Corrigendum to “Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times” [Stochastic Process. Appl. 111 (2004) 237-258]

The purpose of this note is to correct an error in Baltrunas et al. (2004) [1], and to give a more detailed argument to a formula whose validity has been questioned over the years. These details close a gap in the proof of Theorem 4.1 as originally stated, the validity of which is hereby strengthened.     

An investigation of the Si(111)−(√3 × √3)R30°−Ag surface by Li impact collision ion scattering spectroscopy

The Si(111)−(√3 × √3)R30°−Ag surface has been investigated using the technique of Li⁺ impact collision ion scattering spectroscopy. Typical LEED √3 domain sizes were estimated to be on the order of 150 Å for a 1 ML coverage of Ag, with the √3 structure persisting for coverages of Ag up to 35 ML. Silver islanding was found to influence the appearance of the 5 keV Li⁺ ICISS angular scans even for 1 ML coverages of Ag deposited at 480°C. A detailed structural analysis of the Si(111)−√3−Ag surface (0.25 ML deposition) involved the comparison of 5 keV Li⁺ ICISS experimental data along the [11 ], [ 10] and [2 1] azimuths with computer simulations of the scattered ion intensities based on previously proposed models for the √3 surface. Nine structurally different models were tested, and only the missing-top-layer (MTL) and the honeycomb-chained-trimer (HCT) models were found to be consistent with all the experimental results. An estimate of 0.4 Å for the maximum downward vertical displacement of the Ag atoms with resect to the surface Si atoms in the MTL model is made. The effects of increased thermal vibrational amplitude in the simulation of Si---Ag shadowing effects is also discussed. The interpretations of previous noble gas ICISS results are shown to be inconsistent with the present alkali metal ICISS study of the √3 surface.     

A one-dimensional Poisson growth model with non-overlapping intervals

Suppose given a realization of a Poisson process on the line: call the points ‘germs’ because at a given instant ‘grains’ start growing around every germ, stopping for any particular grain when it touches another grain. When all growth stops a fraction e⁻¹ of the line remains uncovered. Let n germs be thrown uniformly and independently onto the circumference of a circle, and let grains grow under a similar protocol. Then the expected fraction of the circle remaining uncovered is the nth partial sum of the usual series for e⁻¹. These results, which sharpen inequalities obtained earlier, have one-sided analogues: the grains on the positive axis alone do not cover the origin with probability e^−1/2, and the conditional probability that the origin is uncovered by these positive grains, given that the germs n and n+1 coincide, is the nth partial sum of the series for e^−1/2. Despite the close similarity of these results to the rencontre, or matching, problem, we have no inclusion–exclusion derivation of them. We give explicitly the distributions for the length of a contiguous block of grains and the number of grains in such a block, and for the length of a grain. The points of the line not covered by any grain constitute a Kingman-type regenerative phenomenon for which the associated p-function p(t) gives the conditional probability that a point at distance t from an uncovered point is also uncovered. These functions enable us to identify a continuous-time Markov chain on the integers for which p(t) is a diagonal transition probability.     

Long range dependence of point processes, with queueing examples

Possible definitions of the long range dependence (LRD) of a stationary point process are discussed. Examples from the standard queueing literature are considered and shown to be amenable to yielding processes with long range count dependence. In particular the effect of the single-server queueing operator, whereby one point process is transformed into another via the mechanism of a simple queue, is examined for possible long range dependence of both the counting and interval properties of the output process. For an infinite server queue, the output is long range count dependent if and only if the input is long range count dependent.     

A Note on Bounds for the Supremum Metric for Discrete Random Variables

For positive or negative integer-valued random variables X and Y with finite second moments the inequality sup \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\sup }\limits_n |\Pr \{ X \le n\} - \Pr \{ Y \le n\} |\, \le \,|EX - EY| + \frac{1}{2}(EX(EX - 1) + (EY(Y - 1)) $\end{document} is established by elementary manipulation, and shown to be tight. Use of generating functions and an inversion formula yields the larger bound with 1/2 replaced by 2/π.     

发光玻璃在X射线实时成像系统中的应用

介绍了以铽（Ｔｂ）激活的高密度发光玻璃和光导纤维发光玻璃的特性。它应用在Ｘ射线实时成像系统中,可大大改善空间分辨能力。用它做的转换屏比一般晶粒状荧光物质做的厚得多,特别适合用于高能Ｘ射线实时成像系统