LET R and R<sub>1</sub> be skew-fields with centres F and F<sub>1</sub>, where F F<sub>1</sub> and |F|】2. By M<sub>n</sub> （R）and I<sub>n</sub>（R） we de...LET R and R<sub>1</sub> be skew-fields with centres F and F<sub>1</sub>, where F F<sub>1</sub> and |F|】2. By M<sub>n</sub> （R）and I<sub>n</sub>（R） we denote the F-space of all n×n matrices over R and the set of all idempotentmatrices in M<sub>n</sub>（R）, respectively. If a linear map L from M<sub>n</sub>（R） to M<sub>m</sub>（R<sub>1</sub>） satisfies L（I<sub>n</sub>（R）） I<sub>m</sub>（R<sub>1</sub>） we call L an idempotence preserver （all such maps will be denoted byL<sub>n</sub>, m（R,R<sub>1</sub>））. To determine the forms of idempotence preservers is one important展开更多
Let M2 be the algebra of all 2 × 2 matrices over a ?eld F of characteristic 2 and |F| > 2. Let P2 be the set of all idempotent matrices in M2. It is shown that if φ : M2 → M2 is an injective map such that A...Let M2 be the algebra of all 2 × 2 matrices over a ?eld F of characteristic 2 and |F| > 2. Let P2 be the set of all idempotent matrices in M2. It is shown that if φ : M2 → M2 is an injective map such that A ? λB ∈ P2 implies φ(A) ? λφ(B) ∈ P2 for any A,B ∈ M2 and λ ∈F, then either φ is of the form φ(A) = TAT? for any A ∈ M2, or φ is of 1 the form φ(A) = TAtT? for any A ∈ M2, where T ∈ M2 is a nonsingular matrix.展开更多
现有的D em pster组合规则及大多数改进规则对两个证据之间存在较大冲突时能有效处理,但是对只存在较小冲突的大量信息源的研究较少,而这类较小的冲突在大量信息源的条件下可能变得很大。本文对信源数目较大时各种组合规则的极限性能进...现有的D em pster组合规则及大多数改进规则对两个证据之间存在较大冲突时能有效处理,但是对只存在较小冲突的大量信息源的研究较少,而这类较小的冲突在大量信息源的条件下可能变得很大。本文对信源数目较大时各种组合规则的极限性能进行了分析和研究,给出了组合规则极限性能的评价标准,指出Sm ets,Y ager和D.P.等规则不适合处理大量信息源的情形,并且提出在大量信息源情况下,可依据不同的结果要求,选择组合规则的策略。展开更多
Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with n ≥ 3. We denote by Mn（R） the ring of all n x n matrices over R. Let （Jn（R）） be the additive subgroup of Mn（...Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with n ≥ 3. We denote by Mn（R） the ring of all n x n matrices over R. Let （Jn（R）） be the additive subgroup of Mn（R） generated additively by all idempotent matrices. Let JJ = （Jn（R）） or Mn（R）. We describe the additive preservers of idempotence from JJ to Mm（R） when 2 is a unit of R. Thereby, we also characterize the Jordan （respectively, ring and ring anti-） homomorphisms from Mn （R） to Mm （R） when 2 is a unit of R.展开更多
A solution is given for the word problem for free idempotent distributive semirings. Using this solution the lattice L(ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns...A solution is given for the word problem for free idempotent distributive semirings. Using this solution the lattice L(ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns out that L(ID) is isomorphic to the direct product of a four-element lattice and a lattice which is itself a subdirect product of four copies of the lattice L (B) of all band varieties. Therefore L(ID) is countably infinite and distributive. Every subvariety of ID is finitely based.展开更多
文摘LET R and R<sub>1</sub> be skew-fields with centres F and F<sub>1</sub>, where F F<sub>1</sub> and |F|】2. By M<sub>n</sub> （R）and I<sub>n</sub>（R） we denote the F-space of all n×n matrices over R and the set of all idempotentmatrices in M<sub>n</sub>（R）, respectively. If a linear map L from M<sub>n</sub>（R） to M<sub>m</sub>（R<sub>1</sub>） satisfies L（I<sub>n</sub>（R）） I<sub>m</sub>（R<sub>1</sub>） we call L an idempotence preserver （all such maps will be denoted byL<sub>n</sub>, m（R,R<sub>1</sub>））. To determine the forms of idempotence preservers is one important
基金Supported by the National Natural Science Foundation of China(1152608411601135)+1 种基金the Natural Science Foundation of Heilongjiang Province(A2015007)the Education Department of Heilongjiang Province(12541605)
基金Supported by the National Science Found of China (10271021)
文摘Let M2 be the algebra of all 2 × 2 matrices over a ?eld F of characteristic 2 and |F| > 2. Let P2 be the set of all idempotent matrices in M2. It is shown that if φ : M2 → M2 is an injective map such that A ? λB ∈ P2 implies φ(A) ? λφ(B) ∈ P2 for any A,B ∈ M2 and λ ∈F, then either φ is of the form φ(A) = TAT? for any A ∈ M2, or φ is of 1 the form φ(A) = TAtT? for any A ∈ M2, where T ∈ M2 is a nonsingular matrix.
文摘现有的D em pster组合规则及大多数改进规则对两个证据之间存在较大冲突时能有效处理,但是对只存在较小冲突的大量信息源的研究较少,而这类较小的冲突在大量信息源的条件下可能变得很大。本文对信源数目较大时各种组合规则的极限性能进行了分析和研究,给出了组合规则极限性能的评价标准,指出Sm ets,Y ager和D.P.等规则不适合处理大量信息源的情形,并且提出在大量信息源情况下,可依据不同的结果要求,选择组合规则的策略。
基金This work is supported in part by the Chinese Natural Science Foundation under Grant No. 10671026 and the Postdoctoral Fund of Heilongjiang Province
文摘Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with n ≥ 3. We denote by Mn（R） the ring of all n x n matrices over R. Let （Jn（R）） be the additive subgroup of Mn（R） generated additively by all idempotent matrices. Let JJ = （Jn（R）） or Mn（R）. We describe the additive preservers of idempotence from JJ to Mm（R） when 2 is a unit of R. Thereby, we also characterize the Jordan （respectively, ring and ring anti-） homomorphisms from Mn （R） to Mm （R） when 2 is a unit of R.
基金Project supported by the National Natural Science Foundation of China (Grant No. 197610O4)the Provincial Applied Fundamental Research Foundation of Yunnan (96a001z).
文摘A solution is given for the word problem for free idempotent distributive semirings. Using this solution the lattice L(ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns out that L(ID) is isomorphic to the direct product of a four-element lattice and a lattice which is itself a subdirect product of four copies of the lattice L (B) of all band varieties. Therefore L(ID) is countably infinite and distributive. Every subvariety of ID is finitely based.
