We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial <i>P</i>(<i>X</i>) over the field C[<i>X</i>]. From a <i>n</i>...We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial <i>P</i>(<i>X</i>) over the field C[<i>X</i>]. From a <i>n</i>×<i>n</i> Fiedler companion matrix <i>C</i>, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix <i>L<sub>r</sub></i>, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of <i>L<sub>r</sub></i>, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.展开更多
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
Let G be a strongly connected directed weighted graph with vertex set{v_(1),v_(2),...,v_(n)},in which each edge e is assigned with an arbitrary nonzero weight w(e).For any two vertices v_i,v_(j )of G,the distance d_(i...Let G be a strongly connected directed weighted graph with vertex set{v_(1),v_(2),...,v_(n)},in which each edge e is assigned with an arbitrary nonzero weight w(e).For any two vertices v_i,v_(j )of G,the distance d_(ij )from v_(i)to v_(j)is defined as dij=P∈P(v_(i),v_(j))min∑w(e) where P(v_(i),v_(j)) denotes the set consisting of all the directed paths from v_(i)to v_(j)in G.Given a nonzero indeterminant q,following the definitions from Yan and Yeh (Adv.Appl.Math.,2007),and Bapat et al.(Linear Algebra Appl.,2006),one can define the exponential distance matrix of G as F^(q)_(G)=(q^(dij))_(n×n),and define the q-distance matrix of G as D_(G)^(q)=(d_(ij)^(q))_(n×n)with d_(ij)^(q)={1-q^(dij)/1-q,if q≠1,dij,if q=1,extending the original definitions only for the undirected unweighted connected graphs.One of the remarkable results about the distance matrices of graphs is due to the Graham-HoffmanHosoya theorem (J.Graph Theory,1977).In this paper,we present some Graham-HoffmanHosoya type theorems for the exponential distance matrix F_(G)^(q)and q-distance matrix D_(G)^(q),extending all the known Graham-Hoffman-Hosoya type theorems.展开更多
Melanocytic matricoma is a very rare adnexal tumor that recapitulates the anagen hair follicle bulb. Few cases of malignant melanocytic matricoma have been reported, thus criteria for malignant potential have not been...Melanocytic matricoma is a very rare adnexal tumor that recapitulates the anagen hair follicle bulb. Few cases of malignant melanocytic matricoma have been reported, thus criteria for malignant potential have not been previously reviewed. We report a case of an 81 year old male that was originally diagnosed as atypical melanocytic matricoma. The site was re-excised with a small focus of residual tumor, but all margins were negative. The re-excision site healed without complication. However, two years after the original biopsy, a new 8 mm firm nodule appeared at the re-excision site, which was subsequently diagnosed as malignant melanocytic matricoma (MMM). In the following paper we will report a new case of MMM and review potential criteria that could be used in the future to establish malignant potential.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.
In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind...In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.展开更多
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
In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of th...In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.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
Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple ...Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.展开更多
A partition reduction method is used to obtain new upper bounds for the inverses of H-matrices and S-strictly diagonally dominant(S-SDD)matrices.The estimates are expressed via the determinants of third order matrices...A partition reduction method is used to obtain new upper bounds for the inverses of H-matrices and S-strictly diagonally dominant(S-SDD)matrices.The estimates are expressed via the determinants of third order matrices.Numerical experiments with various random matrices show that they are stable and better than the estimates presented in literatures.We use these upper bounds to improve known error estimates for linear complementarity problems with H-matrices and S-SDD matrices.展开更多
The class of E＇-matrices introduced in [4] is a subclass of Q0-matrices whose proper principal submatrices are Q--matrices. In this paper, we investigate the relation of the class E＇ to other known matrix classes an...The class of E＇-matrices introduced in [4] is a subclass of Q0-matrices whose proper principal submatrices are Q--matrices. In this paper, we investigate the relation of the class E＇ to other known matrix classes and obtain a series of necessary and sufficient conditions for E＇-matrices.展开更多
The class of generalized α-matrices is presented by Cvetkovi?, L. (2006), and proved to be a subclass of H-matrices. In this paper, we present a new class of matrices-generalized irreducible α-matrices, and prove th...The class of generalized α-matrices is presented by Cvetkovi?, L. (2006), and proved to be a subclass of H-matrices. In this paper, we present a new class of matrices-generalized irreducible α-matrices, and prove that a generalized irreducible α-matrix is an H-matrix. Furthermore, using the generalized arithmetic-geometric mean inequality, we obtain two new classes of H-matrices. As applications of the obtained results, three regions including all the eigenvalues of a matrix are given.展开更多
