On the (non)rigidity of the Frobenius Endomorphism over Gorenstein Rings

It is well-known that for a large class of local rings of positive characteristic, including complete intersection rings, the Frobenius endomorphism can be used as a test for finite projective dimension. In this paper, we exploit this property to study the structure of such rings. One of our results states that the Picard group of the punctured spectrum of such a ring $R$ cannot have $p$-torsion. When $R$ is a local complete intersection, this recovers (with a purely local algebra proof) an analogous statement for complete intersections in projective spaces first given in SGA and also a special case of a conjecture by Gabber. Our method also leads to many simply constructed examples where rigidity for the Frobenius endomorphism does not hold, even when the rings are Gorenstein with isolated singularity. This is in stark contrast to the situation for complete intersection rings. Also, a related length criterion for modules of finite length and finite projective dimension is discussed towards the end.Comment: Minor changes in Example 2.2 and Theorem 2.9. Conjecture 1.2 was added

A short note on the presence of spurious states in finite basis approximations

The genesis of spurious solutions in finite basis approximations to operators which possess a continuum and a point spectrum is discussed and a simple solution for identifying these solutions is suggested

Cheap Food Policy: Fact or Rhetoric?

The term "cheap food policy" has frequently been used as a descriptor for U.S. commodity programs by those who contend these payments to farmers ultimately result in lower food costs for consumers. More recently, farm policy has been criticized for contributing to the obesity problem in the U.S. by making large quantities of fattening foods widely available and relatively inexpensive. This paper econometrically evaluates the impact of direct government payments to farmers from 1960-1999 on the proportion of disposable income consumers spend on food. The model finds the payments do not significantly affect the affordability of food.Agricultural and Food Policy,

Expansions of the real field by open sets: definability versus interpretability

An open set U of the real numbers R is produced such that the expansion (R,+,x,U) of the real field by U defines a Borel isomorph of (R,+,x,N) but does not define N. It follows that (R,+,x,U) defines sets in every level of the projective hierarchy but does not define all projective sets. This result is elaborated in various ways that involve geometric measure theory and working over o-minimal expansions of (R,+,x). In particular, there is a Cantor subset K of R such that for every exponentially bounded o-minimal expansion M of (R,+,x), every subset of R definable in (M,K) either has interior or is Hausdorff null.Comment: 14 page

Space probe/satellite ejection apparatus for spacecraft

An ejection apparatus for spinning and propelling objects for ejection from a spacecraft at a desired velocity and rotational speed is discussed. The apparatus includes a launch cradle on which the space object to be ejected rests. The cradle is rotatably supported by a central hub secured to the upper end of the pneumatic cylinder piston shaft. Release mechanisms consisting of a retractable pin and locking lug is utilized to hold the cradle and object to be ejected. The release mechanism has a fixed barrier member which holds the retractable pin in engagement with the locking lug until release by upward movement of the launch cradle beyond the barrier height

Orbiter windward surface entry Heating: Post-orbital flight test program update

Correlations of orbiter windward surface entry heating data from the first five flights are presented with emphasis on boundary layer transition and the effects of catalytic recombination. Results show that a single roughness boundary layer transition correlation developed for spherical element trips works well for the orbiter tile system. Also, an engineering approach for predicting heating in nonequilibrium flow conditions shows good agreement with the flight test data in the time period of significant heating. The results of these correlations, when used to predict orbiter heating for a high cross mission, indicate that the thermal protection system on the windward surface will perform successfully in such a mission

Pass-Through And The Prediction Of Merger Price Effects

We use Monte Carlo experiments to study how pass-through can improve merger price predictions, focusing on the first order approximation (FOA) proposed in Jaffe and Weyl [2013]. FOA addresses the functional form misspecification that can exist in standard merger simulations. We find that the predictions of FOA are tightly distributed around the true price effects if pass-through is precise, but that measurement error in pass-through diminishes accuracy. As a comparison to FOA, we also study a methodology that uses pass-through to select among functional forms for use in simulation. This alternative also increases accuracy relative to standard merger simulation and proves more robust to measurement error