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
Annual haze in Northern Thailand has become increasingly severe,impacting health and the environment.How-ever,the sources of the haze remain poorly quantified due to limited observational data on aerosol molecular tra...Annual haze in Northern Thailand has become increasingly severe,impacting health and the environment.How-ever,the sources of the haze remain poorly quantified due to limited observational data on aerosol molecular tracers.This study comprehensively investigates chemical composition of PM_(2.5),including both inorganic and organic compounds throughout haze and post-haze periods in 2019 at a rural site of Northern Thailand.Average PM_(2.5) concentrations during haze and post-haze period were 87±36 and 21±11μg/m^(3),respectively.Organic matter was the dominant contributor in PM_(2.5) mass,followed by water soluble inorganic ions and mineral dust.Molecular markers,including levoglucosan,dehydroabietic acid,and 4-nitrocatechol,and ions(Cl^(-),and K^(+)),were used to characterize low haze(PM_(2.5)<100μg/m^(3))and episodic haze(PM_(2.5)>100μg/m^(3)).Low haze is associated with local aerosols from agricultural waste burning,while episodic haze is linked to aged aerosols from mixed agricultural waste,softwood,and hardwood burning.Source apportionment incorporating these molecular markers in receptor modelling(Positive matrix factorization),identified three distinct biomass burning sources:mixed,local,and aged biomass burnings,contributing 31,19 and 13%of PM_(2.5) during haze period.During post-haze period,contributions shifted,with local biomass burning(32%)comparable to secondary sulfate(34%)and mixed dust and traffic sources(26%).These findings demonstrate that both regional and local sources con-tribute to severe haze,highlighting the need for integrated policies for cross-border cooperation as well as stricter regulations to reduce biomass burning in Northern Thailand and Southeast Asia.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Annual haze in Northern Thailand has become increasingly severe,impacting health and the environment.How-ever,the sources of the haze remain poorly quantified due to limited observational data on aerosol molecular tracers.This study comprehensively investigates chemical composition of PM_(2.5),including both inorganic and organic compounds throughout haze and post-haze periods in 2019 at a rural site of Northern Thailand.Average PM_(2.5) concentrations during haze and post-haze period were 87±36 and 21±11μg/m^(3),respectively.Organic matter was the dominant contributor in PM_(2.5) mass,followed by water soluble inorganic ions and mineral dust.Molecular markers,including levoglucosan,dehydroabietic acid,and 4-nitrocatechol,and ions(Cl^(-),and K^(+)),were used to characterize low haze(PM_(2.5)<100μg/m^(3))and episodic haze(PM_(2.5)>100μg/m^(3)).Low haze is associated with local aerosols from agricultural waste burning,while episodic haze is linked to aged aerosols from mixed agricultural waste,softwood,and hardwood burning.Source apportionment incorporating these molecular markers in receptor modelling(Positive matrix factorization),identified three distinct biomass burning sources:mixed,local,and aged biomass burnings,contributing 31,19 and 13%of PM_(2.5) during haze period.During post-haze period,contributions shifted,with local biomass burning(32%)comparable to secondary sulfate(34%)and mixed dust and traffic sources(26%).These findings demonstrate that both regional and local sources con-tribute to severe haze,highlighting the need for integrated policies for cross-border cooperation as well as stricter regulations to reduce biomass burning in Northern Thailand and Southeast Asia.
