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.     

Chapter 15 DEA/AR analysis of the 1988–1989 performance of the Nanjing textiles corporation

This article employs new data envelopment analysis/assurance region (DEA/AR) methods to evaluate the efficiency of the 35 textile factories of the Nanjing Textiles Corporation (NTC), Nanjing, China. The returns to scale (RTS) of these factories were studied without assuming that the optimal DEA solutions were unique. All DMUs are identified with pointsE (Extreme Efficient),E (Efficient but not an extreme point) andF (Frontier but not efficient). We then further identify the nonfrontier DMUs with pointsNE, NE andNF according to whether they are projected onto a point inE, E, orF en route to evaluating their performances. All of the inefficient factories were in classNF and had unique optimal primal-dual solution pairs. Consequently, the solution pairs satisfy the strong complementary slackness condition (SCSC). Application of cone-ratio (CR) ARs reduced significantly the number of factories in classE, and showed that some AR-efficient factories were more flexible in adopting the mixture of central planning and market economies that China currently is trying to use. Also, linked-cone (LC) ARs were applied to measure maximum and minimum profit ratios. The SCSC multiplier space approach was utilized to analyze the sensitivity of the efficiency results to potential errors in the data with and without ARs. The results in this article suggest that collective units had a better performance than state-owned units in the two consecutive years analyzed.This paper was written while the author was at the School of Economics and Management, Southeast University, Nanjing 210018, P.R. China.     

Some remarks on the operator of Foias and Williams

In this paper we study the Foias-Williams operator

where , and is a Hankel operator with symbol . We exhibit a relationship between the similarity of to a contraction and the rate of decay of , the absolute values of the Fourier coefficients of the symbol .

     

Electronic control of stereoselectivity. 20. Crystal and molecular structure of the ferrocene derived from tricyclo[5.2.1.02,6]Deca-2,5,8-triene

Reaction of the isodicyclopentadienide anion and its dehydro congener with Fe(II) leads to a stereochemically homogeneous ferrocene derivative in each instance. Through chemical correlation and X-ray analysis, above-plane complexation is established for both halves within the two sandwich compounds.     

Solid state properties and catalytic behavior of the α- and β-vanadium bronzes

Decomposition of isopropanol (IPA) on V₂O₅, Li_0.02V₂O₅, Na_0.02V₂O₅, Na_0.06V₂O₅, Li_0.33V₂O₅, and Na_0.33V₂O₅ has been studied in the temperature range 186–300°C. The first four catalysts (α-phase) show predominately dehydration, whereas the last two (β-phase) have comparable dehydration and dehydrogenation activity. Dehydration activity increases with alkali metal concentration within the α-phase, but falls sharply on the β-phase catalysts. This difference is attributed to the different rate determining steps for the reaction on the α- and β-phase catalysts. X-ray and ir spectral data show that the β-phase catalysts are much more stable than the α-phase. A mechanism for the dehydration of IPA based on the electrical resistivity, ESR spectra, and kinetic data has been proposed.     

Structure elucidation of triglycerides by chromatographic techniques. Part 1: Capillary GC of ozonized triglycerides

Structure determination of triglycerides according to their number of unsaturated fatty acids (N.U.F.A.) is more easily achieved after ozonolysis of their mixtures (fats and oils) than by capillary gas chromatographic analysis of the mixture as such. Analyses performed before and after ozonolysis of cocoa buttel, hazelnut oil, and a mixture of both fats illustrate the potential of this approach to the structure elucidation of triglycerides by chromatographic techniques.     

An order-disorder transition in Sr2IrD5: Evidence for square pyramidal IrD5 units from powder neutron diffraction data

Neutron diffraction data have been collected on a powdered sample of Sr₂IrD₅ over a range of temperatures. The compound, which is cubic at room temperature, has been found to exhibit a gradual transformation to a tetragonal phase in the temperature range 200-140 K. As a result of the transition, deuterium atoms which randomly occupy sixfold positions in the cubic phase, become tetragonally ordered. A small fraction of the cubic phase remained untransformed at 4.2 K. Both the cubic and tetragonal structures are consistent with square pyramidal IrD₅ units with average Ir---D distances of 1.714 and 1.718 Å, respectively. Agreement factors, R₁, for the two structural analyses are 3.44 and 4.94%.     

Evaluation of the limit of performance of an analytical method based on a statistical calculation of its critical concentrations according to ISO standard 11843: Application to routine control of banned veterinary drug residues in food according to European Decision 657/2002/EC

Traceability of the measurement of analytical parameters capable of evaluating the performance of methods is an important concept for the assessment of quality for the routine control, especially for residue monitoring of non-authorized medicinal substances in food from animal origin. The European Decision no. 657/2002/EC recommends to calculate two statistical limits, CCα and CCβ, which allow to evaluate the critical concentrations above which the method reliably distinguish and quantify a substance taking into account the variability of the method and the statistical risk to take a wrong decision. The calculation, which can be derived from the ISO standard no. 11843 is applied on a routine basis. An example displays a very simple way for evaluating the performance of an LC-MSMS method which has been validated a few years ago and is qualified onto a Micromass Quattro LCZ tandem mass spectrometer to monitor and confirm the nitrofuran metabolite residues in food from animal origin. Community Reference Laboratory for Antimicrobial Veterinary Drug Residue Control in Food from Animal Origin     

Synthesis of homoharringtonine and its derivative by partial esterification of cephalotaxine.

Homoharringtonine $\text{2}$ and dehydrodesoxy homoharringtonine $\text{4}$ were synthesized by partial esterification of cephalotaxine.