Polynomial approximation of functions of matrices and applications

In solving a mathematical problem numerically, we frequently need to operate on a vector by an operator that can be expressed asf(A), whereA is anN ×N matrix [e.g., exp(A), sin(A), A^–-]. Except for very simple matrices, it is impractical to construct the matrixf (A) explicitly. Usually an approximation to it is used. This paper develops an algorithm based upon a polynomial approximation tof (A). First the problem is reduced to a problem of approximatingf (z) by a polynomial in z, where z belongs to a domainD in the complex plane that includes all the eigenvalues ofA. This approximation problem is treated by interpolatingf (z) in a certain set of points that is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problems is described. Since a solution to a linear systemAx=b isx=A ^–1 b, an iterative solution algorithm can be based upon a polynomial approximation tof (A)=A ^–1. We give special attention to this important problem.     

Report on a new OED project: A study of the history of new words in the new OED

The study of the history of new words in theNewOED described in this paper was undertaken in 1986-87, and is based on the material then available. Since then, theNewOED has been finished, and PAT, the inquiry system developed at the University of Waterloo for the investigation of theNewOED data base, has been much altered and improved. Nevertheless, this report should prove useful in indicating the potentiality for analyzing the computerizedNewOED and some of the problems. This project is a study of the ways in which new words are created in English at various periods of time. A chronological dictionary 's created listing words introduced into the language over 50 year increments. These words are then classified by the processes used in forming them to show, in proportional terms, if certain processes are more common at some times than at others.H. M. Logan, Associate Professor, Department of English, University of Waterloo, Waterloo, Ontario, Canada, has written The Dialect of the Middle English Life of St. Katherine (Mouton, 1973), making use of the computer in a study of medieval dialectology. He has also written articles on computer stylistics and literary analysis inCHum, ALLC Journal, Language and Style, College Literature, and on the dictionary inDictionaries.     

An enhanced,acoustic emission-based,single-fiber-composite test

In the single-fiber-composite (SFC) test, a fiber imbedded in a matrix is loaded in tension, resulting in a fragmentation of the fiber. In the conventional version of this test, the final fiber fragmentation length distribution is used with a micro-mechanical model to determine the average fiber/matrix interfacial shear stress. In the enhanced version of this test, one also determines the applied stress at each fiber fracture, and from this, one can evaluate the strength of the fiber at short gage lengths. In our measurement system, we utilize an acoustic emission (AE) technique to detect the fiber fractures and to locate the fiber breaks and so determine both the fiber failure stresses as well as the fiber fragmentation lengths while the test is in progress. Critical to the success of this test is a broadband AE system that utilizes point-like AE sensors, procedures for evaluatingin situ, the wavespeed of the first wave arrival and signal processing techniques for determining the arrival time of this signal as precisely as possible for a broad range of wave shapes. Here we describe the application of such an enhanced SFC test procedure to investigate the failure of a Nicalon fiber in an epoxy matrix.     

基于压缩感知的无线传感器网络的数据编码

近年来,基于压缩感知的无线传感器网络数据编码的研究取得了一定的进展,但大部分研究是基于"单跳"的传输模型或者没有考虑网络内节点之间的合作。本文提出了一种基于压缩感知和分簇的传感器网络数据编码方法。首先,节点根据自己的编号伪随机的产生一个M维的列向量,把感知的数据xi投影到此向量上,然后把自己的编号和投影的数据一同传输给簇头。簇头把收到的数据进行求和,并且把计算后的结果传送给下一个簇头,直到sink节点。通过仿真实验和理论分析,验证了本文提出的方法比传统的方法能更好地减少网络内数据传输量。     

具有随机丢包的网络化多自主体系统的一致性

研究具有随机丢包的网络化多自主体系统的均方一致性问题,其中不同自主体间的通信通道具有相同的丢包情况并且均服从马尔可夫(Markov)分布。首先,利用系统变换和迭代方法,得到了系统达到均方一致的一个初等充要条件。然后,利用矩阵理论和图论知识,如果拓扑图含有有向生成树,则可以将系统的均方一致性转化成一个线性Markov跳变系统的均方稳定性,并且可以建立线性矩阵不等式形式的均方可镇定准则。最后,通过相应的仿真实例说明了所得结论的可行性。     

