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.     

Titius—Bode定则的发展,天体量子论和泛量子理论

太阳系的Titius-Bode定则可以发展为r_n=an~2,令α_1=0.042,n=3,4,5,6是类地行星;令α_2=1.2,n=2,3,4,5,6是类木行星。此时海王星、冥王星都是规则的,且适用于大多数卫星。由此可以完全类比于玻尔原子模型,并得出太阳系量子常数H=(αGM_⊙)~(1/2)和天体薛定谔方程。这样距离规则是行星演化时统计性的结果,宇宙中应普遍存在波粒二象性和形式相似而量子常数各不相同的泛量子理论。     

GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES COOPERATIVE SYSTEM WITH TIME DELAYS

ＧＬＯＢＡＬＡＳＹＭＰＴＯＴＩＣＳＴＡＢＩＬＩＴＹＩＮＮ－ＳＰＥＣＩＥＳＣＯＯＰＥＲＡＴＩＶＥＳＹＳＴＥＭＷＩＴＨＴＩＭＥＤＥＬＡＹＳ￥ＣＵＩＪｉｎｇ＇ａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｕｒｕｍ...     

反馈网络中电位器对调节器性能的影响

通过对各种类型的调节器中含有电位器时传递函数的求解分析,得出接入电位器后对调节器的比例放大系数、微分时间常数及积分时间常数的影响结果,并使多种调节器在形式上得到了统一,根据需要可方便地调节电位器使其性能达到设计的需要.     

周期信号的孔径抖动及其去除

孔径抖动是指模数转换器采样周期之间出现的相位抖动 ,是由各时钟周期边沿出现时刻的不确定性导致的。当输入信号频率较高时孔径抖动是模数转换器信噪比下降的一个重要原因。对数据采集系统中的孔径抖动进行了仿真实验 ,介绍了反卷积算法 ,并利用反卷积算法对周期信号的孔径抖动进行了去除。仿真结果表明该方法是有效可行的     

PASCAL—SPECPK—酸碱离解常数的确定

完成了用分光光度数据确定二元质子酸碱重叠离解常数的程序设计,可快速、准确测定 pK_1和 pK_2,并给出模拟反算的离差及标准误差.程序用 TurboPascal(V5.0)编制.     

超微粒子－有机聚合物薄膜的研究

我们用离子团束－飞行时间质谱（ＩＣＢ－ＴｏＦＭＳ）系统制备了金（Ａｕ）超微粒子－聚乙烯（ＰＥ）薄膜和Ｃ＿（６０）－聚乙烯薄膜。用透射电子显微镜（ＴＥＭ）分析了所制备的样品。它们的结构是Ａｕ超徽粒子镶嵌在多晶的ＰＥ薄膜中，其中Ａｕ原子团呈球形，直径分布在２．０－５．０ｎｍ窄范围内，当沉积基底温度为９０℃时，Ａｕ原子团相互靠近，几乎连接起来，但仍保持原来大小。基底温度为１４０℃蒸积的Ｃ＿（６０）－ｐＥ薄膜具有晶态结构，其晶格常数为１．４５４ｎｍ。     

Why the Afshar experiment does not refute complementarity

A modified version of Young's experiment by Shahriar Afshar demonstrates that, prior to what appears to be a “which-way” measurement, an interference pattern exists. Afshar has claimed that this result constitutes a violation of the Principle of Complementarity. This paper discusses the implications of this experiment and considers how Cramer's Transactional Interpretation easily accommodates the result. It is also shown that the Afshar experiment is analogous in key respects to a spin one-half particle prepared as “spin up along x”, subjected to a nondestructive confirmation of that preparation, and post-selected in a specific state of spin along z. The terminology “which-way” or “which-slit” is critiqued; it is argued that this usage by both Afshar and his critics is misleading and has contributed to confusion surrounding the interpretation of the experiment. Nevertheless, it is concluded that Bohr would have had no more problem accounting for the Afshar result than he would in accounting for the aforementioned pre- and post-selection spin experiment, in which the particle's preparation state is confirmed by a nondestructive measurement prior to post-selection. In addition, some new inferences about the interpretation of delayed choice experiments are drawn from the analysis.     

用玻尔理论测量普朗克常数

提出用玻尔氢原子理论测量普朗克常数的原理和测量结果。