In this paper, the authors prove that the flows of homogeneous vector field Q(x) at infinityare topologically equivalent to the flows of the tangent vector field QT(u) (u∈S2) on thesphere S2, and show the theorems fo...In this paper, the authors prove that the flows of homogeneous vector field Q(x) at infinityare topologically equivalent to the flows of the tangent vector field QT(u) (u∈S2) on thesphere S2, and show the theorems for the global topological classification of Q(x). They derivethe necessary and sufficient conditions for the global asymptotic stability and the boundednessof vector field Q(x), and obtain the criterion for the global topological equivalence of twohomogeneous vector fields.展开更多
The authors extend Hua’s fundamental theorem of the geometry of Hermitian matri- ces to the in?nite-dimensional case. An application to characterizing the corresponding Jordan ring automorphism is also presented.
The authors study a 3×3 rate-type viscoelastic system, which is a relaxation approximationto a 2×2 quasi-linear hyperbolic system, including the well-known p-system. It is shown thatthe rarefaction waves are...The authors study a 3×3 rate-type viscoelastic system, which is a relaxation approximationto a 2×2 quasi-linear hyperbolic system, including the well-known p-system. It is shown thatthe rarefaction waves are nonlinear asymptotically stable in this relaxation approximation.展开更多
The authors consider the irreducibility of the Cowen-Douglas operator T. It is proved that T is irreducible iff the unital C*-algebra generated by some non-zero blocks in the decomposition of T with respect to (Ker Tn...The authors consider the irreducibility of the Cowen-Douglas operator T. It is proved that T is irreducible iff the unital C*-algebra generated by some non-zero blocks in the decomposition of T with respect to (Ker Tn+1 Ker Tn) is M.(C).展开更多
The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further...The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3)Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*, B). Then the functional dimension of (B*, σ(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.展开更多
In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem...In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem, the new quasi-likelihood proposed in this paper is based mainly on a linearly iterative process of some unbiased estimating functions.Some finite sample properties and asymptotic behaviours for this new quasi-likelihood are investigated. These results show that the new quasi-likelihood for parameter of interest is E-sufficient, iteratively efficient and approximately efficient. Some examples are given to illustrate the theoretical results.展开更多
文摘In this paper, the authors prove that the flows of homogeneous vector field Q(x) at infinityare topologically equivalent to the flows of the tangent vector field QT(u) (u∈S2) on thesphere S2, and show the theorems for the global topological classification of Q(x). They derivethe necessary and sufficient conditions for the global asymptotic stability and the boundednessof vector field Q(x), and obtain the criterion for the global topological equivalence of twohomogeneous vector fields.
基金Project supported by the National Natural Science Foundation of China (No.10471082) and the ShanxiProvincial Natural Science Foundation of China.
文摘The authors extend Hua’s fundamental theorem of the geometry of Hermitian matri- ces to the in?nite-dimensional case. An application to characterizing the corresponding Jordan ring automorphism is also presented.
文摘The authors study a 3×3 rate-type viscoelastic system, which is a relaxation approximationto a 2×2 quasi-linear hyperbolic system, including the well-known p-system. It is shown thatthe rarefaction waves are nonlinear asymptotically stable in this relaxation approximation.
文摘The authors consider the irreducibility of the Cowen-Douglas operator T. It is proved that T is irreducible iff the unital C*-algebra generated by some non-zero blocks in the decomposition of T with respect to (Ker Tn+1 Ker Tn) is M.(C).
基金Project supported by the National Natural Science Foundation of China (No.10071088, No.10171098).
文摘The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3)Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*, B). Then the functional dimension of (B*, σ(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.
基金Project supported by the National Natural Science Foundation of China (No.10371059, No.10171051).
文摘In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem, the new quasi-likelihood proposed in this paper is based mainly on a linearly iterative process of some unbiased estimating functions.Some finite sample properties and asymptotic behaviours for this new quasi-likelihood are investigated. These results show that the new quasi-likelihood for parameter of interest is E-sufficient, iteratively efficient and approximately efficient. Some examples are given to illustrate the theoretical results.
