Exponential Sums and Polynomial Congruences Along p-adic Submanifolds

In this article, we consider the estimation of exponential sums along the points of the reduction mod $p^{m}$ of a $p$-adic analytic submanifold of $\mathbb{Z}_{p}^{n}$. More precisely, we extend Igusa's stationary phase method to this type of exponential sums. We also study the number of solutions of a polynomial congruence along the points of the reduction mod $$ of a $p$-adic analytic submanifold of $\mathbb{Z}_{p}^{n}$. In addition, we attach a Poincare series to these numbers, and establish its rationality. In this way, we obtain geometric bounds for the number of solutions of the corresponding polynomial congruences.Comment: Several typos were corrected.To Appear in Finite Fields and its Application

Subsidized Housing, Emergency Shelters, and Homelessness: An Empirical Investigation Using Data from the 1990 Census

This paper uses data on the only systematic count of the homeless throughout the United States to estimate the effect on the rate of homelessness of a wide variety of potentially important determinants, including several major policy responses to homelessness that have not been included in previous studies. It improves upon estimates of the effect of previously studied determinants by using measures that correspond more closely to underlying theoretical constructs, especially by accounting for geographical price differences. It also conducts numerous sensitivity analyses and analyzes the consequences of the undercount of the homeless for point estimates and hypothesis tests. The paper's most important finding from a policy perspective is that targeting the current budget authority for housing assistance on the poorest eligible households will essentially eliminate homelessness among those who apply for assistance. Achieving this goal without concentrating the poorest households in housing projects and without spending more money requires vouchering out project-based assistance. The primary methodological finding of the paper is that the 1990 Decennial Census did not produce sufficiently accurate counts, especially of the street homeless, to permit very precise estimates of the effects of many factors which surely affect the rate of homelessness. The main exceptions are the price of housing and average March temperature. Plausible models of the undercount imply that in regressions with a rate of homelessness as the dependent variable estimators of the coefficients of explanatory variables will be biased towards zero. In regressions with the logarithm of a rate of homelessness as the dependent variable, only the estimator of the constant term will be biased downwards. The unknown magnitude of the undercount precludes predicting the effects of policy interventions on the number of homeless based on the results in this paper and previous studies.Homelessness

On the Physics of Size Selectivity

We demonstrate that two mechanisms used by biological ion channels to select particles by size are driven by entropy. With uncharged particles in an infinite cylinder, we show that a channel that attracts particles is small-particle selective and that a channel that repels water from the wall is large-particle selective. Comparing against extensive density-functional theory calculations of our model, we find that the main physics can be understood with surprisingly simple bulk models that neglect the confining geometry of the channel completely.Comment: 4 pages, 3 figures, Phys. Rev. Lett. (accepted

The role of different negatively charged layers in Ca10(Fe1-xPtxAs)10(Pt3+yAs8) and superconductivity at 30 K in electron-doped (Ca0.8La0.2)10(FeAs)10(Pt3As8)

The recently discovered compounds Ca10(Fe1-xPtxAs)10(Pt3+yAs8) exhibit superconductivity up to 38 K, and contain iron arsenide (FeAs) and platinum arsenide (Pt3+yAs8) layers separated by layers of Ca atoms. We show that high Tc's above 15 K only emerge if the iron-arsenide layers are at most free of platinum-substitution (x \rightarrow 0) in contrast to recent reports. In fact Pt-substitution is detrimental to higher Tc, which increases up to 38 K only by charge doping of pure FeAs layers. We point out, that two different negatively charged layers [(FeAs)10]n- and (Pt3+yAs8)m- compete for the electrons provided by the Ca2+ ions, which is unique in the field of iron-based superconductors. In the parent compound Ca10(FeAs)10(Pt3As8), no excess charge dopes the FeAs-layer, and superconductivity has to be induced by Pt-substitution, albeit below 15 K. In contrast, the additional Pt-atom in the Pt4As8layer shifts the charge balance between the layers equivalent to charge doping by 0.2 electrons per FeAs. Only in this case Tc raises to 38 K, but decreases again if additionally platinum is substituted for iron. This charge doping scenario is supported by our discovery of superconductivity at 30 K in the electron-doped La-1038 compound (Ca0.8La0.2)10(FeAs)10(Pt3As8) without significant Pt-substitution.Comment: 4 pages, 4 figure

