On a new class of multiplicative pseudo-random number generators

In the computing literature, there are few detailed analytical studies of the global statistical characteristics of a class of multiplicative pseudo-random number generators.We comment briefly on normal numbers and study analytically the approximately uniform discrete distribution or (j,)-normality in the sense of Besicovitch for complete periods of fractional parts {x _{0 1} ⁱ /p} on [0, 1] fori=0, 1,..., (p–1)p^–1–1, i.e. in current terminology, generators given byx _{n+1 1} x _n mod p wheren=0, 1,..., (p–1)p ^–1–1,p is any odd prime, (x ₀,p)=1, ₁ is a primitive root modp ², and 1 is any positive integer.We derive the expectationsE(X, ),E(X ², ),E(X _nX_n+k); the varianceV(X, ), and the serial correlation coefficient k. By means of Dedekind sums and some results of H. Rademacher, we investigate the asymptotic properties of k for various lagsk and integers 1 and give numerical illustrations. For the frequently used case =1, we find comparable results to estimates of Coveyou and Jansson as well as a mathematical demonstration of a so-called rule of thumb related to the choice of ₁ for small k.Due to the number of parameters in this class of generators, it may be possible to obtain increased control over the statistical behavior of these pseudo-random sequences both analytically as well as computationally.     

Superconvergence of the iterated collocation methods for Hammerstein equations

In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [16] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also discuss the discrete collocation method for weakly singular Hammerstein equations. Some discrete collocation methods for Hammerstein equations with smooth kernels were given previously in [3, 18].     

具有可变到达率的多重休假Geo~(λ_1,λ_2)/G/1排队分析

本文考虑顾客到达与服务员休假相关的多重休假离散时间排队系统,用更新过程及u-变换分析了系统的队长性质.分别得到系统在三种时点(n~-,n~+,n)处的队长分布的递推解,进而揭示了在不同到达率条件下系统队长分布不再具有随机分解特性,得到了系统在四种时点(n~-,n~+,n,离去时点D_n)处稳态队长分布的重要关系(不同于连续时间排队系统).     

Discrete Green's Function for Lattice Random Walk

A lattice random walk model based on particles scattering on discrete lattice of homogenous space is introduced. The discrete Green's function (DFG) for two-dimensional and three-dimensional lattice random walk of photon is found and proved by mathematical induction. The convolution theorem of photon lattice random walk is presented. They can be used with the method of images to calculate the photon density distribution in semi-infinite and finite slab homogenous turbid media such as tissue.     

Discrete Green's Function for Lattice Random Walk

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Infinite-variate wide-sense Markov processes and functional analysis for bounded operator-forming vectors

Let p, q be arbitrary parameter sets, and let $\text{H}$ be a Hilbert space. We say that x = (xⁱ)_i?q, xⁱ ? $\text{H}$, is a bounded operator-forming vector (?$\text{H}$_F^q) if the Gram matrix 〈x, x〉 = [(xⁱ, x^j)]_i?q,j?q is the matrix of a bounded (necessarily ≥ 0) operator on $\text{l}{}_{\mathrm{q}}{}^2$, the Hilbert space of square-summable complex-valued functions on q. Let A be p × q, i.e., let A be a linear operator from $\text{l}{}_{\mathrm{q}}{}^2$ to $\text{l}{}_{\mathrm{p}}{}^2$. Then exists a linear operator ǎ from (the Banach space) $\text{H}$_F^q to $\text{H}$_F^p on $\text{D}$(A) = {x:x ? $\text{H}$_F^q, $\text{A〈x, x〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is p × q bounded on $\text{l}{}_{\mathrm{q}}{}^2$} such that y = ǎx satisfies y^j?σ(x) = {space spanned by the xⁱ}, 〈y, x〉 = A〈x, x〉 and $\text{〈y, y〉 = A〈x, x〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(A〈x, x〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1$. This is a generalization of our earlier [J. Multivariate Anal.4 (1974), 166–209; 6 (1976), 538–571] results for the case of a spectral measure concentrated on one point. We apply these tools to investigate q-variate wide-sense Markov processes.     

Open dynamic behaviour of financial markets

Open dynamic behaviour of financial markets with internal interactions between agents and with external “fields” from other systems are investigated using the approach of Grossman and Stiglitz for inefficient markets, and Keynes for interference of the market using physics of finance (referred to hereafter as phynance). The simulation results indicate that the NYSE data analyzed in Plerou, V. et al., Nature 421, 130 (2003) can be fitted by an equation of order parameter Φ and local deviation R of type: -(R+0.03) Φ+ 0.6 Φ³ + 0.02 = 0, which is shown to be in remarkable agreement with Plerou's data.     

二维矢量边界推进非结构网格生成方法

提出二维矢量边界推进生成非结构三角形网格方法并证明其可行性.根据流场边界尺度布置边界节点并运用矢量边界推进方法生成背景网格,运用符号面积函数和概率筛选方法布置初始点阵,提出Spring-Laplace方法优化节点位置,同时利用边交换技术优化网格结构.该方法可包含任意点源、线源和内嵌边界,可自由进行局部自适应加密或稀疏,实现任意平面域内与尺度要求一致的高效光滑三角网格剖分.     

ECR离子源六极永磁体的设计研究

分别从材料、结构、尺寸等方面全面地研究了Halbach结构六极永磁铁的设计方法.针对个别磁块可能存在的退磁问题给出了相应的解决方案.通过优化结构,使六极磁铁在离子源等离子体弧腔内壁产生的磁场达到最大.用POISSON,PERMAG,TOSCA等多个磁场模拟程序计算模拟了六极磁场的大小与分布,并给出了一些相应的曲线