In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
We read with the great interest the study by Ababneh et al in which inducedmesenchymal stem cell-derived exosomes were shown to exhibit a stronger andmore sustained anti-proliferative effect by inducing a senescence-l...We read with the great interest the study by Ababneh et al in which inducedmesenchymal stem cell-derived exosomes were shown to exhibit a stronger andmore sustained anti-proliferative effect by inducing a senescence-like state withoutapoptosis.The results obtained by the authors highlight the features of theeffects of senescent drift induction in surrounding tissues.In the light of thesefindings,the role of the properties of extracellular matrix and cellular glycocalyxin responses of human tumors to therapy remain uninvestigated.These extracellularbarriers appear to be significant obstacles to effective cancer therapy,especiallyin relation to the use of unique properties of tumor microenvironment forthe immunotherapy-resistant cancer treatment.展开更多
Peripheral nerve injury causes severe neuroinflammation and has become a global medical challenge.Previous research has demonstrated that porcine decellularized nerve matrix hydrogel exhibits excellent biological prop...Peripheral nerve injury causes severe neuroinflammation and has become a global medical challenge.Previous research has demonstrated that porcine decellularized nerve matrix hydrogel exhibits excellent biological properties and tissue specificity,highlighting its potential as a biomedical material for the repair of severe peripheral nerve injury;however,its role in modulating neuroinflammation post-peripheral nerve injury remains unknown.Here,we aimed to characterize the anti-inflammatory properties of porcine decellularized nerve matrix hydrogel and their underlying molecular mechanisms.Using peripheral nerve injury model rats treated with porcine decellularized nerve matrix hydrogel,we evaluated structural and functional recovery,macrophage phenotype alteration,specific cytokine expression,and changes in related signaling molecules in vivo.Similar parameters were evaluated in vitro using monocyte/macrophage cell lines stimulated with lipopolysaccharide and cultured on porcine decellularized nerve matrix hydrogel-coated plates in complete medium.These comprehensive analyses revealed that porcine decellularized nerve matrix hydrogel attenuated the activation of excessive inflammation at the early stage of peripheral nerve injury and increased the proportion of the M2 subtype in monocytes/macrophages.Additionally,porcine decellularized nerve matrix hydrogel negatively regulated the Toll-like receptor 4/myeloid differentiation factor 88/nuclear factor-κB axis both in vivo and in vitro.Our findings suggest that the efficacious anti-inflammatory properties of porcine decellularized nerve matrix hydrogel induce M2 macrophage polarization via suppression of the Toll-like receptor 4/myeloid differentiation factor 88/nuclear factor-κB pathway,providing new insights into the therapeutic mechanism of porcine decellularized nerve matrix hydrogel in peripheral nerve injury.展开更多
A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. Th...A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold.展开更多
The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covarian...The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.展开更多
The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise w...The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.展开更多
Let R be an associative ring with unity 1. The existence of the Moore-Penrose inverses of block matrices overR is investigated and the sufficient ad necessary conditions for such existence are obtained. Furthermore, ...Let R be an associative ring with unity 1. The existence of the Moore-Penrose inverses of block matrices overR is investigated and the sufficient ad necessary conditions for such existence are obtained. Furthermore, the representation of the Moore-Penrose inverse of M=[0 A C B]is given under the condition of EBF - 0, where E - I - CCT and F - I -AfA. This result generalizes the representation of the Moore-Penrose inverse of the companion matrix M =[0 a In b]due to Pedro Patricio. As for applications, some examples are given to illustrate the obtained results.展开更多
An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new al...An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new algorithm with the cost of (4n + 6) is presented to compute the determinant of a pentadiagonal Toeplitz matrix. The inverse of a pentadiagonal Toeplitz matrix is also considered.展开更多
A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. T...A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.展开更多
By using the classical Cayley-Hamilton theorem,the polynomial equations of the core-EP inverse matrix and Drazin-Moore-Penrose(DMP)inverse matrix are given,respectively.If the characteristic polynomial of the singular...By using the classical Cayley-Hamilton theorem,the polynomial equations of the core-EP inverse matrix and Drazin-Moore-Penrose(DMP)inverse matrix are given,respectively.If the characteristic polynomial of the singular matrix A,p A(s)=det(s E n-A)=s n+a n-1 s n-1+…+a 1 s,is given,then f A(A)=0 and f A(A d,+)=0 in which f A(A)=a 1 x n+a 2 x n-1+…+a n-1 x 2+x,and A and A d,+are the core-EP inverse and the DMP inverse of A,respectively.Furthermore,some properties of the characteristic polynomials of A D∈C n,n and A∈C n,n are derived.展开更多
