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Let $X_1,X_2,\ldots,X_n$ be a sequence of extended negatively dependent random variables with distributions $F_1,F_2,\ldots,F_n$,respectively. Denote by $S_n=X_1+X_2+\cdots+X_n$. This paper establishes the asymptotic relationship for the quantities $\pr(S_n>x)$, $\pr(\max\{X_1,X_2, \ldots,X_n\}>x)$, $\pr(\max\{S_1,S_2$, $\ldots,S_n\}>x)$ and $\tsm_{k=1}^n\pr(X_k>x)$ in the three heavy-tailed cases. Based on this, this paper also investigates the asymptotics for the tail probability of the maximum of randomly weighted sums, and checks its accuracy via Monte Carlo simulations. Finally, as an application to the discrete-time risk model with insurance and financial risks, the asymptotic estimate for the finite-time ruin probability is derived.     

Refined discrete regular variation and its applications

We introduce a new class of the so‐called regularly varying sequences with respect to τ and state its properties. This class, on one hand, generalizes regularly varying sequences. On the other hand, it refines them and makes it possible to do a more sophisticated analysis in applications. We show a close connection with regular variation on time scales; thanks to this relation, we can use the existing theory on time scales to develop discrete regular variation with respect to τ. We reveal also a connection with generalized regularly varying functions. As an application, we study asymptotic behavior of solutions to linear difference equations; we obtain generalization and extension of known results. The theory also yields, in some way, a new view on the tests for convergence and divergence of series; we establish the statement that generalizes Raabe test and Bertrand test.     

Spectral tail processes and max-stable approximations of multivariate regularly varying time series

A regularly varying time series as introduced in Basrak and Segers (2009) is a (multivariate) time series such that all finite dimensional distributions are multivariate regularly varying. The extremal behavior of such a process can then be described by the index of regular variation and the so-called spectral tail process, which is the limiting distribution of the rescaled process, given an extreme event at time 0. As shown in Basrak and Segers (2009), the stationarity of the underlying time series implies a certain structure of the spectral tail process, informally known as the “time change formula”. In this article, we show that on the other hand, every process which satisfies this property is in fact the spectral tail process of an underlying stationary max-stable process. The spectral tail process and the corresponding max-stable process then provide two complementary views on the extremal behavior of a multivariate regularly varying stationary time series.     

Control of multi-node mobile communications networks with time-varying channels via stability methods

Consider a communications network consisting of mobiles and random external data processes, each destined to a particular destination. Each mobile can serve as a node in the multi-hop path from source to destination. At each mobile the data is queued according to the source destination pair. The quality of the connecting channels are randomly varying. Time is divided into small scheduling intervals. At the beginning of each interval, the channels are estimated and this information is used for the decisions concerning allocation of transmission power and/or time, bandwidth, and perhaps antennas, in a queue and channel-state dependent way. Under a natural (and “almost” necessary) “average flow” condition, stochastic stability methods are used to develop scheduling policies that assure stability. The policies are readily implementable and allow a range of tradeoffs between current rates and queue lengths, under very weak conditions. Because of the non-Markovian nature of the problem, we use the perturbed Stochastic Liapunov function method. The choice of Liapunov function allows a choice of the effective performance criteria. All essential factors are incorporated into a “mean rate” function, so that the results cover many different systems. Extensions concerning acknowledgments, multicasting, non-unique routes, and others are given to illustrate the versatility of the method, and a useful method for getting the a priori routes is discussed.     

A new two-dimensional approach to quantitative prediction for collision cross-section of more than 110 singly protonated peptides by a novel moecular electronegativity-interaction vector through quantitative structure-spectrometry relationship studies

Based on two-dimensional topological characters, a novel method called molecular electronegativity-interaction vector (MEIV) is proposed to parameterize molecular structures. Applying MEIV into quantitative structure-spectrometry relationship studies on ion mobility spectrometry collision cross-sections of 113 singly protonated peptides, three models were strictly obtained, with correlative coefficient r and leave-one-out cross-validation q of 0.983, 0.979, 0.981, 0.979 and 0.980, 0.978, respectively. Thus, the MEIV is confirmed to be potent to structural characterizations and property predictions for organic and biologic molecules. Translated from Chinese Journal of Analytical Chemistry, 2006, 34(6) (in Chinese)     

A fast calculation of excitation autoionization cross-sections of Na-like ions

In this work, based on the calculation in detail, two new fitting formulae of total excitation and excitation autoionization cross-sections for Na-like ions (18?Z?39) are given. For discussing the variation of the total excitation autoionization cross-section, a systematic study of the dependence of the overall branching ratio on incident electron energy and nuclear charge is also carried out.     

Some applications of cross-section measures in Minkowski spaces

Summary The purpose of this paper is to establish extremal values for inner and outer radii of the unit ball of a Minkowski space for the Holmes--Thompson and Busemann measures. Furthermore, we confirm a conjecture of C. A. Rogers and G. C. Shephard on ellipsoids.     

与铷（5^2S1／2）原子碰撞产生的铷7^2D态精细结构转移截面

本文报道使用蒸汽泡和两光子两步激发方法,测量原子激发态敏化荧光I_(3/2)~1和直接荧光I_(3/2)~2其与温度的关系,得到与基态(5~2S_(1/2)铷原子碰撞产生的铷7~2D_(5/2)→7~2D_(3/2)和7~2D_(3/2)→7~2D_(5/2)精细结构转移截面分别为:σ_(fs)=4.7×10~(-13)cm~2、σ_(fs)~’=7.0×10~(-13)cm~2;碰撞转移出7~2D双态的转移截面σ_(tr)(5/2)=0.62×10~(-13)cm~2.由计算的7~2D态几何截面σ_(geom)能够相对很好地描述σ_(fs)和σ_(fs)~’的数量级.     

No directed fractal percolation in zero area

We consider the fractal percolation process on the unit square with fixed decimation parameterN and level-dependent retention parameters {p _k}; that is, for allk ⩾ 1, at thek th stage every retained square of side lengthN ¹⁻ k is partitioned intoN ² congruent subsquares, and each of these is retained with probabilityp _k. independent of all others. We show that if Π_k p _k =0 (i.e., if the area of the limiting set vanishes a.s.), then a.s. the limiting set contains no directed crossings of the unit square (a directed crossing is a path that crosses the unit square from left to right, and moves only up, down, and to the right).     

部分线性变系数模型中估计的渐进正态性

作为部分线性模型与变系数模型的推广,部分线性变系数模型是一类应用非常广泛的模型,本文基于Profile最小二乘方法给出了模型中参数分量与非参数分量的估计,并在异方差情形下证明了这些估计的渐进正态性.