Exponential smoothing: Behavior of the ex-post sum of squares near 0 and 1

When using simple exponential smoothing on a given time series the nature of the relationship between the optimal smoothing constant and the autocorrelation structure of the series remains an unresolved question. Although numerical search routines can easily be used to find optimal values of the smoothing constant, they offer little insight into the nature of the relationship between the estimated smoothing constant and the structure of the underlying time series. We suggest that renewed investigations of the ex-post sum of squares function may prove helpful in this pursuit. Results are presented that illustrate how the optimal smoothing constant depends upon the value used to initialize the smoothing and upon the sample autocorrelation coefficients of the observed series. These results are based on a new formula for the derivative of the ex-post sum of squares function. In particular, the derivative is examined near 0 and 1, where great simplifications occur in its form, thereby facilitating investigations near these points. A necessary and sufficient condition is stated for when the ex-post sum of squares must have a positive derivative at 0 and the autocorrelation coefficients of the differenced series are shown to affect the sign of the derivative near 1. Based on these results, a general algorithm is presented as an alternative to grid search routines for minimizing the ex-post sum of squares.     

关于多元Gauss—Weierstrass算子的一致逼近

本文利用一类 K—泛函和光滑模的等价性给出了二元 Gauss—weierstrass 算子在一致逼近意义的正定理、逆空理和特征性。     

中国数学史断代研究的一项新成果：—《明清数学史论文集》简介

本文简介梅荣照主编的《明清数学史论文集》一书，对中国数学史开展断代专题研究，是我国数学史界继承并发展李俨、钱宝琮、严郭杰先生研究成果的宏大计划，持续近三十年，历来为国际科学史界所重视，文集收入论文15篇、附录2篇，其中严敦杰先生遗作7篇，本文对15篇论文逐一作了简介。     

从尚艳到崇雅——论《御览诗》、《极玄集》在中晚唐诗风衍变历程中的座标意义

《御览诗》和《极玄集》分别编成于宪宗元和后期和文宗开成初年。前者喜尚轻艳,追摹齐梁;后者推崇清雅,回归大历。不同的风格特征、相异的审美追求,清晰地透现出中晚唐之际士人心态的变化及诗风衍变的动态历程,在唐诗发展史上极具座标意义。     

Erds 等人的一个定理的新证明

本文给出定理:“在2n—1个整数中,必有n 个数,它们的和被n 整除”的一个新的证明,它无需先讨论n 为素数。     

医院信息管理系统业务量估算与网络流量控制

本文介绍医院信息管理系统组成与设计要求;讨论了信息系统业务量估算,网络流量控制方法,保证信息管理系统数据有效性,快速存储,共享使用与安全可靠性。     

韶关大学男生身体素质现状研究

本文通过对韶关大学93和94级男生五项身体素质成绩的差异研究，并与全省同年级男生进行横向比较，以了解韶关大学男生身体素质现状，并为公共体育教学和为学校发展学生身体素质提供参考依据。     

广告刍议

广告可以创造一种平衡效益。它不仅仅创造你口袋里的平衡，而且创造精神上的平衡。最好的广告是那些树立品牌的广告．它们好就好在能够在消费者心中制造某种平衡，使其超值地购买这种商品，从而为继续开发积累资金，为生产者创造利润等等。     

球对称动态黑洞的广义Stefan-Boltzmann定律

选取超前爱丁顿坐标，采用统计的方法，计算出动态黑洞的瞬时辐出度．结果表明，动态黑洞的瞬时辐出度不仅与假定黑洞处于热力学平衡时的辐出度有关，还与黑洞的事件视界速度、事件视界温度、事件视界附近的熵密度及黑洞的吸收和辐射系数有关．对于球对称动态黑洞，任一时刻黑洞的瞬时辐出度总是正比于黑洞事件视界温度的四次方．