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.     

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.     

The synthesis and structure of potassium cyanotrimethylaluminate

The reaction of KCN with Al(CH₃)₃ to form K[Al(CH₃)₃CN] is greatly facilitated by the presence of an aromatic solvent: for p-xylene a solid complex, K[Al(CH₃)₃CN]·C₆H₄(CH₃)₂, has been isolated. The crystal structure of potassium cyanotrimethylaluminate has been determined from three-dimensional X-ray data measured by counter methods. K[Al(CH₃)₃CN] crystallizes in the monoclinic space group C2/c with cell dimensions a = 19.902(7), b = 9.211(4), c = 9.615(4) Å, β = 107.74(5)°, and p_calcd. = 1.09 g cm^?1 for Z = 8. Least squares refinement gave a conventional weighted R factor of 4.9% for 807 independent reflections. The monomeric [Al(CH₃)₃CN]^? units possess no crystallographic symmetry, and the packing in the unit cell is such that the nitrogen atoms on three such units approach the potassium atom to within 3.11 Å. The average aluminum-methyl carbon bond distance is 1.971 (7) Å, while the aluminum-cyano carbon distance is 2.047 (7) Å. This significant lengthening is attributed to partial electron deficiency in the aluminum-cyano carbon bond.     

σ,π-acetylido complexes via P---C bond cleavage of phosphinoacetylenes: X-ray structure of Fe2(CO)6(CCPh)(PPh2)

Solutions of Co^II salts of organic acids in primary amines absorb molecular oxygen rapidly and irreversibly forming μ-dioxygen—cobalt complexes. Thermolysis leads to a homopolar cleavage of the OO bond with subsequent radical reactions involving ligand amine. After thermolysis the capacity of oxygen uptake is reestablished (catalysis).     

Fluxional behaviour of π-bonded acetylenes

Some cationic five coordinate complexes of formula [Os(CO)(NO)L₂A]PF₆ (L = tertiary phosphine, A = an acetylene) have been prepared by reaction of the appropriate acetylene with [Os(CO)(NO)L₂(acetone)]PF₆; the variable temperature ¹H NMR spectra of some of these indicate that the coordinated π-acetylene undergoes fluxional behaviour.     

Further application of the diazotizationcoupling spectrophotometric technique to the determination of aromatic amines with 8-amino-1 -hydroxynaphthalene-3,6-disulphonic acid and N-(1-naphthyl)-ethylenediamine as coupling agents

Twenty-two aromatic amines are determined by the diazotization-coupling spectrophotometric technique, using 8-amino-1-hydroxynaphthalene-3,6-disulphonic acid (H-acid) and N-(1-naphthyl) ethylenediamine (N-na) as coupling agents. The following are determined by both methods: 2-and 4-ethylaniline, 4-aminobenzonitrile, 3- and 4-aminoacetophenone, 4-aminobenzophenone, 4-iodoaniline, 2,5-dichloroaniline, 4-aminohippuric acid, 2-aminobenzyl alcohol, 3-aminobenzamide, sulphathiazole, 2-, 3- and 4-methoxyaniline and 2,4-, 3,4- and 3,5-dimethylaniline. It is possible to determine 2,3- and 2,5-dimethylaniline only by the H-acid method, but 2,6-dimethylaniline cannot be determined by either method. 2-Aminobenzamide can only be determined by the N-na method. In the application of the H-acid method to the methoxyanilines and dimethylanilines, the colour is developed by adding a large excess of sodium bicarbonate and H-acid. In the application of the N-na method to the ethylanilines, methoxyanilines and 2,4-, 3,4- and 3,5-dimethylanilines, the colour is developed by addition of a large excess of N-na reagent and allowing the solution to stand overnight.     

Synthesis of cyclic hydrocarbons via intramolecular coupling of bis-pentadienyl iron tricarbonyl cations

A general synthesis for the preparation of medium sized cycloalkanes having 1,2-butadienyl substituents is described. The reaction sequence involved acylation of butadiene-iron tricarbonyl with a diacid chloride, reduction of the resultant diketone to a diol derivative and conversion with HBF₄ to an acyclic bis-pentadienyl Fe(C0)₃ dicationic complex. Upon treatment with zinc the dication undergoes intramolecular ring closure to afford the bis-Fe(C0)₃ complex of the 1,2-dibutadienyl cycloalkane. Five-, six- and ten-membered cyclolalkene derivatives have been prepared in this manner.     

Primary methods of measurement in chemical analysis

 Primary methods of measurement have a central function in metrology. They are an essential component in the realisation of the SI units and therefore are indispensable for establishing traceability of measurements of all kinds of physical quantities to the corresponding SI units. This is also true for chemical analysis. Gravimetry, titrimetry, coulometry, and isotope dilution mass spectrometry (IDMS) are evaluated with regard to their potential to be primary methods according to a general definition of primary methods recently given by the Comité Consultatif pour la Quantité de Matière (CCQM). Optical absorption spectrometry and methods based on colligative properties are also considered. A general scheme for establishing traceability of chemical measurements to the SI units using primary methods is discussed. Received: 17 April 1997 · Accepted: 9 August 1997     

Iron-57 Mössbauer effect study of the distribution of divalent and trivalent ions in potassium transition metal fluorides having the tetragonal bronze structure

Mössbauer studies are reported for compounds of the type KM^IIM^IIIF₆ (M = first-row transition metal ion, Zn, or Mg) which have the tetragonal bronze structure. The results of this investigation provide evidence that the trivalent ions are located on the 8(j) sites of the bronze structure and that the divalent ions are distributed over both the 8(j) and 2(c) sites.