线性矩阵方程异类约束最小二乘解的迭代算法

多矩阵变量线性矩阵方程(LME)约束解的计算问题在参数识别、结构设计、振动理论、自动控制理论等领域都有广泛应用。本文借鉴求线性矩阵方程(LME)同类约束最小二乘解的迭代算法,通过构造等价的线性矩阵方程组,建立了求多矩阵变量LME的一种异类约束最小二乘解的迭代算法,并证明了该算法的收敛性。在不考虑舍入误差的情况下,利用该算法不仅可在有限步计算后得到LME的一组异类约束最小二乘解,而且选取特殊初始矩阵时,可求得LME的极小范数异类约束最小二乘解。另外,还可求得指定矩阵在该LME的异类约束最小二乘解集合中的最佳逼近解。算例表明,该算法是有效的。     

Study on diffusion welding SiCp/ZL101 with Cu interlayer

Through the vacuum diffusion welding SiCp/ZL101 aluminum with Cu interlayer,the effect of welding parame-ter and the thickness of Cu on the welded joint property was investigated,and the optimal welding parameters were putforward at the same time.The microstructure of joint was analyzed by means of optical-microscope,scanning electron mi-croscope in order to study the relationship between the macro-properties of joint and the microstructure.The results showthat diffusion welding with Cu interlayer could be used for welding aluminum matrix composites SiCp/ZL101 successfully.     

变频开关电源Fuzzy-PID控制器的设计

针对感应式变频开关电源在对金属材料进行热处理过程中，负载的等效参数和谐振频率发生变化，而变频电源的输出频率不能及时调整和跟踪的问题，结合PID和Fuzzy控制技术的优点，设计Fuzzy-PID控制器对变频电源进行控制，在大偏差时用Fuzzy控制，在小偏差时用PID调节。Fuzzy-PID控制器以单片机8098为核心，采用SPWM专用芯片SA4828，实现变频开关电源的电压、电流双闭环控制，使变频电源不仅具有较快的动态响应、更小的超调，并且具有较高的稳态精度和频率跟踪控制特性。     

Synthesis and characterization of aromatic polyisoimides derived from PMDA and para-diamines. An approach to in situ generated rigid-rod molecular composites

A new concept for the processing and fabrication of rigid-rod molecular composites aiming at the elimination or minimization of phase separation is proposed. This approach calls for a coil-like aromatic polyisoimide which is soluble and compatible with an amorphous matrix polymer or thermosettable oligomer and can undergo facile transformation to the corresponding rigid-rod polyimide in solid composite state, thus imparting the inherently high strength/high modulus properties to the final form. To this end, various synthetic routes were explored to obtain para-diamines which could afford high molecular weight and aprotic-solvent-soluble polyisoimides upon polymerization with pyromellitic dianhydride (PMDA). Four such polyisoimides were prepared, with their inherent viscosities ranging from 0.25 to 1.89 dl g⁻¹ in dimethylacetamide at 30°C. Facile thermally induced isoimide-imide conversion was demonstrated by solid-state (film) Fourier transform infrared spectroscopy. A preliminary evaluation of the compatibility of the polyisoimide/matrix resin was made. In one instance, a film prepared from the polyisoimide derived from PMDA and 3,3′,5,5′-tetramethylbenzidine (TMB) showed no visually detectable phase separation.     

Influence of the composition of the binder and the carbonation on the zeta potential values of hardened cementitious materials

Electroosmotic experiments have been carried out on eight different mixes of hardened cementitious matrixes including concrete, mortar and pastes, different types of binders, carbonated and non-carbonated specimens and different test conditions. From these trials, the zeta potential values have been determined and the optimum experimental parameters and devices have been established. In addition, the influence of the composition of the binder on the zeta potential has been quantified indicating that higher amounts of Al₂O₃ in the binder lead to higher positive values of zeta potential, while the SiO₂ acts just on the opposite side. This has been explained in terms of the different i.e.p. (isoelectric point) for both oxides. Concerning the influence of carbonation, it increases the absolute value of the zeta potential toward more negative values; this behaviour has been attributed to the influence of the specifically adsorbed Ca²⁺ in the negative sites of the surface in the non-carbonated samples.