In this paper a binomial sequence is defined as a special sequence whose renewal lifes are identically distributed with a common geometric distribution. Therefore, it can be regarded as the discrete version of a Poiss...In this paper a binomial sequence is defined as a special sequence whose renewal lifes are identically distributed with a common geometric distribution. Therefore, it can be regarded as the discrete version of a Poisson process. Mainly, we discuss the characterization problem associated with binomial sequences. First, we sketch the properties of some important quantities of a renewal sequence. The emphasis of discussion is laid on the current life, the residual life and the total life. Then, we describe three main approaches to identify a geometric distribution. Finally, based on these concepts and techniques, we give a series of characterization theorems for a binomial sequence. These results are quite similar to those obtained for a Poisson process.展开更多
Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary sets of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods,one...Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary sets of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods,one could establish the exact order of approximation for some special nodes.In the present note we consider the sets of interpolation nodes obtained by adjusting the Chebyshev roots of the second kind on the interval [0,1] and then extending this set to [-1,1] in a symmetric way.We show that in this case the exact order of approximation is O（ 1 n 2 ）.展开更多
We give definitions on increasing, constant and decreasing returns to scale under thegeneralized data envelopment analysis (GDEA) model. The GDEA model possesses cone structures fordescribing evaluators' preferenc...We give definitions on increasing, constant and decreasing returns to scale under thegeneralized data envelopment analysis (GDEA) model. The GDEA model possesses cone structures fordescribing evaluators' preferences toward different decision making units (DMU) and toward differentinput/output categories. The GDEA model contains many important DEA models as its subclasses.Based upon the definition, we discuss and rigorously prove the necessary and sufficient conditionsfor a DMU to have increasing, constant and decreasing returns to scale under a GDEA model, anddiscuss and clarify the differences and relationships of these conditions under different subclasses ofthe GDEA model. Furthermore, we describe a method based on a two-stage linear program to testreturns to scale properties.展开更多
A device is subject to damage caused by environmental shocks.Shocks occur randomly indiscrete time according to a properly defined family of independent random variables.Theincremental damage caused by a shock depends...A device is subject to damage caused by environmental shocks.Shocks occur randomly indiscrete time according to a properly defined family of independent random variables.Theincremental damage caused by a shock depends on the magnitude of the shock.The device has athreshold τ and it fails once the damage exceeds the threshold.The first failure time T of the deviceand its failure rate are examined.If τ is random,under mild conditions we show that the lifedistribution properties of the random threshold are inherited by the first failure time T.For fixed τ,the conditions for the failure rate to increase or to have an increasing average are also found.Finally,as an application of the main results,the additive deterioration models are briefly discussed.展开更多
Fuzzy set systems can be used to solve the problem with uncertain knowledge, and default logic can be used to solve the problem with incomplete knowledge, in some sense. In this paper,based on interval-valued fuzzy se...Fuzzy set systems can be used to solve the problem with uncertain knowledge, and default logic can be used to solve the problem with incomplete knowledge, in some sense. In this paper,based on interval-valued fuzzy sets we introduce a method of inference which combines approximate reasoning and default logic,and give the procedure of transforming monotonic reasoning into default reasoning.展开更多
基金This work was supported by grant No.1880492 from the National Natural Science Foundation of China
文摘In this paper a binomial sequence is defined as a special sequence whose renewal lifes are identically distributed with a common geometric distribution. Therefore, it can be regarded as the discrete version of a Poisson process. Mainly, we discuss the characterization problem associated with binomial sequences. First, we sketch the properties of some important quantities of a renewal sequence. The emphasis of discussion is laid on the current life, the residual life and the total life. Then, we describe three main approaches to identify a geometric distribution. Finally, based on these concepts and techniques, we give a series of characterization theorems for a binomial sequence. These results are quite similar to those obtained for a Poisson process.
基金Supported by the National Natural Science Foundation of China (Grant No. 10601065)
文摘Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary sets of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods,one could establish the exact order of approximation for some special nodes.In the present note we consider the sets of interpolation nodes obtained by adjusting the Chebyshev roots of the second kind on the interval [0,1] and then extending this set to [-1,1] in a symmetric way.We show that in this case the exact order of approximation is O（ 1 n 2 ）.
基金This work was supported by the National Natural Science Foundation of China.
文摘We give definitions on increasing, constant and decreasing returns to scale under thegeneralized data envelopment analysis (GDEA) model. The GDEA model possesses cone structures fordescribing evaluators' preferences toward different decision making units (DMU) and toward differentinput/output categories. The GDEA model contains many important DEA models as its subclasses.Based upon the definition, we discuss and rigorously prove the necessary and sufficient conditionsfor a DMU to have increasing, constant and decreasing returns to scale under a GDEA model, anddiscuss and clarify the differences and relationships of these conditions under different subclasses ofthe GDEA model. Furthermore, we describe a method based on a two-stage linear program to testreturns to scale properties.
基金This work was supported by grant No.1880492 from the National Natural Science Foundation of China
文摘A device is subject to damage caused by environmental shocks.Shocks occur randomly indiscrete time according to a properly defined family of independent random variables.Theincremental damage caused by a shock depends on the magnitude of the shock.The device has athreshold τ and it fails once the damage exceeds the threshold.The first failure time T of the deviceand its failure rate are examined.If τ is random,under mild conditions we show that the lifedistribution properties of the random threshold are inherited by the first failure time T.For fixed τ,the conditions for the failure rate to increase or to have an increasing average are also found.Finally,as an application of the main results,the additive deterioration models are briefly discussed.
文摘Fuzzy set systems can be used to solve the problem with uncertain knowledge, and default logic can be used to solve the problem with incomplete knowledge, in some sense. In this paper,based on interval-valued fuzzy sets we introduce a method of inference which combines approximate reasoning and default logic,and give the procedure of transforming monotonic reasoning into default reasoning.
