A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process

A method for estimating the distribution of scan statistics with high precisìon was introduced in Haiman (2000). Using that method sharp bounds for the errors were also established. This paper is concerned with the application of the method in Haiman (2000) to a two-dimensional Poisson process. The method involves the estimation by simulation of the conditional (fixed number of points) distribution of scan statistics for the particular rectangle sets of size 2 × 2, 2 × 3, 3 × 3, where the unit is the (1 × 1) dimension of the squared scanning window. In order to perform these particular estimations, we develop and test a perfect simulation algorithm. We then perform several numerical applications and compare our results with results obtained by other authors.     

On Analogs of the Tits Alternative for Groups of Homeomorphisms of the Circle and of the Line

In [1] G. Margulis proved Ghys's conjecture stating the validity of the following analog of the Tits alternative: either the group of homeomorphisms of the circle possesses a free subgroup with two generators or there is an invariant probabilistic measure on S ¹ . In the present paper, we prove the following strengthening of Margulis's statement: an invariant probabilistic measure for a group exists if and only if the quotient group does not contain a free subgroup with two generators (here is some specific subgroup of G defined in a canonical way). We also formulate and prove analogs of the Tits alternative for groups of homeomorphisms of the line.     

Parametric amplification at low-frequency pumping and generation of four-mode entangled states

We show that parametric amplification at low-frequency pumping can be implemented in aperiodic nonlinear photonic crystals. In this process, the intensities of the waves with frequencies higher than the pumping frequency increase with increase in the interaction length as in the case of the standard process of parametric amplification at high-frequency pumping. The process under consideration includes a nondegenerate parametric down-conversion followed by two parametric up-conversions in the same pumping wave. As a result, generation at four new frequencies arises. Quantum analysis of the process demonstrates the presence of entanglement in the states of four modes. Talk presented at the oral issue of J. Russ. Laser Res. dedicated to the memory of Professor Vladimir A. Isakov, Professor Alexander S. Shumovsky, and Professor Andrei V. Vinogradov held in Moscow February 21–22, 2008.     

Menger概率n-度量空间中的不动点定理

引进了概率ｎ－度量空间,并将文「１」、「２」的某些主要结果拓广至Ｍｅｎｇｅｒ概率ｎ－度量空间。     

Characterization based on conditional expectations of adjacent order statistics: A unified approach

In this paper, we show a unified approach to the problem of characterizing general distribution functions based on the conditional expectation between adjacent order statistics, or , where is a real, continuous and strictly monotonic function. We have the explicit expression of the distribution function from the above order mean function, and , and we give necessary and sufficient conditions so that any real function can be an order mean function. Our results generalize the results given for the discrete, absolutely continuous and continuous cases. Further, we show stability theorems for these characterizations.

     

量子混沌在谱涨落统计特征上的表象

通过对Ｈｅｎｏｎ－Ｈｅｉｌｅｓ模型、Ｂａｒｂａｎｉｓ模型和刚环转球模型这两类三种守恒体系之对应量子体系的研究，具体地剖析了本征值谱涨落统计特征与体系动力学行为的联系，说明了量子混沌现象的两种表现形式。同时，通过将本质上属于经典耗散系范畴的Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ模型之演化方程哈密顿化，发现其量子对应系本征值谱的涨落统计特征超出了Ｐｏｉｓｓｏｎ－ＧＯＥ（Ｗｉｇｎｅｒ）或ＧＵＥ框架。揭示出经典耗散     

On the spatial-temporal averaging method for modeling transport in porous media

The spatial-temporal averaging procedure is considered with a nonhomogeneous distribution of elementary domains in the spatial-temporal space and the probabilistic interpretation of the ST-averaging is also given. Several averaging theorems and corollaries about the averages of spatial and temporal derivatives are presented and rigorously proved which allow elementary domain to vary in space and time. The macroscopic transport equation in the most general condition and the simplified macroscopic equation under the special form of distributions are developed which may be reduced to the classical macroscopic transport equation as the spatial-temporal average degenerates into the volume average.     

Lattice dynamics of b.c.c. alkaline-earth metals: Barium

Summary The attractive short-range component of the interatomic potential screens the conventional Born-Mayer potential in the framework of the resonance pseudopotential model. The elastic constants are evaluated at the long-wavelength limit of the phonon spectrum and the obtained results are compared with previous experimental values. The numerical calculations show that the attractive component of the potential explains the soft modes in this body-centred cubic (b.c.c.) alkaline-earth metal barium.     

Point processes and multivariate extreme values

A new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions. It is shown that such processes may arise via natural generating procedures, and that, under very weak assumptions, that they can be approximated as closely as desired by appropriate finite models.     

Some asymptotic expansions of moments of order statistics

Series expansions of moments of order statistics are obtained from expansions of the inverse of the distribution function. They are valid for certain types of distributions with regularly varying tails. We show that the expansions converge quickly when the sample size is moderate to large, and we obtain bounds on the rate of convergence. The special case of the Cauchy distribution is treated in more detail.