This article proposes a new algorithm of quaternion and dual quaternion in matrix form. It applies quaternion in special cases of rotated plane, transforming the sine and cosine of the rotation angle into matrix form,...This article proposes a new algorithm of quaternion and dual quaternion in matrix form. It applies quaternion in special cases of rotated plane, transforming the sine and cosine of the rotation angle into matrix form, then exporting flat quaternions base in two matrix form. It establishes serial 6R manipulator kinematic equations in the form of quaternion matrix. Then five variables are eliminated through linear elimination and application of lexicographic Groebner base. Thus, upper bound of the degree of the equation is determined, which is 16. In this way, a 16-degree equation with single variable is obtained without any extraneous root. This is the first time that quaternion matrix modeling has been used in 6R robot inverse kinematics analysis.展开更多
A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical...A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.展开更多
The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions fo...The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions for the existence of such solutions and their general forms are derived.展开更多
This paper presents a recursive procedure to compute the Moore-Penrose inverse of a matrix A. The method is based on the expression for the Moore-Penrose inverse of rank-one modified matrix. The computational complexi...This paper presents a recursive procedure to compute the Moore-Penrose inverse of a matrix A. The method is based on the expression for the Moore-Penrose inverse of rank-one modified matrix. The computational complexity of the method is analyzed and a numerical example is included. A variant of the algorithm with lower computational complexity is also proposed. Both algorithms are tested on randomly generated matrices. Numerical performance confirms our theoretic results.展开更多
Censider the solutions of the matrix inverse problem, which are symmetric positive semide finite on a subspace. Necessary and sufficient conditions for the solvability, as well as the general solution are obtained. Th...Censider the solutions of the matrix inverse problem, which are symmetric positive semide finite on a subspace. Necessary and sufficient conditions for the solvability, as well as the general solution are obtained. The best approximate solution by the above solution set is given. Thus the open problem in [1] is solved.展开更多
Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub&...Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is展开更多
In this article, the expression for the Drazin inverse of a modified matrix is considered and some interesting results are established. This contributes to certain recent results obtained by Y.Wei [9].
In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fra...In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.展开更多
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
文摘We read with the great interest the study by Ababneh et al in which inducedmesenchymal stem cell-derived exosomes were shown to exhibit a stronger andmore sustained anti-proliferative effect by inducing a senescence-like state withoutapoptosis.The results obtained by the authors highlight the features of theeffects of senescent drift induction in surrounding tissues.In the light of thesefindings,the role of the properties of extracellular matrix and cellular glycocalyxin responses of human tumors to therapy remain uninvestigated.These extracellularbarriers appear to be significant obstacles to effective cancer therapy,especiallyin relation to the use of unique properties of tumor microenvironment forthe immunotherapy-resistant cancer treatment.
基金supported by the Shenzhen Hong Kong Joint Funding Project,No.SGDX20230116093645007(to LY)the Shenzhen Science and Technology Innovation Committee International Cooperation Project,No.GJHZ20200731095608025(to LY)+7 种基金Shenzhen Development and Reform Commission’s Intelligent Diagnosis,Treatment and Prevention of Adolescent Spinal Health Public Service Platform,No.S2002Q84500835(to LY)Shenzhen Medical Research Fund,No.B2303005(to LY)Team-based Medical Science Research Program,No.2024YZZ02(to LY)Zhejiang Provincial Natural Science Foundation of China,No.LWQ20H170001(to RL)Basic Research Project of Shenzhen Science and Technology from Shenzhen Science and Technology Innovation Commission,No.JCYJ20210324103010029(to BY)Shenzhen Second People’s Hospital Clinical Research Fund of Guangdong Province High-level Hospital Construction Project,Nos.2023yjlcyj029(to BY),2023yjlcyj021(to LL)Guangdong Basic and Applied Basic Research Foundation,No.2022A1515110679(to LL)China Postdoctoral Science Foundation,No.2022M722203(to GL).
