In This paper we firstly study the M~x/G(M/G)/1 repairable queueing model with adaptive multistage delay vacation from the angle of reliability and discuss the following reliability problems of the service station:(1)The probability that it fails at time t;(2)The failure number during the server busy period;(3)The expected failure number during(0,t] ;(4)The downtime during the server busy period.

By using a new kind of analytic approach-the decomposition method the following reliability indices of the service station are discussed:1) The probability that the service station is during the"generalized busy period";2)The point unavailability at timenand the steady unavailability;3) The expected failure number during(0,n];4) The expected failure number during the"generalized busy period".

The results show that mechanisms of both resonant triad and secondary instability do exist.

Parabolized stability equations(PSE) approach is used to investigate problems of secondary instability in supersonic boundary layers.

Admissibility of parameter estimation on quadratic loss

For general variance components model EY=Xβ,CoυY=mi=1σ 2 iV i,under the quadratic loss L(δ,SXβ)=(δ SXβ)′(δ SXβ),some necessary and sufficient conditions are given to linear estimators of estimable function SXβ being admissible in the classes of linear estimators.

Choose the quadratic loss function,among the homogeneous linear estimator L0={MYN:M,N are m1×n,p×m2 constant matrix,MX1=K},the unipue Minimax admissible estimate of linear estimable function KBL is given.