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*}     

基于RBF网络信道均衡器

在数字通信系统中为了克服信道畸变引起的码间干扰，在接收端必须采用信道均衡技术。在本文中，我们将RBF网络用作均衡器。采用最近邻聚类和直接判决算法来调整隐藏层中心，然后再用LMS算法调整输出层的系数。该算法可以实现在线学习，根据相应的准则增加，删除隐藏层节点。算法事先不必确定隐藏层的节点个数。模拟结果显示，RBF网络均衡器能够正确地将信号从有噪信道中恢复出来，在计算机模拟仿真中其性能与理想贝叶斯均衡器相当。     

Precise rate in the law of iterated logarithm for <Emphasis Type="Italic">ρ</Emphasis>-mixing sequence

Let {X, X _n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set . Suppose lim _n→∞ and , where d=2, if −1<b<0 and d>2(b+1), if b≥0. It is proved that, for any b>−1,

5-桥图F(2,a,a,b,c)的色等价刻画

设P(G，λ)是图G关于变量λ的色多项式，P(G，λ)=P(H，λ)，称G和H色等价，由连接两个顶点的S条内部不交的路组成的图叫S-桥图。本讨论了5-桥图F(2,a,a,b,c)(c≥b≥a 1，a≥2)的色性，完整刻画了这类图的色等价图。     

Multiobjective optimization problem with variational inequality constraints

 We study a general multiobjective optimization problem with variational inequality, equality, inequality and abstract constraints. Fritz John type necessary optimality conditions involving Mordukhovich coderivatives are derived. They lead to Kuhn-Tucker type necessary optimality conditions under additional constraint qualifications including the calmness condition, the error bound constraint qualification, the no nonzero abnormal multiplier constraint qualification, the generalized Mangasarian-Fromovitz constraint qualification, the strong regularity constraint qualification and the linear constraint qualification. We then apply these results to the multiobjective optimization problem with complementarity constraints and the multiobjective bilevel programming problem. Received: November 2000 / Accepted: October 2001 Published online: December 19, 2002 Key Words. Multiobjective optimization – Variational inequality – Complementarity constraint – Constraint qualification – Bilevel programming problem – Preference – Utility function – Subdifferential calculus – Variational principle Research of this paper was supported by NSERC and a University of Victoria Internal Research Grant Research was supported by the National Science Foundation under grants DMS-9704203 and DMS-0102496 Mathematics Subject Classification (2000): Sub49K24, 90C29     

非晶态硒化镉薄膜瞬态光电特性

本文报道用真空热蒸发法淀积的非晶态硒化镉薄膜作光敏介质制备超快光电导探测器。用对撞脉冲锁模Nd:YAG激光器产生的超短光脉冲序列对探测器的响应时间进行检测,结果表明a-CdSe薄膜对皮秒(10^-12秒)级的超短光脉冲作用具有良好的瞬态响应光电特性,探讨a-CdSe薄膜快速弛豫过程的内在机理。     

环形装置中三维MHD平衡与稳定性的计算机模拟

一、引 言 在聚变研究中,环形等离子体的磁约束起着重要作用。目前托卡马克研究的进展令人鼓舞,其理论与实验比较符合,定标关系清楚。但是无论从聚变的最终目标来看,还是从实验的安排考虑,完全轴对称的几何形状给各方面部带来许多不便。人们希望知道如果把环形几何中加进直线段,或者把圆环改成不具有对称性的环形,会对等离子体约束产生何种影响?     

高频单线圈双调谐NMR单晶探头的研制

本文报道了一种测角单晶NMR探头。该探头采用单线圃双调谐电路,工作频率在90MHz-110 MHz连续可调,可进行交叉极化大功率去耦实验。文中提出了一种简单而有效的测角装置,可使单晶绕三个互相垂直轴转动实现单晶的NMR测量。作为典型的应用例子,本文利用该探头实现了单晶DGO(2NH₂CH₂COOH·H₂C₂O₄)屏蔽张量的测量。     

SUPPLEMENT TO “PASSAGE, BLOCKADE, SINK AND SOURCE OF A PLANAR DYNAMICAL SYSTEM”

A Theorem is given on the number of passages passing throgh a multiply-connected region,which corrects a wrong conjecture in a former paper of the author.