Injury to central nervous system(CNS)tissues in adult mam-mals often leads to neuronal loss,scarring,and permanently lost neurologic functions,and this default healing response is increasingly linked to a pro-inflamma...Injury to central nervous system(CNS)tissues in adult mam-mals often leads to neuronal loss,scarring,and permanently lost neurologic functions,and this default healing response is increasingly linked to a pro-inflammatory innate immune response.Extracellular matrix(ECM)technology can reduce inflammation,while increasing functional tissue remodeling in various tissues and organs,including the CNS.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].
For the lower bound about the determinant of Hadamard product of A and B, where A is a n × n real positive definite matrix and B is a n × n M-matrix, Jianzhou Liu [SLAM J. Matrix Anal. Appl., 18(2)(1997): 30...For the lower bound about the determinant of Hadamard product of A and B, where A is a n × n real positive definite matrix and B is a n × n M-matrix, Jianzhou Liu [SLAM J. Matrix Anal. Appl., 18(2)(1997): 305-311]obtained the estimated inequality as follows det(A o B)≥a11b11 nⅡk=2(bkk detAk/detAk-1+detBk/detBk-1(k-1Ei=1 aikaki/aii))=Ln(A,B),where Ak is kth order sequential principal sub-matrix of A. We establish an improved lower bound of the form Yn(A,B)=a11baa nⅡk=2(bkk detAk/detAk-1+akk detBk/detBk-1-detAdetBk/detak-1detBk-1)≥Ln(A,B).For more weaker and practical lower bound, Liu given thatdet(A o B)≥(nⅡi=1 bii)detA+(nⅡi=1 aii)detB(nⅡk=2 k-1Ei=1 aikaki/aiiakk)=(L)n(A,B).We further improve it as Yn(A,B)=(nⅡi=1 bii)detA+(nⅡi=1 aii)detB-(detA)(detB)+max1≤k≤n wn(A,B,k)≥(nⅡi=1 bii)detA+(nⅡi=1 aii)detB-(detA)(detB)≥(L)n(A,B).展开更多
A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential c...A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.展开更多
This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) probl...This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. Three illustrative examples are given to show the effectiveness of our methods.展开更多
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence ...In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.展开更多
The present paper investigated the delay-dependent robust control for linear value bounded uncertain systems with state delay. By introducing the idea of matrix decomposition into the synthesis problem, incorporating ...The present paper investigated the delay-dependent robust control for linear value bounded uncertain systems with state delay. By introducing the idea of matrix decomposition into the synthesis problem, incorporating with Lyapunov-Krasovskii functional method and adding ＂zeros＂ matrix through the correlation of each item in Newton-Leibniz formula, we present a sufficient condition via the feedback stabilization based on linear matrix inequality （LMI）. LMI is a new delay dependent condition that is much less conservative, and it guarantees that the system is robust asymptotically stable via state feedback controller. Neither the model transformation nor the bounding cross terms is employed. Finally, a numerical example is presented and it demonstrates the effectiveness of the offered method.展开更多
This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems. The main consideration...This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set for neutral Markovian jump system as small as possible. By applying Lyapunov functional method, some derived conditions are obtained in the form of matrix inequalities. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.展开更多
The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenva...The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.展开更多
The goal of this study is to propose a method of estimation of bounds for roots of polynomials with complex coefficients. A well-known and easy tool to obtain such information is to use the standard Gershgorin’s theo...The goal of this study is to propose a method of estimation of bounds for roots of polynomials with complex coefficients. A well-known and easy tool to obtain such information is to use the standard Gershgorin’s theorem, however, it doesn’t take into account the structure of the matrix. The modified disks of Gershgorin give the opportunity through some geometrical figures called Ovals of Cassini, to consider the form of the matrix in order to determine appropriated bounds for roots. Furthermore, we have seen that, the Hessenbeg matrices are indicated to estimate good bounds for roots of polynomials as far as we become improved bounds for high values of polynomial’s coefficients. But the bounds are better for small values. The aim of the work was to take advantages of this, after introducing the Dehmer’s bound, to find an appropriated property of the Hessenberg form. To illustrate our results, illustrative examples are given to compare the obtained bounds to those obtained through classical methods like Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds.展开更多
文摘Injury to central nervous system(CNS)tissues in adult mam-mals often leads to neuronal loss,scarring,and permanently lost neurologic functions,and this default healing response is increasingly linked to a pro-inflammatory innate immune response.Extracellular matrix(ECM)technology can reduce inflammation,while increasing functional tissue remodeling in various tissues and organs,including the CNS.
