Suppose Y - N（β, σ^2 In）, where β ∈ R^n and σ^2 〉 0 are unknown. We study the admissibility of linear estimators of mean vector under a quadratic loss function. A necessary and sufficient condition of the admi...Suppose Y - N（β, σ^2 In）, where β ∈ R^n and σ^2 〉 0 are unknown. We study the admissibility of linear estimators of mean vector under a quadratic loss function. A necessary and sufficient condition of the admissible linear estimator is given.展开更多
Let U(n,Q)be the group of all n×n(upper)unitriangular matrices over rational numbers field Q.Let S be a subset of U(n,Q).In this paper,we prove that S is a subgroup of U(n,Q)if and only if the(i,j)-th entry S;sat...Let U(n,Q)be the group of all n×n(upper)unitriangular matrices over rational numbers field Q.Let S be a subset of U(n,Q).In this paper,we prove that S is a subgroup of U(n,Q)if and only if the(i,j)-th entry S;satisfies some condition(see Theorem 3.5).Furthermore,we compute the upper central series and the lower central series for S,and obtain the condition that the upper central series and the lower central series of S coincide.展开更多
The aim of this paper is to determine the structure and to establish the isomorphic invariant of the finitely generated nilpotent group G of infinite cyclic commutator subgroup.Using the structure and invariant of the...The aim of this paper is to determine the structure and to establish the isomorphic invariant of the finitely generated nilpotent group G of infinite cyclic commutator subgroup.Using the structure and invariant of the group which is the central extension of a cyclic group by a free abelian group offinite rank of infinite cyclic center,we provide a decomposition of G as the product of a generalized extraspecial Z-group and its center.By using techniques of lifting isomorphisms of abelian groups and equivalent normal form of the generalized extraspecial Z-groups,we finally obtain the structure and invariants of the group G.展开更多
基金This work is supported by The NNSF of China with Nos.10071090 and 10271013
文摘Suppose Y - N（β, σ^2 In）, where β ∈ R^n and σ^2 〉 0 are unknown. We study the admissibility of linear estimators of mean vector under a quadratic loss function. A necessary and sufficient condition of the admissible linear estimator is given.
基金National Natural Science Foundation of China(Grant Nos.12171142,11971155,12071117)。
文摘Let U(n,Q)be the group of all n×n(upper)unitriangular matrices over rational numbers field Q.Let S be a subset of U(n,Q).In this paper,we prove that S is a subgroup of U(n,Q)if and only if the(i,j)-th entry S;satisfies some condition(see Theorem 3.5).Furthermore,we compute the upper central series and the lower central series for S,and obtain the condition that the upper central series and the lower central series of S coincide.
基金Supported by NSFC(Grant Nos.11631001,11771129,11971155 and 12071117)。
文摘The aim of this paper is to determine the structure and to establish the isomorphic invariant of the finitely generated nilpotent group G of infinite cyclic commutator subgroup.Using the structure and invariant of the group which is the central extension of a cyclic group by a free abelian group offinite rank of infinite cyclic center,we provide a decomposition of G as the product of a generalized extraspecial Z-group and its center.By using techniques of lifting isomorphisms of abelian groups and equivalent normal form of the generalized extraspecial Z-groups,we finally obtain the structure and invariants of the group G.