The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzz...The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.展开更多
The major objective of this work was to establish a structural state-space model to estimate the dynamic origin-destination(O-D) matrices for urban rail transit network, using in- and out-flows at each station from au...The major objective of this work was to establish a structural state-space model to estimate the dynamic origin-destination(O-D) matrices for urban rail transit network, using in- and out-flows at each station from automatic fare collection(AFC) system as the real time observed passenger flow counts. For lacking of measurable passenger flow information, the proposed model employs priori O-D matrices and travel time distribution from historical travel records in AFC system to establish the dynamic system equations. An arriving rate based on travel time distribution is defined to identify the dynamic interrelations between time-varying O-D flows and observed flows, which greatly decreases the computational complexity and improve the model's applicability for large-scale network. This methodology is tested in a real transit network from Beijing subway network in China through comparing the predicted matrices with the true matrices. Case study results indicate that the proposed model is effective and applicative for estimating dynamic O-D matrices for large-scale rail transit network.展开更多
This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is trans...This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.展开更多
Objective:To formulate and evaluate the application of PEGylated mucin in oral bioadhesive drug(OBD) delivery system.Methods:The bioadhesive strength of different formulation ratios of polyethylene glycol(PEG) and muc...Objective:To formulate and evaluate the application of PEGylated mucin in oral bioadhesive drug(OBD) delivery system.Methods:The bioadhesive strength of different formulation ratios of polyethylene glycol(PEG) and mucin was evaluated by tensiometry.Co polymer matrices containing mucin and PEG(PEGylated mucin) in the following ratios of 1:1(A),2:1(B),1:2(C), 0:1(D) and 1:0(E) were prepared by co-precipitation.Microparticles were prepared from the matrices using a size reduction technique.Five different samples were prepared using direct mixtures in the appropriate solvenfs having mucin and PEG ratios of 1:1,2:1,1:2,0:1, 1:0 and labeled as(A-E).The matrices were evaluated for their flow properties and the in vitro bioadhesion characteristics of the samples were examined.Results:The range of flow rates of the matrices was 1.35-2.23 g/sec.The angle of repose was in the range of 37.3-39.9 degree.The bulk and tapped densities were within the ranges of 0.41- 0.49.The Hausner’s quotient(HQ) were 1.12, 1.24,1.14,1.25 and 1.2 for matrix batches A-E respectively,The bioadhesive strength of polymer matrices appeared to be directly related to amount of mucin.The order of bioadhesive strength is 2:1】1:1】1:0】1:2】0:1 of PEG:mucin in both simulated intestine fluid(SEP) and simulated gastrointestinal fluid(SGF).The physical properties of the micrometrics properties of the matrices were within the accepted values.Conclusions:OBD preparation containing PEGylated mucin can be prepared by direct compression and be used in drug delivery to the oral cavity.展开更多
文摘We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial <i>P</i>(<i>X</i>) over the field C[<i>X</i>]. From a <i>n</i>×<i>n</i> Fiedler companion matrix <i>C</i>, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix <i>L<sub>r</sub></i>, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of <i>L<sub>r</sub></i>, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.
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Let G be a strongly connected directed weighted graph with vertex set{v_(1),v_(2),...,v_(n)},in which each edge e is assigned with an arbitrary nonzero weight w(e).For any two vertices v_i,v_(j )of G,the distance d_(ij )from v_(i)to v_(j)is defined as dij=P∈P(v_(i),v_(j))min∑w(e) where P(v_(i),v_(j)) denotes the set consisting of all the directed paths from v_(i)to v_(j)in G.Given a nonzero indeterminant q,following the definitions from Yan and Yeh (Adv.Appl.Math.,2007),and Bapat et al.(Linear Algebra Appl.,2006),one can define the exponential distance matrix of G as F^(q)_(G)=(q^(dij))_(n×n),and define the q-distance matrix of G as D_(G)^(q)=(d_(ij)^(q))_(n×n)with d_(ij)^(q)={1-q^(dij)/1-q,if q≠1,dij,if q=1,extending the original definitions only for the undirected unweighted connected graphs.One of the remarkable results about the distance matrices of graphs is due to the Graham-HoffmanHosoya theorem (J.Graph Theory,1977).In this paper,we present some Graham-HoffmanHosoya type theorems for the exponential distance matrix F_(G)^(q)and q-distance matrix D_(G)^(q),extending all the known Graham-Hoffman-Hosoya type theorems.