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For the lower bound about the determinant of Hadamard product of A and B, where A is a n × n real positive definite matrix and B is a n × n M-matrix, Jianzhou Liu [SLAM J. Matrix Anal. Appl., 18(2)(1997): 305-311]obtained the estimated inequality as follows det(A o B)≥a11b11 nⅡk=2(bkk detAk/detAk-1+detBk/detBk-1(k-1Ei=1 aikaki/aii))=Ln(A,B),where Ak is kth order sequential principal sub-matrix of A. We establish an improved lower bound of the form Yn(A,B)=a11baa nⅡk=2(bkk detAk/detAk-1+akk detBk/detBk-1-detAdetBk/detak-1detBk-1)≥Ln(A,B).For more weaker and practical lower bound, Liu given thatdet(A o B)≥(nⅡi=1 bii)detA+(nⅡi=1 aii)detB(nⅡk=2 k-1Ei=1 aikaki/aiiakk)=(L)n(A,B).We further improve it as Yn(A,B)=(nⅡi=1 bii)detA+(nⅡi=1 aii)detB-(detA)(detB)+max1≤k≤n wn(A,B,k)≥(nⅡi=1 bii)detA+(nⅡi=1 aii)detB-(detA)(detB)≥(L)n(A,B).
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60877055 and 60806041)the Shanghai Rising-Star Program,China (Grant No. 08QA14030)+1 种基金the Innovation Funds for Graduates of Shanghai University,China (Grant No. SHUCX092021)the Foundation of the Science and Technology Commission of Shanghai Municipality,China (Grant No. 08JC14097)
文摘A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.
基金supported by National Natural Science Foundation of China(Nos.61004017 and 60974103)
文摘This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. Three illustrative examples are given to show the effectiveness of our methods.
基金Supported by the National Natural Science Foundation of China (Grant No.11071079)the Natural Science Foundation of Zhejiang Province (Grant No.Y6110043)
文摘In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.
基金Supported by the National Natural Science Foundation of China (60634020)the Natural Science Foundation of Hunan Province (06JJ50145)
文摘The present paper investigated the delay-dependent robust control for linear value bounded uncertain systems with state delay. By introducing the idea of matrix decomposition into the synthesis problem, incorporating with Lyapunov-Krasovskii functional method and adding ＂zeros＂ matrix through the correlation of each item in Newton-Leibniz formula, we present a sufficient condition via the feedback stabilization based on linear matrix inequality （LMI）. LMI is a new delay dependent condition that is much less conservative, and it guarantees that the system is robust asymptotically stable via state feedback controller. Neither the model transformation nor the bounding cross terms is employed. Finally, a numerical example is presented and it demonstrates the effectiveness of the offered method.
文摘This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set for neutral Markovian jump system as small as possible. By applying Lyapunov functional method, some derived conditions are obtained in the form of matrix inequalities. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.
文摘The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.
文摘The goal of this study is to propose a method of estimation of bounds for roots of polynomials with complex coefficients. A well-known and easy tool to obtain such information is to use the standard Gershgorin’s theorem, however, it doesn’t take into account the structure of the matrix. The modified disks of Gershgorin give the opportunity through some geometrical figures called Ovals of Cassini, to consider the form of the matrix in order to determine appropriated bounds for roots. Furthermore, we have seen that, the Hessenbeg matrices are indicated to estimate good bounds for roots of polynomials as far as we become improved bounds for high values of polynomial’s coefficients. But the bounds are better for small values. The aim of the work was to take advantages of this, after introducing the Dehmer’s bound, to find an appropriated property of the Hessenberg form. To illustrate our results, illustrative examples are given to compare the obtained bounds to those obtained through classical methods like Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds.