Radial fall of a test particle onto an evaporating black hole

A test particle falling into a classical black hole crosses the event horizon and ends up in the singularity within finite eigentime. In the `more realistic' case of a `classical' evaporating black hole, an observer falling onto a black hole observes a sudden evaporation of the hole. This illustrates the fact that the discussion of the classical process commonly found in the literature may become obsolete when the black hole has a finite lifetime. The situation is basically the same for more complex cases, e.g. where a particle collides with two merging black holes. It should be pointed out that the model used in this paper is mainly of academic interest, since the description of the physics near a black hole horizon still presents a difficult problem which is not yet fully understood, but our model provides a valuable possibility for students to enter the interesting field of black hole physics and to perform numerical calculations of their own which are not very involved from the computational point of view.Comment: 6 pages, 3 figures, LATE

Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation

We study the stochastic mass-conserving Allen-Cahn equation posed on a bounded two-dimensional domain with additive spatially smooth space-time noise. This equation associated with a small positive parameter describes the stochastic motion of a small almost semicircular droplet attached to domain's boundary and moving towards a point of locally maximum curvature. We apply It\^o calculus to derive the stochastic dynamics of the droplet by utilizing the approximately invariant manifold introduced by Alikakos, Chen and Fusco for the deterministic problem. In the stochastic case depending on the scaling, the motion is driven by the change in the curvature of the boundary and the stochastic forcing. Moreover, under the assumption of a sufficiently small noise strength, we establish stochastic stability of a neighborhood of the manifold of droplets in $L^2$ and $H^1$, which means that with overwhelming probability the solution stays close to the manifold for very long time-scales

Ground states in the Many Interacting Worlds approach

Recently the Many-Interacting-Worlds (MIW) approach to a quantum theory without wave functions was proposed. This approach leads quite naturally to numerical integrators of the Schr\"odinger equation. It has been suggested that such integrators may feature advantages over fixed-grid methods for higher numbers of degrees of freedom. However, as yet, little is known about concrete MIW models for more than one spatial dimension and/or more than one particle. In this work we develop the MIW approach further to treat arbitrary degrees of freedom, and provide a systematic study of a corresponding numerical implementation for computing one-particle ground and excited states in one dimension, and ground states in two spatial dimensions. With this step towards the treatment of higher degrees of freedom we hope to stimulate their further study.Comment: 16 pages, 8 figure

A Panel of Price Indices for Housing, Other Goods, and All Goods for All Areas in the United States 1982-2008

This paper produces a panel of price indices for housing, other produced goods, and all produced goods for each metropolitan area in the United States and the non-metropolitan part of each state from 1982 through 2008 that can be used for estimating behavioral relationships, studying the workings of markets, and assessing differences in the economic circumstances of people living in different areas. Our general approach is to first produce cross-sectional price indices for a single year 2000 and then use BLS time-series price indices to create the panel. Our geographic housing price index for 2000 is based on a large data set with detailed information about the characteristics of dwelling units and their neighborhoods throughout the United States that enables us to overcome many shortcomings of existing interarea housing price indices. For most areas, our price index for all goods other than housing is calculated from the price indices for categories of non-housing goods produced each quarter by the Council for Community and Economic Research. In order to produce a non-housing price index for areas of the United States not covered by their index, we estimate a theoretically-based regression model explaining differences in the composite price index for non-housing goods for areas where it is available and use it to predict a price of other goods for the uncovered areas. The overall consumer price index for all areas is based on the preceding estimates of the price of housing and other goods. The paper also discusses existing interarea price indices available to researchers, and it compares the new housing price index with housing price indices based on alternative methods using the same data and price indices based on alternative data sets. Electronic versions of the price indices are available online.Interarea price indices, interarea housing price indices, geographic cost-of-living differences, geographic price differences