Stationary Probability Distribution of Colored-noise Saturation Model for a Single-mode Dye Laser

It is applied the interpolation procedure to calculate the stationary probability distribution of colored-gain-noise model of a single-mode dye laser which operates above threshold with correlation time τ covering a very wide rang. By use of Stochastic Runge-Kutta Algorithm, it also has carried out numerical simulations of the steady-state properties. Comparing the results of the interpolation procedure and the unified colored-noise approximation with simulation results, the agreement between the results of the interpolation procedure and simulation results is much better than that of the unified colored-noise approximation when correlation time τ covers range from moderate to large.     

一类组合不等式的简证与推广

利用概率方法给出了形如sum from k=1 to n(1/k)>π/4(sum from k=1 to n((-1)k-1Cnk)1/(k～1/2))与sum from k=1 to n(1/k)<2～(1/2)(sum from k=1 to n((-1)k-1Cnk)1/k2)1/2的组合不等式.     

保费收取过程是随机过程的双险种风险模型

研究保费收取过程是一个随机过程的双险种风险模型,得出了Lundberg上界、最终破产概率、不破产所满足的微积分方程、索赔服从指数分布的不破产概率、有限时间不破产所满足的微积分方程.     

Purge efficiency in the determination of trihalomethanes in water by purge-and-trap gas chromatography

Purge-and-trap gas chromatography-mass spectrometry (PT-GC-MS) has become an accepted method for the analysis of trihalomethanes (THMs) in water. The purge-and-trap technique is based on an efficient transfer of volatile organic compounds from the liquid (contained in the purge chamber) to the gaseous phase by bubbling with an inert gas. The aim of this work was to study the purge system's efficiency by means of several consecutive purge cycles lasting 11 min each of the same liquid sample. The concentration range chosen of THMs was very wide [5-200 μg L⁻¹]. The inert gas flow rate was 40 mL min⁻¹, and experiments were performed at temperatures of 25, 35 and 50 °C. Bromoform (CHBr₃), the least volatile compound, needed 19 cycles to be purged quantitatively at a concentration of 200 μg L⁻¹ and only 7 cycles at 5 μg L⁻¹ for a 25 mL sample at 25 °C. Chloroform (CHCl₃), the most volatile compound, required 4 cycles to be fully extracted at 200 μg L⁻¹ and 2 at 5 μg L⁻¹. Finally, Novak's theoretical model, based on the distribution constant between gas and liquid phases, was used to correlate the THMs purging extraction data.     

Skew-Gaussian random field

In this article, we introduce the concept of skewness to the Gaussian random field theory by defining a new two-dimensional non-Gaussian random field called skew-Gaussian random field. We derive the expected Euler characteristic of its excursion set. Moreover, an approximation to the size distribution of one connected component is derived. As an illustration, we present a simulation study to compare the approximation mechanism with the exact one.     

Mathematical modeling of the dissolving and deposition processes during solution seepage in a porous medium

A mathematical model that describes solution seepage in a porous medium and the processes of mineral dissolving and secondary deposition is proposed. Self-similar solutions describing the motion of the leading and trailing fronts, that is, the boundaries of the complete-dissolving zone, are determined. The main features of the processes under consideration are studied and numerical calculations are performed. It is shown that the model describes well the experimental data on mineral leaching by sulfate solutions. The dynamics of mineral extraction from productive solutions in a medium with a nonuniformacidity distribution are investigated. It is shown that, in the elevated-PH zones, the mineral is dissolved; whereas, in the low-acidity zones, secondary deposition of the mineral occurs. In the latter case, after the work has been completed, the bed may contain more or less considerable mineral resources, depending on the extent of the low-PH zone and its proximity to an extraction well.     

CE模型下指数分布步加试验的贝叶斯估计

本文利用Gibbs抽样法得到了CE模型下指数分布场合步进应力加速寿命试验的多层Bayes参数估计,最后通过模拟比较表明多层Bayes估计比最大似然估计更加有效而实用。     

Estimation Methods for the Multivariate <Emphasis Type="Italic">t</Emphasis> Distribution

The known estimation and simulation methods for multivariate t distributions are reviewed. A review of selected applications is also provided. We believe that this review will serve as an important reference and encourage further research activities in the area.     

Batch processor sharing with hyper-exponential service time

We study the Processor Sharing queueing model with a hyper-exponential service time distribution and Poisson batch arrival process. In the case of the hyper-exponential service time distribution we find an analytical expression for the expected conditional response time function and obtain an alternative proof of its concavity with respect to the service time.     

Wigner Transforms and Fractional Fourier Transforms of the First Order Optical Systems

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