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Similar to the Debye-Hueckel plasma, charged groups of oppositely charged polyelectrolytes attract each other. We find exact expression for the correlation free energy of electrostatic attraction in polyelectrolytes within the random phase approximation. ... In this theory we explicitly take into account positions of charged groups on the chains and examine both charge and polymer concentrations fluctuations. ...

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Franco Peracchi IV and GMM under weak instruments Spring 2011 Course outline 1. The instrumental variables (IV) method · · · · · · · · · · · · · · · · · · · · · · · · · · · · Inconsistency of OLS The simple IV estimator The class of IV estimators Sampling properties Estimates of statistical precision Hypothesis testing 2SLS Motivating examples Definitions and basic models The bias of 2SLS Standard asymptotic approximations Alternative asymptotic approximations Detecting weak ...

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