铝硫二元团簇的组分及其光解规律

硫与金属元素所形成的二元团簇具有很多重要的特性,已受到人们的普遍重视.用激光-串级飞行时间质谱仪,我们曾研究了硫与过渡金属钽、铁等的二元团簇.最近我们选取主族金属元素铝,研究了铝硫团簇的形成及其光解,实验结果表明,与钽硫或铁硫团簇相比,铝硫团簇无论在其组份构成还是在其光解方面,都表现出鲜明的特有规律性.实验的主要参数如下:溅射用激光为Nd:YAG 二倍频,其输出强度控制在约10~7W·cm~(-2),激光的重复频率10Hz 样品位于激光束的焦点附近,由焦距f=50cm 的透镜调整其聚焦状     

O(~1D)+Si(CH_3)_3Cl反应生成振动激发的OH(υ≤5)

实验光谱学和理论计算都发现,“重原子”能隔离分子中的某些振动能景,如SiH_4中Si—H振动泛频的“局域模”.Roger 等在研究F 原子与M(CH_2CH=CH_2)_4(M=Sn,Ge)的反应中,发现了Sn,Ge 对过剩能量转移到其它部分有强烈的阻碍作用(在中间态的寿命时间内).最近,在研究O(~1D)+M(CH_3)_4生成OH(v)反应中,观测到类似的现象.M=C 时,Lutz 用激光诱导荧光方法检测OH 的振动分布,振动是冷的,v=1与v=0的布居比为0.05,     

含氢碳原子团簇的初步研究

介绍直接用激光溅射芳香化合物固态样品产生的含氢磷原子团簇离子（C_nH~＋_m），并用飞行时间质谱仪研究了其组成和结构．实验发现，在低质量区（n＝32－56）得到了具有奇偶碳原子数的含氢磷原子簇，而在高质量区（n＞100）除了得到纯碳原子簇以外，还得到了含氢碳原子簇．根据对实验结果的分析提出了两种结构模型：对低质量区的团簇，其结构为芳香基团与富勒烯笼状框架的复合体；对高质量区的团簇，其结构为蜗牛形与圆柱形的复合体．     

CH3I分子束激光裂解产物的分布

The photofragmentation of CH_3I at 249 nm has been investigated by means of our crossed laser-molecular beam apparatus with rotatable supersonic beam source. The measured I~*/I yield ratio is about 4/1. The C—I bond dissociation energy obtained is 56±1 kcal mol~(-1). The vibrational energy distribution of CH_3 fragments has been roughly estimated.     

An asymptotic relationship for ruin probabilities under heavy-tailed claims

The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy \(R(x, \infty ) \sim \rho ^{ - 1} \bar F_e (x)\) if the claim sizes are heavy-tailed, where F_e denotes the equilibrium distribution of the common d.f. F of the i.i.d. claims, ? is the safety loading coefficient of the model and the limit process is for x → ∞. In this paper we obtain a related local asymptotic relationship for the ruin probabilities. In doing this we establish two lemmas regarding the n-fold convolution of subexponential equilibrium distributions, which are of significance on their own right.     

Reinsurance under the LCR and ECOMOR treaties with emphasis on light-tailed claims

Suppose that, over a fixed time interval of interest, an insurance portfolio generates a random number of independent and identically distributed claims. Under the LCR treaty the reinsurance covers the first l largest claims, while under the ECOMOR treaty it covers the first l−1 largest claims in excess of the lth largest one. Assuming that the claim sizes follow an exponential distribution or a distribution with a convolution-equivalent tail, we derive some precise asymptotic estimates for the tail probabilities of the reinsured amounts under both treaties.     

Randomly weighted sums of subexponential random variables with application to capital allocation

We are interested in the tail behavior of the randomly weighted sum \( \sum _{i=1}^{n}\theta _{i}X_{i}\) , in which the primary random variables X ₁, …, X _n are real valued, independent and subexponentially distributed, while the random weights ?? ₁, …, ?? _n are nonnegative and arbitrarily dependent, but independent of X ₁, …, X _n . For various important cases, we prove that the tail probability of \(\sum _{i=1}^{n}\theta _{i}X_{i}\) is asymptotically equivalent to the sum of the tail probabilities of ?? ₁ X ₁, …, ?? _n X _n , which complies with the principle of a single big jump. An application to capital allocation is proposed.     

The product of two dependent random variables with regularly varying or rapidly varying tails

Let X and Y be two nonnegative and dependent random variables following a generalized Farlie-Gumbel-Morgenstern distribution. In this short note, we study the impact of a dependence structure of X and Y on the tail behavior of XY. We quantify the impact as the limit, as x→∞, of the quotient of Pr(XY>x) and Pr(X^∗Y^∗>x), where X^∗ and Y^∗ are independent random variables identically distributed as X and Y, respectively. We obtain an explicit expression for this limit when X is regularly varying or rapidly varying tailed.     

A note on max-sum equivalence

For finitely many independent real-valued random variables, if their maximum follows a subexponential distribution, then the tail probabilities of their sum and maximum are asymptotically equivalent.     

Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model

Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same asymptotic formula holds for the finite-time and infinite-time ruin probabilities. Restricting our attention to the so-called constant investment strategy, we show how the insurer adjusts his investment portfolio to maximize the expected terminal wealth subject to a constraint on the ruin probability.