This paper gives and proofs a theorem, for any matrix A, do elementary column operations, change it to a matrix which is partitioned to two blocks which left one is column full rank and right one is zero matrix. That ...This paper gives and proofs a theorem, for any matrix A, do elementary column operations, change it to a matrix which is partitioned to two blocks which left one is column full rank and right one is zero matrix. That is, use a invertible matrix P to let AP = （B,O）, O is zero matrix with n-r columns, r and n is rank and column number of A, so the P＇s right n-r columns is just the basis of the null space of the matrix A. On the basis of the theorem, lots of problems of linear algebra can be resolved and lots of theorems can be proofed by elementary column operations. Perhaps the textbooks used in universities will have a lot of change with the result of the paper. This result is first found by author in 2010.12.8 in http：//www.paper.edu.cn/index.php/default/releasepaper/content/201012-232, but is not formal published.展开更多
A parallel algorithm for statistical-fairness-based spectrum allocation of cognitive radios is proposedin this paper. The key idea of the algorithm is to pursue the maximum total spectrum utilization of thesystem by a...A parallel algorithm for statistical-fairness-based spectrum allocation of cognitive radios is proposedin this paper. The key idea of the algorithm is to pursue the maximum total spectrum utilization of thesystem by adopting a parallel technique in every spectrum allocation, and to ensure the statistical fairnessrule by deploying a particular scheme during a series of allocations. The simulation results show that theproposed algorithm not only achieves a fairer and more efficient allocation of spectrum resources, but alsohas much shorter allocation duration than the color sensitive graph coloring (CSGC) algorithm.展开更多
文摘This paper gives and proofs a theorem, for any matrix A, do elementary column operations, change it to a matrix which is partitioned to two blocks which left one is column full rank and right one is zero matrix. That is, use a invertible matrix P to let AP = （B,O）, O is zero matrix with n-r columns, r and n is rank and column number of A, so the P＇s right n-r columns is just the basis of the null space of the matrix A. On the basis of the theorem, lots of problems of linear algebra can be resolved and lots of theorems can be proofed by elementary column operations. Perhaps the textbooks used in universities will have a lot of change with the result of the paper. This result is first found by author in 2010.12.8 in http：//www.paper.edu.cn/index.php/default/releasepaper/content/201012-232, but is not formal published.
基金Supported by the National Basic Research Program of China ( No. 2007CB310603)the National High Technology Research and Development Program of China (No. 2006AA10Z258)+1 种基金the Research Fund of NCRL of Southeast University (No. 2008A05&B05a)the UWCL of Ministry of Education of BUPT (No.030801).
文摘A parallel algorithm for statistical-fairness-based spectrum allocation of cognitive radios is proposedin this paper. The key idea of the algorithm is to pursue the maximum total spectrum utilization of thesystem by adopting a parallel technique in every spectrum allocation, and to ensure the statistical fairnessrule by deploying a particular scheme during a series of allocations. The simulation results show that theproposed algorithm not only achieves a fairer and more efficient allocation of spectrum resources, but alsohas much shorter allocation duration than the color sensitive graph coloring (CSGC) algorithm.
