Filters compatible with isomorphism testing

Like the lower central series of a nilpotent group, filters generalize the connection between nilpotent groups and graded Lie rings. However, unlike the case with the lower central series, the associated graded Lie ring may share few features with the original group: e.g. the associated Lie ring can be trivial or arbitrarily large. We determine properties of filters such that every isomorphism between groups is induced by an isomorphism between graded Lie rings.     

继电保护中多路模拟量采集系统的设计

介绍了一种基于高性能浮点DSP芯片TMS320C32、CPLD芯片XC95288和A/D采样芯片AD976组成的多路采集系统的工作原理以及设计方法。通过对第一路施加特殊的电压量,在CCS开发环境下读取采样缓冲区的值,并利用Matlab对采样数据进行了全波傅氏变换。此外,该系统已在继电保护中得到广泛应用,实践表明,该系统能较好地解决多路模拟量的采集,并确保了采样数据的安全可靠性。     

基于TMS320VC5410的最小系统设计

TMS320VC5410是TI公司生产的一款定点数字信号处理(DSP)芯片。基于DSP的最小系统是以其简洁的硬件结构来实现DSP的一般功能,广泛应用于工业生产、教学、科研、电子设计等领域。主要介绍了基于TMS320VC5410的最小系统硬件电路设计方案,阐述了重要电路部分的抗干扰设计和软件调试过程中应注意的若干问题。最后提出了简单易行的软件调试方法以及部分程序代码。     

基于CCS和DSK5402板的音频采集和回放程序设计

为了给程序设计作下基础,本文首先介绍了TI公司的TMS320VC5402和AIC(模拟接口电路)芯片TLC320AD50C的特点,最后着重介绍了利用DSK板上的TMS320C5402和TLC320AD50C实现音频采集并实时回放的软件设计过程,并利用CCS进行了模拟.     

微机械可调谐滤波器的研制

利用 Ga As/Al Ga As分布反馈 Bragg反射镜在 Ga As衬底上制作了一个微机械的调谐滤波器 .该器件在 7V调谐电压下调谐范围达28nm     

Congruence criteria for finite subsets of complex projective and complex hyperbolic spaces

We investigate congruence classes and direct congruence classes of m-tuples in the complex projective space ℂP ⁿ . For direct congruence one allows only isometries which are induced by linear (instead of semilinear) mappings. We establish a canonical bijection between the set of direct congruence classes of m-tuples of points in ℂP ⁿ and the set of equivalence classes of positive semidefinite Hermitean m×m-matrices of rank at most n+1 with 1's on the diagonal. As a corollary we get that the direct congruence class of an m-tuple is uniquely determined by the direct congruence classes of all of its triangles, provided that no pair of points of the m-tuple has distance π/2. Examples show that the situation changes drastically if one replaces direct congruence classes by congruence classes or if distances π/2 are allowed. Finally we do the same kind of investigation also for the complex hyperbolic space ℂH ⁿ . Most of the results are completely analogous, however, there are also some interesting differences. Received: 15 January 1996     

Numerical methods for finding multiple eigenvalues of matrices depending on parameters

Summary. Let be a square matrix dependent on parameters and , of which we choose as the eigenvalue parameter. Many computational problems are equivalent to finding a point such that has a multiple eigenvalue at . An incomplete decomposition of a matrix dependent on several parameters is proposed. Based on the developed theory two new algorithms are presented for computing multiple eigenvalues of with geometric multiplicity . A third algorithm is designed for the computation of multiple eigenvalues with geometric multiplicity but which also appears to have local quadratic convergence to semi-simple eigenvalues. Convergence analyses of these methods are given. Several numerical examples are presented which illustrate the behaviour and applications of our methods. Received December 19, 1994 / Revised version received January 18, 1996     

Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.     

A nilpotent Roth theorem

Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L ²-norm for any u, v∈L ^∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T _-n A∩S ^{- n} A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L ²(X) for all u, v∈L ^∞(X) if and only if T×S is ergodic on X×X and the group generated by T ^-1 S, T ^-2 S ²,..., T ^-c S ^c acts ergodically on X. Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001