Unitary Correlations and the Fejér Kernel

Let M be a unitary matrix with eigenvalues t _j , and let f be a function on the unit circle. Define X _f (M)=f(t _j ). We derive exact and asymptotic formulae for the covariance of X _f and X _g with respect to the measures |(M)|²dM where dM is Haar measure and an irreducible character. The asymptotic results include an analysis of the Fejér kernel which may be of independent interest.     

测量脉冲大电流的四光路光学电流传感器技术

 在传统光学电流传感器技术的基础上，提出了一种四光路光学电流传感器，其通过四路输出信号可准确确定偏转角，使电流的测量范围不受正弦函数的单调性的限制，从而提高了电流的测量范围。配合四光路结构，提出了新的反正切函数数据处理方法，其不存在角度不灵敏区、可纠正原始数据的缺陷，从而提高了测量精度。实测了充电电压为4.5 kV、电容为50 μF和导线有效穿过磁光探头14次的快开快门的总短路电流，其峰值达85 kA，与理论值87 kA能较好地吻合，从而证明了四光路光学电流传感器可有效地测量脉冲大电流。     

快脉冲直线变压器驱动源模块的原理及实验

 介绍了直线型变压器驱动源（LTD）产生快脉冲的基本原理及技术优势，阐述了快脉冲LTD模块设计的要点，设计了输出脉冲上升时间小于100 ns的快脉冲LTD模块，并进行了初步的实验研究。实验得到该LTD模块充电±16 kV时，短路放电的电流峰值为23.7 kA，电流振荡1/4周期为69.6 ns；充电±50 kV驱动0.85 Ω负载时，电流峰值为41.4 kA，上升时间为36.8 ns（10%~90%）和60.8 ns（0~100%）。     

共孔径偏振耦合分光系统中反射镜造成的相位延迟差的测量

 激光信标共孔径发射接收偏振分光系统的动态相位补偿需要测量望远镜各反射镜对s光和p光的相位延迟差。利用Stokes矢量和Mueller矩阵建立了物理模型，并推导出用测得的回光功率计算相位延迟差的解析式。提出一种通过实验测量回光功率计算反射镜相位延迟差的方法，解决了在0～2p范围内唯一确定反射镜相位延迟差的问题。实际测量了两块反射镜的相位延迟差，并将测量结果用于动态相位补偿偏振分光实验，验证了该方法的正确性。分析了偏振分光棱镜、法拉第旋光器以及近似计算这3个主要的测量误差源，并估计总测量误差约为1°。     

Evaluation of uncertainty utilising the component by component approach

 This paper reviews the so-called "component by component approach" of evaluating measurement uncertainty. An overview of the evaluation process is given followed by an in-depth discussion of some of the differences between this approach and the approach of utilising validation data. Some of the advantages and disadvantages of using the component by component approach are outlined at the end. Received: 4 August 1999 · Accepted: 11 November 1999     

环上矩阵的Moore-Penrose逆的注记

讨论带有对合反自同构的环上矩阵的广义逆,给出了矩阵存在Mooore－Penrose逆的条件及Moore－Penrose逆的一些性质和显式．     

On the Relation Between Orthogonal,Symplectic and Unitary Matrix Ensembles

For the unitary ensembles of N×N Hermitian matrices associated with a weight function w there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For the orthogonal and symplectic ensembles of Hermitian matrices there are 2×2 matrix kernels, usually constructed using skew-orthogonal polynomials, which play an analogous role. These matrix kernels are determined by their upper left-hand entries. We derive formulas expressing these entries in terms of the scalar kernel for the corresponding unitary ensembles. We also show that whenever w/w is a rational function the entries are equal to the scalar kernel plus some extra terms whose number equals the order of w/w. General formulas are obtained for these extra terms. We do not use skew-orthogonal polynomials in the derivations     

Representation of the space of polyanalytic functions as a direct sum of orthogonal subspaces. Application to rational approximations

Suppose thatD={z:|z|<1}, L ₂ (D) is the space of functions square-integrable over area inD,A _k (D) is the set of allk-analytic functions inD, (A ₁ (D)=A(D) is the set of all analytic functions inD),A _k L ₂ (D)=L ₂ (D)∩A _k (D),A ₁ L ₂ (D)=AL ₂ (D),

一类非线性代数方程组的并行迭代算法

１．引言考虑非线性代数方程组这里,　　　　　　　　　　　　　　　　　　　　　　　　　　　　为连续的对角映射,二者的导函数均存在,但并不一定连续．这类非线性代数方程组具有丰富的实际背景．譬如,Ｓｔｅｆａｎ问题和许多弱非线性椭圆型偏微分方程,就可归结为（１．１）的数值求解问题．根据方程组（１．１）的特殊结构,并利用矩阵多重分裂思想,文ｔＺ］讨论了一类并行非线性Ｇａｕｓｓ－Ｓｅｉｄｅｌ型迭代算法．这类算法具有很好的数值性质和较高的并行效率·在此基础上,运用松弛加速技术,文［８］进一步研究了一类并行多分…     

Almost-Sure Results for a Class of Dependent Random Variables

The aim of this note is to establish almost-sure Marcinkiewicz-Zygmund type results for a class of random variables indexed by _d ⁺ —the positive d-dimensional lattice points—and having maximal coefficient of correlation strictly smaller than 1. The class of applications include filters of certain Gaussian sequences and Markov processes.