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.     

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．     

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．     

拉萨郊区藏族的跖纹研究

作者研究了拉萨郊区２５０例藏族的跖纹，结果如下：１．拇趾球纹依次为Ｌ〉Ｗ〉Ａ。２．趾间区真实花纹频率为Ⅲ〉Ⅱ〉Ⅳ。３．足小鱼际远侧区真实花纹较多，其他跖区较少。４．在性别、民族和人种间进行了比较，结果显示，藏族有自己的跖纹特点，又呈现蒙古人种的一般特征。     

大豆开花期缺水和遮光处理叶片解剖结构的观察

大豆珍珠塔3号具有双子叶植物叶片结构特征,但在海绵组织最上层有一层特殊细胞——平脉叶肉细胞,此层细胞具有水平运输和气体交换的特殊作用。大豆开花期光照对叶片结构发育起主导作用;水分亦是影响叶片结构发育的重要因素;光弱块水条件下,大豆表现出对光的竞争比对水的竞争更明显。     

Dirichlet公式的简化证明及应用

本文给出了Ｄｉｒｉｃｈｌｅｔ公式的一个简化证明，极易掌握。利用这一公式导出了一个含双参数的级数及其和的表达式。适当选取参数，得出了几个新的收敛级数。     

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。     

我国跨国经营的发展构想

本文在系统阐述当代跨国经营战略调整与发展趋势的基础上，简要剖析了现阶段我国企业跨国经营的主要问题，重点探讨了我国跨国企业发展战略的基本构想。     

家兔髋关节软骨扫描电镜观察

应用扫描电镜对家兔髋关节软骨观察发现:月状面软骨表面和股骨头软骨表面均具由纤维编织而成的网状层,月状面软骨顶部,纤维交错,网状层形态结构复杂而又丰厚;前部与后部次之,股骨头顶部,关节软骨表面的网状层显著低矮、致密,并有一矩形凹陷;下部,网状层呈斑块状,高低错落。     

用“多化一”最小二乘法建立吸附动力学方程

用若干个一元最小二乘法，建立多元经验公式；以吸附动力学方程为例，取得了预期的结果。