The asymptotic stability of delay differential equation x′(t)=Ax(t)+Bx(t τ) is concerned with,where A,B∈C d×d are constant complex matrices, x(t τ)=(x 1(t-τ 1),x 2(t-τ 2),...,x d(t-τ d))T,τ k>...The asymptotic stability of delay differential equation x′(t)=Ax(t)+Bx(t τ) is concerned with,where A,B∈C d×d are constant complex matrices, x(t τ)=(x 1(t-τ 1),x 2(t-τ 2),...,x d(t-τ d))T,τ k>0(k=1,...,d) stand for constant delays. Two criteria through evaluation of a harmonic function on the boundary of a certain region are obtained. The similar results for neutral delay differential equation x′(t)=Lx(t)+Mx(t-τ)+Nx′(t-τ) are also obtained,where L,M and N∈C d×d are constant complex matrices and τ>0 stands for constant delay. Numerical examples are showed to check the results which are more general than those already reported.展开更多
It is known that every tensor has an associated semi-symmetric tensor.The purpose of this paper is to investigate the shared properties of a tensor and its semi-symmetric form.In particular,a corresponding semi-symmet...It is known that every tensor has an associated semi-symmetric tensor.The purpose of this paper is to investigate the shared properties of a tensor and its semi-symmetric form.In particular,a corresponding semi-symmetric tensor has smaller Frobenius norm under some conditions and can be used to get smaller bounds for eigenvalues and solutions of dynamical systems and tensor complementarity problems.In addition,every tensor has the same eigenvalues as its corresponding semi-symmetric form,also a corresponding semi-symmetric tensor inherits properties like being circulant,Toeplitz,Z-tensor,M-tensor,H-tensor and some others.Also,there are a two-way connection for properties like being positive definite,P-tensor,semi-positive,primitive and several others.展开更多
In the theoretical study of numerical solution of stiff ODEs, it usually assumes that the righthand function f(y) satisfy one-side Lipschitz condition < f(y) - f(z),y - z >less than or equal to v(1)parallel to y...In the theoretical study of numerical solution of stiff ODEs, it usually assumes that the righthand function f(y) satisfy one-side Lipschitz condition < f(y) - f(z),y - z >less than or equal to v(1)parallel to y - z parallel to(2),f : Omega subset of or equal to C-m --> C-m, or another related one-side Lipschitz condition [F(Y) - F(Z), Y - Z](D) less than or equal to v'parallel to Y - Z parallel to(D)(2), F : Omega(s) subset of or equal to C-ms --> C-ms, this paper demonstrates that the difference of the two sets of all functions satisfying the above two conditions respectively is at most that v' - v' only is constant independent of stiffness of function f.展开更多
文摘The asymptotic stability of delay differential equation x′(t)=Ax(t)+Bx(t τ) is concerned with,where A,B∈C d×d are constant complex matrices, x(t τ)=(x 1(t-τ 1),x 2(t-τ 2),...,x d(t-τ d))T,τ k>0(k=1,...,d) stand for constant delays. Two criteria through evaluation of a harmonic function on the boundary of a certain region are obtained. The similar results for neutral delay differential equation x′(t)=Lx(t)+Mx(t-τ)+Nx′(t-τ) are also obtained,where L,M and N∈C d×d are constant complex matrices and τ>0 stands for constant delay. Numerical examples are showed to check the results which are more general than those already reported.
文摘It is known that every tensor has an associated semi-symmetric tensor.The purpose of this paper is to investigate the shared properties of a tensor and its semi-symmetric form.In particular,a corresponding semi-symmetric tensor has smaller Frobenius norm under some conditions and can be used to get smaller bounds for eigenvalues and solutions of dynamical systems and tensor complementarity problems.In addition,every tensor has the same eigenvalues as its corresponding semi-symmetric form,also a corresponding semi-symmetric tensor inherits properties like being circulant,Toeplitz,Z-tensor,M-tensor,H-tensor and some others.Also,there are a two-way connection for properties like being positive definite,P-tensor,semi-positive,primitive and several others.
文摘In the theoretical study of numerical solution of stiff ODEs, it usually assumes that the righthand function f(y) satisfy one-side Lipschitz condition < f(y) - f(z),y - z >less than or equal to v(1)parallel to y - z parallel to(2),f : Omega subset of or equal to C-m --> C-m, or another related one-side Lipschitz condition [F(Y) - F(Z), Y - Z](D) less than or equal to v'parallel to Y - Z parallel to(D)(2), F : Omega(s) subset of or equal to C-ms --> C-ms, this paper demonstrates that the difference of the two sets of all functions satisfying the above two conditions respectively is at most that v' - v' only is constant independent of stiffness of function f.
