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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X射线光刻胶的研究

合成了甲基丙烯酸缩水甘油酯与甲基丙烯酸氯乙酯和甲基丙烯酸氯乙酯与甲基丙烯酸甲酯共聚物,并研究了该共聚物的分子量分布、结构和热稳定性能。研究了甲基丙烯酸缩水甘油酯与甲基丙烯酸氯乙酯正性X射线光刻胶。该光刻胶具有热稳定性和高分辨率性。最低线幅宽度为0.1μm。     

Transition from the Fluctuation Mode of Stimulated Resonant Coherent Raman Scattering to the Energy–Stabilized Mode

The equations of the semiclassical theory for the stimulated resonant coherent Raman scattering (SRS) in an extended medium have been solved numerically. The distribution function of the energy of Stokes pulses at different detunings and energies of a laser has been determined. Just as for the nonresonant coherent SRS, in the situation considered there occurs transition from the large–scale fluctuation mode to the mode of relatively small straggling of the energies of Stokes pulses with increase in the pumping energy. With approach to the resonance, the energy required to stabilize the Stokes radiation decreases.     

Optimal Conditional Estimation: Average Case Setting

We consider an estimation problem which appears in the identification of systems by means of restricted complexity models: find the optimal approximation to an element of a linear normed space (a system) based on noisy information, subject to the restriction that approximations (models) can be selected from a prescribed subspace M of the problem element space. In contrast to the worst-case optimization criterion, which may be pessimistic, in this paper the quality of an identification algorithm is measured by its local average performance. Two types of local average errors are considered: for a given information (measurement) y and for a given unknown element x, the latter in two versions. For a wide spectrum of norms in the measurement space, we define an optimal algorithm and give expressions for its average errors which show the dependence on information, information errors, unmodelled dynamics, and norm in the measurement space.     

Review of testing issues in extremes: in honor of Professor Laurens de Haan

As a leading statistician in extreme value theory, Professor Laurens de Haan has made significant contribution in both probability and statistics of extremes. In honor of his 70th birthday, we review testing issues in extremes, which include research done by Professor Laurens de Haan and many others. In comparison with statistical estimation in extremes, research on testing has received less attention. So we also point out some practical questions in this direction.