Probabilistic and Average Linear Widths of Sobolev Space with Gaussian Measure in L \infty-Norm

In this paper we investigate the probabilistic linear $(n,\delta)$-widths and $p$-average linear $n$-widths of the Sobolev space $W^r_2$ equipped with the Gaussian measure $\mu$ in the $L_{\infty}$-norm, and determine the asymptotic equalities \begin{eqnarray*} \lambda_{n,\delta}(W^r_2,\mu,L_{\infty}) &\asymp&\frac{\sqrt{\ln (n/\delta)}}{n^{r+(s-1)/2}},\\[3pt] \lambda^{(a)}_n(W^r_2,\mu,L_{\infty})_p &\asymp&\frac{\sqrt{\ln n}}{n^{r+(s-1)/2}}, \qquad 0 < p < \infty. \end{eqnarray*}     

On the stationary Lp-approximation power to derivatives by radial basis function interpolation

In this paper, we consider approximation to derivatives of a function by using radial basis function interpolation. Most of well-known theories for this problem provide error analysis in terms of the so-called native space, say C_φ. However, if a basis function φ is smooth, the space C_φ is extremely small. Thus, the purpose of this study is to extend this result to functions in the homogenous Sobolev space.     

齐次~Morrey-Herz 空间上分数次积分算子高阶交换子的有界性

在齐次Morrey-Herz空间上建立了高阶交换子~$T^{m}_{b,l}$ 和 ~$M^{m}_{b,l}$的有界性，其中~$T^{m}_{b,l}$ 和 ~$M^{m}_{b,l}$ 是由分数次积分算子和分数次极大算子分别与~BMO($R^{n}$)函数生成的高阶交换子.     

硅色敏器件对复色光色差辨识能力的数值分析

对复色光的光谱功率分布和色敏器件光谱响应的实验曲线进行了函数拟合，采用Mathematica 4．2计算了具有不同峰值波长和半高宽的高斯分布的复色光在色敏器件中产生的电流比．计算结果表明，待测复色光的峰值波长和半高宽变化对两种典型的色敏器件的输出信号影响的权重比分别为100：1和10：1。权重比说明色敏器件的输出电流比随峰值波长和半高宽的变化非常灵敏，但两者权重不同，其中峰值波长的变化影响更为显著，是影响复色光颜色变化的主要因素．数值分析的结果表明，硅双结色敏器件对复色光色差有良好的辨识能力．两种器件权重比的差异说明了器件制作工艺与其辨识能力的关系，为器件合理设计提供了理论依据．     

Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -     

ANTI FUZZY VECTOR SPACES（Ⅱ）

ＡＮＴＩＦＵＺＺＹＶＥＣＴＯＲＳＰＡＣＥＳ（Ⅱ）ＣｈｅｎＹｏｎｇｎｉａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，８３００５４，Ｘｉｎｊｉａｎｇ，Ｐ．Ｒ．Ｃｈｉｎａ）ＡＮＴＩＦＵＺＺＹＶＥＣＴ...     

布尔矩阵维数的缺断区间(英)

本文证明了n维布尔矩阵维数的一个新的缺断区间为这一结果扩充了一些已知的结论．     

光致折射效应中空间电荷场建立过程的研究

本文推导了包含自衍射及非线性吸收影响、用以描述空间电荷场建立过程的微分方程组,阐明了周期性的空间电荷场与光强干涉条纹之间的相位差在建立过程中所起的作用,并推导了描述条纹倾斜和弯曲的微分方程。通过数值计算找到了硅酸铋(BSO)晶体中能量转移的规律,讨论了材料特性对过程快慢的影响,提出了用CW激光来探讨瞬态过程快慢的可能性。     

Numerical analysis of a model of cure process for composites

We consider a composite material composed of fibres included in a resin which becomes solid when it is heated up (reaction of reticulation). The mathematical modelling of the cure process is given by a kinetic equation describing the evolution of the reaction of reticulation coupled with the heat equation. In this paper, we are interested in the computation of approximate solutions. We propose a family of discretized problems depending on two parameters (β₁, β₂) ε [0, 1]² which split the linear and non‐ linear terms in implicit and explicit parts. We prove the stability and convergence of the discretization for any (β₁, β₂) ε [½, 1 ] × [0, 1]. We present also some numerical results. Copyright © 2006 John Wiley & Sons, Ltd.