10,367 research outputs found
Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlev\'e II Equation
We consider the polynomials orthonormal with respect to the weight on the unit circle in the complex plane. The leading coefficient
is found to satisfy a difference-differential (spatially discrete)
equation which is further proved to approach a third order differential
equation by double scaling. The third order differential equation is equivalent
to the Painlev\'e II equation. The leading coefficient and second leading
coefficient of can be expressed asymptotically in terms of the
Painlev\'e II function.Comment: 16 page
Asymptotics of a Class of Solutions to the Cylindrical Toda Equations
The small t asymptotics of a class of solutions to the 2D cylindrical Toda
equations is computed. The solutions, q_k(t), have the representation q_k(t) =
log det(I-lambda K_k) - log det(I-lambda K_{k-1}) where K_k are integral
operators. This class includes the n-periodic cylindrical Toda equations. For
n=2 our results reduce to the previously computed asymptotics of the 2D radial
sinh-Gordon equation and for n=3 (and with an additional symmetry contraint)
they reduce to earlier results for the radial Bullough-Dodd equation.Comment: 29 pages, no figures, LaTeX fil
Reduced O diffusion through Be doped Pt electrodes
Using first principles electronic structure calculations we screen nine
elements for their potential to retard oxygen diffusion through
poly-crystalline Pt (p-Pt) films. We determine that O diffuses preferentially
as interstitial along Pt grain boundaries (GBs). The calculated barriers are
compatible with experimental estimates. We find that Be controls O diffusion
through p-Pt. Beryllium segregates to Pt GBs at interstitial (i) and
substitutional (s) sites. i-Be is slightly less mobile than O and it repels O,
thus stuffing the GB. s-Be has a high diffusion barrier and it forms strong
bonds to O, trapping O in the GB. Experiments confirm our theoretical
predictions.Comment: 3 pages, 2 figure
From Random Matrices to Stochastic Operators
We propose that classical random matrix models are properly viewed as finite
difference schemes for stochastic differential operators. Three particular
stochastic operators commonly arise, each associated with a familiar class of
local eigenvalue behavior. The stochastic Airy operator displays soft edge
behavior, associated with the Airy kernel. The stochastic Bessel operator
displays hard edge behavior, associated with the Bessel kernel. The article
concludes with suggestions for a stochastic sine operator, which would display
bulk behavior, associated with the sine kernel.Comment: 41 pages, 5 figures. Submitted to Journal of Statistical Physics.
Changes in this revision: recomputed Monte Carlo simulations, added reference
[19], fit into margins, performed minor editin
Vulnerability, Risk, and the Transition to Adulthood
Examines whether poverty and single parenthood influence the likelihood of risk behavior and dropping out among youth and how these behaviors affect the trajectory of connectedness and employment patterns in adulthood. Considers policy implications
Infants of Depressed Mothers Living in Poverty: Opportunities to Identify and Serve
Examines the prevalence of depression among mothers in poverty by race/ethnicity, age, family structure, prenatal care and feeding practices, and factors such as domestic violence. Explores intervention points and policy initiatives for support services
Negotiated Trade Restrictions with Private Political Pressure
In this paper we consider a home government with political pressure to restrict trade, at the expense of foreigners. The foreign country is compensated with an income transfer, which can be thought of as a portion of the tariff revenues or quota rents. In this setting the two countries should negotiate over the level of tariff and transfer of rents, depending on the level of political pressure at home. However, if this pressure cannot be directly observed abroad, then the home country may have an incentive to claim arbitrarily high political need and seek corresponding high trade barriers . We resolve this problem by determining incentive compatible trade policies, in which the home government has no incentive to overstate (or understate) the political pressure for protection.
The Use of Replacement Workers in Union Contract Negotiations: The U.S. Experience, 1980-1989
It is argued in many circles that a structural change occurred in U.S. collective bargaining in the 1980s. We investigate the extent to which the hiring of replacement workers can account for this change. For a sample of over 300 major strikes since 1980, we estimate the likelihood of replacements being hired. We find that the risk of replacement declines during tight labor markets, and is lower for bargaining units with more experienced workers. We use the predicted replacement risk as an explanatory variable in a model of the union's choice between the strike and holdout threat. We find that strike usage decreases significantly as the predicted replacement risk increases. We estimate that a ban on the use of replacement workers would have increased strike incidence from 1982-1989 by 3 percentage points, a 30 percent increase.
Kids' Share 2008: How Children Fare in the Federal Budget
Provides an annual analysis of trends in federal spending and tax expenditures on children's programs -- such as food stamps, tax credits, and Head Start -- and assesses the impact of future budget planning on children
Two ways to solve ASEP
The purpose of this article is to describe the two approaches to compute
exact formulas (which are amenable to asymptotic analysis) for the probability
distribution of the current of particles past a given site in the asymmetric
simple exclusion process (ASEP) with step initial data. The first approach is
via a variant of the coordinate Bethe ansatz and was developed in work of Tracy
and Widom in 2008-2009, while the second approach is via a rigorous version of
the replica trick and was developed in work of Borodin, Sasamoto and the author
in 2012.Comment: 10 pages, Chapter in "Topics in percolative and disordered systems
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