The new model for parallel repairable system is introduced, and it is based on the practice problems of maintenance and the idea of Ion-Channel modeling. In the new model, repair times that are sufficiently short （le...The new model for parallel repairable system is introduced, and it is based on the practice problems of maintenance and the idea of Ion-Channel modeling. In the new model, repair times that are sufficiently short （less than some critical value） do not result in system failure, and such a repair interval is omitted from the downtime record. Usually, the underlying process is Markov process if the durations of working and repair time have the negative-exponential distributions, but the new system has not the Markov properties, which is worth to study. The reliability indexes such as instantaneous availability and steady-state availabilities for the new system are given through probability analysis. A numerical example is given to illustrate the results.展开更多
All possible arrangements of cycles of three periodic as well as four periodicHerman rings of transcendental meromorphic functions having at least one omitted value aredetermined. It is shown that if p = 3 or 4, then ...All possible arrangements of cycles of three periodic as well as four periodicHerman rings of transcendental meromorphic functions having at least one omitted value aredetermined. It is shown that if p = 3 or 4, then the number of p-cycles of Herman rings isat most one. We have also proved a result about the non-existence of a 3-cycle and a 4-cycleof Herman rings simultaneously. Finally some examples of functions having no Herman ringare discussed.展开更多
In this paper,we continue to discuss the normality concerning omitted holomorphic function and get the following result.Let F be a family of meromorphic functions on a domain D,k≥4 be a positive integer,and let a(z)a...In this paper,we continue to discuss the normality concerning omitted holomorphic function and get the following result.Let F be a family of meromorphic functions on a domain D,k≥4 be a positive integer,and let a(z)and b(z)be two holomorphic functions on D,where a(z)■0 and f(z)≠∞ whenever a(z)=0.If for any f∈F,f'(z)?a(z)f^k(z)≠b(z),then F is normal on D.展开更多
The absorption of single-cav计y and double-cavity optomechanical systems and periodic optomechanical lattices has previously been investigated extensively. In this paper, we present the absorption of a nonperiodic cav...The absorption of single-cav计y and double-cavity optomechanical systems and periodic optomechanical lattices has previously been investigated extensively. In this paper, we present the absorption of a nonperiodic cavity chain. where the absorption value on the resonance point shows switchable dips or peaks, according to whether the optomechanical interaction is at an odd or even-numbered position in the chain. Meanwhile, the value of absorption due to the optomechanical interaction varies with the number of the bare cavities. The calculated results may have some novel applications, such as detecting the position of the movable mirror in a long cavity chain, which would be useful in quantum information processing based on optomechanical systems.展开更多
基金Sponsored bythe National Natural Science Foundation of China(70671009)the Postgraduate Science and Innovation Project of Beijing Instituteof Technology (GC200818)
文摘The new model for parallel repairable system is introduced, and it is based on the practice problems of maintenance and the idea of Ion-Channel modeling. In the new model, repair times that are sufficiently short （less than some critical value） do not result in system failure, and such a repair interval is omitted from the downtime record. Usually, the underlying process is Markov process if the durations of working and repair time have the negative-exponential distributions, but the new system has not the Markov properties, which is worth to study. The reliability indexes such as instantaneous availability and steady-state availabilities for the new system are given through probability analysis. A numerical example is given to illustrate the results.
基金supported by CSIRDepartment of Science and Technology,Goverment of India through a Fast Track Project(SR-FTP-MS019-2011)respectively
文摘All possible arrangements of cycles of three periodic as well as four periodicHerman rings of transcendental meromorphic functions having at least one omitted value aredetermined. It is shown that if p = 3 or 4, then the number of p-cycles of Herman rings isat most one. We have also proved a result about the non-existence of a 3-cycle and a 4-cycleof Herman rings simultaneously. Finally some examples of functions having no Herman ringare discussed.
基金Supported by the NNSF of China(Grant Nos.11761069 and 11871216)Young Teacher Scientific Research Foundation of Xinjiang Normal University(XJNU201506)“13th Five-Year” Plan for Key Discipline Mathematics Bidding Project(Grant No.17SDKD1104),Xinjiang Normal University
文摘In this paper,we continue to discuss the normality concerning omitted holomorphic function and get the following result.Let F be a family of meromorphic functions on a domain D,k≥4 be a positive integer,and let a(z)and b(z)be two holomorphic functions on D,where a(z)■0 and f(z)≠∞ whenever a(z)=0.If for any f∈F,f'(z)?a(z)f^k(z)≠b(z),then F is normal on D.
文摘The absorption of single-cav计y and double-cavity optomechanical systems and periodic optomechanical lattices has previously been investigated extensively. In this paper, we present the absorption of a nonperiodic cavity chain. where the absorption value on the resonance point shows switchable dips or peaks, according to whether the optomechanical interaction is at an odd or even-numbered position in the chain. Meanwhile, the value of absorption due to the optomechanical interaction varies with the number of the bare cavities. The calculated results may have some novel applications, such as detecting the position of the movable mirror in a long cavity chain, which would be useful in quantum information processing based on optomechanical systems.
