Phase-matched high-order harmonics by interaction of Ar atoms with high-repetition-rate low-energy femtosecond laser pulses

High-order harmonics are generated by coherent interaction of an intense laser and atoms or molecules[1]. With the development of the intense ultrashort pulse laser, the research of high-order harmonic generation has reached the water-window in spectral region[2] and subfemtosecond in time domain[3]. Especially, the generation and application of subfemtosecond pulse led the study of high-order harmonic generation into a completely new world[4, 5]. It has made the study of ultrafast science fro…     

Single-particle light scattering study of polyethyleneglycol-grafted poly(ureaurethane) microcapsule in ethanol

Microcapsules having polyethyleneglycol-grafted poly(ureaurethane) (PUU) membrane and di-2ethylhexyl phthalate core have been prepared, and the structure when they were suspended in dispersing ethanol have been studied by means of single-particle light scattering method. The PUU membrane was synthesized from monomers with aromatic functional groups (microcapsule MC110) and hexamethylene functional groups (microcapsule MC160). Because the outer and inner solvent passed through the membrane easily, the outside and inside of the membrane were the same at the equilibrium state. The thickness of the wall membrane was significantly smaller than that calculated from the overall weight ratio of the wall-forming material and the core solvents. It was attributed to low affinity of PUU membranes and ethanol.     

Thermodynamic equilibrium of the solute distribution in size-exclusion chromatography

Our understanding of the nature of solute retention in size-exclusion chromatography (SEC) is predicated upon an equilibrium, entropy-controlled, size-exclusion mechanism. The entropic nature of the separation depends, in turn, upon the solute distribution coefficient (K(SEC) being at (or close to) thermodynamic equilibrium. Classic experiments to confirm this assumption were performed over thirty years ago. Here, we combine information obtained from both flow and static mixing SEC experiments to show that the solute distribution in SEC is in thermodynamic equilibrium over a molar mass range extending one order of magnitude higher than previously measured (from 2 x 10(3) to 1.1 x 10(6) Da) using crosslinked polystyrene packing material of identical pore size (10(4) A). The differences between our observations and previous ones conducted over three decades ago are ascribed, principally, to advances in stationary phase synthesis and column technology for SEC in particular and, secondarily, to improvements in the performance of the various instrumental components of liquid chromatographic systems in general.     

Factorization of Markov Chains

Existence of following factorization is proved:

深沪股市收益率分布特征的统计分析

本文通过对深沪两地股票市场的股指收益率数据进行分析,发现两地股票收益率分布均呈现"尖峰厚尾"反正态特征,本文通过引入Laplace分布代替过去人们常用的正态分布去刻画收益率分布,结果显示Laplace分布比正态分布拟合效率有了明显的提高。     

On the Almost Intersections of Transient Brownian Motions

Let {B ₁ ^d (t)} and {B ^d ₂(t)} be independent Brownian motions in R ^d starting from 0 and nx respectively, and let w ^d _i (a,b) ={xR ^d : B ^d _i (t)=x for some t(a,b)}, i=1,2. Asymptotic expressions as n for the probability of dist(w ^d ₁(n ² t ₁, n ² t ₂), w ₂ ^d (0,n ² t ₃))1 with d4, respectively for the probability of dist(w ₁ ⁴(n ² t ₁,n ² t ₂),w ₂ ⁴(0,n ² t ₃))1 are obtained. As an application, an improvement of a result due to M. Aizenman concerning the intersections of Wiener sausages in R ⁴ is presented.     

Explicit Expressions for the Ruin Probabilities of Erlang Risk Processes with Pareto Individual Claim Distributions

In this paper we first consider a risk process in which claim inter-arrival times and the time untilthe first claim have an Erlang (2) distribution.An explicit solution is derived for the probability of ultimateruin,given an initial reserve of u when the claim size follows a Pareto distribution.Follow Ramsay,Laplacetransforms and exponential integrals are used to derive the solution,which involves a single integral of realvalued functions along the positive real line,and the integrand is not of an oscillating kind.Then we showthat the ultimate ruin probability can be expressed as the sum of expected values of functions of two differentGamma random variables.Finally,the results are extended to the Erlang(n) case.Numerical examples aregiven to illustrate the main results.     

Two-Parametric Compound Binomial Approximations

We consider two-parametric compound binomial approximation of the generalized Poisson binomial distribution. We show that the accuracy of approximation essentially depends on the symmetry or shifting of distributions and construct asymptotic expansions. For the proofs, we combine the properties of norms with the results for convolutions of symmetric and shifted distributions. In the lattice case, we use the characteristic function method. In the case of almost binomial approximation, we apply Steins method.__________Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 443–466, October–December, 2004.     

The Halász Inequality for Additive Function of Rational Argument

We obtain an upper bound for the quantity . Here I is an interval, is the set of rational numbers q=m/n I such that nx, and f(q) is an arbitrary real-valued additive function of rational argument. The interval I and function f may depend on x3.