Prediction error criterion for selecting variables in a linear regression model

Several criteria, such as CV, C _p , AIC, CAIC, and MAIC, are used for selecting variables in linear regression models. It might be noted that C _p has been proposed as an estimator of the expected standardized prediction error, although the target risk function of CV might be regarded as the expected prediction error R _PE. On the other hand, the target risk function of AIC, CAIC, and MAIC is the expected log-predictive likelihood. In this paper, we propose a prediction error criterion, PE, which is an estimator of the expected prediction error R _PE. Consequently, it is also a competitor of CV. Results of this study show that PE is an unbiased estimator when the true model is contained in the full model. The property is shown without the assumption of normality. In fact, PE is demonstrated as more faithful for its risk function than CV. The prediction error criterion PE is extended to the multivariate case. Furthermore, using simulations, we examine some peculiarities of all these criteria.     

平面图线性色数的一个上界

如果图G的一个正常染色满足染任意两种颜色的顶点集合导出的子图是一些点不交的路的并,则称这个正常染色为图G的线性染色．图G的线性色数用lc（G）表示,是指G的所有线性染色中所用的最少颜色的个数．证明了：若G是一个最大度△（G）≠5,6的平面图,则lc（G）≤2△（G）．     

Multiple expansions of real numbers with digits set $$\left\{ 0,1,q\right\} $$ 0 , 1 , q

Mathematische Zeitschrift - For $$q>1$$ we consider expansions in base q with digits set $$\left\{ 0,1,q\right\} $$ . Let $${{\mathcal {U}}}_q$$ be the set of points which have a unique...     

生鲜供应链中保鲜努力投入及订货定价研究

结合生鲜损耗严重和过度保鲜双重背景,本文在区分保质期和实际有效供货时长的基础上,比较研究了由单一零售商与单一供应商构成的二级生鲜供应链中,两个主体合作与否及主导主体变化对供应链保鲜努力水平和定价的影响机制。研究表明,集中式供应链中,保鲜努力投入随新鲜度(价格)敏感性增强(减弱)而增加,而随有效供货时长增加呈倒U型;供应链的总利润也随新鲜度(价格)敏感性增强(减弱)或有效供货时长上升而增加。分散式供应链中,随新鲜度的敏感性增强,保鲜努力和总利润增加;随价格的敏感性增强,保鲜努力增加而总利润减小;而随有效供货时长上升,保鲜努力先增大后减小,总利润增加。分散式供应链存有搭便车的机会,但因有效供货时长占保质期比例不同,自身投入保鲜努力可能比搭便车更有利。     

A bubble detection technique based on light intensity and Mie scattering theory for spinning solution

A novel bubble detection technique based on light intensity and Mie scattering theory for spinning solution is presented theoretically and experimentally. With the light intensity in every direction, the particle or bubble size distribution can be calculated with the Mie scattering theory. The light intensity distribution in every direction, corresponding to the light intensity received by every assumed annulus of the detector has been calculated theoretically. According to the light intensity distribution, the size distribution of bubbles can be deduced. A series of standardized polystyrene micro-sphere (with 7 μm diameter) solution has been used not only as sample for experiments and calibration, but also as the bubbles in the glycerin. Theoretical and experimental results show that the technique can be used for bubble detection, in order to improve the traditional bubble detection scheme, and to lower production costs.     

Some addition reactions of bisgermavinylidene

The reaction of bisgermavinylidene [(Me₃SiN?PPh₂)₂C?Ge→Ge?C(PPh₂?NSiMe₃)₂] ( 1 ) with AdNCO (Ad = Adamantyl) afforded the [2 + 2] cycloadditon product [(Me₃SiN?PPh₂)₂CGeC(O) NAd] ( 2 ). Similar reaction of 1 with Ph₃SiOH in tetrahydrofuran (THF) yielded the base‐stabilized germanium(II) triphenylsiloxide [H₂C(PPh₂?NSiMe₃)₂Ge(OSiPh₃)₂] ( 3 ). The results suggested that reactive germavinylidene may exist in solution and is capable of forming addition reaction products. The X‐ray structures of 2 and 3 were determined. Copyright © 2007 John Wiley & Sons, Ltd.     

Influence of laser intensity in second-harmonic detection with tunable diode laser multi-pass absorption spectroscopy

Tunable diode laser absorption spectroscopy （TDLAS） has been widely employed in atmospheric trace gases detection. The ratio of the second-harmonic signal to the intensity of laser beam incident to the multi-pass cell is proved to be proportional to the product of the path length and the gas concentration under any condition. A new calibration method based on this relation in TDLAS system for the measurement of trace gas concentration is proposed for the first time. The detection limit and the sensitivity of the system are below 110 and 31ppbv （parts-per-billion in volume）, respectively.     

用于KT-5C托卡马克等离子体电子密度测量的多道HCN激光干涉仪

等离子体的电子密度是聚变等离子体研究中的重要参数。一般采用探测电磁波通过等离子体后产生的相移来求等离子体的电子密度,等离子体引起的相移△(?)与探测弦线上的线积分电子密度n_e有如下的关系: