Chapter 11 Simulation studies of efficiency,returns to scale and misspecification with nonlinear functions in DEA

Using statistically designed experiments, 12,500 observations are generated from a 4-pieced Cobb-Douglas function exhibiting increasing and decreasing returns to scale in its different pieces. Performances of DEA and frontier regressions represented by COLS (Corrected Ordinary Least Squares) are compared at sample sizes ofn=50, 100, 150 and 200. Statistical consistency is exhibited, with performances improving as sample sizes increase. Both DEA and COLS generally give good results at all sample sizes. In evaluating efficiency, DEA generally shows superior performance, with BCC models being best (except at corner points), followed by the CCR model and then by COLS, with log-linear regressions performing better than their translog counterparts at almost all sample sizes. Because of the need to consider locally varying behavior, only the CCR and translog models are used for returns to scale, with CCR being the better performer. An additional set of 7,500 observations were generated under conditions that made it possible to compare efficiency evaluations in the presence of collinearity and with model misspecification in the form of added and omitted variables. Results were similar to the larger experiment: the BCC model is the best performer. However, COLS exhibited surprisingly good performances — which suggests that COLS may have previously unidentified robustness properties — while the CCR model is the poorest performer when one of the variables used to generate the observations is omitted.     

A compact formula for the coupling efficiency associated with mirrors in waveguide lasers

This paper presents a simple theory based on the diffraction integral approach for calculating the coupling efficiency in waveguide lasers which employ plane or spherical mirrors. The results obtained differ only slightly from a full rigorous approach, due to the fact that only less than one percent of the beam energy lies outside the waveguide aperture. The infinite aperture approximation employed here leads to an explicit compact formula for the coupling efficiency, whereas exact calculations lead to expressions requiring numerical integration for their evaluation.     

Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

Effect of column diameter on efficiency in capillary supercritical fluid chromatography

Fused silica capillary columns with internal diameters from 100 to 25 μm were coated with SE-54 and evaluated under supercritical fluid chromatographic conditions using carbon dioxide as mobile phase. Experimental results compared well with theoretical predictions. At ten times the optimum mobile phase velocity and for a capacity factor, k of 3, efficiencies of 2300 to 5600 plates m^?1 were obtained for column diameters of 100 to 25 μm, respectively.     

Effect of Coriolis force on counter-current chromatographic separation by centrifugal partition chromatography

The effect of Coriolis force on the counter-current chromatographic separation was studied using centrifugal partition chromatography (CPC) with four different two-phase solvent systems including n-hexane-acetonitrile (ACN); tert-butyl methyl ether (MtBE)-aqueous 0.1% trifluoroacetic acid (TFA) (1:1); MtBE-ACN-aqueous 0.1% TFA (2:2:3); and 12.5% (w/w) polyethylene glycol (PEG) 1000-12.5% (w/w) dibasic potassium phosphate. Each separation was performed by eluting either the upper phase in the ascending mode or the lower phase in the descending mode, each in clockwise (CW) and counterclockwise column rotation. Better partition efficiencies were attained by the CW rotation in both mobile phases in all the two-phase solvent systems examined. The mathematical analysis also revealed the Coriolis force works favorably under the CW column rotation for both mobile phases. The overall results demonstrated that the Coriolis force produces substantial effects on CPC separation in both organic-aqueous and aqueous-aqueous two-phase systems.     

Monte Carlo simulation of spatial distribution of X rays in multifilm targets. III: optimum design as applied to W/Al‐film targets

The brightness of the X‐ray source in a W/Al‐film target used for X‐ray projection microscopy was studied by an approach using the Monte Carlo simulation. Since continuous X rays generated in a thin film have a specific angular distribution of emission, the brightness of the continuous X‐ray source cannot simply be estimated on the assumption that the angular distribution is homogeneous. The newly developed approach using the Monte Carlo simulation enables the evaluation of the effective source size, angular distribution, and brightness of a continuous X‐ray source with sufficient accuracy that it leads to the optimum design of a high‐brightness X‐ray source for uses such as X‐ray projection microscopy. The Monte Carlo calculations were performed for W(Δz)/Al (200 µm)‐film targets with different thicknesses of W film, Δz, under bombardment of 60 kV electrons. The results have suggested an optimum design consisting of a W (2 µm)/Al (200 µm)‐film target as most promising for providing an X‐ray source of higher brightness than the W (5 µm)/Al (200 µm)‐film target, which has already been in practice for X‐ray projection microscopy. Copyright © 2006 John Wiley & Sons, Ltd.     

The effect of polymers on the phase behavior of balanced microemulsions: diblock-copolymer and comb-polymers

The effect of some amphipilic diblock-copolymers and comb-polymers on a balanced Winsor III microemulsion system is investigated with the quaternary system n-octyl-β-d-glucoside/1-octanol/n-octane/D₂O as basis system. The diblock-copolymers are polyethyleneoxide-co-polydodecenoxide (PEO _x PEDODO _y ) and polyethyleneoxide-co-polybutyleneoxide (PEO _x PEBU _y ), constituted of a straight chain hydrophilic part and a bulky hydrophobic part. Addition of the diblock-copolymer leads to an enhancement of the swelling of the middle phase by uptake of water and oil; a maximum boosting factor of 6 was obtained for PEO₁₁₁PEDODO₂₅. Nuclear magnetic resonance diffusometry yields the self-diffusion coefficients of all the components in the system. The diffusion experiments provide information on how the microstructure of the bicontinuous microemulsion changes upon addition of the polymers. The reduced self-diffusion coefficients of water and oil are sensitive to the type of polymer that is incorporated in the film. For the diblock-copolymers, as mainly used here, the reduced self-diffusion coefficient of oil and water will respond to how the polymer bends the film. When the film bends away from water, the reduced self-diffusion of the water will increase, whereas the oil diffusion will decrease due to the film acting as a barrier, hindering free diffusion. The self-diffusion coefficient of the polymer and surfactant are similar in magnitude and both decrease slightly with increasing polymer concentration.     

凸二次规划的投影收缩算法

对于一般的凸二次规划问题,首先结合该问题的对偶问题给出了解的充分必要条件,然后给出了一种解决该问题的投影收缩算法,并证明了该投影收缩算法的总体收敛性.     

高光谱成像技术的柑橘植株叶片含氮量预测模型

氮素是果树生长发育的一种大量必需元素,及时准确地监控果树的氮营养状况,对果树的合理施肥、增产、优化果实品质以及减缓过量施氮引起的水资源污染具有重要意义。利用高光谱成像技术结合多变量统计学方法,建立了柑橘植株叶片的含氮量预测模型。研究步骤为：高光谱扫描、提取平均光谱曲线、预处理原始光谱数据、采用连续投影法提取特征波段和建立含氮量预测模型。从SG平滑、SNV、MSC、1-Der等11种预处理方法中筛选出的较优预处理方法是SG平滑、Detrending和SG平滑-Detrending。对应这三种最优预处理方法,先采用连续投影法挑选出各自的特征波长,然后将各特征波段下的光谱反射率作为偏最小二乘、多元线性回归和反向传播人工神经网络模型的输入,各自建立三个预测模型。从以上获得的9个预测模型中,得出两个最优模型SG平滑-Detrending-SPA-BPNN(R_p：0.851 3,RMSEP：0.188 1)和Detrending-SPA-BPNN(R_p：0.8609,RMSEP：0.159 5)。结果表明,利用高光谱数据测定柑橘叶片含氮量具有可行性。这为实时、准确地监控柑橘植株生长过程中叶片含氮量的变化以及合理科学的氮肥施加提供了一定的理论基础。