On the distribution of the length of the longest increasing subsequence of random permutations

The authors consider the length, , of the longest increasing subsequence of a random permutation of numbers. The main result in this paper is a proof that the distribution function for , suitably centered and scaled, converges to the Tracy-Widom distribution of the largest eigenvalue of a random GUE matrix. The authors also prove convergence of moments. The proof is based on the steepest descent method for Riemann-Hilbert problems, introduced by Deift and Zhou in 1993 in the context of integrable systems. The applicability of the Riemann-Hilbert technique depends, in turn, on the determinantal formula of Gessel for the Poissonization of the distribution function of .

     

A stochastic model for the HIV epidemic in homosexual populations involving age and race

In this paper, we derive a stochastic model for the HIV epidemic in homosexual populations involving age and race. To account for effects of different mixing patterns, a low risk selection rule is introduced. The model is then formulated in terms of chain multinomial distributions by means of which the means are derived. Some simulation studies by computer indicate clearly that age and race have a significant impact on the HIV epidemic.     

Experimental artefacts in 2D-MAS exchange experiments: non-uniform mixing time within a single 2D run

The practical realization of rotor-synchronized mixing-times in 2D-MAS exchange experiments without the need for a special hardware is reviewed; its consequence for the ‘true mixing time' of the experiment is discussed. We demonstrate influences on experimental rate constants derived from such experiments as well as on the appearance of the 2D-MAS spectra, taken at short mixing times.     

Dispersive flow of disks through a two-dimensional Galton board

We report here an experimental and numerical study of the flow properties of disks driven by gravity through a hexagonal lattice of obstacles, i.e. a Galton board. During the fall, particles experience dissipative collisions that scatter them in random directions. A driven-diffusion regime can be achieved under certain conditions. A characteristic length of the motion and its dependence on geometrical parameters of the system is analyzed in the steady regime. The influence of collective effects on the dispersion process is investigated by comparison between single- and many-particle flows. The characterization of the dynamics and the diffusive properties of the flow in a system like a Galton board can be expanded to other granular systems, particularly static solid particle mixers and will give some insight in understanding granular mixing.     

Mixing Layers in Sink Flow: Effect of Length of Flight on Mixing in a Channel Downstream

We have experimentally and analytically studied transport of a passive scalar in the wake of a thin flat plate located at the centerline of a planar contraction with flat walls. The constant Launder parameter in the contraction, K = 6.25 ×10^− 6, was twice the value required for a turbulent boundary layer to relaminarize. In addition to the mixing analysis inside the contraction, layer mixing is also investigated downstream, where the flow continues inside a constant cross-section channel. In order to generate the passive scalar, the airflow above the plate was heated and the temperature stratification in the wake was traced by measuring the temperature field using constant current anemometry. Using different plate lengths, we found that the degree of mixing, obtained at a given position in the straight channel, is a function of the distance from the plate trailing edge to the contraction outlet. For a plate which does not protrude into the straight channel, we demonstrate the existence of an optimal trailing edge-contraction outlet distance that results in the lowest possible degree of mixing at a given downstream position in the straight channel. This finding is also supported by a semi-empirical relationship based on our developed self-similar solution for mixing layers in planar contractions.     

ρ混合、φ混合、ψ混合线性模型M估计的强相合性

研究了 ρ混合、φ混合、ψ混合样本线性模型中回归参数M估计的强相合性 ,在条件不变的情况下 ,获得与独立情形一样的M估计是强相合的充分条件 ,推广了文 [1 ]定理 2 .     

关于γ—可重排列方面的一个计数公式

本文给也了规格为２＾ｍ的２ｍ个元的γ－可重排列的个数的一个计算公式。     

Nanoparticle nucleation and coagulation in a mixing layer

Numerical simulation of nanoparticle nucleation and coagulation in a mixing layer with sulfuric acid vapor binary system is performed using the large eddy simulation and the direct quadrature method of moment. The distributions of number concentration, volume concentration, and average diameter of nanoparticles are obtained. The results show that the coherent structures have an important effect on the distributions of number concentration, volume concentration and average diameter of nanoparticles via continuously transporting and diffusing the nanoparticles to the area of low particle concentration. In the streamwise direction, the number concentration of nanoparticles decreases, while the volume concentration and the average diameter increase. The distributions of number concentration, volume concentration and average diameter of nanoparticles are spatially inhomogeneous. The characteristic time of nucleation is shorter than that of coagulation. The nucleation takes place more easily in the area of low temperature because where the number concentration of nanoparticles is high, while the intensity of coagulation is mainly affected by the number concentration. Both nucleation and coagulation result in the variation of average diameter of nanoparticles.     

TiO2-Al2O3复合载体的比较研究

对用混胶法和共沉淀法分别制备的ＴｉＯ２－Ａｌ２Ｏ３复合载体（ＴｉＯ２含量为０．０８ｇ／ｇγ－Ａｌ２Ｏ３）进行了对比研究，采用的表征方法有ＸＲＤ，ＸＲＳ，ＬＲＳ等，得出的结论如下：两种载体均保持了γ－Ａｌ２Ｏ３的骨架结构，但ＴｉＯ２的分散状态不尽相同，混胶样品中ＴｉＯ２主要以表面富集的形式分散在γ－Ａｌ２Ｏ３表面，这有利于集二者的优点于一体，共沉淀样品中ＴｉＯ２趋于整个体相均匀分散，这有利于相互作用     

α－混合序列和的强大数律及其应用

研究α－混合序列加权和的强大数律，并将这些结果应用于Ｐｒｉｅｓｔｌｅｙ，Ｍ．Ｂ．和Ｃｈａｏ，Ｍ．Ｔ．（１９７２）提出的非参数回归函数加权核估计，获得较理想结论．