Equations for the angles of arrival and departure for multivariable root loci using frequency-domain methods

Frequency-domain methods are used to study the angles of arrival and departure for multivariable root loci. Explicit equations are obtained. For a special class of poles and zeros, some simpler equations that are generalizations of the single-input-single-output equations are presented.     

Sensitivity of the characteristic gain loci

In the generalized Nyquist stability criterion for linear, time-invariant, multivariable, feedback systems, stability is determined from the characteristic gain loci. This paper examines the sensitivity of the latter, and introduces sets of indices, called sensitivity indices, which characterize the sensitivity of the loci to small system perturbations.     

The asymptotic behaviour of a distributive sorting method

In the distributive sorting method of Dobosiewicz, both the interval between the minimum and the median of the numbers to be sorted and the interval between the median and the maximum are partitioned inton/2 subintervals of equal length; the procedure is then applied recursively on each subinterval containing more than three numbers. We refine and extend previous analyses of this method, e.g., by establishing its asymptotic linear behaviour under various probabilistic assumptions.     

The asymptotic optimal frequency domain filter for edge detection

In an earlier paper by Shanmugam, Dickey, and Green, an edge detection filter was derived which maximized the energy within a specified interval about an edge feature. The initial expression of this filter involved a prolate spheroidal wave function. However, a careful analysis of the application of an asymptotic approximation to this function uncovered a major dimensional error. The corrected derivation of the asymptotic optimal filter forms the subject of this paper. To verify the results, the filter found is compared to a similar filter developed independently by Marr and Hildreth.     

The asymptotic local approach to change detection and model validation

We present a systematic approach for the design of change detection and model validation algorithms for dynamical systems. We show how to associate to any identification algorithm a change detection and a model validation procedure, which are optimal in some asymptotic sense. The foundations of our method go back to the asymptotic local approach in statistics, and our method generalizes this approach.     

Tracking algorithm designed by the local asymptotic approach

The problem of sequential detection of parameter jumps in linear systems with constant noise level is discussed. The detection problem is analyzed by the asymptotic local approach, using the normalized output error sequence as the detection signal. For linear regression, ARMAX, and state-space models, a central limit theorem is proved, transforming the original problem into the problem of detecting an increase in the man of an asymptotically Gaussian distributed scalar process. The performance of the tracking algorithm, which consists of a parameter estimator with decreasing gain and a single Hinkley's detector, has been studied by simulations and compared to the performance of constant- and adaptive-gain parameter estimators. The proposed algorithm seems to be superior in performance, requiring only a little, generally negligible, additional computational effort. The algorithm provides the information about the jump times, and the time delay of jump detection seems to be unaffected by the measurement noise level, provided that this level is not affected by the change     

Dynamic performance,interaction, and the characteristic locus method: a quantitative approach

The characteristic locus method, in addition to its role in the assessment of system stability, is also an effective approach for evaluating tracking accuracy, interaction and dynamic/static loop performance. However, with regard to the evaluation of the latter three, there exists a degree of ambiguity and personal judgement, in addition to a requirement for a priori assumptions about proper problem conditioning. This paper stipulates quantitative bounds/measures of accuracy, interaction and loop assessment that identify the pertinent open-loop system factors affecting the particular performance aspect, and thus provide unambiguous measures to aid system design. Additionally, eigenvector scaling is introduced in order to tighten the bounds.     

Adaptive asymptotic tracking of repetitive signals-a frequencydomain approach

The problem of designing an adaptive tracking controller for repetitive signals is considered. It is assumed that the controlled plant is linear time-invariant (LTI) and that its steady-state behavior can be described by its frequency response. The proposed controller, being able to identify the gain and phase of a plant at selected frequencies, adjusts the input/output (I/O) map at frequencies contained in the reference signal so as to achieve zero steady-state errors. Hence, no structural knowledge of the plant is needed. However, the proposed controller does not alter the transient property of the plant, e.g., locations of poles. The transient property can be improved by adding feedback control action. A combination of the adaptive controller and a feedback LTI controller is studied     

On the generative–discriminative tradeoff approach: Interpretation, asymptotic efficiency and classification performance

The interpretation of generative, discriminative and hybrid approaches to classification is discussed, in particular for the generative–discriminative tradeoff (GDT), a hybrid approach. The asymptotic efficiency of the GDT, relative to that of its generative or discriminative counterpart, is presented theoretically and, by using linear normal discrimination as an example, numerically. On real and simulated datasets, the classification performance of the GDT is compared with those of normal-based linear discriminant analysis (LDA) and linear logistic regression (LLR). Four arguments are made as follows. First, the GDT is a generative model integrating both discriminative and generative learning. It is therefore subject to model misspecification of the data-generating process and hindered by complex optimisation. Secondly, among the three approaches being compared, the asymptotic efficiency of the GDT is higher than that of the discriminative approach but lower than that of the generative approach, when no model misspecification occurs. Thirdly, without model misspecification, LDA performs the best; with model misspecification, LLR or the GDT with an optimal, large weight on its discriminative component may perform the best. Finally, LLR is affected by the imbalance between groups of data.     

Global existence and asymptotic behaviour of the solution of a generalized burger's equation with viscosity

We obtain the global existence and uniqueness for a generalized Burger's equation with viscosity and the initial value being in L^∞ by successive method. Moreover, under certain condition on the initial value the solution tends to the solution of a linear heat equation in H¹.     

