Testing procedures for detection of linear dependencies in efficiency models

The validity of many efficiency measurement methods rely upon the assumption that variables such as input quantities and output mixes are independent of (or uncorrelated with) technical efficiency, however few studies have attempted to test these assumptions. In a recent paper, Wilson (2003) investigates a number of independence tests and finds that they have poor size properties and low power in moderate sample sizes. In this study we discuss the implications of these assumptions in three situations: (i) bootstrapping non-parametric efficiency models; (ii) estimating stochastic frontier models and (iii) obtaining aggregate measures of industry efficiency. We propose a semi-parametric Hausmann-type asymptotic test for linear independence (uncorrelation), and use a Monte Carlo experiment to show that it has good size and power properties in finite samples. We also describe how the test can be generalized in order to detect higher order dependencies, such as heteroscedasticity, so that the test can be used to test for (full) independence when the efficiency distribution has a finite number of moments. Finally, an empirical illustration is provided using data on US electric power generation.     

Persistence of regions with high segment density in polyethylene melts

Proton nuclear magnetic resonance (NMR) spin-spin relaxation measurements were made on three commercial-grade polyethylenes in the melt state, free of solvent. All samples exhibit a three-component relaxation behavior, with components being assigned to amorphous low-molecular weight material (non-network fraction), amorphous entangled network fraction, and an ordered or high-segmental-density fraction, in order of decreasing relaxation times. Sample thermal history is shown to have a considerable effect on the overall relaxation behavior, and therefore on the relative amounts of each of the three components in the melt. An adequate thermal treatment of samples produces an equilibrium melt with invariant composition of the three fractions. The effects of thermal history on the relative amount of high-segment-density regions in the melt parallels its effect on the fraction of crystalline material in the solid polymer. These results are evidence for the persistence of ordered regions in polyethylene at temperatures well above the crystalline melting point of the polymer. We further comment on the nature of the two slower relaxing components and present examples of how the components manifest themselves in other polymer characterization techniques. © 1992 John Wiley & Sons, Inc.     

Preparation of poly(ethylene oxide)‐block‐poly(isoprene) by nitroxide‐mediated free radical polymerization from PEO macroinitiators

Amphiphilic poly(ethylene oxide)‐block‐poly(isoprene) (PEO‐b‐PI) diblock copolymers were prepared by nitroxide‐mediated polymerization of isoprene from alkoxyamine‐terminal poly(ethylene oxide) (PEO). PEO monomethyl ether (M_n ≈ 5200 g/mol) was functionalized by esterification with 2‐bromopropionyl bromide with subsequent copper‐mediated replacement of the terminal bromine with 2,2,5‐trimethyl‐4‐phenyl‐3‐azahexane‐3‐nitroxide. The resulting PEO‐alkoxyamine macroinitiator was used to initiate polymerization of isoprene in bulk and in solution at 125 °C to yield PEO‐b‐PI block copolymers with narrow molecular weight distributions (M_w/M_n ≤ 1.1). Polymerizations were first order in isoprene through 35% conversion. Micellar aggregates of PEO‐b‐PI in aqueous solution were crosslinked by treatment with a water‐soluble redox initiating system, and persistent micellar structures were observed in the dry state by AFM. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2977–2984, 2005     

A Global Optimization Algorithm using Lagrangian Underestimates and the Interval Newton Method

Convex relaxations can be used to obtain lower bounds on the optimal objective function value of nonconvex quadratically constrained quadratic programs. However, for some problems, significantly better bounds can be obtained by minimizing the restricted Lagrangian function for a given estimate of the Lagrange multipliers. The difficulty in utilizing Lagrangian duality within a global optimization context is that the restricted Lagrangian is often nonconvex. Minimizing a convex underestimate of the restricted Lagrangian overcomes this difficulty and facilitates the use of Lagrangian duality within a global optimization framework. A branch-and-bound algorithm is presented that relies on these Lagrangian underestimates to provide lower bounds and on the interval Newton method to facilitate convergence in the neighborhood of the global solution. Computational results show that the algorithm compares favorably to the Reformulation–Linearization Technique for problems with a favorable structure.