Characterization of general summability factors and applications

By (A,B), we denote the set of all sequences ? such that Σ?_nx_n is summable by B whenever Σx_n is summable by A, where A and B are some summability methods. In this paper, we established a simple set of necessary and sufficient conditions for summability factor of type ?∈(A,B), and also deduced various known and some new results as special cases.     

A summability factor theorem involving an almost increasing sequence for generalized absolute summability

In this paper we prove a general theorem on |A;δ|_k-summability factors of infinite series under suitable conditions by using an almost increasing sequence, where A is a lower triangular matrix with non-negative entries. Also, we deduce a similar result for the weighted mean method.     

Some Tauberian theorems for the weighted mean methods of summability

In this paper, we introduce the concept of the weighted generator sequence and prove that certain conditions in terms of weighted generator sequences are Tauberian conditions for the weighted mean summability method.     

On absolute stability of Lur＇e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur‘e form to guarantee the absolute stability of Lur‘e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyaptmov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

On absolute stability of Lur''''e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur'e form to guarantee the absolute stability of Lur'e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs), If those LMIs are feasible, free parameters in the Lyapunov function,such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems.A numerical example is provided to demonstrate the effectiveness of the proposed method.     

Aggregation of infinite sequences

Infinitary aggregation functions acting on sequences and possessing some a priori given properties as additivity, comonotone additivity, symmetry, etc., are investigated. On the other side, we discuss infinitary aggregation functions related to given extended aggregation functions, where special attention is given to triangular norms, triangular conorms and weighted means.     

On transformations of formal power series

Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve recognizability, generalizing the recent results of Zhang [16] to the formal power series setting. We show, for example, that the “square-root” operation, while preserving regularity for formal languages, preserves recognizability for formal power series when the underlying semiring is commutative or locally finite, but not in general.     

On the numerical evaluation of an oscillating infinite series III

An oscillating infinite series involving product of Bessel function J _o(x) and an oscillating infinite series involving trigonometric function sin(x) were evaluated and computed numerically in [1] and [2] respectively. In this paper, an oscillating infinite series involving product of exponential, Bessel and trigonometric functions is evaluated. The series is transformed first into the sum of two infinite integrals by using contour integration and then the infinite integral with oscillating integrand is transformed through some identities into a finite integral containing modified Bessel function K ₁(x). Finally, theset two integrals are evaluated numerically without any computational difficulties at all.     

A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems

This paper deals with absolute stability for a class of nonlinear neutral systems using a discretized Lyapunov functional approach. A delay-dependent absolute stability criterion is obtained and formulated in the form of linear matrix inequalities (LMIs). The criterion is valid not only for systems with small delay, but also for systems with non-small delay. Neither model transformation nor bounding technique for cross terms, nor free weighting matrix method is involved through derivation of the stability criterion. Numerical examples show that for small delay case, the results obtained in this paper significantly improve the estimate of the stability limit over some existing result in the literature; for non-small delay case, the ideal results can also be achieved.     

On the Weighted Mean of a Pair of Strings

String matching and string edit distance are fundamental concepts in structural pattern recognition. In this paper, the weighted mean of a pair of strings is introduced. Given two strings, x and y, where d(x, y) is the edit distance of x and y, the weighted mean of x and y is a string z that has edit distances d(x, z) and d(z, y)to x and y, respectively, such that d(x, z) _ d(z, y) = d(x, y). We’ll show formal properties of the weighted mean, describe a procedure for its computation, and give practical examples. Received: 26 October 2000, Received in revised form: 27 April 2001, Accepted: 20 July 2001     

On the realization of periodic functions

In this article, canonical and spectrally minimal infinite-dimensional state space realizations for periodic functions are considered. It is shown that the periodic functions having ℓ₁ Fourier coefficients are precisely those realizable by a Riesz spectral system (RSS) in which the system operator generates a periodic strongly continuous semigroup and the observation operator is bounded. This realization can easily be converted to a canonical and spectrally minimal form. It is shown how the use of RSS and Cesáro sums of Fourier series allows the construction of a state space realization for a given periodic function merely integrable over its period. Simple finite-dimensional approximations with error bounds are derived for the RSS realization. Regular well-posed linear systems (WPLS) are used to construct a Fuhrmann-type realization for a given periodic function integrable over its period. It is shown that the RSS realizations and WPLS realizations are precisely equally good at coping with the possible ill behavior of a given bounded periodic function integrable over its period, but the WPLS realization is not always spectrally minimal or canonical.     

模式矩阵的FP-DMMFI并行算法在教师科研素养挖掘中的应用

本文为了获取高校教师在科研素养方面与各影响因子的内在关联,在分析Apriori和FP_growth算法的基础上,提出了一种模式矩阵的并行频繁项集挖掘算法(FP-DMMFI算法)。该算法通过映射方式,将频繁项集压缩到模式矩阵中,利用矩阵挖掘频繁信息,从而发现隐藏的、有意义的关联规则信息。并通过实际例子对该算法进行了验证。     

Robust Latent Factor Analysis for Precise Representation of High-Dimensional and Sparse Data

High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.     

皮托管测量影响因素分析 I. 检测杆与安装角的影响

在现场使用中,皮托管不可避免地会偏离其标准使用条件,从而引起附加误差.针对不同型号的皮托管进行了较系统的试验,旨在研究检测杆和安装角对皮托管测量的影响.结果表明,在被测流速较低时,皮托管检测杆直径的大小对全压的测量影响较小,且测量值误差也较小;在皮托管安装角不超过±10°的范围内,流速测量误差为±2%;较小管径检测杆的测量值存在非零安装角时,受流速的影响比较小.这些结论为优化皮托管的测量提供了指导.     

皮托管测量影响因素分析 II. 全压孔与静压孔的影响

为了讨论皮托管全压孔和静压孔几何参数对其测量特性的影响,采用试验和数值模拟相结合的方法,对不同型号的皮托管进行了研究.结果表明:对于皮托管全压,在流速较低时,由较小的全压孔测得的全压较接近参考值,而在流速较大时,大多数全压孔的测量值误差都比较大;对于皮托管静压,由较小外径的检测杆测得的静压值较接近参考值,静压孔不宜布置在太靠近测头或竖直检测杆的地方.这些结论为优化皮托管的测量提供了指导.