We have constructed a class of random sets by statistical contraction operators in this paper.When the probability space is some special product space and the statistical contraction operators are affine or similar,th...We have constructed a class of random sets by statistical contraction operators in this paper.When the probability space is some special product space and the statistical contraction operators are affine or similar,these statistically recursive sets are investigated by many authors.It will be very convenient for us to study their distributions and dimensions and measures using our model in this paper.展开更多
Let X be an infinite-dimensional complex Banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves simil...Let X be an infinite-dimensional complex Banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B（X） such that either Φ（T） = cATA^-1 ＋ ψ（T）I for all T, or Φ（T） = cAT＊A^-1 ＋ ψ（T）I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero.展开更多
Resources shared in e-Science have critical requirements on security.Thus subjective trust management is essential to guarantee users＇ collaborations and communications on such a promising infrastructure.As an import...Resources shared in e-Science have critical requirements on security.Thus subjective trust management is essential to guarantee users＇ collaborations and communications on such a promising infrastructure.As an important nature of subjective trust,uncertainty should be preserved and exhibited in trust definition,representation and evolution.Consider the drawbacks of existing mechanisms based on random mathematics and fuzzy theory,this paper designs an uncertainty enhanced trust evolution strategy based on cloud model theory.We define subjective trust as trust cloud.Then we propose new algorithms to propagate,aggregate and update trust.Furthermore,based on the concept of similar cloud,a method to assess trust level is put forward.The simulation results show the effiectiveness,rationality and efficiency of our proposed strategy.展开更多
文摘We have constructed a class of random sets by statistical contraction operators in this paper.When the probability space is some special product space and the statistical contraction operators are affine or similar,these statistically recursive sets are investigated by many authors.It will be very convenient for us to study their distributions and dimensions and measures using our model in this paper.
文摘Let X be an infinite-dimensional complex Banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B（X） such that either Φ（T） = cATA^-1 ＋ ψ（T）I for all T, or Φ（T） = cAT＊A^-1 ＋ ψ（T）I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero.
基金Supported by the National Natural Science Foundation of China under Grant No.60703048the Open Foundation of State Key Lab of Software Engineering of Wuhan University under Grant No.SKLSE20080720the Open Foundation of State Key Laboratory for Novel Software Technology of Nanjing University under Grant No.KFKT2009B22
文摘Resources shared in e-Science have critical requirements on security.Thus subjective trust management is essential to guarantee users＇ collaborations and communications on such a promising infrastructure.As an important nature of subjective trust,uncertainty should be preserved and exhibited in trust definition,representation and evolution.Consider the drawbacks of existing mechanisms based on random mathematics and fuzzy theory,this paper designs an uncertainty enhanced trust evolution strategy based on cloud model theory.We define subjective trust as trust cloud.Then we propose new algorithms to propagate,aggregate and update trust.Furthermore,based on the concept of similar cloud,a method to assess trust level is put forward.The simulation results show the effiectiveness,rationality and efficiency of our proposed strategy.
