Tail asymptotics for the fundamental period in the MAP/G/1 queue

This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802–813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions. I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008.     

The compound binomial risk model with time-correlated claims

In this paper, we consider the compound binomial risk model with the time-correlated claims. It is assumed that every main claim will produce a by-claim but the occurrence of the by-claim may be delayed. We obtain the recursive formula of the joint distribution of the surplus immediately prior to ruin and deficit at ruin. Furthermore, the ruin probability is given by means of ruin probability and the deficit at ruin of the classical compound binomial risk model. Finally, we derive an upper bound for the ruin probability.     

Regular variation of order 1 nonlinear AR-ARCH models

We prove both geometric ergodicity and regular variation of the stationary distribution for a class of nonlinear stochastic recursions that includes nonlinear AR-ARCH models of order 1. The Lyapounov exponent for the model, the index of regular variation and the spectral measure for the regular variation all are characterized by a simple two-state Markov chain.     

Stationary remaining service time conditional on queue length

In Mandelbaum and Yechiali [The conditional residual service time in the M/G/1 queue, http://www.math.tau.ac.il/∼uriy/publications (No. 30a), 1979] and in Fakinos [The expected remaining service time in a single-server queue, Oper. Res. 30 (1982) 1014-1018] a simple formula is derived for the (stationary) expected remaining service time in a M/G/1 queue, conditional on the number of customers in the system. We give a short new proof of the formula using Rate Conservation Law, and generalize to handle higher moments.     

Direct mass measurements of neutron-deficient 152Sm projectile fragments at the FRS-ESR facility

The FRS-ESR facility at GSI provides one of the most efficient methods for direct mass measurements. In the present experiment, exotic nuclei were produced via fragmentation of ¹⁵²Sm projectiles in a thick beryllium target at 500-600 MeV/u, separated in-flight with the fragment separator FRS, and injected into the storage-cooler ring ESR. Time-resolved Schottky Mass Spectrometry was applied for mass measurements of stored and electron-cooled bare and few-electron ions. 373 different nuclides were identified by means of the spectra of their revolution frequencies. Masses for 18 nuclides (⁸⁴Zr, ⁹²Ru, ⁹⁴Rh, ^107,108,110Sb, ^111,112,114I, ¹¹⁸Ba, ^122,123La, ¹²⁴Ce, ¹²⁷Pr, ¹²⁹Nd, ¹³²Pm, ¹³⁴Sm, ¹³⁷Eu) have been determined for the first time. Masses for ^111,112I and ¹¹³Xe have been obtained via known α-decay energies. The experiment and first results will be presented.     

Second order evolution equations with time-dependent subdifferentials

We study an abstract second order nonlinear evolution equation in a real Hilbert space. We consider time-dependent convex functions and their subdifferentials operating on the first derivative of the unknown function. Introducing appropriate assumptions on the convex functions and other data, we prove the existence and uniqueness of a strong solution, and give some applications of the abstract theorem to hyperbolic variational inequalities with time-dependent constraints.      

On perfectly normal dense subspaces of products

Let M be a separable metric space consisting of more than one point. We construct perfectly normal dense subspaces Z⊂Mc² and (under additional set-theoretic assumption) Y⊂Mc which are not collectionwise Hausdorff.     

An explosion point space without the fixed point property

In 1988 A. Gutek proved that there exist one-point connectifications of hereditarily disconnected spaces that do not have the fixed point property. We improve on this result by constructing a one-point connectification of a totally disconnected space without the fixed point property.