This paper characterizes the multiplication operator semigroup of semiring semigroup by using the tensor product of semigroups, and by using the endomorphism semigroup, and considers some properties of the multiplicat...This paper characterizes the multiplication operator semigroup of semiring semigroup by using the tensor product of semigroups, and by using the endomorphism semigroup, and considers some properties of the multiplication operator semigroup of semiring semigroup.展开更多
The non-probabilistic approach to fatigue life analysis was studied using the convex models-interval, ellipsoidal and multiconvex models. The lower and upper bounds of the fatigue life were obtained by using the secon...The non-probabilistic approach to fatigue life analysis was studied using the convex models-interval, ellipsoidal and multiconvex models. The lower and upper bounds of the fatigue life were obtained by using the second-order Taylor series and Lagrange multiplier method. The solving process for derivatives of the implicit life function was presented. Moreover, a median ellipsoidal model was proposed which can take into account the sample blind zone and almost impossibility of concurrence of some small probability events. The Monte Carlo method for multi-convex model was presented, an important alternative when the analytical method does not work. A project example was given. The feasibility and rationality of the presented approach were verified. It is also revealed that the proposed method is conservative compared to the traditional probabilistic method, but it is a useful complement when it is difficult to obtain the accurate probability densities of parameters.展开更多
文摘This paper characterizes the multiplication operator semigroup of semiring semigroup by using the tensor product of semigroups, and by using the endomorphism semigroup, and considers some properties of the multiplication operator semigroup of semiring semigroup.
基金supported by the Program for New Century Excellent Talents in University of Chinathe Advanced Research Foundation of China (Grant No. 9140A27050109JB1112)
文摘The non-probabilistic approach to fatigue life analysis was studied using the convex models-interval, ellipsoidal and multiconvex models. The lower and upper bounds of the fatigue life were obtained by using the second-order Taylor series and Lagrange multiplier method. The solving process for derivatives of the implicit life function was presented. Moreover, a median ellipsoidal model was proposed which can take into account the sample blind zone and almost impossibility of concurrence of some small probability events. The Monte Carlo method for multi-convex model was presented, an important alternative when the analytical method does not work. A project example was given. The feasibility and rationality of the presented approach were verified. It is also revealed that the proposed method is conservative compared to the traditional probabilistic method, but it is a useful complement when it is difficult to obtain the accurate probability densities of parameters.
