In this paper,the entropy of discrete Heisenberg group actions is considered.Let α be a discrete Heisenberg group action on a compact metric space X.Two types of entropies,h and h(α)are introduced,in which h is defi...In this paper,the entropy of discrete Heisenberg group actions is considered.Let α be a discrete Heisenberg group action on a compact metric space X.Two types of entropies,h and h(α)are introduced,in which h is defined in Ruelle’s way and h(α) is defined via the natural extension of α.It is shown that when X is the torus and α is induced by integer matrices then h is zero and h(α) can be expressed via the eigenvalues of the matrices.展开更多
Small sample size problem is one of the main problems that heavy numerical control(NC) machine tools encounter in their reliability assessment. In order to deal with the small sample size problem, many indirect reliab...Small sample size problem is one of the main problems that heavy numerical control(NC) machine tools encounter in their reliability assessment. In order to deal with the small sample size problem, many indirect reliability data such as reliability data of similar products, expert opinion, and engineers' experience are used in reliability assessment. However, the existing mathematical theories cannot simultaneously process the above reliability data of multiple types, and thus imprecise probability theory is introduced. Imprecise probability theory can simultaneously process multiple reliability data by quantifying multiple uncertainties(stochastic uncertainty,fuzzy uncertainty, epistemic uncertainty, etc.) together. Although imprecise probability theory has so many advantages, the existing natural extension models are complex and the computation result is imprecise. Therefore,they need some improvement for the better application of reliability engineering. This paper proposes an improved imprecise reliability assessment method by introducing empirical probability distributions to natural extension model, and the improved natural extension model is applied to the reliability assessment of heavy NC machine tool spindle to illustrate its effectiveness.展开更多
基金Supported by NSFC (Grant Nos. 12171400, 12126102)。
文摘In this paper,the entropy of discrete Heisenberg group actions is considered.Let α be a discrete Heisenberg group action on a compact metric space X.Two types of entropies,h and h(α)are introduced,in which h is defined in Ruelle’s way and h(α) is defined via the natural extension of α.It is shown that when X is the torus and α is induced by integer matrices then h is zero and h(α) can be expressed via the eigenvalues of the matrices.
基金the National Natural Science Foundation of China(No.51405065)the National Science and Technology Major Project of China(No.2014ZX04014-011)
文摘Small sample size problem is one of the main problems that heavy numerical control(NC) machine tools encounter in their reliability assessment. In order to deal with the small sample size problem, many indirect reliability data such as reliability data of similar products, expert opinion, and engineers' experience are used in reliability assessment. However, the existing mathematical theories cannot simultaneously process the above reliability data of multiple types, and thus imprecise probability theory is introduced. Imprecise probability theory can simultaneously process multiple reliability data by quantifying multiple uncertainties(stochastic uncertainty,fuzzy uncertainty, epistemic uncertainty, etc.) together. Although imprecise probability theory has so many advantages, the existing natural extension models are complex and the computation result is imprecise. Therefore,they need some improvement for the better application of reliability engineering. This paper proposes an improved imprecise reliability assessment method by introducing empirical probability distributions to natural extension model, and the improved natural extension model is applied to the reliability assessment of heavy NC machine tool spindle to illustrate its effectiveness.
