It is proved that the general formulas, obtained recently for the lower bound of the first eigenvalue, can be further bounded by one or two constants depending on the coefficients of the corresponding operators only. ...It is proved that the general formulas, obtained recently for the lower bound of the first eigenvalue, can be further bounded by one or two constants depending on the coefficients of the corresponding operators only. Moreover, the ratio of the upper and lower bounds is no more than four.展开更多
文章在对机群系统的运行特性进行分析的基础上，运用马氏过程描述了机群系统中的高可用性（ High Availability），并从理论上建立了基于生灭过程的机群高可用模型。文中在给出机群高可用管理软件结构的基础上，设计了一种基于集中式结...文章在对机群系统的运行特性进行分析的基础上，运用马氏过程描述了机群系统中的高可用性（ High Availability），并从理论上建立了基于生灭过程的机群高可用模型。文中在给出机群高可用管理软件结构的基础上，设计了一种基于集中式结构的主副容错协议；通过可用度的分析结果得出：机群高可用系统采用了可修复性技术后，只要有一个 HA节点能正常工作，该系统是“可用”的。展开更多
Some complete variational formulas and approximation theorems for the first eigenvalue of elliptic operators in dimension one or a class of Markov chains are presented.
文摘It is proved that the general formulas, obtained recently for the lower bound of the first eigenvalue, can be further bounded by one or two constants depending on the coefficients of the corresponding operators only. Moreover, the ratio of the upper and lower bounds is no more than four.
文摘文章在对机群系统的运行特性进行分析的基础上，运用马氏过程描述了机群系统中的高可用性（ High Availability），并从理论上建立了基于生灭过程的机群高可用模型。文中在给出机群高可用管理软件结构的基础上，设计了一种基于集中式结构的主副容错协议；通过可用度的分析结果得出：机群高可用系统采用了可修复性技术后，只要有一个 HA节点能正常工作，该系统是“可用”的。
基金This work was supported in part bythe National Natural Science Foundation of China (Grant No. 19631060) Mathematical Tian Yuan Foundation, Qiu Shi Science & Technology Foundation, RFDP and MCEC.
文摘Some complete variational formulas and approximation theorems for the first eigenvalue of elliptic operators in dimension one or a class of Markov chains are presented.