On the asymptotic behaviour of solutions of differential equations in a banach space

The purpose of this paper is to consider the asymptotic behaviour of solutions of the initial value problemdu/dt = Au + F(t, u) u(t ₀) =u ₀ t t ₀ in a Banach spaceX with an unbounded, nonlinear operatorA. Conditions are given which guarantee that for sufficiently smallu ₀ the solutions converge to zero. The problem of asymptotic stability is also treated. In the last section there are applications to partial differential equations.     

The response behaviour of a submerged cylindrical shell using the doubly asymptotic approximation method (DAA)

This paper presents experimentally measured and theoretically calculated responses of a flexible cylindrical shell subjected to an impulsive excitation in air and in water. The flat-ended, thin cylindrical shell of overall length 1284 mm, external radius 180 mm, thickness 3 mm is made of mild steel. The predicted responses are derived from a method using the doubly asymptotic approximation (DAA) models in order to uncouple the motion of the fluid from that of the structure. The DAAs enable the radiated pressure to be specified in terms of surface motion of the structure. The method, which employs the DAAs, is applied to determine the responses, i.e. acceleration, velocity and displacement, of the finite length cylindrical shell excited by an impulsive mechanical force. The calculated acceleration responses are compared with the experimental measurements.     

Sufficient conditions for the existence and asymptotic behaviour of solution to a quasi-linear elliptic problem

In this article, we combine the existing regularity theory, perturbation method and the lower and upper solutions method to study the existence and asymptotic behaviour of positive solution to a boundary value problem for the p-Laplacian operator. More exactly, we study the existence and asymptotic behaviour of the positive solution to a quasi-linear elliptic problem of the form?Δ _p u=λ a(x)g(u) in D′(Ω), u>0 in Ω, lim _{x→? Ω} u(x)=0. Under some conditions on a and g, we show that there is a non-negative number Λ₀ such that for all λ∈(0, Λ₀], the problem has a solution u _λ in the sense of distribution, which is bounded from above by some positive numbers μ(λ). Such estimates and the asymptotic behaviour are important in computer programs when we know an algorithm for determining the solution.     

A new approach to computing the Euler characteristic

In this paper we describe a new approach to computing the Euler characteristic of a three dimensional digital image. Our approach is based on computing the change in numbers of black components, tunnels and cavities in 3 × 3 × 3 neighborhood of an object (black) point due to its deletion. The existing algorithms to computing the Euler characteristic of a 3D digital image are based on counting the numbers of all k-dimensional elements (0 ≤ k ≤ 3) in a polyhedral representation of the image. Our approach can be modified for (6,26), (18,6), (6,18) and other connectivity relations of grid points. A parallel implementation of the algorithm is described using the concept of sub-fields.     

The departure process of a quorum queueing system

We study in this paper the departure process of a bulk service queueing system. The server operates under a minimum batch size strategy. We characterize the departure process through the distribution of the interdeparture times of batches and of customers, the distribution of the number of customers in a batch, and the coefficient of correlation between the interdeparture time of a batch and the number of customers in the batch. A numerical illustration is presented.     

测振传感器的低频特性补偿研究

现有的大多数测振传感器不能满足超低频振动测量的需要,有必要扩展其工作频带以满足需要。研究了零极点配置法在941B型测振传感器的应用。通过此方法,拓展了测振传感器的工作频带,尤其是其低频特性得到了拓展,其工作频带由补偿前的0.7~105Hz拓展为补偿后的0.08~109 Hz。在此基础上,利用MATLAB进行了数值仿真,输入不同持续时间的单个半正弦波以及正弦叠加信号,系统在补偿前后的响应表明:低频特性得到明显改善。     

基于字频特征的自动机多模匹配增效算法

针对自动机类多模匹配算法内存占用过多的缺点,分析了DFA存储的列特征,并结合模式串所属字符集的编码范围,提出了按字符频率特征压缩自动机状态空间的多模匹配增效算法.本算法采用了榆入字符阅值映射技术,在保存高频率字符对应列的同时,用位图信息提高对压缩列的检索速度.实验结果表明,在万条配置规则级的环境下,能够同时有效降低内存和CPU利用率.     

Exercise and sleep behaviour A questionnaire approach

This study investigated the effects of daily physical activity levels, including the time of day when the activity was taken and subject fitness, upon sleep behaviour using questionnaires. Three questionnaires were designed, namely a subject screening questionnaire and pre-sleep and post-sleep questionnaires. The pre-sleep questionnaire was completed immediately before the subjects retired to bed and was used to record their daily activity levels and to assess pre-sleep tiredness. The post-sleep questionnaire was designed to obtain information concerning the quantity and quality of sleep as well as post-sleep tiredness.

Eighty volunteers were selected, following screening for ill-health and sleeping problems, and were asked to complete the sleep questionnaires for seven consecutive days. Fifty-one returned their questionnaires and a total of 332 days of data were used for analysis. Subjects were enlisted from sports centres, and all reported a measurable degree of variation in their daily activity levels during the course of the week.

The findings indicated that variations in the daily activity level do not have any major effect upon the tiredness and sleep variables assessed. Time of day of activity was found to have little influence upon these variables, except that the bedtime was delayed by late evening activity. The findings did suggest, however, that fit subjects appear either to need less sleep, or to sleep more efficiently than unfit subjects.     

基于CTD的压电传感器频率特性补偿器

研制了一种以电荷转移器件 (CTD)为核心 ,具有频率特性可随意调节的压电传感器频率特性补偿器。论述了补偿原理、电路设计及其技术难点和相应的解决方法。理论分析与实验表明了该补偿器的有效性、实用性、先进性。