文摘Peripheral nerve injury causes severe neuroinflammation and has become a global medical challenge.Previous research has demonstrated that porcine decellularized nerve matrix hydrogel exhibits excellent biological properties and tissue specificity,highlighting its potential as a biomedical material for the repair of severe peripheral nerve injury;however,its role in modulating neuroinflammation post-peripheral nerve injury remains unknown.Here,we aimed to characterize the anti-inflammatory properties of porcine decellularized nerve matrix hydrogel and their underlying molecular mechanisms.Using peripheral nerve injury model rats treated with porcine decellularized nerve matrix hydrogel,we evaluated structural and functional recovery,macrophage phenotype alteration,specific cytokine expression,and changes in related signaling molecules in vivo.Similar parameters were evaluated in vitro using monocyte/macrophage cell lines stimulated with lipopolysaccharide and cultured on porcine decellularized nerve matrix hydrogel-coated plates in complete medium.These comprehensive analyses revealed that porcine decellularized nerve matrix hydrogel attenuated the activation of excessive inflammation at the early stage of peripheral nerve injury and increased the proportion of the M2 subtype in monocytes/macrophages.Additionally,porcine decellularized nerve matrix hydrogel negatively regulated the Toll-like receptor 4/myeloid differentiation factor 88/nuclear factor-κB axis both in vivo and in vitro.Our findings suggest that the efficacious anti-inflammatory properties of porcine decellularized nerve matrix hydrogel induce M2 macrophage polarization via suppression of the Toll-like receptor 4/myeloid differentiation factor 88/nuclear factor-κB pathway,providing new insights into the therapeutic mechanism of porcine decellularized nerve matrix hydrogel in peripheral nerve injury.
文摘A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold.
文摘The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.
文摘The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.
基金The National Natural Science Foundation of China(No.11371089)the Natural Science Foundation of Jiangsu Province(No.BK20141327)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)the Natural Science Foundation of Jiangsu Higher Education Institutions of China(No.15KJB110021)
文摘Let R be an associative ring with unity 1. The existence of the Moore-Penrose inverses of block matrices overR is investigated and the sufficient ad necessary conditions for such existence are obtained. Furthermore, the representation of the Moore-Penrose inverse of M=[0 A C B]is given under the condition of EBF - 0, where E - I - CCT and F - I -AfA. This result generalizes the representation of the Moore-Penrose inverse of the companion matrix M =[0 a In b]due to Pedro Patricio. As for applications, some examples are given to illustrate the obtained results.
文摘An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new algorithm with the cost of (4n + 6) is presented to compute the determinant of a pentadiagonal Toeplitz matrix. The inverse of a pentadiagonal Toeplitz matrix is also considered.
文摘A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.
基金The China Postdoctoral Science Foundation(No.2015M581690)the National Natural Science Foundation of China(No.11371089)+1 种基金the Natural Science Foundation of Jiangsu Province(No.BK20141327)the Special Fund for Bagui Scholars of Guangxi
文摘By using the classical Cayley-Hamilton theorem,the polynomial equations of the core-EP inverse matrix and Drazin-Moore-Penrose(DMP)inverse matrix are given,respectively.If the characteristic polynomial of the singular matrix A,p A(s)=det(s E n-A)=s n+a n-1 s n-1+…+a 1 s,is given,then f A(A)=0 and f A(A d,+)=0 in which f A(A)=a 1 x n+a 2 x n-1+…+a n-1 x 2+x,and A and A d,+are the core-EP inverse and the DMP inverse of A,respectively.Furthermore,some properties of the characteristic polynomials of A D∈C n,n and A∈C n,n are derived.
文摘This article proposes a new algorithm of quaternion and dual quaternion in matrix form. It applies quaternion in special cases of rotated plane, transforming the sine and cosine of the rotation angle into matrix form, then exporting flat quaternions base in two matrix form. It establishes serial 6R manipulator kinematic equations in the form of quaternion matrix. Then five variables are eliminated through linear elimination and application of lexicographic Groebner base. Thus, upper bound of the degree of the equation is determined, which is 16. In this way, a 16-degree equation with single variable is obtained without any extraneous root. This is the first time that quaternion matrix modeling has been used in 6R robot inverse kinematics analysis.
文摘A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.
文摘The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions for the existence of such solutions and their general forms are derived.
文摘This paper presents a recursive procedure to compute the Moore-Penrose inverse of a matrix A. The method is based on the expression for the Moore-Penrose inverse of rank-one modified matrix. The computational complexity of the method is analyzed and a numerical example is included. A variant of the algorithm with lower computational complexity is also proposed. Both algorithms are tested on randomly generated matrices. Numerical performance confirms our theoretic results.
文摘Censider the solutions of the matrix inverse problem, which are symmetric positive semide finite on a subspace. Necessary and sufficient conditions for the solvability, as well as the general solution are obtained. The best approximate solution by the above solution set is given. Thus the open problem in [1] is solved.
基金The works is supported by the National Natural Science Foundation of China(19871054)
文摘Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is
基金Supported by Grant No. 174007 of the Ministry of Science,Technology and Development,Republic of Serbia
文摘In this article, the expression for the Drazin inverse of a modified matrix is considered and some interesting results are established. This contributes to certain recent results obtained by Y.Wei [9].
文摘In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.
