setting up matrix equations and making matrix transformation, the potential formula derived is a meaningful discovery, which deduces many novel applications. The discovery of potential formula of the hammock network provides new theoretical tools and techniques for related scientific research.
