Computing DEA/AR efficiency and profit ratio measures with an illustrative bank application

This paper describes how the recent, published DEA/AR theory, in conjunction with software, provides measures of radial efficiency and profit ratios, This new DEA theory does not require use of the non-Archimedean principle, i.e., positive infinitesimals, and it allows for analysis of zero data entries. Further, this theory provides a comprehensive classification of the measures for both the efficient and inefficient decision-making units (DMUs). As programmed in the software, the efficiency principles are relative to the Charnes-Cooper-Rhodes ratio model and the Banker-Charnes-Cooper convex model, and the profitability principles are relative to the Thompson-Thrall profit ratio model. An illustrative application to 48 large U.S. banks illustrates some of the most fundamental computations, which are developed for a base option. Additional options may be exercised by the user to more fully utilize the theory. Additions to the software are being made to computer analytic centers and to make multiplier sensitivity analyses. Software utility updates and new DEA theory contributions continue to complement this computational capability.DEA is an advanced operations research method called Data Envelopment Analysis, and AR is an assurance region method used to bound the multipliers in the DEA model. Underlying data have been deposited with the editors.     

Interplanar torsion in the S1<--S0 electronic spectrum of jet cooled 1-phenylimidazole

The S(1)<--S(0) transition of 1-phenylimidazole (1PI) has been studied in a supersonic jet expansion by resonant two-photon ionization. The origin band at 36 075 cm(-1) is accompanied by a low frequency progression associated with torsion about the bond connecting phenyl and imidazole groups. Torsional potentials have been determined for both states. In S(0), phi(min)=37.2+/-0.5 degrees and the planar barrier is 339+/-20 cm(-1), while in S(1), phi(min)=17.6+/-0.5 degrees and the planar barrier is 57+/-2 cm(-1). The transition moment alignment is observed to be consistent with an excited state of L(b) character, in spite of the "off-axis" conjugation provided by the imidazole ring. These results are compared with ab initio calculations on both states, performed using Hartree-Fock, M?ller-Plesset second-order perturbation, density functional theory with the Becke3-Lee-Yang-Parr functional, time-dependent density functional theory, configuration interaction singles, and complete active space self-consistent field methods. Solution-phase UV spectra of neutral and protonated 1PI are also reported.     

Quantitative millimetre wavelength spectrometry at pressures approaching atmospheric: II. Determination of oxygen at atmospheric pressure

A millimetre wavelength (MMW) Fabry-Perot cavity spectrometer described in earlier work has been applied to the measurement of oxygen absorption at 60 GHz and atmospheric pressure in a gas matrix of nitrogen. The spectrometer has also been modified such that the MMW source is stabilised by a sub-harmonic microwave signal transmitted by an infrared carrier on a single mode telecommunications fibre optic. This is a step towards developing an instrument comprising minimal electronic components that can perform MMW spectrometry remotely. Oxygen determinations were achieved by monitoring the change in the quality factor (Q) of a resonant Fabry-Perot cavity due to the presence of an absorbing sample. The MMW absorption of the sample was determined by incrementing the frequency modulation (FM) deviation of the source frequency scanning the cavity resonance profile. The response curve of absorption signal versus fraction of oxygen in nitrogen was found to be linear throughout the working range of 1-100% O₂ (v/v) in N₂ with a slope of (1.407±0.007)×10⁻⁴ m⁻¹ (% O₂)⁻¹. The detection limit (3× standard deviation of the background) was found to be ∼0.8% (v/v). The MMW technique employed is advantageous since, unlike common MMW techniques, there is no vacuum requirement. Application of this method, to the monitoring of oxygen in gas mixtures of practical importance, is proposed. Values of the oxygen spectral absorption coefficients of lines between 55 and 60 GHz were measured at reduced pressure and found to be within ±2% of previous literature values. A pressure correction coefficient for O₂ absorption at 60 GHz in the 45-121 kPa range was obtained and found to be (1.354±0.014)×10⁻⁴ m⁻¹ kPa⁻¹.