Hyers–Ulam stability of linear differential operator with constant coefficients

Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Randomly censored partially linear single-index models

This paper proposes a method for estimation of a class of partially linear single-index models with randomly censored samples. The method provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored. It presents a technique for “dimension reduction” in semiparametric censored regression models and generalizes the existing accelerated failure-time models for survival analysis. The estimation procedure involves three stages: first, transform the censored data into synthetic data or pseudo-responses unbiasedly; second, obtain quasi-likelihood estimates of the regression coefficients in both linear and single-index components by an iteratively algorithm; finally, estimate the unknown nonparametric regression function using techniques for univariate censored nonparametric regression. The estimators for the regression coefficients are shown to be jointly root-n consistent and asymptotically normal. In addition, the estimator for the unknown regression function is a local linear kernel regression estimator and can be estimated with the same efficiency as all the parameters are known. Monte Carlo simulations are conducted to illustrate the proposed methodology.     

托卡马克能量约束及自举电流效应的初步考虑

基于Lee等人的离子温度梯度模导致的反常热能输运系数,本文研究了辅助加热托卡马克等离子体的能量约束行为,并对自举电流的效应作了初步考虑。结果表明,计算得到的能量约束时间随等离子体电流I_p和托卡马克大半径R增大而增长,随注入功率P_t、环向场B_t以及等离子体小半径α的增大而缩短。这些结果与Kaye-Goldston的经验约束定标具有相同的趋势。自举电流的存在总是导致能量约束时间的增加,当自举电流与总电流的比值γ较小时,能量约束时间的增加率约为γ/2。此外,自举电流将造成锯齿反转半径的减小。     

Probabilistic Analysis of Condition Numbers for Linear Programming

In this paper, we provide bounds for the expected value of the log of the condition number C(A) of a linear feasibility problem given by a n × m matrix A (Ref. 1). We show that this expected value is O(min{n, m log n}) if n > m and is O(log n) otherwise. A similar bound applies for the log of the condition number C _R(A) introduced by Renegar (Ref. 2).     

高精度CCD尺寸自动检测系统的光学系统设计

介绍测量精度为±０．００３ｍｍ的ＣＣＤ尺寸检测系统的光学系统设计特点及远心物镜设计原理，并给出了测试结果。     

The many facets of linear programming

We examine the history of linear programming from computational, geometric, and complexity points of view, looking at simplex, ellipsoid, interior-point, and other methods. Received: June 22, 2000 / Accepted: April 4, 2001?Published online October 2, 2001     

电子直线加速器磁控管频率稳定的自适应线性神经元方法

 电子直线加速器电子束能量的稳定与否取决于功率源工作频率的稳定性,磁控管在短时间内的散谱和轻微跳谱造成稳频系统的控制精度下降,最后电子束的扫描均匀度下降。引入自适应线性神经元方法(ADALINE)和噪声对消技术以消除对工作频率长期稳定性的影响,从而保证了电子束的扫描均匀度。     

Constrained control for uncertain linear systems

The linear state feedback synthesis problem for uncertain linear systems with state and control constraints is considered. We assume that the uncertainties are present in both the state and input matrices and they are bounded. The main goal is to find a linear control law assuring that both state and input constraints are fulfilled at each time. The problem is solved by confining the state within a compact and convex positively invariant set contained in the allowable state region.It is shown that, if the controls, the state, and the uncertainties are subject to linear inequality constraints and if a candidate compact and convex polyhedral set is assigned, a feedback matrix assuring that this region is positively invariant for the closed-loop system is found as a solution of a set of linear inequalities for both continuous and discrete time design problems.These results are extended to the case in which additive disturbances are present. The relationship between positive invariance and system stability is investigated and conditions for the existence of positively invariant regions of the polyhedral type are given.The author is grateful to Drs. Vito Cerone and Roberto Tempo for their comments.     

Optical current transducer with bulk type Bi12SiO20 faraday sensor for power systems

Two types of optical current transducers (OCTs) have a bulk Faraday sensor inserted into the gap of an iron core and a porcelain insulator with optical fiber. The sensor consists of Bi₁₂SiO₂₀ (BSO) single crystal, a polarizer, and an analyzer. The OCTs satisfied the target performance requirement for fault location and metering and demonstrated maintained performance at some power utilities in Japan and the US. We have developed a fault location system that immediately detects the fault current with the OCTs, there by locating the fault section. The OCT can easily replace the existing support insulators for the disconnecting switch without any modifications to structure height or bus-bar. For metering requiring 0.3% class accuracy, use of a BSO with right optical rotatory power combined with BSO with left optical rotatory power results in a Faraday sensor with improved temperature characteristics. The OCT demonstrated 0.3% class accuracy for metering described in the current transformer Specifications of IEEE C57–13, 1993.     

Special representations of the group SP(4,q) with minimal degrees

Let G be a finite group. Let p(G) denote the minimal degree of a faithful permutation representation ofG and let q(G) and c(G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers, respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. The purpose of this paper is to calculate p(G), q(G), c(G) and r(G) for the group SP(4,q). This revised version was published online in June 2006 with corrections to the Cover Date.