Availability Analysis of Parallel Repairable System with Omitted Failures

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.

HERMAN RINGS WITH SMALL PERIODS AND OMITTED VALUES

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.

Normal family and the sequence of omitted functions

Let {fn} be a sequence of meromorphic functions on a plane domain D, whose zeros and poles have multiplicity at least 3. Let {hn} be a sequence of meromorphic functions on D, whose poles are multiple, such that {hn} converges locally uniformly in the spherical metric to a function h which is meromorphic and zero-free on D.If fn≠hn, then {fn} is normal on D.

A Normal Criterion Concerning Omitted Holomorphic Function

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.

The critical case for a Berestycki-Lions theorem

We consider the existence of the ground states solutions to the following Schrodinger equation -△u ＋ V（x）u = f（u）, u ∈ H1（RN）, where N ） 3 and f has critical growth. We generalize an earlier theorem due to Berestycki and Lions about tile subcritical case to the current critical case.

A Criterion of Normality Concerning Holomorphic Functions Whose Derivative Omits a Function

The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of holomorphic functions on a domain D C C, all of whose zeros have multiplicity at least k, where k 〉 2 is an integer. And let h（z）≠ 0 be a holomorphic function on D. Assume also that the following two conditions hold for every f ∈F： （a） f（z） = 0 [f^（k）（z）｜ 〈 ｜h（z）｜; （b） f^（k）（z）≠ h（z）. Then F is normal on

How China's Holdings of Foreign Reserves Affect the Value of the US Dollar in Europe and Asia

By January 2009, China held almost US$2tn in foreign reserves. The present paper estimates the marginal effect of China changing its holdings offoreign reserves on the value of the US dollar in Europe and dsia. Because using traditional techniques to find this estimate would be inappropriate due to severe problems resulting from omitted variables, the present paper uses a new approach, bidirectional-reiterative trucated projected least squares, that has been proven to minimize problems associated with omitted variables. It is found that if China would sell 1 percent of its foreign reserves, then the value of the US dollar would fall by 0.44 percent. With such a large effect, China has an incentive to either not sell arty of its US dollar reserves or sell all of its US dollar reserves.

A Criterion of Normality Concerning Holomorphic Functions Whose Derivative Omit a Function II

The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of functions holomorphic on a domain D C, all of whose zeros have multiplicity at least k, where k ≥ 2 is an integer. Let h（z） ≠ 0 and oo be a meromorphic function on D. Assume that the following two conditions hold for every f C Dr ： （a） f（z） = 0 =→ ｜f（k）（z）｜ 〈｜h（z）｜. （b） f（k）（z） ≠ h（z）. Then F is normal on D.

Optomechanical properties of a degenera te nonperiodic cavity chain

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.