A - affirmable 中文 - EN166

affirmable adj.可斷言的，可確定的。

In this thesis , we study some open problems and conjectures about the linear complementarity problem . it consists of the next three aspects : firstly , we study murthys “ open problem whether the augmented matrix is a q0 - matrix for an arbitary square matrix a , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the graves algorithm can be used to solve linear complementarity problem with bisymmetry po - matrices ; secondly , we study murthys “ conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix , we also study pang ' s conjecture , obtain two conditions when r0 - matrices and q - matrices are equivelent and some properties about e0 q - matrices ; lastly , we give a counterexample to prove danao ' s conjecture that if a is a po - matrix , a e “ a p1 * is false , point out some mistakes of murthys in [ 20 ] , obtain when n = 2 or 3 , a e “ a p1 * , i . e . the condition of theorem 3 . 2 of [ 25 ] that a p0 can be deleted and obtain a e “ a is an almost e - matrix if a is a co - matrix or column sufficient matrix 本文分為三個部分，主要研究了線性互補問題的幾個相關的公開問題以及猜想： ( 1 )研究了murthy等在[ 2 ]中提出的公開問題，即對任意的矩陣a ，其擴充矩陣是否為q _ 0 -矩陣，給出了肯定的回答，得到充分矩陣的擴充矩陣是充分矩陣，并討論了graves算法，證明了若a是雙對稱的p _ 0 -矩陣時， lcp ( q ， a )可由graves算法給出； ( 2 )研究了murthy等在[ 6 ]中提出關于半正定矩陣的猜想，給出了半正定矩陣的一些充分條件，并研究了pang ~ -猜想，得到了只r _ 0 -矩陣與q -矩陣的二個等價條件，以及e _ 0 q -矩陣的一些性質； ( 3 )研究了danao在[ 25 ]中提出的danao猜想，即，若a為p _ 0 -矩陣，則，我們給出了反例證明了此猜想當n 4時不成立，指出了murthy等在[ 20 ]中的一些錯誤，得到n = 2 ， 3時，即[ 25 ]中定理3 . 2中a p _ 0的條件可以去掉。
affirmance
In this thesis , we study some open problems and conjectures about the linear complementarity problem . it consists of the next three aspects : firstly , we study murthys “ open problem whether the augmented matrix is a q0 - matrix for an arbitary square matrix a , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the graves algorithm can be used to solve linear complementarity problem with bisymmetry po - matrices ; secondly , we study murthys “ conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix , we also study pang ' s conjecture , obtain two conditions when r0 - matrices and q - matrices are equivelent and some properties about e0 q - matrices ; lastly , we give a counterexample to prove danao ' s conjecture that if a is a po - matrix , a e “ a p1 * is false , point out some mistakes of murthys in [ 20 ] , obtain when n = 2 or 3 , a e “ a p1 * , i . e . the condition of theorem 3 . 2 of [ 25 ] that a p0 can be deleted and obtain a e “ a is an almost e - matrix if a is a co - matrix or column sufficient matrix 本文分為三個部分，主要研究了線性互補問題的幾個相關的公開問題以及猜想： ( 1 )研究了murthy等在[ 2 ]中提出的公開問題，即對任意的矩陣a ，其擴充矩陣是否為q _ 0 -矩陣，給出了肯定的回答，得到充分矩陣的擴充矩陣是充分矩陣，并討論了graves算法，證明了若a是雙對稱的p _ 0 -矩陣時， lcp ( q ， a )可由graves算法給出； ( 2 )研究了murthy等在[ 6 ]中提出關于半正定矩陣的猜想，給出了半正定矩陣的一些充分條件，并研究了pang ~ -猜想，得到了只r _ 0 -矩陣與q -矩陣的二個等價條件，以及e _ 0 q -矩陣的一些性質； ( 3 )研究了danao在[ 25 ]中提出的danao猜想，即，若a為p _ 0 -矩陣，則，我們給出了反例證明了此猜想當n 4時不成立，指出了murthy等在[ 20 ]中的一些錯誤，得到n = 2 ， 3時，即[ 25 ]中定理3 . 2中a p _ 0的條件可以去掉。