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.     

井下导线网陀螺经纬仪定向检测与误差分析

介绍用陀螺定向检测井下导线网测理精度的一个实例，较详细地叙述了应用中考虑的问题和成果的分析。它对应用陀螺定向这一新技术有开拓性的意义     

行列式三种定义方法的等价性

在行列式普通定义的基础上又介绍了归纳定义和公理法定义两种方法，并证明了它们的等价性．     

鲁西北蜜源植物资源调查

首次报导了鲁西北蜜源植物的种类和花期，对充分利用蜜源资源，合理安排养蜂生产具有重要的指导意义．经充分调查并根据孢粉学知识，分析总结出鲁西北共有主要蜜源植物１５种，辅助蜜源植物１０４种，共计１１９种．     

线性驱动下一级相变的重正化群理论

把重正化群理论应用于一受外场驱动而发生一级相变的系统中，结果表明，与有序化过程一样，该系统也由零温不动点所决定，并得到磁化强度及结构函数的新的动力学标度关系．由此可获得滞后回约面积与变场速率的标度关系．     

广西建设抽水蓄能电站的必要性和效益

广西电网需电量迅猛增加，峰谷差越来越大，迫切需要大量调峰容量。由于广西电网电源结构不合理，水电站调节性能差，枯水期出力小，火电机组最小技术出力高，电网调峰能力不足，汛期基荷容量过剩，造成低谷时大量弃水。建设抽水蓄能电站可以发挥其调峰、填谷双重作用，是当前解决电网调峰行之有效的最佳措施，应加紧实施。     

单航片数字转绘在土地详查系统中的应用及其精度评定

土地详查系统是将来建立国土信息系统的一个子系统,建立该系统的关键之一是实现调绘航片的数字转绘,本文通过分析单航片数字转绘的精度,从理论上阐明了以数字转绘代替仪器纠正实现土地详查内业自动化的可靠性。     

Orlicz空间内单边K─泛函与平均模的等价性

本文在Ｏｒｌｉｃｚ空间内对周期函数建立了单边Ｋ─泛函与平均模的等价问题，对多元的情形也可以类似地得到．     

实时实现MPEG2运动估计的DSP处理系统

本文根据ＭＰＥＧ２的图像标准与要求，利用若干大规模集成电路芯片，设计了实时实现活动图像运动估计的ＤＳＰ处理系统板，通过序列图像的测试，证明其工作正常，性能可靠，完全符合ＭＰＥＧ２的技术规范，从而为我国近期实现ＭＰＥＧ２的编解码系统、乃至ＨＤＴＶ实验系统在硬件方面打下了良好的基础。     

3~k元域上的三次方程根的简况

Ｆ是一个３ｋ元域，ｘ３＋ａｘ２＋ｂｘ＋ｃ＝０是Ｆ上的三次方程。该文证明方程ｘ３＋ａｘ２＋ｂｘ＋ｃ＝０在Ｆ中有一根，或一根与二重根，或三个互异的根，或没有根。