We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the...We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).展开更多
Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distri...Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.展开更多
It is proved that the right spread order is closed under the formation of parallel systems with independent and identical components. As an application,the simple upper bounds for both the mean and the variance of the...It is proved that the right spread order is closed under the formation of parallel systems with independent and identical components. As an application,the simple upper bounds for both the mean and the variance of the life length of a parallel system with independent and identical NBUE components are obtained. Furthermore,it is proved that the right spread order is also closed under increasing convex transformations under some conditions.展开更多
It is shown that the total life of a parallel system with independent and identical （i.i.d.） exponential components is smaller in the right spread order than an exponential life with the sane mean as the system. As ...It is shown that the total life of a parallel system with independent and identical （i.i.d.） exponential components is smaller in the right spread order than an exponential life with the sane mean as the system. As applications, simple upper bounds for the mean and the variance of the life length of a parallel system with i.i.d. NBUE components are established, as well as the preservation property of the convolution of NBUE and exponential randorn variables.展开更多
文摘We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).
基金Supported by Program for Young Talents in Artillery College.
文摘Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.
文摘It is proved that the right spread order is closed under the formation of parallel systems with independent and identical components. As an application,the simple upper bounds for both the mean and the variance of the life length of a parallel system with independent and identical NBUE components are obtained. Furthermore,it is proved that the right spread order is also closed under increasing convex transformations under some conditions.
基金Supported by National Natural Science Foundation of China under Grant No.10201010Action Programming of Lanzhou University.
文摘It is shown that the total life of a parallel system with independent and identical （i.i.d.） exponential components is smaller in the right spread order than an exponential life with the sane mean as the system. As applications, simple upper bounds for the mean and the variance of the life length of a parallel system with i.i.d. NBUE components are established, as well as the preservation property of the convolution of NBUE and exponential randorn variables.
