A Generalization of the Mean Size Formula of Wavelet Packets in Lp

The purpose of this paper is to investigate the mean size formula of wavelet packets in Lp for 0 〈 p ≤ ∞. We generalize a mean size formula of wavelet packets given in terms of the p-norm joint spectral radius and we also give some asymptotic formulas for the Lp-norm or quasi-norm on the subdivision trees. All results will be given in the general setting,     

Photoluminescence linewidth broadening due to alloy/thickness fluctuation of CdxZn1 − xSe/ZnSe triple quantum wells

Photoluminescence (PL) linewidth broadening of Cd_xZn_{1 − x}Se/ZnSe triple quantum wells, grown on GaAs substrates by molecular beam epitaxy (MBE), has been investigated. Various quantum well (QW) samples have been prepared with different QW thickness and composition (Cd-composition). Measured and calculated PL linewidth are compared. Both composition and thickness fluctuations are considered for the calculation with the parameters such as the volume of exciton, nominal thickness and composition of QWs. Surface roughness measured by atomic force microscopy (AFM) is used to estimate the interface roughness. Results show that when Cd-composition increases additional linewidth broadening due to Zn/Cd interdiffusion is enhanced.     

Order restricted randomized designs for control versus treatment comparison

We develop a method of randomizing units to treatments that relies on subjective judgement or on possible coarse modeling to produce restrictions on the randomization. The procedure thus fits within the general framework of ranked set sampling. However, instead of selecting a single unit from each set for full measurement, all units within a set are used. The units within a set are assigned to different treatments. Such an assignment translates the positive dependence among units within a set into a reduction in variation of contrasting features of the treatments. A test for treatment versus control comparison, with controlled familywise error rate, is developed along with the associated confidence intervals. The new procedure is shown to be superior to corresponding procedures based on completely randomized or ranked set sample designs. The superiority appears both in asymptotic relative efficiency and in power for finite sample sizes. Importantly, this test does not rely on perfect rankings; rather, the information in the data on the quality of rankings is exploited to maintain the level of the test when rankings are imperfect. The asymptotic relative efficiency of the test is not affected by estimation of the quality of rankings, and the finite sample performance is only mildly affected.     

When should you sack a football manager? Results from a simple model applied to the English Premiership

What strategy should a football (soccer, in American parlance) club adopt when deciding whether to sack its manager? This paper introduces a simple model assuming that a club's objective is to maximize the number of league points that it scores per season. The club's strategy consists of three choices: the length of the honeymoon period during which it will not consider sacking a new manager, the level of the performance trapdoor below which the manager get the sack, and the weight that it will give to more recent games compared to earlier ones. Some data from the last six seasons of the English Premiership are used to calibrate the model. At this early stage of the research, the best strategy appears to have only a short honeymoon period of eight games (much less than the actual shortest period of 12 games), to set the trapdoor at 0.74 points per game, and to put 47% of the weight on the last five games. A club adopting this strategy would obtain on average 56.8 points per season, compared to a Premiership average of 51.8 points.     

On Bayes and unbiased estimators of loss

We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In 3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988, On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly, that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss. Research supported by NSF Grant DMS-97-04524.     

3,7-二硝基亚氨基-2,4-二氮杂双环[3,3,0]辛烷的放热分解反应动力学

在程序升温条件下 ,用DSC研究了标题化合物的放热分解反应动力学 .用线性最小二乘法、迭代法以及二分法与最小二乘法相结合的方法 ,以积分方程、微分方程和放热速率方程拟合DSC数据 .在逻辑选择建立了微分和积分机理函数的最可几一般表达式后 ,用放热速率方程得到相应的表观活化能 (Ea)、指前因子 (A)和反应级数 (n)的值 .结果表明 :该反应的微分形式的经验动力学模式函数、Ea 和A值分别为 (1-α) 0 .44、2 30 .4kJ/mol和 10 18.16s-1.借助加热速率和所得动力学参数值 ,提出了标题化合物放热分解反应的动力学方程 .该化合物的热爆炸临界温度为 30 2 .6℃ .上述动力学参数对分析、评价标题化合物的稳定性和热变化规律十分有用 .     

Synthesis and characterization of new bis(1-aryliminomethylenylnaphthalen-2-oxy)nickel complexes and their catalytic behavior for vinyl polymerization of norbornene

The synthesized 1-aryliminomethylenylnaphthalen-2-ol derivatives reacted with nickel chloride to form bis(1-aryliminomethylenylnaphthalen-2-oxy)nickel complexes. All resultant compounds were structurally characterized by elemental analyses, IR and H NMR, and the structures of the formed complexes were elucidated by X-ray crystal structure analysis. The complexes show high catalytic activities for the vinyl polymerization of norbornene in the presence of methylaluminoxane. The catalytic activity variations have been followed by gas chromatography through monitoring the conversion of norbornene.