A number theoretic characterization of EE-smooth and (FRS) morphisms: estimates on the number of Z/pkZ\mathbb{Z}/p^{k}\mathbb{Z}-points

We provide uniform estimates on the number of $\mathbb{Z}/p^{k}\mathbb{Z}$-points lying on fibers of flat morphisms between smooth varieties whose fibers have rational singularities, termed (FRS) morphisms. For each individual fiber, the estimates were known by work of Avni and Aizenbud, but we render them uniform over all fibers. The proof technique for individual fibers is based on Hironaka's resolution of singularities and Denef's formula, but breaks down in the uniform case. Instead, we use recent results from the theory of motivic integration. Our estimates are moreover equivalent to the (FRS) property, just like in the absolute case by Avni and Aizenbud. In addition, we define new classes of morphisms, called $E$-smooth morphisms ($E\in\mathbb{N}$), which refine the (FRS) property, and use the methods we developed to provide uniform number-theoretic estimates as above for their fibers. Similar estimates are given for fibers of $\varepsilon$-jet flat morphisms, improving previous results by the last two authors.Comment: 27 pages, comments welcome; v2: the new notion of E-smooth morphisms was added, and uniform estimates on the number of points lying on the fibers of $E$-smooth and $\varepsilon$-jet flat morphisms are given (Theorems 4.11 and 4.12

Improvements on dimension growth results and effective Hilbert's irreducibility theorem

We sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree $d$, over any global field. In particular, we focus on the the affine hypersurface situation by relaxing the condition on the top degree homogeneous part of the polynomial describing the affine hypersurface. Our work sharpens the dependence on the degree in the bounds, compared to~\cite{CCDN-dgc}. We also formulate a conjecture about plane curves which gives a conjectural approach to the uniform degree $3$ case (the only case which remains open). For induction on dimension, we develop a higher dimensional effective version of Hilbert's irreducibility theorem.Comment: 35 page

Learning from Asiana 214--Minimizing Strike/Rollover for Aircraft Rescue and Firefighting

Following the crash of Asiana flight 214 on July 6, 2013, the National Transportation Safety Board (NTSB) provided a recommendation to the Aircraft Rescue & Fire Fighting Working Group (ARFFWG) to develop best practices to avoid strike/rollover of seriously injured or deceased persons in mass casualty situations. This paper summarizes the research process and the technical committee’s conclusions. The qualitative inquiry used participatory research and evaluation from medico-legal professionals and the expert committee comprised of 21 aircraft rescue and firefighting experts. Key informants were complemented by documentary analysis, including FAA Advisory Circulars, regulations, standards, medical and aircraft rescue industry publications. The research provides specific committee recommendations for establishing control zones in the mass casualty environment, using START for triage, surveillance, transportation, training and certification of both ARFF personnel and incident command, and airport emergency planning strategies. A best practice for ARFF personnel, which is a tactical procedure for task prioritization at aircraft crash incidents, is also proposed. The authors suggest future pilot testing for evaluation of these best practices following NTSB’s consent with the committee’s recommendations

Nonlinear pricing of storable goods

This paper develops a model of nonlinear pricing of storable goods. We show that storability imposes novel constraints on a monopolist’s ability to extract surplus. We then show that the attempt to relax these constraints can generate cyclical patterns in pricing and sales, even when consumers are homogeneous. Thus, the model provides a novel explanation for sales that does not rely on discrimination motives. Enriching the model to allow for buyer heterogeneity in storage technology, delivers the prediction that larger containers are more likely to be on sale. This prediction is consistent with observed patterns in scanner data

Mode-coupling and nonlinear Landau damping effects in auroral Farley-Buneman turbulence

The fundamental problem of Farley-Buneman turbulence in the auroral $E$-region has been discussed and debated extensively in the past two decades. In the present paper we intend to clarify the different steps that the auroral $E$-region plasma has to undergo before reaching a steady state. The mode-coupling calculation, for Farley-Buneman turbulence, is developed in order to place it in perspective and to estimate its magnitude relative to the anomalous effects which arise through the nonlinear wave-particle interaction. This nonlinear effect, known as nonlinear ``Landau damping'' is due to the coupling of waves which produces other waves which in turn lose energy to the bulk of the particles by Landau damping. This leads to a decay of the wave energy and consequently a heating of the plasma. An equation governing the evolution of the field spectrum is derived and a physical interpration for each of its terms is provided