In this study,the authors consider an M/M/1 queuing system with attached inventory under an(s,S)control policy.The server takes multiple vacations whenever the inventory is depleted.It is assumed that the lead time an...In this study,the authors consider an M/M/1 queuing system with attached inventory under an(s,S)control policy.The server takes multiple vacations whenever the inventory is depleted.It is assumed that the lead time and the vacation time follow exponential distributions.The authors formulate the model as a quasi-birth-and-dearth(QBD)process and derive the stability condition of the system.Then,the stationary distribution in product form for the joint process of the queue length,the inventory level,and the server’s status is obtained.Furthermore,the conditional distributions of the inventory level when the server is on and operational,and when it is off due to a vacation,are derived.Using the stationary distribution,the authors obtain some performance measures of the system.The authors investigate analytically the effect of the server’s vacation on the performance measures.Finally,several numerical examples are presented to investigate the effects of some parameters on the performance measures,the optimal policy,and the optimal cost.展开更多
A new production form for a hierarchy of nonlinear evolution equations (NLEEs) is given in this paper. The form contains productions of isospectral and non-isospectral hierarchy. Under this form a generalized structur...A new production form for a hierarchy of nonlinear evolution equations (NLEEs) is given in this paper. The form contains productions of isospectral and non-isospectral hierarchy. Under this form a generalized structure of Lax representations for the hierarchy of NLEEs is this presented. As a concrete example, the Levi-hierarchy of evolution equations are discussed at the end of this paper.展开更多
The paper presents a design method that ensures the ingenuity of the product form as well as the whole and exact expression of user’s needs. The key idea is to establish an automatic design system which can transform...The paper presents a design method that ensures the ingenuity of the product form as well as the whole and exact expression of user’s needs. The key idea is to establish an automatic design system which can transform the user’s language needs into the product features in real-time. A rifle was taken as a research instance and soldiers were chosen as evaluation customers. The theory of fuzzy set and semantic difference are adopted to evaluate the relationship between user’s needs and product features as well as their alternatives. FAHP (fuzzy analytic hierarchy process) is utilized to judge the user’s satisfactory forms. This method can also be applied to other product form designs.展开更多
In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finall...In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.展开更多
基金supported in part by the Natural Science Foundation of China under Grant No.71971189the Natural Science Foundation of Hebei Province under Grant No.A2019203313+1 种基金the Key Project of Scientific Research in Higher Education of Hebei Province of China under Grant No.ZD2018042in part by MEXT,Japan。
文摘In this study,the authors consider an M/M/1 queuing system with attached inventory under an(s,S)control policy.The server takes multiple vacations whenever the inventory is depleted.It is assumed that the lead time and the vacation time follow exponential distributions.The authors formulate the model as a quasi-birth-and-dearth(QBD)process and derive the stability condition of the system.Then,the stationary distribution in product form for the joint process of the queue length,the inventory level,and the server’s status is obtained.Furthermore,the conditional distributions of the inventory level when the server is on and operational,and when it is off due to a vacation,are derived.Using the stationary distribution,the authors obtain some performance measures of the system.The authors investigate analytically the effect of the server’s vacation on the performance measures.Finally,several numerical examples are presented to investigate the effects of some parameters on the performance measures,the optimal policy,and the optimal cost.
文摘A new production form for a hierarchy of nonlinear evolution equations (NLEEs) is given in this paper. The form contains productions of isospectral and non-isospectral hierarchy. Under this form a generalized structure of Lax representations for the hierarchy of NLEEs is this presented. As a concrete example, the Levi-hierarchy of evolution equations are discussed at the end of this paper.
文摘The paper presents a design method that ensures the ingenuity of the product form as well as the whole and exact expression of user’s needs. The key idea is to establish an automatic design system which can transform the user’s language needs into the product features in real-time. A rifle was taken as a research instance and soldiers were chosen as evaluation customers. The theory of fuzzy set and semantic difference are adopted to evaluate the relationship between user’s needs and product features as well as their alternatives. FAHP (fuzzy analytic hierarchy process) is utilized to judge the user’s satisfactory forms. This method can also be applied to other product form designs.
文摘In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.
