Pseudoinverse in clustering problems

The clustering of vector observations of hyperplanes is studied. Different cases of correspondence distances are proposed and investigated, including the algebraic Jack Knife one. The efficiency, constructivity, and explicit form of formulas are provided by using the pseudoinverse technique including the pseudoinverse-perturbation theory. Results important for the application of pseudoinverse and related operators are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 73–92, July–August 2007.     

A singular loop transformation framework based on non-singular matrices

In this paper, we discuss a loop transformation framework that is based on integer non-singular matrices. The transformations included in this framework are called Λ-transformations and include permutation, skewing and reversal, as well as a transformation calledloop scaling. This framework is more general than existing ones; however, it is also more difficult to generate code in our framework. This paper shows how integer lattice theory can be used to generate efficient code. An added advantage of our framework over existing ones is that there is a simple completion algorithm which, given a partial transformation matrix, produces a full transformation matrix that satisfies all dependences. This completion procedure has applications in parallelization and in the generation of code for NUMA machines. This work was supported by the Cornell Theory Center, NSF Presidential Young Investigator award #CCR-8958543. by NSF Grant #CCR-9008526, and by a grant from the Hewlett-Packard Company.     

Bilateral polynomial matrix equations in two indeterminates

Two special cases of the bilateral 2-D polynomial matrix equationDU +VN=C whenC=I andC=I with being a -stable 2-D polynomial, which are related respectively to deadbeat and asymptotic control problems of 2-D systems, are first considered. By generalizing the concepts of factor coprimeness, zero coprimeness and zero skew primeness in the 2-D polynomial ring to the ring of causal -stable 2-D rational functions, a constructive solution of these two problems mentioned is proposed. Based on these results, we derive a solvability condition for the bilateral equiation whereC is a general 2-D polynomial matrix. The general solutions are investigated as well.     

工矿供电系统谐波治理新方法研究

针对现有无源滤波器滤波效果较差,易出现谐振过电压、谐波放大等现象的问题,提出一种基于基波谐振原理的谐波治理新方法。该方法在电网与无源滤波器之间的三相线路中分别串联一组由电感和电容组成的基波谐振电路,迫使谐波电流最大限度地流入无源滤波器,从而大幅提升滤波器的效率。实验结果表明,增加基波谐振电路后,电流畸变率从10.6%下降为0.942%,滤波效果更佳。     

用简化的Goertzel来实现正弦基波与谐波

通过对Goertzel算法的优化和运用查表法处理来加快其运算速度。在硬件电路的基础上,用C语言完成了实际应用的算法程序。采用Atmel公司51系列外接晶振时钟频率可高达24MHz的单片机AT89C2051-24SU,运算后输出了一定频率的正弦基波及其多次谐波组成的波形。     

Citations do not solve problems.

D. T. Cambell and D. W. Fiske (1959) made the now-obvious statement that measures of the same variable made by different methods should agree (converge) and certainly should agree better than measures of different variables made by those several methods. Almost everyone accepted that statement, yet the multitrait–multimethod matrices published today show little or no improvement over the published examples cited in 1959. The article raised the conceptual problem of how a variable and its measurement should be linked and the methodological problem of clarifying the nature of methods and their effects. Given these unresolved problems, it is perhaps not surprising that the question of the appropriate statistical analysis of these matrices has also no consensual answer. Perhaps methods and traits or contents are so thoroughly intertwined that their interaction cannot be adequately analyzed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

基于锁相放大器原理的基波无功检测方法研究

无功补偿控制系统需要快速、准确地检测出系统基波无功功率以及功率因数等参数,用以控制无功补偿设备输出系统所需的基波无功功率。针对现有检测方法受电网以及无功补偿设备本身产生的谐波影响而造成计算结果准确度降低、计算速度慢等问题,基于锁相放大器原理,提出一种适用于无功控制系统的快速、准确的基波无功功率以及功率因数检测方法;在Matlab上进行了仿真分析,对比了含有多种谐波时,不同信噪比下各参数的最大误差,并搭建了实验平台,以Fluke-435-II电能质量分析仪验证该方法的准确性;经仿真和实验表明,该方法可以在含有谐波时准确、快速地检测出系统的基波无功功率及功率因数,为无功补偿系统的无功检测提供了理论依据和实用方法。     

煤气化联合循环发电示范状况和煤气化工艺对比

煤炭气化已被确认为制取管道煤气或合成气的技术。经多方研究已被工业化规模生产和煤气化联合循环发电所证实。本文评述了煤的基本性质对气化效率的影响，煤气化联合循环发电示范厂现状和各种选定用于煤气化联合循环发电的第二代煤气化方法的对比。本文最后阐述了煤气化联合循环发电用于改造高能耗的以煤、油和天然气为燃料的中小规模电厂的现实性。     

FREQUENCY DOMAIN TESTS OF MULTIVARIATE GAUSSIANITY AND LINEARITY

A stationary multivariate time series { X _t } is defined as linear if it can be written in the form X _t = ∑^∞ _{j =−∞} A _j e _{t − j} where A _j are square matrices and e _t are independent and identically distributed random vectors. If the e _t } are normally distributed, then { X _t is a multivariate Gaussian linear process. This paper is concerned with the testing of departures of a vector stationary process from multivariate Gaussianity and linearity using the bispectral approach. First the definition and properties of cumulants of random matrices are used to obtain the expressions for the higher-order cumulant and spectral vectors of a linear vector process as defined above. Then it is shown that linearity of a vector process implies constancy of the modulus square of its normalized higher-order spectra whereas the component of such a vector process does not necessarily have a linear representation. Finally, statistics for the testing of multivariate Gaussianity and linearity are proposed.     

MDS矩阵和对合MDS矩阵的新构造方法

首先对Lacan等人给出的由Vandermonde矩阵构造MDS码的方法进行了研究, 指出了其中存在的问题, 给出了由两个Vandermonde矩阵构造MDS矩阵的充要条件; 然后利用矩阵乘的方法, 给出了由标量乘Vandermonde矩阵构造MDS矩阵的充要条件; 最后在Sajadieh等人给出的由两个Vandermonde矩阵构造对合MDS矩阵方法的基础之上, 给出了标量乘Vandermonde矩阵构造对合MDS矩阵的方法。对标量乘矩阵来讲, 可以通过调控标量中分量的大小来调整标量乘矩阵元素大小和元素重量大小来满足其软、硬件实现性能, 因此该构造MDS矩阵及对合MDS矩阵的方法具有实用价值。