Neutrino propagation in matter using the wave packet approach

We study the oscillations and conversions of relativistic neutrinos propagating in matter of variable density using the wave packet formalism. We show how the oscillation and coherence lengths are modified in comparison with the case of oscillations in vacuum. Secondly, we demonstrate how the equation of motion for two neutrino flavors can be formally solved for almost arbitrary density profile. We calculate finally how the use of wave packets alters the nonadiabatic level crossing probabilities. For the most common physical environments the corrections due to the width of the wave packet do not lead to observable effects.Comment: 21 pages, LATEX, no figure

Firm and industry level profit efficiency analysis under incomplete price data: A nonparametric approach based on absolute and uniform shadow prices

We discuss the nonparametric approach to profit efficiency analysis at the firm and industry levels in the absence of complete price information. Two new insights are developed. First, we measure profit inefficiency in monetary terms using absolute shadow prices. Second, we evaluate all firms using the same input-output prices. This allows us to aggregate firm-level profit inefficiencies to the overall industry inefficiency. Besides the measurement of profit losses, the presented approach enables one to recover absolute price information from quantity data. We conduct a series of Monte Carlo simulations to study the performance of the proposed approach in controlled production environments