文摘Melanocytic matricoma is a very rare adnexal tumor that recapitulates the anagen hair follicle bulb. Few cases of malignant melanocytic matricoma have been reported, thus criteria for malignant potential have not been previously reviewed. We report a case of an 81 year old male that was originally diagnosed as atypical melanocytic matricoma. The site was re-excised with a small focus of residual tumor, but all margins were negative. The re-excision site healed without complication. However, two years after the original biopsy, a new 8 mm firm nodule appeared at the re-excision site, which was subsequently diagnosed as malignant melanocytic matricoma (MMM). In the following paper we will report a new case of MMM and review potential criteria that could be used in the future to establish malignant potential.
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In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.
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In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.
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.
基金The NSF (10571114) of Chinathe Natural Science Basic Research Plan (2005A1) of Shaanxi Province of China
文摘Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.
基金Supported by the Scientific Research Project of Education Department of Hunan Province(Grant No.21C0837).
文摘A partition reduction method is used to obtain new upper bounds for the inverses of H-matrices and S-strictly diagonally dominant(S-SDD)matrices.The estimates are expressed via the determinants of third order matrices.Numerical experiments with various random matrices show that they are stable and better than the estimates presented in literatures.We use these upper bounds to improve known error estimates for linear complementarity problems with H-matrices and S-SDD matrices.
基金Supported by the YSF of Guangdong University of Technology(062058)
文摘The class of E＇-matrices introduced in [4] is a subclass of Q0-matrices whose proper principal submatrices are Q--matrices. In this paper, we investigate the relation of the class E＇ to other known matrix classes and obtain a series of necessary and sufficient conditions for E＇-matrices.
文摘The class of generalized α-matrices is presented by Cvetkovi?, L. (2006), and proved to be a subclass of H-matrices. In this paper, we present a new class of matrices-generalized irreducible α-matrices, and prove that a generalized irreducible α-matrix is an H-matrix. Furthermore, using the generalized arithmetic-geometric mean inequality, we obtain two new classes of H-matrices. As applications of the obtained results, three regions including all the eigenvalues of a matrix are given.
基金This work was partially supported by the Natural Science Foundation of China （No. 611 74094） the Tianjin Natural Science Foundation of China （No. 13JCYBJC1 7400） the Program for New Century Excellent Talents in University of China （No. NCET-10-0506）.
文摘The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.
基金Project(51478036)supported by the National Natural Science Foundation of ChinaProject(20120009110016)supported by Research Fund for Doctoral Program of Higher EducationChina
文摘The major objective of this work was to establish a structural state-space model to estimate the dynamic origin-destination(O-D) matrices for urban rail transit network, using in- and out-flows at each station from automatic fare collection(AFC) system as the real time observed passenger flow counts. For lacking of measurable passenger flow information, the proposed model employs priori O-D matrices and travel time distribution from historical travel records in AFC system to establish the dynamic system equations. An arriving rate based on travel time distribution is defined to identify the dynamic interrelations between time-varying O-D flows and observed flows, which greatly decreases the computational complexity and improve the model's applicability for large-scale network. This methodology is tested in a real transit network from Beijing subway network in China through comparing the predicted matrices with the true matrices. Case study results indicate that the proposed model is effective and applicative for estimating dynamic O-D matrices for large-scale rail transit network.
基金the National Natural Science Foundation of China (No.60874024, 60574013).
文摘This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.
文摘Objective:To formulate and evaluate the application of PEGylated mucin in oral bioadhesive drug(OBD) delivery system.Methods:The bioadhesive strength of different formulation ratios of polyethylene glycol(PEG) and mucin was evaluated by tensiometry.Co polymer matrices containing mucin and PEG(PEGylated mucin) in the following ratios of 1:1(A),2:1(B),1:2(C), 0:1(D) and 1:0(E) were prepared by co-precipitation.Microparticles were prepared from the matrices using a size reduction technique.Five different samples were prepared using direct mixtures in the appropriate solvenfs having mucin and PEG ratios of 1:1,2:1,1:2,0:1, 1:0 and labeled as(A-E).The matrices were evaluated for their flow properties and the in vitro bioadhesion characteristics of the samples were examined.Results:The range of flow rates of the matrices was 1.35-2.23 g/sec.The angle of repose was in the range of 37.3-39.9 degree.The bulk and tapped densities were within the ranges of 0.41- 0.49.The Hausner’s quotient(HQ) were 1.12, 1.24,1.14,1.25 and 1.2 for matrix batches A-E respectively,The bioadhesive strength of polymer matrices appeared to be directly related to amount of mucin.The order of bioadhesive strength is 2:1】1:1】1:0】1:2】0:1 of PEG:mucin in both simulated intestine fluid(SEP) and simulated gastrointestinal fluid(SGF).The physical properties of the micrometrics properties of the matrices were within the accepted values.Conclusions:OBD preparation containing PEGylated mucin can be prepared by direct compression and be used in drug delivery to the oral cavity.
