Discrete threshold growth dynamics are omnivorous for box neighborhoods

In the discrete threshold model for crystal growth in the plane we begin with some set of seed crystals and observe crystal growth over time by generating a sequence of subsets of by a deterministic rule. This rule is as follows: a site crystallizes when a threshold number of crystallized points appear in the site's prescribed neighborhood. The growth dynamics generated by this model are said to be omnivorous if finite and imply . In this paper we prove that the dynamics are omnivorous when the neighborhood is a box (i.e. when, for some fixed , the neighborhood of is . This result has important implications in the study of the first passage time when is chosen randomly with a sparse Bernoulli density and in the study of the limiting shape to which converges.

     

Linear phase transition in random linear constraint satisfaction problems

Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and a constraint is chosen from also uniformly at random. This procedure is repeated m times independently. We are interested in whether the resulting linear programming problem is feasible. We prove that the feasibility property experiences a linear phase transition, when n and m = cn for a constant c. Namely, there exists a critical value c^* such that, when c < c^*, the problem is feasible or is asymptotically almost feasible, as n, but, when c>c^*, the distance to feasibility is at least a positive constant independent of n. Our result is obtained using the combination of a powerful local weak convergence method developed in Aldous [Ald92], [Ald01], Aldous and Steele [AS03], Steele [Ste02] and martingale techniques. By exploiting a linear programming duality, our theorem implies the following result in the context of sparse random graphs G(n, cn) on n nodes with cn edges, where edges are equipped with randomly generated weights. Let (n, c) denote maximum weight matching in G(n, cn). We prove that when c is a constant and n , the limit lim_n (n, c)/n, exists, with high probability. We further extend this result to maximum weight b-matchings also in G(n, cn).     

短脉冲激光辐照下SiO2损伤微观机理简化模型

 从电子密度速率方程出发，建立短脉冲激光辐照下SiO₂材料中导带电子增长简化模型，计算了SiO₂中光致电离速率和电子雪崩速率，得到SiO₂激光损伤阈值与脉冲宽度的关系，计算分析了光致电离和碰撞电离两种电离机制在导带电子累积过程中的不同作用。结果表明：脉冲较长，碰撞电离几乎能提供全部的导带电子，激光损伤阈值与脉宽的0.5次方成正比；脉冲较短时，导带电子主要由碰撞电离产生，光致电离提供碰撞电离的初始电子，激光损伤阈值随着脉宽的减小，先增加后减小。     

Picosecond stimulated Raman scattering of BaWO4 crystal

In single-pass configuration, a picosecond pulse laser was used to investigate the stimulated Raman scattering in different BaWO₄ crystals. Using the thresholds for the first Stokes line along the a- and c-axis, the Raman gain coefficients of the BaWO₄ crystals were calculated along their respective direction. The higher Stokes (fourth) and anti-Stokes (third) lines were observed. Compared with other well-known Raman crystals, such as KGd(WO₄)₂ and Ba(NO₃)₂, BaWO₄ has favorable properties for scattering the pump radiation with picosecond pulse duration. The Raman gain coefficients of BaWO₄ are different, but do not vary for different transmission directions, which means that this Raman material can be selected more freely.     

Asymmetric conditional volatility in international stock markets

Recent studies show that a negative shock in stock prices will generate more volatility than a positive shock of similar magnitude. The aim of this paper is to appraise the hypothesis under which the conditional mean and the conditional variance of stock returns are asymmetric functions of past information. We compare the results for the Portuguese Stock Market Index PSI 20 with six other Stock Market Indices, namely the SP 500, FTSE 100, DAX 30, CAC 40, ASE 20, and IBEX 35. In order to assess asymmetric volatility we use autoregressive conditional heteroskedasticity specifications known as TARCH and EGARCH. We also test for asymmetry after controlling for the effect of macroeconomic factors on stock market returns using TAR and M-TAR specifications within a VAR framework. Our results show that the conditional variance is an asymmetric function of past innovations raising proportionately more during market declines, a phenomenon known as the leverage effect. However, when we control for the effect of changes in macroeconomic variables, we find no significant evidence of asymmetric behaviour of the stock market returns. There are some signs that the Portuguese Stock Market tends to show somewhat less market efficiency than other markets since the effect of the shocks appear to take a longer time to dissipate.     

三能级光纤激光器速率方程组的阈值解析解

 在考虑了泵浦损耗及激光损耗的情况下,解析求解了阈值泵浦下的三能级光纤激光器速率方程组,获得了泵浦功率阈值的显函数解析表达式,泵浦功率沿光纤变化的隐函数表达式,以及用功率变化表示的各个能级的粒子数密度随位置变化的显函数表达式。并利用这些表达式对光纤激光器的阈值特性进行了研究,研究表明：泵浦功率阈值随泵浦损耗系数增大而增大;激光上能级粒子数密度随归一化位置呈下降趋势,而下能级粒子数密度的变化与此相反;泵浦功率阈值越大(光纤长度越长),净增益系数随归一位置下降就越快。所获得的结果适用于单包层和双包层光纤激光器。     

连续照明时成像对比度与气象条件的关系

 通过同轴激光连续照明成像模型分析了大气后向散射对成像对比度的影响，得出了考虑散射因素时成像对比度的计算公式。基于不同气象条件下大气粒子散射特点，讨论了霾和雾两种不同天气时成像对比度随照明距离的变化规律，并与实验结果进行了对比，计算结果与实验吻合较好。     

Classical Risk Model with Threshold Dividend Strategy

In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.