In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise c...In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.展开更多
We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigen...We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigenvector)of tridiagonal matrices,isospectral transforms and sharp bounds for speed stability of birth-death processes.展开更多
In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial ...On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.展开更多
The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability ...The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.展开更多
过程支持系统(PSS,Process Support System)是一个支持定义、执行和监控业务过程的软件系统,其中通过过程模型描述过程的各种控制结构。在基于CMM的过程支持系统——CPMS(CMM Based Process ManagementSystem)中,由于CMM中庇护性过程的...过程支持系统(PSS,Process Support System)是一个支持定义、执行和监控业务过程的软件系统,其中通过过程模型描述过程的各种控制结构。在基于CMM的过程支持系统——CPMS(CMM Based Process ManagementSystem)中,由于CMM中庇护性过程的存在,简单的过程模型的控制结构已显得不够灵活有效,需要在过程模型中加入一些新的机制以丰富其对CMM庇护性过程的支持。本文介绍了一种对CMM庇护性过程支持的机制——例程处理机制,其设计在借鉴了程序设计语言中异常处理机制的基础上,又结合了庇护性过程的实际需要对异常处理机制进行了部分修改。最后本文还给出了系统对例程处理机制的实现。展开更多
This study investigates the influence of the elastic modulus(E)of the composite strata on the trough width coefficient(i).It is hypothesized that,in composite strata,the relationship between the trough width coefficie...This study investigates the influence of the elastic modulus(E)of the composite strata on the trough width coefficient(i).It is hypothesized that,in composite strata,the relationship between the trough width coefficient(i)and the stratum thickness(H)follows a piecewise linear trend.Specifically,within strata of identical elastic modulus(E),i exhibits a linear correlation with H,while variations in E affect the slope of this correlation.Building upon the non-iterative analytical method(NIAM)for evaluating tunnel excavation responses in composite strata,this study proposes two novel approaches:the crucial point method(CPM)and the standard curve method(SCM).These methods incorporate the elastic modulus into the estimation of i.The values of i obtained via NIAM and refined through CPM and SCM are validated against field data using the parameter K.The results are consistent with existing research findings,thereby confirming the reliability of the proposed methodology.Furthermore,the study investigates the relationship between tunnel depth(h0)and tunnel radius(R),and explores the interactions among the layer number of stratum(n),elastic modulus(E),and layer thickness(H).A reduction coefficient(η)is introduced to improve the model's accuracy.The proposed approach is applied to nine tunnel engineering cases,and comparisons with measured data demonstrate its accuracy and practical applicability.展开更多
文摘In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11771046,12101186)Beijing Natural Science Foundation(Grant No.1254039).
文摘We display sharp bounds for upper and lower spectrum of a Hermitizable tridiagonal matrix.The representations are brought to light by exploiting the characteristic for eigenpairs(eigenvalue and its corresponding eigenvector)of tridiagonal matrices,isospectral transforms and sharp bounds for speed stability of birth-death processes.
文摘In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
文摘On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.
文摘The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.
文摘过程支持系统(PSS,Process Support System)是一个支持定义、执行和监控业务过程的软件系统,其中通过过程模型描述过程的各种控制结构。在基于CMM的过程支持系统——CPMS(CMM Based Process ManagementSystem)中,由于CMM中庇护性过程的存在,简单的过程模型的控制结构已显得不够灵活有效,需要在过程模型中加入一些新的机制以丰富其对CMM庇护性过程的支持。本文介绍了一种对CMM庇护性过程支持的机制——例程处理机制,其设计在借鉴了程序设计语言中异常处理机制的基础上,又结合了庇护性过程的实际需要对异常处理机制进行了部分修改。最后本文还给出了系统对例程处理机制的实现。
基金support from the National Natural Science Foundation of China(Grant No.52278387).
文摘This study investigates the influence of the elastic modulus(E)of the composite strata on the trough width coefficient(i).It is hypothesized that,in composite strata,the relationship between the trough width coefficient(i)and the stratum thickness(H)follows a piecewise linear trend.Specifically,within strata of identical elastic modulus(E),i exhibits a linear correlation with H,while variations in E affect the slope of this correlation.Building upon the non-iterative analytical method(NIAM)for evaluating tunnel excavation responses in composite strata,this study proposes two novel approaches:the crucial point method(CPM)and the standard curve method(SCM).These methods incorporate the elastic modulus into the estimation of i.The values of i obtained via NIAM and refined through CPM and SCM are validated against field data using the parameter K.The results are consistent with existing research findings,thereby confirming the reliability of the proposed methodology.Furthermore,the study investigates the relationship between tunnel depth(h0)and tunnel radius(R),and explores the interactions among the layer number of stratum(n),elastic modulus(E),and layer thickness(H).A reduction coefficient(η)is introduced to improve the model's accuracy.The proposed approach is applied to nine tunnel engineering cases,and comparisons with measured data demonstrate its accuracy and practical applicability.
