A multiple window scan statistic for time series models

In this article we extend the results derived for scan statistics in Wang and Glaz (2014) for independent normal observations. We investigate the performance of two approximations for the distribution of fixed window scan statistics for time series models. An R algorithm for computing multivariate normal probabilities established in Genz and Bretz (2009) can be used along with proposed approximations to implement fixed window scan statistics for ARMA models. The accuracy of these approximations is investigated via simulation. Moreover, a multiple window scan statistic is defined for detecting a local change in the mean of a Gaussian white noise component in ARMA models, when the appropriate length of the scanning window is unknown. Based on the numerical results, for power comparisons of the scan statistics, we can conclude that when the window size of a local change is unknown, the multiple window scan statistic outperforms the fixed window scan statistics.     

一类具幂指积系数微分算子谱的离散性

应用算子直和分解法和二次型比较的方法,研究了一类具幂指积系数微分算子谱的离散性,得到了该类微分算子的谱是离散的一些充分条件.     

运用多目标规划优化功放的预失真模型

预失真技术是克服功率放大器非线性失真的一种非常有效的方法.许多研究者从数学建模的思想角度出发,建立了关于功放与预失真的各类级数模型,以实现线性增益输出.但是在应用通信系统中,这些模型不能有效地动态实现功放效率尽可能高的要求.在和记忆多项式模型的基础上,创新地运用多目标规划的方法优化功放的预失真模型.在满足一定的线性化输出的同时,尽可能地得到更高的功放效率,而且能同时计算出增益系数与模型参数.对于数据量为1000的无记忆功放得到增益倍数为1.82649,预失真模型的NMSE值为-41.5633.数据量为73920的有记忆功放得到增益倍数为9.5969,预失真模型的NMSE值为-24.3682.     

On some Diophantine fourier series

We continue our study on arithmetical Fourier series by considering two Fourier series which are related to Diophantine analysis. The first one was studied by Hardy and Littlewood in connection with the classification of numbers and the second one was studied by Hartman and Wintner by Lebesgue integration theory.     

Sums Over States of the Atoms and Singly and Doubly Charged Ions of Rare-Earth Elements

The sums over states of the atoms and singly and doubly charged ions of rare-earth elements that are required for a theoretical study of thermochemical processes in high-temperature plasma spectral sources are calculated in the temperature range 2500–12,000 K.     

Some Alternating Double Binomial Sums

We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.     

Modelling and control of flexible joint robot based on Takagi–Sugeno fuzzy approach and its stability analysis via sum of squares

This article proposes a Takagi–Sugeno (T-S) fuzzy model of single-link rotary flexible joint robot. The proposed control method is based on parallel distributed control. The parameters of T-S controller are improved by distributed population genetic algorithm (GA) with chaos GA. Using Hermite–Biehler theorem in distributed population, GA is made to have a fast convergence. Dividing search space into several sub-spaces causes a better response, and chaos disturbance helps the whole algorithm to reach a best answer. The stability of the controller is analysed via the sum of squares programming, and finally, it is implemented on the plant.     

关于预测误差平方和最小准则的几点看法

在应用桃棣荣等提出的预测误差平方和（ＰＲＥＳＳ）最小准则逐步算法的过程中，发现单纯应用ＰＲＥＳＳ值来控制引进因子数目有时不很有效。因此建议：１）当引进因子过多时，采用赤池信息准则对因子数做进一步控制。２）当引进因子过少时，取消原算法中关于ＰＲＥＳＳ值上界的规定和增加候选因子数以增加引进因子数。最后，对应用ＰＲＥＳＳ准则时所选因子的优良性进行了讨论     

一个素变数的Diophantine不等式

设１＜Ｃ＜１３／１２．本文证明了存在Ｎ（Ｃ）＞０使得对任意实数Ｎ＞Ｎ（Ｃ），下面的不等式｜＋＋　－Ｎ｜＜Ｎ－　　　　）ｌｏｇｓＮ有素数解ｐ１，ｐ２，ｐ３，其中ｓ＝２（１５）．