Statistical Properties of Stimulated Raman Scattering in a Nonlinear Regime

Statistical properties of the Raman scattering of an intense step pulse are investigated by numerical solution of the equations of a semi-classical theory with assignment of a random Gaussian distribution of the initial polarization over the sample. The probability density functions of the intensity, energy, delay time, and width of a Stokes pulse and also of the position, height, and width of the spectral peaks of the first incidental Stokes component with the preservation of the phase memory of scattering centers are calculated. The influence of collisional dephasing on the fluctuation of these characteristics is considered.     

Conditions for the convergence in distribution of maxima of stationary normal processes

The asymptotic distribution of the maximum M_n=max_1?t?nξ_t in a stationary normal sequence ξ₁,ξ,… depends on the correlation r_t between ξ₀ and ξ_t. It is well known that if r_t log t → 0 as t → ∞ or if Σr²_t<∞, then the limiting distribution is the same as for a sequence of independent normal variables. Here it is shown that this also follows from a weaker condition, which only puts a restriction on the number of t-values for which rt log t islarge. The condition gives some insight into what is essential for this asymptotic behaviour of maxima. Similar results are obtained for a stationary normal process in continuous time.     

The Spearman footrule and a Markov chain property

An equivalent representation of the Spearman footrule is considered and a characterization in terms of a Markov chain is established. A martingale approach is thereby incorporated in the study of the asymptotic normality of the statistics.     

Synchronized abandonments in a single server unreliable queue

We consider a single server unreliable queue represented by a 2-dimensional continuous-time Markov chain. At failure times, the present customers leave the system. Moreover, customers become impatient and perform synchronized abandonments, as long as the server is down. We analyze this model and derive the main performance measures using results from the basic q-hypergeometric series.     

The Wigner Function as Distribution Function

Some entangled states have nonnegative Wigner representative function. The latter allow being viewed as a distribution function of local hidden variables. It is argued herewith that the interpretation of expectation values using such distribution functions as local hidden variable theory requires restrictions pertaining to the observables under study. The reasoning lead to support the view that violation of Bell’s inequalities that is always possible for entangled states hinges not only on the states involved but also whether the dynamical variables have their values defined even when they cannot be measured.     

Water absorption kinetics in different wettability conditions studied at pore and sample scales in porous media by NMR with portable single-sided and laboratory imaging devices

NMR relaxation time distributions of water (1)H obtained by a portable single-sided surface device have been compared with MRI internal images obtained with a laboratory imaging apparatus on the same biocalcarenite (Lecce Stone) samples during capillary water uptake. The aim of this work was to check the ability of NMR methods to quantitatively follow the absorption phenomenon under different wettability conditions of the internal pore surfaces. Stone wettability changes were obtained by capillary absorption of a chloroform solution of Paraloid PB72, a hydrophobic acrylic resin frequently used to protect monuments and buildings, through one face of each sample. Both relaxation and imaging data have been found in good quantitative agreement each other and with masses of water determined by weighing the samples. In particular the Washburn model of water capillary rise applied to the imaging data allowed us to quantify the sorptivity in both treated and untreated samples. Combining relaxation and imaging data, a synergetic improvement of our understanding of the water absorption kinetics at both pore and sample scales is obtained. Since relaxation data have been taken over the course of time without interrupting the absorption process, simply by keeping the portable device on the surface opposite to the absorption, the results show that the single-sided NMR technique is a powerful tool for in situ evaluation of water-repellent treatments frequently used for consolidation and/or protection of stone artifacts.     

On the Capability of the Generalized Gamma Function to Represent Spray Drop‐Size Distribution

The three‐parameter, Generalized Gamma function solution of a recent MEF formulation used to derive liquid spray drop‐size distribution, is applied to sprays resulting from three different atomization processes. The objectives of these applications are to determine the sign of the parameters for which this function reports a more reliable fit and to further understand the parameter stability problem reported elsewhere. It is found that the lack of stability of the parameters is related to a characteristic feature of the mathematical function and appears for a series of spray drop‐size distributions with constant shape. For each situation analyzed in the present study, the Generalized Gamma function provides a very good fit with parameters that are either constant or correlated to the working conditions. As far as the sign of the parameters is concerned, the results show that the best formulation is a function of the spray and that it is impossible to know, a priori, which parameter sign will report the best fit. Finally, for one situation, it is found that the Generalized Gamma function allows extrapolation of drop sizes outside the measured values. All of the results converge to conclude that the three‐parameter Generalized Gamma function, which is identical to the well‐known Nukiyama‐Tanasawa distribution, accumulates valuable attributes to represent liquid spray drop‐size distributions.     

线偏振激光场中原子的多光子电离的光电子角分布研究

非微扰量子电动力学的发展使我们可以利用精确的波函数和非微扰的散射理论来研究多光子电离问题.文章作者及其合作者发展了光电子角分布的处理方法,利用复合相位Bessel函数来表征光电子的跃迁几率幅,将光电子的角分布与复合相位Bessel函数直接联系起来.研究发现,复合相位Bessel函数的性质决定了光电子角分布的主要特点及其随激光强度、频率以及光电子能量的演化.该理论不但证实了实验上已经观测到的各种光电子角分布,而且还预言了实验上尚未观测到的光电子角分布,确立了光电子角分布的标度定律.     

On log-normal convolutions: An analytical–numerical method with applications to economic capital determination

We put forward an efficient algorithm for approximating the sums of independent and log-normally distributed random variables. Namely, by combining tools from probability theory and numerical analysis, we are able to compute the cumulative distribution functions of the just-mentioned sums to a high precision and in a relatively short computing time. We illustrate the effectiveness of the new method in the contexts of the individual and collective risk models, aggregate economic capital determination, and economic capital allocation.     

NMR analysis and triad sequence distributions of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

Polyhydroxyalkanoates (PHAs) are considered promising “green” alternatives to synthetic polymers because they are bio-derived, biodegradable and biocompatible. The properties of bacterial PHA copolymers depend on their microstructures, which can be modified with the use of different fermentation processes and feed materials. Thus, it is desirable to have an improved testing method for the determination of PHA microstructures. In this work, a detailed NMR analysis of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) microstructure was made. Previously only two of the hydroxyvalerate ¹³C NMR peaks have been assigned at the triad level. In this work, three of the ¹³C hydroxyvalerate peaks and two of the hydroxybutyrate peaks were found to be split into four peaks each due to comonomer sequence effects. Using eight copolymer samples with a wide compositional range, we were able to assign all these peaks to B-centered and V-centered triad sequences. Through curve deconvolution, the triad intensities were determined. These triad sequence intensities can then be analyzed via both the first-order Markovian and two-component Bernoullian models to obtain more in-depth information on copolymer composition and comonomer reactivities.